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

Average Error: 5.4 → 0.1

Time: 13.1s

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 r31626997 = 1.0;
        double r31626998 = x;
        double r31626999 = r31626997 - r31626998;
        double r31627000 = 3.0;
        double r31627001 = r31627000 - r31626998;
        double r31627002 = r31626999 * r31627001;
        double r31627003 = y;
        double r31627004 = r31627003 * r31627000;
        double r31627005 = r31627002 / r31627004;
        return r31627005;
}

↓

double f(double x, double y) {
        double r31627006 = 3.0;
        double r31627007 = x;
        double r31627008 = r31627006 - r31627007;
        double r31627009 = r31627008 / r31627006;
        double r31627010 = 1.0;
        double r31627011 = r31627010 - r31627007;
        double r31627012 = y;
        double r31627013 = r31627011 / r31627012;
        double r31627014 = r31627009 * r31627013;
        return r31627014;
}

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)))