Analysing Machine Learning Models With Imandra¶

In this notebook we show how Imandra can be used to analyse and reason about models that have been learnt from data, an important and exciting topic bridging the gap between formal methods and machine learning (ML). Brief notes and some links are included, but for a fuller explanation (with code snippets included for reference) see our corresponding Medium post. You can also find all of our code for both learning and analysing our models on GitHub.

To illustrate this approach we'll be looking at (relatively simple) examples from two of the most common tasks within supervised learning (and ML more generally): classification and regression. In particular, we'll show how two of the most common kinds of model used to perform these tasks, random forests and neural networks, can be analysed using Imandra. For each task we'll use a real-world benchmark dataset from the UCI Machine Learning Repository and create our models using Python with some standard ML libraries.

We'll mostly be working with reals in this notebook so we'll start by installing a pretty printer so that we're not overrun with digits.

Try this!

In [1]:

let pp_approx fmt r = CCFormat.fprintf fmt "%s" (Real.to_string_approx r) [@@program]
#install_printer pp_approx

Out[1]:

val pp_approx : Format.formatter -> real -> unit = <fun>

Classification¶

In a classification task we want to learn to predict the label of a datapoint based on previous data. In the classic Wisconsin Breast Cancer (Diagnostic) dataset) the task is to predict whether the cancer is benign or malignant based on the features of cell nuclei. In the dataset we have the following variables:

1. ID number
2. Diagnosis (malignant or benign)
3-32. Real values for the mean, standard error, and the 'worst' value for each cell nucleus'
      a) Radius
      b) Texture
      c) Perimeter
      d) Area
      e) Smoothness
      f) Compactness
      g) Concavity
      h) Concave points
      i) Symmetry
      j) Fractal dimension

As is standard practice we pre-process the data before learning. First we standardise each variable to have zero mean and unit variance, then remove all but one from sets of highly correlated variables, along with those that have low mutual information with respect to the target variable. The data is split into training (80%) and test (20%) sets and we use Scikit-Learn to learn a random forest of 3 decision trees of maximum depth 3. As this is a relatively straightforward problem even this simple model achieves a fairly high accuracy. Using a short Python script each tree is then converted to Imandra Modelling Language (IML) and can be reasoned about using Imandra.

Try this!

In [2]:

let tree_0 (f_0 : real) (f_1 : real) (f_2 : real) (f_3 : real) (f_4 : real) (f_5 : real) (f_6 : real) = let open Real in
  if f_2 <=. (-0.10815) then
    if f_0 <=. (0.26348) then
      if f_6 <=. (-0.06176) then
        (236.0, 1.0)
      else
        (17.0, 5.0)
    else
      if f_3 <=. (-0.54236) then
        (8.0, 2.0)
      else
        (3.0, 7.0)
  else
    if f_6 <=. (0.09812) then
      if f_6 <=. (-0.17063) then
        (24.0, 0.0)
      else
        (4.0, 2.0)
    else
      if f_2 <=. (2.65413) then
        (6.0, 128.0)
      else
        (7.0, 5.0);;

let tree_1 (f_0 : real) (f_1 : real) (f_2 : real) (f_3 : real) (f_4 : real) (f_5 : real) (f_6 : real) = let open Real in
  if f_5 <=. (-0.05799) then
    if f_0 <=. (0.68524) then
      if f_1 <=. (-0.83180) then
        (110.0, 3.0)
      else
        (137.0, 0.0)
    else
      if f_3 <=. (0.45504) then
        (1.0, 8.0)
      else
        (0.0, 7.0)
  else
    if f_0 <=. (-0.18668) then
      if f_6 <=. (0.45214) then
        (39.0, 0.0)
      else
        (2.0, 11.0)
    else
      if f_6 <=. (-0.00009) then
        (8.0, 4.0)
      else
        (5.0, 120.0);;

let tree_2 (f_0 : real) (f_1 : real) (f_2 : real) (f_3 : real) (f_4 : real) (f_5 : real) (f_6 : real) = let open Real in
  if f_2 <=. (0.10459) then
    if f_5 <=. (-0.38015) then
      if f_5 <=. (-0.60659) then
        (139.0, 1.0)
      else
        (44.0, 3.0)
    else
      if f_6 <=. (-0.07927) then
        (38.0, 2.0)
      else
        (25.0, 17.0)
  else
    if f_6 <=. (0.46888) then
      if f_3 <=. (0.41642) then
        (28.0, 3.0)
      else
        (1.0, 4.0)
    else
      if f_2 <=. (1.74327) then
        (3.0, 122.0)
      else
        (4.0, 21.0);;

let rf (f_0, f_1, f_2, f_3, f_4, f_5, f_6) = let open Real in
let (a_0, b_0) = tree_0 f_0 f_1 f_2 f_3 f_4 f_5 f_6 in
let (a_1, b_1) = tree_1 f_0 f_1 f_2 f_3 f_4 f_5 f_6 in
let (a_2, b_2) = tree_2 f_0 f_1 f_2 f_3 f_4 f_5 f_6 in
let a = a_0 + a_1 + a_2 in
let b = b_0 + b_1 + b_2 in
(a, b);;

Out[2]:

val tree_0 :
  real -> real -> real -> real -> real -> real -> real -> real * real = <fun>
val tree_1 :
  real -> real -> real -> real -> real -> real -> real -> real * real = <fun>
val tree_2 :
  real -> real -> real -> real -> real -> real -> real -> real * real = <fun>
val rf : real * real * real * real * real * real * real -> real * real =
  <fun>

We can create a custom input type in Imandra for our model, so that we can keep track of the different features of our data.

Try this!

In [3]:

type rf_input = {
  radius_mean : real;
  compactness_mean : real;
  concavity_mean : real;
  radius_se : real;
  compactness_worst : real;
  concavity_worst : real;
  concave_points_worst : real;
}

Out[3]:

type rf_input = {
  radius_mean : real;
  compactness_mean : real;
  concavity_mean : real;
  radius_se : real;
  compactness_worst : real;
  concavity_worst : real;
  concave_points_worst : real;
}

However, remember that we also processed our data before learning. To make things easier we'll add in a function applying this transformation to each input variable. Here we simply use some multiplicative and additive scaling values extracted during our data pre-processing stage. After that we can define a full model which combines these pre-processing steps and the random forest.

Try this!

In [4]:

let process_rf_input input = let open Real in
let f_0 = (input.radius_mean          - 14.12729) / 3.52405 in
let f_1 = (input.compactness_mean     - 0.10434)  / 0.05281 in
let f_2 = (input.concavity_mean       - 0.08880)  / 0.07972 in
let f_3 = (input.radius_se            - 0.40517)  / 0.27731 in
let f_4 = (input.compactness_worst    - 0.25427)  / 0.15734 in
let f_5 = (input.concavity_worst      - 0.27219)  / 0.20862 in
let f_6 = (input.concave_points_worst - 0.11461)  / 0.06573 in
(f_0, f_1, f_2, f_3, f_4, f_5, f_6)

let process_rf_output c =
let (a, b) = c in
if a >. b then "benign" else "malignant"

let rf_model input = input |> process_rf_input |> rf |> process_rf_output

Out[4]:

val process_rf_input :
  rf_input -> real * real * real * real * real * real * real = <fun>
val process_rf_output : real * real -> string = <fun>
val rf_model : rf_input -> string = <fun>

As our model is fully executable we can both query it as well as find counterexamples, prove properties, apply logical side-conditions, decompose its regions, and more. As a quick sanity check to make sure everything is working, let's run a datum from our dataset through the model. In particular, we'll input (17.99, 0.2776, 0.3001, 1.095, 0.6656, 0.7119, 0.2654) which is classified as malignant in the data.

Try this!

In [5]:

let x = {
  radius_mean = 17.99;
  compactness_mean = 0.2776;
  concavity_mean = 0.3001;
  radius_se = 1.095;
  compactness_worst = 0.6656;
  concavity_worst = 0.7119;
  concave_points_worst = 0.7119;
}

let y = rf_model x

Out[5]:

val x : rf_input =
  {radius_mean = 17.99; compactness_mean = 0.2776; concavity_mean = 0.3001;
   radius_se = 1.095; compactness_worst = 0.6656; concavity_worst = 0.7119;
   concave_points_worst = 0.7119}
val y : string = "malignant"

Great, just what we'd expect. Now we'll use Imandra to generate an example datapoint for us given that diagnosis is benign.

Try this!

In [6]:

instance (fun x -> rf_model x = "benign")

Out[6]:

- : rf_input -> bool = <fun>
module CX : sig val x : rf_input end

Instance (after 0 steps, 0.026s):
let x : rf_input =
  {radius_mean = (-216972096653/500000000);
   compactness_mean = (-140469793679/500000000);
   concavity_mean = (-4048959910859/500000000); radius_se = 5853;
   compactness_worst = 9; concavity_worst = (-5709271784029/5000000000);
   concave_points_worst = (-47569488241/78125000)}

Instance

call graph
proof

digraph "call graph" {
goal [label="let (_x_0 : real) = x.concavity_mean in\llet (_x_1 : real) = x.concave_points_worst in\llet (_x_2 : real) = x.radius_se in\llet (_x_3 : real) = x.radius_mean in\llet (_x_4 : (Real.t * Real.t))\l    = if _x_0 \<= 40089141/500000000\l      then\l        if _x_3 \<= 7527903347/500000000\l        then if _x_1 \<= 8636759/78125000 then … else …\l        else if _x_2 \<= 636920371/2500000000 then … else …\l      else\l      if _x_1 \<= 302648569/2500000000\l      then if _x_1 \<= 1033944901/10000000000 then … else …\l      else if _x_0 \<= 750968109/2500000000 then … else …\lin\llet (_x_5 : real) = x.concavity_worst in\llet (_x_6 : (Real.t * Real.t))\l    = if _x_5 \<= 1300460631/5000000000\l      then\l        if _x_3 \<= 8271055011/500000000\l        then if x.compactness_mean \<= 30206321/500000000 then … else …\l        else if _x_2 \<= 166049107/312500000 then … else …\l      else\l      if _x_3 \<= 6734710173/500000000\l      then if _x_1 \<= 721645811/5000000000 then … else …\l      else if _x_1 \<= 1146040843/10000000000 then … else …\lin\llet (_x_7 : (Real.t * Real.t))\l    = if _x_0 \<= 242844787/2500000000\l      then\l        if _x_5 \<= 192883107/1000000000\l        then if _x_5 \<= 728215971/5000000000 then … else …\l        else if _x_1 \<= 1093995829/10000000000 then … else …\l      else\l      if _x_1 \<= 181786853/1250000000\l      then if _x_2 \<= 2603237151/5000000000 then … else …\l      else if _x_0 \<= 569433711/2500000000 then … else …\lin\l(if _x_4.0 +. _x_6.0 +. _x_7.0 \<= _x_4.1 +. _x_6.1 +. _x_7.1 then \"malignant\"\l else \"benign\")\l= \"benign\"",shape=box,style=filled,color="cyan",fontname="courier",fontsize=14];
}

proof attempt

ground_instances:

definitions:

inductions:

search_time:

0.026s

details:

Expand

smt_stats:

num checks:	2
arith assert lower:	7
arith tableau max rows:	1
arith tableau max columns:	39
arith pivots:	3
rlimit count:	3538
mk clause:	63
datatype occurs check:	25
mk bool var:	148
arith assert upper:	15
decisions:	21
propagations:	42
datatype accessor ax:	28
arith num rows:	1
datatype constructor ax:	4
num allocs:	7626406
final checks:	1
added eqs:	93
arith eq adapter:	6
time:	0.014000
memory:	16.940000
max memory:	17.510000

Expand

start[0.026s]
  let (_x_0 : real) = ….2 in
  let (_x_1 : (Real.t * Real.t)) = if _x_0 <= (-2163/20000) then … else …
  in
  let (_x_2 : (Real.t * Real.t))
      = if ….5 <= (-5799/100000) then … else …
  in
  let (_x_3 : (Real.t * Real.t)) = if _x_0 <= 10459/100000 then … else …
  in
  (if _x_1.0 +. _x_2.0 +. _x_3.0 > _x_1.1 +. _x_2.1 +. _x_3.1 then "benign"
   else "malignant")
  = "benign"

simplify

into:	let (_x_0 : real) = ( :var_0: ).concavity_mean in let (_x_1 : real) = ( :var_0: ).concave_points_worst in let (_x_2 : real) = ( :var_0: ).radius_se in let (_x_3 : real) = ( :var_0: ).radius_mean in let (_x_4 : (Real.t * Real.t)) = if _x_0 <= 40089141/500000000 then if _x_3 <= 7527903347/500000000 then if _x_1 <= 8636759/78125000 then … else … else if _x_2 <= 636920371/2500000000 then … else … else if _x_1 <= 302648569/2500000000 then if _x_1 <= 1033944901/10000000000 then … else … else if _x_0 <= 750968109/2500000000 then … else … in let (_x_5 : real) = ( :var_0: ).concavity_worst in let (_x_6 : (Real.t * Real.t)) = if _x_5 <= 1300460631/5000000000 then if _x_3 <= 8271055011/500000000 then if ( :var_0: ).compactness_mean <= 30206321/500000000 then … else … else if _x_2 <= 166049107/312500000 then … else … else if _x_3 <= 6734710173/500000000 then if _x_1 <= 721645811/5000000000 then … else … else if _x_1 <= 1146040843/10000000000 then … else … in let (_x_7 : (Real.t * Real.t)) = if _x_0 <= 242844787/2500000000 then if _x_5 <= 192883107/1000000000 then if _x_5 <= 728215971/5000000000 then … else … else if _x_1 <= 1093995829/10000000000 then … else … else if _x_1 <= 181786853/1250000000 then if _x_2 <= 2603237151/5000000000 then … else … else if _x_0 <= 569433711/2500000000 then … else … in (if _x_4.0 +. _x_6.0 +. _x_7.0 <= _x_4.1 +. _x_6.1 +. _x_7.1 then "malignant" else "benign") = "benign"
expansions:	[]
rewrite_steps:
forward_chaining:

Sat (Some let x : rf_input = {radius_mean = (Q.of_string "-216972096653/500000000"); compactness_mean = (Q.of_string "-140469793679/500000000"); concavity_mean = (Q.of_string "-4048959910859/500000000"); radius_se = (Q.of_nativeint (5853n)); compactness_worst = (Q.of_nativeint (9n)); concavity_worst = (Q.of_string "-5709271784029/5000000000"); concave_points_worst = (Q.of_string "-47569488241/78125000")} )

digraph "proof" {
p_2 [label="Start (let (_x_0 : real) = ….2 in\l       let (_x_1 : (Real.t * Real.t))\l           = if _x_0 \<= (-2163/20000) then … else …\l       in\l       let (_x_2 : (Real.t * Real.t))\l           = if ….5 \<= (-5799/100000) then … else …\l       in\l       let (_x_3 : (Real.t * Real.t))\l           = if _x_0 \<= 10459/100000 then … else …\l       in\l       (if _x_1.0 +. _x_2.0 +. _x_3.0 \> _x_1.1 +. _x_2.1 +. _x_3.1\l        then \"benign\" else \"malignant\")\l       = \"benign\" :time 0.026s)",shape=box,style=filled,fontname="courier",fontsize=14];
p_2 -> p_1 [label=""];
p_1 [label="Simplify (let (_x_0 : real) = ( :var_0: ).concavity_mean in\l          let (_x_1 : real) = ( :var_0: ).concave_points_worst in\l          let (_x_2 : real) = ( :var_0: ).radius_se in\l          let (_x_3 : real) = ( :var_0: ).radius_mean in\l          let (_x_4 : (Real.t * Real.t))\l              = if _x_0 \<= 40089141/500000000\l                then\l                  if _x_3 \<= 7527903347/500000000\l                  then if _x_1 \<= 8636759/78125000 then … else …\l                  else if _x_2 \<= 636920371/2500000000 then … else …\l                else\l                if _x_1 \<= 302648569/2500000000\l                then if _x_1 \<= 1033944901/10000000000 then … else …\l                else if _x_0 \<= 750968109/2500000000 then … else …\l          in\l          let (_x_5 : real) = ( :var_0: ).concavity_worst in\l          let (_x_6 : (Real.t * Real.t))\l              = if _x_5 \<= 1300460631/5000000000\l                then\l                  if _x_3 \<= 8271055011/500000000\l                  then\l                    if ( :var_0: ).compactness_mean \<= 30206321/500000000\l                    then … else …\l                  else if _x_2 \<= 166049107/312500000 then … else …\l                else\l                if _x_3 \<= 6734710173/500000000\l                then if _x_1 \<= 721645811/5000000000 then … else …\l                else if _x_1 \<= 1146040843/10000000000 then … else …\l          in\l          let (_x_7 : (Real.t * Real.t))\l              = if _x_0 \<= 242844787/2500000000\l                then\l                  if _x_5 \<= 192883107/1000000000\l                  then if _x_5 \<= 728215971/5000000000 then … else …\l                  else if _x_1 \<= 1093995829/10000000000 then … else …\l                else\l                if _x_1 \<= 181786853/1250000000\l                then if _x_2 \<= 2603237151/5000000000 then … else …\l                else if _x_0 \<= 569433711/2500000000 then … else …\l          in\l          (if _x_4.0 +. _x_6.0 +. _x_7.0 \<= _x_4.1 +. _x_6.1 +. _x_7.1\l           then \"malignant\" else \"benign\")\l          = \"benign\" :expansions [] :rw [] :fc [])",shape=box,style=filled,fontname="courier",fontsize=14];
p_1 -> p_0 [label=""];
p_0 [label="Sat (Some let x : rf_input =\l  \{radius_mean = (Q.of_string \"-216972096653/500000000\");\l   compactness_mean = (Q.of_string \"-140469793679/500000000\");\l   concavity_mean = (Q.of_string \"-4048959910859/500000000\");\l   radius_se = (Q.of_nativeint (5853n));\l   compactness_worst = (Q.of_nativeint (9n));\l   concavity_worst = (Q.of_string \"-5709271784029/5000000000\");\l   concave_points_worst = (Q.of_string \"-47569488241/78125000\")\}\l)",shape=box,style=filled,fontname="courier",fontsize=14];
}

Try this!

In [7]:

CX.x

Out[7]:

- : rf_input =
{radius_mean = -433.944193306; compactness_mean = -280.939587358;
 concavity_mean = -8097.91982172; radius_se = 5853.; compactness_worst = 9.;
 concavity_worst = -1141.85435681; concave_points_worst = -608.889449485}

This looks a bit funny however; notice how the unspecified input variables are unbounded in a way that doesn't make sense with respect to the data. In general we might only care about the performance of our model when some reasonable bounds are placed on the input (for example, the mean radius can't be negative, and if the values for this variable in our dataset range between 6.98 and 28.11 we wouldn't really expect any value greater than, say, 35). Using the description of each variable in the dataset we can form a condition describing valid and reasonable inputs to our model. In machine learning more generally, we are typically only interested in the performance and quality of a model over some particular distribution of data, which we often have particular prior beliefs about.

Try this!

In [8]:

let is_valid_rf input =
  5.0 <=. input.radius_mean && input.radius_mean <=. 35.0 &&
  0.0 <=. input.compactness_mean && input.compactness_mean <=. 0.4 &&
  0.0 <=. input.concavity_mean && input.concavity_mean <=. 0.5 &&
  0.0 <=. input.radius_se && input.radius_se <=. 3.5 &&
  0.0 <=. input.compactness_worst && input.compactness_worst <=. 1.2 &&
  0.0 <=. input.concavity_worst && input.concavity_worst <=. 1.5 &&
  0.0 <=. input.concave_points_worst && input.concave_points_worst <=. 0.35

instance (fun x -> rf_model x = "benign" && is_valid_rf x)

Out[8]:

val is_valid_rf : rf_input -> bool = <fun>
- : rf_input -> bool = <fun>
module CX : sig val x : rf_input end

Instance (after 0 steps, 0.016s):
let x : rf_input =
  {radius_mean = 15370932811137/2500000000000;
   compactness_mean = 13562638129/5000000000000;
   concavity_mean = 11265048621/5000000000000; radius_se = 40971/20000;
   compactness_worst = 321/5000;
   concavity_worst = 443483526339/50000000000000;
   concave_points_worst = 34970237191/390625000000}

Instance

call graph
proof

digraph "call graph" {
goal [label="let (_x_0 : real) = x.concavity_mean in\llet (_x_1 : real) = x.concave_points_worst in\llet (_x_2 : real) = x.radius_se in\llet (_x_3 : real) = x.radius_mean in\llet (_x_4 : (Real.t * Real.t))\l    = if _x_0 \<= 40089141/500000000\l      then\l        if _x_3 \<= 7527903347/500000000\l        then if _x_1 \<= 8636759/78125000 then … else …\l        else if _x_2 \<= 636920371/2500000000 then … else …\l      else\l      if _x_1 \<= 302648569/2500000000\l      then if _x_1 \<= 1033944901/10000000000 then … else …\l      else if _x_0 \<= 750968109/2500000000 then … else …\lin\llet (_x_5 : real) = x.compactness_mean in\llet (_x_6 : real) = x.concavity_worst in\llet (_x_7 : (Real.t * Real.t))\l    = if _x_6 \<= 1300460631/5000000000\l      then\l        if _x_3 \<= 8271055011/500000000\l        then if _x_5 \<= 30206321/500000000 then … else …\l        else if _x_2 \<= 166049107/312500000 then … else …\l      else\l      if _x_3 \<= 6734710173/500000000\l      then if _x_1 \<= 721645811/5000000000 then … else …\l      else if _x_1 \<= 1146040843/10000000000 then … else …\lin\llet (_x_8 : (Real.t * Real.t))\l    = if _x_0 \<= 242844787/2500000000\l      then\l        if _x_6 \<= 192883107/1000000000\l        then if _x_6 \<= 728215971/5000000000 then … else …\l        else if _x_1 \<= 1093995829/10000000000 then … else …\l      else\l      if _x_1 \<= 181786853/1250000000\l      then if _x_2 \<= 2603237151/5000000000 then … else …\l      else if _x_0 \<= 569433711/2500000000 then … else …\lin\llet (_x_9 : real) = x.compactness_worst in\l((if _x_4.0 +. _x_7.0 +. _x_8.0 \<= _x_4.1 +. _x_7.1 +. _x_8.1\l  then \"malignant\" else \"benign\")\l = \"benign\")\l&& (5 \<= _x_3) && (_x_3 \<= 35) && (0 \<= _x_5) && (_x_5 \<= 2/5) && (0 \<= _x_0)\l&& (_x_0 \<= 1/2) && (0 \<= _x_2) && (_x_2 \<= 7/2) && (0 \<= _x_9)\l&& (_x_9 \<= 6/5) && (0 \<= _x_6) && (_x_6 \<= 3/2) && (0 \<= _x_1)\l&& (_x_1 \<= 7/20)",shape=box,style=filled,color="cyan",fontname="courier",fontsize=14];
}

proof attempt

ground_instances:

definitions:

inductions:

search_time:

0.016s

details:

Expand

smt_stats:

num checks:	2
arith assert lower:	14
arith tableau max rows:	1
arith tableau max columns:	39
arith pivots:	3
rlimit count:	4512
mk clause:	63
datatype occurs check:	25
mk bool var:	162
arith assert upper:	22
decisions:	21
propagations:	42
datatype accessor ax:	28
arith num rows:	1
datatype constructor ax:	4
num allocs:	15439415
final checks:	1
added eqs:	93
arith eq adapter:	6
time:	0.009000
memory:	17.500000
max memory:	18.160000

Expand

start[0.016s]
  let (_x_0 : real) = ….2 in
  let (_x_1 : (Real.t * Real.t)) = if _x_0 <= (-2163/20000) then … else …
  in
  let (_x_2 : (Real.t * Real.t))
      = if ….5 <= (-5799/100000) then … else …
  in
  let (_x_3 : (Real.t * Real.t)) = if _x_0 <= 10459/100000 then … else …
  in
  let (_x_4 : real) = ( :var_0: ).radius_mean in
  let (_x_5 : real) = ( :var_0: ).compactness_mean in
  let (_x_6 : real) = ( :var_0: ).concavity_mean in
  let (_x_7 : real) = ( :var_0: ).radius_se in
  let (_x_8 : real) = ( :var_0: ).compactness_worst in
  let (_x_9 : real) = ( :var_0: ).concavity_worst in
  let (_x_10 : real) = ( :var_0: ).concave_points_worst in
  ((if _x_1.0 +. _x_2.0 +. _x_3.0 > _x_1.1 +. _x_2.1 +. _x_3.1 then "benign"
    else "malignant")
   = "benign")
  && ((5 <= _x_4)
      && ((_x_4 <= 35)
          && ((0 <= _x_5)
              && ((_x_5 <= 2/5)
                  && ((0 <= _x_6)
                      && ((_x_6 <= 1/2)
                          && ((0 <= _x_7)
                              && ((_x_7 <= 7/2)
                                  && ((0 <= _x_8)
                                      && ((_x_8 <= 6/5)
                                          && ((0 <= _x_9)
                                              && ((_x_9 <= 3/2)
                                                  && ((0 <= _x_10)
                                                      && (_x_10 <= 7/20))))))))))))))

simplify

into:	let (_x_0 : real) = ( :var_0: ).concavity_mean in let (_x_1 : real) = ( :var_0: ).concave_points_worst in let (_x_2 : real) = ( :var_0: ).radius_se in let (_x_3 : real) = ( :var_0: ).radius_mean in let (_x_4 : (Real.t * Real.t)) = if _x_0 <= 40089141/500000000 then if _x_3 <= 7527903347/500000000 then if _x_1 <= 8636759/78125000 then … else … else if _x_2 <= 636920371/2500000000 then … else … else if _x_1 <= 302648569/2500000000 then if _x_1 <= 1033944901/10000000000 then … else … else if _x_0 <= 750968109/2500000000 then … else … in let (_x_5 : real) = ( :var_0: ).compactness_mean in let (_x_6 : real) = ( :var_0: ).concavity_worst in let (_x_7 : (Real.t * Real.t)) = if _x_6 <= 1300460631/5000000000 then if _x_3 <= 8271055011/500000000 then if _x_5 <= 30206321/500000000 then … else … else if _x_2 <= 166049107/312500000 then … else … else if _x_3 <= 6734710173/500000000 then if _x_1 <= 721645811/5000000000 then … else … else if _x_1 <= 1146040843/10000000000 then … else … in let (_x_8 : (Real.t * Real.t)) = if _x_0 <= 242844787/2500000000 then if _x_6 <= 192883107/1000000000 then if _x_6 <= 728215971/5000000000 then … else … else if _x_1 <= 1093995829/10000000000 then … else … else if _x_1 <= 181786853/1250000000 then if _x_2 <= 2603237151/5000000000 then … else … else if _x_0 <= 569433711/2500000000 then … else … in let (_x_9 : real) = ( :var_0: ).compactness_worst in ((if _x_4.0 +. _x_7.0 +. _x_8.0 <= _x_4.1 +. _x_7.1 +. _x_8.1 then "malignant" else "benign") = "benign") && (5 <= _x_3) && (_x_3 <= 35) && (0 <= _x_5) && (_x_5 <= 2/5) && (0 <= _x_0) && (_x_0 <= 1/2) && (0 <= _x_2) && (_x_2 <= 7/2) && (0 <= _x_9) && (_x_9 <= 6/5) && (0 <= _x_6) && (_x_6 <= 3/2) && (0 <= _x_1) && (_x_1 <= 7/20)
expansions:	[]
rewrite_steps:
forward_chaining:

Sat (Some let x : rf_input = {radius_mean = (Q.of_string "15370932811137/2500000000000"); compactness_mean = (Q.of_string "13562638129/5000000000000"); concavity_mean = (Q.of_string "11265048621/5000000000000"); radius_se = (Q.of_string "40971/20000"); compactness_worst = (Q.of_string "321/5000"); concavity_worst = (Q.of_string "443483526339/50000000000000"); concave_points_worst = (Q.of_string "34970237191/390625000000")} )

digraph "proof" {
p_5 [label="Start (let (_x_0 : real) = ….2 in\l       let (_x_1 : (Real.t * Real.t))\l           = if _x_0 \<= (-2163/20000) then … else …\l       in\l       let (_x_2 : (Real.t * Real.t))\l           = if ….5 \<= (-5799/100000) then … else …\l       in\l       let (_x_3 : (Real.t * Real.t))\l           = if _x_0 \<= 10459/100000 then … else …\l       in\l       let (_x_4 : real) = ( :var_0: ).radius_mean in\l       let (_x_5 : real) = ( :var_0: ).compactness_mean in\l       let (_x_6 : real) = ( :var_0: ).concavity_mean in\l       let (_x_7 : real) = ( :var_0: ).radius_se in\l       let (_x_8 : real) = ( :var_0: ).compactness_worst in\l       let (_x_9 : real) = ( :var_0: ).concavity_worst in\l       let (_x_10 : real) = ( :var_0: ).concave_points_worst in\l       ((if _x_1.0 +. _x_2.0 +. _x_3.0 \> _x_1.1 +. _x_2.1 +. _x_3.1\l         then \"benign\" else \"malignant\")\l        = \"benign\")\l       && ((5 \<= _x_4)\l           && ((_x_4 \<= 35)\l               && ((0 \<= _x_5)\l                   && ((_x_5 \<= 2/5)\l                       && ((0 \<= _x_6)\l                           && ((_x_6 \<= 1/2)\l                               && ((0 \<= _x_7)\l                                   && ((_x_7 \<= 7/2)\l                                       && ((0 \<= _x_8)\l                                           && ((_x_8 \<= 6/5)\l                                               && ((0 \<= _x_9)\l                                                   && ((_x_9 \<= 3/2)\l                                                       && ((0 \<= _x_10)\l                                                           && (_x_10 \<= 7/20))))))))))))))\l       :time 0.016s)",shape=box,style=filled,fontname="courier",fontsize=14];
p_5 -> p_4 [label=""];
p_4 [label="Simplify (let (_x_0 : real) = ( :var_0: ).concavity_mean in\l          let (_x_1 : real) = ( :var_0: ).concave_points_worst in\l          let (_x_2 : real) = ( :var_0: ).radius_se in\l          let (_x_3 : real) = ( :var_0: ).radius_mean in\l          let (_x_4 : (Real.t * Real.t))\l              = if _x_0 \<= 40089141/500000000\l                then\l                  if _x_3 \<= 7527903347/500000000\l                  then if _x_1 \<= 8636759/78125000 then … else …\l                  else if _x_2 \<= 636920371/2500000000 then … else …\l                else\l                if _x_1 \<= 302648569/2500000000\l                then if _x_1 \<= 1033944901/10000000000 then … else …\l                else if _x_0 \<= 750968109/2500000000 then … else …\l          in\l          let (_x_5 : real) = ( :var_0: ).compactness_mean in\l          let (_x_6 : real) = ( :var_0: ).concavity_worst in\l          let (_x_7 : (Real.t * Real.t))\l              = if _x_6 \<= 1300460631/5000000000\l                then\l                  if _x_3 \<= 8271055011/500000000\l                  then if _x_5 \<= 30206321/500000000 then … else …\l                  else if _x_2 \<= 166049107/312500000 then … else …\l                else\l                if _x_3 \<= 6734710173/500000000\l                then if _x_1 \<= 721645811/5000000000 then … else …\l                else if _x_1 \<= 1146040843/10000000000 then … else …\l          in\l          let (_x_8 : (Real.t * Real.t))\l              = if _x_0 \<= 242844787/2500000000\l                then\l                  if _x_6 \<= 192883107/1000000000\l                  then if _x_6 \<= 728215971/5000000000 then … else …\l                  else if _x_1 \<= 1093995829/10000000000 then … else …\l                else\l                if _x_1 \<= 181786853/1250000000\l                then if _x_2 \<= 2603237151/5000000000 then … else …\l                else if _x_0 \<= 569433711/2500000000 then … else …\l          in\l          let (_x_9 : real) = ( :var_0: ).compactness_worst in\l          ((if _x_4.0 +. _x_7.0 +. _x_8.0 \<= _x_4.1 +. _x_7.1 +. _x_8.1\l            then \"malignant\" else \"benign\")\l           = \"benign\")\l          && (5 \<= _x_3) && (_x_3 \<= 35) && (0 \<= _x_5) && (_x_5 \<= 2/5)\l          && (0 \<= _x_0) && (_x_0 \<= 1/2) && (0 \<= _x_2) && (_x_2 \<= 7/2)\l          && (0 \<= _x_9) && (_x_9 \<= 6/5) && (0 \<= _x_6) && (_x_6 \<= 3/2)\l          && (0 \<= _x_1) && (_x_1 \<= 7/20) :expansions [] :rw [] :fc [])",shape=box,style=filled,fontname="courier",fontsize=14];
p_4 -> p_3 [label=""];
p_3 [label="Sat (Some let x : rf_input =\l  \{radius_mean = (Q.of_string \"15370932811137/2500000000000\");\l   compactness_mean = (Q.of_string \"13562638129/5000000000000\");\l   concavity_mean = (Q.of_string \"11265048621/5000000000000\");\l   radius_se = (Q.of_string \"40971/20000\");\l   compactness_worst = (Q.of_string \"321/5000\");\l   concavity_worst = (Q.of_string \"443483526339/50000000000000\");\l   concave_points_worst = (Q.of_string \"34970237191/390625000000\")\}\l)",shape=box,style=filled,fontname="courier",fontsize=14];
}

Try this!

In [9]:

CX.x

Out[9]:

- : rf_input =
{radius_mean = 6.14837312445; compactness_mean = 0.0027125276258;
 concavity_mean = 0.0022530097242; radius_se = 2.04855;
 compactness_worst = 0.0642; concavity_worst = 0.00886967052678;
 concave_points_worst = 0.089523807209}

This looks much better. Now let's move on to reasoning about our model in more interesting ways. One thing we can do is check the validity of certain constraints we might want our model to satisfy. For example, if the surface of a cell nucleus has many, large concave sections then is a particularly negative sign indicating that the cancer is likely to be malignant. We can use Imandra to easily verify that our model always classifies a sample of highly concave cells as malignant.

Try this!

