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

Average Error: 5.6 → 0.2

Time: 14.6s

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 r438083 = 1.0;
        double r438084 = x;
        double r438085 = r438083 - r438084;
        double r438086 = 3.0;
        double r438087 = r438086 - r438084;
        double r438088 = r438085 * r438087;
        double r438089 = y;
        double r438090 = r438089 * r438086;
        double r438091 = r438088 / r438090;
        return r438091;
}

↓

double f(double x, double y) {
        double r438092 = 1.0;
        double r438093 = y;
        double r438094 = 1.0;
        double r438095 = x;
        double r438096 = r438094 - r438095;
        double r438097 = r438093 / r438096;
        double r438098 = r438092 / r438097;
        double r438099 = 3.0;
        double r438100 = r438099 - r438095;
        double r438101 = r438100 / r438099;
        double r438102 = r438098 * r438101;
        return r438102;
}

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)))