Random Jason Timeout Test 004

Average Error: 34.5 → 34.5

Time: 14.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.882583458996196e-203
  2. c = -1.7792650320053334e+66

Math

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

↓

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

C

double f(double a, double c) {
        double r12280 = c;
        double r12281 = cosh(r12280);
        double r12282 = a;
        double r12283 = log1p(r12282);
        double r12284 = fmod(r12281, r12283);
        return r12284;
}

↓

double f(double a, double c) {
        double r12285 = exp(1.0);
        double r12286 = c;
        double r12287 = cosh(r12286);
        double r12288 = log(r12287);
        double r12289 = exp(r12288);
        double r12290 = a;
        double r12291 = log1p(r12290);
        double r12292 = fmod(r12289, r12291);
        double r12293 = log(r12292);
        double r12294 = cbrt(r12293);
        double r12295 = r12294 * r12294;
        double r12296 = r12295 * r12294;
        double r12297 = pow(r12285, r12296);
        return r12297;
}

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

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

5. Applied add-exp-log 34.5

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

7. Applied pow1 34.5

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

8. Applied log-pow 34.5

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

9. Applied exp-prod 34.5

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

10. Simplified 34.5

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

12. Applied add-cube-cbrt 34.5

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

13. Final simplification 34.5

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))