Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 5.1s

Precision: 64

• could not determine a ground truth for program body

  1. a = 2.8168093462857454e+294
  2. b = 2.725542050564335e+252

Math

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

↓

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

C

double f(double a, double b) {
        double r6472 = b;
        double r6473 = atan2(r6472, r6472);
        double r6474 = sqrt(r6473);
        double r6475 = a;
        double r6476 = r6472 - r6475;
        double r6477 = pow(r6474, r6476);
        double r6478 = sin(r6477);
        return r6478;
}

↓

double f(double a, double b) {
        double r6479 = b;
        double r6480 = atan2(r6479, r6479);
        double r6481 = sqrt(r6480);
        double r6482 = sqrt(r6481);
        double r6483 = cbrt(r6479);
        double r6484 = r6483 * r6483;
        double r6485 = a;
        double r6486 = cbrt(r6485);
        double r6487 = r6486 * r6486;
        double r6488 = r6486 * r6487;
        double r6489 = -r6488;
        double r6490 = fma(r6484, r6483, r6489);
        double r6491 = pow(r6482, r6490);
        double r6492 = -r6485;
        double r6493 = 1.0;
        double r6494 = r6485 * r6493;
        double r6495 = fma(r6492, r6493, r6494);
        double r6496 = pow(r6482, r6495);
        double r6497 = r6479 - r6485;
        double r6498 = pow(r6482, r6497);
        double r6499 = r6496 * r6498;
        double r6500 = r6491 * r6499;
        double r6501 = sin(r6500);
        return r6501;
}

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

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

8. Applied add-cube-cbrt 0.1

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

9. Applied prod-diff 0.1

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

10. Applied unpow-prod-up 11.1

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

11. Applied associate-*l* 11.1

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

12. Simplified 0.1

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

13. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))