In [10]:

verify (fun x -> is_valid_rf x
        && x.concavity_mean >=. 0.4
        && x.concavity_worst >=. 1.0
        && x.concave_points_worst >=. 0.25
        ==> rf_model x = "malignant")

Out[10]:

- : rf_input -> bool = <fun>

Proved

proof
call graph

proof

ground_instances:

definitions:

inductions:

search_time:

0.014s

details:

Expand

smt_stats:

num checks:	2
arith assert lower:	30
arith tableau max rows:	1
arith tableau max columns:	40
arith pivots:	2
rlimit count:	4443
mk clause:	50
mk bool var:	171
arith assert upper:	16
decisions:	9
propagations:	26
conflicts:	2
datatype accessor ax:	28
arith conflicts:	2
arith num rows:	1
datatype constructor ax:	4
num allocs:	26223887
added eqs:	102
del clause:	4
arith eq adapter:	8
time:	0.007000
memory:	17.920000
max memory:	18.600000

Expand

start[0.014s]
  let (_x_0 : real) = ( :var_0: ).radius_mean in
  let (_x_1 : real) = ( :var_0: ).compactness_mean in
  let (_x_2 : real) = ( :var_0: ).concavity_mean in
  let (_x_3 : real) = ( :var_0: ).radius_se in
  let (_x_4 : real) = ( :var_0: ).compactness_worst in
  let (_x_5 : real) = ( :var_0: ).concavity_worst in
  let (_x_6 : real) = ( :var_0: ).concave_points_worst in
  let (_x_7 : real) = ….2 in
  let (_x_8 : (Real.t * Real.t)) = if _x_7 <= (-2163/20000) then … else …
  in
  let (_x_9 : (Real.t * Real.t))
      = if ….5 <= (-5799/100000) then … else …
  in
  let (_x_10 : (Real.t * Real.t)) = if _x_7 <= 10459/100000 then … else …
  in
  (5 <= _x_0)
  && ((_x_0 <= 35)
      && ((0 <= _x_1)
          && ((_x_1 <= 2/5)
              && ((0 <= _x_2)
                  && ((_x_2 <= 1/2)
                      && ((0 <= _x_3)
                          && ((_x_3 <= 7/2)
                              && ((0 <= _x_4)
                                  && ((_x_4 <= 6/5)
                                      && ((0 <= _x_5)
                                          && ((_x_5 <= 3/2)
                                              && ((0 <= _x_6)
                                                  && (_x_6 <= 7/20)))))))))))))
  && ((_x_2 >= 2/5) && ((_x_5 >= 1) && (_x_6 >= 1/4)))
  ==> (if _x_8.0 +. _x_9.0 +. _x_10.0 > _x_8.1 +. _x_9.1 +. _x_10.1
       then "benign" else "malignant")
      = "malignant"

simplify

into:	let (_x_0 : real) = ( :var_0: ).radius_mean in let (_x_1 : real) = ( :var_0: ).compactness_mean in let (_x_2 : real) = ( :var_0: ).concavity_mean in let (_x_3 : real) = ( :var_0: ).radius_se in let (_x_4 : real) = ( :var_0: ).compactness_worst in let (_x_5 : real) = ( :var_0: ).concavity_worst in let (_x_6 : real) = ( :var_0: ).concave_points_worst in let (_x_7 : (Real.t * Real.t)) = if _x_2 <= 40089141/500000000 then if _x_0 <= 7527903347/500000000 then if _x_6 <= 8636759/78125000 then … else … else if _x_3 <= 636920371/2500000000 then … else … else if _x_6 <= 302648569/2500000000 then if _x_6 <= 1033944901/10000000000 then … else … else if _x_2 <= 750968109/2500000000 then … else … in let (_x_8 : (Real.t * Real.t)) = if _x_5 <= 1300460631/5000000000 then if _x_0 <= 8271055011/500000000 then if _x_1 <= 30206321/500000000 then … else … else if _x_3 <= 166049107/312500000 then … else … else if _x_0 <= 6734710173/500000000 then if _x_6 <= 721645811/5000000000 then … else … else if _x_6 <= 1146040843/10000000000 then … else … in let (_x_9 : (Real.t * Real.t)) = if _x_2 <= 242844787/2500000000 then if _x_5 <= 192883107/1000000000 then if _x_5 <= 728215971/5000000000 then … else … else if _x_6 <= 1093995829/10000000000 then … else … else if _x_6 <= 181786853/1250000000 then if _x_3 <= 2603237151/5000000000 then … else … else if _x_2 <= 569433711/2500000000 then … else … in not ((5 <= _x_0) && (_x_0 <= 35) && (0 <= _x_1) && (_x_1 <= 2/5) && (0 <= _x_2) && (_x_2 <= 1/2) && (0 <= _x_3) && (_x_3 <= 7/2) && (0 <= _x_4) && (_x_4 <= 6/5) && (0 <= _x_5) && (_x_5 <= 3/2) && (0 <= _x_6) && (_x_6 <= 7/20) && (_x_2 >= 2/5) && (_x_5 >= 1) && (_x_6 >= 1/4)) \|\| ((if _x_7.0 +. _x_8.0 +. _x_9.0 <= _x_7.1 +. _x_8.1 +. _x_9.1 then "malignant" else "benign") = "malignant")
expansions:	[]
rewrite_steps:
forward_chaining:

Unsat

digraph "proof" {
p_8 [label="Start (let (_x_0 : real) = ( :var_0: ).radius_mean in\l       let (_x_1 : real) = ( :var_0: ).compactness_mean in\l       let (_x_2 : real) = ( :var_0: ).concavity_mean in\l       let (_x_3 : real) = ( :var_0: ).radius_se in\l       let (_x_4 : real) = ( :var_0: ).compactness_worst in\l       let (_x_5 : real) = ( :var_0: ).concavity_worst in\l       let (_x_6 : real) = ( :var_0: ).concave_points_worst in\l       let (_x_7 : real) = ….2 in\l       let (_x_8 : (Real.t * Real.t))\l           = if _x_7 \<= (-2163/20000) then … else …\l       in\l       let (_x_9 : (Real.t * Real.t))\l           = if ….5 \<= (-5799/100000) then … else …\l       in\l       let (_x_10 : (Real.t * Real.t))\l           = if _x_7 \<= 10459/100000 then … else …\l       in\l       (5 \<= _x_0)\l       && ((_x_0 \<= 35)\l           && ((0 \<= _x_1)\l               && ((_x_1 \<= 2/5)\l                   && ((0 \<= _x_2)\l                       && ((_x_2 \<= 1/2)\l                           && ((0 \<= _x_3)\l                               && ((_x_3 \<= 7/2)\l                                   && ((0 \<= _x_4)\l                                       && ((_x_4 \<= 6/5)\l                                           && ((0 \<= _x_5)\l                                               && ((_x_5 \<= 3/2)\l                                                   && ((0 \<= _x_6)\l                                                       && (_x_6 \<= 7/20)))))))))))))\l       && ((_x_2 \>= 2/5) && ((_x_5 \>= 1) && (_x_6 \>= 1/4)))\l       ==\> (if _x_8.0 +. _x_9.0 +. _x_10.0 \> _x_8.1 +. _x_9.1 +. _x_10.1\l            then \"benign\" else \"malignant\")\l           = \"malignant\"\l       :time 0.014s)",shape=box,style=filled,fontname="courier",fontsize=14];
p_8 -> p_7 [label=""];
p_7 [label="Simplify (let (_x_0 : real) = ( :var_0: ).radius_mean in\l          let (_x_1 : real) = ( :var_0: ).compactness_mean in\l          let (_x_2 : real) = ( :var_0: ).concavity_mean in\l          let (_x_3 : real) = ( :var_0: ).radius_se in\l          let (_x_4 : real) = ( :var_0: ).compactness_worst in\l          let (_x_5 : real) = ( :var_0: ).concavity_worst in\l          let (_x_6 : real) = ( :var_0: ).concave_points_worst in\l          let (_x_7 : (Real.t * Real.t))\l              = if _x_2 \<= 40089141/500000000\l                then\l                  if _x_0 \<= 7527903347/500000000\l                  then if _x_6 \<= 8636759/78125000 then … else …\l                  else if _x_3 \<= 636920371/2500000000 then … else …\l                else\l                if _x_6 \<= 302648569/2500000000\l                then if _x_6 \<= 1033944901/10000000000 then … else …\l                else if _x_2 \<= 750968109/2500000000 then … else …\l          in\l          let (_x_8 : (Real.t * Real.t))\l              = if _x_5 \<= 1300460631/5000000000\l                then\l                  if _x_0 \<= 8271055011/500000000\l                  then if _x_1 \<= 30206321/500000000 then … else …\l                  else if _x_3 \<= 166049107/312500000 then … else …\l                else\l                if _x_0 \<= 6734710173/500000000\l                then if _x_6 \<= 721645811/5000000000 then … else …\l                else if _x_6 \<= 1146040843/10000000000 then … else …\l          in\l          let (_x_9 : (Real.t * Real.t))\l              = if _x_2 \<= 242844787/2500000000\l                then\l                  if _x_5 \<= 192883107/1000000000\l                  then if _x_5 \<= 728215971/5000000000 then … else …\l                  else if _x_6 \<= 1093995829/10000000000 then … else …\l                else\l                if _x_6 \<= 181786853/1250000000\l                then if _x_3 \<= 2603237151/5000000000 then … else …\l                else if _x_2 \<= 569433711/2500000000 then … else …\l          in\l          not\l          ((5 \<= _x_0) && (_x_0 \<= 35) && (0 \<= _x_1) && (_x_1 \<= 2/5)\l           && (0 \<= _x_2) && (_x_2 \<= 1/2) && (0 \<= _x_3) && (_x_3 \<= 7/2)\l           && (0 \<= _x_4) && (_x_4 \<= 6/5) && (0 \<= _x_5) && (_x_5 \<= 3/2)\l           && (0 \<= _x_6) && (_x_6 \<= 7/20) && (_x_2 \>= 2/5) && (_x_5 \>= 1)\l           && (_x_6 \>= 1/4))\l          \|\| ((if _x_7.0 +. _x_8.0 +. _x_9.0 \<= _x_7.1 +. _x_8.1 +. _x_9.1\l               then \"malignant\" else \"benign\")\l              = \"malignant\")\l          :expansions [] :rw [] :fc [])",shape=box,style=filled,fontname="courier",fontsize=14];
p_7 -> p_6 [label=""];
p_6 [label="Unsat",shape=box,style=filled,fontname="courier",fontsize=14];
}

digraph "call graph" {
goal [label="let (_x_0 : real) = x.radius_mean in\llet (_x_1 : real) = x.compactness_mean in\llet (_x_2 : real) = x.concavity_mean in\llet (_x_3 : real) = x.radius_se in\llet (_x_4 : real) = x.compactness_worst in\llet (_x_5 : real) = x.concavity_worst in\llet (_x_6 : real) = x.concave_points_worst in\llet (_x_7 : real) = ….concave_points_worst in\llet (_x_8 : (Real.t * Real.t))\l    = if _x_0 \<= 6734710173/500000000\l      then if _x_7 \<= 721645811/5000000000 then … else …\l      else if _x_7 \<= 1146040843/10000000000 then … else …\lin\llet (_x_9 : real) = ….concavity_mean in\llet (_x_10 : real) = ….radius_se in\llet (_x_11 : real) = ….concavity_worst in\llet (_x_12 : (Real.t * Real.t))\l    = if _x_9 \<= 242844787/2500000000\l      then\l        if _x_11 \<= 192883107/1000000000\l        then if _x_11 \<= 728215971/5000000000 then … else …\l        else if _x_7 \<= 1093995829/10000000000 then … else …\l      else\l      if _x_7 \<= 181786853/1250000000\l      then if _x_10 \<= 2603237151/5000000000 then … else …\l      else if _x_9 \<= 569433711/2500000000 then … else …\lin\llet (_x_13 : real) = ….radius_mean in\lnot\l(not\l ((5 \<= _x_0) && (_x_0 \<= 35) && (0 \<= _x_1) && (_x_1 \<= 2/5) && (0 \<= _x_2)\l  && (_x_2 \<= 1/2) && (0 \<= _x_3) && (_x_3 \<= 7/2) && (0 \<= _x_4)\l  && (_x_4 \<= 6/5) && (0 \<= _x_5) && (_x_5 \<= 3/2) && (0 \<= _x_6)\l  && (_x_6 \<= 7/20) && (_x_2 \>= 2/5) && (_x_5 \>= 1) && (_x_6 \>= 1/4))\l \|\| ((if (if _x_2 \<= 40089141/500000000\l          then\l            if _x_0 \<= 7527903347/500000000\l            then if _x_6 \<= 8636759/78125000 then … else …\l            else if _x_3 \<= 636920371/2500000000 then … else …\l          else\l          if _x_6 \<= 302648569/2500000000\l          then if _x_6 \<= 1033944901/10000000000 then … else …\l          else if _x_2 \<= 750968109/2500000000 then … else …).0\l         +. (if _x_5 \<= 1300460631/5000000000\l             then\l               if _x_0 \<= 8271055011/500000000\l               then if _x_1 \<= 30206321/500000000 then … else …\l               else if _x_3 \<= 166049107/312500000 then … else …\l             else _x_8).0\l         +. _x_12.0\l         \<= (if _x_9 \<= 40089141/500000000\l             then\l               if _x_13 \<= 7527903347/500000000\l               then if _x_7 \<= 8636759/78125000 then … else …\l               else if _x_10 \<= 636920371/2500000000 then … else …\l             else\l             if _x_7 \<= 302648569/2500000000\l             then if _x_7 \<= 1033944901/10000000000 then … else …\l             else if _x_9 \<= 750968109/2500000000 then … else …).1\l            +. (if _x_11 \<= 1300460631/5000000000\l                then\l                  if _x_13 \<= 8271055011/500000000\l                  then\l                    if ….compactness_mean \<= 30206321/500000000 then …\l                    else …\l                  else if _x_10 \<= 166049107/312500000 then … else …\l                else _x_8).1\l            +. _x_12.1\l      then \"malignant\" else \"benign\")\l     = \"malignant\"))",shape=box,style=filled,color="cyan",fontname="courier",fontsize=14];
}

The nested if ... then ... else statements in how the trees are defined mean that they are a prime candidate for Imandra's region decomposition functionality. As well as the total model we can of course also decompose the individual trees making up the ensemble.

Try this!

In [11]:

Modular_decomp.top ~assuming:"is_valid_rf" "rf_model"

Out[11]:

- : Modular_decomp_intf.decomp_ref = <abstr>

Voronoi (174 of 174)
Table

{
  "regions": [
    {
      "constraints": [
        "0 <= input.compactness_mean <= 2/5",
        "0 <= input.compactness_worst <= 6/5",
        "0 <= input.concave_points_worst <= 7/20",
        "0 <= input.concavity_mean <= 1/2",
        "0 <= input.concavity_worst <= 3/2", "0 <= input.radius_se <= 7/2",
        "5 <= input.radius_mean <= 35"
      ],
      "region": null,
      "groups": [
        {
          "constraints": [
            "0 <= input.compactness_mean <= 2/5",
            "0 <= input.compactness_worst <= 6/5",
            "0 <= input.concave_points_worst <= 7/20",
            "0 <= input.concavity_mean <= 1/2",
            "0 <= input.concavity_worst <= 3/2",
            "0 <= input.radius_se <= 7/2", "5 <= input.radius_mean <= 35",
            "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
            "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000"
          ],
          "region": null,
          "groups": [
            {
              "constraints": [
                "0 <= input.compactness_mean <= 2/5",
                "0 <= input.compactness_worst <= 6/5",
                "0 <= input.concave_points_worst <= 7/20",
                "0 <= input.concavity_mean <= 1/2",
                "0 <= input.concavity_worst <= 3/2",
                "0 <= input.radius_se <= 7/2",
                "5 <= input.radius_mean <= 35",
                "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000"
              ],
              "region": null,
              "groups": [
                {
                  "constraints": [
                    "0 <= input.compactness_mean <= 2/5",
                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.concave_points_worst <= 7/20",
                    "0 <= input.concavity_mean <= 1/2",
                    "0 <= input.concavity_worst <= 3/2",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                    "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                    "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                    "((input.concave_points_worst - 11461/100000) / 6573/100000) > 5861/12500"
                  ],
                  "region": null,
                  "groups": [
                    {
                      "constraints": [
                        "0 <= input.compactness_mean <= 2/5",
                        "0 <= input.compactness_worst <= 6/5",
                        "0 <= input.concave_points_worst <= 7/20",
                        "0 <= input.concavity_mean <= 1/2",
                        "0 <= input.concavity_worst <= 3/2",
                        "0 <= input.radius_se <= 7/2",
                        "5 <= input.radius_mean <= 35",
                        "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                        "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                        "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                        "((input.concave_points_worst - 11461/100000) / 6573/100000) > 5861/12500",
                        "174327/100000 < ((input.concavity_mean - 111/1250) / 1993/25000) <= 265413/100000"
                      ],
                      "region": {
                        "constraints": [
                          "174327/100000 < ((input.concavity_mean - 111/1250) / 1993/25000) <= 265413/100000",
                          "((input.concave_points_worst - 11461/100000) / 6573/100000) > 5861/12500",
                          "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                          "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                          "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                          "5 <= input.radius_mean <= 35",
                          "0 <= input.compactness_mean <= 2/5",
                          "0 <= input.concavity_mean <= 1/2",
                          "0 <= input.radius_se <= 7/2",
                          "0 <= input.compactness_worst <= 6/5",
                          "0 <= input.concavity_worst <= 3/2",
                          "0 <= input.concave_points_worst <= 7/20"
                        ],
                        "invariant": "F = \"malignant\""
                      },
                      "groups": [],
                      "label": "3",
                      "weight": 1
                    },
                    {
                      "constraints": [
                        "0 <= input.compactness_mean <= 2/5",
                        "0 <= input.compactness_worst <= 6/5",
                        "0 <= input.concave_points_worst <= 7/20",
                        "0 <= input.concavity_mean <= 1/2",
                        "0 <= input.concavity_worst <= 3/2",
                        "0 <= input.radius_se <= 7/2",
                        "5 <= input.radius_mean <= 35",
                        "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                        "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                        "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                        "((input.concave_points_worst - 11461/100000) / 6573/100000) > 5861/12500",
                        "10459/100000 < ((input.concavity_mean - 111/1250) / 1993/25000) <= 174327/100000"
                      ],
                      "region": {
                        "constraints": [
                          "10459/100000 < ((input.concavity_mean - 111/1250) / 1993/25000) <= 174327/100000",
                          "((input.concave_points_worst - 11461/100000) / 6573/100000) > 5861/12500",
                          "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                          "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                          "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                          "5 <= input.radius_mean <= 35",
                          "0 <= input.compactness_mean <= 2/5",
                          "0 <= input.concavity_mean <= 1/2",
                          "0 <= input.radius_se <= 7/2",
                          "0 <= input.compactness_worst <= 6/5",
                          "0 <= input.concavity_worst <= 3/2",
                          "0 <= input.concave_points_worst <= 7/20"
                        ],
                        "invariant": "F = \"malignant\""
                      },
                      "groups": [],
                      "label": "2",
                      "weight": 1
                    },
                    {
                      "constraints": [
                        "0 <= input.compactness_mean <= 2/5",
                        "0 <= input.compactness_worst <= 6/5",
                        "0 <= input.concave_points_worst <= 7/20",
                        "0 <= input.concavity_mean <= 1/2",
                        "0 <= input.concavity_worst <= 3/2",
                        "0 <= input.radius_se <= 7/2",
                        "5 <= input.radius_mean <= 35",
                        "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                        "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                        "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                        "((input.concave_points_worst - 11461/100000) / 6573/100000) > 5861/12500",
                        "((input.concavity_mean - 111/1250) / 1993/25000) > 265413/100000"
                      ],
                      "region": {
                        "constraints": [
                          "((input.concavity_mean - 111/1250) / 1993/25000) > 265413/100000",
                          "((input.concave_points_worst - 11461/100000) / 6573/100000) > 5861/12500",
                          "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                          "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                          "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                          "5 <= input.radius_mean <= 35",
                          "0 <= input.compactness_mean <= 2/5",
                          "0 <= input.concavity_mean <= 1/2",
                          "0 <= input.radius_se <= 7/2",
                          "0 <= input.compactness_worst <= 6/5",
                          "0 <= input.concavity_worst <= 3/2",
                          "0 <= input.concave_points_worst <= 7/20"
                        ],
                        "invariant": "F = \"benign\""
                      },
                      "groups": [],
                      "label": "1",
                      "weight": 1
                    }
                  ],
                  "label": "",
                  "weight": 3
                },
                {
                  "constraints": [
                    "0 <= input.compactness_mean <= 2/5",
                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.concave_points_worst <= 7/20",
                    "0 <= input.concavity_mean <= 1/2",
                    "0 <= input.concavity_worst <= 3/2",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                    "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                    "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                    "((input.radius_se - 40517/100000) / 27731/100000) > 20821/50000",
                    "2453/25000 < ((input.concave_points_worst - 11461/100000) / 6573/100000) <= 5861/12500"
                  ],
                  "region": null,
                  "groups": [
                    {
                      "constraints": [
                        "0 <= input.compactness_mean <= 2/5",
                        "0 <= input.compactness_worst <= 6/5",
                        "0 <= input.concave_points_worst <= 7/20",
                        "0 <= input.concavity_mean <= 1/2",
                        "0 <= input.concavity_worst <= 3/2",
                        "0 <= input.radius_se <= 7/2",
                        "5 <= input.radius_mean <= 35",
                        "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                        "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                        "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                        "((input.radius_se - 40517/100000) / 27731/100000) > 20821/50000",
                        "2453/25000 < ((input.concave_points_worst - 11461/100000) / 6573/100000) <= 5861/12500",
                        "10459/100000 < ((input.concavity_mean - 111/1250) / 1993/25000) <= 265413/100000"
                      ],
                      "region": {
                        "constraints": [
                          "10459/100000 < ((input.concavity_mean - 111/1250) / 1993/25000) <= 265413/100000",
                          "2453/25000 < ((input.concave_points_worst - 11461/100000) / 6573/100000) <= 5861/12500",
                          "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                          "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                          "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                          "((input.radius_se - 40517/100000) / 27731/100000) > 20821/50000",
                          "5 <= input.radius_mean <= 35",
                          "0 <= input.compactness_mean <= 2/5",
                          "0 <= input.concavity_mean <= 1/2",
                          "0 <= input.radius_se <= 7/2",
                          "0 <= input.compactness_worst <= 6/5",
                          "0 <= input.concavity_worst <= 3/2",
                          "0 <= input.concave_points_worst <= 7/20"
                        ],
                        "invariant": "F = \"benign\""
                      },
                      "groups": [],
                      "label": "3.2",
                      "weight": 1
                    },
                    {
                      "constraints": [
                        "0 <= input.compactness_mean <= 2/5",
                        "0 <= input.compactness_worst <= 6/5",
                        "0 <= input.concave_points_worst <= 7/20",
                        "0 <= input.concavity_mean <= 1/2",
                        "0 <= input.concavity_worst <= 3/2",
                        "0 <= input.radius_se <= 7/2",
                        "5 <= input.radius_mean <= 35",
                        "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                        "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                        "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                        "((input.radius_se - 40517/100000) / 27731/100000) > 20821/50000",
                        "2453/25000 < ((input.concave_points_worst - 11461/100000) / 6573/100000) <= 5861/12500",
                        "((input.concavity_mean - 111/1250) / 1993/25000) > 265413/100000"
                      ],
                      "region": {
                        "constraints": [
                          "((input.concavity_mean - 111/1250) / 1993/25000) > 265413/100000",
                          "2453/25000 < ((input.concave_points_worst - 11461/100000) / 6573/100000) <= 5861/12500",
                          "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                          "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                          "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                          "((input.radius_se - 40517/100000) / 27731/100000) > 20821/50000",
                          "5 <= input.radius_mean <= 35",
                          "0 <= input.compactness_mean <= 2/5",
                          "0 <= input.concavity_mean <= 1/2",
                          "0 <= input.radius_se <= 7/2",
                          "0 <= input.compactness_worst <= 6/5",
                          "0 <= input.concavity_worst <= 3/2",
                          "0 <= input.concave_points_worst <= 7/20"
                        ],
                        "invariant": "F = \"benign\""
                      },
                      "groups": [],
                      "label": "3.1",
                      "weight": 1
                    }
                  ],
                  "label": "",
                  "weight": 2
                },
                {
                  "constraints": [
                    "0 <= input.compactness_mean <= 2/5",
                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.concave_points_worst <= 7/20",
                    "0 <= input.concavity_mean <= 1/2",
                    "0 <= input.concavity_worst <= 3/2",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                    "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                    "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                    "((input.radius_se - 40517/100000) / 27731/100000) <= 20821/50000",
                    "2453/25000 < ((input.concave_points_worst - 11461/100000) / 6573/100000) <= 5861/12500"
                  ],
                  "region": null,
                  "groups": [
                    {
                      "constraints": [
                        "0 <= input.compactness_mean <= 2/5",
                        "0 <= input.compactness_worst <= 6/5",
                        "0 <= input.concave_points_worst <= 7/20",
                        "0 <= input.concavity_mean <= 1/2",
                        "0 <= input.concavity_worst <= 3/2",
                        "0 <= input.radius_se <= 7/2",
                        "5 <= input.radius_mean <= 35",
                        "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                        "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                        "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                        "((input.radius_se - 40517/100000) / 27731/100000) <= 20821/50000",
                        "2453/25000 < ((input.concave_points_worst - 11461/100000) / 6573/100000) <= 5861/12500",
                        "10459/100000 < ((input.concavity_mean - 111/1250) / 1993/25000) <= 265413/100000"
                      ],
                      "region": {
                        "constraints": [
                          "10459/100000 < ((input.concavity_mean - 111/1250) / 1993/25000) <= 265413/100000",
                          "2453/25000 < ((input.concave_points_worst - 11461/100000) / 6573/100000) <= 5861/12500",
                          "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                          "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                          "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                          "((input.radius_se - 40517/100000) / 27731/100000) <= 20821/50000",
                          "5 <= input.radius_mean <= 35",
                          "0 <= input.compactness_mean <= 2/5",
                          "0 <= input.concavity_mean <= 1/2",
                          "0 <= input.radius_se <= 7/2",
                          "0 <= input.compactness_worst <= 6/5",
                          "0 <= input.concavity_worst <= 3/2",
                          "0 <= input.concave_points_worst <= 7/20"
                        ],
                        "invariant": "F = \"benign\""
                      },
                      "groups": [],
                      "label": "2.2",
                      "weight": 1
                    },
                    {
                      "constraints": [
                        "0 <= input.compactness_mean <= 2/5",
                        "0 <= input.compactness_worst <= 6/5",
                        "0 <= input.concave_points_worst <= 7/20",
                        "0 <= input.concavity_mean <= 1/2",
                        "0 <= input.concavity_worst <= 3/2",
                        "0 <= input.radius_se <= 7/2",
                        "5 <= input.radius_mean <= 35",
                        "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                        "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                        "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                        "((input.radius_se - 40517/100000) / 27731/100000) <= 20821/50000",
                        "2453/25000 < ((input.concave_points_worst - 11461/100000) / 6573/100000) <= 5861/12500",
                        "((input.concavity_mean - 111/1250) / 1993/25000) > 265413/100000"
                      ],
                      "region": {
                        "constraints": [
                          "((input.concavity_mean - 111/1250) / 1993/25000) > 265413/100000",
                          "2453/25000 < ((input.concave_points_worst - 11461/100000) / 6573/100000) <= 5861/12500",
                          "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                          "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                          "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                          "((input.radius_se - 40517/100000) / 27731/100000) <= 20821/50000",
                          "5 <= input.radius_mean <= 35",
                          "0 <= input.compactness_mean <= 2/5",
                          "0 <= input.concavity_mean <= 1/2",
                          "0 <= input.radius_se <= 7/2",
                          "0 <= input.compactness_worst <= 6/5",
                          "0 <= input.concavity_worst <= 3/2",
                          "0 <= input.concave_points_worst <= 7/20"
                        ],
                        "invariant": "F = \"benign\""
                      },
                      "groups": [],
                      "label": "2.1",
                      "weight": 1
                    }
                  ],
                  "label": "",
                  "weight": 2
                },
                {
                  "constraints": [
                    "0 <= input.compactness_mean <= 2/5",
                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.concave_points_worst <= 7/20",
                    "0 <= input.concavity_mean <= 1/2",
                    "0 <= input.concavity_worst <= 3/2",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                    "((input.concavity_worst - 27219/100000) / 10431/50000) <= -5799/100000",
                    "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                    "((input.concavity_mean - 111/1250) / 1993/25000) > 10459/100000"
                  ],
                  "region": null,
                  "groups": [
                    {
                      "constraints": [
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                              "weight": 1
                            }
                          ],
                          "label": "",
                          "weight": 2
                        }
                      ],
                      "label": "",
                      "weight": 4
                    }
                  ],
                  "label": "",
                  "weight": 9
                }
              ],
              "label": "",
              "weight": 20
            }
          ],
          "label": "",
          "weight": 56
        }
      ],
      "label": "",
      "weight": 174
    }
  ]
}

Regions details

No group selected.

Concrete regions are numbered
Unnumbered regions are groups whose children share a particular constraint
Click on a region to view its details
Double click on a region to zoom in on it
Shift+double click to zoom out
Hit escape to reset back to the top

decomp of (rf_model input


"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"

Try this!

In [12]:

Modular_decomp.top "tree_0"

Out[12]:

- : Modular_decomp_intf.decomp_ref = <abstr>

Voronoi (8 of 8)
Table

{
  "regions": [
    {
      "constraints": [ "f_6 > 2453/25000" ],
      "region": null,
      "groups": [
        {
          "constraints": [ "f_6 > 2453/25000", "f_2 > 265413/100000" ],
          "region": {
            "constraints": [ "f_2 > 265413/100000", "f_6 > 2453/25000" ],
            "invariant": "F = (7,\n5)"
          },
          "groups": [],
          "label": "2",
          "weight": 1
        },
        {
          "constraints": [
            "f_6 > 2453/25000", "-2163/20000 < f_2 <= 265413/100000"
          ],
          "region": {
            "constraints": [
              "-2163/20000 < f_2 <= 265413/100000", "f_6 > 2453/25000"
            ],
            "invariant": "F = (6,\n128)"
          },
          "groups": [],
          "label": "1",
          "weight": 1
        }
      ],
      "label": "",
      "weight": 2
    },
    {
      "constraints": [ "f_2 > -2163/20000" ],
      "region": null,
      "groups": [
        {
          "constraints": [ "f_2 > -2163/20000", "f_6 <= -17063/100000" ],
          "region": {
            "constraints": [ "f_6 <= -17063/100000", "f_2 > -2163/20000" ],
            "invariant": "F = (24,\n0)"
          },
          "groups": [],
          "label": "2.2",
          "weight": 1
        },
        {
          "constraints": [
            "f_2 > -2163/20000", "-17063/100000 < f_6 <= 2453/25000"
          ],
          "region": {
            "constraints": [
              "-17063/100000 < f_6 <= 2453/25000", "f_2 > -2163/20000"
            ],
            "invariant": "F = (4,\n2)"
          },
          "groups": [],
          "label": "2.1",
          "weight": 1
        }
      ],
      "label": "",
      "weight": 2
    },
    {
      "constraints": [ "f_2 <= -2163/20000" ],
      "region": null,
      "groups": [
        {
          "constraints": [ "f_2 <= -2163/20000", "f_0 > 6587/25000" ],
          "region": null,
          "groups": [
            {
              "constraints": [
                "f_2 <= -2163/20000", "f_0 > 6587/25000",
                "f_3 > -13559/25000"
              ],
              "region": {
                "constraints": [
                  "f_2 <= -2163/20000", "f_3 > -13559/25000",
                  "f_0 > 6587/25000"
                ],
                "invariant": "F = (3,\n7)"
              },
              "groups": [],
              "label": "1.2",
              "weight": 1
            },
            {
              "constraints": [
                "f_2 <= -2163/20000", "f_0 > 6587/25000",
                "f_3 <= -13559/25000"
              ],
              "region": {
                "constraints": [
                  "f_3 <= -13559/25000", "f_2 <= -2163/20000",
                  "f_0 > 6587/25000"
                ],
                "invariant": "F = (8,\n2)"
              },
              "groups": [],
              "label": "1.1",
              "weight": 1
            }
          ],
          "label": "",
          "weight": 2
        },
        {
          "constraints": [ "f_2 <= -2163/20000", "f_0 <= 6587/25000" ],
          "region": null,
          "groups": [
            {
              "constraints": [
                "f_2 <= -2163/20000", "f_0 <= 6587/25000", "f_6 > -193/3125"
              ],
              "region": {
                "constraints": [
                  "f_0 <= 6587/25000", "f_2 <= -2163/20000",
                  "f_6 > -193/3125"
                ],
                "invariant": "F = (17,\n5)"
              },
              "groups": [],
              "label": "1.1.2",
              "weight": 1
            },
            {
              "constraints": [
                "f_2 <= -2163/20000", "f_0 <= 6587/25000", "f_6 <= -193/3125"
              ],
              "region": {
                "constraints": [
                  "f_6 <= -193/3125", "f_0 <= 6587/25000",
                  "f_2 <= -2163/20000"
                ],
                "invariant": "F = (236,\n1)"
              },
              "groups": [],
              "label": "1.1.1",
              "weight": 1
            }
          ],
          "label": "",
          "weight": 2
        }
      ],
      "label": "",
      "weight": 4
    }
  ]
}

Regions details

No group selected.

Concrete regions are numbered
Unnumbered regions are groups whose children share a particular constraint
Click on a region to view its details
Double click on a region to zoom in on it
Shift+double click to zoom out
Hit escape to reset back to the top

decomp of (tree_0 f_0, f_1, f_2, f_3, f_4, f_5, f_6

Reg_id	Constraints	Invariant
0	f_6 <= -193/3125 f_0 <= 6587/25000 f_2 <= -2163/20000	(236, 1)
1	f_0 <= 6587/25000 f_2 <= -2163/20000 f_6 > -193/3125	(17, 5)
2	f_3 <= -13559/25000 f_2 <= -2163/20000 f_0 > 6587/25000	(8, 2)
3	f_2 <= -2163/20000 f_3 > -13559/25000 f_0 > 6587/25000	(3, 7)
4	f_6 <= -17063/100000 f_2 > -2163/20000	(24, 0)
5	-17063/100000 < f_6 <= 2453/25000 f_2 > -2163/20000	(4, 2)
6	-2163/20000 < f_2 <= 265413/100000 f_6 > 2453/25000	(6, 128)
7	f_2 > 265413/100000 f_6 > 2453/25000	(7, 5)

We can also use side conditions on the region decomposition of our model by using the ~assuming: flag. One application here is in simulating partial observability. Perhaps we know most of the measurements for a particular set of cells and we'd like to see how the classification of the input depends on the remaining features. Let's imagine that we only have the concavity measurements for a particular patient's cell sample and we'd like to see how the output of our model depends on the values of the other features.

Try this!

In [13]:

let partial_observation x =
  is_valid_rf x &&
  x.concavity_mean = 0.04295 &&
  x.concavity_worst = 0.26000 &&
  x.concave_points_worst = 0.11460;;

Modular_decomp.top ~prune:true ~assuming:"partial_observation" "rf_model" [@@program];;

Out[13]:

val partial_observation : rf_input -> bool = <fun>
- : Modular_decomp_intf.decomp_ref = <abstr>

Voronoi (174 of 174)
Table

{
  "regions": [
    {
      "constraints": [
        "0 <= input.compactness_mean <= 2/5",
        "0 <= input.compactness_worst <= 6/5", "0 <= input.radius_se <= 7/2",
        "5 <= input.radius_mean <= 35",
        "input.concave_points_worst = 573/5000",
        "input.concavity_mean = 859/20000", "input.concavity_worst = 13/50"
      ],
      "region": null,
      "groups": [
        {
          "constraints": [
            "0 <= input.compactness_mean <= 2/5",
            "0 <= input.compactness_worst <= 6/5",
            "0 <= input.radius_se <= 7/2", "5 <= input.radius_mean <= 35",
            "input.concave_points_worst = 573/5000",
            "input.concavity_mean = 859/20000",
            "input.concavity_worst = 13/50",
            "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000"
          ],
          "region": null,
          "groups": [
            {
              "constraints": [
                "0 <= input.compactness_mean <= 2/5",
                "0 <= input.compactness_worst <= 6/5",
                "0 <= input.radius_se <= 7/2",
                "5 <= input.radius_mean <= 35",
                "input.concave_points_worst = 573/5000",
                "input.concavity_mean = 859/20000",
                "input.concavity_worst = 13/50",
                "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                "((input.radius_mean - 1412729/100000) / 70481/20000) <= 6587/25000"
              ],
              "region": {
                "constraints": [
                  "((input.radius_mean - 1412729/100000) / 70481/20000) <= 6587/25000",
                  "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                  "0 <= input.compactness_worst <= 6/5",
                  "0 <= input.radius_se <= 7/2",
                  "0 <= input.compactness_mean <= 2/5",
                  "5 <= input.radius_mean <= 35",
                  "input.concavity_mean = 859/20000",
                  "input.concavity_worst = 13/50",
                  "input.concave_points_worst = 573/5000"
                ],
                "invariant": "F = \"benign\""
              },
              "groups": [],
              "label": "2",
              "weight": 1
            },
            {
              "constraints": [
                "0 <= input.compactness_mean <= 2/5",
                "0 <= input.compactness_worst <= 6/5",
                "0 <= input.radius_se <= 7/2",
                "5 <= input.radius_mean <= 35",
                "input.concave_points_worst = 573/5000",
                "input.concavity_mean = 859/20000",
                "input.concavity_worst = 13/50",
                "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                "6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000"
              ],
              "region": null,
              "groups": [
                {
                  "constraints": [
                    "0 <= input.compactness_mean <= 2/5",
                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "input.concave_points_worst = 573/5000",
                    "input.concavity_mean = 859/20000",
                    "input.concavity_worst = 13/50",
                    "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                    "6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                    "((input.radius_se - 40517/100000) / 27731/100000) > -13559/25000"
                  ],
                  "region": {
                    "constraints": [
                      "6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                      "((input.radius_se - 40517/100000) / 27731/100000) > -13559/25000",
                      "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                      "0 <= input.compactness_worst <= 6/5",
                      "0 <= input.radius_se <= 7/2",
                      "0 <= input.compactness_mean <= 2/5",
                      "5 <= input.radius_mean <= 35",
                      "input.concavity_mean = 859/20000",
                      "input.concavity_worst = 13/50",
                      "input.concave_points_worst = 573/5000"
                    ],
                    "invariant": "F = \"benign\""
                  },
                  "groups": [],
                  "label": "1.2",
                  "weight": 1
                },
                {
                  "constraints": [
                    "0 <= input.compactness_mean <= 2/5",
                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "input.concave_points_worst = 573/5000",
                    "input.concavity_mean = 859/20000",
                    "input.concavity_worst = 13/50",
                    "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                    "6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                    "((input.radius_se - 40517/100000) / 27731/100000) <= -13559/25000"
                  ],
                  "region": {
                    "constraints": [
                      "6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                      "((input.radius_se - 40517/100000) / 27731/100000) <= -13559/25000",
                      "((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000",
                      "0 <= input.compactness_worst <= 6/5",
                      "0 <= input.radius_se <= 7/2",
                      "0 <= input.compactness_mean <= 2/5",
                      "5 <= input.radius_mean <= 35",
                      "input.concavity_mean = 859/20000",
                      "input.concavity_worst = 13/50",
                      "input.concave_points_worst = 573/5000"
                    ],
                    "invariant": "F = \"benign\""
                  },
                  "groups": [],
                  "label": "1.1",
                  "weight": 1
                }
              ],
              "label": "",
              "weight": 2
            }
          ],
          "label": "",
          "weight": 3
        },
        {
          "constraints": [
            "0 <= input.compactness_mean <= 2/5",
            "0 <= input.compactness_worst <= 6/5",
            "0 <= input.radius_se <= 7/2", "5 <= input.radius_mean <= 35",
            "input.concave_points_worst = 573/5000",
            "input.concavity_mean = 859/20000",
            "input.concavity_worst = 13/50",
            "((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000"
          ],
          "region": null,
          "groups": [
            {
              "constraints": [
                "0 <= input.compactness_mean <= 2/5",
                "0 <= input.compactness_worst <= 6/5",
                "0 <= input.radius_se <= 7/2",
                "5 <= input.radius_mean <= 35",
                "input.concave_points_worst = 573/5000",
                "input.concavity_mean = 859/20000",
                "input.concavity_worst = 13/50",
                "((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000",
                "((input.radius_mean - 1412729/100000) / 70481/20000) <= 6587/25000"
              ],
              "region": {
                "constraints": [
                  "((input.radius_mean - 1412729/100000) / 70481/20000) <= 6587/25000",
                  "((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000",
                  "0 <= input.compactness_worst <= 6/5",
                  "0 <= input.radius_se <= 7/2",
                  "0 <= input.compactness_mean <= 2/5",
                  "5 <= input.radius_mean <= 35",
                  "input.concavity_mean = 859/20000",
                  "input.concavity_worst = 13/50",
                  "input.concave_points_worst = 573/5000"
                ],
                "invariant": "F = \"benign\""
              },
              "groups": [],
              "label": "3.2",
              "weight": 1
            },
            {
              "constraints": [
                "0 <= input.compactness_mean <= 2/5",
                "0 <= input.compactness_worst <= 6/5",
                "0 <= input.radius_se <= 7/2",
                "5 <= input.radius_mean <= 35",
                "input.concave_points_worst = 573/5000",
                "input.concavity_mean = 859/20000",
                "input.concavity_worst = 13/50",
                "((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000",
                "6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000"
              ],
              "region": null,
              "groups": [
                {
                  "constraints": [
                    "0 <= input.compactness_mean <= 2/5",
                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "input.concave_points_worst = 573/5000",
                    "input.concavity_mean = 859/20000",
                    "input.concavity_worst = 13/50",
                    "((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000",
                    "6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                    "((input.radius_se - 40517/100000) / 27731/100000) > -13559/25000"
                  ],
                  "region": {
                    "constraints": [
                      "6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                      "((input.radius_se - 40517/100000) / 27731/100000) > -13559/25000",
                      "((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000",
                      "0 <= input.compactness_worst <= 6/5",
                      "0 <= input.radius_se <= 7/2",
                      "0 <= input.compactness_mean <= 2/5",
                      "5 <= input.radius_mean <= 35",
                      "input.concavity_mean = 859/20000",
                      "input.concavity_worst = 13/50",
                      "input.concave_points_worst = 573/5000"
                    ],
                    "invariant": "F = \"benign\""
                  },
                  "groups": [],
                  "label": "3.1.2",
                  "weight": 1
                },
                {
                  "constraints": [
                    "0 <= input.compactness_mean <= 2/5",
                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "input.concave_points_worst = 573/5000",
                    "input.concavity_mean = 859/20000",
                    "input.concavity_worst = 13/50",
                    "((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000",
                    "6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                    "((input.radius_se - 40517/100000) / 27731/100000) <= -13559/25000"
                  ],
                  "region": {
                    "constraints": [
                      "6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000",
                      "((input.radius_se - 40517/100000) / 27731/100000) <= -13559/25000",
                      "((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000",
                      "0 <= input.compactness_worst <= 6/5",
                      "0 <= input.radius_se <= 7/2",
                      "0 <= input.compactness_mean <= 2/5",
                      "5 <= input.radius_mean <= 35",
                      "input.concavity_mean = 859/20000",
                      "input.concavity_worst = 13/50",
                      "input.concave_points_worst = 573/5000"
                    ],
                    "invariant": "F = \"benign\""
                  },
                  "groups": [],
                  "label": "3.1.1",
                  "weight": 1
                }
              ],
              "label": "",
              "weight": 2
            }
          ],
          "label": "",
          "weight": 3
        },
        {
          "constraints": [
            "0 <= input.compactness_mean <= 2/5",
            "0 <= input.compactness_worst <= 6/5",
            "0 <= input.radius_se <= 7/2", "5 <= input.radius_mean <= 35",
            "input.concave_points_worst = 573/5000",
            "input.concavity_mean = 859/20000",
            "input.concavity_worst = 13/50",
            "((input.radius_mean - 1412729/100000) / 70481/20000) > 17131/25000"
          ],
          "region": null,
          "groups": [
            {
              "constraints": [
                "0 <= input.compactness_mean <= 2/5",
                "0 <= input.compactness_worst <= 6/5",
                "0 <= input.radius_se <= 7/2",
                "5 <= input.radius_mean <= 35",
                "input.concave_points_worst = 573/5000",
                "input.concavity_mean = 859/20000",
                "input.concavity_worst = 13/50",
                "((input.radius_mean - 1412729/100000) / 70481/20000) > 17131/25000",
                "-13559/25000 < ((input.radius_se - 40517/100000) / 27731/100000) <= 1422/3125"
              ],
              "region": {
                "constraints": [
                  "((input.radius_mean - 1412729/100000) / 70481/20000) > 17131/25000",
                  "-13559/25000 < ((input.radius_se - 40517/100000) / 27731/100000) <= 1422/3125",
                  "0 <= input.compactness_worst <= 6/5",
                  "0 <= input.radius_se <= 7/2",
                  "0 <= input.compactness_mean <= 2/5",
                  "5 <= input.radius_mean <= 35",
                  "input.concavity_mean = 859/20000",
                  "input.concavity_worst = 13/50",
                  "input.concave_points_worst = 573/5000"
                ],
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                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "input.concave_points_worst = 573/5000",
                    "input.concavity_mean = 859/20000",
                    "input.concavity_worst = 13/50", "false",
                    "((input.radius_mean - 1412729/100000) / 70481/20000) > 17131/25000",
                    "((input.radius_se - 40517/100000) / 27731/100000) <= 20821/50000"
                  ],
                  "region": null,
                  "groups": [],
                  "label": "",
                  "weight": 4
                },
                {
                  "constraints": [
                    "0 <= input.compactness_mean <= 2/5",
                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "input.concave_points_worst = 573/5000",
                    "input.concavity_mean = 859/20000",
                    "input.concavity_worst = 13/50", "false",
                    "((input.radius_mean - 1412729/100000) / 70481/20000) > 17131/25000",
                    "((input.radius_se - 40517/100000) / 27731/100000) <= 1422/3125"
                  ],
                  "region": null,
                  "groups": [],
                  "label": "",
                  "weight": 13
                },
                {
                  "constraints": [
                    "0 <= input.compactness_mean <= 2/5",
                    "0 <= input.compactness_worst <= 6/5",
                    "0 <= input.radius_se <= 7/2",
                    "5 <= input.radius_mean <= 35",
                    "input.concave_points_worst = 573/5000",
                    "input.concavity_mean = 859/20000",
                    "input.concavity_worst = 13/50", "false",
                    "((input.radius_mean - 1412729/100000) / 70481/20000) > 17131/25000",
                    "((input.radius_se - 40517/100000) / 27731/100000) > 1422/3125"
                  ],
                  "region": null,
                  "groups": [],
                  "label": "",
                  "weight": 20
                }
              ],
              "label": "",
              "weight": 47
            }
          ],
          "label": "",
          "weight": 165
        }
      ],
      "label": "",
      "weight": 174
    }
  ]
}

Regions details

No group selected.

