Random Jason Timeout Test 004

Average Error: 34.1 → 34.1

Time: 24.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = 2.8774590365534544e-144
  2. c = 3.0260304830237114e+184

Math

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

↓

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

C

double f(double a, double c) {
        double r11443 = c;
        double r11444 = cosh(r11443);
        double r11445 = a;
        double r11446 = log1p(r11445);
        double r11447 = fmod(r11444, r11446);
        return r11447;
}

↓

double f(double a, double c) {
        double r11448 = exp(1.0);
        double r11449 = 2.0;
        double r11450 = c;
        double r11451 = cosh(r11450);
        double r11452 = a;
        double r11453 = log1p(r11452);
        double r11454 = fmod(r11451, r11453);
        double r11455 = log(r11454);
        double r11456 = r11455 / r11449;
        double r11457 = r11449 * r11456;
        double r11458 = pow(r11448, r11457);
        return r11458;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.1

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

3. Applied add-exp-log 34.1

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

5. Applied pow1 34.1

   \[\leadsto e^{\log \color{blue}{\left({\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}^{1}\right)}}\]

6. Applied log-pow 34.1

   \[\leadsto e^{\color{blue}{1 \cdot \log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

7. Applied exp-prod 34.1

   \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\right)}}\]

8. Simplified 34.1

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

10. Applied add-cube-cbrt 34.1

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

11. Final simplification 34.1

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

Reproduce

herbie shell --seed 2019304 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))