Average Error: 16.0 → 0.8
Time: 37.0s
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 r6984539 = g;
        double r6984540 = 2.0;
        double r6984541 = a;
        double r6984542 = r6984540 * r6984541;
        double r6984543 = r6984539 / r6984542;
        double r6984544 = cbrt(r6984543);
        return r6984544;
}
↓
double f(double g, double a) {
        double r6984545 = -0.5;
        double r6984546 = cbrt(r6984545);
        double r6984547 = -1.0;
        double r6984548 = a;
        double r6984549 = r6984547 / r6984548;
        double r6984550 = cbrt(r6984549);
        double r6984551 = r6984546 * r6984550;
        double r6984552 = g;
        double r6984553 = cbrt(r6984552);
        double r6984554 = r6984551 * r6984553;
        return r6984554;
}

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 16.0

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

  3. Applied div-inv16.0

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around -inf 34.7

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

  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 2019168 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))