Concrete regions are numbered
Unnumbered regions are groups whose children share a particular constraint
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Double click on a region to zoom in on it
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decomp of (rf_model input


"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"malignant"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"

Voronoi (9 of 9)
Table

Regions details

No group selected.

Concrete regions are numbered
Unnumbered regions are groups whose children share a particular constraint
Click on a region to view its details
Double click on a region to zoom in on it
Shift+double click to zoom out
Hit escape to reset back to the top

decomp of (rf_model input


"malignant"
"malignant"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"
"benign"

Regression¶

In a regression task we want to learn to predict the value(s) of some variable(s) based on previous data. In the commonly used Forest Fires dataset the aim is to predict the area burned by forest fires, in the northeast region of Portugal, by using meteorological and other data. This is a fairly difficult task and while the neural network below doesn't achieve state-of-the-art performance, it's enough to demonstrate how we can analyse relatively simple models in Imandra. In the dataset we have the following variables:

1. X-axis spatial coordinate (within the Montesinho park map)
2. Y-axis spatial coordinate (within the Montesinho park map)
3. Month
4. Day
5. FFMC index (from the FWI system)
6. DMC index (from the FWI system)
7. DC index (from the FWI system)
8. ISI index (from the FWI system)
9. Temperature
10. Relative percentage humidity
11. Wind speed
12. Rainfall
13. Area of forest burned

We again pre-process the data before learning by first transforming the month and day variables into a numerical value and applying a sine transformation (so that similar times are close in value), as well as removing outliers and applying an approximate logarithmic transformation to the area variable (as recommended in the dataset description). Each variable is scaled to lie between 0 and 1, and those with high correlations and/or low mutual information respect to the target variable are removed. We then split the data into training (80%) and test (20%) sets and use Keras to learn a simple feed-forward neural network with one (6 neuron) hidden layer, ReLU activation functions, and stochastic gradient descent to optimise the mean squared error. After saving our model as a .h5 file we use a short Python script to extract the network into an IML file and reason about it using Imandra.

Try this!

In [14]:

let relu x = Real.(if x > 0.0 then x else 0.0);;

let linear x = Real.(x)

let layer_0 (x_0, x_1, x_2, x_3, x_4, x_5) = let open Real in
  let y_0 = relu @@ (0.20124)*x_0 + (-0.15722)*x_1 + (-0.19063)*x_2 + (-0.54562)*x_3 + (0.03425)*x_4 + (0.50104)*x_5 + -0.02768 in
  let y_1 = relu @@ (0.29103)*x_0 + (0.03180)*x_1 + (-0.16336)*x_2 + (0.17919)*x_3 + (0.32971)*x_4 + (-0.43206)*x_5 + -0.02620 in
  let y_2 = relu @@ (0.66419)*x_0 + (0.25399)*x_1 + (0.00449)*x_2 + (0.03841)*x_3 + (-0.51482)*x_4 + (0.58299)*x_5 + 0.11858 in
  let y_3 = relu @@ (0.47598)*x_0 + (-0.36142)*x_1 + (0.38981)*x_2 + (0.27632)*x_3 + (-0.61231)*x_4 + (-0.03662)*x_5 + -0.02890 in
  let y_4 = relu @@ (0.10277)*x_0 + (-0.28841)*x_1 + (0.04637)*x_2 + (0.28808)*x_3 + (0.05957)*x_4 + (-0.22041)*x_5 + 0.18270 in
  let y_5 = relu @@ (0.55604)*x_0 + (-0.04015)*x_1 + (0.10557)*x_2 + (0.60757)*x_3 + (-0.32314)*x_4 + (0.47933)*x_5 + -0.24876 in
  (y_0, y_1, y_2, y_3, y_4, y_5)

let layer_1 (x_0, x_1, x_2, x_3, x_4, x_5) = let open Real in
  let y_0 = linear @@ (0.28248)*x_0 + (-0.25208)*x_1 + (-0.50075)*x_2 + (-0.07092)*x_3 + (-0.43189)*x_4 + (0.60065)*x_5 + 0.47136 in
  (y_0)

let nn (x_0, x_1, x_2, x_3, x_4, x_5) = let open Real in
  (x_0, x_1, x_2, x_3, x_4, x_5) |> layer_0 |> layer_1

Out[14]:

val relu : real -> real = <fun>
val linear : 'a -> 'a = <fun>
val layer_0 :
  real * real * real * real * real * real ->
  real * real * real * real * real * real = <fun>
val layer_1 : real * real * real * real * real * real -> real = <fun>
val nn : real * real * real * real * real * real -> real = <fun>

Given the description of the dataset above we can again create some custom input types in Imandra for our model.

Try this!

In [15]:

type month = Jan | Feb | Mar | Apr | May | Jun| Jul | Aug | Sep | Oct | Nov | Dec

type day = Mon | Tue | Wed | Thu | Fri | Sat | Sun

type nn_input = {
  month : month;
  day : day;
  dmc : real;
  temp : real;
  rh : real;
  rain : real
}

Out[15]:

type month =
    Jan
  | Feb
  | Mar
  | Apr
  | May
  | Jun
  | Jul
  | Aug
  | Sep
  | Oct
  | Nov
  | Dec
type day = Mon | Tue | Wed | Thu | Fri | Sat | Sun
type nn_input = {
  month : month;
  day : day;
  dmc : real;
  temp : real;
  rh : real;
  rain : real;
}

As before, because we pre-processed our data, we'll add in a function applying this transform to each input variable. Equally, we'll need to convert back to hectares for our output variable, again using some minimum and maximum values extracted during our data pre-processing stage. After that we define a full model which combines these pre/post-processing steps and the network above.

Try this!

In [16]:

let month_2_num = let open Real in function
  | Jan -> 0.134
  | Feb -> 0.500
  | Mar -> 1.000
  | Apr -> 1.500
  | May -> 1.866
  | Jun -> 2.000
  | Jul -> 1.866
  | Aug -> 1.500
  | Sep -> 1.000
  | Oct -> 0.500
  | Nov -> 0.133
  | Dec -> 0.000

let day_2_num = let open Real in function
  | Mon -> 0.377
  | Tue -> 1.223
  | Wed -> 1.901
  | Thu -> 1.901
  | Fri -> 1.223
  | Sat -> 0.377
  | Sun -> 0.000

let process_nn_input input = let open Real in
  let real_month = month_2_num input.month in
  let real_day = day_2_num input.day in
  let x_0 = (real_month - 0.0)  / (2.0   - 0.0)  in
  let x_1 = (real_day   - 0.0)  / (1.901 - 0.0)  in
  let x_2 = (input.dmc  - 1.1)  / (291.3 - 1.1)  in
  let x_3 = (input.temp - 2.2)  / (33.3  - 2.2)  in
  let x_4 = (input.rh   - 15.0) / (100.0 - 15.0) in
  let x_5 = (input.rain - 0.0)  / (6.40  - 0.0)  in
  (x_0, x_1, x_2, x_3, x_4, x_5)

let process_nn_output y_0 = let open Real in
  let y = 4.44323 * y_0 in
  if y <= 1.0 then (y - 0.00000) * 1.71828 else
  if y <= 2.0 then (y - 0.63212) * 4.67077 else
  if y <= 3.0 then (y - 1.49679) * 12.69648 else
  if y <= 4.0 then (y - 2.44700) * 34.51261 else
  (y - 3.42868) * 93.81501

let nn_model input = input |> process_nn_input |> nn |> process_nn_output

Out[16]:

val month_2_num : month -> real = <fun>
val day_2_num : day -> real = <fun>
val process_nn_input : nn_input -> real * real * real * real * real * real =
  <fun>
val process_nn_output : real -> real = <fun>
val nn_model : nn_input -> real = <fun>

Let's start as in the previous section by running a datum from our dataset through the model. In particular, we'll input x = (Aug, Sat, 231.1, 26.9, 31.0, 0.0) which has an area of y = 4.96 hectares in the data.

Try this!

In [17]:

let x = {
  month = Aug;
  day = Sat;
  dmc = 231.1;
  temp = 26.9;
  rh = 31.0;
  rain = 0.0
}

let y = nn_model x

Out[17]:

val x : nn_input =
  {month = Aug; day = Sat; dmc = 231.1; temp = 26.9; rh = 31.; rain = 0.}
val y : real = 2.1368837387

Our answer is both roughly similar to the recorded datapoint value and also to the value we get from our original Keras model, 2.13683266556. The small disparity here is due to our rounding the weight values in our network to 5 decimal places when we extracted them to IML, though it wasn't necessary to do so. Now we'll use Imandra to generate an example for us with some particular side conditions.

Try this!

In [18]:

instance (fun x -> nn_model x >. 20.0 && x.temp = 20.0 && x.month = May)

Out[18]:

- : nn_input -> bool = <fun>
module CX : sig val x : nn_input end

Instance (after 0 steps, 0.036s):
let x : nn_input =
  {month = May; day = Mon;
   dmc =
   5504175945856158301941488984049755357/5071988086553252496827564580975000;
   temp = 20;
   rh = 6938343360970919031635529463866329/25359940432766262484137822904875;
   rain =
   6689442348868569273582309835512268/633998510819156562103445572621875}

Instance

call graph
proof

digraph "call graph" {
goal [label="let (_x_0 : month) = x.month in\llet (_x_1 : bool) = _x_0 = Mar in\llet (_x_2 : bool) = _x_0 = Feb in\llet (_x_3 : bool) = _x_0 = Jan in\llet (_x_4 : real)\l    = if _x_3 then 67/500\l      else\l      if _x_2 then 1/2\l      else if _x_1 then 1 else if _x_0 = Apr then 3/2 else …\lin\llet (_x_5 : real) = 5031/50000 * _x_4 in\llet (_x_6 : day) = x.day in\llet (_x_7 : bool) = (_x_6 = Wed) \|\| (_x_6 = Thu) in\llet (_x_8 : bool) = _x_6 = Tue in\llet (_x_9 : bool) = _x_6 = Mon in\llet (_x_10 : real)\l    = (-7861/95050)\l      * (if _x_9 then 377/1000\l         else if _x_8 then 1223/1000 else if _x_7 then 1901/1000 else …)\lin\llet (_x_11 : real) = x.dmc in\llet (_x_12 : real) = (-19063/29020000) * _x_11 in\llet (_x_13 : real) = x.temp in\llet (_x_14 : real) = (-27281/1555000) * _x_13 in\llet (_x_15 : real) = x.rh in\llet (_x_16 : real) = 137/340000 * _x_15 in\llet (_x_17 : real) = x.rain in\llet (_x_18 : real) = 6263/80000 * _x_17 in\llet (_x_19 : real)\l    = 1716983137/306857480000 +. _x_5 +. _x_10 +. _x_12 +. _x_14 +. _x_16\l      +. _x_18\lin\llet (_x_20 : real)\l    = if _x_9 then 377/1000\l      else\l      if _x_8 then 1223/1000\l      else if _x_7 then 1901/1000 else if _x_6 = Fri then 1223/1000 else …\lin\llet (_x_21 : real) = 29103/200000 * _x_4 in\llet (_x_22 : real) = 159/9505 * _x_20 in\llet (_x_23 : real) = (-1021/1813750) * _x_11 in\llet (_x_24 : real) = 17919/3110000 * _x_13 in\llet (_x_25 : real) = 32971/8500000 * _x_15 in\llet (_x_26 : real) = (-21603/320000) * _x_17 in\llet (_x_27 : real)\l    = if _x_21 +. _x_22 +. _x_23 +. _x_24 +. _x_25 +. _x_26\l         \<= 73983893263/767143700000\l      then 0\l      else\l        (-73983893263/767143700000) +. _x_21 +. _x_22 +. _x_23 +. _x_24\l        +. _x_25 +. _x_26\lin\llet (_x_28 : real) = 66419/200000 * _x_4 in\llet (_x_29 : real) = 25399/190100 * _x_20 in\llet (_x_30 : real) = 449/29020000 * _x_11 in\llet (_x_31 : real) = 3841/3110000 * _x_13 in\llet (_x_32 : real) = (-25741/4250000) * _x_15 in\llet (_x_33 : real) = 58299/640000 * _x_17 in\llet (_x_34 : real)\l    = if _x_28 +. _x_29 +. _x_30 +. _x_31 +. _x_32 +. _x_33\l         \<= (-317131778543/1534287400000)\l      then 0\l      else\l        317131778543/1534287400000 +. _x_28 +. _x_29 +. _x_30 +. _x_31\l        +. _x_32 +. _x_33\lin\llet (_x_35 : real) = 23799/100000 * _x_4 in\llet (_x_36 : real) = (-18071/95050) * _x_20 in\llet (_x_37 : real) = 38981/29020000 * _x_11 in\llet (_x_38 : real) = 1727/194375 * _x_13 in\llet (_x_39 : real) = (-61231/8500000) * _x_15 in\llet (_x_40 : real) = (-1831/320000) * _x_17 in\llet (_x_41 : real)\l    = if _x_35 +. _x_36 +. _x_37 +. _x_38 +. _x_39 +. _x_40\l         \<= (-89188713933/1534287400000)\l      then 0\l      else\l        89188713933/1534287400000 +. _x_35 +. _x_36 +. _x_37 +. _x_38\l        +. _x_39 +. _x_40\lin\llet (_x_42 : real) = 10277/200000 * _x_4 in\llet (_x_43 : real) = (-28841/190100) * _x_20 in\llet (_x_44 : real) = 4637/29020000 * _x_11 in\llet (_x_45 : real) = 3601/388750 * _x_13 in\llet (_x_46 : real) = 5957/8500000 * _x_15 in\llet (_x_47 : real) = (-22041/640000) * _x_17 in\llet (_x_48 : real)\l    = if _x_42 +. _x_43 +. _x_44 +. _x_45 +. _x_46 +. _x_47\l         \<= (-372238333/2454859840)\l      then 0\l      else\l        372238333/2454859840 +. _x_42 +. _x_43 +. _x_44 +. _x_45 +. _x_46\l        +. _x_47\lin\llet (_x_49 : real) = 13901/50000 * _x_4 in\llet (_x_50 : real) = (-803/38020) * _x_20 in\llet (_x_51 : real) = 10557/29020000 * _x_11 in\llet (_x_52 : real) = 60757/3110000 * _x_13 in\llet (_x_53 : real) = (-16157/4250000) * _x_15 in\llet (_x_54 : real) = 47933/640000 * _x_17 in\llet (_x_55 : real)\l    = if _x_49 +. _x_50 +. _x_51 +. _x_52 +. _x_53 +. _x_54\l         \<= 72146699557/306857480000\l      then 0\l      else\l        (-72146699557/306857480000) +. _x_49 +. _x_50 +. _x_51 +. _x_52\l        +. _x_53 +. _x_54\lin\llet (_x_56 : real)\l    = 1568904513/1250000000\l      * (if _x_5 +. (-7861/95050) * _x_20 +. _x_12 +. _x_14 +. _x_16 +. _x_18\l            \<= (-1716983137/306857480000)\l         then 0 else _x_19)\l      +. (-1400061773/1250000000) * _x_27 +. (-889978969/400000000) * _x_34\l      +. (-787784679/2500000000) * _x_41\l      +. (-19189866047/10000000000) * _x_48 +. 5337652199/2000000000 * _x_55\lin\llet (_x_57 : real)\l    = if 5031/50000\l         * (if _x_3 then 67/500\l            else if _x_2 then 1/2 else if _x_1 then 1 else …)\l         +. _x_10 +. _x_12 +. _x_14 +. _x_16 +. _x_18\l         \<= (-1716983137/306857480000)\l      then 0 else _x_19\lin\lnot\l((if _x_56 \<= (-341987779/312500000)\l  then\l    28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_57\l    +. (-60142453582761/31250000000000) * _x_27\l    +. (-38230826571333/10000000000000) * _x_34\l    +. (-33840866455803/62500000000000) * _x_41\l    +. (-824339075780979/250000000000000) * _x_48\l    +. 229289525512443/50000000000000 * _x_55\l  else\l  if _x_56 \<= (-29487779/312500000)\l  then\l    213430965464483/31250000000000 +. 732799213218501/125000000000000 * _x_57\l    +. (-653936652747521/125000000000000) * _x_27\l    +. (-415688706903613/40000000000000) * _x_34\l    +. (-367956104513283/250000000000000) * _x_41\l    +. (-8963145063634619/1000000000000000) * _x_48\l    +. 2493094576152323/200000000000000 * _x_55\l  else\l  if _x_56 \<= 283012221/312500000\l  then\l    1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_57\l    +. (-111099101872869/7812500000000) * _x_27\l    +. (-70622501127057/2500000000000) * _x_34\l    +. (-62513077632687/15625000000000) * _x_41\l    +. (-1522773440427591/62500000000000) * _x_48\l    +. 423558714947247/12500000000000 * _x_55\l  else if _x_56 \<= 595512221/312500000 then … else …)\l \<= 20)\l&& (_x_13 = 20) && (_x_0 = May)",shape=box,style=filled,color="cyan",fontname="courier",fontsize=14];
}

proof attempt

ground_instances:

definitions:

inductions:

search_time:

0.036s

details:

Expand

smt_stats:

num checks:	1
arith assert lower:	78
arith tableau max rows:	24
arith tableau max columns:	122
arith pivots:	65
rlimit count:	66129
mk clause:	148
datatype occurs check:	8
mk bool var:	209
arith assert upper:	122
datatype splits:	6
decisions:	171
arith row summations:	569
arith bound prop:	4
propagations:	256
conflicts:	27
arith fixed eqs:	23
datatype accessor ax:	10
minimized lits:	16
arith conflicts:	10
arith num rows:	24
arith assert diseq:	11
datatype constructor ax:	10
final checks:	1
added eqs:	153
del clause:	60
arith eq adapter:	71
time:	0.028000
memory:	22.550000
max memory:	23.340000
num allocs:	35892153702.000000

Expand

start[0.036s]
  let (_x_0 : real)
      = 5031/25000 * … +. (-7861/50000) * … +. (-19063/100000) * …
        +. (-27281/50000) * … +. 137/4000 * … +. 6263/12500 * …
        +. (-173/6250)
  in
  let (_x_1 : real)
      = 29103/100000 * … +. 159/5000 * … +. (-1021/6250) * …
        +. 17919/100000 * … +. 32971/100000 * … +. (-21603/50000) * …
        +. (-131/5000)
  in
  let (_x_2 : real)
      = 66419/100000 * … +. 25399/100000 * … +. 449/100000 * …
        +. 3841/100000 * … +. (-25741/50000) * … +. 58299/100000 * …
        +. 5929/50000
  in
  let (_x_3 : real)
      = 23799/50000 * … +. (-18071/50000) * … +. 38981/100000 * …
        +. 1727/6250 * … +. (-61231/100000) * … +. (-1831/50000) * …
        +. (-289/10000)
  in
  let (_x_4 : real)
      = 10277/100000 * … +. (-28841/100000) * … +. 4637/100000 * …
        +. 3601/12500 * … +. 5957/100000 * … +. (-22041/100000) * …
        +. 1827/10000
  in
  let (_x_5 : real)
      = 13901/25000 * … +. (-803/20000) * … +. 10557/100000 * …
        +. 60757/100000 * … +. (-16157/50000) * … +. 47933/100000 * …
        +. (-6219/25000)
  in
  let (_x_6 : real)
      = 444323/100000
        * (3531/12500 * (if _x_0 > 0 then _x_0 else 0)
           +. (-3151/12500) * (if _x_1 > 0 then _x_1 else 0)
           +. (-2003/4000) * (if _x_2 > 0 then _x_2 else 0)
           +. (-1773/25000) * (if _x_3 > 0 then _x_3 else 0)
           +. (-43189/100000) * (if _x_4 > 0 then _x_4 else 0)
           +. 12013/20000 * (if _x_5 > 0 then _x_5 else 0) +. 1473/3125)
  in
  ((if _x_6 <= 1 then (_x_6 - 0) * 42957/25000
    else
    if _x_6 <= 2 then (_x_6 - 15803/25000) * 467077/100000
    else
    if _x_6 <= 3 then (_x_6 - 149679/100000) * 79353/6250
    else if _x_6 <= 4 then … else …)
   > 20)
  && ((( :var_0: ).temp = 20) && (( :var_0: ).month = May))

simplify

into:	let (_x_0 : month) = ( :var_0: ).month in let (_x_1 : real) = if _x_0 = Jan then 67/500 else if _x_0 = Feb then 1/2 else if _x_0 = Mar then 1 else if _x_0 = Apr then 3/2 else … in let (_x_2 : real) = 5031/50000 * _x_1 in let (_x_3 : day) = ( :var_0: ).day in let (_x_4 : real) = if _x_3 = Mon then 377/1000 else if _x_3 = Tue then 1223/1000 else if (_x_3 = Wed) \|\| (_x_3 = Thu) then 1901/1000 else if _x_3 = Fri then 1223/1000 else … in let (_x_5 : real) = (-7861/95050) * _x_4 in let (_x_6 : real) = ( :var_0: ).dmc in let (_x_7 : real) = (-19063/29020000) * _x_6 in let (_x_8 : real) = ( :var_0: ).temp in let (_x_9 : real) = (-27281/1555000) * _x_8 in let (_x_10 : real) = ( :var_0: ).rh in let (_x_11 : real) = 137/340000 * _x_10 in let (_x_12 : real) = ( :var_0: ).rain in let (_x_13 : real) = 6263/80000 * _x_12 in let (_x_14 : real) = if _x_2 +. _x_5 +. _x_7 +. _x_9 +. _x_11 +. _x_13 <= (-1716983137/306857480000) then 0 else 1716983137/306857480000 +. _x_2 +. _x_5 +. _x_7 +. _x_9 +. _x_11 +. _x_13 in let (_x_15 : real) = 29103/200000 * _x_1 in let (_x_16 : real) = 159/9505 * _x_4 in let (_x_17 : real) = (-1021/1813750) * _x_6 in let (_x_18 : real) = 17919/3110000 * _x_8 in let (_x_19 : real) = 32971/8500000 * _x_10 in let (_x_20 : real) = (-21603/320000) * _x_12 in let (_x_21 : real) = if _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19 +. _x_20 <= 73983893263/767143700000 then 0 else (-73983893263/767143700000) +. _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19 +. _x_20 in let (_x_22 : real) = 66419/200000 * _x_1 in let (_x_23 : real) = 25399/190100 * _x_4 in let (_x_24 : real) = 449/29020000 * _x_6 in let (_x_25 : real) = 3841/3110000 * _x_8 in let (_x_26 : real) = (-25741/4250000) * _x_10 in let (_x_27 : real) = 58299/640000 * _x_12 in let (_x_28 : real) = if _x_22 +. _x_23 +. _x_24 +. _x_25 +. _x_26 +. _x_27 <= (-317131778543/1534287400000) then 0 else 317131778543/1534287400000 +. _x_22 +. _x_23 +. _x_24 +. _x_25 +. _x_26 +. _x_27 in let (_x_29 : real) = 23799/100000 * _x_1 in let (_x_30 : real) = (-18071/95050) * _x_4 in let (_x_31 : real) = 38981/29020000 * _x_6 in let (_x_32 : real) = 1727/194375 * _x_8 in let (_x_33 : real) = (-61231/8500000) * _x_10 in let (_x_34 : real) = (-1831/320000) * _x_12 in let (_x_35 : real) = if _x_29 +. _x_30 +. _x_31 +. _x_32 +. _x_33 +. _x_34 <= (-89188713933/1534287400000) then 0 else 89188713933/1534287400000 +. _x_29 +. _x_30 +. _x_31 +. _x_32 +. _x_33 +. _x_34 in let (_x_36 : real) = 10277/200000 * _x_1 in let (_x_37 : real) = (-28841/190100) * _x_4 in let (_x_38 : real) = 4637/29020000 * _x_6 in let (_x_39 : real) = 3601/388750 * _x_8 in let (_x_40 : real) = 5957/8500000 * _x_10 in let (_x_41 : real) = (-22041/640000) * _x_12 in let (_x_42 : real) = if _x_36 +. _x_37 +. _x_38 +. _x_39 +. _x_40 +. _x_41 <= (-372238333/2454859840) then 0 else 372238333/2454859840 +. _x_36 +. _x_37 +. _x_38 +. _x_39 +. _x_40 +. _x_41 in let (_x_43 : real) = 13901/50000 * _x_1 in let (_x_44 : real) = (-803/38020) * _x_4 in let (_x_45 : real) = 10557/29020000 * _x_6 in let (_x_46 : real) = 60757/3110000 * _x_8 in let (_x_47 : real) = (-16157/4250000) * _x_10 in let (_x_48 : real) = 47933/640000 * _x_12 in let (_x_49 : real) = if _x_43 +. _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48 <= 72146699557/306857480000 then 0 else (-72146699557/306857480000) +. _x_43 +. _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48 in let (_x_50 : real) = 1568904513/1250000000 * _x_14 +. (-1400061773/1250000000) * _x_21 +. (-889978969/400000000) * _x_28 +. (-787784679/2500000000) * _x_35 +. (-19189866047/10000000000) * _x_42 +. 5337652199/2000000000 * _x_49 in not ((if _x_50 <= (-341987779/312500000) then 28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_14 +. (-60142453582761/31250000000000) * _x_21 +. (-38230826571333/10000000000000) * _x_28 +. (-33840866455803/62500000000000) * _x_35 +. (-824339075780979/250000000000000) * _x_42 +. 229289525512443/50000000000000 * _x_49 else if _x_50 <= (-29487779/312500000) then 213430965464483/31250000000000 +. 732799213218501/125000000000000 * _x_14 +. (-653936652747521/125000000000000) * _x_21 +. (-415688706903613/40000000000000) * _x_28 +. (-367956104513283/250000000000000) * _x_35 +. (-8963145063634619/1000000000000000) * _x_42 +. 2493094576152323/200000000000000 * _x_49 else if _x_50 <= 283012221/312500000 then 1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_14 +. (-111099101872869/7812500000000) * _x_21 +. (-70622501127057/2500000000000) * _x_28 +. (-62513077632687/15625000000000) * _x_35 +. (-1522773440427591/62500000000000) * _x_42 +. 423558714947247/12500000000000 * _x_49 else if _x_50 <= 595512221/312500000 then … else …) <= 20) && (_x_8 = 20) && (_x_0 = May)
expansions:	[]
rewrite_steps:
forward_chaining:

Sat (Some let x : nn_input = {month = May; day = Mon; dmc = (Q.of_string "5504175945856158301941488984049755357/5071988086553252496827564580975000"); temp = (Q.of_nativeint (20n)); rh = (Q.of_string "6938343360970919031635529463866329/25359940432766262484137822904875"); rain = (Q.of_string "6689442348868569273582309835512268/633998510819156562103445572621875")} )

digraph "proof" {
p_359 [label="Start (let (_x_0 : real)\l           = 5031/25000 * … +. (-7861/50000) * … +. (-19063/100000) * …\l             +. (-27281/50000) * … +. 137/4000 * … +. 6263/12500 * …\l             +. (-173/6250)\l       in\l       let (_x_1 : real)\l           = 29103/100000 * … +. 159/5000 * … +. (-1021/6250) * …\l             +. 17919/100000 * … +. 32971/100000 * …\l             +. (-21603/50000) * … +. (-131/5000)\l       in\l       let (_x_2 : real)\l           = 66419/100000 * … +. 25399/100000 * … +. 449/100000 * …\l             +. 3841/100000 * … +. (-25741/50000) * …\l             +. 58299/100000 * … +. 5929/50000\l       in\l       let (_x_3 : real)\l           = 23799/50000 * … +. (-18071/50000) * … +. 38981/100000 * …\l             +. 1727/6250 * … +. (-61231/100000) * …\l             +. (-1831/50000) * … +. (-289/10000)\l       in\l       let (_x_4 : real)\l           = 10277/100000 * … +. (-28841/100000) * … +. 4637/100000 * …\l             +. 3601/12500 * … +. 5957/100000 * …\l             +. (-22041/100000) * … +. 1827/10000\l       in\l       let (_x_5 : real)\l           = 13901/25000 * … +. (-803/20000) * … +. 10557/100000 * …\l             +. 60757/100000 * … +. (-16157/50000) * …\l             +. 47933/100000 * … +. (-6219/25000)\l       in\l       let (_x_6 : real)\l           = 444323/100000\l             * (3531/12500 * (if _x_0 \> 0 then _x_0 else 0)\l                +. (-3151/12500) * (if _x_1 \> 0 then _x_1 else 0)\l                +. (-2003/4000) * (if _x_2 \> 0 then _x_2 else 0)\l                +. (-1773/25000) * (if _x_3 \> 0 then _x_3 else 0)\l                +. (-43189/100000) * (if _x_4 \> 0 then _x_4 else 0)\l                +. 12013/20000 * (if _x_5 \> 0 then _x_5 else 0) +. 1473/3125)\l       in\l       ((if _x_6 \<= 1 then (_x_6 - 0) * 42957/25000\l         else\l         if _x_6 \<= 2 then (_x_6 - 15803/25000) * 467077/100000\l         else\l         if _x_6 \<= 3 then (_x_6 - 149679/100000) * 79353/6250\l         else if _x_6 \<= 4 then … else …)\l        \> 20)\l       && ((( :var_0: ).temp = 20) && (( :var_0: ).month = May)) :time 0.036s)",shape=box,style=filled,fontname="courier",fontsize=14];
p_359 -> p_358 [label=""];
p_358 [label="Simplify (let (_x_0 : month) = ( :var_0: ).month in\l          let (_x_1 : real)\l              = if _x_0 = Jan then 67/500\l                else\l                if _x_0 = Feb then 1/2\l                else\l                if _x_0 = Mar then 1 else if _x_0 = Apr then 3/2 else …\l          in\l          let (_x_2 : real) = 5031/50000 * _x_1 in\l          let (_x_3 : day) = ( :var_0: ).day in\l          let (_x_4 : real)\l              = if _x_3 = Mon then 377/1000\l                else\l                if _x_3 = Tue then 1223/1000\l                else\l                if (_x_3 = Wed) \|\| (_x_3 = Thu) then 1901/1000\l                else if _x_3 = Fri then 1223/1000 else …\l          in\l          let (_x_5 : real) = (-7861/95050) * _x_4 in\l          let (_x_6 : real) = ( :var_0: ).dmc in\l          let (_x_7 : real) = (-19063/29020000) * _x_6 in\l          let (_x_8 : real) = ( :var_0: ).temp in\l          let (_x_9 : real) = (-27281/1555000) * _x_8 in\l          let (_x_10 : real) = ( :var_0: ).rh in\l          let (_x_11 : real) = 137/340000 * _x_10 in\l          let (_x_12 : real) = ( :var_0: ).rain in\l          let (_x_13 : real) = 6263/80000 * _x_12 in\l          let (_x_14 : real)\l              = if _x_2 +. _x_5 +. _x_7 +. _x_9 +. _x_11 +. _x_13\l                   \<= (-1716983137/306857480000)\l                then 0\l                else\l                  1716983137/306857480000 +. _x_2 +. _x_5 +. _x_7 +. _x_9\l                  +. _x_11 +. _x_13\l          in\l          let (_x_15 : real) = 29103/200000 * _x_1 in\l          let (_x_16 : real) = 159/9505 * _x_4 in\l          let (_x_17 : real) = (-1021/1813750) * _x_6 in\l          let (_x_18 : real) = 17919/3110000 * _x_8 in\l          let (_x_19 : real) = 32971/8500000 * _x_10 in\l          let (_x_20 : real) = (-21603/320000) * _x_12 in\l          let (_x_21 : real)\l              = if _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19 +. _x_20\l                   \<= 73983893263/767143700000\l                then 0\l                else\l                  (-73983893263/767143700000) +. _x_15 +. _x_16 +. _x_17\l                  +. _x_18 +. _x_19 +. _x_20\l          in\l          let (_x_22 : real) = 66419/200000 * _x_1 in\l          let (_x_23 : real) = 25399/190100 * _x_4 in\l          let (_x_24 : real) = 449/29020000 * _x_6 in\l          let (_x_25 : real) = 3841/3110000 * _x_8 in\l          let (_x_26 : real) = (-25741/4250000) * _x_10 in\l          let (_x_27 : real) = 58299/640000 * _x_12 in\l          let (_x_28 : real)\l              = if _x_22 +. _x_23 +. _x_24 +. _x_25 +. _x_26 +. _x_27\l                   \<= (-317131778543/1534287400000)\l                then 0\l                else\l                  317131778543/1534287400000 +. _x_22 +. _x_23 +. _x_24\l                  +. _x_25 +. _x_26 +. _x_27\l          in\l          let (_x_29 : real) = 23799/100000 * _x_1 in\l          let (_x_30 : real) = (-18071/95050) * _x_4 in\l          let (_x_31 : real) = 38981/29020000 * _x_6 in\l          let (_x_32 : real) = 1727/194375 * _x_8 in\l          let (_x_33 : real) = (-61231/8500000) * _x_10 in\l          let (_x_34 : real) = (-1831/320000) * _x_12 in\l          let (_x_35 : real)\l              = if _x_29 +. _x_30 +. _x_31 +. _x_32 +. _x_33 +. _x_34\l                   \<= (-89188713933/1534287400000)\l                then 0\l                else\l                  89188713933/1534287400000 +. _x_29 +. _x_30 +. _x_31\l                  +. _x_32 +. _x_33 +. _x_34\l          in\l          let (_x_36 : real) = 10277/200000 * _x_1 in\l          let (_x_37 : real) = (-28841/190100) * _x_4 in\l          let (_x_38 : real) = 4637/29020000 * _x_6 in\l          let (_x_39 : real) = 3601/388750 * _x_8 in\l          let (_x_40 : real) = 5957/8500000 * _x_10 in\l          let (_x_41 : real) = (-22041/640000) * _x_12 in\l          let (_x_42 : real)\l              = if _x_36 +. _x_37 +. _x_38 +. _x_39 +. _x_40 +. _x_41\l                   \<= (-372238333/2454859840)\l                then 0\l                else\l                  372238333/2454859840 +. _x_36 +. _x_37 +. _x_38 +. _x_39\l                  +. _x_40 +. _x_41\l          in\l          let (_x_43 : real) = 13901/50000 * _x_1 in\l          let (_x_44 : real) = (-803/38020) * _x_4 in\l          let (_x_45 : real) = 10557/29020000 * _x_6 in\l          let (_x_46 : real) = 60757/3110000 * _x_8 in\l          let (_x_47 : real) = (-16157/4250000) * _x_10 in\l          let (_x_48 : real) = 47933/640000 * _x_12 in\l          let (_x_49 : real)\l              = if _x_43 +. _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48\l                   \<= 72146699557/306857480000\l                then 0\l                else\l                  (-72146699557/306857480000) +. _x_43 +. _x_44 +. _x_45\l                  +. _x_46 +. _x_47 +. _x_48\l          in\l          let (_x_50 : real)\l              = 1568904513/1250000000 * _x_14\l                +. (-1400061773/1250000000) * _x_21\l                +. (-889978969/400000000) * _x_28\l                +. (-787784679/2500000000) * _x_35\l                +. (-19189866047/10000000000) * _x_42\l                +. 5337652199/2000000000 * _x_49\l          in\l          not\l          ((if _x_50 \<= (-341987779/312500000)\l            then\l              28114831522503/7812500000000\l              +. 67395431164941/31250000000000 * _x_14\l              +. (-60142453582761/31250000000000) * _x_21\l              +. (-38230826571333/10000000000000) * _x_28\l              +. (-33840866455803/62500000000000) * _x_35\l              +. (-824339075780979/250000000000000) * _x_42\l              +. 229289525512443/50000000000000 * _x_49\l            else\l            if _x_50 \<= (-29487779/312500000)\l            then\l              213430965464483/31250000000000\l              +. 732799213218501/125000000000000 * _x_14\l              +. (-653936652747521/125000000000000) * _x_21\l              +. (-415688706903613/40000000000000) * _x_28\l              +. (-367956104513283/250000000000000) * _x_35\l              +. (-8963145063634619/1000000000000000) * _x_42\l              +. 2493094576152323/200000000000000 * _x_49\l            else\l            if _x_50 \<= 283012221/312500000\l            then\l              1852306369389/244140625000\l              +. 124497279820089/7812500000000 * _x_14\l              +. (-111099101872869/7812500000000) * _x_21\l              +. (-70622501127057/2500000000000) * _x_28\l              +. (-62513077632687/15625000000000) * _x_35\l              +. (-1522773440427591/62500000000000) * _x_42\l              +. 423558714947247/12500000000000 * _x_49\l            else if _x_50 \<= 595512221/312500000 then … else …)\l           \<= 20)\l          && (_x_8 = 20) && (_x_0 = May) :expansions [] :rw [] :fc [])",shape=box,style=filled,fontname="courier",fontsize=14];
p_358 -> p_357 [label=""];
p_357 [label="Sat (Some let x : nn_input =\l  \{month = May; day = Mon;\l   dmc =\l   (Q.of_string \"5504175945856158301941488984049755357/5071988086553252496827564580975000\");\l   temp = (Q.of_nativeint (20n));\l   rh =\l   (Q.of_string \"6938343360970919031635529463866329/25359940432766262484137822904875\");\l   rain =\l   (Q.of_string \"6689442348868569273582309835512268/633998510819156562103445572621875\")\}\l)",shape=box,style=filled,fontname="courier",fontsize=14];
}

Try this!

