Average Error: 61.1 → 60.2
Time: 50.5s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
double f(double a) {
        double r21962 = a;
        double r21963 = cosh(r21962);
        double r21964 = r21962 * r21962;
        double r21965 = fmod(r21963, r21964);
        double r21966 = log1p(r21962);
        double r21967 = pow(r21965, r21966);
        double r21968 = acos(r21967);
        return r21968;
}
↓
double f(double a) {
        double r21969 = a;
        double r21970 = cosh(r21969);
        double r21971 = 2.0;
        double r21972 = pow(r21969, r21971);
        double r21973 = fmod(r21970, r21972);
        double r21974 = exp(r21973);
        double r21975 = log(r21974);
        double r21976 = log1p(r21969);
        double r21977 = pow(r21975, r21976);
        double r21978 = acos(r21977);
        return r21978;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.1

    \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  2. Using strategy rm

  3. Applied add-log-exp60.2

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

  4. Simplified60.2

    \[\leadsto \cos^{-1} \left({\left(\log \color{blue}{\left(e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

  5. Final simplification60.2

    \[\leadsto \cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))