Average Error: 61.1 → 59.3
Time: 37.0s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}
double code(double a) {
	return ((double) acos(((double) pow(((double) fmod(((double) cosh(a)), ((double) (a * a)))), ((double) log1p(a))))));
}
↓
double code(double a) {
	return ((double) (((double) fma(((double) (((double) M_PI) * ((double) M_PI))), 0.25, ((double) (((double) -(1.0)) * ((double) pow(((double) cbrt(((double) asin(((double) pow(((double) fmod(((double) cosh(a)), ((double) (a * a)))), ((double) log1p(a)))))))), 6.0)))))) / ((double) fma(((double) M_PI), 0.5, ((double) asin(((double) pow(((double) fmod(((double) cosh(a)), ((double) pow(a, 2.0)))), ((double) log1p(a))))))))));
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.1

    \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  2. Using strategy rm

  3. Applied add-log-exp60.2

    \[\leadsto \cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  4. Using strategy rm

  5. Applied acos-asin60.2

    \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
  6. Using strategy rm

  7. Applied flip--60.2

    \[\leadsto \color{blue}{\frac{\frac{\pi}{2} \cdot \frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}{\frac{\pi}{2} + \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\]

  8. Simplified60.2

    \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}}{\frac{\pi}{2} + \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]

  9. Simplified60.2

    \[\leadsto \frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\color{blue}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}}\]
  10. Using strategy rm

  11. Applied rem-log-exp59.3

    \[\leadsto \frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\color{blue}{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

  12. Final simplification59.3

    \[\leadsto \frac{\mathsf{fma}\left(\pi \cdot \pi, \frac{1}{4}, \left(-1\right) \cdot {\left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}^{6}\right)}{\mathsf{fma}\left(\pi, \frac{1}{2}, \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

Reproduce

herbie shell --seed 2020122 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))