Random Jason Timeout Test 004

Average Error: 33.7 → 33.7

Time: 23.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. a = 6.621422423638233e-193
  2. c = -2.5562774200050244e+255

Math

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

↓

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

C

double f(double a, double c) {
        double r15698 = c;
        double r15699 = cosh(r15698);
        double r15700 = a;
        double r15701 = log1p(r15700);
        double r15702 = fmod(r15699, r15701);
        return r15702;
}

↓

double f(double a, double c) {
        double r15703 = exp(1.0);
        double r15704 = c;
        double r15705 = cosh(r15704);
        double r15706 = a;
        double r15707 = log1p(r15706);
        double r15708 = fmod(r15705, r15707);
        double r15709 = log(r15708);
        double r15710 = 2.0;
        double r15711 = pow(r15709, r15710);
        double r15712 = cbrt(r15711);
        double r15713 = pow(r15703, r15712);
        double r15714 = cbrt(r15709);
        double r15715 = 3.0;
        double r15716 = pow(r15714, r15715);
        double r15717 = cbrt(r15716);
        double r15718 = pow(r15713, r15717);
        return r15718;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.7

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

3. Applied add-exp-log 33.7

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

5. Applied pow1 33.7

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

6. Applied log-pow 33.7

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

7. Applied exp-prod 33.7

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

8. Simplified 33.7

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

10. Applied add-cbrt-cube 33.7

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

11. Simplified 33.7

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

13. Applied add-cube-cbrt 33.7

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

14. Applied unpow-prod-down 33.7

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

15. Applied cbrt-prod 33.7

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

16. Applied pow-unpow 33.7

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

17. Simplified 33.7

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

18. Final simplification 33.7

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

Reproduce

herbie shell --seed 2020043 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))