Random Jason Timeout Test 003

Average Error: 0.1 → 0.2

Time: 21.9s

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 r1763724 = b;
        double r1763725 = atan2(r1763724, r1763724);
        double r1763726 = sqrt(r1763725);
        double r1763727 = a;
        double r1763728 = r1763724 - r1763727;
        double r1763729 = pow(r1763726, r1763728);
        double r1763730 = sin(r1763729);
        return r1763730;
}

↓

double f(double a, double b) {
        double r1763731 = b;
        double r1763732 = atan2(r1763731, r1763731);
        double r1763733 = sqrt(r1763732);
        double r1763734 = sqrt(r1763733);
        double r1763735 = a;
        double r1763736 = r1763731 - r1763735;
        double r1763737 = r1763736 + r1763736;
        double r1763738 = pow(r1763734, r1763737);
        double r1763739 = r1763738 * r1763738;
        double r1763740 = r1763738 * r1763739;
        double r1763741 = cbrt(r1763740);
        double r1763742 = sin(r1763741);
        return r1763742;
}

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 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))