Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 4.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 3.490165826213844e+274
  2. b = 1.0262914181209274e-117

Math

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

↓

\[\sin \left(\sqrt[3]{{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}^{3} \cdot {\left({\left(\sqrt{\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)}\right)}^{3}}\right)\]

C

double f(double a, double b) {
        double r5775 = b;
        double r5776 = atan2(r5775, r5775);
        double r5777 = sqrt(r5776);
        double r5778 = a;
        double r5779 = r5775 - r5778;
        double r5780 = pow(r5777, r5779);
        double r5781 = sin(r5780);
        return r5781;
}

↓

double f(double a, double b) {
        double r5782 = b;
        double r5783 = atan2(r5782, r5782);
        double r5784 = sqrt(r5783);
        double r5785 = sqrt(r5784);
        double r5786 = a;
        double r5787 = r5782 - r5786;
        double r5788 = pow(r5785, r5787);
        double r5789 = 3.0;
        double r5790 = pow(r5788, r5789);
        double r5791 = cbrt(r5784);
        double r5792 = r5791 * r5791;
        double r5793 = r5792 * r5791;
        double r5794 = sqrt(r5793);
        double r5795 = pow(r5794, r5787);
        double r5796 = pow(r5795, r5789);
        double r5797 = r5790 * r5796;
        double r5798 = cbrt(r5797);
        double r5799 = sin(r5798);
        return r5799;
}

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-cbrt-cube 0.1

   \[\leadsto \sin \color{blue}{\left(\sqrt[3]{\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right) \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}\right)}\]

4. Simplified 0.1

   \[\leadsto \sin \left(\sqrt[3]{\color{blue}{{\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}^{3}}}\right)\]
5. Using strategy rm

6. Applied add-sqr-sqrt 0.1

   \[\leadsto \sin \left(\sqrt[3]{{\left({\left(\sqrt{\color{blue}{\sqrt{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)}\right)}^{3}}\right)\]

7. Applied sqrt-prod 0.1

   \[\leadsto \sin \left(\sqrt[3]{{\left({\color{blue}{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}}^{\left(b - a\right)}\right)}^{3}}\right)\]

8. Applied unpow-prod-down 0.1

   \[\leadsto \sin \left(\sqrt[3]{{\color{blue}{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}}^{3}}\right)\]

9. Applied unpow-prod-down 0.1

   \[\leadsto \sin \left(\sqrt[3]{\color{blue}{{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}^{3} \cdot {\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}^{3}}}\right)\]
10. Using strategy rm

11. Applied add-cube-cbrt 0.1

    \[\leadsto \sin \left(\sqrt[3]{{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}^{3} \cdot {\left({\left(\sqrt{\color{blue}{\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}}\right)}^{\left(b - a\right)}\right)}^{3}}\right)\]

12. Final simplification 0.1

    \[\leadsto \sin \left(\sqrt[3]{{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}^{3} \cdot {\left({\left(\sqrt{\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)}\right)}^{3}}\right)\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))