Average Error: 33.9 → 33.6
Time: 17.3s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[e^{\log \left(\left(\cosh c\right) \bmod \left(\left(\left({\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)}}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)\right)}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
e^{\log \left(\left(\cosh c\right) \bmod \left(\left(\left({\left(\sqrt[3]{\mathsf{log1p}\left(a\right)} \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\sqrt[3]{\mathsf{log1p}\left(a\right)}}\right) \cdot \sqrt[3]{\mathsf{log1p}\left(a\right)}\right) \cdot \sqrt[3]{\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 exp(log(fmod(cosh(c), (((pow((cbrt(log1p(a)) * cbrt(log1p(a))), 0.3333333333333333) * cbrt(cbrt(log1p(a)))) * cbrt(log1p(a))) * cbrt(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-cube-cbrt33.6

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

  5. Applied add-cube-cbrt33.6

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

  6. Applied cbrt-prod33.6

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

  8. Applied pow1/333.6

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

  10. Applied add-exp-log33.6

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

  11. Final simplification33.6

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

Reproduce

herbie shell --seed 2020075 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))