Random Jason Timeout Test 012

Average Error: 60.3 → 59.1

Time: 44.1s

Precision: 64

• could not determine a ground truth for program body

  1. a = 2.5636690231409943e+180

Math

\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]

↓

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

C

double f(double a) {
        double r149591 = a;
        double r149592 = cosh(r149591);
        double r149593 = r149591 * r149591;
        double r149594 = fmod(r149592, r149593);
        double r149595 = log1p(r149591);
        double r149596 = pow(r149594, r149595);
        double r149597 = acos(r149596);
        return r149597;
}

↓

double f(double a) {
        double r149598 = a;
        double r149599 = cosh(r149598);
        double r149600 = r149598 * r149598;
        double r149601 = fmod(r149599, r149600);
        double r149602 = sqrt(r149601);
        double r149603 = exp(r149602);
        double r149604 = sqrt(r149603);
        double r149605 = log(r149604);
        double r149606 = sqrt(r149604);
        double r149607 = log(r149606);
        double r149608 = r149607 + r149607;
        double r149609 = r149605 + r149608;
        double r149610 = r149609 * r149602;
        double r149611 = log1p(r149598);
        double r149612 = pow(r149610, r149611);
        double r149613 = acos(r149612);
        return r149613;
}

Error

Bits error versus a

Derivation

1. Initial program 60.3

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

3. Applied add-log-exp 59.4

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

5. Applied add-sqr-sqrt 59.4

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

6. Applied exp-prod 59.4

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

7. Applied log-pow 59.1

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

9. Applied add-sqr-sqrt 59.1

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

10. Applied log-prod 59.1

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

12. Applied add-sqr-sqrt 59.1

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

13. Applied log-prod 59.1

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

14. Final simplification 59.1

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))