Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 27.2s

Precision: 64

• could not determine a ground truth for program body

  1. a = 2.946875762806093e+147
  2. b = 1.0173158586829269e-80

Math

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

↓

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

C

double f(double a, double b) {
        double r799124 = b;
        double r799125 = atan2(r799124, r799124);
        double r799126 = sqrt(r799125);
        double r799127 = a;
        double r799128 = r799124 - r799127;
        double r799129 = pow(r799126, r799128);
        double r799130 = sin(r799129);
        return r799130;
}

↓

double f(double a, double b) {
        double r799131 = b;
        double r799132 = atan2(r799131, r799131);
        double r799133 = sqrt(r799132);
        double r799134 = sqrt(r799133);
        double r799135 = a;
        double r799136 = r799131 - r799135;
        double r799137 = pow(r799134, r799136);
        double r799138 = cbrt(r799137);
        double r799139 = r799138 * r799138;
        double r799140 = r799139 * r799139;
        double r799141 = r799140 * r799139;
        double r799142 = sin(r799141);
        return r799142;
}

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

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

8. Applied add-cube-cbrt 0.1

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

9. Applied swap-sqr 0.1

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

10. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019144 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))