Average Error: 34.3 → 34.3
Time: 27.0s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[{\left(e^{\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\right)}^{\left(\sqrt[3]{\sqrt[3]{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\right)}\]
double f(double a, double c) {
        double r101610 = c;
        double r101611 = cosh(r101610);
        double r101612 = a;
        double r101613 = log1p(r101612);
        double r101614 = fmod(r101611, r101613);
        return r101614;
}
↓
double f(double a, double c) {
        double r101615 = c;
        double r101616 = cosh(r101615);
        double r101617 = a;
        double r101618 = log1p(r101617);
        double r101619 = fmod(r101616, r101618);
        double r101620 = log(r101619);
        double r101621 = cbrt(r101620);
        double r101622 = r101621 * r101621;
        double r101623 = exp(r101622);
        double r101624 = r101620 * r101620;
        double r101625 = r101624 * r101620;
        double r101626 = cbrt(r101625);
        double r101627 = cbrt(r101626);
        double r101628 = pow(r101623, r101627);
        return r101628;
}


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

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.3

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

  3. Applied add-exp-log34.3

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

  5. Applied add-cube-cbrt34.3

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

  6. Applied exp-prod34.3

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

  8. Applied add-cbrt-cube34.3

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

  9. Final simplification34.3

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

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))