Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 20.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.4565393843068548e+200
  2. b = 1.837913291573934e-184

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 r2058454 = b;
        double r2058455 = atan2(r2058454, r2058454);
        double r2058456 = sqrt(r2058455);
        double r2058457 = a;
        double r2058458 = r2058454 - r2058457;
        double r2058459 = pow(r2058456, r2058458);
        double r2058460 = sin(r2058459);
        return r2058460;
}

↓

double f(double a, double b) {
        double r2058461 = b;
        double r2058462 = atan2(r2058461, r2058461);
        double r2058463 = a;
        double r2058464 = r2058461 - r2058463;
        double r2058465 = 0.5;
        double r2058466 = r2058464 * r2058465;
        double r2058467 = pow(r2058462, r2058466);
        double r2058468 = sin(r2058467);
        return r2058468;
}

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 2019172 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))