In [19]:

CX.x

Out[19]:

- : nn_input =
{month = May; day = Mon; dmc = 1085.21074023; temp = 20.; rh = 273.594623748;
 rain = 10.5511956806}

Notice how the unspecified input variables are unbounded, just as in our original classification instances. Using the description of each variable in the data (plus some reasonable assumptions about Portugal's climate) we can form the following condition describing valid inputs to the network.

Try this!

In [20]:

let is_valid_nn input =
  0.0 <=. input.dmc && input.dmc <=. 500.0 &&
  0.0 <=. input.temp && input.temp <=. 40.0 &&
  0.0 <=. input.rh && input.rh <=. 100.0 &&
  0.0 <=. input.rain && input.rain <=. 15.0

instance (fun x -> nn_model x >. 20.0 && x.temp = 20.0 && x.month = May && is_valid_nn x)

Out[20]:

val is_valid_nn : nn_input -> bool = <fun>
- : nn_input -> bool = <fun>
module CX : sig val x : nn_input end

Instance (after 0 steps, 0.093s):
let x : nn_input =
  {month = May; day = Sun;
   dmc =
   10320016944192717928085378625498323/104479107528761825932953783127500;
   temp = 20; rh = 100;
   rain = 59292603493829172244694194140464/5223955376438091296647689156375}

Instance

call graph
proof

digraph "call graph" {
goal [label="let (_x_0 : month) = x.month in\llet (_x_1 : bool) = _x_0 = Mar in\llet (_x_2 : bool) = _x_0 = Feb in\llet (_x_3 : bool) = _x_0 = Jan in\llet (_x_4 : real)\l    = if _x_3 then 67/500\l      else\l      if _x_2 then 1/2\l      else if _x_1 then 1 else if _x_0 = Apr then 3/2 else …\lin\llet (_x_5 : real) = 5031/50000 * _x_4 in\llet (_x_6 : day) = x.day in\llet (_x_7 : bool) = (_x_6 = Wed) \|\| (_x_6 = Thu) in\llet (_x_8 : bool) = _x_6 = Tue in\llet (_x_9 : bool) = _x_6 = Mon in\llet (_x_10 : real)\l    = if _x_9 then 377/1000\l      else\l      if _x_8 then 1223/1000\l      else if _x_7 then 1901/1000 else if _x_6 = Fri then 1223/1000 else …\lin\llet (_x_11 : real) = (-7861/95050) * _x_10 in\llet (_x_12 : real) = x.dmc in\llet (_x_13 : real) = (-19063/29020000) * _x_12 in\llet (_x_14 : real) = x.temp in\llet (_x_15 : real) = (-27281/1555000) * _x_14 in\llet (_x_16 : real) = x.rh in\llet (_x_17 : real) = 137/340000 * _x_16 in\llet (_x_18 : real) = x.rain in\llet (_x_19 : real) = 6263/80000 * _x_18 in\llet (_x_20 : real)\l    = if _x_3 then 67/500 else if _x_2 then 1/2 else if _x_1 then 1 else …\lin\llet (_x_21 : real)\l    = if _x_9 then 377/1000\l      else if _x_8 then 1223/1000 else if _x_7 then 1901/1000 else …\lin\llet (_x_22 : real) = (-1021/1813750) * _x_12 in\llet (_x_23 : real) = 17919/3110000 * _x_14 in\llet (_x_24 : real) = 32971/8500000 * _x_16 in\llet (_x_25 : real) = (-21603/320000) * _x_18 in\llet (_x_26 : real)\l    = if 29103/200000 * _x_4 +. 159/9505 * _x_10 +. _x_22 +. _x_23 +. _x_24\l         +. _x_25 \<= 73983893263/767143700000\l      then 0\l      else\l        (-73983893263/767143700000) +. 29103/200000 * _x_20\l        +. 159/9505 * _x_21 +. _x_22 +. _x_23 +. _x_24 +. _x_25\lin\llet (_x_27 : real) = 66419/200000 * _x_4 in\llet (_x_28 : real) = 25399/190100 * _x_10 in\llet (_x_29 : real) = 449/29020000 * _x_12 in\llet (_x_30 : real) = 3841/3110000 * _x_14 in\llet (_x_31 : real) = (-25741/4250000) * _x_16 in\llet (_x_32 : real) = 58299/640000 * _x_18 in\llet (_x_33 : real)\l    = if _x_27 +. _x_28 +. _x_29 +. _x_30 +. _x_31 +. _x_32\l         \<= (-317131778543/1534287400000)\l      then 0\l      else\l        317131778543/1534287400000 +. _x_27 +. _x_28 +. _x_29 +. _x_30\l        +. _x_31 +. _x_32\lin\llet (_x_34 : real) = 23799/100000 * _x_4 in\llet (_x_35 : real) = (-18071/95050) * _x_10 in\llet (_x_36 : real) = 38981/29020000 * _x_12 in\llet (_x_37 : real) = 1727/194375 * _x_14 in\llet (_x_38 : real) = (-61231/8500000) * _x_16 in\llet (_x_39 : real) = (-1831/320000) * _x_18 in\llet (_x_40 : real)\l    = if _x_34 +. _x_35 +. _x_36 +. _x_37 +. _x_38 +. _x_39\l         \<= (-89188713933/1534287400000)\l      then 0\l      else\l        89188713933/1534287400000 +. _x_34 +. _x_35 +. _x_36 +. _x_37\l        +. _x_38 +. _x_39\lin\llet (_x_41 : real) = 10277/200000 * _x_4 in\llet (_x_42 : real) = (-28841/190100) * _x_10 in\llet (_x_43 : real) = 4637/29020000 * _x_12 in\llet (_x_44 : real) = 3601/388750 * _x_14 in\llet (_x_45 : real) = 5957/8500000 * _x_16 in\llet (_x_46 : real) = (-22041/640000) * _x_18 in\llet (_x_47 : real)\l    = if _x_41 +. _x_42 +. _x_43 +. _x_44 +. _x_45 +. _x_46\l         \<= (-372238333/2454859840)\l      then 0\l      else\l        372238333/2454859840 +. _x_41 +. _x_42 +. _x_43 +. _x_44 +. _x_45\l        +. _x_46\lin\llet (_x_48 : real) = 13901/50000 * _x_4 in\llet (_x_49 : real) = (-803/38020) * _x_10 in\llet (_x_50 : real) = 10557/29020000 * _x_12 in\llet (_x_51 : real) = 60757/3110000 * _x_14 in\llet (_x_52 : real) = (-16157/4250000) * _x_16 in\llet (_x_53 : real) = 47933/640000 * _x_18 in\llet (_x_54 : real)\l    = if _x_48 +. _x_49 +. _x_50 +. _x_51 +. _x_52 +. _x_53\l         \<= 72146699557/306857480000\l      then 0\l      else\l        (-72146699557/306857480000) +. _x_48 +. _x_49 +. _x_50 +. _x_51\l        +. _x_52 +. _x_53\lin\llet (_x_55 : real)\l    = 1568904513/1250000000\l      * (if _x_5 +. _x_11 +. _x_13 +. _x_15 +. _x_17 +. _x_19\l            \<= (-1716983137/306857480000)\l         then 0\l         else\l           (1716983137/306857480000 +. _x_5 +. _x_11 +. _x_13 +. _x_15\l            +. _x_17 +. _x_19))\l      +. (-1400061773/1250000000) * _x_26 +. (-889978969/400000000) * _x_33\l      +. (-787784679/2500000000) * _x_40\l      +. (-19189866047/10000000000) * _x_47 +. 5337652199/2000000000 * _x_54\lin\llet (_x_56 : real) = 5031/50000 * _x_20 in\llet (_x_57 : real) = (-7861/95050) * _x_21 in\llet (_x_58 : real)\l    = if _x_56 +. _x_57 +. _x_13 +. _x_15 +. _x_17 +. _x_19\l         \<= (-1716983137/306857480000)\l      then 0\l      else\l        1716983137/306857480000 +. _x_56 +. _x_57 +. _x_13 +. _x_15 +. _x_17\l        +. _x_19\lin\lnot\l((if _x_55 \<= (-341987779/312500000)\l  then\l    28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_58\l    +. (-60142453582761/31250000000000) * _x_26\l    +. (-38230826571333/10000000000000) * _x_33\l    +. (-33840866455803/62500000000000) * _x_40\l    +. (-824339075780979/250000000000000) * _x_47\l    +. 229289525512443/50000000000000 * _x_54\l  else\l  if _x_55 \<= (-29487779/312500000)\l  then\l    213430965464483/31250000000000 +. 732799213218501/125000000000000 * _x_58\l    +. (-653936652747521/125000000000000) * _x_26\l    +. (-415688706903613/40000000000000) * _x_33\l    +. (-367956104513283/250000000000000) * _x_40\l    +. (-8963145063634619/1000000000000000) * _x_47\l    +. 2493094576152323/200000000000000 * _x_54\l  else\l  if _x_55 \<= 283012221/312500000\l  then\l    1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_58\l    +. (-111099101872869/7812500000000) * _x_26\l    +. (-70622501127057/2500000000000) * _x_33\l    +. (-62513077632687/15625000000000) * _x_40\l    +. (-1522773440427591/62500000000000) * _x_47\l    +. 423558714947247/12500000000000 * _x_54\l  else if _x_55 \<= 595512221/312500000 then … else …)\l \<= 20)\l&& (_x_14 = 20) && (_x_0 = May) && (0 \<= _x_12) && (_x_12 \<= 500)\l&& (0 \<= _x_14) && (_x_14 \<= 40) && (0 \<= _x_16) && (_x_16 \<= 100)\l&& (0 \<= _x_18) && (_x_18 \<= 15)",shape=box,style=filled,color="cyan",fontname="courier",fontsize=14];
}

proof attempt

ground_instances:

definitions:

inductions:

search_time:

0.093s

details:

Expand

smt_stats:

num checks:	1
arith assert lower:	131
arith tableau max rows:	24
arith tableau max columns:	122
arith pivots:	163
rlimit count:	264779
mk clause:	191
datatype occurs check:	8
mk bool var:	254
arith assert upper:	121
datatype splits:	10
decisions:	207
arith row summations:	2168
arith bound prop:	8
propagations:	375
conflicts:	47
arith fixed eqs:	38
datatype accessor ax:	11
minimized lits:	16
arith conflicts:	21
arith num rows:	24
arith assert diseq:	15
datatype constructor ax:	20
final checks:	1
added eqs:	248
del clause:	83
arith eq adapter:	93
time:	0.085000
memory:	23.340000
max memory:	24.210000
num allocs:	36445086188.000000

Expand

start[0.093s]
  let (_x_0 : real)
      = 5031/25000 * … +. (-7861/50000) * … +. (-19063/100000) * …
        +. (-27281/50000) * … +. 137/4000 * … +. 6263/12500 * …
        +. (-173/6250)
  in
  let (_x_1 : real)
      = 29103/100000 * … +. 159/5000 * … +. (-1021/6250) * …
        +. 17919/100000 * … +. 32971/100000 * … +. (-21603/50000) * …
        +. (-131/5000)
  in
  let (_x_2 : real)
      = 66419/100000 * … +. 25399/100000 * … +. 449/100000 * …
        +. 3841/100000 * … +. (-25741/50000) * … +. 58299/100000 * …
        +. 5929/50000
  in
  let (_x_3 : real)
      = 23799/50000 * … +. (-18071/50000) * … +. 38981/100000 * …
        +. 1727/6250 * … +. (-61231/100000) * … +. (-1831/50000) * …
        +. (-289/10000)
  in
  let (_x_4 : real)
      = 10277/100000 * … +. (-28841/100000) * … +. 4637/100000 * …
        +. 3601/12500 * … +. 5957/100000 * … +. (-22041/100000) * …
        +. 1827/10000
  in
  let (_x_5 : real)
      = 13901/25000 * … +. (-803/20000) * … +. 10557/100000 * …
        +. 60757/100000 * … +. (-16157/50000) * … +. 47933/100000 * …
        +. (-6219/25000)
  in
  let (_x_6 : real)
      = 444323/100000
        * (3531/12500 * (if _x_0 > 0 then _x_0 else 0)
           +. (-3151/12500) * (if _x_1 > 0 then _x_1 else 0)
           +. (-2003/4000) * (if _x_2 > 0 then _x_2 else 0)
           +. (-1773/25000) * (if _x_3 > 0 then _x_3 else 0)
           +. (-43189/100000) * (if _x_4 > 0 then _x_4 else 0)
           +. 12013/20000 * (if _x_5 > 0 then _x_5 else 0) +. 1473/3125)
  in
  let (_x_7 : real) = ( :var_0: ).temp in
  let (_x_8 : real) = ( :var_0: ).dmc in
  let (_x_9 : real) = ( :var_0: ).rh in
  let (_x_10 : real) = ( :var_0: ).rain in
  ((if _x_6 <= 1 then (_x_6 - 0) * 42957/25000
    else
    if _x_6 <= 2 then (_x_6 - 15803/25000) * 467077/100000
    else
    if _x_6 <= 3 then (_x_6 - 149679/100000) * 79353/6250
    else if _x_6 <= 4 then … else …)
   > 20)
  && ((_x_7 = 20)
      && ((( :var_0: ).month = May)
          && ((0 <= _x_8)
              && ((_x_8 <= 500)
                  && ((0 <= _x_7)
                      && ((_x_7 <= 40)
                          && ((0 <= _x_9)
                              && ((_x_9 <= 100)
                                  && ((0 <= _x_10) && (_x_10 <= 15))))))))))

simplify

into:	let (_x_0 : month) = ( :var_0: ).month in let (_x_1 : real) = if _x_0 = Jan then 67/500 else if _x_0 = Feb then 1/2 else if _x_0 = Mar then 1 else if _x_0 = Apr then 3/2 else … in let (_x_2 : real) = 5031/50000 * _x_1 in let (_x_3 : day) = ( :var_0: ).day in let (_x_4 : real) = if _x_3 = Mon then 377/1000 else if _x_3 = Tue then 1223/1000 else if (_x_3 = Wed) \|\| (_x_3 = Thu) then 1901/1000 else if _x_3 = Fri then 1223/1000 else … in let (_x_5 : real) = (-7861/95050) * _x_4 in let (_x_6 : real) = ( :var_0: ).dmc in let (_x_7 : real) = (-19063/29020000) * _x_6 in let (_x_8 : real) = ( :var_0: ).temp in let (_x_9 : real) = (-27281/1555000) * _x_8 in let (_x_10 : real) = ( :var_0: ).rh in let (_x_11 : real) = 137/340000 * _x_10 in let (_x_12 : real) = ( :var_0: ).rain in let (_x_13 : real) = 6263/80000 * _x_12 in let (_x_14 : real) = if _x_2 +. _x_5 +. _x_7 +. _x_9 +. _x_11 +. _x_13 <= (-1716983137/306857480000) then 0 else 1716983137/306857480000 +. _x_2 +. _x_5 +. _x_7 +. _x_9 +. _x_11 +. _x_13 in let (_x_15 : real) = 29103/200000 * _x_1 in let (_x_16 : real) = 159/9505 * _x_4 in let (_x_17 : real) = (-1021/1813750) * _x_6 in let (_x_18 : real) = 17919/3110000 * _x_8 in let (_x_19 : real) = 32971/8500000 * _x_10 in let (_x_20 : real) = (-21603/320000) * _x_12 in let (_x_21 : real) = if _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19 +. _x_20 <= 73983893263/767143700000 then 0 else (-73983893263/767143700000) +. _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19 +. _x_20 in let (_x_22 : real) = 66419/200000 * _x_1 in let (_x_23 : real) = 25399/190100 * _x_4 in let (_x_24 : real) = 449/29020000 * _x_6 in let (_x_25 : real) = 3841/3110000 * _x_8 in let (_x_26 : real) = (-25741/4250000) * _x_10 in let (_x_27 : real) = 58299/640000 * _x_12 in let (_x_28 : real) = if _x_22 +. _x_23 +. _x_24 +. _x_25 +. _x_26 +. _x_27 <= (-317131778543/1534287400000) then 0 else 317131778543/1534287400000 +. _x_22 +. _x_23 +. _x_24 +. _x_25 +. _x_26 +. _x_27 in let (_x_29 : real) = 23799/100000 * _x_1 in let (_x_30 : real) = (-18071/95050) * _x_4 in let (_x_31 : real) = 38981/29020000 * _x_6 in let (_x_32 : real) = 1727/194375 * _x_8 in let (_x_33 : real) = (-61231/8500000) * _x_10 in let (_x_34 : real) = (-1831/320000) * _x_12 in let (_x_35 : real) = if _x_29 +. _x_30 +. _x_31 +. _x_32 +. _x_33 +. _x_34 <= (-89188713933/1534287400000) then 0 else 89188713933/1534287400000 +. _x_29 +. _x_30 +. _x_31 +. _x_32 +. _x_33 +. _x_34 in let (_x_36 : real) = 10277/200000 * _x_1 in let (_x_37 : real) = (-28841/190100) * _x_4 in let (_x_38 : real) = 4637/29020000 * _x_6 in let (_x_39 : real) = 3601/388750 * _x_8 in let (_x_40 : real) = 5957/8500000 * _x_10 in let (_x_41 : real) = (-22041/640000) * _x_12 in let (_x_42 : real) = if _x_36 +. _x_37 +. _x_38 +. _x_39 +. _x_40 +. _x_41 <= (-372238333/2454859840) then 0 else 372238333/2454859840 +. _x_36 +. _x_37 +. _x_38 +. _x_39 +. _x_40 +. _x_41 in let (_x_43 : real) = 13901/50000 * _x_1 in let (_x_44 : real) = (-803/38020) * _x_4 in let (_x_45 : real) = 10557/29020000 * _x_6 in let (_x_46 : real) = 60757/3110000 * _x_8 in let (_x_47 : real) = (-16157/4250000) * _x_10 in let (_x_48 : real) = 47933/640000 * _x_12 in let (_x_49 : real) = if _x_43 +. _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48 <= 72146699557/306857480000 then 0 else (-72146699557/306857480000) +. _x_43 +. _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48 in let (_x_50 : real) = 1568904513/1250000000 * _x_14 +. (-1400061773/1250000000) * _x_21 +. (-889978969/400000000) * _x_28 +. (-787784679/2500000000) * _x_35 +. (-19189866047/10000000000) * _x_42 +. 5337652199/2000000000 * _x_49 in not ((if _x_50 <= (-341987779/312500000) then 28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_14 +. (-60142453582761/31250000000000) * _x_21 +. (-38230826571333/10000000000000) * _x_28 +. (-33840866455803/62500000000000) * _x_35 +. (-824339075780979/250000000000000) * _x_42 +. 229289525512443/50000000000000 * _x_49 else if _x_50 <= (-29487779/312500000) then 213430965464483/31250000000000 +. 732799213218501/125000000000000 * _x_14 +. (-653936652747521/125000000000000) * _x_21 +. (-415688706903613/40000000000000) * _x_28 +. (-367956104513283/250000000000000) * _x_35 +. (-8963145063634619/1000000000000000) * _x_42 +. 2493094576152323/200000000000000 * _x_49 else if _x_50 <= 283012221/312500000 then 1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_14 +. (-111099101872869/7812500000000) * _x_21 +. (-70622501127057/2500000000000) * _x_28 +. (-62513077632687/15625000000000) * _x_35 +. (-1522773440427591/62500000000000) * _x_42 +. 423558714947247/12500000000000 * _x_49 else if _x_50 <= 595512221/312500000 then … else …) <= 20) && (_x_8 = 20) && (_x_0 = May) && (0 <= _x_6) && (_x_6 <= 500) && (0 <= _x_8) && (_x_8 <= 40) && (0 <= _x_10) && (_x_10 <= 100) && (0 <= _x_12) && (_x_12 <= 15)
expansions:	[]
rewrite_steps:
forward_chaining:

Sat (Some let x : nn_input = {month = May; day = Sun; dmc = (Q.of_string "10320016944192717928085378625498323/104479107528761825932953783127500"); temp = (Q.of_nativeint (20n)); rh = (Q.of_nativeint (100n)); rain = (Q.of_string "59292603493829172244694194140464/5223955376438091296647689156375")} )

digraph "proof" {
p_362 [label="Start (let (_x_0 : real)\l           = 5031/25000 * … +. (-7861/50000) * … +. (-19063/100000) * …\l             +. (-27281/50000) * … +. 137/4000 * … +. 6263/12500 * …\l             +. (-173/6250)\l       in\l       let (_x_1 : real)\l           = 29103/100000 * … +. 159/5000 * … +. (-1021/6250) * …\l             +. 17919/100000 * … +. 32971/100000 * …\l             +. (-21603/50000) * … +. (-131/5000)\l       in\l       let (_x_2 : real)\l           = 66419/100000 * … +. 25399/100000 * … +. 449/100000 * …\l             +. 3841/100000 * … +. (-25741/50000) * …\l             +. 58299/100000 * … +. 5929/50000\l       in\l       let (_x_3 : real)\l           = 23799/50000 * … +. (-18071/50000) * … +. 38981/100000 * …\l             +. 1727/6250 * … +. (-61231/100000) * …\l             +. (-1831/50000) * … +. (-289/10000)\l       in\l       let (_x_4 : real)\l           = 10277/100000 * … +. (-28841/100000) * … +. 4637/100000 * …\l             +. 3601/12500 * … +. 5957/100000 * …\l             +. (-22041/100000) * … +. 1827/10000\l       in\l       let (_x_5 : real)\l           = 13901/25000 * … +. (-803/20000) * … +. 10557/100000 * …\l             +. 60757/100000 * … +. (-16157/50000) * …\l             +. 47933/100000 * … +. (-6219/25000)\l       in\l       let (_x_6 : real)\l           = 444323/100000\l             * (3531/12500 * (if _x_0 \> 0 then _x_0 else 0)\l                +. (-3151/12500) * (if _x_1 \> 0 then _x_1 else 0)\l                +. (-2003/4000) * (if _x_2 \> 0 then _x_2 else 0)\l                +. (-1773/25000) * (if _x_3 \> 0 then _x_3 else 0)\l                +. (-43189/100000) * (if _x_4 \> 0 then _x_4 else 0)\l                +. 12013/20000 * (if _x_5 \> 0 then _x_5 else 0) +. 1473/3125)\l       in\l       let (_x_7 : real) = ( :var_0: ).temp in\l       let (_x_8 : real) = ( :var_0: ).dmc in\l       let (_x_9 : real) = ( :var_0: ).rh in\l       let (_x_10 : real) = ( :var_0: ).rain in\l       ((if _x_6 \<= 1 then (_x_6 - 0) * 42957/25000\l         else\l         if _x_6 \<= 2 then (_x_6 - 15803/25000) * 467077/100000\l         else\l         if _x_6 \<= 3 then (_x_6 - 149679/100000) * 79353/6250\l         else if _x_6 \<= 4 then … else …)\l        \> 20)\l       && ((_x_7 = 20)\l           && ((( :var_0: ).month = May)\l               && ((0 \<= _x_8)\l                   && ((_x_8 \<= 500)\l                       && ((0 \<= _x_7)\l                           && ((_x_7 \<= 40)\l                               && ((0 \<= _x_9)\l                                   && ((_x_9 \<= 100)\l                                       && ((0 \<= _x_10) && (_x_10 \<= 15))))))))))\l       :time 0.093s)",shape=box,style=filled,fontname="courier",fontsize=14];
p_362 -> p_361 [label=""];
p_361 [label="Simplify (let (_x_0 : month) = ( :var_0: ).month in\l          let (_x_1 : real)\l              = if _x_0 = Jan then 67/500\l                else\l                if _x_0 = Feb then 1/2\l                else\l                if _x_0 = Mar then 1 else if _x_0 = Apr then 3/2 else …\l          in\l          let (_x_2 : real) = 5031/50000 * _x_1 in\l          let (_x_3 : day) = ( :var_0: ).day in\l          let (_x_4 : real)\l              = if _x_3 = Mon then 377/1000\l                else\l                if _x_3 = Tue then 1223/1000\l                else\l                if (_x_3 = Wed) \|\| (_x_3 = Thu) then 1901/1000\l                else if _x_3 = Fri then 1223/1000 else …\l          in\l          let (_x_5 : real) = (-7861/95050) * _x_4 in\l          let (_x_6 : real) = ( :var_0: ).dmc in\l          let (_x_7 : real) = (-19063/29020000) * _x_6 in\l          let (_x_8 : real) = ( :var_0: ).temp in\l          let (_x_9 : real) = (-27281/1555000) * _x_8 in\l          let (_x_10 : real) = ( :var_0: ).rh in\l          let (_x_11 : real) = 137/340000 * _x_10 in\l          let (_x_12 : real) = ( :var_0: ).rain in\l          let (_x_13 : real) = 6263/80000 * _x_12 in\l          let (_x_14 : real)\l              = if _x_2 +. _x_5 +. _x_7 +. _x_9 +. _x_11 +. _x_13\l                   \<= (-1716983137/306857480000)\l                then 0\l                else\l                  1716983137/306857480000 +. _x_2 +. _x_5 +. _x_7 +. _x_9\l                  +. _x_11 +. _x_13\l          in\l          let (_x_15 : real) = 29103/200000 * _x_1 in\l          let (_x_16 : real) = 159/9505 * _x_4 in\l          let (_x_17 : real) = (-1021/1813750) * _x_6 in\l          let (_x_18 : real) = 17919/3110000 * _x_8 in\l          let (_x_19 : real) = 32971/8500000 * _x_10 in\l          let (_x_20 : real) = (-21603/320000) * _x_12 in\l          let (_x_21 : real)\l              = if _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19 +. _x_20\l                   \<= 73983893263/767143700000\l                then 0\l                else\l                  (-73983893263/767143700000) +. _x_15 +. _x_16 +. _x_17\l                  +. _x_18 +. _x_19 +. _x_20\l          in\l          let (_x_22 : real) = 66419/200000 * _x_1 in\l          let (_x_23 : real) = 25399/190100 * _x_4 in\l          let (_x_24 : real) = 449/29020000 * _x_6 in\l          let (_x_25 : real) = 3841/3110000 * _x_8 in\l          let (_x_26 : real) = (-25741/4250000) * _x_10 in\l          let (_x_27 : real) = 58299/640000 * _x_12 in\l          let (_x_28 : real)\l              = if _x_22 +. _x_23 +. _x_24 +. _x_25 +. _x_26 +. _x_27\l                   \<= (-317131778543/1534287400000)\l                then 0\l                else\l                  317131778543/1534287400000 +. _x_22 +. _x_23 +. _x_24\l                  +. _x_25 +. _x_26 +. _x_27\l          in\l          let (_x_29 : real) = 23799/100000 * _x_1 in\l          let (_x_30 : real) = (-18071/95050) * _x_4 in\l          let (_x_31 : real) = 38981/29020000 * _x_6 in\l          let (_x_32 : real) = 1727/194375 * _x_8 in\l          let (_x_33 : real) = (-61231/8500000) * _x_10 in\l          let (_x_34 : real) = (-1831/320000) * _x_12 in\l          let (_x_35 : real)\l              = if _x_29 +. _x_30 +. _x_31 +. _x_32 +. _x_33 +. _x_34\l                   \<= (-89188713933/1534287400000)\l                then 0\l                else\l                  89188713933/1534287400000 +. _x_29 +. _x_30 +. _x_31\l                  +. _x_32 +. _x_33 +. _x_34\l          in\l          let (_x_36 : real) = 10277/200000 * _x_1 in\l          let (_x_37 : real) = (-28841/190100) * _x_4 in\l          let (_x_38 : real) = 4637/29020000 * _x_6 in\l          let (_x_39 : real) = 3601/388750 * _x_8 in\l          let (_x_40 : real) = 5957/8500000 * _x_10 in\l          let (_x_41 : real) = (-22041/640000) * _x_12 in\l          let (_x_42 : real)\l              = if _x_36 +. _x_37 +. _x_38 +. _x_39 +. _x_40 +. _x_41\l                   \<= (-372238333/2454859840)\l                then 0\l                else\l                  372238333/2454859840 +. _x_36 +. _x_37 +. _x_38 +. _x_39\l                  +. _x_40 +. _x_41\l          in\l          let (_x_43 : real) = 13901/50000 * _x_1 in\l          let (_x_44 : real) = (-803/38020) * _x_4 in\l          let (_x_45 : real) = 10557/29020000 * _x_6 in\l          let (_x_46 : real) = 60757/3110000 * _x_8 in\l          let (_x_47 : real) = (-16157/4250000) * _x_10 in\l          let (_x_48 : real) = 47933/640000 * _x_12 in\l          let (_x_49 : real)\l              = if _x_43 +. _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48\l                   \<= 72146699557/306857480000\l                then 0\l                else\l                  (-72146699557/306857480000) +. _x_43 +. _x_44 +. _x_45\l                  +. _x_46 +. _x_47 +. _x_48\l          in\l          let (_x_50 : real)\l              = 1568904513/1250000000 * _x_14\l                +. (-1400061773/1250000000) * _x_21\l                +. (-889978969/400000000) * _x_28\l                +. (-787784679/2500000000) * _x_35\l                +. (-19189866047/10000000000) * _x_42\l                +. 5337652199/2000000000 * _x_49\l          in\l          not\l          ((if _x_50 \<= (-341987779/312500000)\l            then\l              28114831522503/7812500000000\l              +. 67395431164941/31250000000000 * _x_14\l              +. (-60142453582761/31250000000000) * _x_21\l              +. (-38230826571333/10000000000000) * _x_28\l              +. (-33840866455803/62500000000000) * _x_35\l              +. (-824339075780979/250000000000000) * _x_42\l              +. 229289525512443/50000000000000 * _x_49\l            else\l            if _x_50 \<= (-29487779/312500000)\l            then\l              213430965464483/31250000000000\l              +. 732799213218501/125000000000000 * _x_14\l              +. (-653936652747521/125000000000000) * _x_21\l              +. (-415688706903613/40000000000000) * _x_28\l              +. (-367956104513283/250000000000000) * _x_35\l              +. (-8963145063634619/1000000000000000) * _x_42\l              +. 2493094576152323/200000000000000 * _x_49\l            else\l            if _x_50 \<= 283012221/312500000\l            then\l              1852306369389/244140625000\l              +. 124497279820089/7812500000000 * _x_14\l              +. (-111099101872869/7812500000000) * _x_21\l              +. (-70622501127057/2500000000000) * _x_28\l              +. (-62513077632687/15625000000000) * _x_35\l              +. (-1522773440427591/62500000000000) * _x_42\l              +. 423558714947247/12500000000000 * _x_49\l            else if _x_50 \<= 595512221/312500000 then … else …)\l           \<= 20)\l          && (_x_8 = 20) && (_x_0 = May) && (0 \<= _x_6) && (_x_6 \<= 500)\l          && (0 \<= _x_8) && (_x_8 \<= 40) && (0 \<= _x_10) && (_x_10 \<= 100)\l          && (0 \<= _x_12) && (_x_12 \<= 15) :expansions [] :rw [] :fc [])",shape=box,style=filled,fontname="courier",fontsize=14];
p_361 -> p_360 [label=""];
p_360 [label="Sat (Some let x : nn_input =\l  \{month = May; day = Sun;\l   dmc =\l   (Q.of_string \"10320016944192717928085378625498323/104479107528761825932953783127500\");\l   temp = (Q.of_nativeint (20n)); rh = (Q.of_nativeint (100n));\l   rain =\l   (Q.of_string \"59292603493829172244694194140464/5223955376438091296647689156375\")\}\l)",shape=box,style=filled,fontname="courier",fontsize=14];
}

Try this!

In [21]:

CX.x;;

nn_model CX.x

Out[21]:

- : nn_input =
{month = May; day = Sun; dmc = 98.7758910685; temp = 20.; rh = 100.;
 rain = 11.3501359068}
- : real = 20.0272890315

These constraints mean it is slightly harder for Imandra to find a particular instance satisfying our original demand, but nonetheless it's possible. Now let's try something a bit more interesting. First of all let's check for one desirable property of the model, namely that it never outputs a negative area as a prediction.

Try this!

