Average Error: 34.4 → 34.4
Time: 13.2s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[{\left(\sqrt[3]{\sqrt{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}} \cdot \sqrt[3]{\sqrt{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{3} \cdot \sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
{\left(\sqrt[3]{\sqrt{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}} \cdot \sqrt[3]{\sqrt{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{3} \cdot \sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}
double code(double a, double c) {
	return fmod(cosh(c), log1p(a));
}
↓
double code(double a, double c) {
	return (pow((cbrt(sqrt(sqrt(fmod(cosh(c), log1p(a))))) * cbrt(sqrt(sqrt(fmod(cosh(c), log1p(a)))))), 3.0) * sqrt(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 34.4

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

  3. Applied add-sqr-sqrt34.4

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

  5. Applied add-sqr-sqrt34.4

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

  6. Applied sqrt-prod34.4

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

  7. Applied associate-*r*34.4

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

  8. Simplified34.4

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

  10. Applied add-cube-cbrt34.4

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

  11. Applied unpow-prod-down34.4

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

  12. Applied associate-*l*34.4

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

  13. Simplified34.4

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

  14. Final simplification34.4

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

Reproduce

herbie shell --seed 2020091 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))