Average Error: 34.4 → 34.4
Time: 41.5s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\left(\sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot {\left(\cosh c\right)}^{\left(2 \cdot \frac{1}{6}\right)}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\left(\sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot {\left(\cosh c\right)}^{\left(2 \cdot \frac{1}{6}\right)}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}
double f(double a, double c) {
        double r19890 = c;
        double r19891 = cosh(r19890);
        double r19892 = a;
        double r19893 = log1p(r19892);
        double r19894 = fmod(r19891, r19893);
        return r19894;
}
↓
double f(double a, double c) {
        double r19895 = c;
        double r19896 = cosh(r19895);
        double r19897 = cbrt(r19896);
        double r19898 = r19897 * r19897;
        double r19899 = r19898 * r19897;
        double r19900 = a;
        double r19901 = log1p(r19900);
        double r19902 = fmod(r19899, r19901);
        double r19903 = cbrt(r19902);
        double r19904 = r19903 * r19903;
        double r19905 = 2.0;
        double r19906 = 1.0;
        double r19907 = 6.0;
        double r19908 = r19906 / r19907;
        double r19909 = r19905 * r19908;
        double r19910 = pow(r19896, r19909);
        double r19911 = r19898 * r19910;
        double r19912 = fmod(r19911, r19901);
        double r19913 = cbrt(r19912);
        double r19914 = r19904 * r19913;
        return r19914;
}

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.4

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

  3. Applied add-cube-cbrt34.4

    \[\leadsto \left(\color{blue}{\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
  4. Using strategy rm

  5. Applied add-cube-cbrt34.4

    \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

  6. Taylor expanded around inf 34.4

    \[\leadsto \left(\sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \color{blue}{{\left(\frac{1}{2} \cdot \left(e^{c} + e^{-c}\right)\right)}^{\frac{1}{3}}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

  7. Simplified34.4

    \[\leadsto \left(\sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \color{blue}{{\left(\cosh c\right)}^{\left(2 \cdot \frac{1}{6}\right)}}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]
  8. Using strategy rm

  9. Applied add-exp-log34.4

    \[\leadsto \left(\sqrt[3]{\color{blue}{e^{\log \left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}} \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot {\left(\cosh c\right)}^{\left(2 \cdot \frac{1}{6}\right)}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

  10. Final simplification34.4

    \[\leadsto \left(\sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot {\left(\cosh c\right)}^{\left(2 \cdot \frac{1}{6}\right)}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))