Average Error: 15.2 → 0.9
Time: 22.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{1}{a}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{1}{a}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right)
double f(double g, double a) {
        double r91191 = g;
        double r91192 = 2.0;
        double r91193 = a;
        double r91194 = r91192 * r91193;
        double r91195 = r91191 / r91194;
        double r91196 = cbrt(r91195);
        return r91196;
}
↓
double f(double g, double a) {
        double r91197 = 1.0;
        double r91198 = a;
        double r91199 = r91197 / r91198;
        double r91200 = cbrt(r91199);
        double r91201 = g;
        double r91202 = cbrt(r91201);
        double r91203 = 2.0;
        double r91204 = r91197 / r91203;
        double r91205 = cbrt(r91204);
        double r91206 = r91202 * r91205;
        double r91207 = r91200 * r91206;
        return r91207;
}

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 15.2

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

  3. Applied div-inv15.3

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

  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-sqr-sqrt0.9

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

  7. Applied times-frac0.9

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

  8. Applied cbrt-prod0.9

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

  9. Applied associate-*r*0.9

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

  10. Simplified0.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))