Average Error: 15.5 → 0.8
Time: 16.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r3517068 = g;
        double r3517069 = 2.0;
        double r3517070 = a;
        double r3517071 = r3517069 * r3517070;
        double r3517072 = r3517068 / r3517071;
        double r3517073 = cbrt(r3517072);
        return r3517073;
}
↓
double f(double g, double a) {
        double r3517074 = 0.5;
        double r3517075 = cbrt(r3517074);
        double r3517076 = 1.0;
        double r3517077 = a;
        double r3517078 = r3517076 / r3517077;
        double r3517079 = cbrt(r3517078);
        double r3517080 = r3517075 * r3517079;
        double r3517081 = g;
        double r3517082 = cbrt(r3517081);
        double r3517083 = r3517080 * r3517082;
        return r3517083;
}

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 15.5

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  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. Simplified0.8

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

  6. Taylor expanded around 0 33.4

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

  7. Simplified0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2019133 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))