Average Error: 15.6 → 0.9
Time: 4.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\frac{\sqrt[3]{g}}{\sqrt{\sqrt[3]{2}} \cdot \sqrt{\sqrt[3]{2}}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\frac{\sqrt[3]{g}}{\sqrt{\sqrt[3]{2}} \cdot \sqrt{\sqrt[3]{2}}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r99579 = g;
        double r99580 = 2.0;
        double r99581 = a;
        double r99582 = r99580 * r99581;
        double r99583 = r99579 / r99582;
        double r99584 = cbrt(r99583);
        return r99584;
}
↓
double f(double g, double a) {
        double r99585 = g;
        double r99586 = cbrt(r99585);
        double r99587 = 2.0;
        double r99588 = cbrt(r99587);
        double r99589 = sqrt(r99588);
        double r99590 = r99589 * r99589;
        double r99591 = r99586 / r99590;
        double r99592 = a;
        double r99593 = cbrt(r99592);
        double r99594 = r99591 / r99593;
        return r99594;
}

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.6

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

  3. Applied cbrt-div0.9

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

  5. Applied cbrt-prod1.1

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

  6. Applied associate-/r*1.1

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

  8. Applied add-sqr-sqrt0.9

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

  9. Final simplification0.9

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

Reproduce

herbie shell --seed 2020100 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))