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

Average Error: 5.2 → 0.1

Time: 15.5s

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 r28957427 = 1.0;
        double r28957428 = x;
        double r28957429 = r28957427 - r28957428;
        double r28957430 = 3.0;
        double r28957431 = r28957430 - r28957428;
        double r28957432 = r28957429 * r28957431;
        double r28957433 = y;
        double r28957434 = r28957433 * r28957430;
        double r28957435 = r28957432 / r28957434;
        return r28957435;
}

↓

double f(double x, double y) {
        double r28957436 = 3.0;
        double r28957437 = x;
        double r28957438 = r28957436 - r28957437;
        double r28957439 = r28957438 / r28957436;
        double r28957440 = 1.0;
        double r28957441 = r28957440 - r28957437;
        double r28957442 = y;
        double r28957443 = r28957441 / r28957442;
        double r28957444 = r28957439 * r28957443;
        return r28957444;
}

Error

Bits error versus x

Bits error versus y

Target

Original	5.2
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 5.2

   \[\frac{\left(1.0 - x\right) \cdot \left(3.0 - x\right)}{y \cdot 3.0}\]
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 2019162 +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)))