Random Jason Timeout Test 004

Average Error: 33.9 → 34.0

Time: 13.4s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.5211905892621495e-43
  2. c = -31625873581007.836

Math

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

↓

\[\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left({\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(\left(\sqrt[3]{\sqrt{4}} \cdot \sqrt[3]{\sqrt{4}}\right) \cdot \left(\sqrt[3]{\sqrt{4}} \cdot \sqrt[3]{\sqrt{4}}\right)\right)}\right)}^{\left(\sqrt[3]{4}\right)}\]

C

double f(double a, double c) {
        double r6867 = c;
        double r6868 = cosh(r6867);
        double r6869 = a;
        double r6870 = log1p(r6869);
        double r6871 = fmod(r6868, r6870);
        return r6871;
}

↓

double f(double a, double c) {
        double r6872 = c;
        double r6873 = cosh(r6872);
        double r6874 = a;
        double r6875 = log1p(r6874);
        double r6876 = fmod(r6873, r6875);
        double r6877 = sqrt(r6876);
        double r6878 = cbrt(r6877);
        double r6879 = r6878 * r6878;
        double r6880 = 4.0;
        double r6881 = sqrt(r6880);
        double r6882 = cbrt(r6881);
        double r6883 = r6882 * r6882;
        double r6884 = r6883 * r6883;
        double r6885 = pow(r6878, r6884);
        double r6886 = cbrt(r6880);
        double r6887 = pow(r6885, r6886);
        double r6888 = r6879 * r6887;
        return r6888;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.9

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

3. Applied add-sqr-sqrt 34.0

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

5. Applied add-cube-cbrt 34.0

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

6. Applied associate-*l* 34.0

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

7. Simplified 34.0

   \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot \color{blue}{{\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{4}}\]
8. Using strategy rm

9. Applied add-cube-cbrt 34.0

   \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\color{blue}{\left(\left(\sqrt[3]{4} \cdot \sqrt[3]{4}\right) \cdot \sqrt[3]{4}\right)}}\]

10. Applied pow-unpow 34.0

    \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot \color{blue}{{\left({\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(\sqrt[3]{4} \cdot \sqrt[3]{4}\right)}\right)}^{\left(\sqrt[3]{4}\right)}}\]
11. Using strategy rm

12. Applied add-sqr-sqrt 34.0

    \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left({\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(\sqrt[3]{4} \cdot \sqrt[3]{\color{blue}{\sqrt{4} \cdot \sqrt{4}}}\right)}\right)}^{\left(\sqrt[3]{4}\right)}\]

13. Applied cbrt-prod 34.0

    \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left({\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(\sqrt[3]{4} \cdot \color{blue}{\left(\sqrt[3]{\sqrt{4}} \cdot \sqrt[3]{\sqrt{4}}\right)}\right)}\right)}^{\left(\sqrt[3]{4}\right)}\]

14. Applied add-sqr-sqrt 34.0

    \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left({\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(\sqrt[3]{\color{blue}{\sqrt{4} \cdot \sqrt{4}}} \cdot \left(\sqrt[3]{\sqrt{4}} \cdot \sqrt[3]{\sqrt{4}}\right)\right)}\right)}^{\left(\sqrt[3]{4}\right)}\]

15. Applied cbrt-prod 34.0

    \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left({\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(\color{blue}{\left(\sqrt[3]{\sqrt{4}} \cdot \sqrt[3]{\sqrt{4}}\right)} \cdot \left(\sqrt[3]{\sqrt{4}} \cdot \sqrt[3]{\sqrt{4}}\right)\right)}\right)}^{\left(\sqrt[3]{4}\right)}\]

16. Applied swap-sqr 34.0

    \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left({\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\color{blue}{\left(\left(\sqrt[3]{\sqrt{4}} \cdot \sqrt[3]{\sqrt{4}}\right) \cdot \left(\sqrt[3]{\sqrt{4}} \cdot \sqrt[3]{\sqrt{4}}\right)\right)}}\right)}^{\left(\sqrt[3]{4}\right)}\]

17. Final simplification 34.0

    \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot {\left({\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(\left(\sqrt[3]{\sqrt{4}} \cdot \sqrt[3]{\sqrt{4}}\right) \cdot \left(\sqrt[3]{\sqrt{4}} \cdot \sqrt[3]{\sqrt{4}}\right)\right)}\right)}^{\left(\sqrt[3]{4}\right)}\]

Reproduce

herbie shell --seed 2020002 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))