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

Average Error: 5.6 → 0.2

Time: 2.7s

Precision: 64

Math

\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]

↓

\[\left(\left(1 - x\right) \cdot \frac{1}{y}\right) \cdot \frac{3 - x}{3}\]

C

double f(double x, double y) {
        double r671705 = 1.0;
        double r671706 = x;
        double r671707 = r671705 - r671706;
        double r671708 = 3.0;
        double r671709 = r671708 - r671706;
        double r671710 = r671707 * r671709;
        double r671711 = y;
        double r671712 = r671711 * r671708;
        double r671713 = r671710 / r671712;
        return r671713;
}

↓

double f(double x, double y) {
        double r671714 = 1.0;
        double r671715 = x;
        double r671716 = r671714 - r671715;
        double r671717 = 1.0;
        double r671718 = y;
        double r671719 = r671717 / r671718;
        double r671720 = r671716 * r671719;
        double r671721 = 3.0;
        double r671722 = r671721 - r671715;
        double r671723 = r671722 / r671721;
        double r671724 = r671720 * r671723;
        return r671724;
}

Error

Bits error versus x

Bits error versus y

Target

Original	5.6
Target	0.1
Herbie	0.2

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

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-frac 0.1

   \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}}\]
4. Using strategy rm

5. Applied div-inv 0.2

   \[\leadsto \color{blue}{\left(\left(1 - x\right) \cdot \frac{1}{y}\right)} \cdot \frac{3 - x}{3}\]

6. Final simplification 0.2

   \[\leadsto \left(\left(1 - x\right) \cdot \frac{1}{y}\right) \cdot \frac{3 - x}{3}\]

Reproduce

herbie shell --seed 2020062 +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)))