In [22]:

verify (fun x -> is_valid_nn x ==> nn_model x >=. 0.0)

Out[22]:

- : nn_input -> bool = <fun>

Proved

proof
call graph

proof

ground_instances:

definitions:

inductions:

search_time:

0.490s

details:

Expand

smt_stats:

arith offset eqs:	20
num checks:	1
arith assert lower:	446
arith tableau max rows:	24
arith tableau max columns:	138
arith pivots:	625
rlimit count:	1359433
mk clause:	586
restarts:	1
mk bool var:	498
arith assert upper:	385
datatype splits:	51
decisions:	663
arith row summations:	7832
arith bound prop:	20
propagations:	2849
conflicts:	142
arith fixed eqs:	80
datatype accessor ax:	18
minimized lits:	171
arith conflicts:	88
arith num rows:	24
arith assert diseq:	220
datatype constructor ax:	9
added eqs:	1161
del clause:	272
arith eq adapter:	207
time:	0.480000
memory:	24.070000
max memory:	24.950000
num allocs:	37065453164.000000

Expand

start[0.490s]
  let (_x_0 : real) = ( :var_0: ).dmc in
  let (_x_1 : real) = ( :var_0: ).temp in
  let (_x_2 : real) = ( :var_0: ).rh in
  let (_x_3 : real) = ( :var_0: ).rain in
  let (_x_4 : real)
      = 5031/25000 * … +. (-7861/50000) * … +. (-19063/100000) * …
        +. (-27281/50000) * … +. 137/4000 * … +. 6263/12500 * …
        +. (-173/6250)
  in
  let (_x_5 : real)
      = 29103/100000 * … +. 159/5000 * … +. (-1021/6250) * …
        +. 17919/100000 * … +. 32971/100000 * … +. (-21603/50000) * …
        +. (-131/5000)
  in
  let (_x_6 : real)
      = 66419/100000 * … +. 25399/100000 * … +. 449/100000 * …
        +. 3841/100000 * … +. (-25741/50000) * … +. 58299/100000 * …
        +. 5929/50000
  in
  let (_x_7 : real)
      = 23799/50000 * … +. (-18071/50000) * … +. 38981/100000 * …
        +. 1727/6250 * … +. (-61231/100000) * … +. (-1831/50000) * …
        +. (-289/10000)
  in
  let (_x_8 : real)
      = 10277/100000 * … +. (-28841/100000) * … +. 4637/100000 * …
        +. 3601/12500 * … +. 5957/100000 * … +. (-22041/100000) * …
        +. 1827/10000
  in
  let (_x_9 : real)
      = 13901/25000 * … +. (-803/20000) * … +. 10557/100000 * …
        +. 60757/100000 * … +. (-16157/50000) * … +. 47933/100000 * …
        +. (-6219/25000)
  in
  let (_x_10 : real)
      = 444323/100000
        * (3531/12500 * (if _x_4 > 0 then _x_4 else 0)
           +. (-3151/12500) * (if _x_5 > 0 then _x_5 else 0)
           +. (-2003/4000) * (if _x_6 > 0 then _x_6 else 0)
           +. (-1773/25000) * (if _x_7 > 0 then _x_7 else 0)
           +. (-43189/100000) * (if _x_8 > 0 then _x_8 else 0)
           +. 12013/20000 * (if _x_9 > 0 then _x_9 else 0) +. 1473/3125)
  in
  (0 <= _x_0)
  && ((_x_0 <= 500)
      && ((0 <= _x_1)
          && ((_x_1 <= 40)
              && ((0 <= _x_2)
                  && ((_x_2 <= 100) && ((0 <= _x_3) && (_x_3 <= 15)))))))
  ==> (if _x_10 <= 1 then (_x_10 - 0) * 42957/25000
       else
       if _x_10 <= 2 then (_x_10 - 15803/25000) * 467077/100000
       else
       if _x_10 <= 3 then (_x_10 - 149679/100000) * 79353/6250
       else if _x_10 <= 4 then … else …)
      >= 0

simplify

into:	let (_x_0 : real) = ( :var_0: ).dmc in let (_x_1 : real) = ( :var_0: ).temp in let (_x_2 : real) = ( :var_0: ).rh in let (_x_3 : real) = ( :var_0: ).rain in let (_x_4 : month) = ( :var_0: ).month in let (_x_5 : bool) = _x_4 = Mar in let (_x_6 : bool) = _x_4 = Feb in let (_x_7 : bool) = _x_4 = Jan in let (_x_8 : real) = if _x_7 then 67/500 else if _x_6 then 1/2 else if _x_5 then 1 else if _x_4 = Apr then 3/2 else … in let (_x_9 : real) = 5031/50000 * _x_8 in let (_x_10 : day) = ( :var_0: ).day in let (_x_11 : bool) = (_x_10 = Wed) \|\| (_x_10 = Thu) in let (_x_12 : bool) = _x_10 = Tue in let (_x_13 : bool) = _x_10 = Mon in let (_x_14 : real) = if _x_13 then 377/1000 else if _x_12 then 1223/1000 else if _x_11 then 1901/1000 else if _x_10 = Fri then 1223/1000 else … in let (_x_15 : real) = (-7861/95050) * _x_14 in let (_x_16 : real) = (-19063/29020000) * _x_0 in let (_x_17 : real) = (-27281/1555000) * _x_1 in let (_x_18 : real) = 137/340000 * _x_2 in let (_x_19 : real) = 6263/80000 * _x_3 in let (_x_20 : real) = 29103/200000 * _x_8 in let (_x_21 : real) = 159/9505 * _x_14 in let (_x_22 : real) = (-1021/1813750) * _x_0 in let (_x_23 : real) = 17919/3110000 * _x_1 in let (_x_24 : real) = 32971/8500000 * _x_2 in let (_x_25 : real) = (-21603/320000) * _x_3 in let (_x_26 : real) = 66419/200000 * _x_8 in let (_x_27 : real) = 25399/190100 * _x_14 in let (_x_28 : real) = 449/29020000 * _x_0 in let (_x_29 : real) = 3841/3110000 * _x_1 in let (_x_30 : real) = (-25741/4250000) * _x_2 in let (_x_31 : real) = 58299/640000 * _x_3 in let (_x_32 : real) = 23799/100000 * _x_8 in let (_x_33 : real) = (-18071/95050) * _x_14 in let (_x_34 : real) = 38981/29020000 * _x_0 in let (_x_35 : real) = 1727/194375 * _x_1 in let (_x_36 : real) = (-61231/8500000) * _x_2 in let (_x_37 : real) = (-1831/320000) * _x_3 in let (_x_38 : real) = if _x_7 then 67/500 else if _x_6 then 1/2 else if _x_5 then 1 else … in let (_x_39 : real) = if _x_13 then 377/1000 else if _x_12 then 1223/1000 else if _x_11 then 1901/1000 else … in let (_x_40 : real) = 4637/29020000 * _x_0 in let (_x_41 : real) = 3601/388750 * _x_1 in let (_x_42 : real) = 5957/8500000 * _x_2 in let (_x_43 : real) = (-22041/640000) * _x_3 in let (_x_44 : real) = if 10277/200000 * _x_8 +. (-28841/190100) * _x_14 +. _x_40 +. _x_41 +. _x_42 +. _x_43 <= (-372238333/2454859840) then 0 else 372238333/2454859840 +. 10277/200000 * _x_38 +. (-28841/190100) * _x_39 +. _x_40 +. _x_41 +. _x_42 +. _x_43 in let (_x_45 : real) = 13901/50000 * _x_8 in let (_x_46 : real) = (-803/38020) * _x_14 in let (_x_47 : real) = 10557/29020000 * _x_0 in let (_x_48 : real) = 60757/3110000 * _x_1 in let (_x_49 : real) = (-16157/4250000) * _x_2 in let (_x_50 : real) = 47933/640000 * _x_3 in let (_x_51 : real) = if _x_45 +. _x_46 +. _x_47 +. _x_48 +. _x_49 +. _x_50 <= 72146699557/306857480000 then 0 else (-72146699557/306857480000) +. _x_45 +. _x_46 +. _x_47 +. _x_48 +. _x_49 +. _x_50 in let (_x_52 : real) = 1568904513/1250000000 * (if _x_9 +. _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19 <= (-1716983137/306857480000) then 0 else (1716983137/306857480000 +. _x_9 +. _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19)) +. (-1400061773/1250000000) * (if _x_20 +. _x_21 +. _x_22 +. _x_23 +. _x_24 +. _x_25 <= 73983893263/767143700000 then 0 else ((-73983893263/767143700000) +. _x_20 +. _x_21 +. _x_22 +. _x_23 +. _x_24 +. _x_25)) +. (-889978969/400000000) * (if _x_26 +. _x_27 +. _x_28 +. _x_29 +. _x_30 +. _x_31 <= (-317131778543/1534287400000) then 0 else (317131778543/1534287400000 +. _x_26 +. _x_27 +. _x_28 +. _x_29 +. _x_30 +. _x_31)) +. (-787784679/2500000000) * (if _x_32 +. _x_33 +. _x_34 +. _x_35 +. _x_36 +. _x_37 <= (-89188713933/1534287400000) then 0 else (89188713933/1534287400000 +. _x_32 +. _x_33 +. _x_34 +. _x_35 +. _x_36 +. _x_37)) +. (-19189866047/10000000000) * _x_44 +. 5337652199/2000000000 * _x_51 in let (_x_53 : real) = 5031/50000 * _x_38 in let (_x_54 : real) = (-7861/95050) * _x_39 in let (_x_55 : real) = if _x_53 +. _x_54 +. _x_16 +. _x_17 +. _x_18 +. _x_19 <= (-1716983137/306857480000) then 0 else 1716983137/306857480000 +. _x_53 +. _x_54 +. _x_16 +. _x_17 +. _x_18 +. _x_19 in let (_x_56 : real) = 29103/200000 * _x_38 in let (_x_57 : real) = 159/9505 * _x_39 in let (_x_58 : real) = if _x_56 +. _x_57 +. _x_22 +. _x_23 +. _x_24 +. _x_25 <= 73983893263/767143700000 then 0 else (-73983893263/767143700000) +. _x_56 +. _x_57 +. _x_22 +. _x_23 +. _x_24 +. _x_25 in let (_x_59 : real) = 66419/200000 * _x_38 in let (_x_60 : real) = 25399/190100 * _x_39 in let (_x_61 : real) = if _x_59 +. _x_60 +. _x_28 +. _x_29 +. _x_30 +. _x_31 <= (-317131778543/1534287400000) then 0 else 317131778543/1534287400000 +. _x_59 +. _x_60 +. _x_28 +. _x_29 +. _x_30 +. _x_31 in let (_x_62 : real) = 23799/100000 * _x_38 in let (_x_63 : real) = (-18071/95050) * _x_39 in let (_x_64 : real) = if _x_62 +. _x_63 +. _x_34 +. _x_35 +. _x_36 +. _x_37 <= (-89188713933/1534287400000) then 0 else 89188713933/1534287400000 +. _x_62 +. _x_63 +. _x_34 +. _x_35 +. _x_36 +. _x_37 in not ((0 <= _x_0) && (_x_0 <= 500) && (0 <= _x_1) && (_x_1 <= 40) && (0 <= _x_2) && (_x_2 <= 100) && (0 <= _x_3) && (_x_3 <= 15)) \|\| ((if _x_52 <= (-341987779/312500000) then 28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_55 +. (-60142453582761/31250000000000) * _x_58 +. (-38230826571333/10000000000000) * _x_61 +. (-33840866455803/62500000000000) * _x_64 +. (-824339075780979/250000000000000) * _x_44 +. 229289525512443/50000000000000 * _x_51 else if _x_52 <= (-29487779/312500000) then 213430965464483/31250000000000 +. 732799213218501/125000000000000 * _x_55 +. (-653936652747521/125000000000000) * _x_58 +. (-415688706903613/40000000000000) * _x_61 +. (-367956104513283/250000000000000) * _x_64 +. (-8963145063634619/1000000000000000) * _x_44 +. 2493094576152323/200000000000000 * _x_51 else if _x_52 <= 283012221/312500000 then 1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_55 +. (-111099101872869/7812500000000) * _x_58 +. (-70622501127057/2500000000000) * _x_61 +. (-62513077632687/15625000000000) * _x_64 +. (-1522773440427591/62500000000000) * _x_44 +. 423558714947247/12500000000000 * _x_51 else if _x_52 <= 595512221/312500000 then … else …) >= 0)
expansions:	[]
rewrite_steps:
forward_chaining:

Unsat

digraph "proof" {
p_365 [label="Start (let (_x_0 : real) = ( :var_0: ).dmc in\l       let (_x_1 : real) = ( :var_0: ).temp in\l       let (_x_2 : real) = ( :var_0: ).rh in\l       let (_x_3 : real) = ( :var_0: ).rain in\l       let (_x_4 : real)\l           = 5031/25000 * … +. (-7861/50000) * … +. (-19063/100000) * …\l             +. (-27281/50000) * … +. 137/4000 * … +. 6263/12500 * …\l             +. (-173/6250)\l       in\l       let (_x_5 : real)\l           = 29103/100000 * … +. 159/5000 * … +. (-1021/6250) * …\l             +. 17919/100000 * … +. 32971/100000 * …\l             +. (-21603/50000) * … +. (-131/5000)\l       in\l       let (_x_6 : real)\l           = 66419/100000 * … +. 25399/100000 * … +. 449/100000 * …\l             +. 3841/100000 * … +. (-25741/50000) * …\l             +. 58299/100000 * … +. 5929/50000\l       in\l       let (_x_7 : real)\l           = 23799/50000 * … +. (-18071/50000) * … +. 38981/100000 * …\l             +. 1727/6250 * … +. (-61231/100000) * …\l             +. (-1831/50000) * … +. (-289/10000)\l       in\l       let (_x_8 : real)\l           = 10277/100000 * … +. (-28841/100000) * … +. 4637/100000 * …\l             +. 3601/12500 * … +. 5957/100000 * …\l             +. (-22041/100000) * … +. 1827/10000\l       in\l       let (_x_9 : real)\l           = 13901/25000 * … +. (-803/20000) * … +. 10557/100000 * …\l             +. 60757/100000 * … +. (-16157/50000) * …\l             +. 47933/100000 * … +. (-6219/25000)\l       in\l       let (_x_10 : real)\l           = 444323/100000\l             * (3531/12500 * (if _x_4 \> 0 then _x_4 else 0)\l                +. (-3151/12500) * (if _x_5 \> 0 then _x_5 else 0)\l                +. (-2003/4000) * (if _x_6 \> 0 then _x_6 else 0)\l                +. (-1773/25000) * (if _x_7 \> 0 then _x_7 else 0)\l                +. (-43189/100000) * (if _x_8 \> 0 then _x_8 else 0)\l                +. 12013/20000 * (if _x_9 \> 0 then _x_9 else 0) +. 1473/3125)\l       in\l       (0 \<= _x_0)\l       && ((_x_0 \<= 500)\l           && ((0 \<= _x_1)\l               && ((_x_1 \<= 40)\l                   && ((0 \<= _x_2)\l                       && ((_x_2 \<= 100) && ((0 \<= _x_3) && (_x_3 \<= 15)))))))\l       ==\> (if _x_10 \<= 1 then (_x_10 - 0) * 42957/25000\l            else\l            if _x_10 \<= 2 then (_x_10 - 15803/25000) * 467077/100000\l            else\l            if _x_10 \<= 3 then (_x_10 - 149679/100000) * 79353/6250\l            else if _x_10 \<= 4 then … else …)\l           \>= 0\l       :time 0.490s)",shape=box,style=filled,fontname="courier",fontsize=14];
p_365 -> p_364 [label=""];
p_364 [label="Simplify (let (_x_0 : real) = ( :var_0: ).dmc in\l          let (_x_1 : real) = ( :var_0: ).temp in\l          let (_x_2 : real) = ( :var_0: ).rh in\l          let (_x_3 : real) = ( :var_0: ).rain in\l          let (_x_4 : month) = ( :var_0: ).month in\l          let (_x_5 : bool) = _x_4 = Mar in\l          let (_x_6 : bool) = _x_4 = Feb in\l          let (_x_7 : bool) = _x_4 = Jan in\l          let (_x_8 : real)\l              = if _x_7 then 67/500\l                else\l                if _x_6 then 1/2\l                else if _x_5 then 1 else if _x_4 = Apr then 3/2 else …\l          in\l          let (_x_9 : real) = 5031/50000 * _x_8 in\l          let (_x_10 : day) = ( :var_0: ).day in\l          let (_x_11 : bool) = (_x_10 = Wed) \|\| (_x_10 = Thu) in\l          let (_x_12 : bool) = _x_10 = Tue in\l          let (_x_13 : bool) = _x_10 = Mon in\l          let (_x_14 : real)\l              = if _x_13 then 377/1000\l                else\l                if _x_12 then 1223/1000\l                else\l                if _x_11 then 1901/1000\l                else if _x_10 = Fri then 1223/1000 else …\l          in\l          let (_x_15 : real) = (-7861/95050) * _x_14 in\l          let (_x_16 : real) = (-19063/29020000) * _x_0 in\l          let (_x_17 : real) = (-27281/1555000) * _x_1 in\l          let (_x_18 : real) = 137/340000 * _x_2 in\l          let (_x_19 : real) = 6263/80000 * _x_3 in\l          let (_x_20 : real) = 29103/200000 * _x_8 in\l          let (_x_21 : real) = 159/9505 * _x_14 in\l          let (_x_22 : real) = (-1021/1813750) * _x_0 in\l          let (_x_23 : real) = 17919/3110000 * _x_1 in\l          let (_x_24 : real) = 32971/8500000 * _x_2 in\l          let (_x_25 : real) = (-21603/320000) * _x_3 in\l          let (_x_26 : real) = 66419/200000 * _x_8 in\l          let (_x_27 : real) = 25399/190100 * _x_14 in\l          let (_x_28 : real) = 449/29020000 * _x_0 in\l          let (_x_29 : real) = 3841/3110000 * _x_1 in\l          let (_x_30 : real) = (-25741/4250000) * _x_2 in\l          let (_x_31 : real) = 58299/640000 * _x_3 in\l          let (_x_32 : real) = 23799/100000 * _x_8 in\l          let (_x_33 : real) = (-18071/95050) * _x_14 in\l          let (_x_34 : real) = 38981/29020000 * _x_0 in\l          let (_x_35 : real) = 1727/194375 * _x_1 in\l          let (_x_36 : real) = (-61231/8500000) * _x_2 in\l          let (_x_37 : real) = (-1831/320000) * _x_3 in\l          let (_x_38 : real)\l              = if _x_7 then 67/500\l                else if _x_6 then 1/2 else if _x_5 then 1 else …\l          in\l          let (_x_39 : real)\l              = if _x_13 then 377/1000\l                else\l                if _x_12 then 1223/1000 else if _x_11 then 1901/1000 else …\l          in\l          let (_x_40 : real) = 4637/29020000 * _x_0 in\l          let (_x_41 : real) = 3601/388750 * _x_1 in\l          let (_x_42 : real) = 5957/8500000 * _x_2 in\l          let (_x_43 : real) = (-22041/640000) * _x_3 in\l          let (_x_44 : real)\l              = if 10277/200000 * _x_8 +. (-28841/190100) * _x_14 +. _x_40\l                   +. _x_41 +. _x_42 +. _x_43 \<= (-372238333/2454859840)\l                then 0\l                else\l                  372238333/2454859840 +. 10277/200000 * _x_38\l                  +. (-28841/190100) * _x_39 +. _x_40 +. _x_41 +. _x_42\l                  +. _x_43\l          in\l          let (_x_45 : real) = 13901/50000 * _x_8 in\l          let (_x_46 : real) = (-803/38020) * _x_14 in\l          let (_x_47 : real) = 10557/29020000 * _x_0 in\l          let (_x_48 : real) = 60757/3110000 * _x_1 in\l          let (_x_49 : real) = (-16157/4250000) * _x_2 in\l          let (_x_50 : real) = 47933/640000 * _x_3 in\l          let (_x_51 : real)\l              = if _x_45 +. _x_46 +. _x_47 +. _x_48 +. _x_49 +. _x_50\l                   \<= 72146699557/306857480000\l                then 0\l                else\l                  (-72146699557/306857480000) +. _x_45 +. _x_46 +. _x_47\l                  +. _x_48 +. _x_49 +. _x_50\l          in\l          let (_x_52 : real)\l              = 1568904513/1250000000\l                * (if _x_9 +. _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19\l                      \<= (-1716983137/306857480000)\l                   then 0\l                   else\l                     (1716983137/306857480000 +. _x_9 +. _x_15 +. _x_16\l                      +. _x_17 +. _x_18 +. _x_19))\l                +. (-1400061773/1250000000)\l                   * (if _x_20 +. _x_21 +. _x_22 +. _x_23 +. _x_24 +. _x_25\l                         \<= 73983893263/767143700000\l                      then 0\l                      else\l                        ((-73983893263/767143700000) +. _x_20 +. _x_21\l                         +. _x_22 +. _x_23 +. _x_24 +. _x_25))\l                +. (-889978969/400000000)\l                   * (if _x_26 +. _x_27 +. _x_28 +. _x_29 +. _x_30 +. _x_31\l                         \<= (-317131778543/1534287400000)\l                      then 0\l                      else\l                        (317131778543/1534287400000 +. _x_26 +. _x_27\l                         +. _x_28 +. _x_29 +. _x_30 +. _x_31))\l                +. (-787784679/2500000000)\l                   * (if _x_32 +. _x_33 +. _x_34 +. _x_35 +. _x_36 +. _x_37\l                         \<= (-89188713933/1534287400000)\l                      then 0\l                      else\l                        (89188713933/1534287400000 +. _x_32 +. _x_33 +. _x_34\l                         +. _x_35 +. _x_36 +. _x_37))\l                +. (-19189866047/10000000000) * _x_44\l                +. 5337652199/2000000000 * _x_51\l          in\l          let (_x_53 : real) = 5031/50000 * _x_38 in\l          let (_x_54 : real) = (-7861/95050) * _x_39 in\l          let (_x_55 : real)\l              = if _x_53 +. _x_54 +. _x_16 +. _x_17 +. _x_18 +. _x_19\l                   \<= (-1716983137/306857480000)\l                then 0\l                else\l                  1716983137/306857480000 +. _x_53 +. _x_54 +. _x_16 +. _x_17\l                  +. _x_18 +. _x_19\l          in\l          let (_x_56 : real) = 29103/200000 * _x_38 in\l          let (_x_57 : real) = 159/9505 * _x_39 in\l          let (_x_58 : real)\l              = if _x_56 +. _x_57 +. _x_22 +. _x_23 +. _x_24 +. _x_25\l                   \<= 73983893263/767143700000\l                then 0\l                else\l                  (-73983893263/767143700000) +. _x_56 +. _x_57 +. _x_22\l                  +. _x_23 +. _x_24 +. _x_25\l          in\l          let (_x_59 : real) = 66419/200000 * _x_38 in\l          let (_x_60 : real) = 25399/190100 * _x_39 in\l          let (_x_61 : real)\l              = if _x_59 +. _x_60 +. _x_28 +. _x_29 +. _x_30 +. _x_31\l                   \<= (-317131778543/1534287400000)\l                then 0\l                else\l                  317131778543/1534287400000 +. _x_59 +. _x_60 +. _x_28\l                  +. _x_29 +. _x_30 +. _x_31\l          in\l          let (_x_62 : real) = 23799/100000 * _x_38 in\l          let (_x_63 : real) = (-18071/95050) * _x_39 in\l          let (_x_64 : real)\l              = if _x_62 +. _x_63 +. _x_34 +. _x_35 +. _x_36 +. _x_37\l                   \<= (-89188713933/1534287400000)\l                then 0\l                else\l                  89188713933/1534287400000 +. _x_62 +. _x_63 +. _x_34\l                  +. _x_35 +. _x_36 +. _x_37\l          in\l          not\l          ((0 \<= _x_0) && (_x_0 \<= 500) && (0 \<= _x_1) && (_x_1 \<= 40)\l           && (0 \<= _x_2) && (_x_2 \<= 100) && (0 \<= _x_3) && (_x_3 \<= 15))\l          \|\| ((if _x_52 \<= (-341987779/312500000)\l               then\l                 28114831522503/7812500000000\l                 +. 67395431164941/31250000000000 * _x_55\l                 +. (-60142453582761/31250000000000) * _x_58\l                 +. (-38230826571333/10000000000000) * _x_61\l                 +. (-33840866455803/62500000000000) * _x_64\l                 +. (-824339075780979/250000000000000) * _x_44\l                 +. 229289525512443/50000000000000 * _x_51\l               else\l               if _x_52 \<= (-29487779/312500000)\l               then\l                 213430965464483/31250000000000\l                 +. 732799213218501/125000000000000 * _x_55\l                 +. (-653936652747521/125000000000000) * _x_58\l                 +. (-415688706903613/40000000000000) * _x_61\l                 +. (-367956104513283/250000000000000) * _x_64\l                 +. (-8963145063634619/1000000000000000) * _x_44\l                 +. 2493094576152323/200000000000000 * _x_51\l               else\l               if _x_52 \<= 283012221/312500000\l               then\l                 1852306369389/244140625000\l                 +. 124497279820089/7812500000000 * _x_55\l                 +. (-111099101872869/7812500000000) * _x_58\l                 +. (-70622501127057/2500000000000) * _x_61\l                 +. (-62513077632687/15625000000000) * _x_64\l                 +. (-1522773440427591/62500000000000) * _x_44\l                 +. 423558714947247/12500000000000 * _x_51\l               else if _x_52 \<= 595512221/312500000 then … else …)\l              \>= 0)\l          :expansions [] :rw [] :fc [])",shape=box,style=filled,fontname="courier",fontsize=14];
p_364 -> p_363 [label=""];
p_363 [label="Unsat",shape=box,style=filled,fontname="courier",fontsize=14];
}

digraph "call graph" {
goal [label="let (_x_0 : real) = x.dmc in\llet (_x_1 : real) = x.temp in\llet (_x_2 : real) = x.rh in\llet (_x_3 : real) = x.rain in\llet (_x_4 : month) = x.month in\llet (_x_5 : bool) = _x_4 = Mar in\llet (_x_6 : bool) = _x_4 = Feb in\llet (_x_7 : bool) = _x_4 = Jan in\llet (_x_8 : real)\l    = if _x_7 then 67/500\l      else\l      if _x_6 then 1/2\l      else if _x_5 then 1 else if _x_4 = Apr then 3/2 else …\lin\llet (_x_9 : real) = 5031/50000 * _x_8 in\llet (_x_10 : day) = x.day in\llet (_x_11 : bool) = (_x_10 = Wed) \|\| (_x_10 = Thu) in\llet (_x_12 : bool) = _x_10 = Tue in\llet (_x_13 : bool) = _x_10 = Mon in\llet (_x_14 : real)\l    = if _x_13 then 377/1000\l      else\l      if _x_12 then 1223/1000\l      else\l      if _x_11 then 1901/1000 else if _x_10 = Fri then 1223/1000 else …\lin\llet (_x_15 : real) = (-7861/95050) * _x_14 in\llet (_x_16 : real) = (-19063/29020000) * _x_0 in\llet (_x_17 : real) = (-27281/1555000) * _x_1 in\llet (_x_18 : real) = 137/340000 * _x_2 in\llet (_x_19 : real) = 6263/80000 * _x_3 in\llet (_x_20 : real) = 29103/200000 * _x_8 in\llet (_x_21 : real) = 159/9505 * _x_14 in\llet (_x_22 : real) = (-1021/1813750) * _x_0 in\llet (_x_23 : real) = 17919/3110000 * _x_1 in\llet (_x_24 : real) = 32971/8500000 * _x_2 in\llet (_x_25 : real) = (-21603/320000) * _x_3 in\llet (_x_26 : real) = 66419/200000 * _x_8 in\llet (_x_27 : real) = 25399/190100 * _x_14 in\llet (_x_28 : real) = 449/29020000 * _x_0 in\llet (_x_29 : real) = 3841/3110000 * _x_1 in\llet (_x_30 : real) = (-25741/4250000) * _x_2 in\llet (_x_31 : real) = 58299/640000 * _x_3 in\llet (_x_32 : real) = 23799/100000 * _x_8 in\llet (_x_33 : real) = (-18071/95050) * _x_14 in\llet (_x_34 : real) = 38981/29020000 * _x_0 in\llet (_x_35 : real) = 1727/194375 * _x_1 in\llet (_x_36 : real) = (-61231/8500000) * _x_2 in\llet (_x_37 : real) = (-1831/320000) * _x_3 in\llet (_x_38 : real)\l    = 89188713933/1534287400000 +. _x_32 +. _x_33 +. _x_34 +. _x_35 +. _x_36\l      +. _x_37\lin\llet (_x_39 : real) = 10277/200000 * _x_8 in\llet (_x_40 : real) = (-28841/190100) * _x_14 in\llet (_x_41 : real) = 4637/29020000 * _x_0 in\llet (_x_42 : real) = 3601/388750 * _x_1 in\llet (_x_43 : real) = 5957/8500000 * _x_2 in\llet (_x_44 : real) = (-22041/640000) * _x_3 in\llet (_x_45 : real)\l    = if _x_39 +. _x_40 +. _x_41 +. _x_42 +. _x_43 +. _x_44\l         \<= (-372238333/2454859840)\l      then 0\l      else\l        372238333/2454859840 +. _x_39 +. _x_40 +. _x_41 +. _x_42 +. _x_43\l        +. _x_44\lin\llet (_x_46 : real) = 13901/50000 * _x_8 in\llet (_x_47 : real) = (-803/38020) * _x_14 in\llet (_x_48 : real) = 10557/29020000 * _x_0 in\llet (_x_49 : real) = 60757/3110000 * _x_1 in\llet (_x_50 : real) = (-16157/4250000) * _x_2 in\llet (_x_51 : real) = 47933/640000 * _x_3 in\llet (_x_52 : real)\l    = if _x_46 +. _x_47 +. _x_48 +. _x_49 +. _x_50 +. _x_51\l         \<= 72146699557/306857480000\l      then 0\l      else\l        (-72146699557/306857480000) +. _x_46 +. _x_47 +. _x_48 +. _x_49\l        +. _x_50 +. _x_51\lin\llet (_x_53 : real)\l    = 1568904513/1250000000\l      * (if _x_9 +. _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19\l            \<= (-1716983137/306857480000)\l         then 0\l         else\l           (1716983137/306857480000 +. _x_9 +. _x_15 +. _x_16 +. _x_17\l            +. _x_18 +. _x_19))\l      +. (-1400061773/1250000000)\l         * (if _x_20 +. _x_21 +. _x_22 +. _x_23 +. _x_24 +. _x_25\l               \<= 73983893263/767143700000\l            then 0\l            else\l              ((-73983893263/767143700000) +. _x_20 +. _x_21 +. _x_22\l               +. _x_23 +. _x_24 +. _x_25))\l      +. (-889978969/400000000)\l         * (if _x_26 +. _x_27 +. _x_28 +. _x_29 +. _x_30 +. _x_31\l               \<= (-317131778543/1534287400000)\l            then 0\l            else\l              (317131778543/1534287400000 +. _x_26 +. _x_27 +. _x_28 +. _x_29\l               +. _x_30 +. _x_31))\l      +. (-787784679/2500000000)\l         * (if _x_32 +. _x_33 +. _x_34 +. _x_35 +. _x_36 +. _x_37\l               \<= (-89188713933/1534287400000)\l            then 0 else _x_38)\l      +. (-19189866047/10000000000) * _x_45 +. 5337652199/2000000000 * _x_52\lin\llet (_x_54 : real)\l    = if _x_7 then 67/500 else if _x_6 then 1/2 else if _x_5 then 1 else …\lin\llet (_x_55 : real) = 5031/50000 * _x_54 in\llet (_x_56 : real)\l    = if _x_13 then 377/1000\l      else if _x_12 then 1223/1000 else if _x_11 then 1901/1000 else …\lin\llet (_x_57 : real) = (-7861/95050) * _x_56 in\llet (_x_58 : real)\l    = if _x_55 +. _x_57 +. _x_16 +. _x_17 +. _x_18 +. _x_19\l         \<= (-1716983137/306857480000)\l      then 0\l      else\l        1716983137/306857480000 +. _x_55 +. _x_57 +. _x_16 +. _x_17 +. _x_18\l        +. _x_19\lin\llet (_x_59 : real) = 29103/200000 * _x_54 in\llet (_x_60 : real) = 159/9505 * _x_56 in\llet (_x_61 : real)\l    = if _x_59 +. _x_60 +. _x_22 +. _x_23 +. _x_24 +. _x_25\l         \<= 73983893263/767143700000\l      then 0\l      else\l        (-73983893263/767143700000) +. _x_59 +. _x_60 +. _x_22 +. _x_23\l        +. _x_24 +. _x_25\lin\llet (_x_62 : real) = 66419/200000 * _x_54 in\llet (_x_63 : real) = 25399/190100 * _x_56 in\llet (_x_64 : real)\l    = if _x_62 +. _x_63 +. _x_28 +. _x_29 +. _x_30 +. _x_31\l         \<= (-317131778543/1534287400000)\l      then 0\l      else\l        317131778543/1534287400000 +. _x_62 +. _x_63 +. _x_28 +. _x_29\l        +. _x_30 +. _x_31\lin\llet (_x_65 : real)\l    = if 23799/100000 * _x_54 +. (-18071/95050) * _x_56 +. _x_34 +. _x_35\l         +. _x_36 +. _x_37 \<= (-89188713933/1534287400000)\l      then 0 else _x_38\lin\lnot\l(not\l ((0 \<= _x_0) && (_x_0 \<= 500) && (0 \<= _x_1) && (_x_1 \<= 40) && (0 \<= _x_2)\l  && (_x_2 \<= 100) && (0 \<= _x_3) && (_x_3 \<= 15))\l \|\| ((if _x_53 \<= (-341987779/312500000)\l      then\l        28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_58\l        +. (-60142453582761/31250000000000) * _x_61\l        +. (-38230826571333/10000000000000) * _x_64\l        +. (-33840866455803/62500000000000) * _x_65\l        +. (-824339075780979/250000000000000) * _x_45\l        +. 229289525512443/50000000000000 * _x_52\l      else\l      if _x_53 \<= (-29487779/312500000)\l      then\l        213430965464483/31250000000000\l        +. 732799213218501/125000000000000 * _x_58\l        +. (-653936652747521/125000000000000) * _x_61\l        +. (-415688706903613/40000000000000) * _x_64\l        +. (-367956104513283/250000000000000) * _x_65\l        +. (-8963145063634619/1000000000000000) * _x_45\l        +. 2493094576152323/200000000000000 * _x_52\l      else\l      if _x_53 \<= 283012221/312500000\l      then\l        1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_58\l        +. (-111099101872869/7812500000000) * _x_61\l        +. (-70622501127057/2500000000000) * _x_64\l        +. (-62513077632687/15625000000000) * _x_65\l        +. (-1522773440427591/62500000000000) * _x_45\l        +. 423558714947247/12500000000000 * _x_52\l      else if _x_53 \<= 595512221/312500000 then … else …)\l     \>= 0))",shape=box,style=filled,color="cyan",fontname="courier",fontsize=14];
}

Finally, we'll try something slightly more ambitious and test a hypothesis. All other things remaining equal, we would expect that the higher the temperature, the larger the area of forest that would be burned. Due to the imperfections in our model (because of limited data, stochasticity in training, the complicated patterns present in natural physical phenomena, and so on) this assertion is in fact easily falsifiable by Imandra.

Try this!

In [23]:

verify (fun a b ->
        is_valid_nn a &&
        is_valid_nn b &&
        a.month = b.month &&
        a.day = b.day &&
        a.dmc = b.dmc &&
        a.rh = b.rh &&
        a.rain = b.rain &&
        a.temp >=. b.temp ==>
        nn_model a >=. nn_model b)

Out[23]:

- : nn_input -> nn_input -> bool = <fun>
module CX : sig val a : nn_input val b : nn_input end

Counterexample (after 0 steps, 0.072s):
let a : nn_input =
  {month = Feb; day = Mon;
   dmc = 477530538943470675292449136343/52265269828627920420809925120;
   temp =
   16456572619172832889468514796852129522445874981486473/843088427862816291297913293280956091559763750558720;
   rh =
   104614291401820088872242530073475835587789055/1417405504169645763458544629343803680909824;
   rain = 0}
let b : nn_input =
  {month = Feb; day = Mon;
   dmc = 477530538943470675292449136343/52265269828627920420809925120;
   temp =
   53415521146114949327048139937483913145890495777/2775279977164166404851830384255167607221435392;
   rh =
   104614291401820088872242530073475835587789055/1417405504169645763458544629343803680909824;
   rain = 0}

