Average Error: 60.5 → 59.4
Time: 46.3s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\left(\log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \log \left(\sqrt{e^{\sqrt{\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}}}\right)\right) \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)\]
double f(double a) {
        double r99785 = a;
        double r99786 = cosh(r99785);
        double r99787 = r99785 * r99785;
        double r99788 = fmod(r99786, r99787);
        double r99789 = log1p(r99785);
        double r99790 = pow(r99788, r99789);
        double r99791 = acos(r99790);
        return r99791;
}
↓
double f(double a) {
        double r99792 = a;
        double r99793 = cosh(r99792);
        double r99794 = r99792 * r99792;
        double r99795 = fmod(r99793, r99794);
        double r99796 = sqrt(r99795);
        double r99797 = exp(r99796);
        double r99798 = sqrt(r99797);
        double r99799 = log(r99798);
        double r99800 = exp(r99795);
        double r99801 = log(r99800);
        double r99802 = sqrt(r99801);
        double r99803 = exp(r99802);
        double r99804 = sqrt(r99803);
        double r99805 = log(r99804);
        double r99806 = r99799 + r99805;
        double r99807 = r99806 * r99796;
        double r99808 = log1p(r99792);
        double r99809 = pow(r99807, r99808);
        double r99810 = acos(r99809);
        return r99810;
}


\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)
↓
\cos^{-1} \left({\left(\left(\log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \log \left(\sqrt{e^{\sqrt{\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}}}\right)\right) \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)

Error

Bits error versus a

Derivation

  1. Initial program 60.5

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

  3. Applied add-log-exp59.6

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

  5. Applied add-sqr-sqrt59.6

    \[\leadsto \cos^{-1} \left({\left(\log \left(e^{\color{blue}{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]

  6. Applied exp-prod59.6

    \[\leadsto \cos^{-1} \left({\left(\log \color{blue}{\left({\left(e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)}^{\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)\]

  7. Applied log-pow59.3

    \[\leadsto \cos^{-1} \left({\color{blue}{\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \log \left(e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right)\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt59.3

    \[\leadsto \cos^{-1} \left({\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \log \color{blue}{\left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}} \cdot \sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)\]

  10. Applied log-prod59.3

    \[\leadsto \cos^{-1} \left({\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \color{blue}{\left(\log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)\]
  11. Using strategy rm

  12. Applied add-log-exp59.4

    \[\leadsto \cos^{-1} \left({\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \left(\log \left(\sqrt{e^{\sqrt{\color{blue}{\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}}}}\right) + \log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right)\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]

  13. Final simplification59.4

    \[\leadsto \cos^{-1} \left({\left(\left(\log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \log \left(\sqrt{e^{\sqrt{\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}}}\right)\right) \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)\]

Reproduce

herbie shell --seed 2019102 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))