Average Error: 15.5 → 0.8
Time: 10.7s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a} \cdot {\left(\sqrt[3]{0.5}\right)}^{3}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a} \cdot {\left(\sqrt[3]{0.5}\right)}^{3}}
double f(double g, double a) {
        double r127123 = g;
        double r127124 = 2.0;
        double r127125 = a;
        double r127126 = r127124 * r127125;
        double r127127 = r127123 / r127126;
        double r127128 = cbrt(r127127);
        return r127128;
}
↓
double f(double g, double a) {
        double r127129 = g;
        double r127130 = cbrt(r127129);
        double r127131 = 1.0;
        double r127132 = a;
        double r127133 = r127131 / r127132;
        double r127134 = 0.5;
        double r127135 = cbrt(r127134);
        double r127136 = 3.0;
        double r127137 = pow(r127135, r127136);
        double r127138 = r127133 * r127137;
        double r127139 = cbrt(r127138);
        double r127140 = r127130 * r127139;
        return r127140;
}

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 15.5

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  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. Taylor expanded around 0 34.9

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

  6. Simplified0.9

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{0.5} \cdot \sqrt[3]{\frac{1}{a}}\right)}\]
  7. Using strategy rm

  8. Applied add-cbrt-cube1.0

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

  9. Simplified0.8

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

  10. Final simplification0.8

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

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))