Average Error: 61.0 → 60.1
Time: 28.1s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\cos^{-1} \left({\left(\log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \left(\log \left(\sqrt{\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \left(\log \left(\sqrt{\sqrt{\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}}\right) + \log \left(\sqrt{\sqrt{\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}}\right)\right)\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\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(\log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \left(\log \left(\sqrt{\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \left(\log \left(\sqrt{\sqrt{\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}}\right) + \log \left(\sqrt{\sqrt{\sqrt{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\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((log(sqrt(exp(fmod(cosh(a), (a * a))))) + (log(sqrt(sqrt(exp(fmod(cosh(a), (a * a)))))) + (log(sqrt(sqrt(sqrt(exp(fmod(cosh(a), (a * a))))))) + log(sqrt(sqrt(sqrt(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 61.0

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

  3. Applied add-log-exp60.1

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

  5. Applied add-sqr-sqrt60.1

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

  6. Applied log-prod60.1

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

  8. Applied add-sqr-sqrt60.1

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

  9. Applied sqrt-prod60.1

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

  10. Applied log-prod60.1

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

  12. Applied add-sqr-sqrt60.1

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

  13. Applied sqrt-prod60.1

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

  14. Applied sqrt-prod60.1

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

  15. Applied log-prod60.1

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

  16. Final simplification60.1

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

Reproduce

herbie shell --seed 2020092 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))