Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 36.7s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.5337538126839207e+211
  2. b = 1.1947132001406549e-195

Math

\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]

↓

\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]

C

double f(double a, double b) {
        double r227453 = b;
        double r227454 = atan2(r227453, r227453);
        double r227455 = sqrt(r227454);
        double r227456 = a;
        double r227457 = r227453 - r227456;
        double r227458 = pow(r227455, r227457);
        double r227459 = sin(r227458);
        return r227459;
}

↓

double f(double a, double b) {
        double r227460 = b;
        double r227461 = atan2(r227460, r227460);
        double r227462 = a;
        double r227463 = r227460 - r227462;
        double r227464 = 0.5;
        double r227465 = r227463 * r227464;
        double r227466 = pow(r227461, r227465);
        double r227467 = sin(r227466);
        return r227467;
}

Error

Bits error versus a

Bits error versus b

Derivation

1. Initial program 0.1

   \[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
2. Using strategy rm

3. Applied pow1/2 0.1

   \[\leadsto \sin \left({\color{blue}{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{2}}\right)}}^{\left(b - a\right)}\right)\]

4. Applied pow-pow 0.1

   \[\leadsto \sin \color{blue}{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)}\]

5. Final simplification 0.1

   \[\leadsto \sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))