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

Average Error: 5.6 → 0.1

Time: 2.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r616222 = 1.0;
        double r616223 = x;
        double r616224 = r616222 - r616223;
        double r616225 = 3.0;
        double r616226 = r616225 - r616223;
        double r616227 = r616224 * r616226;
        double r616228 = y;
        double r616229 = r616228 * r616225;
        double r616230 = r616227 / r616229;
        return r616230;
}

↓

double f(double x, double y) {
        double r616231 = 1.0;
        double r616232 = y;
        double r616233 = r616231 / r616232;
        double r616234 = x;
        double r616235 = r616234 / r616232;
        double r616236 = r616233 - r616235;
        double r616237 = 3.0;
        double r616238 = r616237 - r616234;
        double r616239 = r616238 / r616237;
        double r616240 = r616236 * r616239;
        return r616240;
}

Error

Bits error versus x

Bits error versus y

Target

Original	5.6
Target	0.1
Herbie	0.1

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

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-sub 0.1

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

6. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020062 
(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)))