Average Error: 16.2 → 0.8
Time: 13.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{\sqrt{1}}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{\sqrt{1}}{a}}
double f(double g, double a) {
        double r140285 = g;
        double r140286 = 2.0;
        double r140287 = a;
        double r140288 = r140286 * r140287;
        double r140289 = r140285 / r140288;
        double r140290 = cbrt(r140289);
        return r140290;
}
↓
double f(double g, double a) {
        double r140291 = g;
        double r140292 = cbrt(r140291);
        double r140293 = 1.0;
        double r140294 = 2.0;
        double r140295 = r140293 / r140294;
        double r140296 = cbrt(r140295);
        double r140297 = r140292 * r140296;
        double r140298 = sqrt(r140293);
        double r140299 = a;
        double r140300 = r140298 / r140299;
        double r140301 = cbrt(r140300);
        double r140302 = r140297 * r140301;
        return r140302;
}

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 16.2

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

  3. Applied div-inv16.2

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

  4. Applied cbrt-prod0.9

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.9

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

  7. Applied times-frac0.8

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

  8. Applied cbrt-prod0.8

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

  9. Applied associate-*r*0.8

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

  10. Simplified0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))