Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 4.7s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.8264699465001106e+111
  2. b = 2.317654564211401e+40

Math

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

↓

\[\sin \left(\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)}\right) \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{4} \cdot \left(b - a\right)\right)}\right)\]

C

double f(double a, double b) {
        double r20982 = b;
        double r20983 = atan2(r20982, r20982);
        double r20984 = sqrt(r20983);
        double r20985 = a;
        double r20986 = r20982 - r20985;
        double r20987 = pow(r20984, r20986);
        double r20988 = sin(r20987);
        return r20988;
}

↓

double f(double a, double b) {
        double r20989 = b;
        double r20990 = atan2(r20989, r20989);
        double r20991 = sqrt(r20990);
        double r20992 = sqrt(r20991);
        double r20993 = a;
        double r20994 = r20989 - r20993;
        double r20995 = 2.0;
        double r20996 = r20994 / r20995;
        double r20997 = pow(r20992, r20996);
        double r20998 = r20997 * r20997;
        double r20999 = 0.25;
        double r21000 = r20999 * r20994;
        double r21001 = pow(r20990, r21000);
        double r21002 = r20998 * r21001;
        double r21003 = sin(r21002);
        return r21003;
}

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 sqr-pow 0.1

   \[\leadsto \sin \left(\color{blue}{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]
8. Using strategy rm

9. Applied pow1/2 0.1

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

10. Applied sqrt-pow1 0.1

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

11. Applied pow-pow 0.1

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

12. Simplified 0.1

    \[\leadsto \sin \left(\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)}\right) \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\color{blue}{\left(\frac{1}{4} \cdot \left(b - a\right)\right)}}\right)\]

13. Final simplification 0.1

    \[\leadsto \sin \left(\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)}\right) \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{4} \cdot \left(b - a\right)\right)}\right)\]

Reproduce

herbie shell --seed 2020035 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))