Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 15.1s

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 r6907 = b;
        double r6908 = atan2(r6907, r6907);
        double r6909 = sqrt(r6908);
        double r6910 = a;
        double r6911 = r6907 - r6910;
        double r6912 = pow(r6909, r6911);
        double r6913 = sin(r6912);
        return r6913;
}

↓

double f(double a, double b) {
        double r6914 = b;
        double r6915 = atan2(r6914, r6914);
        double r6916 = sqrt(r6915);
        double r6917 = sqrt(r6916);
        double r6918 = 2.0;
        double r6919 = a;
        double r6920 = r6914 - r6919;
        double r6921 = r6918 * r6920;
        double r6922 = pow(r6917, r6921);
        double r6923 = sin(r6922);
        double r6924 = log(r6923);
        double r6925 = exp(r6924);
        return r6925;
}

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 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))