Average Error: 15.8 → 0.8
Time: 11.1s
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 r134232 = g;
        double r134233 = 2.0;
        double r134234 = a;
        double r134235 = r134233 * r134234;
        double r134236 = r134232 / r134235;
        double r134237 = cbrt(r134236);
        return r134237;
}
↓
double f(double g, double a) {
        double r134238 = g;
        double r134239 = cbrt(r134238);
        double r134240 = 2.0;
        double r134241 = a;
        double r134242 = r134240 * r134241;
        double r134243 = cbrt(r134242);
        double r134244 = r134239 / r134243;
        return r134244;
}

Error

Bits error versus g

Bits error versus a

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Your Program's Arguments

Results

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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. Using strategy rm

  6. Applied cbrt-div0.9

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

  7. Applied associate-*r/0.8

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

  8. Simplified0.8

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

  9. Final simplification0.8

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

Reproduce

herbie shell --seed 2019291 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))