Average Error: 14.6 → 0.9
Time: 19.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{g}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{g}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r3571171 = g;
        double r3571172 = 2.0;
        double r3571173 = a;
        double r3571174 = r3571172 * r3571173;
        double r3571175 = r3571171 / r3571174;
        double r3571176 = cbrt(r3571175);
        return r3571176;
}
↓
double f(double g, double a) {
        double r3571177 = 0.5;
        double r3571178 = cbrt(r3571177);
        double r3571179 = g;
        double r3571180 = cbrt(r3571179);
        double r3571181 = r3571178 * r3571180;
        double r3571182 = a;
        double r3571183 = cbrt(r3571182);
        double r3571184 = r3571181 / r3571183;
        return r3571184;
}

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 14.6

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

  3. Applied div-inv14.6

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

  4. Applied cbrt-prod0.8

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

  5. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\sqrt[3]{\frac{\frac{1}{2}}{a}}}\]
  6. Using strategy rm

  7. Applied cbrt-div0.9

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

  8. Applied associate-*r/0.9

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

  9. Final simplification0.9

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))