Random Jason Timeout Test 012

Average Error: 61.0 → 60.1

Time: 28.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.611838088146848e+293

Math

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

↓

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

C

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) acos(((double) (((double) (((double) cbrt(((double) pow(((double) log(((double) exp(((double) fmod(((double) cosh(a)), ((double) (a * a)))))))), ((double) log1p(a)))))) * ((double) cbrt(((double) pow(((double) log(((double) exp(((double) fmod(((double) cosh(a)), ((double) (a * a)))))))), ((double) log1p(a)))))))) * ((double) cbrt(((double) pow(((double) fmod(((double) cosh(a)), ((double) (a * a)))), ((double) log1p(a))))))))));
}

Error

Bits error versus a

Derivation

1. Initial program 61.0

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

3. Applied add-log-exp 60.1

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

5. Applied add-cube-cbrt 60.1

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

7. Applied rem-log-exp 60.1

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

8. Final simplification 60.1

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

Reproduce

herbie shell --seed 2020113 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))