Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 26.6s

Precision: 64

• could not determine a ground truth for program body

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

Math

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

↓

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

C

double f(double a, double b) {
        double r626642 = b;
        double r626643 = atan2(r626642, r626642);
        double r626644 = sqrt(r626643);
        double r626645 = a;
        double r626646 = r626642 - r626645;
        double r626647 = pow(r626644, r626646);
        double r626648 = sin(r626647);
        return r626648;
}

↓

double f(double a, double b) {
        double r626649 = b;
        double r626650 = atan2(r626649, r626649);
        double r626651 = sqrt(r626650);
        double r626652 = sqrt(r626651);
        double r626653 = a;
        double r626654 = r626649 - r626653;
        double r626655 = pow(r626652, r626654);
        double r626656 = log(r626650);
        double r626657 = cbrt(r626656);
        double r626658 = r626657 * r626657;
        double r626659 = 4.0;
        double r626660 = r626659 / r626654;
        double r626661 = r626660 / r626657;
        double r626662 = r626658 / r626661;
        double r626663 = exp(r626662);
        double r626664 = r626655 * r626663;
        double r626665 = sin(r626664);
        return r626665;
}

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

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

4. Applied unpow-prod-down 0.1

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

5. Taylor expanded around inf 0.1

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

6. Simplified 0.1

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

8. Applied add-cube-cbrt 0.1

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

9. Applied associate-/l* 0.1

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

10. Final simplification 0.1

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

Reproduce

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