Average Error: 34.0 → 34.0
Time: 29.8s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot e^{\sqrt[3]{{\left(\log \left(\sqrt[3]{{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{2}{3}}}\right) + \log \left(\sqrt[3]{\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\right)}^{3}}}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot e^{\sqrt[3]{{\left(\log \left(\sqrt[3]{{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{2}{3}}}\right) + \log \left(\sqrt[3]{\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\right)}^{3}}}
double f(double a, double c) {
        double r14838 = c;
        double r14839 = cosh(r14838);
        double r14840 = a;
        double r14841 = log1p(r14840);
        double r14842 = fmod(r14839, r14841);
        return r14842;
}
↓
double f(double a, double c) {
        double r14843 = c;
        double r14844 = cosh(r14843);
        double r14845 = a;
        double r14846 = log1p(r14845);
        double r14847 = fmod(r14844, r14846);
        double r14848 = cbrt(r14847);
        double r14849 = r14848 * r14848;
        double r14850 = 0.6666666666666666;
        double r14851 = pow(r14847, r14850);
        double r14852 = cbrt(r14851);
        double r14853 = log(r14852);
        double r14854 = cbrt(r14848);
        double r14855 = log(r14854);
        double r14856 = r14853 + r14855;
        double r14857 = 3.0;
        double r14858 = pow(r14856, r14857);
        double r14859 = cbrt(r14858);
        double r14860 = exp(r14859);
        double r14861 = r14849 * r14860;
        return r14861;
}

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-cube-cbrt34.0

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

  5. Applied add-exp-log34.0

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

  7. Applied add-cbrt-cube34.0

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

  8. Simplified34.0

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

  10. Applied add-cube-cbrt34.0

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

  11. Applied cbrt-prod34.0

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

  12. Applied log-prod34.0

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

  13. Simplified34.0

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

  14. Final simplification34.0

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

Reproduce

herbie shell --seed 2019235 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))