Random Jason Timeout Test 004

Average Error: 34.3 → 34.3

Time: 38.4s

Precision: 64

• could not determine a ground truth for program body

  1. a = 2.457824670046789e-148
  2. c = -8.762345834154966e+296

Math

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

↓

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

C

double f(double a, double c) {
        double r13605 = c;
        double r13606 = cosh(r13605);
        double r13607 = a;
        double r13608 = log1p(r13607);
        double r13609 = fmod(r13606, r13608);
        return r13609;
}

↓

double f(double a, double c) {
        double r13610 = exp(1.0);
        double r13611 = c;
        double r13612 = cosh(r13611);
        double r13613 = a;
        double r13614 = log1p(r13613);
        double r13615 = fmod(r13612, r13614);
        double r13616 = log(r13615);
        double r13617 = 3.0;
        double r13618 = pow(r13616, r13617);
        double r13619 = cbrt(r13618);
        double r13620 = pow(r13619, r13617);
        double r13621 = cbrt(r13620);
        double r13622 = pow(r13610, r13621);
        return r13622;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.3

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

3. Applied add-exp-log 34.3

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

5. Applied add-cbrt-cube 34.3

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

6. Simplified 34.3

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

8. Applied pow1 34.3

   \[\leadsto e^{\sqrt[3]{{\left(\log \color{blue}{\left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{1}\right)}\right)}^{3}}}\]

9. Applied log-pow 34.3

   \[\leadsto e^{\sqrt[3]{{\color{blue}{\left(1 \cdot \log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}}^{3}}}\]

10. Applied unpow-prod-down 34.3

    \[\leadsto e^{\sqrt[3]{\color{blue}{{1}^{3} \cdot {\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{3}}}}\]

11. Applied cbrt-prod 34.3

    \[\leadsto e^{\color{blue}{\sqrt[3]{{1}^{3}} \cdot \sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{3}}}}\]

12. Applied exp-prod 34.3

    \[\leadsto \color{blue}{{\left(e^{\sqrt[3]{{1}^{3}}}\right)}^{\left(\sqrt[3]{{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}^{3}}\right)}}\]

13. Simplified 34.3

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

15. Applied add-cbrt-cube 34.3

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

16. Simplified 34.3

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

17. Final simplification 34.3

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))