Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 16.9s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. a = 7.113723716624242e+188
  2. b = 3.1812150306990062e-208

Math

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

↓

\[e^{\log \left(\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)\right)}\]

C

double f(double a, double b) {
        double r19749 = b;
        double r19750 = atan2(r19749, r19749);
        double r19751 = sqrt(r19750);
        double r19752 = a;
        double r19753 = r19749 - r19752;
        double r19754 = pow(r19751, r19753);
        double r19755 = sin(r19754);
        return r19755;
}

↓

double f(double a, double b) {
        double r19756 = b;
        double r19757 = atan2(r19756, r19756);
        double r19758 = sqrt(r19757);
        double r19759 = sqrt(r19758);
        double r19760 = 2.0;
        double r19761 = a;
        double r19762 = r19756 - r19761;
        double r19763 = r19760 * r19762;
        double r19764 = pow(r19759, r19763);
        double r19765 = sin(r19764);
        double r19766 = log(r19765);
        double r19767 = exp(r19766);
        return r19767;
}

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-exp-log 0.1

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

8. Simplified 0.1

   \[\leadsto e^{\color{blue}{\log \left(\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)\right)}}\]

9. Final simplification 0.1

   \[\leadsto e^{\log \left(\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)\right)}\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))