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

Average Error: 5.4 → 0.1

Time: 18.5s

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 r31122559 = 1.0;
        double r31122560 = x;
        double r31122561 = r31122559 - r31122560;
        double r31122562 = 3.0;
        double r31122563 = r31122562 - r31122560;
        double r31122564 = r31122561 * r31122563;
        double r31122565 = y;
        double r31122566 = r31122565 * r31122562;
        double r31122567 = r31122564 / r31122566;
        return r31122567;
}

↓

double f(double x, double y) {
        double r31122568 = 3.0;
        double r31122569 = x;
        double r31122570 = r31122568 - r31122569;
        double r31122571 = r31122570 / r31122568;
        double r31122572 = 1.0;
        double r31122573 = r31122572 - r31122569;
        double r31122574 = y;
        double r31122575 = r31122573 / r31122574;
        double r31122576 = r31122571 * r31122575;
        return r31122576;
}

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 +o rules:numerics
(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)))