Random Jason Timeout Test 004

Average Error: 33.8 → 33.4

Time: 33.3s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.2059558245150868e+23
  2. c = 1.774174898164156e+151

Math

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

↓

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

C

double f(double a, double c) {
        double r468635 = c;
        double r468636 = cosh(r468635);
        double r468637 = a;
        double r468638 = log1p(r468637);
        double r468639 = fmod(r468636, r468638);
        return r468639;
}

↓

double f(double a, double c) {
        double r468640 = c;
        double r468641 = cosh(r468640);
        double r468642 = a;
        double r468643 = log1p(r468642);
        double r468644 = cbrt(r468643);
        double r468645 = r468644 * r468644;
        double r468646 = r468644 * r468645;
        double r468647 = fmod(r468641, r468646);
        double r468648 = log(r468647);
        double r468649 = r468648 * r468648;
        double r468650 = r468648 * r468649;
        double r468651 = cbrt(r468650);
        double r468652 = exp(r468651);
        double r468653 = sqrt(r468652);
        double r468654 = sqrt(r468647);
        double r468655 = r468653 * r468654;
        return r468655;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.8

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

3. Applied add-cube-cbrt 33.4

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

5. Applied add-sqr-sqrt 33.4

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

7. Applied add-exp-log 33.4

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

9. Applied add-cbrt-cube 33.4

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

10. Final simplification 33.4

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

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))