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

Average Error: 5.7 → 0.1

Time: 15.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r31015862 = 1.0;
        double r31015863 = x;
        double r31015864 = r31015862 - r31015863;
        double r31015865 = 3.0;
        double r31015866 = r31015865 - r31015863;
        double r31015867 = r31015864 * r31015866;
        double r31015868 = y;
        double r31015869 = r31015868 * r31015865;
        double r31015870 = r31015867 / r31015869;
        return r31015870;
}

↓

double f(double x, double y) {
        double r31015871 = 3.0;
        double r31015872 = x;
        double r31015873 = r31015871 - r31015872;
        double r31015874 = r31015873 / r31015871;
        double r31015875 = 1.0;
        double r31015876 = r31015875 - r31015872;
        double r31015877 = y;
        double r31015878 = r31015876 / r31015877;
        double r31015879 = r31015874 * r31015878;
        return r31015879;
}

Error

Bits error versus x

Bits error versus y

Target

Original	5.7
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 5.7

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
2. Using strategy rm

3. Applied times-frac 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019170 +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)))