Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 13.0s

Precision: 64

• could not determine a ground truth for program body

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

Math

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

↓

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

C

double f(double a, double b) {
        double r12894 = b;
        double r12895 = atan2(r12894, r12894);
        double r12896 = sqrt(r12895);
        double r12897 = a;
        double r12898 = r12894 - r12897;
        double r12899 = pow(r12896, r12898);
        double r12900 = sin(r12899);
        return r12900;
}

↓

double f(double a, double b) {
        double r12901 = b;
        double r12902 = atan2(r12901, r12901);
        double r12903 = sqrt(r12902);
        double r12904 = sqrt(r12903);
        double r12905 = a;
        double r12906 = r12901 - r12905;
        double r12907 = 2.0;
        double r12908 = r12906 * r12907;
        double r12909 = pow(r12904, r12908);
        double r12910 = sin(r12909);
        return r12910;
}

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 *-un-lft-identity 0.1

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

8. Applied sqrt-prod 0.1

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

9. Applied sqrt-prod 0.1

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

10. Applied unpow-prod-down 0.1

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

11. Applied *-un-lft-identity 0.1

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

12. Applied sqrt-prod 0.1

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

13. Applied sqrt-prod 0.1

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

14. Applied unpow-prod-down 0.1

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

15. Applied swap-sqr 0.1

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

16. Simplified 0.1

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

17. Simplified 0.1

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

18. Final simplification 0.1

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

Reproduce

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