Average Error: 34.4 → 34.5
Time: 14.5s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[e^{\left(\sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
e^{\left(\sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}
double code(double a, double c) {
	return ((double) fmod(((double) cosh(c)), ((double) log1p(a))));
}
↓
double code(double a, double c) {
	return ((double) exp(((double) (((double) (((double) cbrt(((double) log(((double) fmod(((double) (((double) exp(((double) log(((double) (0.041666666666666664 * ((double) pow(c, 4.0)))))))) + ((double) (((double) (0.5 * ((double) pow(c, 2.0)))) + 1.0)))), ((double) log1p(a)))))))) * ((double) cbrt(((double) log(((double) fmod(((double) (((double) exp(((double) log(((double) (0.041666666666666664 * ((double) pow(c, 4.0)))))))) + ((double) (((double) (0.5 * ((double) pow(c, 2.0)))) + 1.0)))), ((double) log1p(a)))))))))) * ((double) cbrt(((double) log(((double) fmod(((double) (((double) exp(((double) log(((double) (0.041666666666666664 * ((double) pow(c, 4.0)))))))) + ((double) (((double) (0.5 * ((double) pow(c, 2.0)))) + 1.0)))), ((double) 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. Taylor expanded around 0 34.5

    \[\leadsto \left(\color{blue}{\left(\frac{1}{24} \cdot {c}^{4} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
  3. Using strategy rm

  4. Applied add-exp-log49.0

    \[\leadsto \left(\left(\frac{1}{24} \cdot {\color{blue}{\left(e^{\log c}\right)}}^{4} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  5. Applied pow-exp49.0

    \[\leadsto \left(\left(\frac{1}{24} \cdot \color{blue}{e^{\log c \cdot 4}} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  6. Applied add-exp-log49.0

    \[\leadsto \left(\left(\color{blue}{e^{\log \frac{1}{24}}} \cdot e^{\log c \cdot 4} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  7. Applied prod-exp49.0

    \[\leadsto \left(\left(\color{blue}{e^{\log \frac{1}{24} + \log c \cdot 4}} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  8. Simplified34.5

    \[\leadsto \left(\left(e^{\color{blue}{\log \left(\frac{1}{24} \cdot {c}^{4}\right)}} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
  9. Using strategy rm

  10. Applied add-exp-log34.5

    \[\leadsto \color{blue}{e^{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]
  11. Using strategy rm

  12. Applied add-cube-cbrt34.5

    \[\leadsto e^{\color{blue}{\left(\sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\]

  13. Final simplification34.5

    \[\leadsto e^{\left(\sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(e^{\log \left(\frac{1}{24} \cdot {c}^{4}\right)} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

Reproduce

herbie shell --seed 2020123 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))