Average Error: 5.6 → 0.1
Time: 11.1s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y \cdot \frac{3}{3 - x}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y \cdot \frac{3}{3 - x}}
double f(double x, double y) {
        double r686908 = 1.0;
        double r686909 = x;
        double r686910 = r686908 - r686909;
        double r686911 = 3.0;
        double r686912 = r686911 - r686909;
        double r686913 = r686910 * r686912;
        double r686914 = y;
        double r686915 = r686914 * r686911;
        double r686916 = r686913 / r686915;
        return r686916;
}
↓
double f(double x, double y) {
        double r686917 = 1.0;
        double r686918 = x;
        double r686919 = r686917 - r686918;
        double r686920 = y;
        double r686921 = 3.0;
        double r686922 = r686921 - r686918;
        double r686923 = r686921 / r686922;
        double r686924 = r686920 * r686923;
        double r686925 = r686919 / r686924;
        return r686925;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.6
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.6

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

  3. Applied associate-/l*0.3

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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)))