Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 20.1s

Precision: 64

• could not determine a ground truth for program body

  1. a = 7.015171298646812e+194
  2. b = 4.52205504228614e-15

Math

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

↓

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

C

double f(double a, double b) {
        double r527597 = b;
        double r527598 = atan2(r527597, r527597);
        double r527599 = sqrt(r527598);
        double r527600 = a;
        double r527601 = r527597 - r527600;
        double r527602 = pow(r527599, r527601);
        double r527603 = sin(r527602);
        return r527603;
}

↓

double f(double a, double b) {
        double r527604 = b;
        double r527605 = atan2(r527604, r527604);
        double r527606 = sqrt(r527605);
        double r527607 = sqrt(r527606);
        double r527608 = a;
        double r527609 = r527604 - r527608;
        double r527610 = pow(r527607, r527609);
        double r527611 = cbrt(r527610);
        double r527612 = r527611 * r527611;
        double r527613 = r527612 * r527612;
        double r527614 = r527613 * r527612;
        double r527615 = sin(r527614);
        return r527615;
}

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

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

8. Applied add-cube-cbrt 0.1

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

9. Applied swap-sqr 0.1

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

10. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019152 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))