Average Error: 61.2 → 60.3
Time: 36.6s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\log \left(e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\log \left(e^{\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)}\right)
double f(double a) {
        double r7805 = a;
        double r7806 = cosh(r7805);
        double r7807 = r7805 * r7805;
        double r7808 = fmod(r7806, r7807);
        double r7809 = log1p(r7805);
        double r7810 = pow(r7808, r7809);
        double r7811 = acos(r7810);
        return r7811;
}
↓
double f(double a) {
        double r7812 = a;
        double r7813 = cosh(r7812);
        double r7814 = 2.0;
        double r7815 = pow(r7812, r7814);
        double r7816 = fmod(r7813, r7815);
        double r7817 = exp(r7816);
        double r7818 = log(r7817);
        double r7819 = log1p(r7812);
        double r7820 = pow(r7818, r7819);
        double r7821 = acos(r7820);
        double r7822 = exp(r7821);
        double r7823 = log(r7822);
        return r7823;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.2

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

  3. Applied add-log-exp60.3

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

  5. Applied add-log-exp60.3

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

  6. Simplified61.2

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

  8. Applied add-log-exp60.3

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

  9. Final simplification60.3

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))