Average Error: 61.1 → 60.2
Time: 29.5s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left(\left(\sqrt[3]{{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}} \cdot \sqrt[3]{{\left(e^{\log \left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{3}}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right)\]
\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(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}} \cdot \sqrt[3]{{\left(e^{\log \left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{3}}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right)
double code(double a) {
	return ((double) acos(((double) pow(((double) fmod(((double) cosh(a)), ((double) (a * a)))), ((double) log1p(a))))));
}
↓
double code(double a) {
	return ((double) acos(((double) (((double) (((double) cbrt(((double) pow(((double) log(((double) exp(((double) fmod(((double) cosh(a)), ((double) (a * a)))))))), ((double) log1p(a)))))) * ((double) cbrt(((double) pow(((double) exp(((double) log(((double) fmod(((double) cosh(a)), ((double) (a * a)))))))), ((double) log1p(a)))))))) * ((double) cbrt(((double) pow(((double) cbrt(((double) pow(((double) fmod(((double) cosh(a)), ((double) (a * a)))), 3.0)))), ((double) 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 61.1

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

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

  7. Applied add-cbrt-cube60.2

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

  8. Simplified60.2

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

  10. Applied add-exp-log60.2

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

  11. Simplified60.2

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

  12. Final simplification60.2

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

Reproduce

herbie shell --seed 2020114 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))