added my_cosine example in regression tests (purely logic version)

.gitignore

@@ -145,7 +145,6 @@ why.conf
 /tests/test-claude/
 
 # /examples/
-/examples/my_cosine/
 /examples/genealogy/
 /examples/programs/course/
 /examples/programs/wcet_hull/

examples/my_cosine/my_cosine.why_CosineSingle_MethodError_1.v

-(* Beware! Only edit allowed sections below    *)
 (* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
 Require Import ZArith.
 Require Import Rbase.
 Require Import Rbasic_fun.
 Require Import R_sqrt.
 Require Import Rtrigo.
 Require Import AltSeries. (* for def of pi *)
-Axiom Refl : forall (x:R), (x <= x)%R.
-
-Axiom Trans : forall (x:R) (y:R) (z:R), (x <= y)%R -> ((y <= z)%R ->
-  (x <= z)%R).
-
-Axiom Antisymm : forall (x:R) (y:R), (x <= y)%R -> ((y <= x)%R -> (x = y)).
-
-Axiom Total : forall (x:R) (y:R), (x <= y)%R \/ (y <= x)%R.
-
 Axiom Abs_le : forall (x:R) (y:R), ((Rabs x) <= y)%R <-> (((-y)%R <= x)%R /\
   (x <= y)%R).
 
-Axiom Abs_pos : forall (x:R), ((Rabs x) >= (0)%R)%R.
+Axiom Sqrt_positive : forall (x:R), ((0)%R <= x)%R -> ((0)%R <= (sqrt x))%R.
 
-Axiom Sqrt_positive : forall (x:R), (x >= (0)%R)%R -> ((sqrt x) >= (0)%R)%R.
+Axiom Sqrt_square : forall (x:R), ((0)%R <= x)%R -> ((Rsqr (sqrt x)) = x).
 
-Axiom Sqrt_square : forall (x:R), (x >= (0)%R)%R -> ((Rsqr (sqrt x)) = x).
-
-Axiom Square_sqrt : forall (x:R), (x >= (0)%R)%R -> ((sqrt (x * x)%R) = x).
+Axiom Square_sqrt : forall (x:R), ((0)%R <= x)%R -> ((sqrt (x * x)%R) = x).
 
 Axiom Pythagorean_identity : forall (x:R),
   (((Rsqr (Rtrigo_def.cos x)) + (Rsqr (Rtrigo_def.sin x)))%R = (1)%R).
@@ -73,21 +62,18 @@ Axiom Sin_sum : forall (x:R) (y:R),
 
 Parameter atan: R  -> R.
 
+
 Axiom Tan_atan : forall (x:R), ((Rtrigo.tan (atan x)) = x).
 
 Inductive mode  :=
-  | nearestTiesToEven : mode 
-  | toZero : mode 
-  | up : mode 
-  | down : mode 
-  | nearTiesToAway : mode .
+  | NearestTiesToEven : mode 
+  | ToZero : mode 
+  | Up : mode 
+  | Down : mode 
+  | NearTiesToAway : mode .
 
 Parameter single : Type.
 
-Definition max_single: R := (33554430 * 10141204801825835211973625643008)%R.
-
-Definition max_int: Z := 16777216%Z.
-
 Axiom Zero : ((IZR 0%Z) = (0)%R).
 
 Axiom One : ((IZR 1%Z) = (1)%R).
@@ -98,47 +84,53 @@ Axiom Sub : forall (x:Z) (y:Z), ((IZR (x - y)%Z) = ((IZR x) - (IZR y))%R).
 
 Axiom Mul : forall (x:Z) (y:Z), ((IZR (x * y)%Z) = ((IZR x) * (IZR y))%R).
 
-Axiom Neg : forall (x:Z) (y:Z), ((IZR (-x)%Z) = (-(IZR x))%R).
+Axiom Neg : forall (x:Z), ((IZR (-x)%Z) = (-(IZR x))%R).
 
 Parameter round: mode -> R  -> R.
 
+
 Parameter round_logic: mode -> R  -> single.
 
+
 Parameter value: single  -> R.
 
+
 Parameter exact: single  -> R.
 
+
 Parameter model: single  -> R.
 
+
 Definition round_error(x:single): R := (Rabs ((value x) - (exact x))%R).
 
 Definition total_error(x:single): R := (Rabs ((value x) - (model x))%R).
 
