Random Jason Timeout Test 004

Average Error: 34.2 → 34.2

Time: 15.3s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.8761317066315612e+62
  2. c = -9.598405931812191e+260

Math

\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

↓

\[\sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

C

double f(double a, double c) {
        double r16331 = c;
        double r16332 = cosh(r16331);
        double r16333 = a;
        double r16334 = log1p(r16333);
        double r16335 = fmod(r16332, r16334);
        return r16335;
}

↓

double f(double a, double c) {
        double r16336 = c;
        double r16337 = cosh(r16336);
        double r16338 = cbrt(r16337);
        double r16339 = r16338 * r16338;
        double r16340 = sqrt(r16339);
        double r16341 = sqrt(r16338);
        double r16342 = sqrt(r16337);
        double r16343 = r16341 * r16342;
        double r16344 = r16340 * r16343;
        double r16345 = a;
        double r16346 = log1p(r16345);
        double r16347 = fmod(r16344, r16346);
        double r16348 = sqrt(r16347);
        double r16349 = r16348 * r16348;
        return r16349;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.2

   \[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
2. Using strategy rm

3. Applied add-sqr-sqrt 34.2

   \[\leadsto \left(\color{blue}{\left(\sqrt{\cosh c} \cdot \sqrt{\cosh c}\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
4. Using strategy rm

5. Applied add-cube-cbrt 34.2

   \[\leadsto \left(\left(\sqrt{\color{blue}{\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}}} \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

6. Applied sqrt-prod 34.2

   \[\leadsto \left(\left(\color{blue}{\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \sqrt{\sqrt[3]{\cosh c}}\right)} \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

7. Applied associate-*l* 34.2

   \[\leadsto \left(\color{blue}{\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
8. Using strategy rm

9. Applied add-sqr-sqrt 34.2

   \[\leadsto \color{blue}{\sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

10. Final simplification 34.2

    \[\leadsto \sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

Reproduce

herbie shell --seed 2020035 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))