Average Error: 16.1 → 0.9
Time: 18.2s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}
double f(double g, double a) {
        double r4610614 = g;
        double r4610615 = 2.0;
        double r4610616 = a;
        double r4610617 = r4610615 * r4610616;
        double r4610618 = r4610614 / r4610617;
        double r4610619 = cbrt(r4610618);
        return r4610619;
}
↓
double f(double g, double a) {
        double r4610620 = g;
        double r4610621 = cbrt(r4610620);
        double r4610622 = 1.0;
        double r4610623 = a;
        double r4610624 = 2.0;
        double r4610625 = r4610623 * r4610624;
        double r4610626 = r4610622 / r4610625;
        double r4610627 = cbrt(r4610626);
        double r4610628 = r4610621 * r4610627;
        return r4610628;
}

Error

Bits error versus g

Bits error versus a

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Your Program's Arguments

Results

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Derivation

  1. Initial program 16.1

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

  3. Applied div-inv16.1

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

  4. Applied cbrt-prod0.9

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

  6. Applied add-cbrt-cube1.0

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

  7. Simplified0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019170 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))