Average Error: 15.3 → 0.8
Time: 15.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{-1} \cdot \sqrt[3]{-g}}{\sqrt[3]{a \cdot 2}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{-1} \cdot \sqrt[3]{-g}}{\sqrt[3]{a \cdot 2}}
double f(double g, double a) {
        double r5059405 = g;
        double r5059406 = 2.0;
        double r5059407 = a;
        double r5059408 = r5059406 * r5059407;
        double r5059409 = r5059405 / r5059408;
        double r5059410 = cbrt(r5059409);
        return r5059410;
}
↓
double f(double g, double a) {
        double r5059411 = -1.0;
        double r5059412 = cbrt(r5059411);
        double r5059413 = g;
        double r5059414 = -r5059413;
        double r5059415 = cbrt(r5059414);
        double r5059416 = r5059412 * r5059415;
        double r5059417 = a;
        double r5059418 = 2.0;
        double r5059419 = r5059417 * r5059418;
        double r5059420 = cbrt(r5059419);
        double r5059421 = r5059416 / r5059420;
        return r5059421;
}

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 cbrt-div0.8

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

  4. Taylor expanded around -inf 34.6

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

  5. Simplified0.8

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

  6. Final simplification0.8

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

Reproduce

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