Random Jason Timeout Test 012

Average Error: 61.2 → 58.7

Time: 28.4s

Precision: 64

• could not determine a ground truth for program body

  1. a = 5.683788269687683e+223

Math

\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \le 8.9406967163085964 \cdot 10^{-8}:\\ \;\;\;\;\cos^{-1} \left(\left(\sqrt[3]{{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}} \cdot \sqrt[3]{{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right) \cdot \sqrt[3]{{\left(2 \cdot \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)\\ \end{array}\]

C

double code(double a) {
	return acos(pow(fmod(cosh(a), (a * a)), log1p(a)));
}

↓

double code(double a) {
	double temp;
	if ((acos(pow(fmod(cosh(a), (a * a)), log1p(a))) <= 8.940696716308596e-08)) {
		temp = acos(((cbrt(pow(log(exp(fmod(cosh(a), (a * a)))), log1p(a))) * cbrt(pow(log(exp(fmod(cosh(a), (a * a)))), log1p(a)))) * cbrt(pow(((2.0 * log(cbrt(exp(fmod(cosh(a), (a * a)))))) + log(cbrt(exp(fmod(cosh(a), (a * a)))))), log1p(a)))));
	} else {
		temp = acos(pow(fmod(cosh(a), (a * a)), log(exp(log1p(a)))));
	}
	return temp;
}

Error

Bits error versus a

Derivation

1. Split input into 2 regimes

2. if (acos (pow (fmod (cosh a) (* a a)) (log1p a))) < 8.940696716308596e-08

   1. Initial program 61.6

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

   3. Applied add-log-exp 58.9

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

   5. Applied add-cube-cbrt 58.9

      \[\leadsto \cos^{-1} \color{blue}{\left(\left(\sqrt[3]{{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}} \cdot \sqrt[3]{{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right) \cdot \sqrt[3]{{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right)}\]
   6. Using strategy rm

   7. Applied add-cube-cbrt 58.9

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

   8. Applied log-prod 58.9

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

   9. Simplified 58.9

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

   if 8.940696716308596e-08 < (acos (pow (fmod (cosh a) (* a a)) (log1p a)))

   1. Initial program 60.9

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

   3. Applied add-log-exp 58.5

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

4. Final simplification 58.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \le 8.9406967163085964 \cdot 10^{-8}:\\ \;\;\;\;\cos^{-1} \left(\left(\sqrt[3]{{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}} \cdot \sqrt[3]{{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right) \cdot \sqrt[3]{{\left(2 \cdot \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right) + \log \left(\sqrt[3]{e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))