 Definition no_overflow(m:mode) (x:R): Prop := ((Rabs (round m
-  x)) <= (max_single ))%R.
+  x)) <= (33554430 * 10141204801825835211973625643008)%R)%R.
 
 Axiom Bounded_real_no_overflow : forall (m:mode) (x:R),
-  ((Rabs x) <= (max_single ))%R -> (no_overflow m x).
+  ((Rabs x) <= (33554430 * 10141204801825835211973625643008)%R)%R ->
+  (no_overflow m x).
 
 Axiom Round_monotonic : forall (m:mode) (x:R) (y:R), (x <= y)%R -> ((round m
   x) <= (round m y))%R.
 
 Axiom Exact_rounding_for_integers : forall (m:mode) (i:Z),
-  (((-(max_int ))%Z <= i)%Z /\ (i <= (max_int ))%Z) -> ((round m
+  (((-16777216%Z)%Z <= i)%Z /\ (i <= 16777216%Z)%Z) -> ((round m
   (IZR i)) = (IZR i)).
 
-Axiom Round_down_le : forall (x:R), ((round (down ) x) <= x)%R.
+Axiom Round_down_le : forall (x:R), ((round (Down ) x) <= x)%R.
 
-Axiom Round_up_ge : forall (x:R), ((round (up ) x) >= x)%R.
+Axiom Round_up_ge : forall (x:R), (x <= (round (Up ) x))%R.
 
-Axiom Round_down_neg : forall (x:R), ((round (down ) (-x)%R) = (-(round (up )
+Axiom Round_down_neg : forall (x:R), ((round (Down ) (-x)%R) = (-(round (Up )
   x))%R).
 
-Axiom Round_up_neg : forall (x:R), ((round (up ) (-x)%R) = (-(round (down )
+Axiom Round_up_neg : forall (x:R), ((round (Up ) (-x)%R) = (-(round (Down )
   x))%R).
 
 Theorem MethodError : forall (x:R), ((Rabs x) <= (1 / 32)%R)%R ->
-  ((Rabs (((1)%R - ((x * x)%R * (05 / 10)%R)%R)%R - (Rtrigo_def.cos x))%R) <= (1 / 16777216)%R)%R.
+  ((Rabs (((1)%R - ((05 / 10)%R * (x * x)%R)%R)%R - (Rtrigo_def.cos x))%R) <= (1 / 16777216)%R)%R.
 (* YOU MAY EDIT THE PROOF BELOW *)
 intros x H.
 Require Import Interval_tactic.

examples/my_cosine/why3session.xml

+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE why3session SYSTEM "why3session.dtd">
+<why3session name="examples/my_cosine/why3session.xml">
+ <file name="../my_cosine.why" verified="false" expanded="true">
+  <theory name="CosineSingle" verified="false" expanded="true">
+   <goal name="MethodError" sum="03308e96177082a1d3da02e1d9af1b90" proved="true" expanded="true">
+    <proof prover="coq" timelimit="2" edited="my_cosine.why_CosineSingle_MethodError_1.v" obsolete="false">
+     <result status="valid" time="3.93"/>
+    </proof>
+   </goal>
+   <goal name="TotalErrorFullyExpanded" sum="2fc170302406d4bec35227d00816a288" proved="true" expanded="true">
+    <proof prover="gappa" timelimit="2" edited="" obsolete="false">
+     <result status="valid" time="0.02"/>
+    </proof>
+   </goal>
+   <goal name="TotalErrorExpanded" sum="aad0006d76fec58b87bf9c270f975fb4" proved="true" expanded="true">
+    <proof prover="alt-ergo" timelimit="2" edited="" obsolete="false">
+     <result status="valid" time="0.81"/>
+    </proof>
+    <proof prover="gappa" timelimit="2" edited="" obsolete="false">
+     <result status="unknown" time="0.01"/>
+    </proof>
+   </goal>
+   <goal name="TotalError" sum="0851711761327bfdfc8ed8a6b0c1fa03" proved="false" expanded="true">
+    <proof prover="alt-ergo" timelimit="2" edited="" obsolete="false">
+     <result status="timeout" time="2.08"/>
+    </proof>
+    <proof prover="gappa" timelimit="2" edited="" obsolete="false">
+     <result status="unknown" time="0.01"/>
+    </proof>
+   </goal>
+  </theory>
+ </file>
+</why3session>