Average Error: 61.3 → 60.5
Time: 37.5s
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 r8743 = a;
        double r8744 = cosh(r8743);
        double r8745 = r8743 * r8743;
        double r8746 = fmod(r8744, r8745);
        double r8747 = log1p(r8743);
        double r8748 = pow(r8746, r8747);
        double r8749 = acos(r8748);
        return r8749;
}
↓
double f(double a) {
        double r8750 = a;
        double r8751 = cosh(r8750);
        double r8752 = 2.0;
        double r8753 = pow(r8750, r8752);
        double r8754 = fmod(r8751, r8753);
        double r8755 = 3.0;
        double r8756 = pow(r8754, r8755);
        double r8757 = cbrt(r8756);
        double r8758 = log1p(r8750);
        double r8759 = pow(r8757, r8758);
        double r8760 = acos(r8759);
        return r8760;
}

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))))