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

Average Error: 32.3 → 0.4

Time: 21.8s

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 r28057304 = x;
        double r28057305 = r28057304 * r28057304;
        double r28057306 = y;
        double r28057307 = r28057306 * r28057306;
        double r28057308 = r28057305 / r28057307;
        double r28057309 = z;
        double r28057310 = r28057309 * r28057309;
        double r28057311 = t;
        double r28057312 = r28057311 * r28057311;
        double r28057313 = r28057310 / r28057312;
        double r28057314 = r28057308 + r28057313;
        return r28057314;
}

↓

double f(double x, double y, double z, double t) {
        double r28057315 = z;
        double r28057316 = t;
        double r28057317 = r28057315 / r28057316;
        double r28057318 = x;
        double r28057319 = y;
        double r28057320 = r28057318 / r28057319;
        double r28057321 = r28057320 * r28057320;
        double r28057322 = fma(r28057317, r28057317, r28057321);
        return r28057322;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	32.3
Target	0.4
Herbie	0.4

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

Derivation

1. Initial program 32.3

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

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 2019162 +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))))