Average Error: 15.2 → 0.9
Time: 14.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}
double f(double g, double a) {
        double r3650278 = g;
        double r3650279 = 2.0;
        double r3650280 = a;
        double r3650281 = r3650279 * r3650280;
        double r3650282 = r3650278 / r3650281;
        double r3650283 = cbrt(r3650282);
        return r3650283;
}
↓
double f(double g, double a) {
        double r3650284 = g;
        double r3650285 = cbrt(r3650284);
        double r3650286 = 2.0;
        double r3650287 = a;
        double r3650288 = r3650286 * r3650287;
        double r3650289 = cbrt(r3650288);
        double r3650290 = r3650285 / r3650289;
        return r3650290;
}

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 15.2

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

  3. Applied cbrt-div0.9

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

  5. Applied *-un-lft-identity0.9

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

  6. Applied associate-/r*0.9

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

  7. Simplified0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019135 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))