Average Error: 5.4 → 0.2
Time: 20.4s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \frac{\frac{3 - x}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \frac{\frac{3 - x}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}
double f(double x, double y) {
        double r77745969 = 1.0;
        double r77745970 = x;
        double r77745971 = r77745969 - r77745970;
        double r77745972 = 3.0;
        double r77745973 = r77745972 - r77745970;
        double r77745974 = r77745971 * r77745973;
        double r77745975 = y;
        double r77745976 = r77745975 * r77745972;
        double r77745977 = r77745974 / r77745976;
        return r77745977;
}
↓
double f(double x, double y) {
        double r77745978 = 1.0;
        double r77745979 = x;
        double r77745980 = r77745978 - r77745979;
        double r77745981 = y;
        double r77745982 = r77745980 / r77745981;
        double r77745983 = 3.0;
        double r77745984 = r77745983 - r77745979;
        double r77745985 = cbrt(r77745983);
        double r77745986 = r77745985 * r77745985;
        double r77745987 = r77745984 / r77745986;
        double r77745988 = r77745987 / r77745985;
        double r77745989 = r77745982 * r77745988;
        return r77745989;
}

Error

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Results

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Target

Original5.4
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.4

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.1

    \[\leadsto \frac{1 - x}{y} \cdot \frac{3 - x}{\color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}}}\]

  6. Applied associate-/r*0.2

    \[\leadsto \frac{1 - x}{y} \cdot \color{blue}{\frac{\frac{3 - x}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}}\]

  7. Final simplification0.2

    \[\leadsto \frac{1 - x}{y} \cdot \frac{\frac{3 - x}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))