Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3

Average Error: 5.6 → 0.1

Time: 12.3s

Precision: 64

Math

\[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]

↓

\[\frac{3.0 - x}{3.0} \cdot \frac{1.0 - x}{y}\]

C

double f(double x, double y) {
        double r27197769 = 1.0;
        double r27197770 = x;
        double r27197771 = r27197769 - r27197770;
        double r27197772 = 3.0;
        double r27197773 = r27197772 - r27197770;
        double r27197774 = r27197771 * r27197773;
        double r27197775 = y;
        double r27197776 = r27197775 * r27197772;
        double r27197777 = r27197774 / r27197776;
        return r27197777;
}

↓

double f(double x, double y) {
        double r27197778 = 3.0;
        double r27197779 = x;
        double r27197780 = r27197778 - r27197779;
        double r27197781 = r27197780 / r27197778;
        double r27197782 = 1.0;
        double r27197783 = r27197782 - r27197779;
        double r27197784 = y;
        double r27197785 = r27197783 / r27197784;
        double r27197786 = r27197781 * r27197785;
        return r27197786;
}

Error

Bits error versus x

Bits error versus y

Target

Original	5.6
Target	0.1
Herbie	0.1

\[\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}\]

Derivation

1. Initial program 5.6

   \[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
2. Using strategy rm

3. Applied times-frac 0.1

   \[\leadsto \color{blue}{\frac{1.0 - x}{y} \cdot \frac{3.0 - x}{3.0}}\]

4. Final simplification 0.1

   \[\leadsto \frac{3.0 - x}{3.0} \cdot \frac{1.0 - x}{y}\]

Reproduce

herbie shell --seed 2019165 
(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)))