Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 14.6s

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

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

↓

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

C

double f(double a, double b) {
        double r9279 = b;
        double r9280 = atan2(r9279, r9279);
        double r9281 = sqrt(r9280);
        double r9282 = a;
        double r9283 = r9279 - r9282;
        double r9284 = pow(r9281, r9283);
        double r9285 = sin(r9284);
        return r9285;
}

↓

double f(double a, double b) {
        double r9286 = b;
        double r9287 = atan2(r9286, r9286);
        double r9288 = sqrt(r9287);
        double r9289 = sqrt(r9288);
        double r9290 = a;
        double r9291 = r9286 - r9290;
        double r9292 = pow(r9289, r9291);
        double r9293 = log(r9292);
        double r9294 = exp(r9293);
        double r9295 = log(r9287);
        double r9296 = r9291 * r9295;
        double r9297 = 0.25;
        double r9298 = r9296 * r9297;
        double r9299 = exp(r9298);
        double r9300 = r9294 * r9299;
        double r9301 = sin(r9300);
        return r9301;
}

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

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

12. Applied add-exp-log 0.1

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

13. Applied pow-exp 0.1

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

14. Simplified 0.1

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

16. Applied add-exp-log 0.1

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

17. Applied pow-exp 0.1

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

18. Simplified 0.1

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

19. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))