Random Jason Timeout Test 004

Average Error: 33.9 → 33.9

Time: 1.1m

Precision: 64

• could not determine a ground truth for program body

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

Math

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

↓

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

C

double f(double a, double c) {
        double r1055179 = c;
        double r1055180 = cosh(r1055179);
        double r1055181 = a;
        double r1055182 = log1p(r1055181);
        double r1055183 = fmod(r1055180, r1055182);
        return r1055183;
}

↓

double f(double a, double c) {
        double r1055184 = c;
        double r1055185 = cosh(r1055184);
        double r1055186 = a;
        double r1055187 = log1p(r1055186);
        double r1055188 = fmod(r1055185, r1055187);
        double r1055189 = log(r1055188);
        double r1055190 = exp(r1055189);
        double r1055191 = sqrt(r1055190);
        double r1055192 = r1055189 * r1055189;
        double r1055193 = r1055189 * r1055192;
        double r1055194 = cbrt(r1055193);
        double r1055195 = exp(r1055194);
        double r1055196 = sqrt(r1055195);
        double r1055197 = r1055191 * r1055196;
        return r1055197;
}

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

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

8. Final simplification 33.9

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

Reproduce

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