Average Error: 61.3 → 60.3
Time: 37.3s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\frac{\left(-2 \cdot \left({\left(\frac{1}{2} \cdot \pi\right)}^{3} - {\left(\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}\right) + \frac{1}{4} \cdot {\pi}^{3}\right) + \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \left(\pi \cdot \left(\frac{1}{2} \cdot \pi + \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)}{2 \cdot \left(\frac{1}{4} \cdot \left(\pi \cdot \pi\right)\right) + 2 \cdot \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \frac{1}{2} \cdot \pi\right)\right)}\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\frac{\left(-2 \cdot \left({\left(\frac{1}{2} \cdot \pi\right)}^{3} - {\left(\cos^{-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)}^{3}\right) + \frac{1}{4} \cdot {\pi}^{3}\right) + \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \left(\pi \cdot \left(\frac{1}{2} \cdot \pi + \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)\right)}{2 \cdot \left(\frac{1}{4} \cdot \left(\pi \cdot \pi\right)\right) + 2 \cdot \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \frac{1}{2} \cdot \pi\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) (((double) (((double) (-2.0 * ((double) (((double) pow(((double) (0.5 * ((double) M_PI))), 3.0)) - ((double) pow(((double) acos(((double) pow(((double) log(((double) exp(((double) fmod(((double) cosh(a)), ((double) (a * a)))))))), ((double) log1p(a)))))), 3.0)))))) + ((double) (0.25 * ((double) pow(((double) M_PI), 3.0)))))) + ((double) (((double) acos(((double) pow(((double) fmod(((double) cosh(a)), ((double) pow(a, 2.0)))), ((double) log1p(a)))))) * ((double) (((double) M_PI) * ((double) (((double) (0.5 * ((double) M_PI))) + ((double) acos(((double) pow(((double) fmod(((double) cosh(a)), ((double) pow(a, 2.0)))), ((double) log1p(a)))))))))))))) / ((double) (((double) (2.0 * ((double) (0.25 * ((double) (((double) M_PI) * ((double) M_PI))))))) + ((double) (2.0 * ((double) (((double) acos(((double) pow(((double) fmod(((double) cosh(a)), ((double) pow(a, 2.0)))), ((double) log1p(a)))))) * ((double) (((double) acos(((double) pow(((double) fmod(((double) cosh(a)), ((double) pow(a, 2.0)))), ((double) log1p(a)))))) + ((double) (0.5 * ((double) M_PI)))))))))))));
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.3

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

  3. Applied add-log-exp60.3

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

  5. Applied acos-asin60.3

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

  7. Applied asin-acos60.3

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

  8. Simplified60.3

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

  10. Applied flip3--60.3

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

  11. Applied frac-sub60.3

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

  12. Simplified60.3

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

  13. Simplified60.3

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

  14. Final simplification60.3

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

Reproduce

herbie shell --seed 2020124 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))