Average Error: 34.6 → 34.6
Time: 29.9s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[e^{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]
double f(double a, double c) {
        double r98705 = c;
        double r98706 = cosh(r98705);
        double r98707 = a;
        double r98708 = log1p(r98707);
        double r98709 = fmod(r98706, r98708);
        return r98709;
}
↓
double f(double a, double c) {
        double r98710 = c;
        double r98711 = cosh(r98710);
        double r98712 = a;
        double r98713 = log1p(r98712);
        double r98714 = fmod(r98711, r98713);
        double r98715 = log(r98714);
        double r98716 = cbrt(r98715);
        double r98717 = r98716 * r98716;
        double r98718 = r98717 * r98716;
        double r98719 = exp(r98718);
        return r98719;
}


\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)
↓
e^{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.6

    \[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
  2. Using strategy rm

  3. Applied add-exp-log34.6

    \[\leadsto \color{blue}{e^{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt34.6

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

  6. Taylor expanded around 0 34.6

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

  7. Final simplification34.6

    \[\leadsto e^{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]

Reproduce

herbie shell --seed 2019102 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))