Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 26.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.0362876411490344e+263
  2. b = 9.656044930860567e+126

Math

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

↓

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

C

double f(double a, double b) {
        double r1299463 = b;
        double r1299464 = atan2(r1299463, r1299463);
        double r1299465 = sqrt(r1299464);
        double r1299466 = a;
        double r1299467 = r1299463 - r1299466;
        double r1299468 = pow(r1299465, r1299467);
        double r1299469 = sin(r1299468);
        return r1299469;
}

↓

double f(double a, double b) {
        double r1299470 = b;
        double r1299471 = atan2(r1299470, r1299470);
        double r1299472 = sqrt(r1299471);
        double r1299473 = sqrt(r1299472);
        double r1299474 = a;
        double r1299475 = r1299470 - r1299474;
        double r1299476 = pow(r1299473, r1299475);
        double r1299477 = sqrt(r1299476);
        double r1299478 = 0.25;
        double r1299479 = log(r1299471);
        double r1299480 = r1299478 * r1299479;
        double r1299481 = r1299475 * r1299480;
        double r1299482 = exp(r1299481);
        double r1299483 = sqrt(r1299482);
        double r1299484 = r1299477 * r1299483;
        double r1299485 = r1299484 * r1299476;
        double r1299486 = sin(r1299485);
        return r1299486;
}

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-sqr-sqrt 0.1

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

8. Taylor expanded around inf 0.1

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

9. Simplified 0.1

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

10. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019146 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))