Random Jason Timeout Test 004

Average Error: 34.2 → 34.2

Time: 31.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = -2.217850508686917e-110
  2. c = 3.920658959644529e+183

Math

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

↓

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

C

double f(double a, double c) {
        double r365769 = c;
        double r365770 = cosh(r365769);
        double r365771 = a;
        double r365772 = log1p(r365771);
        double r365773 = fmod(r365770, r365772);
        return r365773;
}

↓

double f(double a, double c) {
        double r365774 = c;
        double r365775 = cosh(r365774);
        double r365776 = a;
        double r365777 = log1p(r365776);
        double r365778 = fmod(r365775, r365777);
        double r365779 = log(r365778);
        double r365780 = cbrt(r365779);
        double r365781 = r365780 * r365780;
        double r365782 = r365780 * r365781;
        double r365783 = r365779 * r365779;
        double r365784 = r365782 * r365783;
        double r365785 = cbrt(r365784);
        double r365786 = exp(r365785);
        return r365786;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.2

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

3. Applied add-exp-log 34.2

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

5. Applied add-cbrt-cube 34.2

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

7. Applied add-cube-cbrt 34.2

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

8. Final simplification 34.2

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

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))