Random Jason Timeout Test 004

Average Error: 33.4 → 33.4

Time: 33.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = -2.737455125593724e-285
  2. c = 37258.21705967671

Math

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

↓

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

C

double f(double a, double c) {
        double r841223 = c;
        double r841224 = cosh(r841223);
        double r841225 = a;
        double r841226 = log1p(r841225);
        double r841227 = fmod(r841224, r841226);
        return r841227;
}

↓

double f(double a, double c) {
        double r841228 = exp(1.0);
        double r841229 = c;
        double r841230 = cosh(r841229);
        double r841231 = a;
        double r841232 = log1p(r841231);
        double r841233 = fmod(r841230, r841232);
        double r841234 = sqrt(r841233);
        double r841235 = log(r841234);
        double r841236 = pow(r841228, r841235);
        double r841237 = r841236 * r841236;
        return r841237;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.4

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

3. Applied add-exp-log 33.4

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

5. Applied pow1 33.4

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

6. Applied log-pow 33.4

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

7. Applied exp-prod 33.4

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

8. Simplified 33.4

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

10. Applied add-sqr-sqrt 33.4

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

11. Applied log-prod 33.4

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

12. Applied unpow-prod-up 33.4

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

14. Applied add-log-exp 33.4

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

15. Simplified 33.4

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

16. Final simplification 33.4

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

Reproduce

herbie shell --seed 2019129 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))