Average Error: 34.6 → 34.6
Time: 28.9s
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 r104060 = c;
        double r104061 = cosh(r104060);
        double r104062 = a;
        double r104063 = log1p(r104062);
        double r104064 = fmod(r104061, r104063);
        return r104064;
}
↓
double f(double a, double c) {
        double r104065 = c;
        double r104066 = cosh(r104065);
        double r104067 = a;
        double r104068 = log1p(r104067);
        double r104069 = fmod(r104066, r104068);
        double r104070 = log(r104069);
        double r104071 = cbrt(r104070);
        double r104072 = r104071 * r104071;
        double r104073 = r104072 * r104071;
        double r104074 = exp(r104073);
        return r104074;
}


\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 -inf 34.6

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

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