Random Jason Timeout Test 015

Average Error: 0.1 → 0.2

Time: 40.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 9.137530169746875e+200
  2. b = 1.4011542472758516e-71

Math

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

↓

\[\sin \left(\sqrt[3]{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\left(b - a\right) + \left(b - a\right)\right)} \cdot \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\left(b - a\right) + \left(b - a\right)\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\left(b - a\right) + \left(b - a\right)\right)}\right)}\right)\]

C

double f(double a, double b) {
        double r1367674 = b;
        double r1367675 = atan2(r1367674, r1367674);
        double r1367676 = sqrt(r1367675);
        double r1367677 = a;
        double r1367678 = r1367674 - r1367677;
        double r1367679 = pow(r1367676, r1367678);
        double r1367680 = sin(r1367679);
        return r1367680;
}

↓

double f(double a, double b) {
        double r1367681 = b;
        double r1367682 = atan2(r1367681, r1367681);
        double r1367683 = sqrt(r1367682);
        double r1367684 = sqrt(r1367683);
        double r1367685 = a;
        double r1367686 = r1367681 - r1367685;
        double r1367687 = r1367686 + r1367686;
        double r1367688 = pow(r1367684, r1367687);
        double r1367689 = r1367688 * r1367688;
        double r1367690 = r1367688 * r1367689;
        double r1367691 = cbrt(r1367690);
        double r1367692 = sin(r1367691);
        return r1367692;
}

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 pow-prod-up 0.1

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

9. Applied add-cbrt-cube 0.2

   \[\leadsto \sin \color{blue}{\left(\sqrt[3]{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\left(b - a\right) + \left(b - a\right)\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\left(b - a\right) + \left(b - a\right)\right)}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\left(b - a\right) + \left(b - a\right)\right)}}\right)}\]

10. Final simplification 0.2

    \[\leadsto \sin \left(\sqrt[3]{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\left(b - a\right) + \left(b - a\right)\right)} \cdot \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\left(b - a\right) + \left(b - a\right)\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\left(b - a\right) + \left(b - a\right)\right)}\right)}\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))