Refuted

call graph
proof

digraph "call graph" {
goal [label="let (_x_0 : real) = a.dmc in\llet (_x_1 : real) = a.temp in\llet (_x_2 : real) = a.rh in\llet (_x_3 : real) = a.rain in\llet (_x_4 : real) = b.dmc in\llet (_x_5 : real) = b.temp in\llet (_x_6 : real) = b.rh in\llet (_x_7 : real) = b.rain in\llet (_x_8 : month) = a.month in\llet (_x_9 : month) = b.month in\llet (_x_10 : day) = a.day in\llet (_x_11 : day) = b.day in\llet (_x_12 : real)\l    = if _x_8 = Jan then 67/500\l      else\l      if _x_8 = Feb then 1/2\l      else if _x_8 = Mar then 1 else if _x_8 = Apr then 3/2 else …\lin\llet (_x_13 : real) = 5031/50000 * _x_12 in\llet (_x_14 : real)\l    = if _x_10 = Mon then 377/1000\l      else\l      if _x_10 = Tue then 1223/1000\l      else\l      if (_x_10 = Wed) \|\| (_x_10 = Thu) then 1901/1000\l      else if _x_10 = Fri then 1223/1000 else …\lin\llet (_x_15 : real) = (-7861/95050) * _x_14 in\llet (_x_16 : real) = (-19063/29020000) * _x_0 in\llet (_x_17 : real) = (-27281/1555000) * _x_1 in\llet (_x_18 : real) = 137/340000 * _x_2 in\llet (_x_19 : real) = 6263/80000 * _x_3 in\llet (_x_20 : real)\l    = if _x_13 +. _x_15 +. _x_16 +. _x_17 +. _x_18 +. _x_19\l         \<= (-1716983137/306857480000)\l      then 0\l      else\l        1716983137/306857480000 +. _x_13 +. _x_15 +. _x_16 +. _x_17 +. _x_18\l        +. _x_19\lin\llet (_x_21 : real) = 29103/200000 * _x_12 in\llet (_x_22 : real) = 159/9505 * _x_14 in\llet (_x_23 : real) = (-1021/1813750) * _x_0 in\llet (_x_24 : real) = 17919/3110000 * _x_1 in\llet (_x_25 : real) = 32971/8500000 * _x_2 in\llet (_x_26 : real) = (-21603/320000) * _x_3 in\llet (_x_27 : real)\l    = if _x_21 +. _x_22 +. _x_23 +. _x_24 +. _x_25 +. _x_26\l         \<= 73983893263/767143700000\l      then 0\l      else\l        (-73983893263/767143700000) +. _x_21 +. _x_22 +. _x_23 +. _x_24\l        +. _x_25 +. _x_26\lin\llet (_x_28 : real) = 66419/200000 * _x_12 in\llet (_x_29 : real) = 25399/190100 * _x_14 in\llet (_x_30 : real) = 449/29020000 * _x_0 in\llet (_x_31 : real) = 3841/3110000 * _x_1 in\llet (_x_32 : real) = (-25741/4250000) * _x_2 in\llet (_x_33 : real) = 58299/640000 * _x_3 in\llet (_x_34 : real)\l    = if _x_28 +. _x_29 +. _x_30 +. _x_31 +. _x_32 +. _x_33\l         \<= (-317131778543/1534287400000)\l      then 0\l      else\l        317131778543/1534287400000 +. _x_28 +. _x_29 +. _x_30 +. _x_31\l        +. _x_32 +. _x_33\lin\llet (_x_35 : real) = 23799/100000 * _x_12 in\llet (_x_36 : real) = (-18071/95050) * _x_14 in\llet (_x_37 : real) = 38981/29020000 * _x_0 in\llet (_x_38 : real) = 1727/194375 * _x_1 in\llet (_x_39 : real) = (-61231/8500000) * _x_2 in\llet (_x_40 : real) = (-1831/320000) * _x_3 in\llet (_x_41 : real)\l    = if _x_35 +. _x_36 +. _x_37 +. _x_38 +. _x_39 +. _x_40\l         \<= (-89188713933/1534287400000)\l      then 0\l      else\l        89188713933/1534287400000 +. _x_35 +. _x_36 +. _x_37 +. _x_38\l        +. _x_39 +. _x_40\lin\llet (_x_42 : real) = 10277/200000 * _x_12 in\llet (_x_43 : real) = (-28841/190100) * _x_14 in\llet (_x_44 : real) = 4637/29020000 * _x_0 in\llet (_x_45 : real) = 3601/388750 * _x_1 in\llet (_x_46 : real) = 5957/8500000 * _x_2 in\llet (_x_47 : real) = (-22041/640000) * _x_3 in\llet (_x_48 : real)\l    = if _x_42 +. _x_43 +. _x_44 +. _x_45 +. _x_46 +. _x_47\l         \<= (-372238333/2454859840)\l      then 0\l      else\l        372238333/2454859840 +. _x_42 +. _x_43 +. _x_44 +. _x_45 +. _x_46\l        +. _x_47\lin\llet (_x_49 : real) = 13901/50000 * _x_12 in\llet (_x_50 : real) = (-803/38020) * _x_14 in\llet (_x_51 : real) = 10557/29020000 * _x_0 in\llet (_x_52 : real) = 60757/3110000 * _x_1 in\llet (_x_53 : real) = (-16157/4250000) * _x_2 in\llet (_x_54 : real) = 47933/640000 * _x_3 in\llet (_x_55 : real)\l    = if _x_49 +. _x_50 +. _x_51 +. _x_52 +. _x_53 +. _x_54\l         \<= 72146699557/306857480000\l      then 0\l      else\l        (-72146699557/306857480000) +. _x_49 +. _x_50 +. _x_51 +. _x_52\l        +. _x_53 +. _x_54\lin\llet (_x_56 : real)\l    = 1568904513/1250000000 * _x_20 +. (-1400061773/1250000000) * _x_27\l      +. (-889978969/400000000) * _x_34 +. (-787784679/2500000000) * _x_41\l      +. (-19189866047/10000000000) * _x_48 +. 5337652199/2000000000 * _x_55\lin\llet (_x_57 : bool) = _x_9 = Mar in\llet (_x_58 : bool) = _x_9 = Feb in\llet (_x_59 : bool) = _x_9 = Jan in\llet (_x_60 : real)\l    = if _x_59 then 67/500\l      else\l      if _x_58 then 1/2\l      else if _x_57 then 1 else if _x_9 = Apr then 3/2 else …\lin\llet (_x_61 : real) = 5031/50000 * _x_60 in\llet (_x_62 : bool) = (_x_11 = Wed) \|\| (_x_11 = Thu) in\llet (_x_63 : bool) = _x_11 = Tue in\llet (_x_64 : bool) = _x_11 = Mon in\llet (_x_65 : real)\l    = if _x_64 then 377/1000\l      else\l      if _x_63 then 1223/1000\l      else\l      if _x_62 then 1901/1000 else if _x_11 = Fri then 1223/1000 else …\lin\llet (_x_66 : real) = (-7861/95050) * _x_65 in\llet (_x_67 : real) = (-19063/29020000) * _x_4 in\llet (_x_68 : real) = (-27281/1555000) * _x_5 in\llet (_x_69 : real) = 137/340000 * _x_6 in\llet (_x_70 : real) = 6263/80000 * _x_7 in\llet (_x_71 : real) = 29103/200000 * _x_60 in\llet (_x_72 : real) = 159/9505 * _x_65 in\llet (_x_73 : real) = (-1021/1813750) * _x_4 in\llet (_x_74 : real) = 17919/3110000 * _x_5 in\llet (_x_75 : real) = 32971/8500000 * _x_6 in\llet (_x_76 : real) = (-21603/320000) * _x_7 in\llet (_x_77 : real)\l    = if _x_59 then 67/500\l      else if _x_58 then 1/2 else if _x_57 then 1 else …\lin\llet (_x_78 : real) = 25399/190100 * _x_65 in\llet (_x_79 : real) = 449/29020000 * _x_4 in\llet (_x_80 : real) = 3841/3110000 * _x_5 in\llet (_x_81 : real) = (-25741/4250000) * _x_6 in\llet (_x_82 : real) = 58299/640000 * _x_7 in\llet (_x_83 : real)\l    = if 66419/200000 * _x_60 +. _x_78 +. _x_79 +. _x_80 +. _x_81 +. _x_82\l         \<= (-317131778543/1534287400000)\l      then 0\l      else\l        317131778543/1534287400000 +. 66419/200000 * _x_77 +. _x_78 +. _x_79\l        +. _x_80 +. _x_81 +. _x_82\lin\llet (_x_84 : real) = 23799/100000 * _x_60 in\llet (_x_85 : real) = (-18071/95050) * _x_65 in\llet (_x_86 : real) = 38981/29020000 * _x_4 in\llet (_x_87 : real) = 1727/194375 * _x_5 in\llet (_x_88 : real) = (-61231/8500000) * _x_6 in\llet (_x_89 : real) = (-1831/320000) * _x_7 in\llet (_x_90 : real)\l    = if _x_84 +. _x_85 +. _x_86 +. _x_87 +. _x_88 +. _x_89\l         \<= (-89188713933/1534287400000)\l      then 0\l      else\l        89188713933/1534287400000 +. _x_84 +. _x_85 +. _x_86 +. _x_87\l        +. _x_88 +. _x_89\lin\llet (_x_91 : real) = 10277/200000 * _x_60 in\llet (_x_92 : real) = (-28841/190100) * _x_65 in\llet (_x_93 : real) = 4637/29020000 * _x_4 in\llet (_x_94 : real) = 3601/388750 * _x_5 in\llet (_x_95 : real) = 5957/8500000 * _x_6 in\llet (_x_96 : real) = (-22041/640000) * _x_7 in\llet (_x_97 : real)\l    = if _x_91 +. _x_92 +. _x_93 +. _x_94 +. _x_95 +. _x_96\l         \<= (-372238333/2454859840)\l      then 0\l      else\l        372238333/2454859840 +. _x_91 +. _x_92 +. _x_93 +. _x_94 +. _x_95\l        +. _x_96\lin\llet (_x_98 : real) = 13901/50000 * _x_60 in\llet (_x_99 : real) = (-803/38020) * _x_65 in\llet (_x_100 : real) = 10557/29020000 * _x_4 in\llet (_x_101 : real) = 60757/3110000 * _x_5 in\llet (_x_102 : real) = (-16157/4250000) * _x_6 in\llet (_x_103 : real) = 47933/640000 * _x_7 in\llet (_x_104 : real)\l    = if _x_98 +. _x_99 +. _x_100 +. _x_101 +. _x_102 +. _x_103\l         \<= 72146699557/306857480000\l      then 0\l      else\l        (-72146699557/306857480000) +. _x_98 +. _x_99 +. _x_100 +. _x_101\l        +. _x_102 +. _x_103\lin\llet (_x_105 : real)\l    = 1568904513/1250000000\l      * (if _x_61 +. _x_66 +. _x_67 +. _x_68 +. _x_69 +. _x_70\l            \<= (-1716983137/306857480000)\l         then 0\l         else\l           (1716983137/306857480000 +. _x_61 +. _x_66 +. _x_67 +. _x_68\l            +. _x_69 +. _x_70))\l      +. (-1400061773/1250000000)\l         * (if _x_71 +. _x_72 +. _x_73 +. _x_74 +. _x_75 +. _x_76\l               \<= 73983893263/767143700000\l            then 0\l            else\l              ((-73983893263/767143700000) +. _x_71 +. _x_72 +. _x_73\l               +. _x_74 +. _x_75 +. _x_76))\l      +. (-889978969/400000000) * _x_83 +. (-787784679/2500000000) * _x_90\l      +. (-19189866047/10000000000) * _x_97 +. 5337652199/2000000000 * _x_104\lin\llet (_x_106 : real) = 5031/50000 * _x_77 in\llet (_x_107 : real)\l    = if _x_64 then 377/1000\l      else if _x_63 then 1223/1000 else if _x_62 then 1901/1000 else …\lin\llet (_x_108 : real) = (-7861/95050) * _x_107 in\llet (_x_109 : real)\l    = if _x_106 +. _x_108 +. _x_67 +. _x_68 +. _x_69 +. _x_70\l         \<= (-1716983137/306857480000)\l      then 0\l      else\l        1716983137/306857480000 +. _x_106 +. _x_108 +. _x_67 +. _x_68\l        +. _x_69 +. _x_70\lin\llet (_x_110 : real) = 29103/200000 * _x_77 in\llet (_x_111 : real) = 159/9505 * _x_107 in\llet (_x_112 : real)\l    = if _x_110 +. _x_111 +. _x_73 +. _x_74 +. _x_75 +. _x_76\l         \<= 73983893263/767143700000\l      then 0\l      else\l        (-73983893263/767143700000) +. _x_110 +. _x_111 +. _x_73 +. _x_74\l        +. _x_75 +. _x_76\lin\lnot\l(not\l ((0 \<= _x_0) && (_x_0 \<= 500) && (0 \<= _x_1) && (_x_1 \<= 40) && (0 \<= _x_2)\l  && (_x_2 \<= 100) && (0 \<= _x_3) && (_x_3 \<= 15) && (0 \<= _x_4)\l  && (_x_4 \<= 500) && (0 \<= _x_5) && (_x_5 \<= 40) && (0 \<= _x_6)\l  && (_x_6 \<= 100) && (0 \<= _x_7) && (_x_7 \<= 15) && (_x_8 = _x_9)\l  && (_x_10 = _x_11) && (_x_0 = _x_4) && (_x_2 = _x_6) && (_x_3 = _x_7)\l  && (_x_1 \>= _x_5))\l \|\| ((if _x_56 \<= (-341987779/312500000)\l      then\l        28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_20\l        +. (-60142453582761/31250000000000) * _x_27\l        +. (-38230826571333/10000000000000) * _x_34\l        +. (-33840866455803/62500000000000) * _x_41\l        +. (-824339075780979/250000000000000) * _x_48\l        +. 229289525512443/50000000000000 * _x_55\l      else\l      if _x_56 \<= (-29487779/312500000)\l      then\l        213430965464483/31250000000000\l        +. 732799213218501/125000000000000 * _x_20\l        +. (-653936652747521/125000000000000) * _x_27\l        +. (-415688706903613/40000000000000) * _x_34\l        +. (-367956104513283/250000000000000) * _x_41\l        +. (-8963145063634619/1000000000000000) * _x_48\l        +. 2493094576152323/200000000000000 * _x_55\l      else\l      if _x_56 \<= 283012221/312500000\l      then\l        1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_20\l        +. (-111099101872869/7812500000000) * _x_27\l        +. (-70622501127057/2500000000000) * _x_34\l        +. (-62513077632687/15625000000000) * _x_41\l        +. (-1522773440427591/62500000000000) * _x_48\l        +. 423558714947247/12500000000000 * _x_55\l      else if _x_56 \<= 595512221/312500000 then … else …)\l     \>= (if _x_105 \<= (-341987779/312500000)\l         then\l           28114831522503/7812500000000\l           +. 67395431164941/31250000000000 * _x_109\l           +. (-60142453582761/31250000000000) * _x_112\l           +. (-38230826571333/10000000000000) * _x_83\l           +. (-33840866455803/62500000000000) * _x_90\l           +. (-824339075780979/250000000000000) * _x_97\l           +. 229289525512443/50000000000000 * _x_104\l         else\l         if _x_105 \<= (-29487779/312500000)\l         then\l           213430965464483/31250000000000\l           +. 732799213218501/125000000000000 * _x_109\l           +. (-653936652747521/125000000000000) * _x_112\l           +. (-415688706903613/40000000000000) * _x_83\l           +. (-367956104513283/250000000000000) * _x_90\l           +. (-8963145063634619/1000000000000000) * _x_97\l           +. 2493094576152323/200000000000000 * _x_104\l         else\l         if _x_105 \<= 283012221/312500000\l         then\l           1852306369389/244140625000\l           +. 124497279820089/7812500000000 * _x_109\l           +. (-111099101872869/7812500000000) * _x_112\l           +. (-70622501127057/2500000000000) * _x_83\l           +. (-62513077632687/15625000000000) * _x_90\l           +. (-1522773440427591/62500000000000) * _x_97\l           +. 423558714947247/12500000000000 * _x_104\l         else if _x_105 \<= 595512221/312500000 then … else …)))",shape=box,style=filled,color="cyan",fontname="courier",fontsize=14];
}

proof attempt

ground_instances:

definitions:

inductions:

search_time:

0.072s

details:

Expand

smt_stats:

arith offset eqs:	3
num checks:	1
arith assert lower:	42
arith tableau max rows:	48
arith tableau max columns:	185
arith pivots:	56
rlimit count:	173362
mk clause:	119
datatype occurs check:	17
mk bool var:	214
arith assert upper:	41
datatype splits:	8
decisions:	65
arith row summations:	977
arith bound prop:	1
propagations:	94
conflicts:	7
arith fixed eqs:	8
datatype accessor ax:	19
minimized lits:	5
arith conflicts:	4
arith num rows:	48
arith assert diseq:	1
datatype constructor ax:	7
final checks:	1
added eqs:	77
del clause:	14
arith eq adapter:	26
time:	0.062000
memory:	24.710000
max memory:	25.810000
num allocs:	37948863577.000000

Expand

start[0.072s]
  let (_x_0 : real) = ( :var_0: ).dmc in
  let (_x_1 : real) = ( :var_0: ).temp in
  let (_x_2 : real) = ( :var_0: ).rh in
  let (_x_3 : real) = ( :var_0: ).rain in
  let (_x_4 : real) = ( :var_1: ).dmc in
  let (_x_5 : real) = ( :var_1: ).temp in
  let (_x_6 : real) = ( :var_1: ).rh in
  let (_x_7 : real) = ( :var_1: ).rain in
  let (_x_8 : real)
      = 5031/25000 * … +. (-7861/50000) * … +. (-19063/100000) * …
        +. (-27281/50000) * … +. 137/4000 * … +. 6263/12500 * …
        +. (-173/6250)
  in
  let (_x_9 : real)
      = 29103/100000 * … +. 159/5000 * … +. (-1021/6250) * …
        +. 17919/100000 * … +. 32971/100000 * … +. (-21603/50000) * …
        +. (-131/5000)
  in
  let (_x_10 : real)
      = 66419/100000 * … +. 25399/100000 * … +. 449/100000 * …
        +. 3841/100000 * … +. (-25741/50000) * … +. 58299/100000 * …
        +. 5929/50000
  in
  let (_x_11 : real)
      = 23799/50000 * … +. (-18071/50000) * … +. 38981/100000 * …
        +. 1727/6250 * … +. (-61231/100000) * … +. (-1831/50000) * …
        +. (-289/10000)
  in
  let (_x_12 : real)
      = 10277/100000 * … +. (-28841/100000) * … +. 4637/100000 * …
        +. 3601/12500 * … +. 5957/100000 * … +. (-22041/100000) * …
        +. 1827/10000
  in
  let (_x_13 : real)
      = 13901/25000 * … +. (-803/20000) * … +. 10557/100000 * …
        +. 60757/100000 * … +. (-16157/50000) * … +. 47933/100000 * …
        +. (-6219/25000)
  in
  let (_x_14 : real)
      = 444323/100000
        * (3531/12500 * (if _x_8 > 0 then _x_8 else 0)
           +. (-3151/12500) * (if _x_9 > 0 then _x_9 else 0)
           +. (-2003/4000) * (if _x_10 > 0 then _x_10 else 0)
           +. (-1773/25000) * (if _x_11 > 0 then _x_11 else 0)
           +. (-43189/100000) * (if _x_12 > 0 then _x_12 else 0)
           +. 12013/20000 * (if _x_13 > 0 then _x_13 else 0) +. 1473/3125)
  in
  let (_x_15 : real)
      = if _x_14 <= 1 then (_x_14 - 0) * 42957/25000
        else
        if _x_14 <= 2 then (_x_14 - 15803/25000) * 467077/100000
        else
        if _x_14 <= 3 then (_x_14 - 149679/100000) * 79353/6250
        else if _x_14 <= 4 then … else …
  in
  (0 <= _x_0)
  && ((_x_0 <= 500)
      && ((0 <= _x_1)
          && ((_x_1 <= 40)
              && ((0 <= _x_2)
                  && ((_x_2 <= 100) && ((0 <= _x_3) && (_x_3 <= 15)))))))
  && ((0 <= _x_4)
      && ((_x_4 <= 500)
          && ((0 <= _x_5)
              && ((_x_5 <= 40)
                  && ((0 <= _x_6)
                      && ((_x_6 <= 100) && ((0 <= _x_7) && (_x_7 <= 15)))))))
      && ((( :var_0: ).month = ( :var_1: ).month)
          && ((( :var_0: ).day = ( :var_1: ).day)
              && ((_x_0 = _x_4)
                  && ((_x_2 = _x_6) && ((_x_3 = _x_7) && (_x_1 >= _x_5)))))))
  ==> _x_15 >= _x_15

simplify

into:	let (_x_0 : real) = ( :var_0: ).dmc in let (_x_1 : real) = ( :var_0: ).temp in let (_x_2 : real) = ( :var_0: ).rh in let (_x_3 : real) = ( :var_0: ).rain in let (_x_4 : real) = ( :var_1: ).dmc in let (_x_5 : real) = ( :var_1: ).temp in let (_x_6 : real) = ( :var_1: ).rh in let (_x_7 : real) = ( :var_1: ).rain in let (_x_8 : month) = ( :var_0: ).month in let (_x_9 : month) = ( :var_1: ).month in let (_x_10 : day) = ( :var_0: ).day in let (_x_11 : day) = ( :var_1: ).day in let (_x_12 : bool) = _x_8 = Mar in let (_x_13 : bool) = _x_8 = Feb in let (_x_14 : bool) = _x_8 = Jan in let (_x_15 : bool) = (_x_10 = Wed) \|\| (_x_10 = Thu) in let (_x_16 : bool) = _x_10 = Tue in let (_x_17 : bool) = _x_10 = Mon in let (_x_18 : real) = (-19063/29020000) * _x_0 in let (_x_19 : real) = (-27281/1555000) * _x_1 in let (_x_20 : real) = 137/340000 * _x_2 in let (_x_21 : real) = 6263/80000 * _x_3 in let (_x_22 : real) = if _x_14 then 67/500 else if _x_13 then 1/2 else if _x_12 then 1 else if _x_8 = Apr then 3/2 else … in let (_x_23 : real) = if _x_17 then 377/1000 else if _x_16 then 1223/1000 else if _x_15 then 1901/1000 else if _x_10 = Fri then 1223/1000 else … in let (_x_24 : real) = if 5031/50000 * _x_22 +. (-7861/95050) * _x_23 +. _x_18 +. _x_19 +. _x_20 +. _x_21 <= (-1716983137/306857480000) then 0 else 1716983137/306857480000 +. 5031/50000 * (if _x_14 then 67/500 else if _x_13 then 1/2 else if _x_12 then 1 else …) +. (-7861/95050) * (if _x_17 then 377/1000 else if _x_16 then 1223/1000 else if _x_15 then 1901/1000 else …) +. _x_18 +. _x_19 +. _x_20 +. _x_21 in let (_x_25 : real) = 29103/200000 * _x_22 in let (_x_26 : real) = 159/9505 * _x_23 in let (_x_27 : real) = (-1021/1813750) * _x_0 in let (_x_28 : real) = 17919/3110000 * _x_1 in let (_x_29 : real) = 32971/8500000 * _x_2 in let (_x_30 : real) = (-21603/320000) * _x_3 in let (_x_31 : real) = if _x_25 +. _x_26 +. _x_27 +. _x_28 +. _x_29 +. _x_30 <= 73983893263/767143700000 then 0 else (-73983893263/767143700000) +. _x_25 +. _x_26 +. _x_27 +. _x_28 +. _x_29 +. _x_30 in let (_x_32 : real) = 66419/200000 * _x_22 in let (_x_33 : real) = 25399/190100 * _x_23 in let (_x_34 : real) = 449/29020000 * _x_0 in let (_x_35 : real) = 3841/3110000 * _x_1 in let (_x_36 : real) = (-25741/4250000) * _x_2 in let (_x_37 : real) = 58299/640000 * _x_3 in let (_x_38 : real) = if _x_32 +. _x_33 +. _x_34 +. _x_35 +. _x_36 +. _x_37 <= (-317131778543/1534287400000) then 0 else 317131778543/1534287400000 +. _x_32 +. _x_33 +. _x_34 +. _x_35 +. _x_36 +. _x_37 in let (_x_39 : real) = 23799/100000 * _x_22 in let (_x_40 : real) = (-18071/95050) * _x_23 in let (_x_41 : real) = 38981/29020000 * _x_0 in let (_x_42 : real) = 1727/194375 * _x_1 in let (_x_43 : real) = (-61231/8500000) * _x_2 in let (_x_44 : real) = (-1831/320000) * _x_3 in let (_x_45 : real) = if _x_39 +. _x_40 +. _x_41 +. _x_42 +. _x_43 +. _x_44 <= (-89188713933/1534287400000) then 0 else 89188713933/1534287400000 +. _x_39 +. _x_40 +. _x_41 +. _x_42 +. _x_43 +. _x_44 in let (_x_46 : real) = 10277/200000 * _x_22 in let (_x_47 : real) = (-28841/190100) * _x_23 in let (_x_48 : real) = 4637/29020000 * _x_0 in let (_x_49 : real) = 3601/388750 * _x_1 in let (_x_50 : real) = 5957/8500000 * _x_2 in let (_x_51 : real) = (-22041/640000) * _x_3 in let (_x_52 : real) = if _x_46 +. _x_47 +. _x_48 +. _x_49 +. _x_50 +. _x_51 <= (-372238333/2454859840) then 0 else 372238333/2454859840 +. _x_46 +. _x_47 +. _x_48 +. _x_49 +. _x_50 +. _x_51 in let (_x_53 : real) = 13901/50000 * _x_22 in let (_x_54 : real) = (-803/38020) * _x_23 in let (_x_55 : real) = 10557/29020000 * _x_0 in let (_x_56 : real) = 60757/3110000 * _x_1 in let (_x_57 : real) = (-16157/4250000) * _x_2 in let (_x_58 : real) = 47933/640000 * _x_3 in let (_x_59 : real) = if _x_53 +. _x_54 +. _x_55 +. _x_56 +. _x_57 +. _x_58 <= 72146699557/306857480000 then 0 else (-72146699557/306857480000) +. _x_53 +. _x_54 +. _x_55 +. _x_56 +. _x_57 +. _x_58 in let (_x_60 : real) = 1568904513/1250000000 * _x_24 +. (-1400061773/1250000000) * _x_31 +. (-889978969/400000000) * _x_38 +. (-787784679/2500000000) * _x_45 +. (-19189866047/10000000000) * _x_52 +. 5337652199/2000000000 * _x_59 in let (_x_61 : bool) = _x_9 = Mar in let (_x_62 : bool) = _x_9 = Feb in let (_x_63 : bool) = _x_9 = Jan in let (_x_64 : real) = if _x_63 then 67/500 else if _x_62 then 1/2 else if _x_61 then 1 else if _x_9 = Apr then 3/2 else … in let (_x_65 : real) = 5031/50000 * _x_64 in let (_x_66 : bool) = (_x_11 = Wed) \|\| (_x_11 = Thu) in let (_x_67 : bool) = _x_11 = Tue in let (_x_68 : bool) = _x_11 = Mon in let (_x_69 : real) = if _x_68 then 377/1000 else if _x_67 then 1223/1000 else if _x_66 then 1901/1000 else if _x_11 = Fri then 1223/1000 else … in let (_x_70 : real) = (-7861/95050) * _x_69 in let (_x_71 : real) = (-19063/29020000) * _x_4 in let (_x_72 : real) = (-27281/1555000) * _x_5 in let (_x_73 : real) = 137/340000 * _x_6 in let (_x_74 : real) = 6263/80000 * _x_7 in let (_x_75 : real) = 29103/200000 * _x_64 in let (_x_76 : real) = 159/9505 * _x_69 in let (_x_77 : real) = (-1021/1813750) * _x_4 in let (_x_78 : real) = 17919/3110000 * _x_5 in let (_x_79 : real) = 32971/8500000 * _x_6 in let (_x_80 : real) = (-21603/320000) * _x_7 in let (_x_81 : real) = if _x_63 then 67/500 else if _x_62 then 1/2 else if _x_61 then 1 else … in let (_x_82 : real) = if _x_68 then 377/1000 else if _x_67 then 1223/1000 else if _x_66 then 1901/1000 else … in let (_x_83 : real) = 449/29020000 * _x_4 in let (_x_84 : real) = 3841/3110000 * _x_5 in let (_x_85 : real) = (-25741/4250000) * _x_6 in let (_x_86 : real) = 58299/640000 * _x_7 in let (_x_87 : real) = if 66419/200000 * _x_64 +. 25399/190100 * _x_69 +. _x_83 +. _x_84 +. _x_85 +. _x_86 <= (-317131778543/1534287400000) then 0 else 317131778543/1534287400000 +. 66419/200000 * _x_81 +. 25399/190100 * _x_82 +. _x_83 +. _x_84 +. _x_85 +. _x_86 in let (_x_88 : real) = 23799/100000 * _x_64 in let (_x_89 : real) = (-18071/95050) * _x_69 in let (_x_90 : real) = 38981/29020000 * _x_4 in let (_x_91 : real) = 1727/194375 * _x_5 in let (_x_92 : real) = (-61231/8500000) * _x_6 in let (_x_93 : real) = (-1831/320000) * _x_7 in let (_x_94 : real) = if _x_88 +. _x_89 +. _x_90 +. _x_91 +. _x_92 +. _x_93 <= (-89188713933/1534287400000) then 0 else 89188713933/1534287400000 +. _x_88 +. _x_89 +. _x_90 +. _x_91 +. _x_92 +. _x_93 in let (_x_95 : real) = 10277/200000 * _x_64 in let (_x_96 : real) = (-28841/190100) * _x_69 in let (_x_97 : real) = 4637/29020000 * _x_4 in let (_x_98 : real) = 3601/388750 * _x_5 in let (_x_99 : real) = 5957/8500000 * _x_6 in let (_x_100 : real) = (-22041/640000) * _x_7 in let (_x_101 : real) = if _x_95 +. _x_96 +. _x_97 +. _x_98 +. _x_99 +. _x_100 <= (-372238333/2454859840) then 0 else 372238333/2454859840 +. _x_95 +. _x_96 +. _x_97 +. _x_98 +. _x_99 +. _x_100 in let (_x_102 : real) = 13901/50000 * _x_64 in let (_x_103 : real) = (-803/38020) * _x_69 in let (_x_104 : real) = 10557/29020000 * _x_4 in let (_x_105 : real) = 60757/3110000 * _x_5 in let (_x_106 : real) = (-16157/4250000) * _x_6 in let (_x_107 : real) = 47933/640000 * _x_7 in let (_x_108 : real) = if _x_102 +. _x_103 +. _x_104 +. _x_105 +. _x_106 +. _x_107 <= 72146699557/306857480000 then 0 else (-72146699557/306857480000) +. _x_102 +. _x_103 +. _x_104 +. _x_105 +. _x_106 +. _x_107 in let (_x_109 : real) = 1568904513/1250000000 * (if _x_65 +. _x_70 +. _x_71 +. _x_72 +. _x_73 +. _x_74 <= (-1716983137/306857480000) then 0 else (1716983137/306857480000 +. _x_65 +. _x_70 +. _x_71 +. _x_72 +. _x_73 +. _x_74)) +. (-1400061773/1250000000) * (if _x_75 +. _x_76 +. _x_77 +. _x_78 +. _x_79 +. _x_80 <= 73983893263/767143700000 then 0 else ((-73983893263/767143700000) +. _x_75 +. _x_76 +. _x_77 +. _x_78 +. _x_79 +. _x_80)) +. (-889978969/400000000) * _x_87 +. (-787784679/2500000000) * _x_94 +. (-19189866047/10000000000) * _x_101 +. 5337652199/2000000000 * _x_108 in let (_x_110 : real) = 5031/50000 * _x_81 in let (_x_111 : real) = (-7861/95050) * _x_82 in let (_x_112 : real) = if _x_110 +. _x_111 +. _x_71 +. _x_72 +. _x_73 +. _x_74 <= (-1716983137/306857480000) then 0 else 1716983137/306857480000 +. _x_110 +. _x_111 +. _x_71 +. _x_72 +. _x_73 +. _x_74 in let (_x_113 : real) = 29103/200000 * _x_81 in let (_x_114 : real) = 159/9505 * _x_82 in let (_x_115 : real) = if _x_113 +. _x_114 +. _x_77 +. _x_78 +. _x_79 +. _x_80 <= 73983893263/767143700000 then 0 else (-73983893263/767143700000) +. _x_113 +. _x_114 +. _x_77 +. _x_78 +. _x_79 +. _x_80 in not ((0 <= _x_0) && (_x_0 <= 500) && (0 <= _x_1) && (_x_1 <= 40) && (0 <= _x_2) && (_x_2 <= 100) && (0 <= _x_3) && (_x_3 <= 15) && (0 <= _x_4) && (_x_4 <= 500) && (0 <= _x_5) && (_x_5 <= 40) && (0 <= _x_6) && (_x_6 <= 100) && (0 <= _x_7) && (_x_7 <= 15) && (_x_8 = _x_9) && (_x_10 = _x_11) && (_x_0 = _x_4) && (_x_2 = _x_6) && (_x_3 = _x_7) && (_x_1 >= _x_5)) \|\| ((if _x_60 <= (-341987779/312500000) then 28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_24 +. (-60142453582761/31250000000000) * _x_31 +. (-38230826571333/10000000000000) * _x_38 +. (-33840866455803/62500000000000) * _x_45 +. (-824339075780979/250000000000000) * _x_52 +. 229289525512443/50000000000000 * _x_59 else if _x_60 <= (-29487779/312500000) then 213430965464483/31250000000000 +. 732799213218501/125000000000000 * _x_24 +. (-653936652747521/125000000000000) * _x_31 +. (-415688706903613/40000000000000) * _x_38 +. (-367956104513283/250000000000000) * _x_45 +. (-8963145063634619/1000000000000000) * _x_52 +. 2493094576152323/200000000000000 * _x_59 else if _x_60 <= 283012221/312500000 then 1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_24 +. (-111099101872869/7812500000000) * _x_31 +. (-70622501127057/2500000000000) * _x_38 +. (-62513077632687/15625000000000) * _x_45 +. (-1522773440427591/62500000000000) * _x_52 +. 423558714947247/12500000000000 * _x_59 else if _x_60 <= 595512221/312500000 then … else …) >= (if _x_109 <= (-341987779/312500000) then 28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_112 +. (-60142453582761/31250000000000) * _x_115 +. (-38230826571333/10000000000000) * _x_87 +. (-33840866455803/62500000000000) * _x_94 +. (-824339075780979/250000000000000) * _x_101 +. 229289525512443/50000000000000 * _x_108 else if _x_109 <= (-29487779/312500000) then 213430965464483/31250000000000 +. 732799213218501/125000000000000 * _x_112 +. (-653936652747521/125000000000000) * _x_115 +. (-415688706903613/40000000000000) * _x_87 +. (-367956104513283/250000000000000) * _x_94 +. (-8963145063634619/1000000000000000) * _x_101 +. 2493094576152323/200000000000000 * _x_108 else if _x_109 <= 283012221/312500000 then 1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_112 +. (-111099101872869/7812500000000) * _x_115 +. (-70622501127057/2500000000000) * _x_87 +. (-62513077632687/15625000000000) * _x_94 +. (-1522773440427591/62500000000000) * _x_101 +. 423558714947247/12500000000000 * _x_108 else if _x_109 <= 595512221/312500000 then … else …))
expansions:	[]
rewrite_steps:
forward_chaining:

Sat (Some let a : nn_input = {month = Feb; day = Mon; dmc = (Q.of_string "477530538943470675292449136343/52265269828627920420809925120"); temp = (Q.of_string "16456572619172832889468514796852129522445874981486473/843088427862816291297913293280956091559763750558720"); rh = (Q.of_string "104614291401820088872242530073475835587789055/1417405504169645763458544629343803680909824"); rain = (Q.of_nativeint (0n))} let b : nn_input = {month = Feb; day = Mon; dmc = (Q.of_string "477530538943470675292449136343/52265269828627920420809925120"); temp = (Q.of_string "53415521146114949327048139937483913145890495777/2775279977164166404851830384255167607221435392"); rh = (Q.of_string "104614291401820088872242530073475835587789055/1417405504169645763458544629343803680909824"); rain = (Q.of_nativeint (0n))} )

