Random Jason Timeout Test 004

Average Error: 34.1 → 34.1

Time: 13.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 3.043105375567236e+91
  2. c = -5.968297493912559e+121

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 r12670 = c;
        double r12671 = cosh(r12670);
        double r12672 = a;
        double r12673 = log1p(r12672);
        double r12674 = fmod(r12671, r12673);
        return r12674;
}

↓

double f(double a, double c) {
        double r12675 = exp(1.0);
        double r12676 = c;
        double r12677 = cosh(r12676);
        double r12678 = a;
        double r12679 = log1p(r12678);
        double r12680 = fmod(r12677, r12679);
        double r12681 = log(r12680);
        double r12682 = pow(r12675, r12681);
        return r12682;
}

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. Final simplification 34.1

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

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))