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

Average Error: 33.9 → 0.4

Time: 20.0s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r38928118 = x;
        double r38928119 = r38928118 * r38928118;
        double r38928120 = y;
        double r38928121 = r38928120 * r38928120;
        double r38928122 = r38928119 / r38928121;
        double r38928123 = z;
        double r38928124 = r38928123 * r38928123;
        double r38928125 = t;
        double r38928126 = r38928125 * r38928125;
        double r38928127 = r38928124 / r38928126;
        double r38928128 = r38928122 + r38928127;
        return r38928128;
}

↓

double f(double x, double y, double z, double t) {
        double r38928129 = x;
        double r38928130 = y;
        double r38928131 = r38928129 / r38928130;
        double r38928132 = z;
        double r38928133 = t;
        double r38928134 = r38928132 / r38928133;
        double r38928135 = r38928134 * r38928134;
        double r38928136 = fma(r38928131, r38928131, r38928135);
        return r38928136;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	33.9
Target	0.4
Herbie	0.4

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

Derivation

1. Initial program 33.9

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

2. Simplified 0.4

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

3. Final simplification 0.4

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

Reproduce

herbie shell --seed 2019174 +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) 2.0) (pow (/ z t) 2.0))

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