Average Error: 33.8 → 33.8
Time: 32.2s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\left(\left(\sqrt{e^{e^{\log \left(\log \left(\cosh c\right)\right)}}} \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\left(\left(\sqrt{e^{e^{\log \left(\log \left(\cosh c\right)\right)}}} \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
double f(double a, double c) {
        double r20698 = c;
        double r20699 = cosh(r20698);
        double r20700 = a;
        double r20701 = log1p(r20700);
        double r20702 = fmod(r20699, r20701);
        return r20702;
}
↓
double f(double a, double c) {
        double r20703 = c;
        double r20704 = cosh(r20703);
        double r20705 = log(r20704);
        double r20706 = log(r20705);
        double r20707 = exp(r20706);
        double r20708 = exp(r20707);
        double r20709 = sqrt(r20708);
        double r20710 = sqrt(r20704);
        double r20711 = r20709 * r20710;
        double r20712 = a;
        double r20713 = log1p(r20712);
        double r20714 = fmod(r20711, r20713);
        return r20714;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 33.8

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

  3. Applied add-sqr-sqrt33.8

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

  5. Applied add-exp-log33.8

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

  7. Applied add-exp-log33.8

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

  8. Final simplification33.8

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

Reproduce

herbie shell --seed 2019208 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))