digraph "proof" {
p_368 [label="Start (let (_x_0 : real) = ( :var_0: ).dmc in\l       let (_x_1 : real) = ( :var_0: ).temp in\l       let (_x_2 : real) = ( :var_0: ).rh in\l       let (_x_3 : real) = ( :var_0: ).rain in\l       let (_x_4 : real) = ( :var_1: ).dmc in\l       let (_x_5 : real) = ( :var_1: ).temp in\l       let (_x_6 : real) = ( :var_1: ).rh in\l       let (_x_7 : real) = ( :var_1: ).rain in\l       let (_x_8 : real)\l           = 5031/25000 * … +. (-7861/50000) * … +. (-19063/100000) * …\l             +. (-27281/50000) * … +. 137/4000 * … +. 6263/12500 * …\l             +. (-173/6250)\l       in\l       let (_x_9 : real)\l           = 29103/100000 * … +. 159/5000 * … +. (-1021/6250) * …\l             +. 17919/100000 * … +. 32971/100000 * …\l             +. (-21603/50000) * … +. (-131/5000)\l       in\l       let (_x_10 : real)\l           = 66419/100000 * … +. 25399/100000 * … +. 449/100000 * …\l             +. 3841/100000 * … +. (-25741/50000) * …\l             +. 58299/100000 * … +. 5929/50000\l       in\l       let (_x_11 : real)\l           = 23799/50000 * … +. (-18071/50000) * … +. 38981/100000 * …\l             +. 1727/6250 * … +. (-61231/100000) * …\l             +. (-1831/50000) * … +. (-289/10000)\l       in\l       let (_x_12 : real)\l           = 10277/100000 * … +. (-28841/100000) * … +. 4637/100000 * …\l             +. 3601/12500 * … +. 5957/100000 * …\l             +. (-22041/100000) * … +. 1827/10000\l       in\l       let (_x_13 : real)\l           = 13901/25000 * … +. (-803/20000) * … +. 10557/100000 * …\l             +. 60757/100000 * … +. (-16157/50000) * …\l             +. 47933/100000 * … +. (-6219/25000)\l       in\l       let (_x_14 : real)\l           = 444323/100000\l             * (3531/12500 * (if _x_8 \> 0 then _x_8 else 0)\l                +. (-3151/12500) * (if _x_9 \> 0 then _x_9 else 0)\l                +. (-2003/4000) * (if _x_10 \> 0 then _x_10 else 0)\l                +. (-1773/25000) * (if _x_11 \> 0 then _x_11 else 0)\l                +. (-43189/100000) * (if _x_12 \> 0 then _x_12 else 0)\l                +. 12013/20000 * (if _x_13 \> 0 then _x_13 else 0)\l                +. 1473/3125)\l       in\l       let (_x_15 : real)\l           = if _x_14 \<= 1 then (_x_14 - 0) * 42957/25000\l             else\l             if _x_14 \<= 2 then (_x_14 - 15803/25000) * 467077/100000\l             else\l             if _x_14 \<= 3 then (_x_14 - 149679/100000) * 79353/6250\l             else if _x_14 \<= 4 then … else …\l       in\l       (0 \<= _x_0)\l       && ((_x_0 \<= 500)\l           && ((0 \<= _x_1)\l               && ((_x_1 \<= 40)\l                   && ((0 \<= _x_2)\l                       && ((_x_2 \<= 100) && ((0 \<= _x_3) && (_x_3 \<= 15)))))))\l       && ((0 \<= _x_4)\l           && ((_x_4 \<= 500)\l               && ((0 \<= _x_5)\l                   && ((_x_5 \<= 40)\l                       && ((0 \<= _x_6)\l                           && ((_x_6 \<= 100) && ((0 \<= _x_7) && (_x_7 \<= 15)))))))\l           && ((( :var_0: ).month = ( :var_1: ).month)\l               && ((( :var_0: ).day = ( :var_1: ).day)\l                   && ((_x_0 = _x_4)\l                       && ((_x_2 = _x_6) && ((_x_3 = _x_7) && (_x_1 \>= _x_5)))))))\l       ==\> _x_15 \>= _x_15 :time 0.072s)",shape=box,style=filled,fontname="courier",fontsize=14];
p_368 -> p_367 [label=""];
p_367 [label="Simplify (let (_x_0 : real) = ( :var_0: ).dmc in\l          let (_x_1 : real) = ( :var_0: ).temp in\l          let (_x_2 : real) = ( :var_0: ).rh in\l          let (_x_3 : real) = ( :var_0: ).rain in\l          let (_x_4 : real) = ( :var_1: ).dmc in\l          let (_x_5 : real) = ( :var_1: ).temp in\l          let (_x_6 : real) = ( :var_1: ).rh in\l          let (_x_7 : real) = ( :var_1: ).rain in\l          let (_x_8 : month) = ( :var_0: ).month in\l          let (_x_9 : month) = ( :var_1: ).month in\l          let (_x_10 : day) = ( :var_0: ).day in\l          let (_x_11 : day) = ( :var_1: ).day in\l          let (_x_12 : bool) = _x_8 = Mar in\l          let (_x_13 : bool) = _x_8 = Feb in\l          let (_x_14 : bool) = _x_8 = Jan in\l          let (_x_15 : bool) = (_x_10 = Wed) \|\| (_x_10 = Thu) in\l          let (_x_16 : bool) = _x_10 = Tue in\l          let (_x_17 : bool) = _x_10 = Mon in\l          let (_x_18 : real) = (-19063/29020000) * _x_0 in\l          let (_x_19 : real) = (-27281/1555000) * _x_1 in\l          let (_x_20 : real) = 137/340000 * _x_2 in\l          let (_x_21 : real) = 6263/80000 * _x_3 in\l          let (_x_22 : real)\l              = if _x_14 then 67/500\l                else\l                if _x_13 then 1/2\l                else if _x_12 then 1 else if _x_8 = Apr then 3/2 else …\l          in\l          let (_x_23 : real)\l              = if _x_17 then 377/1000\l                else\l                if _x_16 then 1223/1000\l                else\l                if _x_15 then 1901/1000\l                else if _x_10 = Fri then 1223/1000 else …\l          in\l          let (_x_24 : real)\l              = if 5031/50000 * _x_22 +. (-7861/95050) * _x_23 +. _x_18\l                   +. _x_19 +. _x_20 +. _x_21 \<= (-1716983137/306857480000)\l                then 0\l                else\l                  1716983137/306857480000\l                  +. 5031/50000\l                     * (if _x_14 then 67/500\l                        else if _x_13 then 1/2 else if _x_12 then 1 else …)\l                  +. (-7861/95050)\l                     * (if _x_17 then 377/1000\l                        else\l                        if _x_16 then 1223/1000\l                        else if _x_15 then 1901/1000 else …)\l                  +. _x_18 +. _x_19 +. _x_20 +. _x_21\l          in\l          let (_x_25 : real) = 29103/200000 * _x_22 in\l          let (_x_26 : real) = 159/9505 * _x_23 in\l          let (_x_27 : real) = (-1021/1813750) * _x_0 in\l          let (_x_28 : real) = 17919/3110000 * _x_1 in\l          let (_x_29 : real) = 32971/8500000 * _x_2 in\l          let (_x_30 : real) = (-21603/320000) * _x_3 in\l          let (_x_31 : real)\l              = if _x_25 +. _x_26 +. _x_27 +. _x_28 +. _x_29 +. _x_30\l                   \<= 73983893263/767143700000\l                then 0\l                else\l                  (-73983893263/767143700000) +. _x_25 +. _x_26 +. _x_27\l                  +. _x_28 +. _x_29 +. _x_30\l          in\l          let (_x_32 : real) = 66419/200000 * _x_22 in\l          let (_x_33 : real) = 25399/190100 * _x_23 in\l          let (_x_34 : real) = 449/29020000 * _x_0 in\l          let (_x_35 : real) = 3841/3110000 * _x_1 in\l          let (_x_36 : real) = (-25741/4250000) * _x_2 in\l          let (_x_37 : real) = 58299/640000 * _x_3 in\l          let (_x_38 : real)\l              = if _x_32 +. _x_33 +. _x_34 +. _x_35 +. _x_36 +. _x_37\l                   \<= (-317131778543/1534287400000)\l                then 0\l                else\l                  317131778543/1534287400000 +. _x_32 +. _x_33 +. _x_34\l                  +. _x_35 +. _x_36 +. _x_37\l          in\l          let (_x_39 : real) = 23799/100000 * _x_22 in\l          let (_x_40 : real) = (-18071/95050) * _x_23 in\l          let (_x_41 : real) = 38981/29020000 * _x_0 in\l          let (_x_42 : real) = 1727/194375 * _x_1 in\l          let (_x_43 : real) = (-61231/8500000) * _x_2 in\l          let (_x_44 : real) = (-1831/320000) * _x_3 in\l          let (_x_45 : real)\l              = if _x_39 +. _x_40 +. _x_41 +. _x_42 +. _x_43 +. _x_44\l                   \<= (-89188713933/1534287400000)\l                then 0\l                else\l                  89188713933/1534287400000 +. _x_39 +. _x_40 +. _x_41\l                  +. _x_42 +. _x_43 +. _x_44\l          in\l          let (_x_46 : real) = 10277/200000 * _x_22 in\l          let (_x_47 : real) = (-28841/190100) * _x_23 in\l          let (_x_48 : real) = 4637/29020000 * _x_0 in\l          let (_x_49 : real) = 3601/388750 * _x_1 in\l          let (_x_50 : real) = 5957/8500000 * _x_2 in\l          let (_x_51 : real) = (-22041/640000) * _x_3 in\l          let (_x_52 : real)\l              = if _x_46 +. _x_47 +. _x_48 +. _x_49 +. _x_50 +. _x_51\l                   \<= (-372238333/2454859840)\l                then 0\l                else\l                  372238333/2454859840 +. _x_46 +. _x_47 +. _x_48 +. _x_49\l                  +. _x_50 +. _x_51\l          in\l          let (_x_53 : real) = 13901/50000 * _x_22 in\l          let (_x_54 : real) = (-803/38020) * _x_23 in\l          let (_x_55 : real) = 10557/29020000 * _x_0 in\l          let (_x_56 : real) = 60757/3110000 * _x_1 in\l          let (_x_57 : real) = (-16157/4250000) * _x_2 in\l          let (_x_58 : real) = 47933/640000 * _x_3 in\l          let (_x_59 : real)\l              = if _x_53 +. _x_54 +. _x_55 +. _x_56 +. _x_57 +. _x_58\l                   \<= 72146699557/306857480000\l                then 0\l                else\l                  (-72146699557/306857480000) +. _x_53 +. _x_54 +. _x_55\l                  +. _x_56 +. _x_57 +. _x_58\l          in\l          let (_x_60 : real)\l              = 1568904513/1250000000 * _x_24\l                +. (-1400061773/1250000000) * _x_31\l                +. (-889978969/400000000) * _x_38\l                +. (-787784679/2500000000) * _x_45\l                +. (-19189866047/10000000000) * _x_52\l                +. 5337652199/2000000000 * _x_59\l          in\l          let (_x_61 : bool) = _x_9 = Mar in\l          let (_x_62 : bool) = _x_9 = Feb in\l          let (_x_63 : bool) = _x_9 = Jan in\l          let (_x_64 : real)\l              = if _x_63 then 67/500\l                else\l                if _x_62 then 1/2\l                else if _x_61 then 1 else if _x_9 = Apr then 3/2 else …\l          in\l          let (_x_65 : real) = 5031/50000 * _x_64 in\l          let (_x_66 : bool) = (_x_11 = Wed) \|\| (_x_11 = Thu) in\l          let (_x_67 : bool) = _x_11 = Tue in\l          let (_x_68 : bool) = _x_11 = Mon in\l          let (_x_69 : real)\l              = if _x_68 then 377/1000\l                else\l                if _x_67 then 1223/1000\l                else\l                if _x_66 then 1901/1000\l                else if _x_11 = Fri then 1223/1000 else …\l          in\l          let (_x_70 : real) = (-7861/95050) * _x_69 in\l          let (_x_71 : real) = (-19063/29020000) * _x_4 in\l          let (_x_72 : real) = (-27281/1555000) * _x_5 in\l          let (_x_73 : real) = 137/340000 * _x_6 in\l          let (_x_74 : real) = 6263/80000 * _x_7 in\l          let (_x_75 : real) = 29103/200000 * _x_64 in\l          let (_x_76 : real) = 159/9505 * _x_69 in\l          let (_x_77 : real) = (-1021/1813750) * _x_4 in\l          let (_x_78 : real) = 17919/3110000 * _x_5 in\l          let (_x_79 : real) = 32971/8500000 * _x_6 in\l          let (_x_80 : real) = (-21603/320000) * _x_7 in\l          let (_x_81 : real)\l              = if _x_63 then 67/500\l                else if _x_62 then 1/2 else if _x_61 then 1 else …\l          in\l          let (_x_82 : real)\l              = if _x_68 then 377/1000\l                else\l                if _x_67 then 1223/1000 else if _x_66 then 1901/1000 else …\l          in\l          let (_x_83 : real) = 449/29020000 * _x_4 in\l          let (_x_84 : real) = 3841/3110000 * _x_5 in\l          let (_x_85 : real) = (-25741/4250000) * _x_6 in\l          let (_x_86 : real) = 58299/640000 * _x_7 in\l          let (_x_87 : real)\l              = if 66419/200000 * _x_64 +. 25399/190100 * _x_69 +. _x_83\l                   +. _x_84 +. _x_85 +. _x_86\l                   \<= (-317131778543/1534287400000)\l                then 0\l                else\l                  317131778543/1534287400000 +. 66419/200000 * _x_81\l                  +. 25399/190100 * _x_82 +. _x_83 +. _x_84 +. _x_85 +. _x_86\l          in\l          let (_x_88 : real) = 23799/100000 * _x_64 in\l          let (_x_89 : real) = (-18071/95050) * _x_69 in\l          let (_x_90 : real) = 38981/29020000 * _x_4 in\l          let (_x_91 : real) = 1727/194375 * _x_5 in\l          let (_x_92 : real) = (-61231/8500000) * _x_6 in\l          let (_x_93 : real) = (-1831/320000) * _x_7 in\l          let (_x_94 : real)\l              = if _x_88 +. _x_89 +. _x_90 +. _x_91 +. _x_92 +. _x_93\l                   \<= (-89188713933/1534287400000)\l                then 0\l                else\l                  89188713933/1534287400000 +. _x_88 +. _x_89 +. _x_90\l                  +. _x_91 +. _x_92 +. _x_93\l          in\l          let (_x_95 : real) = 10277/200000 * _x_64 in\l          let (_x_96 : real) = (-28841/190100) * _x_69 in\l          let (_x_97 : real) = 4637/29020000 * _x_4 in\l          let (_x_98 : real) = 3601/388750 * _x_5 in\l          let (_x_99 : real) = 5957/8500000 * _x_6 in\l          let (_x_100 : real) = (-22041/640000) * _x_7 in\l          let (_x_101 : real)\l              = if _x_95 +. _x_96 +. _x_97 +. _x_98 +. _x_99 +. _x_100\l                   \<= (-372238333/2454859840)\l                then 0\l                else\l                  372238333/2454859840 +. _x_95 +. _x_96 +. _x_97 +. _x_98\l                  +. _x_99 +. _x_100\l          in\l          let (_x_102 : real) = 13901/50000 * _x_64 in\l          let (_x_103 : real) = (-803/38020) * _x_69 in\l          let (_x_104 : real) = 10557/29020000 * _x_4 in\l          let (_x_105 : real) = 60757/3110000 * _x_5 in\l          let (_x_106 : real) = (-16157/4250000) * _x_6 in\l          let (_x_107 : real) = 47933/640000 * _x_7 in\l          let (_x_108 : real)\l              = if _x_102 +. _x_103 +. _x_104 +. _x_105 +. _x_106 +. _x_107\l                   \<= 72146699557/306857480000\l                then 0\l                else\l                  (-72146699557/306857480000) +. _x_102 +. _x_103 +. _x_104\l                  +. _x_105 +. _x_106 +. _x_107\l          in\l          let (_x_109 : real)\l              = 1568904513/1250000000\l                * (if _x_65 +. _x_70 +. _x_71 +. _x_72 +. _x_73 +. _x_74\l                      \<= (-1716983137/306857480000)\l                   then 0\l                   else\l                     (1716983137/306857480000 +. _x_65 +. _x_70 +. _x_71\l                      +. _x_72 +. _x_73 +. _x_74))\l                +. (-1400061773/1250000000)\l                   * (if _x_75 +. _x_76 +. _x_77 +. _x_78 +. _x_79 +. _x_80\l                         \<= 73983893263/767143700000\l                      then 0\l                      else\l                        ((-73983893263/767143700000) +. _x_75 +. _x_76\l                         +. _x_77 +. _x_78 +. _x_79 +. _x_80))\l                +. (-889978969/400000000) * _x_87\l                +. (-787784679/2500000000) * _x_94\l                +. (-19189866047/10000000000) * _x_101\l                +. 5337652199/2000000000 * _x_108\l          in\l          let (_x_110 : real) = 5031/50000 * _x_81 in\l          let (_x_111 : real) = (-7861/95050) * _x_82 in\l          let (_x_112 : real)\l              = if _x_110 +. _x_111 +. _x_71 +. _x_72 +. _x_73 +. _x_74\l                   \<= (-1716983137/306857480000)\l                then 0\l                else\l                  1716983137/306857480000 +. _x_110 +. _x_111 +. _x_71\l                  +. _x_72 +. _x_73 +. _x_74\l          in\l          let (_x_113 : real) = 29103/200000 * _x_81 in\l          let (_x_114 : real) = 159/9505 * _x_82 in\l          let (_x_115 : real)\l              = if _x_113 +. _x_114 +. _x_77 +. _x_78 +. _x_79 +. _x_80\l                   \<= 73983893263/767143700000\l                then 0\l                else\l                  (-73983893263/767143700000) +. _x_113 +. _x_114 +. _x_77\l                  +. _x_78 +. _x_79 +. _x_80\l          in\l          not\l          ((0 \<= _x_0) && (_x_0 \<= 500) && (0 \<= _x_1) && (_x_1 \<= 40)\l           && (0 \<= _x_2) && (_x_2 \<= 100) && (0 \<= _x_3) && (_x_3 \<= 15)\l           && (0 \<= _x_4) && (_x_4 \<= 500) && (0 \<= _x_5) && (_x_5 \<= 40)\l           && (0 \<= _x_6) && (_x_6 \<= 100) && (0 \<= _x_7) && (_x_7 \<= 15)\l           && (_x_8 = _x_9) && (_x_10 = _x_11) && (_x_0 = _x_4)\l           && (_x_2 = _x_6) && (_x_3 = _x_7) && (_x_1 \>= _x_5))\l          \|\| ((if _x_60 \<= (-341987779/312500000)\l               then\l                 28114831522503/7812500000000\l                 +. 67395431164941/31250000000000 * _x_24\l                 +. (-60142453582761/31250000000000) * _x_31\l                 +. (-38230826571333/10000000000000) * _x_38\l                 +. (-33840866455803/62500000000000) * _x_45\l                 +. (-824339075780979/250000000000000) * _x_52\l                 +. 229289525512443/50000000000000 * _x_59\l               else\l               if _x_60 \<= (-29487779/312500000)\l               then\l                 213430965464483/31250000000000\l                 +. 732799213218501/125000000000000 * _x_24\l                 +. (-653936652747521/125000000000000) * _x_31\l                 +. (-415688706903613/40000000000000) * _x_38\l                 +. (-367956104513283/250000000000000) * _x_45\l                 +. (-8963145063634619/1000000000000000) * _x_52\l                 +. 2493094576152323/200000000000000 * _x_59\l               else\l               if _x_60 \<= 283012221/312500000\l               then\l                 1852306369389/244140625000\l                 +. 124497279820089/7812500000000 * _x_24\l                 +. (-111099101872869/7812500000000) * _x_31\l                 +. (-70622501127057/2500000000000) * _x_38\l                 +. (-62513077632687/15625000000000) * _x_45\l                 +. (-1522773440427591/62500000000000) * _x_52\l                 +. 423558714947247/12500000000000 * _x_59\l               else if _x_60 \<= 595512221/312500000 then … else …)\l              \>= (if _x_109 \<= (-341987779/312500000)\l                  then\l                    28114831522503/7812500000000\l                    +. 67395431164941/31250000000000 * _x_112\l                    +. (-60142453582761/31250000000000) * _x_115\l                    +. (-38230826571333/10000000000000) * _x_87\l                    +. (-33840866455803/62500000000000) * _x_94\l                    +. (-824339075780979/250000000000000) * _x_101\l                    +. 229289525512443/50000000000000 * _x_108\l                  else\l                  if _x_109 \<= (-29487779/312500000)\l                  then\l                    213430965464483/31250000000000\l                    +. 732799213218501/125000000000000 * _x_112\l                    +. (-653936652747521/125000000000000) * _x_115\l                    +. (-415688706903613/40000000000000) * _x_87\l                    +. (-367956104513283/250000000000000) * _x_94\l                    +. (-8963145063634619/1000000000000000) * _x_101\l                    +. 2493094576152323/200000000000000 * _x_108\l                  else\l                  if _x_109 \<= 283012221/312500000\l                  then\l                    1852306369389/244140625000\l                    +. 124497279820089/7812500000000 * _x_112\l                    +. (-111099101872869/7812500000000) * _x_115\l                    +. (-70622501127057/2500000000000) * _x_87\l                    +. (-62513077632687/15625000000000) * _x_94\l                    +. (-1522773440427591/62500000000000) * _x_101\l                    +. 423558714947247/12500000000000 * _x_108\l                  else if _x_109 \<= 595512221/312500000 then … else …))\l          :expansions [] :rw [] :fc [])",shape=box,style=filled,fontname="courier",fontsize=14];
p_367 -> p_366 [label=""];
p_366 [label="Sat (Some let a : nn_input =\l  \{month = Feb; day = Mon;\l   dmc =\l   (Q.of_string \"477530538943470675292449136343/52265269828627920420809925120\");\l   temp =\l   (Q.of_string \"16456572619172832889468514796852129522445874981486473/843088427862816291297913293280956091559763750558720\");\l   rh =\l   (Q.of_string \"104614291401820088872242530073475835587789055/1417405504169645763458544629343803680909824\");\l   rain = (Q.of_nativeint (0n))\}\llet b : nn_input =\l  \{month = Feb; day = Mon;\l   dmc =\l   (Q.of_string \"477530538943470675292449136343/52265269828627920420809925120\");\l   temp =\l   (Q.of_string \"53415521146114949327048139937483913145890495777/2775279977164166404851830384255167607221435392\");\l   rh =\l   (Q.of_string \"104614291401820088872242530073475835587789055/1417405504169645763458544629343803680909824\");\l   rain = (Q.of_nativeint (0n))\}\l)",shape=box,style=filled,fontname="courier",fontsize=14];
}

Try this!

In [24]:

CX.a.temp;;
CX.b.temp;;
nn_model CX.a;;
nn_model CX.b;;

Out[24]:

- : real = 19.5193909385
- : real = 19.2468945784
- : real = 1.70564871031
- : real = 1.71828

Although the network doesn't satisfy our original verification statement we can restrict our setting in a sensible way in order to prove something slightly weaker:

There is very little data from winter months, and so the model is unlikely to generalise well here, hence we'll only consider non-winter months
We'll increase the tolerance in temperature to 10 degrees celsius
We'll increase the tolerance in area burned to 25 hectares

Try this!

In [25]:

let winter month = month = Oct || month = Nov || month = Dec || month = Jan || month = Feb

verify (fun a b ->
        is_valid_nn a &&
        is_valid_nn b &&
        a.month = b.month &&
        not (winter a.month) &&
        a.day = b.day &&
        a.dmc = b.dmc &&
        a.rh = b.rh &&
        a.rain = b.rain &&
        (a.temp -. 10.0) >=. b.temp ==>
        (nn_model a +. 25.0) >=. nn_model b)

Out[25]:

val winter : month -> bool = <fun>
- : nn_input -> nn_input -> bool = <fun>

Proved

proof
call graph

proof

ground_instances:

definitions:

inductions:

search_time:

11.196s

details:

Expand

smt_stats:

arith offset eqs:	63
num checks:	1
arith assert lower:	3086
arith tableau max rows:	63
arith tableau max columns:	199
arith pivots:	4522
rlimit count:	35004873
mk clause:	1441
restarts:	4
mk bool var:	1117
arith assert upper:	2318
datatype splits:	61
decisions:	1692
arith row summations:	133849
arith bound prop:	115
propagations:	15347
conflicts:	455
arith fixed eqs:	793
datatype accessor ax:	20
minimized lits:	774
arith conflicts:	322
arith num rows:	63
arith assert diseq:	1179
datatype constructor ax:	24
added eqs:	6082
del clause:	807
arith eq adapter:	446
time:	11.186000
memory:	26.690000
max memory:	28.550000
num allocs:	42791677606.000000

Expand

start[11.196s]
  let (_x_0 : real) = ( :var_0: ).dmc in
  let (_x_1 : real) = ( :var_0: ).temp in
  let (_x_2 : real) = ( :var_0: ).rh in
  let (_x_3 : real) = ( :var_0: ).rain in
  let (_x_4 : real) = ( :var_1: ).dmc in
  let (_x_5 : real) = ( :var_1: ).temp in
  let (_x_6 : real) = ( :var_1: ).rh in
  let (_x_7 : real) = ( :var_1: ).rain in
  let (_x_8 : month) = ( :var_0: ).month in
  let (_x_9 : real)
      = 5031/25000 * … +. (-7861/50000) * … +. (-19063/100000) * …
        +. (-27281/50000) * … +. 137/4000 * … +. 6263/12500 * …
        +. (-173/6250)
  in
  let (_x_10 : real)
      = 29103/100000 * … +. 159/5000 * … +. (-1021/6250) * …
        +. 17919/100000 * … +. 32971/100000 * … +. (-21603/50000) * …
        +. (-131/5000)
  in
  let (_x_11 : real)
      = 66419/100000 * … +. 25399/100000 * … +. 449/100000 * …
        +. 3841/100000 * … +. (-25741/50000) * … +. 58299/100000 * …
        +. 5929/50000
  in
  let (_x_12 : real)
      = 23799/50000 * … +. (-18071/50000) * … +. 38981/100000 * …
        +. 1727/6250 * … +. (-61231/100000) * … +. (-1831/50000) * …
        +. (-289/10000)
  in
  let (_x_13 : real)
      = 10277/100000 * … +. (-28841/100000) * … +. 4637/100000 * …
        +. 3601/12500 * … +. 5957/100000 * … +. (-22041/100000) * …
        +. 1827/10000
  in
  let (_x_14 : real)
      = 13901/25000 * … +. (-803/20000) * … +. 10557/100000 * …
        +. 60757/100000 * … +. (-16157/50000) * … +. 47933/100000 * …
        +. (-6219/25000)
  in
  let (_x_15 : real)
      = 444323/100000
        * (3531/12500 * (if _x_9 > 0 then _x_9 else 0)
           +. (-3151/12500) * (if _x_10 > 0 then _x_10 else 0)
           +. (-2003/4000) * (if _x_11 > 0 then _x_11 else 0)
           +. (-1773/25000) * (if _x_12 > 0 then _x_12 else 0)
           +. (-43189/100000) * (if _x_13 > 0 then _x_13 else 0)
           +. 12013/20000 * (if _x_14 > 0 then _x_14 else 0) +. 1473/3125)
  in
  let (_x_16 : real)
      = if _x_15 <= 1 then (_x_15 - 0) * 42957/25000
        else
        if _x_15 <= 2 then (_x_15 - 15803/25000) * 467077/100000
        else
        if _x_15 <= 3 then (_x_15 - 149679/100000) * 79353/6250
        else if _x_15 <= 4 then … else …
  in
  (0 <= _x_0)
  && ((_x_0 <= 500)
      && ((0 <= _x_1)
          && ((_x_1 <= 40)
              && ((0 <= _x_2)
                  && ((_x_2 <= 100) && ((0 <= _x_3) && (_x_3 <= 15)))))))
  && ((0 <= _x_4)
      && ((_x_4 <= 500)
          && ((0 <= _x_5)
              && ((_x_5 <= 40)
                  && ((0 <= _x_6)
                      && ((_x_6 <= 100) && ((0 <= _x_7) && (_x_7 <= 15)))))))
      && ((_x_8 = ( :var_1: ).month)
          && (not
              ((_x_8 = Oct)
               || ((_x_8 = Nov)
                   || ((_x_8 = Dec) || ((_x_8 = Jan) || (_x_8 = Feb)))))
              && ((( :var_0: ).day = ( :var_1: ).day)
                  && ((_x_0 = _x_4)
                      && ((_x_2 = _x_6)
                          && ((_x_3 = _x_7) && (_x_1 - 10 >= _x_5))))))))
  ==> _x_16 +. 25 >= _x_16

simplify

into:	let (_x_0 : real) = ( :var_0: ).dmc in let (_x_1 : real) = ( :var_0: ).temp in let (_x_2 : real) = ( :var_0: ).rh in let (_x_3 : real) = ( :var_0: ).rain in let (_x_4 : real) = ( :var_1: ).dmc in let (_x_5 : real) = ( :var_1: ).temp in let (_x_6 : real) = ( :var_1: ).rh in let (_x_7 : real) = ( :var_1: ).rain in let (_x_8 : month) = ( :var_0: ).month in let (_x_9 : month) = ( :var_1: ).month in let (_x_10 : bool) = _x_8 = Jan in let (_x_11 : bool) = _x_8 = Feb in let (_x_12 : day) = ( :var_0: ).day in let (_x_13 : day) = ( :var_1: ).day in let (_x_14 : real) = if _x_10 then 67/500 else if _x_11 then 1/2 else if _x_8 = Mar then 1 else if _x_8 = Apr then 3/2 else … in let (_x_15 : real) = 5031/50000 * _x_14 in let (_x_16 : real) = if _x_12 = Mon then 377/1000 else if _x_12 = Tue then 1223/1000 else if (_x_12 = Wed) \|\| (_x_12 = Thu) then 1901/1000 else if _x_12 = Fri then 1223/1000 else … in let (_x_17 : real) = (-7861/95050) * _x_16 in let (_x_18 : real) = (-19063/29020000) * _x_0 in let (_x_19 : real) = (-27281/1555000) * _x_1 in let (_x_20 : real) = 137/340000 * _x_2 in let (_x_21 : real) = 6263/80000 * _x_3 in let (_x_22 : real) = if _x_15 +. _x_17 +. _x_18 +. _x_19 +. _x_20 +. _x_21 <= (-1716983137/306857480000) then 0 else 1716983137/306857480000 +. _x_15 +. _x_17 +. _x_18 +. _x_19 +. _x_20 +. _x_21 in let (_x_23 : real) = 29103/200000 * _x_14 in let (_x_24 : real) = 159/9505 * _x_16 in let (_x_25 : real) = (-1021/1813750) * _x_0 in let (_x_26 : real) = 17919/3110000 * _x_1 in let (_x_27 : real) = 32971/8500000 * _x_2 in let (_x_28 : real) = (-21603/320000) * _x_3 in let (_x_29 : real) = if _x_23 +. _x_24 +. _x_25 +. _x_26 +. _x_27 +. _x_28 <= 73983893263/767143700000 then 0 else (-73983893263/767143700000) +. _x_23 +. _x_24 +. _x_25 +. _x_26 +. _x_27 +. _x_28 in let (_x_30 : real) = 66419/200000 * _x_14 in let (_x_31 : real) = 25399/190100 * _x_16 in let (_x_32 : real) = 449/29020000 * _x_0 in let (_x_33 : real) = 3841/3110000 * _x_1 in let (_x_34 : real) = (-25741/4250000) * _x_2 in let (_x_35 : real) = 58299/640000 * _x_3 in let (_x_36 : real) = if _x_30 +. _x_31 +. _x_32 +. _x_33 +. _x_34 +. _x_35 <= (-317131778543/1534287400000) then 0 else 317131778543/1534287400000 +. _x_30 +. _x_31 +. _x_32 +. _x_33 +. _x_34 +. _x_35 in let (_x_37 : real) = 23799/100000 * _x_14 in let (_x_38 : real) = (-18071/95050) * _x_16 in let (_x_39 : real) = 38981/29020000 * _x_0 in let (_x_40 : real) = 1727/194375 * _x_1 in let (_x_41 : real) = (-61231/8500000) * _x_2 in let (_x_42 : real) = (-1831/320000) * _x_3 in let (_x_43 : real) = if _x_37 +. _x_38 +. _x_39 +. _x_40 +. _x_41 +. _x_42 <= (-89188713933/1534287400000) then 0 else 89188713933/1534287400000 +. _x_37 +. _x_38 +. _x_39 +. _x_40 +. _x_41 +. _x_42 in let (_x_44 : real) = 10277/200000 * _x_14 in let (_x_45 : real) = (-28841/190100) * _x_16 in let (_x_46 : real) = 4637/29020000 * _x_0 in let (_x_47 : real) = 3601/388750 * _x_1 in let (_x_48 : real) = 5957/8500000 * _x_2 in let (_x_49 : real) = (-22041/640000) * _x_3 in let (_x_50 : real) = if _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48 +. _x_49 <= (-372238333/2454859840) then 0 else 372238333/2454859840 +. _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48 +. _x_49 in let (_x_51 : real) = 13901/50000 * _x_14 in let (_x_52 : real) = (-803/38020) * _x_16 in let (_x_53 : real) = 10557/29020000 * _x_0 in let (_x_54 : real) = 60757/3110000 * _x_1 in let (_x_55 : real) = (-16157/4250000) * _x_2 in let (_x_56 : real) = 47933/640000 * _x_3 in let (_x_57 : real) = if _x_51 +. _x_52 +. _x_53 +. _x_54 +. _x_55 +. _x_56 <= 72146699557/306857480000 then 0 else (-72146699557/306857480000) +. _x_51 +. _x_52 +. _x_53 +. _x_54 +. _x_55 +. _x_56 in let (_x_58 : real) = 1568904513/1250000000 * _x_22 +. (-1400061773/1250000000) * _x_29 +. (-889978969/400000000) * _x_36 +. (-787784679/2500000000) * _x_43 +. (-19189866047/10000000000) * _x_50 +. 5337652199/2000000000 * _x_57 in let (_x_59 : bool) = _x_9 = Mar in let (_x_60 : bool) = _x_9 = Feb in let (_x_61 : bool) = _x_9 = Jan in let (_x_62 : real) = if _x_13 = Mon then 377/1000 else if _x_13 = Tue then 1223/1000 else if (_x_13 = Wed) \|\| (_x_13 = Thu) then 1901/1000 else if _x_13 = Fri then 1223/1000 else … in let (_x_63 : real) = (-7861/95050) * _x_62 in let (_x_64 : real) = (-19063/29020000) * _x_4 in let (_x_65 : real) = (-27281/1555000) * _x_5 in let (_x_66 : real) = 137/340000 * _x_6 in let (_x_67 : real) = 6263/80000 * _x_7 in let (_x_68 : real) = if _x_61 then 67/500 else if _x_60 then 1/2 else if _x_59 then 1 else if _x_9 = Apr then 3/2 else … in let (_x_69 : real) = if 5031/50000 * _x_68 +. _x_63 +. _x_64 +. _x_65 +. _x_66 +. _x_67 <= (-1716983137/306857480000) then 0 else 1716983137/306857480000 +. 5031/50000 * (if _x_61 then 67/500 else if _x_60 then 1/2 else if _x_59 then 1 else …) +. _x_63 +. _x_64 +. _x_65 +. _x_66 +. _x_67 in let (_x_70 : real) = 29103/200000 * _x_68 in let (_x_71 : real) = 159/9505 * _x_62 in let (_x_72 : real) = (-1021/1813750) * _x_4 in let (_x_73 : real) = 17919/3110000 * _x_5 in let (_x_74 : real) = 32971/8500000 * _x_6 in let (_x_75 : real) = (-21603/320000) * _x_7 in let (_x_76 : real) = if _x_70 +. _x_71 +. _x_72 +. _x_73 +. _x_74 +. _x_75 <= 73983893263/767143700000 then 0 else (-73983893263/767143700000) +. _x_70 +. _x_71 +. _x_72 +. _x_73 +. _x_74 +. _x_75 in let (_x_77 : real) = 66419/200000 * _x_68 in let (_x_78 : real) = 25399/190100 * _x_62 in let (_x_79 : real) = 449/29020000 * _x_4 in let (_x_80 : real) = 3841/3110000 * _x_5 in let (_x_81 : real) = (-25741/4250000) * _x_6 in let (_x_82 : real) = 58299/640000 * _x_7 in let (_x_83 : real) = if _x_77 +. _x_78 +. _x_79 +. _x_80 +. _x_81 +. _x_82 <= (-317131778543/1534287400000) then 0 else 317131778543/1534287400000 +. _x_77 +. _x_78 +. _x_79 +. _x_80 +. _x_81 +. _x_82 in let (_x_84 : real) = 23799/100000 * _x_68 in let (_x_85 : real) = (-18071/95050) * _x_62 in let (_x_86 : real) = 38981/29020000 * _x_4 in let (_x_87 : real) = 1727/194375 * _x_5 in let (_x_88 : real) = (-61231/8500000) * _x_6 in let (_x_89 : real) = (-1831/320000) * _x_7 in let (_x_90 : real) = if _x_84 +. _x_85 +. _x_86 +. _x_87 +. _x_88 +. _x_89 <= (-89188713933/1534287400000) then 0 else 89188713933/1534287400000 +. _x_84 +. _x_85 +. _x_86 +. _x_87 +. _x_88 +. _x_89 in let (_x_91 : real) = 10277/200000 * _x_68 in let (_x_92 : real) = (-28841/190100) * _x_62 in let (_x_93 : real) = 4637/29020000 * _x_4 in let (_x_94 : real) = 3601/388750 * _x_5 in let (_x_95 : real) = 5957/8500000 * _x_6 in let (_x_96 : real) = (-22041/640000) * _x_7 in let (_x_97 : real) = if _x_91 +. _x_92 +. _x_93 +. _x_94 +. _x_95 +. _x_96 <= (-372238333/2454859840) then 0 else 372238333/2454859840 +. _x_91 +. _x_92 +. _x_93 +. _x_94 +. _x_95 +. _x_96 in let (_x_98 : real) = 13901/50000 * _x_68 in let (_x_99 : real) = (-803/38020) * _x_62 in let (_x_100 : real) = 10557/29020000 * _x_4 in let (_x_101 : real) = 60757/3110000 * _x_5 in let (_x_102 : real) = (-16157/4250000) * _x_6 in let (_x_103 : real) = 47933/640000 * _x_7 in let (_x_104 : real) = if _x_98 +. _x_99 +. _x_100 +. _x_101 +. _x_102 +. _x_103 <= 72146699557/306857480000 then 0 else (-72146699557/306857480000) +. _x_98 +. _x_99 +. _x_100 +. _x_101 +. _x_102 +. _x_103 in let (_x_105 : real) = 1568904513/1250000000 * _x_69 +. (-1400061773/1250000000) * _x_76 +. (-889978969/400000000) * _x_83 +. (-787784679/2500000000) * _x_90 +. (-19189866047/10000000000) * _x_97 +. 5337652199/2000000000 * _x_104 in not ((0 <= _x_0) && (_x_0 <= 500) && (0 <= _x_1) && (_x_1 <= 40) && (0 <= _x_2) && (_x_2 <= 100) && (0 <= _x_3) && (_x_3 <= 15) && (0 <= _x_4) && (_x_4 <= 500) && (0 <= _x_5) && (_x_5 <= 40) && (0 <= _x_6) && (_x_6 <= 100) && (0 <= _x_7) && (_x_7 <= 15) && (_x_8 = _x_9) && not ((_x_8 = Oct) \|\| (_x_8 = Nov) \|\| (_x_8 = Dec) \|\| _x_10 \|\| _x_11) && (_x_12 = _x_13) && (_x_0 = _x_4) && (_x_2 = _x_6) && (_x_3 = _x_7) && (_x_1 >= 10 +. _x_5)) \|\| ((if _x_58 <= (-341987779/312500000) then 28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_22 +. (-60142453582761/31250000000000) * _x_29 +. (-38230826571333/10000000000000) * _x_36 +. (-33840866455803/62500000000000) * _x_43 +. (-824339075780979/250000000000000) * _x_50 +. 229289525512443/50000000000000 * _x_57 else if _x_58 <= (-29487779/312500000) then 213430965464483/31250000000000 +. 732799213218501/125000000000000 * _x_22 +. (-653936652747521/125000000000000) * _x_29 +. (-415688706903613/40000000000000) * _x_36 +. (-367956104513283/250000000000000) * _x_43 +. (-8963145063634619/1000000000000000) * _x_50 +. 2493094576152323/200000000000000 * _x_57 else if _x_58 <= 283012221/312500000 then 1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_22 +. (-111099101872869/7812500000000) * _x_29 +. (-70622501127057/2500000000000) * _x_36 +. (-62513077632687/15625000000000) * _x_43 +. (-1522773440427591/62500000000000) * _x_50 +. 423558714947247/12500000000000 * _x_57 else if _x_58 <= 595512221/312500000 then … else …) >= (-25) +. (if _x_105 <= (-341987779/312500000) then 28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_69 +. (-60142453582761/31250000000000) * _x_76 +. (-38230826571333/10000000000000) * _x_83 +. (-33840866455803/62500000000000) * _x_90 +. (-824339075780979/250000000000000) * _x_97 +. 229289525512443/50000000000000 * _x_104 else if _x_105 <= (-29487779/312500000) then 213430965464483/31250000000000 +. 732799213218501/125000000000000 * _x_69 +. (-653936652747521/125000000000000) * _x_76 +. (-415688706903613/40000000000000) * _x_83 +. (-367956104513283/250000000000000) * _x_90 +. (-8963145063634619/1000000000000000) * _x_97 +. 2493094576152323/200000000000000 * _x_104 else if _x_105 <= 283012221/312500000 then 1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_69 +. (-111099101872869/7812500000000) * _x_76 +. (-70622501127057/2500000000000) * _x_83 +. (-62513077632687/15625000000000) * _x_90 +. (-1522773440427591/62500000000000) * _x_97 +. 423558714947247/12500000000000 * _x_104 else if _x_105 <= 595512221/312500000 then … else …))
expansions:	[]
rewrite_steps:
forward_chaining:

