Average Error: 15.3 → 0.8
Time: 15.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{0.5} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{0.5} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r4800087 = g;
        double r4800088 = 2.0;
        double r4800089 = a;
        double r4800090 = r4800088 * r4800089;
        double r4800091 = r4800087 / r4800090;
        double r4800092 = cbrt(r4800091);
        return r4800092;
}
↓
double f(double g, double a) {
        double r4800093 = 0.5;
        double r4800094 = cbrt(r4800093);
        double r4800095 = 1.0;
        double r4800096 = a;
        double r4800097 = r4800095 / r4800096;
        double r4800098 = cbrt(r4800097);
        double r4800099 = r4800094 * r4800098;
        double r4800100 = g;
        double r4800101 = cbrt(r4800100);
        double r4800102 = r4800099 * r4800101;
        return r4800102;
}

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 15.3

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  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. Taylor expanded around 0 34.5

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

  6. Simplified0.8

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

  7. Final simplification0.8

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))