Random Jason Timeout Test 004

Average Error: 34.2 → 33.9

Time: 55.3s

Precision: 64

• could not determine a ground truth for program body

  1. a = 5.0362447883134526e+148
  2. c = 1.0422426701817188e+213

Math

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

↓

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

C

double f(double a, double c) {
        double r1420744 = c;
        double r1420745 = cosh(r1420744);
        double r1420746 = a;
        double r1420747 = log1p(r1420746);
        double r1420748 = fmod(r1420745, r1420747);
        return r1420748;
}

↓

double f(double a, double c) {
        double r1420749 = c;
        double r1420750 = cosh(r1420749);
        double r1420751 = a;
        double r1420752 = log1p(r1420751);
        double r1420753 = cbrt(r1420752);
        double r1420754 = r1420753 * r1420753;
        double r1420755 = cbrt(r1420753);
        double r1420756 = cbrt(r1420754);
        double r1420757 = log(r1420756);
        double r1420758 = exp(r1420757);
        double r1420759 = r1420755 * r1420758;
        double r1420760 = cbrt(r1420759);
        double r1420761 = r1420760 * r1420755;
        double r1420762 = r1420755 * r1420761;
        double r1420763 = r1420754 * r1420762;
        double r1420764 = fmod(r1420750, r1420763);
        return r1420764;
}

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-cube-cbrt 33.9

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

5. Applied add-cube-cbrt 33.9

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

7. Applied add-cube-cbrt 33.9

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

8. Applied cbrt-prod 33.9

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

10. Applied add-exp-log 33.9

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

11. Final simplification 33.9

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

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))