Average Error: 15.5 → 0.8
Time: 12.9s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)
double f(double g, double a) {
        double r134652 = g;
        double r134653 = 2.0;
        double r134654 = a;
        double r134655 = r134653 * r134654;
        double r134656 = r134652 / r134655;
        double r134657 = cbrt(r134656);
        return r134657;
}
↓
double f(double g, double a) {
        double r134658 = g;
        double r134659 = cbrt(r134658);
        double r134660 = -0.5;
        double r134661 = cbrt(r134660);
        double r134662 = -1.0;
        double r134663 = a;
        double r134664 = r134662 / r134663;
        double r134665 = cbrt(r134664);
        double r134666 = r134661 * r134665;
        double r134667 = r134659 * r134666;
        return r134667;
}

Error

Bits error versus g

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.5

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

  3. Applied div-inv15.5

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

  4. Applied cbrt-prod0.8

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

  5. Taylor expanded around -inf 34.2

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left({\left(\frac{-1}{a}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{-0.5}\right)}\]

  6. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)}\]

  7. Final simplification0.8

    \[\leadsto \sqrt[3]{g} \cdot \left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))