Average Error: 34.3 → 34.3
Time: 31.0s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[e^{\log \left(\left(\mathsf{expm1}\left(\left(e^{\log \left(\mathsf{log1p}\left(\left(\cosh c\right)\right)\right)}\right)\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
e^{\log \left(\left(\mathsf{expm1}\left(\left(e^{\log \left(\mathsf{log1p}\left(\left(\cosh c\right)\right)\right)}\right)\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}
double f(double a, double c) {
        double r216013 = c;
        double r216014 = cosh(r216013);
        double r216015 = a;
        double r216016 = log1p(r216015);
        double r216017 = fmod(r216014, r216016);
        return r216017;
}
↓
double f(double a, double c) {
        double r216018 = c;
        double r216019 = cosh(r216018);
        double r216020 = log1p(r216019);
        double r216021 = log(r216020);
        double r216022 = exp(r216021);
        double r216023 = expm1(r216022);
        double r216024 = a;
        double r216025 = log1p(r216024);
        double r216026 = fmod(r216023, r216025);
        double r216027 = log(r216026);
        double r216028 = exp(r216027);
        return r216028;
}

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

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

  5. Applied expm1-log1p-u34.3

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

  7. Applied add-exp-log34.3

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

  8. Final simplification34.3

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))