Random Jason Timeout Test 012

Average Error: 61.2 → 59.5

Time: 39.8s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. a = 6.651092020437287e+111

Math

\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

↓

\[\frac{\pi}{2} - \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]

C

double f(double a) {
        double r6425 = a;
        double r6426 = cosh(r6425);
        double r6427 = r6425 * r6425;
        double r6428 = fmod(r6426, r6427);
        double r6429 = log1p(r6425);
        double r6430 = pow(r6428, r6429);
        double r6431 = acos(r6430);
        return r6431;
}

↓

double f(double a) {
        double r6432 = atan2(1.0, 0.0);
        double r6433 = 2.0;
        double r6434 = r6432 / r6433;
        double r6435 = a;
        double r6436 = cosh(r6435);
        double r6437 = pow(r6435, r6433);
        double r6438 = fmod(r6436, r6437);
        double r6439 = log1p(r6435);
        double r6440 = pow(r6438, r6439);
        double r6441 = asin(r6440);
        double r6442 = sqrt(r6441);
        double r6443 = r6442 * r6442;
        double r6444 = r6434 - r6443;
        return r6444;
}

Error

Bits error versus a

Derivation

1. Initial program 61.2

   \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
2. Using strategy rm

3. Applied add-log-exp 60.3

   \[\leadsto \cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
4. Using strategy rm

5. Applied acos-asin 60.3

   \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]

6. Simplified 61.2

   \[\leadsto \frac{\pi}{2} - \color{blue}{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
7. Using strategy rm

8. Applied add-sqr-sqrt 59.5

   \[\leadsto \frac{\pi}{2} - \color{blue}{\sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\]

9. Final simplification 59.5

   \[\leadsto \frac{\pi}{2} - \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))