2-ancestry mixing, zero discriminant

Average Error: 15.6 → 0.9

Time: 17.9s

Precision: 64

Math

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

↓

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

C

double f(double g, double a) {
        double r2728628 = g;
        double r2728629 = 2.0;
        double r2728630 = a;
        double r2728631 = r2728629 * r2728630;
        double r2728632 = r2728628 / r2728631;
        double r2728633 = cbrt(r2728632);
        return r2728633;
}

↓

double f(double g, double a) {
        double r2728634 = 1.0;
        double r2728635 = a;
        double r2728636 = 2.0;
        double r2728637 = r2728635 * r2728636;
        double r2728638 = cbrt(r2728637);
        double r2728639 = r2728634 / r2728638;
        double r2728640 = g;
        double r2728641 = cbrt(r2728640);
        double r2728642 = r2728634 / r2728641;
        double r2728643 = r2728639 / r2728642;
        return r2728643;
}

Error

Bits error versus g

Bits error versus a

Derivation

1. Initial program 15.6

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

3. Applied cbrt-div 0.9

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

5. Applied *-un-lft-identity 0.9

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

6. Applied associate-/l* 0.9

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

8. Applied div-inv 0.9

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

9. Applied associate-/r* 0.9

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

10. Final simplification 0.9

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

Reproduce

herbie shell --seed 2019153 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))