Average Error: 61.2 → 59.0
Time: 37.0s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le 1.5952721721417026 \cdot 10^{-162}:\\ \;\;\;\;\cos^{-1} \left({\left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)}^{\left(\log \left(e^{\sqrt{\mathsf{log1p}\left(a\right)}}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{2} - \sin^{-1} \left({\left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)\\ \end{array}\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\begin{array}{l}
\mathbf{if}\;a \le 1.5952721721417026 \cdot 10^{-162}:\\
\;\;\;\;\cos^{-1} \left({\left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)}^{\left(\log \left(e^{\sqrt{\mathsf{log1p}\left(a\right)}}\right)\right)}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{\pi}{2} - \sin^{-1} \left({\left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)\\

\end{array}
double code(double a) {
	return acos(pow(fmod(cosh(a), (a * a)), log1p(a)));
}
↓
double code(double a) {
	double VAR;
	if ((a <= 1.5952721721417026e-162)) {
		VAR = acos(pow(pow(log(exp(fmod(cosh(a), (a * a)))), sqrt(log1p(a))), log(exp(sqrt(log1p(a))))));
	} else {
		VAR = ((((double) M_PI) / 2.0) - asin(pow(pow(log(exp(fmod(cosh(a), (a * a)))), sqrt(log1p(a))), sqrt(log1p(a)))));
	}
	return VAR;
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if a < 1.5952721721417026e-162

    1. Initial program 64.0

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

    3. Applied add-log-exp64.0

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

    5. Applied add-sqr-sqrt64.0

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

    6. Applied pow-unpow64.0

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

    8. Applied add-log-exp61.3

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

    if 1.5952721721417026e-162 < a

    1. Initial program 58.6

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

    3. Applied add-log-exp56.9

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

    5. Applied add-sqr-sqrt56.9

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

    6. Applied pow-unpow56.9

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

    8. Applied acos-asin56.9

      \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left({\left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification59.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le 1.5952721721417026 \cdot 10^{-162}:\\ \;\;\;\;\cos^{-1} \left({\left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)}^{\left(\log \left(e^{\sqrt{\mathsf{log1p}\left(a\right)}}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{2} - \sin^{-1} \left({\left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)}^{\left(\sqrt{\mathsf{log1p}\left(a\right)}\right)}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))