Random Jason Timeout Test 004

Average Error: 34.0 → 34.0

Time: 33.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = -8.629504245900419e-173
  2. c = -1.5889599578209953e+300

Math

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

↓

\[{\left({e}^{\left(\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{2}}\right)}\right)}^{\left(\sqrt[3]{{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{3}}\right)}\]

C

double f(double a, double c) {
        double r15910 = c;
        double r15911 = cosh(r15910);
        double r15912 = a;
        double r15913 = log1p(r15912);
        double r15914 = fmod(r15911, r15913);
        return r15914;
}

↓

double f(double a, double c) {
        double r15915 = exp(1.0);
        double r15916 = c;
        double r15917 = cosh(r15916);
        double r15918 = a;
        double r15919 = log1p(r15918);
        double r15920 = fmod(r15917, r15919);
        double r15921 = log(r15920);
        double r15922 = 2.0;
        double r15923 = pow(r15921, r15922);
        double r15924 = cbrt(r15923);
        double r15925 = pow(r15915, r15924);
        double r15926 = cbrt(r15921);
        double r15927 = 3.0;
        double r15928 = pow(r15926, r15927);
        double r15929 = cbrt(r15928);
        double r15930 = pow(r15925, r15929);
        return r15930;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.0

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

3. Applied add-exp-log 34.0

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

5. Applied pow1 34.0

   \[\leadsto e^{\log \color{blue}{\left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{1}\right)}}\]

6. Applied log-pow 34.0

   \[\leadsto e^{\color{blue}{1 \cdot \log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

7. Applied exp-prod 34.0

   \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}}\]

8. Simplified 34.0

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

10. Applied add-cbrt-cube 34.0

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

11. Simplified 34.0

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

13. Applied add-cube-cbrt 34.0

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

14. Applied unpow-prod-down 34.0

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

15. Applied cbrt-prod 34.0

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

16. Applied pow-unpow 34.0

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

17. Simplified 34.0

    \[\leadsto {\color{blue}{\left({e}^{\left(\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{2}}\right)}\right)}}^{\left(\sqrt[3]{{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{3}}\right)}\]

18. Final simplification 34.0

    \[\leadsto {\left({e}^{\left(\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{2}}\right)}\right)}^{\left(\sqrt[3]{{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{3}}\right)}\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))