Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 5.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.6197547301821798e+147
  2. b = 4.2985835605462347e-277

Math

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

↓

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

C

double f(double a, double b) {
        double r9430 = b;
        double r9431 = atan2(r9430, r9430);
        double r9432 = sqrt(r9431);
        double r9433 = a;
        double r9434 = r9430 - r9433;
        double r9435 = pow(r9432, r9434);
        double r9436 = sin(r9435);
        return r9436;
}

↓

double f(double a, double b) {
        double r9437 = b;
        double r9438 = atan2(r9437, r9437);
        double r9439 = sqrt(r9438);
        double r9440 = sqrt(r9439);
        double r9441 = a;
        double r9442 = r9437 - r9441;
        double r9443 = pow(r9440, r9442);
        double r9444 = cbrt(r9438);
        double r9445 = r9444 * r9444;
        double r9446 = sqrt(r9445);
        double r9447 = sqrt(r9446);
        double r9448 = pow(r9447, r9442);
        double r9449 = sqrt(r9444);
        double r9450 = sqrt(r9449);
        double r9451 = pow(r9450, r9442);
        double r9452 = r9448 * r9451;
        double r9453 = r9443 * r9452;
        double r9454 = sin(r9453);
        return r9454;
}

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 add-cube-cbrt 0.1

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

8. Applied sqrt-prod 0.1

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

9. Applied sqrt-prod 0.1

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

10. Applied unpow-prod-down 0.1

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

11. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))