Random Jason Timeout Test 004

Average Error: 33.9 → 33.9

Time: 38.4s

Precision: 64

• could not determine a ground truth for program body

  1. a = -1.3952531104493216e-235
  2. c = 1.242935524573972e+38

Math

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

↓

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

C

double f(double a, double c) {
        double r932176 = c;
        double r932177 = cosh(r932176);
        double r932178 = a;
        double r932179 = log1p(r932178);
        double r932180 = fmod(r932177, r932179);
        return r932180;
}

↓

double f(double a, double c) {
        double r932181 = c;
        double r932182 = cosh(r932181);
        double r932183 = a;
        double r932184 = log1p(r932183);
        double r932185 = fmod(r932182, r932184);
        double r932186 = log(r932185);
        double r932187 = r932186 * r932186;
        double r932188 = r932187 * r932186;
        double r932189 = cbrt(r932188);
        double r932190 = exp(r932189);
        double r932191 = sqrt(r932190);
        double r932192 = exp(r932186);
        double r932193 = sqrt(r932192);
        double r932194 = r932191 * r932193;
        return r932194;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.9

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

3. Applied add-exp-log 33.9

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

5. Applied add-sqr-sqrt 33.9

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

7. Applied add-cbrt-cube 33.9

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

8. Final simplification 33.9

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

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))