Random Jason Timeout Test 004

Average Error: 34.2 → 34.2

Time: 1.8m

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.1907736260088357e+136
  2. c = -1.0340574268486961e+306

Math

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

↓

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

C

double f(double a, double c) {
        double r1268997 = c;
        double r1268998 = cosh(r1268997);
        double r1268999 = a;
        double r1269000 = log1p(r1268999);
        double r1269001 = fmod(r1268998, r1269000);
        return r1269001;
}

↓

double f(double a, double c) {
        double r1269002 = c;
        double r1269003 = cosh(r1269002);
        double r1269004 = a;
        double r1269005 = log1p(r1269004);
        double r1269006 = fmod(r1269003, r1269005);
        return r1269006;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.2

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

3. Applied add-exp-log 34.2

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

5. Applied pow1 34.2

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

6. Applied log-pow 34.2

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

7. Applied exp-prod 34.2

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

8. Simplified 34.2

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

9. Taylor expanded around 0 34.2

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

10. Final simplification 34.2

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))