Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 24.9s

Precision: 64

• could not determine a ground truth for program body

  1. a = 7.953652505345186e+78
  2. b = 2.911049425072326e-200

Math

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

↓

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

C

double f(double a, double b) {
        double r17099 = b;
        double r17100 = atan2(r17099, r17099);
        double r17101 = sqrt(r17100);
        double r17102 = a;
        double r17103 = r17099 - r17102;
        double r17104 = pow(r17101, r17103);
        double r17105 = sin(r17104);
        return r17105;
}

↓

double f(double a, double b) {
        double r17106 = b;
        double r17107 = atan2(r17106, r17106);
        double r17108 = 0.5;
        double r17109 = a;
        double r17110 = r17106 - r17109;
        double r17111 = r17108 * r17110;
        double r17112 = pow(r17107, r17111);
        double r17113 = sin(r17112);
        return r17113;
}

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

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))