Average Error: 5.6 → 0.1
Time: 7.5s
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 r669863 = 1.0;
        double r669864 = x;
        double r669865 = r669863 - r669864;
        double r669866 = 3.0;
        double r669867 = r669866 - r669864;
        double r669868 = r669865 * r669867;
        double r669869 = y;
        double r669870 = r669869 * r669866;
        double r669871 = r669868 / r669870;
        return r669871;
}
↓
double f(double x, double y) {
        double r669872 = 1.0;
        double r669873 = x;
        double r669874 = r669872 - r669873;
        double r669875 = y;
        double r669876 = r669874 / r669875;
        double r669877 = 3.0;
        double r669878 = r669877 - r669873;
        double r669879 = r669878 / r669877;
        double r669880 = r669876 * r669879;
        return r669880;
}

Error

Bits error versus x

Bits error versus y

Try it out

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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 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 2020045 
(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)))