Random Jason Timeout Test 004

Average Error: 34.3 → 34.3

Time: 39.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.940605716246613e+111
  2. c = 5.5812662725677215e+112

Math

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

↓

\[{\left(e^{\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(2 \cdot \frac{\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}{2}\right)}\]

C

double f(double a, double c) {
        double r11187 = c;
        double r11188 = cosh(r11187);
        double r11189 = a;
        double r11190 = log1p(r11189);
        double r11191 = fmod(r11188, r11190);
        return r11191;
}

↓

double f(double a, double c) {
        double r11192 = c;
        double r11193 = cosh(r11192);
        double r11194 = a;
        double r11195 = log1p(r11194);
        double r11196 = fmod(r11193, r11195);
        double r11197 = log(r11196);
        double r11198 = cbrt(r11197);
        double r11199 = r11198 * r11198;
        double r11200 = exp(r11199);
        double r11201 = 2.0;
        double r11202 = r11198 / r11201;
        double r11203 = r11201 * r11202;
        double r11204 = pow(r11200, r11203);
        return r11204;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.3

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

3. Applied add-exp-log 34.3

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

5. Applied add-cube-cbrt 34.3

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

6. Applied exp-prod 34.3

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

8. Applied add-cube-cbrt 34.3

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

9. Final simplification 34.3

   \[\leadsto {\left(e^{\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(2 \cdot \frac{\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}{2}\right)}\]

Reproduce

herbie shell --seed 2019294 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))