Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 4.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 3.711862644908055e+285
  2. b = 1.5653616039360228e+281

Math

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

↓

\[\sin \left(e^{2 \cdot \left(\left(b - a\right) \cdot \log \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{4}}\right)\right)}\right)\]

C

double f(double a, double b) {
        double r11416 = b;
        double r11417 = atan2(r11416, r11416);
        double r11418 = sqrt(r11417);
        double r11419 = a;
        double r11420 = r11416 - r11419;
        double r11421 = pow(r11418, r11420);
        double r11422 = sin(r11421);
        return r11422;
}

↓

double f(double a, double b) {
        double r11423 = 2.0;
        double r11424 = b;
        double r11425 = a;
        double r11426 = r11424 - r11425;
        double r11427 = atan2(r11424, r11424);
        double r11428 = 0.25;
        double r11429 = pow(r11427, r11428);
        double r11430 = log(r11429);
        double r11431 = r11426 * r11430;
        double r11432 = r11423 * r11431;
        double r11433 = exp(r11432);
        double r11434 = sin(r11433);
        return r11434;
}

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. Taylor expanded around inf 0.1

    \[\leadsto \color{blue}{\sin \left(e^{2 \cdot \left(\left(b - a\right) \cdot \log \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{4}}\right)\right)}\right)}\]

19. Final simplification 0.1

    \[\leadsto \sin \left(e^{2 \cdot \left(\left(b - a\right) \cdot \log \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{4}}\right)\right)}\right)\]

Reproduce

herbie shell --seed 2019346 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))