Average Error: 33.4 → 33.4
Time: 35.5s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[{e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)} \cdot {e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
{e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)} \cdot {e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}
double f(double a, double c) {
        double r925238 = c;
        double r925239 = cosh(r925238);
        double r925240 = a;
        double r925241 = log1p(r925240);
        double r925242 = fmod(r925239, r925241);
        return r925242;
}
↓
double f(double a, double c) {
        double r925243 = exp(1.0);
        double r925244 = c;
        double r925245 = cosh(r925244);
        double r925246 = a;
        double r925247 = log1p(r925246);
        double r925248 = fmod(r925245, r925247);
        double r925249 = sqrt(r925248);
        double r925250 = log(r925249);
        double r925251 = pow(r925243, r925250);
        double r925252 = r925251 * r925251;
        return r925252;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 33.4

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

  3. Applied add-exp-log33.4

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

  5. Applied *-un-lft-identity33.4

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

  6. Applied exp-prod33.4

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

  7. Simplified33.4

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

  9. Applied add-sqr-sqrt33.4

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

  10. Applied log-prod33.4

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

  11. Applied unpow-prod-up33.4

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

  12. Final simplification33.4

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

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))