Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 4.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.1400289630919464e+77
  2. b = 9.354890242965149e-94

Math

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

↓

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

C

double f(double a, double b) {
        double r4984 = b;
        double r4985 = atan2(r4984, r4984);
        double r4986 = sqrt(r4985);
        double r4987 = a;
        double r4988 = r4984 - r4987;
        double r4989 = pow(r4986, r4988);
        double r4990 = sin(r4989);
        return r4990;
}

↓

double f(double a, double b) {
        double r4991 = b;
        double r4992 = atan2(r4991, r4991);
        double r4993 = sqrt(r4992);
        double r4994 = sqrt(r4993);
        double r4995 = a;
        double r4996 = r4991 - r4995;
        double r4997 = pow(r4994, r4996);
        double r4998 = cbrt(r4994);
        double r4999 = r4998 * r4998;
        double r5000 = pow(r4999, r4996);
        double r5001 = pow(r4998, r4996);
        double r5002 = r5000 * r5001;
        double r5003 = r4997 * r5002;
        double r5004 = sin(r5003);
        return r5004;
}

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

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

8. Applied unpow-prod-down 0.1

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

9. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019362 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))