Average Error: 61.1 → 60.2
Time: 26.5s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[e^{\left(\sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}}\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
e^{\left(\sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\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)\right)\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\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)\right)\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\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)\right)\right)}}
double code(double a) {
	return acos(pow(fmod(cosh(a), (a * a)), log1p(a)));
}
↓
double code(double a) {
	return exp(((cbrt(log1p(expm1(log(acos(pow(log(exp(fmod(cosh(a), (a * a)))), log1p(a))))))) * cbrt(log1p(expm1(log(acos(pow(log(exp(fmod(cosh(a), (a * a)))), log1p(a)))))))) * cbrt(log1p(expm1(log(acos(pow(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 61.1

    \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  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-exp-log60.2

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

  7. Applied log1p-expm1-u60.2

    \[\leadsto e^{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt60.2

    \[\leadsto e^{\color{blue}{\left(\sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}}}\]

  10. Final simplification60.2

    \[\leadsto e^{\left(\sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left(\log \left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)\right)}}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))