Average Error: 60.9 → 60.0
Time: 50.4s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}\right) + \log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\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(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}\right) + \log \left(\sqrt{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 r17803 = a;
        double r17804 = cosh(r17803);
        double r17805 = r17803 * r17803;
        double r17806 = fmod(r17804, r17805);
        double r17807 = log1p(r17803);
        double r17808 = pow(r17806, r17807);
        double r17809 = acos(r17808);
        return r17809;
}
↓
double f(double a) {
        double r17810 = a;
        double r17811 = cosh(r17810);
        double r17812 = 2.0;
        double r17813 = pow(r17810, r17812);
        double r17814 = fmod(r17811, r17813);
        double r17815 = exp(r17814);
        double r17816 = sqrt(r17815);
        double r17817 = log(r17816);
        double r17818 = r17817 + r17817;
        double r17819 = log1p(r17810);
        double r17820 = pow(r17818, r17819);
        double r17821 = acos(r17820);
        return r17821;
}

Error

Bits error versus a

Derivation

  1. Initial program 60.9

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

  3. Applied add-log-exp60.0

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

  4. Simplified60.0

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

  6. Applied add-sqr-sqrt60.1

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

  7. Applied log-prod60.0

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

  8. Final simplification60.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))