Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1

Average Error: 32.5 → 0.4

Time: 13.7s

Precision: 64

Math

\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]

↓

\[\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x}{y} \cdot \frac{x}{y}\right)\]

C

double f(double x, double y, double z, double t) {
        double r10719445 = x;
        double r10719446 = r10719445 * r10719445;
        double r10719447 = y;
        double r10719448 = r10719447 * r10719447;
        double r10719449 = r10719446 / r10719448;
        double r10719450 = z;
        double r10719451 = r10719450 * r10719450;
        double r10719452 = t;
        double r10719453 = r10719452 * r10719452;
        double r10719454 = r10719451 / r10719453;
        double r10719455 = r10719449 + r10719454;
        return r10719455;
}

↓

double f(double x, double y, double z, double t) {
        double r10719456 = z;
        double r10719457 = t;
        double r10719458 = r10719456 / r10719457;
        double r10719459 = x;
        double r10719460 = y;
        double r10719461 = r10719459 / r10719460;
        double r10719462 = r10719461 * r10719461;
        double r10719463 = fma(r10719458, r10719458, r10719462);
        return r10719463;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	32.5
Target	0.4
Herbie	0.4

\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

1. Initial program 32.5

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]

2. Simplified 0.4

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x}{y} \cdot \frac{x}{y}\right)}\]

3. Final simplification 0.4

   \[\leadsto \mathsf{fma}\left(\frac{z}{t}, \frac{z}{t}, \frac{x}{y} \cdot \frac{x}{y}\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"

  :herbie-target
  (+ (pow (/ x y) 2) (pow (/ z t) 2))

  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))