Random Jason Timeout Test 004

Average Error: 34.4 → 34.4

Time: 19.5s

Precision: 64

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

• could not determine a ground truth for program body

  1. a = -2.113572165822749e-307
  2. c = -2.5020242176796438e+231

Math

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

↓

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

C

double f(double a, double c) {
        double r13459 = c;
        double r13460 = cosh(r13459);
        double r13461 = a;
        double r13462 = log1p(r13461);
        double r13463 = fmod(r13460, r13462);
        return r13463;
}

↓

double f(double a, double c) {
        double r13464 = exp(1.0);
        double r13465 = c;
        double r13466 = cosh(r13465);
        double r13467 = a;
        double r13468 = log1p(r13467);
        double r13469 = fmod(r13466, r13468);
        double r13470 = log(r13469);
        double r13471 = 3.0;
        double r13472 = pow(r13470, r13471);
        double r13473 = cbrt(r13472);
        double r13474 = pow(r13464, r13473);
        return r13474;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.4

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

3. Applied add-exp-log 34.4

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

5. Applied pow1 34.4

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

6. Applied log-pow 34.4

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

7. Applied exp-prod 34.4

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

8. Simplified 34.4

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

10. Applied add-cbrt-cube 34.4

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

11. Simplified 34.4

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

12. Final simplification 34.4

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))