Random Jason Timeout Test 012

Average Error: 61.0 → 60.1

Time: 50.3s

Precision: 64

• could not determine a ground truth for program body

  1. a = 6.699398910899426e+285

Math

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

↓

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

C

double f(double a) {
        double r18610 = a;
        double r18611 = cosh(r18610);
        double r18612 = r18610 * r18610;
        double r18613 = fmod(r18611, r18612);
        double r18614 = log1p(r18610);
        double r18615 = pow(r18613, r18614);
        double r18616 = acos(r18615);
        return r18616;
}

↓

double f(double a) {
        double r18617 = a;
        double r18618 = cosh(r18617);
        double r18619 = 2.0;
        double r18620 = pow(r18617, r18619);
        double r18621 = fmod(r18618, r18620);
        double r18622 = exp(r18621);
        double r18623 = sqrt(r18622);
        double r18624 = log(r18623);
        double r18625 = r18617 * r18617;
        double r18626 = fmod(r18618, r18625);
        double r18627 = exp(r18626);
        double r18628 = sqrt(r18627);
        double r18629 = log(r18628);
        double r18630 = 0.5;
        double r18631 = r18629 * r18630;
        double r18632 = sqrt(r18623);
        double r18633 = log(r18632);
        double r18634 = r18631 + r18633;
        double r18635 = r18624 + r18634;
        double r18636 = log1p(r18617);
        double r18637 = pow(r18635, r18636);
        double r18638 = acos(r18637);
        return r18638;
}

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. Simplified 60.1

   \[\leadsto \cos^{-1} \left({\left(\log \color{blue}{\left(e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}\right)}\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
5. Using strategy rm

6. Applied add-sqr-sqrt 60.1

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

7. Applied log-prod 60.1

   \[\leadsto \cos^{-1} \left({\color{blue}{\left(\log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}\right) + \log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
8. Using strategy rm

9. Applied add-sqr-sqrt 60.1

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

10. Applied sqrt-prod 60.2

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

11. Applied log-prod 60.2

    \[\leadsto \cos^{-1} \left({\left(\color{blue}{\left(\log \left(\sqrt{\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}}\right) + \log \left(\sqrt{\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}}\right)\right)} + \log \left(\sqrt{e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
12. Using strategy rm

13. Applied pow1/2 60.2

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

14. Applied log-pow 60.1

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

15. Simplified 60.1

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

16. Final simplification 60.1

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))