Random Jason Timeout Test 004

Average Error: 33.8 → 33.8

Time: 13.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = -3.1006725809079922e-214
  2. c = 4.130937424398548e+69

Math

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

↓

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

C

double f(double a, double c) {
        double r17208 = c;
        double r17209 = cosh(r17208);
        double r17210 = a;
        double r17211 = log1p(r17210);
        double r17212 = fmod(r17209, r17211);
        return r17212;
}

↓

double f(double a, double c) {
        double r17213 = exp(1.0);
        double r17214 = c;
        double r17215 = cosh(r17214);
        double r17216 = a;
        double r17217 = log1p(r17216);
        double r17218 = fmod(r17215, r17217);
        double r17219 = log(r17218);
        double r17220 = pow(r17213, r17219);
        return r17220;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.8

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

3. Applied add-exp-log 33.8

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

5. Applied pow1 33.8

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

6. Applied log-pow 33.8

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

7. Applied exp-prod 33.8

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

8. Simplified 33.8

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

9. Final simplification 33.8

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))