Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 15.4s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.0354753041264744e+289
  2. b = 1.805639974384451e-278

Math

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

↓

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

C

double f(double a, double b) {
        double r15430 = b;
        double r15431 = atan2(r15430, r15430);
        double r15432 = sqrt(r15431);
        double r15433 = a;
        double r15434 = r15430 - r15433;
        double r15435 = pow(r15432, r15434);
        double r15436 = sin(r15435);
        return r15436;
}

↓

double f(double a, double b) {
        double r15437 = b;
        double r15438 = a;
        double r15439 = r15437 - r15438;
        double r15440 = atan2(r15437, r15437);
        double r15441 = sqrt(r15440);
        double r15442 = sqrt(r15441);
        double r15443 = log(r15442);
        double r15444 = r15439 * r15443;
        double r15445 = exp(r15444);
        double r15446 = 0.25;
        double r15447 = r15439 * r15446;
        double r15448 = pow(r15440, r15447);
        double r15449 = r15445 * r15448;
        double r15450 = sin(r15449);
        return r15450;
}

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

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

15. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019195 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))