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

Average Error: 5.6 → 0.2

Time: 2.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r632507 = 1.0;
        double r632508 = x;
        double r632509 = r632507 - r632508;
        double r632510 = 3.0;
        double r632511 = r632510 - r632508;
        double r632512 = r632509 * r632511;
        double r632513 = y;
        double r632514 = r632513 * r632510;
        double r632515 = r632512 / r632514;
        return r632515;
}

↓

double f(double x, double y) {
        double r632516 = 1.0;
        double r632517 = x;
        double r632518 = r632516 - r632517;
        double r632519 = 1.0;
        double r632520 = y;
        double r632521 = r632519 / r632520;
        double r632522 = r632518 * r632521;
        double r632523 = 3.0;
        double r632524 = r632523 - r632517;
        double r632525 = r632524 / r632523;
        double r632526 = r632522 * r632525;
        return r632526;
}

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 div-inv 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020062 +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)))