Average Error: 5.3 → 0.1
Time: 13.5s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \frac{3 - x}{3}
double f(double x, double y) {
        double r457978 = 1.0;
        double r457979 = x;
        double r457980 = r457978 - r457979;
        double r457981 = 3.0;
        double r457982 = r457981 - r457979;
        double r457983 = r457980 * r457982;
        double r457984 = y;
        double r457985 = r457984 * r457981;
        double r457986 = r457983 / r457985;
        return r457986;
}
↓
double f(double x, double y) {
        double r457987 = 1.0;
        double r457988 = x;
        double r457989 = r457987 - r457988;
        double r457990 = y;
        double r457991 = r457989 / r457990;
        double r457992 = 3.0;
        double r457993 = r457992 - r457988;
        double r457994 = r457993 / r457992;
        double r457995 = r457991 * r457994;
        return r457995;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 5.3

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

  3. Applied times-frac0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1 x) y) (/ (- 3 x) 3))

  (/ (* (- 1 x) (- 3 x)) (* y 3)))