Average Error: 34.4 → 34.4
Time: 14.5s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(e^{\sqrt[3]{{\left(\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{3}}\right)}^{3}}}\right)\right)\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(e^{\sqrt[3]{{\left(\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{3}}\right)}^{3}}}\right)\right)
double f(double a, double c) {
        double r9879 = c;
        double r9880 = cosh(r9879);
        double r9881 = a;
        double r9882 = log1p(r9881);
        double r9883 = fmod(r9880, r9882);
        return r9883;
}
↓
double f(double a, double c) {
        double r9884 = c;
        double r9885 = cosh(r9884);
        double r9886 = a;
        double r9887 = log1p(r9886);
        double r9888 = fmod(r9885, r9887);
        double r9889 = log(r9888);
        double r9890 = 3.0;
        double r9891 = pow(r9889, r9890);
        double r9892 = cbrt(r9891);
        double r9893 = pow(r9892, r9890);
        double r9894 = cbrt(r9893);
        double r9895 = exp(r9894);
        double r9896 = log1p(r9895);
        double r9897 = expm1(r9896);
        return r9897;
}

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 expm1-log1p-u34.4

    \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)\right)}\]
  4. Using strategy rm

  5. Applied add-exp-log34.4

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)\right)\]
  6. Using strategy rm

  7. Applied add-cbrt-cube34.4

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(e^{\color{blue}{\sqrt[3]{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)\right)\]

  8. Simplified34.4

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(e^{\sqrt[3]{\color{blue}{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{3}}}}\right)\right)\]
  9. Using strategy rm

  10. Applied add-cbrt-cube34.4

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(e^{\sqrt[3]{{\color{blue}{\left(\sqrt[3]{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}}^{3}}}\right)\right)\]

  11. Simplified34.4

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(e^{\sqrt[3]{{\left(\sqrt[3]{\color{blue}{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{3}}}\right)}^{3}}}\right)\right)\]

  12. Final simplification34.4

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(e^{\sqrt[3]{{\left(\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{3}}\right)}^{3}}}\right)\right)\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))