Random Jason Timeout Test 004

Average Error: 33.7 → 33.7

Time: 24.5s

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 r17274 = c;
        double r17275 = cosh(r17274);
        double r17276 = a;
        double r17277 = log1p(r17276);
        double r17278 = fmod(r17275, r17277);
        return r17278;
}

↓

double f(double a, double c) {
        double r17279 = exp(1.0);
        double r17280 = c;
        double r17281 = cosh(r17280);
        double r17282 = a;
        double r17283 = log1p(r17282);
        double r17284 = fmod(r17281, r17283);
        double r17285 = log(r17284);
        double r17286 = 2.0;
        double r17287 = pow(r17285, r17286);
        double r17288 = cbrt(r17287);
        double r17289 = pow(r17279, r17288);
        double r17290 = cbrt(r17285);
        double r17291 = 3.0;
        double r17292 = pow(r17290, r17291);
        double r17293 = cbrt(r17292);
        double r17294 = pow(r17289, r17293);
        return r17294;
}

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