Random Jason Timeout Test 015

Average Error: 0.1 → 0.2

Time: 21.0s

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 r1439574 = b;
        double r1439575 = atan2(r1439574, r1439574);
        double r1439576 = sqrt(r1439575);
        double r1439577 = a;
        double r1439578 = r1439574 - r1439577;
        double r1439579 = pow(r1439576, r1439578);
        double r1439580 = sin(r1439579);
        return r1439580;
}

↓

double f(double a, double b) {
        double r1439581 = b;
        double r1439582 = atan2(r1439581, r1439581);
        double r1439583 = sqrt(r1439582);
        double r1439584 = sqrt(r1439583);
        double r1439585 = a;
        double r1439586 = r1439581 - r1439585;
        double r1439587 = r1439586 + r1439586;
        double r1439588 = pow(r1439584, r1439587);
        double r1439589 = r1439588 * r1439588;
        double r1439590 = r1439588 * r1439589;
        double r1439591 = cbrt(r1439590);
        double r1439592 = sin(r1439591);
        return r1439592;
}

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 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))