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

Average Error: 5.6 → 0.2

Time: 17.0s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r421232 = 1.0;
        double r421233 = x;
        double r421234 = r421232 - r421233;
        double r421235 = 3.0;
        double r421236 = r421235 - r421233;
        double r421237 = r421234 * r421236;
        double r421238 = y;
        double r421239 = r421238 * r421235;
        double r421240 = r421237 / r421239;
        return r421240;
}

↓

double f(double x, double y) {
        double r421241 = 1.0;
        double r421242 = y;
        double r421243 = 1.0;
        double r421244 = x;
        double r421245 = r421243 - r421244;
        double r421246 = r421242 / r421245;
        double r421247 = r421241 / r421246;
        double r421248 = 3.0;
        double r421249 = r421248 - r421244;
        double r421250 = r421249 / r421248;
        double r421251 = r421247 * r421250;
        return r421251;
}

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 clear-num 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019323 +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)))