Average Error: 61.2 → 59.3
Time: 27.5s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\frac{\mathsf{fma}\left(-\pi, \mathsf{fma}\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right), \mathsf{fma}\left(\frac{1}{2}, \pi, \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right), \frac{1}{4} \cdot \left(\pi \cdot \pi\right)\right), 2 \cdot \left({\left(\frac{1}{2} \cdot \pi\right)}^{3} - {\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}\right)\right)}{\left(-\mathsf{fma}\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right), \mathsf{fma}\left(\frac{1}{2}, \pi, \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right), \frac{1}{4} \cdot \left(\pi \cdot \pi\right)\right)\right) \cdot 2}\]
\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, \mathsf{fma}\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right), \mathsf{fma}\left(\frac{1}{2}, \pi, \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right), \frac{1}{4} \cdot \left(\pi \cdot \pi\right)\right), 2 \cdot \left({\left(\frac{1}{2} \cdot \pi\right)}^{3} - {\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}\right)\right)}{\left(-\mathsf{fma}\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right), \mathsf{fma}\left(\frac{1}{2}, \pi, \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right), \frac{1}{4} \cdot \left(\pi \cdot \pi\right)\right)\right) \cdot 2}
double code(double a) {
	return acos(pow(fmod(cosh(a), (a * a)), log1p(a)));
}
↓
double code(double a) {
	return (fma(-((double) M_PI), fma(acos(pow(fmod(cosh(a), pow(a, 2.0)), log1p(a))), fma(0.5, ((double) M_PI), acos(pow(fmod(cosh(a), (a * a)), log1p(a)))), (0.25 * (((double) M_PI) * ((double) M_PI)))), (2.0 * (pow((0.5 * ((double) M_PI)), 3.0) - pow(acos(pow(fmod(cosh(a), (a * a)), log1p(a))), 3.0)))) / (-fma(acos(pow(fmod(cosh(a), pow(a, 2.0)), log1p(a))), fma(0.5, ((double) M_PI), acos(pow(fmod(cosh(a), (a * a)), log1p(a)))), (0.25 * (((double) M_PI) * ((double) M_PI)))) * 2.0));
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.2

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

  3. Applied acos-asin61.2

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

  5. Applied asin-acos61.2

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

  6. Simplified61.2

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

  8. Applied flip3--61.2

    \[\leadsto \frac{\pi}{2} - \color{blue}{\frac{{\left(\frac{1}{2} \cdot \pi\right)}^{3} - {\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{\left(\frac{1}{2} \cdot \pi\right) \cdot \left(\frac{1}{2} \cdot \pi\right) + \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \left(\frac{1}{2} \cdot \pi\right) \cdot \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}}\]

  9. Applied frac-2neg61.2

    \[\leadsto \color{blue}{\frac{-\pi}{-2}} - \frac{{\left(\frac{1}{2} \cdot \pi\right)}^{3} - {\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{\left(\frac{1}{2} \cdot \pi\right) \cdot \left(\frac{1}{2} \cdot \pi\right) + \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \left(\frac{1}{2} \cdot \pi\right) \cdot \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}\]

  10. Applied frac-sub61.2

    \[\leadsto \color{blue}{\frac{\left(-\pi\right) \cdot \left(\left(\frac{1}{2} \cdot \pi\right) \cdot \left(\frac{1}{2} \cdot \pi\right) + \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \left(\frac{1}{2} \cdot \pi\right) \cdot \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right) - \left(-2\right) \cdot \left({\left(\frac{1}{2} \cdot \pi\right)}^{3} - {\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}\right)}{\left(-2\right) \cdot \left(\left(\frac{1}{2} \cdot \pi\right) \cdot \left(\frac{1}{2} \cdot \pi\right) + \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \left(\frac{1}{2} \cdot \pi\right) \cdot \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)}}\]

  11. Simplified59.3

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

  12. Simplified59.3

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

  13. Final simplification59.3

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

Reproduce

herbie shell --seed 2020071 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))