Average Error: 61.1 → 60.3
Time: 32.0s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\left(\sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right) \cdot \sqrt[3]{\cos^{-1} \left({\left(2 \cdot \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\left(\sqrt[3]{\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)} \cdot \sqrt[3]{\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) \cdot \sqrt[3]{\cos^{-1} \left({\left(2 \cdot \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}
double f(double a) {
        double r13134 = a;
        double r13135 = cosh(r13134);
        double r13136 = r13134 * r13134;
        double r13137 = fmod(r13135, r13136);
        double r13138 = log1p(r13134);
        double r13139 = pow(r13137, r13138);
        double r13140 = acos(r13139);
        return r13140;
}
↓
double f(double a) {
        double r13141 = a;
        double r13142 = cosh(r13141);
        double r13143 = r13141 * r13141;
        double r13144 = fmod(r13142, r13143);
        double r13145 = exp(r13144);
        double r13146 = log(r13145);
        double r13147 = log1p(r13141);
        double r13148 = pow(r13146, r13147);
        double r13149 = acos(r13148);
        double r13150 = cbrt(r13149);
        double r13151 = r13150 * r13150;
        double r13152 = 2.0;
        double r13153 = cbrt(r13145);
        double r13154 = log(r13153);
        double r13155 = r13152 * r13154;
        double r13156 = r13155 + r13154;
        double r13157 = pow(r13156, r13147);
        double r13158 = acos(r13157);
        double r13159 = cbrt(r13158);
        double r13160 = r13151 * r13159;
        return r13160;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.1

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

  3. Applied add-log-exp60.2

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

  5. Applied add-cube-cbrt60.2

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

  7. Applied add-cube-cbrt60.3

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

  8. Applied log-prod60.3

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

  9. Simplified60.3

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

  10. Final simplification60.3

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

Reproduce

herbie shell --seed 2019322 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))