Average Error: 15.4 → 0.8
Time: 27.9s
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 r4707332 = g;
        double r4707333 = 2.0;
        double r4707334 = a;
        double r4707335 = r4707333 * r4707334;
        double r4707336 = r4707332 / r4707335;
        double r4707337 = cbrt(r4707336);
        return r4707337;
}
↓
double f(double g, double a) {
        double r4707338 = g;
        double r4707339 = cbrt(r4707338);
        double r4707340 = 2.0;
        double r4707341 = a;
        double r4707342 = r4707340 * r4707341;
        double r4707343 = cbrt(r4707342);
        double r4707344 = r4707339 / r4707343;
        return r4707344;
}

Error

Bits error versus g

Bits error versus a

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Results

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Derivation

  1. Initial program 15.4

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

  3. Applied cbrt-div0.8

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

  5. Applied div-inv0.8

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

  7. Applied un-div-inv0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2019200 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))