Average Error: 15.8 → 0.8
Time: 16.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{-1}{a}} \cdot \sqrt[3]{-0.5}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{-1}{a}} \cdot \sqrt[3]{-0.5}\right)
double f(double g, double a) {
        double r92333 = g;
        double r92334 = 2.0;
        double r92335 = a;
        double r92336 = r92334 * r92335;
        double r92337 = r92333 / r92336;
        double r92338 = cbrt(r92337);
        return r92338;
}
↓
double f(double g, double a) {
        double r92339 = g;
        double r92340 = cbrt(r92339);
        double r92341 = -1.0;
        double r92342 = a;
        double r92343 = r92341 / r92342;
        double r92344 = cbrt(r92343);
        double r92345 = -0.5;
        double r92346 = cbrt(r92345);
        double r92347 = r92344 * r92346;
        double r92348 = r92340 * r92347;
        return r92348;
}

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 15.8

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

  3. Applied div-inv15.8

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around -inf 34.3

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

  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

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))