Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 26.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.0362876411490344e+263
  2. b = 9.656044930860567e+126

Math

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

↓

\[\sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \sqrt{e^{\left(b - a\right) \cdot \left(\log \left(\tan^{-1}_* \frac{b}{b}\right) \cdot \frac{1}{4}\right)}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

C

double f(double a, double b) {
        double r812695 = b;
        double r812696 = atan2(r812695, r812695);
        double r812697 = sqrt(r812696);
        double r812698 = a;
        double r812699 = r812695 - r812698;
        double r812700 = pow(r812697, r812699);
        double r812701 = sin(r812700);
        return r812701;
}

↓

double f(double a, double b) {
        double r812702 = b;
        double r812703 = atan2(r812702, r812702);
        double r812704 = sqrt(r812703);
        double r812705 = sqrt(r812704);
        double r812706 = a;
        double r812707 = r812702 - r812706;
        double r812708 = pow(r812705, r812707);
        double r812709 = sqrt(r812708);
        double r812710 = log(r812703);
        double r812711 = 0.25;
        double r812712 = r812710 * r812711;
        double r812713 = r812707 * r812712;
        double r812714 = exp(r812713);
        double r812715 = sqrt(r812714);
        double r812716 = r812709 * r812715;
        double r812717 = r812716 * r812708;
        double r812718 = sin(r812717);
        return r812718;
}

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 add-sqr-sqrt 0.1

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

4. Applied sqrt-prod 0.1

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

5. Applied unpow-prod-down 0.1

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

7. Applied add-sqr-sqrt 0.1

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

8. Taylor expanded around inf 0.1

   \[\leadsto \sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \color{blue}{\sqrt{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{4}}\right)}^{\left(b - a\right)}}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

9. Simplified 0.1

   \[\leadsto \sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \color{blue}{\sqrt{e^{\left(\frac{1}{4} \cdot \log \left(\tan^{-1}_* \frac{b}{b}\right)\right) \cdot \left(b - a\right)}}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

10. Final simplification 0.1

    \[\leadsto \sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \sqrt{e^{\left(b - a\right) \cdot \left(\log \left(\tan^{-1}_* \frac{b}{b}\right) \cdot \frac{1}{4}\right)}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))