Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 4.3s

Precision: 64

• could not determine a ground truth for program body

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

Math

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

↓

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

C

double f(double a, double b) {
        double r14790 = b;
        double r14791 = atan2(r14790, r14790);
        double r14792 = sqrt(r14791);
        double r14793 = a;
        double r14794 = r14790 - r14793;
        double r14795 = pow(r14792, r14794);
        double r14796 = sin(r14795);
        return r14796;
}

↓

double f(double a, double b) {
        double r14797 = b;
        double r14798 = atan2(r14797, r14797);
        double r14799 = sqrt(r14798);
        double r14800 = cbrt(r14799);
        double r14801 = r14800 * r14800;
        double r14802 = r14801 * r14800;
        double r14803 = sqrt(r14802);
        double r14804 = a;
        double r14805 = r14797 - r14804;
        double r14806 = pow(r14803, r14805);
        double r14807 = 3.0;
        double r14808 = pow(r14806, r14807);
        double r14809 = sqrt(r14799);
        double r14810 = pow(r14809, r14805);
        double r14811 = pow(r14810, r14807);
        double r14812 = r14808 * r14811;
        double r14813 = cbrt(r14812);
        double r14814 = sin(r14813);
        return r14814;
}

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

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

12. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))