Average Error: 61.1 → 60.2
Time: 49.3s
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 r15024 = a;
        double r15025 = cosh(r15024);
        double r15026 = r15024 * r15024;
        double r15027 = fmod(r15025, r15026);
        double r15028 = log1p(r15024);
        double r15029 = pow(r15027, r15028);
        double r15030 = acos(r15029);
        return r15030;
}
↓
double f(double a) {
        double r15031 = a;
        double r15032 = cosh(r15031);
        double r15033 = 2.0;
        double r15034 = pow(r15031, r15033);
        double r15035 = fmod(r15032, r15034);
        double r15036 = exp(r15035);
        double r15037 = log(r15036);
        double r15038 = log1p(r15031);
        double r15039 = pow(r15037, r15038);
        double r15040 = acos(r15039);
        return r15040;
}

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 2019174 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))