Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 4.7s

Precision: 64

• could not determine a ground truth for program body

  1. a = 8.677094401051118e+132
  2. b = 1.662100557100748e-24

Math

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

↓

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

C

double code(double a, double b) {
	return sin(pow(sqrt(atan2(b, b)), (b - a)));
}

↓

double code(double a, double b) {
	return sin((pow(fabs(cbrt(sqrt(atan2(b, b)))), (2.0 * (b - a))) * pow(sqrt(cbrt(sqrt(atan2(b, b)))), (2.0 * (b - a)))));
}

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

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

8. Applied sqrt-prod 0.1

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

9. Applied unpow-prod-down 0.1

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

10. Applied add-cube-cbrt 0.1

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

11. Applied sqrt-prod 0.1

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

12. Applied unpow-prod-down 0.1

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

13. Applied swap-sqr 0.1

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

14. Simplified 0.1

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

15. Simplified 0.1

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

16. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020075 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))