Average Error: 34.0 → 34.0
Time: 30.4s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[{e}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
{e}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}
double f(double a, double c) {
        double r12523 = c;
        double r12524 = cosh(r12523);
        double r12525 = a;
        double r12526 = log1p(r12525);
        double r12527 = fmod(r12524, r12526);
        return r12527;
}
↓
double f(double a, double c) {
        double r12528 = exp(1.0);
        double r12529 = c;
        double r12530 = cosh(r12529);
        double r12531 = a;
        double r12532 = log1p(r12531);
        double r12533 = fmod(r12530, r12532);
        double r12534 = log(r12533);
        double r12535 = pow(r12528, r12534);
        return r12535;
}

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-exp-log34.0

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

  5. Applied pow134.0

    \[\leadsto e^{\log \color{blue}{\left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{1}\right)}}\]

  6. Applied log-pow34.0

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

  7. Applied exp-prod34.0

    \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}}\]

  8. Simplified34.0

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

  10. Applied pow134.0

    \[\leadsto {e}^{\left(\log \color{blue}{\left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{1}\right)}\right)}\]

  11. Applied log-pow34.0

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

  12. Final simplification34.0

    \[\leadsto {e}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}\]

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))