Random Jason Timeout Test 004

Average Error: 33.8 → 33.4

Time: 35.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.2059558245150868e+23
  2. c = 1.774174898164156e+151

Math

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

↓

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

C

double f(double a, double c) {
        double r685897 = c;
        double r685898 = cosh(r685897);
        double r685899 = a;
        double r685900 = log1p(r685899);
        double r685901 = fmod(r685898, r685900);
        return r685901;
}

↓

double f(double a, double c) {
        double r685902 = c;
        double r685903 = cosh(r685902);
        double r685904 = a;
        double r685905 = log1p(r685904);
        double r685906 = cbrt(r685905);
        double r685907 = r685906 * r685906;
        double r685908 = r685906 * r685907;
        double r685909 = fmod(r685903, r685908);
        double r685910 = sqrt(r685909);
        double r685911 = log(r685909);
        double r685912 = r685911 * r685911;
        double r685913 = r685912 * r685911;
        double r685914 = cbrt(r685913);
        double r685915 = exp(r685914);
        double r685916 = sqrt(r685915);
        double r685917 = r685910 * r685916;
        return r685917;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.8

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

3. Applied add-cube-cbrt 33.4

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

5. Applied add-sqr-sqrt 33.4

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

7. Applied add-exp-log 33.4

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

9. Applied add-cbrt-cube 33.4

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

10. Final simplification 33.4

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

Reproduce

herbie shell --seed 2019132 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))