Random Jason Timeout Test 004

Average Error: 34.0 → 33.6

Time: 32.7s

Precision: 64

• could not determine a ground truth for program body

  1. a = -4.273686323627727e-248
  2. c = 1.9440266393072233e+190

Math

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

↓

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

C

double f(double a, double c) {
        double r702915 = c;
        double r702916 = cosh(r702915);
        double r702917 = a;
        double r702918 = log1p(r702917);
        double r702919 = fmod(r702916, r702918);
        return r702919;
}

↓

double f(double a, double c) {
        double r702920 = c;
        double r702921 = cosh(r702920);
        double r702922 = a;
        double r702923 = log1p(r702922);
        double r702924 = cbrt(r702923);
        double r702925 = r702924 * r702924;
        double r702926 = r702924 * r702925;
        double r702927 = fmod(r702921, r702926);
        return r702927;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.0

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

3. Applied add-cube-cbrt 33.6

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

4. Final simplification 33.6

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

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))