Average Error: 34.6 → 34.6
Time: 14.7s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[e^{\sqrt[3]{{\left(2 \cdot \sqrt[3]{{\left(\log \left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{1}{3}}\right)\right)}^{3}} + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}^{3}}}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
e^{\sqrt[3]{{\left(2 \cdot \sqrt[3]{{\left(\log \left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{1}{3}}\right)\right)}^{3}} + \log \left(\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 r11839 = c;
        double r11840 = cosh(r11839);
        double r11841 = a;
        double r11842 = log1p(r11841);
        double r11843 = fmod(r11840, r11842);
        return r11843;
}
↓
double f(double a, double c) {
        double r11844 = 2.0;
        double r11845 = c;
        double r11846 = cosh(r11845);
        double r11847 = a;
        double r11848 = log1p(r11847);
        double r11849 = fmod(r11846, r11848);
        double r11850 = 0.3333333333333333;
        double r11851 = pow(r11849, r11850);
        double r11852 = log(r11851);
        double r11853 = 3.0;
        double r11854 = pow(r11852, r11853);
        double r11855 = cbrt(r11854);
        double r11856 = r11844 * r11855;
        double r11857 = cbrt(r11849);
        double r11858 = log(r11857);
        double r11859 = r11856 + r11858;
        double r11860 = pow(r11859, r11853);
        double r11861 = cbrt(r11860);
        double r11862 = exp(r11861);
        return r11862;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.6

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

  3. Applied add-exp-log34.6

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

  5. Applied add-cbrt-cube34.6

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

  6. Simplified34.6

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

  8. Applied add-cube-cbrt34.6

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

  9. Applied log-prod34.6

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

  10. Simplified34.6

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

  12. Applied add-cbrt-cube34.6

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

  13. Simplified34.6

    \[\leadsto e^{\sqrt[3]{{\left(2 \cdot \sqrt[3]{\color{blue}{{\left(\log \left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{1}{3}}\right)\right)}^{3}}} + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}^{3}}}\]

  14. Final simplification34.6

    \[\leadsto e^{\sqrt[3]{{\left(2 \cdot \sqrt[3]{{\left(\log \left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{1}{3}}\right)\right)}^{3}} + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}^{3}}}\]

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))