Random Jason Timeout Test 004

Average Error: 34.2 → 34.2

Time: 1.3m

Precision: 64

• could not determine a ground truth for program body

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

Math

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

↓

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

C

double f(double a, double c) {
        double r14200 = c;
        double r14201 = cosh(r14200);
        double r14202 = a;
        double r14203 = log1p(r14202);
        double r14204 = fmod(r14201, r14203);
        return r14204;
}

↓

double f(double a, double c) {
        double r14205 = exp(1.0);
        double r14206 = c;
        double r14207 = cosh(r14206);
        double r14208 = a;
        double r14209 = log1p(r14208);
        double r14210 = fmod(r14207, r14209);
        double r14211 = log(r14210);
        double r14212 = pow(r14205, r14211);
        return r14212;
}

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. Using strategy rm

10. Applied *-un-lft-identity 34.2

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

11. Final simplification 34.2

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

Reproduce

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