Random Jason Timeout Test 012

Average Error: 60.4 → 59.5

Time: 41.7s

Precision: 64

• could not determine a ground truth for program body

  1. a = 8.049456502996968e+74

Math

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

↓

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

C

double f(double a) {
        double r119676 = a;
        double r119677 = cosh(r119676);
        double r119678 = r119676 * r119676;
        double r119679 = fmod(r119677, r119678);
        double r119680 = log1p(r119676);
        double r119681 = pow(r119679, r119680);
        double r119682 = acos(r119681);
        return r119682;
}

↓

double f(double a) {
        double r119683 = a;
        double r119684 = cosh(r119683);
        double r119685 = r119683 * r119683;
        double r119686 = fmod(r119684, r119685);
        double r119687 = exp(r119686);
        double r119688 = sqrt(r119687);
        double r119689 = log(r119688);
        double r119690 = 0.5;
        double r119691 = log(r119687);
        double r119692 = r119690 * r119691;
        double r119693 = r119689 + r119692;
        double r119694 = log1p(r119683);
        double r119695 = pow(r119693, r119694);
        double r119696 = acos(r119695);
        return r119696;
}

Error

Bits error versus a

Derivation

1. Initial program 60.4

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

3. Applied add-log-exp 59.5

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

5. Applied add-sqr-sqrt 59.5

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

6. Applied log-prod 59.5

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

8. Applied pow1 59.5

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

9. Applied sqrt-pow1 59.5

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

10. Applied log-pow 59.5

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

11. Simplified 59.5

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

12. Final simplification 59.5

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

Reproduce

herbie shell --seed 2019121 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))