Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 21.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 8.504910344707986e+189
  2. b = 1.9244747225358218e-24

Math

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

↓

\[\sin \left(e^{\frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4} \cdot \left(\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \left(b - a\right)\right) \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

C

double f(double a, double b) {
        double r614640 = b;
        double r614641 = atan2(r614640, r614640);
        double r614642 = sqrt(r614641);
        double r614643 = a;
        double r614644 = r614640 - r614643;
        double r614645 = pow(r614642, r614644);
        double r614646 = sin(r614645);
        return r614646;
}

↓

double f(double a, double b) {
        double r614647 = b;
        double r614648 = atan2(r614647, r614647);
        double r614649 = log(r614648);
        double r614650 = cbrt(r614649);
        double r614651 = 4.0;
        double r614652 = r614650 / r614651;
        double r614653 = a;
        double r614654 = r614647 - r614653;
        double r614655 = r614650 * r614654;
        double r614656 = r614655 * r614650;
        double r614657 = r614652 * r614656;
        double r614658 = exp(r614657);
        double r614659 = sqrt(r614648);
        double r614660 = sqrt(r614659);
        double r614661 = pow(r614660, r614654);
        double r614662 = r614658 * r614661;
        double r614663 = sin(r614662);
        return r614663;
}

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. Taylor expanded around -inf 0.1

   \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \color{blue}{e^{\log \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{4}}\right) \cdot \left(b - a\right)}}\right)\]

7. Simplified 0.1

   \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \color{blue}{e^{\left(b - a\right) \cdot \frac{\log \left(\tan^{-1}_* \frac{b}{b}\right)}{4}}}\right)\]
8. Using strategy rm

9. Applied *-un-lft-identity 0.1

   \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\left(b - a\right) \cdot \frac{\log \left(\tan^{-1}_* \frac{b}{b}\right)}{\color{blue}{1 \cdot 4}}}\right)\]

10. Applied add-cube-cbrt 0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\left(b - a\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}\right) \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}}{1 \cdot 4}}\right)\]

11. Applied times-frac 0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\left(b - a\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{1} \cdot \frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4}\right)}}\right)\]

12. Applied associate-*r* 0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\color{blue}{\left(\left(b - a\right) \cdot \frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{1}\right) \cdot \frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4}}}\right)\]

13. Simplified 0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\color{blue}{\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \left(b - a\right)\right)\right)} \cdot \frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4}}\right)\]

14. Final simplification 0.1

    \[\leadsto \sin \left(e^{\frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4} \cdot \left(\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \left(b - a\right)\right) \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

Reproduce

herbie shell --seed 2019151 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))