Random Jason Timeout Test 012

Average Error: 61.3 → 60.4

Time: 29.3s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.023379392650477e+110

Math

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

↓

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

C

double f(double a) {
        double r2738 = a;
        double r2739 = cosh(r2738);
        double r2740 = r2738 * r2738;
        double r2741 = fmod(r2739, r2740);
        double r2742 = log1p(r2738);
        double r2743 = pow(r2741, r2742);
        double r2744 = acos(r2743);
        return r2744;
}

↓

double f(double a) {
        double r2745 = a;
        double r2746 = cosh(r2745);
        double r2747 = r2745 * r2745;
        double r2748 = fmod(r2746, r2747);
        double r2749 = exp(r2748);
        double r2750 = log(r2749);
        double r2751 = log1p(r2745);
        double r2752 = pow(r2750, r2751);
        double r2753 = acos(r2752);
        double r2754 = exp(r2753);
        double r2755 = sqrt(r2754);
        double r2756 = log(r2755);
        double r2757 = r2756 + r2756;
        return r2757;
}

Error

Bits error versus a

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-exp 60.4

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

5. Applied add-log-exp 60.4

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

7. Applied add-sqr-sqrt 60.4

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

8. Applied log-prod 60.4

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

9. Final simplification 60.4

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

Reproduce

herbie shell --seed 2020062 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))