Average Error: 33.9 → 33.9
Time: 14.8s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[e^{\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{2} \cdot \left(2 \cdot \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
e^{\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{2} \cdot \left(2 \cdot \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}}
double code(double a, double c) {
	return fmod(cosh(c), log1p(a));
}
↓
double code(double a, double c) {
	return exp(cbrt((pow(log(fmod(cosh(c), log1p(a))), 2.0) * ((2.0 * log(cbrt(fmod(cosh(c), log1p(a))))) + log(cbrt(fmod(cosh(c), log1p(a))))))));
}

Error

Bits error versus a

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 33.9

    \[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
  2. Using strategy rm

  3. Applied add-exp-log33.9

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

  5. Applied add-cbrt-cube33.9

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

  6. Simplified33.9

    \[\leadsto e^{\sqrt[3]{\color{blue}{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{3}}}}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt33.9

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

  9. Applied unpow-prod-down33.9

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

  10. Simplified33.9

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

  11. Simplified33.9

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

  13. Applied add-cube-cbrt33.9

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

  14. Applied log-prod33.9

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

  15. Simplified33.9

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

  16. Final simplification33.9

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

Reproduce

herbie shell --seed 2020105 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))