Random Jason Timeout Test 004

Average Error: 34.5 → 34.5

Time: 14.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = -1.6114834637609747e-176
  2. c = -3.4877376356874454e+65

Math

\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

↓

\[{\left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{1}{3}}\right)}^{3}\]

C

double f(double a, double c) {
        double r12679 = c;
        double r12680 = cosh(r12679);
        double r12681 = a;
        double r12682 = log1p(r12681);
        double r12683 = fmod(r12680, r12682);
        return r12683;
}

↓

double f(double a, double c) {
        double r12684 = c;
        double r12685 = cosh(r12684);
        double r12686 = a;
        double r12687 = log1p(r12686);
        double r12688 = fmod(r12685, r12687);
        double r12689 = 0.3333333333333333;
        double r12690 = pow(r12688, r12689);
        double r12691 = 3.0;
        double r12692 = pow(r12690, r12691);
        return r12692;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.5

   \[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
2. Using strategy rm

3. Applied add-exp-log 34.5

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

5. Applied pow1 34.5

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

6. Applied log-pow 34.5

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

7. Applied exp-prod 34.5

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

8. Simplified 34.5

   \[\leadsto {\color{blue}{e}}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}\]
9. Using strategy rm

10. Applied add-cube-cbrt 34.5

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

11. Applied log-prod 34.5

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

12. Simplified 34.5

    \[\leadsto {e}^{\left(\color{blue}{2 \cdot \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)} + \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}\]
13. Using strategy rm

14. Applied pow1 34.5

    \[\leadsto {e}^{\left(2 \cdot \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) + \log \color{blue}{\left({\left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}^{1}\right)}\right)}\]

15. Applied log-pow 34.5

    \[\leadsto {e}^{\left(2 \cdot \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) + \color{blue}{1 \cdot \log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)}\right)}\]

16. Applied distribute-rgt-out 34.5

    \[\leadsto {e}^{\color{blue}{\left(\log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \left(2 + 1\right)\right)}}\]

17. Applied pow-unpow 34.5

    \[\leadsto \color{blue}{{\left({e}^{\left(\log \left(\sqrt[3]{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\right)}\right)}^{\left(2 + 1\right)}}\]

18. Simplified 34.5

    \[\leadsto {\color{blue}{\left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{1}{3}}\right)}}^{\left(2 + 1\right)}\]

19. Final simplification 34.5

    \[\leadsto {\left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{\frac{1}{3}}\right)}^{3}\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))