Unsat

digraph "proof" {
p_371 [label="Start (let (_x_0 : real) = ( :var_0: ).dmc in\l       let (_x_1 : real) = ( :var_0: ).temp in\l       let (_x_2 : real) = ( :var_0: ).rh in\l       let (_x_3 : real) = ( :var_0: ).rain in\l       let (_x_4 : real) = ( :var_1: ).dmc in\l       let (_x_5 : real) = ( :var_1: ).temp in\l       let (_x_6 : real) = ( :var_1: ).rh in\l       let (_x_7 : real) = ( :var_1: ).rain in\l       let (_x_8 : month) = ( :var_0: ).month in\l       let (_x_9 : real)\l           = 5031/25000 * … +. (-7861/50000) * … +. (-19063/100000) * …\l             +. (-27281/50000) * … +. 137/4000 * … +. 6263/12500 * …\l             +. (-173/6250)\l       in\l       let (_x_10 : real)\l           = 29103/100000 * … +. 159/5000 * … +. (-1021/6250) * …\l             +. 17919/100000 * … +. 32971/100000 * …\l             +. (-21603/50000) * … +. (-131/5000)\l       in\l       let (_x_11 : real)\l           = 66419/100000 * … +. 25399/100000 * … +. 449/100000 * …\l             +. 3841/100000 * … +. (-25741/50000) * …\l             +. 58299/100000 * … +. 5929/50000\l       in\l       let (_x_12 : real)\l           = 23799/50000 * … +. (-18071/50000) * … +. 38981/100000 * …\l             +. 1727/6250 * … +. (-61231/100000) * …\l             +. (-1831/50000) * … +. (-289/10000)\l       in\l       let (_x_13 : real)\l           = 10277/100000 * … +. (-28841/100000) * … +. 4637/100000 * …\l             +. 3601/12500 * … +. 5957/100000 * …\l             +. (-22041/100000) * … +. 1827/10000\l       in\l       let (_x_14 : real)\l           = 13901/25000 * … +. (-803/20000) * … +. 10557/100000 * …\l             +. 60757/100000 * … +. (-16157/50000) * …\l             +. 47933/100000 * … +. (-6219/25000)\l       in\l       let (_x_15 : real)\l           = 444323/100000\l             * (3531/12500 * (if _x_9 \> 0 then _x_9 else 0)\l                +. (-3151/12500) * (if _x_10 \> 0 then _x_10 else 0)\l                +. (-2003/4000) * (if _x_11 \> 0 then _x_11 else 0)\l                +. (-1773/25000) * (if _x_12 \> 0 then _x_12 else 0)\l                +. (-43189/100000) * (if _x_13 \> 0 then _x_13 else 0)\l                +. 12013/20000 * (if _x_14 \> 0 then _x_14 else 0)\l                +. 1473/3125)\l       in\l       let (_x_16 : real)\l           = if _x_15 \<= 1 then (_x_15 - 0) * 42957/25000\l             else\l             if _x_15 \<= 2 then (_x_15 - 15803/25000) * 467077/100000\l             else\l             if _x_15 \<= 3 then (_x_15 - 149679/100000) * 79353/6250\l             else if _x_15 \<= 4 then … else …\l       in\l       (0 \<= _x_0)\l       && ((_x_0 \<= 500)\l           && ((0 \<= _x_1)\l               && ((_x_1 \<= 40)\l                   && ((0 \<= _x_2)\l                       && ((_x_2 \<= 100) && ((0 \<= _x_3) && (_x_3 \<= 15)))))))\l       && ((0 \<= _x_4)\l           && ((_x_4 \<= 500)\l               && ((0 \<= _x_5)\l                   && ((_x_5 \<= 40)\l                       && ((0 \<= _x_6)\l                           && ((_x_6 \<= 100) && ((0 \<= _x_7) && (_x_7 \<= 15)))))))\l           && ((_x_8 = ( :var_1: ).month)\l               && (not\l                   ((_x_8 = Oct)\l                    \|\| ((_x_8 = Nov)\l                        \|\| ((_x_8 = Dec) \|\| ((_x_8 = Jan) \|\| (_x_8 = Feb)))))\l                   && ((( :var_0: ).day = ( :var_1: ).day)\l                       && ((_x_0 = _x_4)\l                           && ((_x_2 = _x_6)\l                               && ((_x_3 = _x_7) && (_x_1 - 10 \>= _x_5))))))))\l       ==\> _x_16 +. 25 \>= _x_16 :time 11.196s)",shape=box,style=filled,fontname="courier",fontsize=14];
p_371 -> p_370 [label=""];
p_370 [label="Simplify (let (_x_0 : real) = ( :var_0: ).dmc in\l          let (_x_1 : real) = ( :var_0: ).temp in\l          let (_x_2 : real) = ( :var_0: ).rh in\l          let (_x_3 : real) = ( :var_0: ).rain in\l          let (_x_4 : real) = ( :var_1: ).dmc in\l          let (_x_5 : real) = ( :var_1: ).temp in\l          let (_x_6 : real) = ( :var_1: ).rh in\l          let (_x_7 : real) = ( :var_1: ).rain in\l          let (_x_8 : month) = ( :var_0: ).month in\l          let (_x_9 : month) = ( :var_1: ).month in\l          let (_x_10 : bool) = _x_8 = Jan in\l          let (_x_11 : bool) = _x_8 = Feb in\l          let (_x_12 : day) = ( :var_0: ).day in\l          let (_x_13 : day) = ( :var_1: ).day in\l          let (_x_14 : real)\l              = if _x_10 then 67/500\l                else\l                if _x_11 then 1/2\l                else\l                if _x_8 = Mar then 1 else if _x_8 = Apr then 3/2 else …\l          in\l          let (_x_15 : real) = 5031/50000 * _x_14 in\l          let (_x_16 : real)\l              = if _x_12 = Mon then 377/1000\l                else\l                if _x_12 = Tue then 1223/1000\l                else\l                if (_x_12 = Wed) \|\| (_x_12 = Thu) then 1901/1000\l                else if _x_12 = Fri then 1223/1000 else …\l          in\l          let (_x_17 : real) = (-7861/95050) * _x_16 in\l          let (_x_18 : real) = (-19063/29020000) * _x_0 in\l          let (_x_19 : real) = (-27281/1555000) * _x_1 in\l          let (_x_20 : real) = 137/340000 * _x_2 in\l          let (_x_21 : real) = 6263/80000 * _x_3 in\l          let (_x_22 : real)\l              = if _x_15 +. _x_17 +. _x_18 +. _x_19 +. _x_20 +. _x_21\l                   \<= (-1716983137/306857480000)\l                then 0\l                else\l                  1716983137/306857480000 +. _x_15 +. _x_17 +. _x_18 +. _x_19\l                  +. _x_20 +. _x_21\l          in\l          let (_x_23 : real) = 29103/200000 * _x_14 in\l          let (_x_24 : real) = 159/9505 * _x_16 in\l          let (_x_25 : real) = (-1021/1813750) * _x_0 in\l          let (_x_26 : real) = 17919/3110000 * _x_1 in\l          let (_x_27 : real) = 32971/8500000 * _x_2 in\l          let (_x_28 : real) = (-21603/320000) * _x_3 in\l          let (_x_29 : real)\l              = if _x_23 +. _x_24 +. _x_25 +. _x_26 +. _x_27 +. _x_28\l                   \<= 73983893263/767143700000\l                then 0\l                else\l                  (-73983893263/767143700000) +. _x_23 +. _x_24 +. _x_25\l                  +. _x_26 +. _x_27 +. _x_28\l          in\l          let (_x_30 : real) = 66419/200000 * _x_14 in\l          let (_x_31 : real) = 25399/190100 * _x_16 in\l          let (_x_32 : real) = 449/29020000 * _x_0 in\l          let (_x_33 : real) = 3841/3110000 * _x_1 in\l          let (_x_34 : real) = (-25741/4250000) * _x_2 in\l          let (_x_35 : real) = 58299/640000 * _x_3 in\l          let (_x_36 : real)\l              = if _x_30 +. _x_31 +. _x_32 +. _x_33 +. _x_34 +. _x_35\l                   \<= (-317131778543/1534287400000)\l                then 0\l                else\l                  317131778543/1534287400000 +. _x_30 +. _x_31 +. _x_32\l                  +. _x_33 +. _x_34 +. _x_35\l          in\l          let (_x_37 : real) = 23799/100000 * _x_14 in\l          let (_x_38 : real) = (-18071/95050) * _x_16 in\l          let (_x_39 : real) = 38981/29020000 * _x_0 in\l          let (_x_40 : real) = 1727/194375 * _x_1 in\l          let (_x_41 : real) = (-61231/8500000) * _x_2 in\l          let (_x_42 : real) = (-1831/320000) * _x_3 in\l          let (_x_43 : real)\l              = if _x_37 +. _x_38 +. _x_39 +. _x_40 +. _x_41 +. _x_42\l                   \<= (-89188713933/1534287400000)\l                then 0\l                else\l                  89188713933/1534287400000 +. _x_37 +. _x_38 +. _x_39\l                  +. _x_40 +. _x_41 +. _x_42\l          in\l          let (_x_44 : real) = 10277/200000 * _x_14 in\l          let (_x_45 : real) = (-28841/190100) * _x_16 in\l          let (_x_46 : real) = 4637/29020000 * _x_0 in\l          let (_x_47 : real) = 3601/388750 * _x_1 in\l          let (_x_48 : real) = 5957/8500000 * _x_2 in\l          let (_x_49 : real) = (-22041/640000) * _x_3 in\l          let (_x_50 : real)\l              = if _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48 +. _x_49\l                   \<= (-372238333/2454859840)\l                then 0\l                else\l                  372238333/2454859840 +. _x_44 +. _x_45 +. _x_46 +. _x_47\l                  +. _x_48 +. _x_49\l          in\l          let (_x_51 : real) = 13901/50000 * _x_14 in\l          let (_x_52 : real) = (-803/38020) * _x_16 in\l          let (_x_53 : real) = 10557/29020000 * _x_0 in\l          let (_x_54 : real) = 60757/3110000 * _x_1 in\l          let (_x_55 : real) = (-16157/4250000) * _x_2 in\l          let (_x_56 : real) = 47933/640000 * _x_3 in\l          let (_x_57 : real)\l              = if _x_51 +. _x_52 +. _x_53 +. _x_54 +. _x_55 +. _x_56\l                   \<= 72146699557/306857480000\l                then 0\l                else\l                  (-72146699557/306857480000) +. _x_51 +. _x_52 +. _x_53\l                  +. _x_54 +. _x_55 +. _x_56\l          in\l          let (_x_58 : real)\l              = 1568904513/1250000000 * _x_22\l                +. (-1400061773/1250000000) * _x_29\l                +. (-889978969/400000000) * _x_36\l                +. (-787784679/2500000000) * _x_43\l                +. (-19189866047/10000000000) * _x_50\l                +. 5337652199/2000000000 * _x_57\l          in\l          let (_x_59 : bool) = _x_9 = Mar in\l          let (_x_60 : bool) = _x_9 = Feb in\l          let (_x_61 : bool) = _x_9 = Jan in\l          let (_x_62 : real)\l              = if _x_13 = Mon then 377/1000\l                else\l                if _x_13 = Tue then 1223/1000\l                else\l                if (_x_13 = Wed) \|\| (_x_13 = Thu) then 1901/1000\l                else if _x_13 = Fri then 1223/1000 else …\l          in\l          let (_x_63 : real) = (-7861/95050) * _x_62 in\l          let (_x_64 : real) = (-19063/29020000) * _x_4 in\l          let (_x_65 : real) = (-27281/1555000) * _x_5 in\l          let (_x_66 : real) = 137/340000 * _x_6 in\l          let (_x_67 : real) = 6263/80000 * _x_7 in\l          let (_x_68 : real)\l              = if _x_61 then 67/500\l                else\l                if _x_60 then 1/2\l                else if _x_59 then 1 else if _x_9 = Apr then 3/2 else …\l          in\l          let (_x_69 : real)\l              = if 5031/50000 * _x_68 +. _x_63 +. _x_64 +. _x_65 +. _x_66\l                   +. _x_67 \<= (-1716983137/306857480000)\l                then 0\l                else\l                  1716983137/306857480000\l                  +. 5031/50000\l                     * (if _x_61 then 67/500\l                        else if _x_60 then 1/2 else if _x_59 then 1 else …)\l                  +. _x_63 +. _x_64 +. _x_65 +. _x_66 +. _x_67\l          in\l          let (_x_70 : real) = 29103/200000 * _x_68 in\l          let (_x_71 : real) = 159/9505 * _x_62 in\l          let (_x_72 : real) = (-1021/1813750) * _x_4 in\l          let (_x_73 : real) = 17919/3110000 * _x_5 in\l          let (_x_74 : real) = 32971/8500000 * _x_6 in\l          let (_x_75 : real) = (-21603/320000) * _x_7 in\l          let (_x_76 : real)\l              = if _x_70 +. _x_71 +. _x_72 +. _x_73 +. _x_74 +. _x_75\l                   \<= 73983893263/767143700000\l                then 0\l                else\l                  (-73983893263/767143700000) +. _x_70 +. _x_71 +. _x_72\l                  +. _x_73 +. _x_74 +. _x_75\l          in\l          let (_x_77 : real) = 66419/200000 * _x_68 in\l          let (_x_78 : real) = 25399/190100 * _x_62 in\l          let (_x_79 : real) = 449/29020000 * _x_4 in\l          let (_x_80 : real) = 3841/3110000 * _x_5 in\l          let (_x_81 : real) = (-25741/4250000) * _x_6 in\l          let (_x_82 : real) = 58299/640000 * _x_7 in\l          let (_x_83 : real)\l              = if _x_77 +. _x_78 +. _x_79 +. _x_80 +. _x_81 +. _x_82\l                   \<= (-317131778543/1534287400000)\l                then 0\l                else\l                  317131778543/1534287400000 +. _x_77 +. _x_78 +. _x_79\l                  +. _x_80 +. _x_81 +. _x_82\l          in\l          let (_x_84 : real) = 23799/100000 * _x_68 in\l          let (_x_85 : real) = (-18071/95050) * _x_62 in\l          let (_x_86 : real) = 38981/29020000 * _x_4 in\l          let (_x_87 : real) = 1727/194375 * _x_5 in\l          let (_x_88 : real) = (-61231/8500000) * _x_6 in\l          let (_x_89 : real) = (-1831/320000) * _x_7 in\l          let (_x_90 : real)\l              = if _x_84 +. _x_85 +. _x_86 +. _x_87 +. _x_88 +. _x_89\l                   \<= (-89188713933/1534287400000)\l                then 0\l                else\l                  89188713933/1534287400000 +. _x_84 +. _x_85 +. _x_86\l                  +. _x_87 +. _x_88 +. _x_89\l          in\l          let (_x_91 : real) = 10277/200000 * _x_68 in\l          let (_x_92 : real) = (-28841/190100) * _x_62 in\l          let (_x_93 : real) = 4637/29020000 * _x_4 in\l          let (_x_94 : real) = 3601/388750 * _x_5 in\l          let (_x_95 : real) = 5957/8500000 * _x_6 in\l          let (_x_96 : real) = (-22041/640000) * _x_7 in\l          let (_x_97 : real)\l              = if _x_91 +. _x_92 +. _x_93 +. _x_94 +. _x_95 +. _x_96\l                   \<= (-372238333/2454859840)\l                then 0\l                else\l                  372238333/2454859840 +. _x_91 +. _x_92 +. _x_93 +. _x_94\l                  +. _x_95 +. _x_96\l          in\l          let (_x_98 : real) = 13901/50000 * _x_68 in\l          let (_x_99 : real) = (-803/38020) * _x_62 in\l          let (_x_100 : real) = 10557/29020000 * _x_4 in\l          let (_x_101 : real) = 60757/3110000 * _x_5 in\l          let (_x_102 : real) = (-16157/4250000) * _x_6 in\l          let (_x_103 : real) = 47933/640000 * _x_7 in\l          let (_x_104 : real)\l              = if _x_98 +. _x_99 +. _x_100 +. _x_101 +. _x_102 +. _x_103\l                   \<= 72146699557/306857480000\l                then 0\l                else\l                  (-72146699557/306857480000) +. _x_98 +. _x_99 +. _x_100\l                  +. _x_101 +. _x_102 +. _x_103\l          in\l          let (_x_105 : real)\l              = 1568904513/1250000000 * _x_69\l                +. (-1400061773/1250000000) * _x_76\l                +. (-889978969/400000000) * _x_83\l                +. (-787784679/2500000000) * _x_90\l                +. (-19189866047/10000000000) * _x_97\l                +. 5337652199/2000000000 * _x_104\l          in\l          not\l          ((0 \<= _x_0) && (_x_0 \<= 500) && (0 \<= _x_1) && (_x_1 \<= 40)\l           && (0 \<= _x_2) && (_x_2 \<= 100) && (0 \<= _x_3) && (_x_3 \<= 15)\l           && (0 \<= _x_4) && (_x_4 \<= 500) && (0 \<= _x_5) && (_x_5 \<= 40)\l           && (0 \<= _x_6) && (_x_6 \<= 100) && (0 \<= _x_7) && (_x_7 \<= 15)\l           && (_x_8 = _x_9)\l           && not\l              ((_x_8 = Oct) \|\| (_x_8 = Nov) \|\| (_x_8 = Dec) \|\| _x_10 \|\| _x_11)\l           && (_x_12 = _x_13) && (_x_0 = _x_4) && (_x_2 = _x_6)\l           && (_x_3 = _x_7) && (_x_1 \>= 10 +. _x_5))\l          \|\| ((if _x_58 \<= (-341987779/312500000)\l               then\l                 28114831522503/7812500000000\l                 +. 67395431164941/31250000000000 * _x_22\l                 +. (-60142453582761/31250000000000) * _x_29\l                 +. (-38230826571333/10000000000000) * _x_36\l                 +. (-33840866455803/62500000000000) * _x_43\l                 +. (-824339075780979/250000000000000) * _x_50\l                 +. 229289525512443/50000000000000 * _x_57\l               else\l               if _x_58 \<= (-29487779/312500000)\l               then\l                 213430965464483/31250000000000\l                 +. 732799213218501/125000000000000 * _x_22\l                 +. (-653936652747521/125000000000000) * _x_29\l                 +. (-415688706903613/40000000000000) * _x_36\l                 +. (-367956104513283/250000000000000) * _x_43\l                 +. (-8963145063634619/1000000000000000) * _x_50\l                 +. 2493094576152323/200000000000000 * _x_57\l               else\l               if _x_58 \<= 283012221/312500000\l               then\l                 1852306369389/244140625000\l                 +. 124497279820089/7812500000000 * _x_22\l                 +. (-111099101872869/7812500000000) * _x_29\l                 +. (-70622501127057/2500000000000) * _x_36\l                 +. (-62513077632687/15625000000000) * _x_43\l                 +. (-1522773440427591/62500000000000) * _x_50\l                 +. 423558714947247/12500000000000 * _x_57\l               else if _x_58 \<= 595512221/312500000 then … else …)\l              \>= (-25)\l                 +. (if _x_105 \<= (-341987779/312500000)\l                     then\l                       28114831522503/7812500000000\l                       +. 67395431164941/31250000000000 * _x_69\l                       +. (-60142453582761/31250000000000) * _x_76\l                       +. (-38230826571333/10000000000000) * _x_83\l                       +. (-33840866455803/62500000000000) * _x_90\l                       +. (-824339075780979/250000000000000) * _x_97\l                       +. 229289525512443/50000000000000 * _x_104\l                     else\l                     if _x_105 \<= (-29487779/312500000)\l                     then\l                       213430965464483/31250000000000\l                       +. 732799213218501/125000000000000 * _x_69\l                       +. (-653936652747521/125000000000000) * _x_76\l                       +. (-415688706903613/40000000000000) * _x_83\l                       +. (-367956104513283/250000000000000) * _x_90\l                       +. (-8963145063634619/1000000000000000) * _x_97\l                       +. 2493094576152323/200000000000000 * _x_104\l                     else\l                     if _x_105 \<= 283012221/312500000\l                     then\l                       1852306369389/244140625000\l                       +. 124497279820089/7812500000000 * _x_69\l                       +. (-111099101872869/7812500000000) * _x_76\l                       +. (-70622501127057/2500000000000) * _x_83\l                       +. (-62513077632687/15625000000000) * _x_90\l                       +. (-1522773440427591/62500000000000) * _x_97\l                       +. 423558714947247/12500000000000 * _x_104\l                     else if _x_105 \<= 595512221/312500000 then … else …))\l          :expansions [] :rw [] :fc [])",shape=box,style=filled,fontname="courier",fontsize=14];
p_370 -> p_369 [label=""];
p_369 [label="Unsat",shape=box,style=filled,fontname="courier",fontsize=14];
}

digraph "call graph" {
goal [label="let (_x_0 : real) = a.dmc in\llet (_x_1 : real) = a.temp in\llet (_x_2 : real) = a.rh in\llet (_x_3 : real) = a.rain in\llet (_x_4 : real) = b.dmc in\llet (_x_5 : real) = b.temp in\llet (_x_6 : real) = b.rh in\llet (_x_7 : real) = b.rain in\llet (_x_8 : month) = a.month in\llet (_x_9 : month) = b.month in\llet (_x_10 : bool) = _x_8 = Jan in\llet (_x_11 : bool) = _x_8 = Feb in\llet (_x_12 : day) = a.day in\llet (_x_13 : day) = b.day in\llet (_x_14 : bool) = _x_8 = Mar in\llet (_x_15 : real)\l    = if _x_12 = Mon then 377/1000\l      else\l      if _x_12 = Tue then 1223/1000\l      else\l      if (_x_12 = Wed) \|\| (_x_12 = Thu) then 1901/1000\l      else if _x_12 = Fri then 1223/1000 else …\lin\llet (_x_16 : real) = (-7861/95050) * _x_15 in\llet (_x_17 : real) = (-19063/29020000) * _x_0 in\llet (_x_18 : real) = (-27281/1555000) * _x_1 in\llet (_x_19 : real) = 137/340000 * _x_2 in\llet (_x_20 : real) = 6263/80000 * _x_3 in\llet (_x_21 : real)\l    = if _x_10 then 67/500\l      else\l      if _x_11 then 1/2\l      else if _x_14 then 1 else if _x_8 = Apr then 3/2 else …\lin\llet (_x_22 : real)\l    = if 5031/50000 * _x_21 +. _x_16 +. _x_17 +. _x_18 +. _x_19 +. _x_20\l         \<= (-1716983137/306857480000)\l      then 0\l      else\l        1716983137/306857480000\l        +. 5031/50000\l           * (if _x_10 then 67/500\l              else if _x_11 then 1/2 else if _x_14 then 1 else …)\l        +. _x_16 +. _x_17 +. _x_18 +. _x_19 +. _x_20\lin\llet (_x_23 : real) = 29103/200000 * _x_21 in\llet (_x_24 : real) = 159/9505 * _x_15 in\llet (_x_25 : real) = (-1021/1813750) * _x_0 in\llet (_x_26 : real) = 17919/3110000 * _x_1 in\llet (_x_27 : real) = 32971/8500000 * _x_2 in\llet (_x_28 : real) = (-21603/320000) * _x_3 in\llet (_x_29 : real)\l    = if _x_23 +. _x_24 +. _x_25 +. _x_26 +. _x_27 +. _x_28\l         \<= 73983893263/767143700000\l      then 0\l      else\l        (-73983893263/767143700000) +. _x_23 +. _x_24 +. _x_25 +. _x_26\l        +. _x_27 +. _x_28\lin\llet (_x_30 : real) = 66419/200000 * _x_21 in\llet (_x_31 : real) = 25399/190100 * _x_15 in\llet (_x_32 : real) = 449/29020000 * _x_0 in\llet (_x_33 : real) = 3841/3110000 * _x_1 in\llet (_x_34 : real) = (-25741/4250000) * _x_2 in\llet (_x_35 : real) = 58299/640000 * _x_3 in\llet (_x_36 : real)\l    = if _x_30 +. _x_31 +. _x_32 +. _x_33 +. _x_34 +. _x_35\l         \<= (-317131778543/1534287400000)\l      then 0\l      else\l        317131778543/1534287400000 +. _x_30 +. _x_31 +. _x_32 +. _x_33\l        +. _x_34 +. _x_35\lin\llet (_x_37 : real) = 23799/100000 * _x_21 in\llet (_x_38 : real) = (-18071/95050) * _x_15 in\llet (_x_39 : real) = 38981/29020000 * _x_0 in\llet (_x_40 : real) = 1727/194375 * _x_1 in\llet (_x_41 : real) = (-61231/8500000) * _x_2 in\llet (_x_42 : real) = (-1831/320000) * _x_3 in\llet (_x_43 : real)\l    = if _x_37 +. _x_38 +. _x_39 +. _x_40 +. _x_41 +. _x_42\l         \<= (-89188713933/1534287400000)\l      then 0\l      else\l        89188713933/1534287400000 +. _x_37 +. _x_38 +. _x_39 +. _x_40\l        +. _x_41 +. _x_42\lin\llet (_x_44 : real) = 10277/200000 * _x_21 in\llet (_x_45 : real) = (-28841/190100) * _x_15 in\llet (_x_46 : real) = 4637/29020000 * _x_0 in\llet (_x_47 : real) = 3601/388750 * _x_1 in\llet (_x_48 : real) = 5957/8500000 * _x_2 in\llet (_x_49 : real) = (-22041/640000) * _x_3 in\llet (_x_50 : real)\l    = if _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48 +. _x_49\l         \<= (-372238333/2454859840)\l      then 0\l      else\l        372238333/2454859840 +. _x_44 +. _x_45 +. _x_46 +. _x_47 +. _x_48\l        +. _x_49\lin\llet (_x_51 : real) = 13901/50000 * _x_21 in\llet (_x_52 : real) = (-803/38020) * _x_15 in\llet (_x_53 : real) = 10557/29020000 * _x_0 in\llet (_x_54 : real) = 60757/3110000 * _x_1 in\llet (_x_55 : real) = (-16157/4250000) * _x_2 in\llet (_x_56 : real) = 47933/640000 * _x_3 in\llet (_x_57 : real)\l    = if _x_51 +. _x_52 +. _x_53 +. _x_54 +. _x_55 +. _x_56\l         \<= 72146699557/306857480000\l      then 0\l      else\l        (-72146699557/306857480000) +. _x_51 +. _x_52 +. _x_53 +. _x_54\l        +. _x_55 +. _x_56\lin\llet (_x_58 : real)\l    = 1568904513/1250000000 * _x_22 +. (-1400061773/1250000000) * _x_29\l      +. (-889978969/400000000) * _x_36 +. (-787784679/2500000000) * _x_43\l      +. (-19189866047/10000000000) * _x_50 +. 5337652199/2000000000 * _x_57\lin\llet (_x_59 : bool) = _x_9 = Mar in\llet (_x_60 : bool) = _x_9 = Feb in\llet (_x_61 : bool) = _x_9 = Jan in\llet (_x_62 : real)\l    = if _x_61 then 67/500\l      else\l      if _x_60 then 1/2\l      else if _x_59 then 1 else if _x_9 = Apr then 3/2 else …\lin\llet (_x_63 : real) = 5031/50000 * _x_62 in\llet (_x_64 : bool) = (_x_13 = Wed) \|\| (_x_13 = Thu) in\llet (_x_65 : bool) = _x_13 = Tue in\llet (_x_66 : bool) = _x_13 = Mon in\llet (_x_67 : real)\l    = if _x_66 then 377/1000\l      else\l      if _x_65 then 1223/1000\l      else\l      if _x_64 then 1901/1000 else if _x_13 = Fri then 1223/1000 else …\lin\llet (_x_68 : real) = (-7861/95050) * _x_67 in\llet (_x_69 : real) = (-19063/29020000) * _x_4 in\llet (_x_70 : real) = (-27281/1555000) * _x_5 in\llet (_x_71 : real) = 137/340000 * _x_6 in\llet (_x_72 : real) = 6263/80000 * _x_7 in\llet (_x_73 : real) = 29103/200000 * _x_62 in\llet (_x_74 : real) = 159/9505 * _x_67 in\llet (_x_75 : real) = (-1021/1813750) * _x_4 in\llet (_x_76 : real) = 17919/3110000 * _x_5 in\llet (_x_77 : real) = 32971/8500000 * _x_6 in\llet (_x_78 : real) = (-21603/320000) * _x_7 in\llet (_x_79 : real)\l    = if _x_61 then 67/500\l      else if _x_60 then 1/2 else if _x_59 then 1 else …\lin\llet (_x_80 : real)\l    = if _x_66 then 377/1000\l      else if _x_65 then 1223/1000 else if _x_64 then 1901/1000 else …\lin\llet (_x_81 : real) = 449/29020000 * _x_4 in\llet (_x_82 : real) = 3841/3110000 * _x_5 in\llet (_x_83 : real) = (-25741/4250000) * _x_6 in\llet (_x_84 : real) = 58299/640000 * _x_7 in\llet (_x_85 : real)\l    = if 66419/200000 * _x_62 +. 25399/190100 * _x_67 +. _x_81 +. _x_82\l         +. _x_83 +. _x_84 \<= (-317131778543/1534287400000)\l      then 0\l      else\l        317131778543/1534287400000 +. 66419/200000 * _x_79\l        +. 25399/190100 * _x_80 +. _x_81 +. _x_82 +. _x_83 +. _x_84\lin\llet (_x_86 : real) = 23799/100000 * _x_62 in\llet (_x_87 : real) = (-18071/95050) * _x_67 in\llet (_x_88 : real) = 38981/29020000 * _x_4 in\llet (_x_89 : real) = 1727/194375 * _x_5 in\llet (_x_90 : real) = (-61231/8500000) * _x_6 in\llet (_x_91 : real) = (-1831/320000) * _x_7 in\llet (_x_92 : real) = 10277/200000 * _x_62 in\llet (_x_93 : real) = (-28841/190100) * _x_67 in\llet (_x_94 : real) = 4637/29020000 * _x_4 in\llet (_x_95 : real) = 3601/388750 * _x_5 in\llet (_x_96 : real) = 5957/8500000 * _x_6 in\llet (_x_97 : real) = (-22041/640000) * _x_7 in\llet (_x_98 : real) = 13901/50000 * _x_62 in\llet (_x_99 : real) = (-803/38020) * _x_67 in\llet (_x_100 : real) = 10557/29020000 * _x_4 in\llet (_x_101 : real) = 60757/3110000 * _x_5 in\llet (_x_102 : real) = (-16157/4250000) * _x_6 in\llet (_x_103 : real) = 47933/640000 * _x_7 in\llet (_x_104 : real)\l    = 1568904513/1250000000\l      * (if _x_63 +. _x_68 +. _x_69 +. _x_70 +. _x_71 +. _x_72\l            \<= (-1716983137/306857480000)\l         then 0\l         else\l           (1716983137/306857480000 +. _x_63 +. _x_68 +. _x_69 +. _x_70\l            +. _x_71 +. _x_72))\l      +. (-1400061773/1250000000)\l         * (if _x_73 +. _x_74 +. _x_75 +. _x_76 +. _x_77 +. _x_78\l               \<= 73983893263/767143700000\l            then 0\l            else\l              ((-73983893263/767143700000) +. _x_73 +. _x_74 +. _x_75\l               +. _x_76 +. _x_77 +. _x_78))\l      +. (-889978969/400000000) * _x_85\l      +. (-787784679/2500000000)\l         * (if _x_86 +. _x_87 +. _x_88 +. _x_89 +. _x_90 +. _x_91\l               \<= (-89188713933/1534287400000)\l            then 0\l            else\l              (89188713933/1534287400000 +. _x_86 +. _x_87 +. _x_88 +. _x_89\l               +. _x_90 +. _x_91))\l      +. (-19189866047/10000000000)\l         * (if _x_92 +. _x_93 +. _x_94 +. _x_95 +. _x_96 +. _x_97\l               \<= (-372238333/2454859840)\l            then 0\l            else\l              (372238333/2454859840 +. _x_92 +. _x_93 +. _x_94 +. _x_95\l               +. _x_96 +. _x_97))\l      +. 5337652199/2000000000\l         * (if _x_98 +. _x_99 +. _x_100 +. _x_101 +. _x_102 +. _x_103\l               \<= 72146699557/306857480000\l            then 0\l            else\l              ((-72146699557/306857480000) +. _x_98 +. _x_99 +. _x_100\l               +. _x_101 +. _x_102 +. _x_103))\lin\llet (_x_105 : real) = if _x_61 then 67/500 else if _x_60 then 1/2 else … in\llet (_x_106 : real) = 5031/50000 * _x_105 in\llet (_x_107 : real)\l    = (-7861/95050)\l      * (if _x_66 then 377/1000 else if _x_65 then 1223/1000 else …)\lin\llet (_x_108 : real)\l    = if _x_106 +. _x_107 +. _x_69 +. _x_70 +. _x_71 +. _x_72\l         \<= (-1716983137/306857480000)\l      then 0\l      else\l        1716983137/306857480000 +. _x_106 +. _x_107 +. _x_69 +. _x_70\l        +. _x_71 +. _x_72\lin\llet (_x_109 : real) = 159/9505 * _x_80 in\llet (_x_110 : real)\l    = if 29103/200000 * _x_79 +. _x_109 +. _x_75 +. _x_76 +. _x_77 +. _x_78\l         \<= 73983893263/767143700000\l      then 0\l      else\l        (-73983893263/767143700000) +. 29103/200000 * _x_105 +. _x_109\l        +. _x_75 +. _x_76 +. _x_77 +. _x_78\lin\llet (_x_111 : real) = 23799/100000 * _x_79 in\llet (_x_112 : real) = (-18071/95050) * _x_80 in\llet (_x_113 : real)\l    = if _x_111 +. _x_112 +. _x_88 +. _x_89 +. _x_90 +. _x_91\l         \<= (-89188713933/1534287400000)\l      then 0\l      else\l        89188713933/1534287400000 +. _x_111 +. _x_112 +. _x_88 +. _x_89\l        +. _x_90 +. _x_91\lin\llet (_x_114 : real) = 10277/200000 * _x_79 in\llet (_x_115 : real) = (-28841/190100) * _x_80 in\llet (_x_116 : real)\l    = if _x_114 +. _x_115 +. _x_94 +. _x_95 +. _x_96 +. _x_97\l         \<= (-372238333/2454859840)\l      then 0\l      else\l        372238333/2454859840 +. _x_114 +. _x_115 +. _x_94 +. _x_95 +. _x_96\l        +. _x_97\lin\llet (_x_117 : real) = 13901/50000 * _x_79 in\llet (_x_118 : real) = (-803/38020) * _x_80 in\llet (_x_119 : real)\l    = if _x_117 +. _x_118 +. _x_100 +. _x_101 +. _x_102 +. _x_103\l         \<= 72146699557/306857480000\l      then 0\l      else\l        (-72146699557/306857480000) +. _x_117 +. _x_118 +. _x_100 +. _x_101\l        +. _x_102 +. _x_103\lin\llet (_x_120 : real) = 5031/50000 * _x_79 in\llet (_x_121 : real) = (-7861/95050) * _x_80 in\lnot\l(not\l ((0 \<= _x_0) && (_x_0 \<= 500) && (0 \<= _x_1) && (_x_1 \<= 40) && (0 \<= _x_2)\l  && (_x_2 \<= 100) && (0 \<= _x_3) && (_x_3 \<= 15) && (0 \<= _x_4)\l  && (_x_4 \<= 500) && (0 \<= _x_5) && (_x_5 \<= 40) && (0 \<= _x_6)\l  && (_x_6 \<= 100) && (0 \<= _x_7) && (_x_7 \<= 15) && (_x_8 = _x_9)\l  && not ((_x_8 = Oct) \|\| (_x_8 = Nov) \|\| (_x_8 = Dec) \|\| _x_10 \|\| _x_11)\l  && (_x_12 = _x_13) && (_x_0 = _x_4) && (_x_2 = _x_6) && (_x_3 = _x_7)\l  && (_x_1 \>= 10 +. _x_5))\l \|\| ((if _x_58 \<= (-341987779/312500000)\l      then\l        28114831522503/7812500000000 +. 67395431164941/31250000000000 * _x_22\l        +. (-60142453582761/31250000000000) * _x_29\l        +. (-38230826571333/10000000000000) * _x_36\l        +. (-33840866455803/62500000000000) * _x_43\l        +. (-824339075780979/250000000000000) * _x_50\l        +. 229289525512443/50000000000000 * _x_57\l      else\l      if _x_58 \<= (-29487779/312500000)\l      then\l        213430965464483/31250000000000\l        +. 732799213218501/125000000000000 * _x_22\l        +. (-653936652747521/125000000000000) * _x_29\l        +. (-415688706903613/40000000000000) * _x_36\l        +. (-367956104513283/250000000000000) * _x_43\l        +. (-8963145063634619/1000000000000000) * _x_50\l        +. 2493094576152323/200000000000000 * _x_57\l      else\l      if _x_58 \<= 283012221/312500000\l      then\l        1852306369389/244140625000 +. 124497279820089/7812500000000 * _x_22\l        +. (-111099101872869/7812500000000) * _x_29\l        +. (-70622501127057/2500000000000) * _x_36\l        +. (-62513077632687/15625000000000) * _x_43\l        +. (-1522773440427591/62500000000000) * _x_50\l        +. 423558714947247/12500000000000 * _x_57\l      else if _x_58 \<= 595512221/312500000 then … else …)\l     \>= (-25)\l        +. (if _x_104 \<= (-341987779/312500000)\l            then\l              28114831522503/7812500000000\l              +. 67395431164941/31250000000000\l                 * (if _x_120 +. _x_121 +. _x_69 +. _x_70 +. _x_71 +. _x_72\l                       \<= (-1716983137/306857480000)\l                    then 0\l                    else\l                      (1716983137/306857480000 +. _x_120 +. _x_121 +. _x_69\l                       +. _x_70 +. _x_71 +. _x_72))\l              +. (-60142453582761/31250000000000) * _x_110\l              +. (-38230826571333/10000000000000) * _x_85\l              +. (-33840866455803/62500000000000) * _x_113\l              +. (-824339075780979/250000000000000) * _x_116\l              +. 229289525512443/50000000000000 * _x_119\l            else\l            if _x_104 \<= (-29487779/312500000)\l            then\l              213430965464483/31250000000000\l              +. 732799213218501/125000000000000 * _x_108\l              +. (-653936652747521/125000000000000) * _x_110\l              +. (-415688706903613/40000000000000) * _x_85\l              +. (-367956104513283/250000000000000) * _x_113\l              +. (-8963145063634619/1000000000000000) * _x_116\l              +. 2493094576152323/200000000000000 * _x_119\l            else\l            if _x_104 \<= 283012221/312500000\l            then\l              1852306369389/244140625000\l              +. 124497279820089/7812500000000 * _x_108\l              +. (-111099101872869/7812500000000) * _x_110\l              +. (-70622501127057/2500000000000) * _x_85\l              +. (-62513077632687/15625000000000) * _x_113\l              +. (-1522773440427591/62500000000000) * _x_116\l              +. 423558714947247/12500000000000 * _x_119\l            else if _x_104 \<= 595512221/312500000 then … else …)))",shape=box,style=filled,color="cyan",fontname="courier",fontsize=14];
}

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Reg_id	Constraints	Invariant
0	((input.radius_mean - 1412729/100000) / 70481/20000) > 17131/25000 ((input.radius_se - 40517/100000) / 27731/100000) > 1422/3125 0 <= input.compactness_worst <= 6/5 0 <= input.radius_se <= 7/2 0 <= input.compactness_mean <= 2/5 5 <= input.radius_mean <= 35 input.concavity_mean = 859/20000 input.concavity_worst = 13/50 input.concave_points_worst = 573/5000	"malignant"
1	((input.radius_mean - 1412729/100000) / 70481/20000) > 17131/25000 -13559/25000 < ((input.radius_se - 40517/100000) / 27731/100000) <= 1422/3125 0 <= input.compactness_worst <= 6/5 0 <= input.radius_se <= 7/2 0 <= input.compactness_mean <= 2/5 5 <= input.radius_mean <= 35 input.concavity_mean = 859/20000 input.concavity_worst = 13/50 input.concave_points_worst = 573/5000	"malignant"
2	((input.radius_mean - 1412729/100000) / 70481/20000) > 17131/25000 ((input.radius_se - 40517/100000) / 27731/100000) <= -13559/25000 0 <= input.compactness_worst <= 6/5 0 <= input.radius_se <= 7/2 0 <= input.compactness_mean <= 2/5 5 <= input.radius_mean <= 35 input.concavity_mean = 859/20000 input.concavity_worst = 13/50 input.concave_points_worst = 573/5000	"benign"
3	((input.radius_mean - 1412729/100000) / 70481/20000) <= 6587/25000 ((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000 0 <= input.compactness_worst <= 6/5 0 <= input.radius_se <= 7/2 0 <= input.compactness_mean <= 2/5 5 <= input.radius_mean <= 35 input.concavity_mean = 859/20000 input.concavity_worst = 13/50 input.concave_points_worst = 573/5000	"benign"
4	6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000 ((input.radius_se - 40517/100000) / 27731/100000) <= -13559/25000 ((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000 0 <= input.compactness_worst <= 6/5 0 <= input.radius_se <= 7/2 0 <= input.compactness_mean <= 2/5 5 <= input.radius_mean <= 35 input.concavity_mean = 859/20000 input.concavity_worst = 13/50 input.concave_points_worst = 573/5000	"benign"
5	6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000 ((input.radius_se - 40517/100000) / 27731/100000) > -13559/25000 ((input.compactness_mean - 5217/50000) / 5281/100000) > -4159/5000 0 <= input.compactness_worst <= 6/5 0 <= input.radius_se <= 7/2 0 <= input.compactness_mean <= 2/5 5 <= input.radius_mean <= 35 input.concavity_mean = 859/20000 input.concavity_worst = 13/50 input.concave_points_worst = 573/5000	"benign"
6	((input.radius_mean - 1412729/100000) / 70481/20000) <= 6587/25000 ((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000 0 <= input.compactness_worst <= 6/5 0 <= input.radius_se <= 7/2 0 <= input.compactness_mean <= 2/5 5 <= input.radius_mean <= 35 input.concavity_mean = 859/20000 input.concavity_worst = 13/50 input.concave_points_worst = 573/5000	"benign"
7	6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000 ((input.radius_se - 40517/100000) / 27731/100000) <= -13559/25000 ((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000 0 <= input.compactness_worst <= 6/5 0 <= input.radius_se <= 7/2 0 <= input.compactness_mean <= 2/5 5 <= input.radius_mean <= 35 input.concavity_mean = 859/20000 input.concavity_worst = 13/50 input.concave_points_worst = 573/5000	"benign"
8	6587/25000 < ((input.radius_mean - 1412729/100000) / 70481/20000) <= 17131/25000 ((input.radius_se - 40517/100000) / 27731/100000) > -13559/25000 ((input.compactness_mean - 5217/50000) / 5281/100000) <= -4159/5000 0 <= input.compactness_worst <= 6/5 0 <= input.radius_se <= 7/2 0 <= input.compactness_mean <= 2/5 5 <= input.radius_mean <= 35 input.concavity_mean = 859/20000 input.concavity_worst = 13/50 input.concave_points_worst = 573/5000	"benign"