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

Average Error: 5.4 → 0.1

Time: 19.2s

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 r30004068 = 1.0;
        double r30004069 = x;
        double r30004070 = r30004068 - r30004069;
        double r30004071 = 3.0;
        double r30004072 = r30004071 - r30004069;
        double r30004073 = r30004070 * r30004072;
        double r30004074 = y;
        double r30004075 = r30004074 * r30004071;
        double r30004076 = r30004073 / r30004075;
        return r30004076;
}

↓

double f(double x, double y) {
        double r30004077 = 3.0;
        double r30004078 = x;
        double r30004079 = r30004077 - r30004078;
        double r30004080 = r30004079 / r30004077;
        double r30004081 = 1.0;
        double r30004082 = r30004081 - r30004078;
        double r30004083 = y;
        double r30004084 = r30004082 / r30004083;
        double r30004085 = r30004080 * r30004084;
        return r30004085;
}

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)))