Average Error: 61.3 → 60.4
Time: 42.1s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\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 \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
double f(double a) {
        double r8780 = a;
        double r8781 = cosh(r8780);
        double r8782 = r8780 * r8780;
        double r8783 = fmod(r8781, r8782);
        double r8784 = log1p(r8780);
        double r8785 = pow(r8783, r8784);
        double r8786 = acos(r8785);
        return r8786;
}
↓
double f(double a) {
        double r8787 = a;
        double r8788 = cosh(r8787);
        double r8789 = r8787 * r8787;
        double r8790 = fmod(r8788, r8789);
        double r8791 = exp(r8790);
        double r8792 = log(r8791);
        double r8793 = log1p(r8787);
        double r8794 = pow(r8792, r8793);
        double r8795 = acos(r8794);
        return r8795;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.3

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

  3. Applied add-log-exp60.4

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

  4. Final simplification60.4

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))