Average Error: 34.8 → 34.9
Time: 12.7s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
↓
\[\left(\left(\left(\frac{1}{24} \cdot {c}^{2}\right) \cdot {c}^{2} + \left(\frac{1}{2} \cdot {c}^{2} + 1\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)
↓
\left(\left(\left(\frac{1}{24} \cdot {c}^{2}\right) \cdot {c}^{2} + \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 fmod(cosh(c), log1p(a));
}
↓
double code(double a, double c) {
	return fmod((((0.041666666666666664 * pow(c, 2.0)) * pow(c, 2.0)) + ((0.5 * pow(c, 2.0)) + 1.0)), 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 34.8

    \[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

  2. Taylor expanded around 0 34.9

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

  4. Applied sqr-pow34.9

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

  5. Applied associate-*r*34.9

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

  6. Simplified34.9

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

  7. Final simplification34.9

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

Reproduce

herbie shell --seed 2020071 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))