Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 4.5s

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 r15833 = b;
        double r15834 = atan2(r15833, r15833);
        double r15835 = sqrt(r15834);
        double r15836 = a;
        double r15837 = r15833 - r15836;
        double r15838 = pow(r15835, r15837);
        double r15839 = sin(r15838);
        return r15839;
}

↓

double f(double a, double b) {
        double r15840 = b;
        double r15841 = atan2(r15840, r15840);
        double r15842 = sqrt(r15841);
        double r15843 = sqrt(r15842);
        double r15844 = a;
        double r15845 = r15840 - r15844;
        double r15846 = pow(r15843, r15845);
        double r15847 = cbrt(r15843);
        double r15848 = r15847 * r15847;
        double r15849 = pow(r15848, r15845);
        double r15850 = pow(r15847, r15845);
        double r15851 = r15849 * r15850;
        double r15852 = r15846 * r15851;
        double r15853 = sin(r15852);
        return r15853;
}

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 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))