Average Error: 34.3 → 34.3
Time: 33.3s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\left(\left(e^{e^{\log \left(\log \left(\cosh c\right)\right)}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\left(\left(e^{e^{\log \left(\log \left(\cosh c\right)\right)}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
double f(double a, double c) {
        double r578355 = c;
        double r578356 = cosh(r578355);
        double r578357 = a;
        double r578358 = log1p(r578357);
        double r578359 = fmod(r578356, r578358);
        return r578359;
}
↓
double f(double a, double c) {
        double r578360 = c;
        double r578361 = cosh(r578360);
        double r578362 = log(r578361);
        double r578363 = log(r578362);
        double r578364 = exp(r578363);
        double r578365 = exp(r578364);
        double r578366 = a;
        double r578367 = log1p(r578366);
        double r578368 = fmod(r578365, r578367);
        return r578368;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.3

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

  3. Applied add-exp-log34.3

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

  5. Applied add-exp-log34.3

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

  6. Final simplification34.3

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

Reproduce

herbie shell --seed 2019124 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))