Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 19.9s

Precision: 64

• could not determine a ground truth for program body

  1. a = 3.11214772715739e+301
  2. b = 1.3033505323871184e+57

Math

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

↓

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

C

double f(double a, double b) {
        double r1247286 = b;
        double r1247287 = atan2(r1247286, r1247286);
        double r1247288 = sqrt(r1247287);
        double r1247289 = a;
        double r1247290 = r1247286 - r1247289;
        double r1247291 = pow(r1247288, r1247290);
        double r1247292 = sin(r1247291);
        return r1247292;
}

↓

double f(double a, double b) {
        double r1247293 = b;
        double r1247294 = atan2(r1247293, r1247293);
        double r1247295 = sqrt(r1247294);
        double r1247296 = sqrt(r1247295);
        double r1247297 = a;
        double r1247298 = r1247293 - r1247297;
        double r1247299 = pow(r1247296, r1247298);
        double r1247300 = cbrt(r1247298);
        double r1247301 = r1247300 * r1247300;
        double r1247302 = pow(r1247296, r1247301);
        double r1247303 = r1247293 + r1247297;
        double r1247304 = r1247303 * r1247298;
        double r1247305 = cbrt(r1247304);
        double r1247306 = cbrt(r1247303);
        double r1247307 = r1247305 / r1247306;
        double r1247308 = pow(r1247302, r1247307);
        double r1247309 = r1247299 * r1247308;
        double r1247310 = sin(r1247309);
        return r1247310;
}

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

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

8. Applied pow-unpow 0.1

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

10. Applied flip-- 3.9

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

11. Applied cbrt-div 3.9

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

12. Simplified 0.1

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

13. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))