Random Jason Timeout Test 003

Average Error: 0.2 → 0.1

Time: 31.2s

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.313660165890731e+245
  2. b = 7.161382394770597e-199

Math

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

↓

\[\sin \left({\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{b - a}{4}\right)}\right)\]

C

double f(double a, double b) {
        double r2528792 = b;
        double r2528793 = atan2(r2528792, r2528792);
        double r2528794 = sqrt(r2528793);
        double r2528795 = a;
        double r2528796 = r2528792 - r2528795;
        double r2528797 = pow(r2528794, r2528796);
        double r2528798 = sin(r2528797);
        return r2528798;
}

↓

double f(double a, double b) {
        double r2528799 = b;
        double r2528800 = atan2(r2528799, r2528799);
        double r2528801 = sqrt(r2528800);
        double r2528802 = sqrt(r2528801);
        double r2528803 = a;
        double r2528804 = r2528799 - r2528803;
        double r2528805 = cbrt(r2528804);
        double r2528806 = r2528805 * r2528805;
        double r2528807 = pow(r2528802, r2528806);
        double r2528808 = pow(r2528807, r2528805);
        double r2528809 = 4.0;
        double r2528810 = r2528804 / r2528809;
        double r2528811 = pow(r2528800, r2528810);
        double r2528812 = r2528808 * r2528811;
        double r2528813 = sin(r2528812);
        return r2528813;
}

Error

Bits error versus a

Bits error versus b

Derivation

1. Initial program 0.2

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

3. Applied add-sqr-sqrt 0.2

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

4. Applied sqrt-prod 0.2

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

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 pow1/2 0.1

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

8. Applied sqrt-pow1 0.1

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

9. Applied pow-pow 0.1

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

10. Simplified 0.1

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

12. Applied add-cube-cbrt 0.1

    \[\leadsto \sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{b - a}{4}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\color{blue}{\left(\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right) \cdot \sqrt[3]{b - a}\right)}}\right)\]

13. Applied pow-unpow 0.1

    \[\leadsto \sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{b - a}{4}\right)} \cdot \color{blue}{{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)}}\right)\]

14. Final simplification 0.1

    \[\leadsto \sin \left({\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{b - a}{4}\right)}\right)\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))