Average Error: 15.5 → 0.8
Time: 17.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r4930659 = g;
        double r4930660 = 2.0;
        double r4930661 = a;
        double r4930662 = r4930660 * r4930661;
        double r4930663 = r4930659 / r4930662;
        double r4930664 = cbrt(r4930663);
        return r4930664;
}
↓
double f(double g, double a) {
        double r4930665 = 0.5;
        double r4930666 = a;
        double r4930667 = r4930665 / r4930666;
        double r4930668 = cbrt(r4930667);
        double r4930669 = g;
        double r4930670 = cbrt(r4930669);
        double r4930671 = r4930668 * r4930670;
        return r4930671;
}

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 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-prod0.9

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

  5. Simplified0.8

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

  6. Taylor expanded around 0 34.4

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

  7. Simplified0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2019141 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))