Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 25.7s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.201272836446736e+303
  2. b = 4.859928888733039e+49

Math

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

↓

\[\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left({\left(\sqrt[3]{b}\right)}^{3} - a\right)\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(a - a\right)\right)}\right)\]

C

double f(double a, double b) {
        double r28694 = b;
        double r28695 = atan2(r28694, r28694);
        double r28696 = sqrt(r28695);
        double r28697 = a;
        double r28698 = r28694 - r28697;
        double r28699 = pow(r28696, r28698);
        double r28700 = sin(r28699);
        return r28700;
}

↓

double f(double a, double b) {
        double r28701 = b;
        double r28702 = atan2(r28701, r28701);
        double r28703 = sqrt(r28702);
        double r28704 = sqrt(r28703);
        double r28705 = 2.0;
        double r28706 = cbrt(r28701);
        double r28707 = 3.0;
        double r28708 = pow(r28706, r28707);
        double r28709 = a;
        double r28710 = r28708 - r28709;
        double r28711 = r28705 * r28710;
        double r28712 = pow(r28704, r28711);
        double r28713 = r28709 - r28709;
        double r28714 = r28705 * r28713;
        double r28715 = pow(r28704, r28714);
        double r28716 = r28712 * r28715;
        double r28717 = sin(r28716);
        return r28717;
}

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-cube-cbrt 0.1

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

9. Applied prod-diff 0.1

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

10. Applied unpow-prod-up 11.1

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

11. Applied add-cube-cbrt 11.1

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

12. Applied add-cube-cbrt 11.1

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

13. Applied prod-diff 11.1

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

14. Applied unpow-prod-up 11.1

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

15. Applied swap-sqr 11.1

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

16. Simplified 11.1

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

17. Simplified 0.1

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

18. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))