Average Error: 61.0 → 60.1
Time: 50.4s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \left(\frac{1}{2} \cdot \log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}\right) + \log \left(\sqrt{\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}}\right)\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\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 \cdot a\right)\right)}}\right) + \left(\frac{1}{2} \cdot \log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}\right) + \log \left(\sqrt{\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}}\right)\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
double f(double a) {
        double r20811 = a;
        double r20812 = cosh(r20811);
        double r20813 = r20811 * r20811;
        double r20814 = fmod(r20812, r20813);
        double r20815 = log1p(r20811);
        double r20816 = pow(r20814, r20815);
        double r20817 = acos(r20816);
        return r20817;
}
↓
double f(double a) {
        double r20818 = a;
        double r20819 = cosh(r20818);
        double r20820 = r20818 * r20818;
        double r20821 = fmod(r20819, r20820);
        double r20822 = exp(r20821);
        double r20823 = sqrt(r20822);
        double r20824 = log(r20823);
        double r20825 = 0.5;
        double r20826 = 2.0;
        double r20827 = pow(r20818, r20826);
        double r20828 = fmod(r20819, r20827);
        double r20829 = exp(r20828);
        double r20830 = sqrt(r20829);
        double r20831 = log(r20830);
        double r20832 = r20825 * r20831;
        double r20833 = sqrt(r20830);
        double r20834 = log(r20833);
        double r20835 = r20832 + r20834;
        double r20836 = r20824 + r20835;
        double r20837 = log1p(r20818);
        double r20838 = pow(r20836, r20837);
        double r20839 = acos(r20838);
        return r20839;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.0

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

  3. Applied add-log-exp60.1

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

  5. Applied add-sqr-sqrt60.1

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

  6. Applied log-prod60.1

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

  8. Applied add-sqr-sqrt60.1

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

  9. Applied sqrt-prod60.2

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

  10. Applied log-prod60.2

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

  11. Simplified60.2

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

  12. Simplified60.2

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

  14. Applied pow160.2

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

  15. Applied sqrt-pow160.2

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

  16. Applied log-pow60.1

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

  17. Final simplification60.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))