Average Error: 61.2 → 60.1
Time: 37.6s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)} \cdot {\left(2 \cdot \log \left(\sqrt[3]{e^{\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \log \left(\sqrt[3]{e^{\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt[3]{\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}}}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\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(\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)} \cdot {\left(2 \cdot \log \left(\sqrt[3]{e^{\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \log \left(\sqrt[3]{e^{\sqrt[3]{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt[3]{\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}}}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
double code(double a) {
	return acos(pow(fmod(cosh(a), (a * a)), log1p(a)));
}
↓
double code(double a) {
	return acos((pow(cbrt(fmod(cosh(a), (a * a))), log1p(a)) * pow(((2.0 * log(cbrt(exp((cbrt(fmod(cosh(a), (a * a))) * cbrt(fmod(cosh(a), (a * a)))))))) + log(cbrt(exp((cbrt(fmod(cosh(a), (a * a))) * cbrt(log(exp(fmod(cosh(a), (a * a)))))))))), log1p(a))));
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.2

    \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  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

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

  6. Applied exp-prod60.2

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

  7. Applied log-pow60.1

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

  8. Applied unpow-prod-down60.1

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

  10. Applied add-cube-cbrt60.1

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

  11. Applied log-prod60.1

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

  12. Simplified60.1

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

  14. Applied add-log-exp60.1

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

  15. Final simplification60.1

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

Reproduce

herbie shell --seed 2020105 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))