2-ancestry mixing, zero discriminant

Average Error: 15.5 → 0.8

Time: 12.0s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\sqrt[3]{\frac{g}{2 \cdot a}}\]

↓

\[\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{g}\]

C

double f(double g, double a) {
        double r127904 = g;
        double r127905 = 2.0;
        double r127906 = a;
        double r127907 = r127905 * r127906;
        double r127908 = r127904 / r127907;
        double r127909 = cbrt(r127908);
        return r127909;
}

↓

double f(double g, double a) {
        double r127910 = 1.0;
        double r127911 = 2.0;
        double r127912 = r127910 / r127911;
        double r127913 = cbrt(r127912);
        double r127914 = a;
        double r127915 = r127910 / r127914;
        double r127916 = cbrt(r127915);
        double r127917 = r127913 * r127916;
        double r127918 = g;
        double r127919 = cbrt(r127918);
        double r127920 = r127917 * r127919;
        return r127920;
}

Error

Bits error versus g

Bits error versus a

Derivation

1. Initial program 15.5

   \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
2. Using strategy rm

3. Applied div-inv 15.5

   \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}}\]

4. Applied cbrt-prod 0.8

   \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}}\]
5. Using strategy rm

6. Applied add-sqr-sqrt 0.8

   \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{2 \cdot a}}\]

7. Applied times-frac 0.8

   \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\color{blue}{\frac{\sqrt{1}}{2} \cdot \frac{\sqrt{1}}{a}}}\]

8. Applied cbrt-prod 0.8

   \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{\frac{\sqrt{1}}{2}} \cdot \sqrt[3]{\frac{\sqrt{1}}{a}}\right)}\]

9. Applied associate-*r* 0.8

   \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{\sqrt{1}}{2}}\right) \cdot \sqrt[3]{\frac{\sqrt{1}}{a}}}\]

10. Simplified 0.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right)} \cdot \sqrt[3]{\frac{\sqrt{1}}{a}}\]
11. Using strategy rm

12. Applied pow1 0.8

    \[\leadsto \left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \color{blue}{{\left(\sqrt[3]{\frac{\sqrt{1}}{a}}\right)}^{1}}\]

13. Applied pow1 0.8

    \[\leadsto \left(\sqrt[3]{g} \cdot \color{blue}{{\left(\sqrt[3]{\frac{1}{2}}\right)}^{1}}\right) \cdot {\left(\sqrt[3]{\frac{\sqrt{1}}{a}}\right)}^{1}\]

14. Applied pow1 0.8

    \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{g}\right)}^{1}} \cdot {\left(\sqrt[3]{\frac{1}{2}}\right)}^{1}\right) \cdot {\left(\sqrt[3]{\frac{\sqrt{1}}{a}}\right)}^{1}\]

15. Applied pow-prod-down 0.8

    \[\leadsto \color{blue}{{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right)}^{1}} \cdot {\left(\sqrt[3]{\frac{\sqrt{1}}{a}}\right)}^{1}\]

16. Applied pow-prod-down 0.8

    \[\leadsto \color{blue}{{\left(\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{\sqrt{1}}{a}}\right)}^{1}}\]

17. Simplified 0.8

    \[\leadsto {\color{blue}{\left(\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right)\right)}}^{1}\]

18. Final simplification 0.8

    \[\leadsto \left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{g}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))