Random Jason Timeout Test 004

Average Error: 34.4 → 34.4

Time: 46.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 2.73300969175321e+146
  2. c = -1.4512726209800046e+108

Math

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

↓

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

C

double f(double a, double c) {
        double r12049 = c;
        double r12050 = cosh(r12049);
        double r12051 = a;
        double r12052 = log1p(r12051);
        double r12053 = fmod(r12050, r12052);
        return r12053;
}

↓

double f(double a, double c) {
        double r12054 = c;
        double r12055 = cosh(r12054);
        double r12056 = a;
        double r12057 = log1p(r12056);
        double r12058 = fmod(r12055, r12057);
        return r12058;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.4

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

3. Applied add-exp-log 34.4

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

5. Applied add-cbrt-cube 34.4

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

6. Simplified 34.4

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

8. Applied add-cbrt-cube 34.4

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

9. Simplified 34.4

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

10. Final simplification 34.4

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

Reproduce

herbie shell --seed 2019298 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))