Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 26.3s

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 r17105 = b;
        double r17106 = atan2(r17105, r17105);
        double r17107 = sqrt(r17106);
        double r17108 = a;
        double r17109 = r17105 - r17108;
        double r17110 = pow(r17107, r17109);
        double r17111 = sin(r17110);
        return r17111;
}

↓

double f(double a, double b) {
        double r17112 = b;
        double r17113 = atan2(r17112, r17112);
        double r17114 = 0.5;
        double r17115 = a;
        double r17116 = r17112 - r17115;
        double r17117 = r17114 * r17116;
        double r17118 = pow(r17113, r17117);
        double r17119 = sin(r17118);
        return r17119;
}

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))))