Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 16.0s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. a = 5.619679650686545e+73
  2. b = 2.700807754743675e-33

Math

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

↓

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

C

double f(double a, double b) {
        double r17369 = b;
        double r17370 = atan2(r17369, r17369);
        double r17371 = sqrt(r17370);
        double r17372 = a;
        double r17373 = r17369 - r17372;
        double r17374 = pow(r17371, r17373);
        double r17375 = sin(r17374);
        return r17375;
}

↓

double f(double a, double b) {
        double r17376 = b;
        double r17377 = atan2(r17376, r17376);
        double r17378 = sqrt(r17377);
        double r17379 = sqrt(r17378);
        double r17380 = a;
        double r17381 = r17376 - r17380;
        double r17382 = pow(r17379, r17381);
        double r17383 = log(r17382);
        double r17384 = exp(r17383);
        double r17385 = log(r17377);
        double r17386 = 4.0;
        double r17387 = r17381 / r17386;
        double r17388 = r17385 * r17387;
        double r17389 = exp(r17388);
        double r17390 = r17384 * r17389;
        double r17391 = sin(r17390);
        return r17391;
}

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 pow1/2 0.1

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

8. Applied sqrt-pow1 0.1

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

9. Applied pow-pow 0.1

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

10. Simplified 0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\color{blue}{\left(\left(b - a\right) \cdot \frac{1}{4}\right)}}\right)\]
11. Using strategy rm

12. Applied add-exp-log 0.1

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

13. Applied pow-exp 0.1

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

14. Simplified 0.1

    \[\leadsto \sin \left(e^{\color{blue}{\log \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{4}\right)}\right)\]
15. Using strategy rm

16. Applied add-exp-log 0.1

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

17. Applied pow-exp 0.1

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

18. Simplified 0.1

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

19. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))