Average Error: 15.1 → 0.9
Time: 17.7s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{1}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{1}{a}}
double f(double g, double a) {
        double r4596279 = g;
        double r4596280 = 2.0;
        double r4596281 = a;
        double r4596282 = r4596280 * r4596281;
        double r4596283 = r4596279 / r4596282;
        double r4596284 = cbrt(r4596283);
        return r4596284;
}
↓
double f(double g, double a) {
        double r4596285 = g;
        double r4596286 = cbrt(r4596285);
        double r4596287 = 0.5;
        double r4596288 = cbrt(r4596287);
        double r4596289 = r4596286 * r4596288;
        double r4596290 = 1.0;
        double r4596291 = a;
        double r4596292 = r4596290 / r4596291;
        double r4596293 = cbrt(r4596292);
        double r4596294 = r4596289 * r4596293;
        return r4596294;
}

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 15.1

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

  3. Applied div-inv15.1

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

  4. Applied cbrt-prod0.9

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

  5. Simplified0.9

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

  6. Taylor expanded around inf 49.2

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

  7. Simplified0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019138 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))