Average Error: 34.3 → 34.3
Time: 33.5s
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 r604201 = c;
        double r604202 = cosh(r604201);
        double r604203 = a;
        double r604204 = log1p(r604203);
        double r604205 = fmod(r604202, r604204);
        return r604205;
}
↓
double f(double a, double c) {
        double r604206 = c;
        double r604207 = cosh(r604206);
        double r604208 = log(r604207);
        double r604209 = log(r604208);
        double r604210 = exp(r604209);
        double r604211 = exp(r604210);
        double r604212 = a;
        double r604213 = log1p(r604212);
        double r604214 = fmod(r604211, r604213);
        return r604214;
}

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