Random Jason Timeout Test 004

Average Error: 34.2 → 34.2

Time: 14.2s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.1741963849460375e-217
  2. c = -2.3820831826475924e+172

Math

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

↓

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

C

double f(double a, double c) {
        double r12321 = c;
        double r12322 = cosh(r12321);
        double r12323 = a;
        double r12324 = log1p(r12323);
        double r12325 = fmod(r12322, r12324);
        return r12325;
}

↓

double f(double a, double c) {
        double r12326 = c;
        double r12327 = cosh(r12326);
        double r12328 = a;
        double r12329 = log1p(r12328);
        double r12330 = fmod(r12327, r12329);
        double r12331 = log(r12330);
        double r12332 = exp(r12331);
        double r12333 = sqrt(r12332);
        double r12334 = sqrt(r12333);
        double r12335 = 3.0;
        double r12336 = pow(r12334, r12335);
        double r12337 = log(r12336);
        double r12338 = exp(r12337);
        double r12339 = sqrt(r12330);
        double r12340 = sqrt(r12339);
        double r12341 = r12338 * r12340;
        return r12341;
}

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

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

5. Applied add-sqr-sqrt 34.2

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

6. Applied sqrt-prod 34.2

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

7. Applied associate-*r* 34.2

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

8. Simplified 34.2

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

10. Applied add-exp-log 34.2

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

11. Applied pow-exp 34.2

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

12. Simplified 34.2

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

14. Applied add-exp-log 34.2

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

15. Final simplification 34.2

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

Reproduce

herbie shell --seed 2020049 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))