Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 15.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.5337538126839207e+211
  2. b = 1.1947132001406549e-195

Math

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

↓

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

C

double f(double a, double b) {
        double r14508 = b;
        double r14509 = atan2(r14508, r14508);
        double r14510 = sqrt(r14509);
        double r14511 = a;
        double r14512 = r14508 - r14511;
        double r14513 = pow(r14510, r14512);
        double r14514 = sin(r14513);
        return r14514;
}

↓

double f(double a, double b) {
        double r14515 = b;
        double r14516 = atan2(r14515, r14515);
        double r14517 = sqrt(r14516);
        double r14518 = sqrt(r14517);
        double r14519 = 2.0;
        double r14520 = a;
        double r14521 = -r14520;
        double r14522 = r14520 + r14521;
        double r14523 = r14519 * r14522;
        double r14524 = pow(r14518, r14523);
        double r14525 = r14515 - r14520;
        double r14526 = r14525 * r14519;
        double r14527 = pow(r14518, r14526);
        double r14528 = r14524 * r14527;
        double r14529 = sin(r14528);
        return r14529;
}

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-cube-cbrt 0.1

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

8. Applied add-sqr-sqrt 0.1

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

9. Applied prod-diff 0.1

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

10. Applied unpow-prod-up 11.6

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

11. Applied add-cube-cbrt 11.6

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

12. Applied add-sqr-sqrt 11.6

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

13. Applied prod-diff 11.6

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

14. Applied unpow-prod-up 11.6

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

15. Applied swap-sqr 11.6

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

16. Simplified 11.6

    \[\leadsto \sin \left(\color{blue}{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}} \cdot \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\mathsf{fma}\left(-\sqrt[3]{a}, \sqrt[3]{a} \cdot \sqrt[3]{a}, \sqrt[3]{a} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right)\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\mathsf{fma}\left(-\sqrt[3]{a}, \sqrt[3]{a} \cdot \sqrt[3]{a}, \sqrt[3]{a} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right)\right)}\right)\right)\]

17. Simplified 0.1

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

18. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))