Average Error: 61.3 → 60.5
Time: 36.3s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\sqrt[3]{{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{3}}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\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(\sqrt[3]{{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{3}}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
double f(double a) {
        double r6721 = a;
        double r6722 = cosh(r6721);
        double r6723 = r6721 * r6721;
        double r6724 = fmod(r6722, r6723);
        double r6725 = log1p(r6721);
        double r6726 = pow(r6724, r6725);
        double r6727 = acos(r6726);
        return r6727;
}
↓
double f(double a) {
        double r6728 = a;
        double r6729 = cosh(r6728);
        double r6730 = 2.0;
        double r6731 = pow(r6728, r6730);
        double r6732 = fmod(r6729, r6731);
        double r6733 = 3.0;
        double r6734 = pow(r6732, r6733);
        double r6735 = cbrt(r6734);
        double r6736 = log1p(r6728);
        double r6737 = pow(r6735, r6736);
        double r6738 = acos(r6737);
        return r6738;
}

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-exp60.3

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

  5. Applied add-cbrt-cube60.3

    \[\leadsto \cos^{-1} \left({\color{blue}{\left(\sqrt[3]{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right) \cdot \log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right) \cdot \log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

  6. Simplified60.5

    \[\leadsto \cos^{-1} \left({\left(\sqrt[3]{\color{blue}{{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{3}}}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

  7. Final simplification60.5

    \[\leadsto \cos^{-1} \left({\left(\sqrt[3]{{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{3}}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))