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

Average Error: 5.4 → 0.1

Time: 14.8s

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 r33435732 = 1.0;
        double r33435733 = x;
        double r33435734 = r33435732 - r33435733;
        double r33435735 = 3.0;
        double r33435736 = r33435735 - r33435733;
        double r33435737 = r33435734 * r33435736;
        double r33435738 = y;
        double r33435739 = r33435738 * r33435735;
        double r33435740 = r33435737 / r33435739;
        return r33435740;
}

↓

double f(double x, double y) {
        double r33435741 = 3.0;
        double r33435742 = x;
        double r33435743 = r33435741 - r33435742;
        double r33435744 = r33435743 / r33435741;
        double r33435745 = 1.0;
        double r33435746 = r33435745 - r33435742;
        double r33435747 = y;
        double r33435748 = r33435746 / r33435747;
        double r33435749 = r33435744 * r33435748;
        return r33435749;
}

Error

Bits error versus x

Bits error versus y

Target

Original	5.4
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 5.4

   \[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
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 2019163 
(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)))