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

Average Error: 33.7 → 0.4

Time: 24.4s

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 r25949940 = x;
        double r25949941 = r25949940 * r25949940;
        double r25949942 = y;
        double r25949943 = r25949942 * r25949942;
        double r25949944 = r25949941 / r25949943;
        double r25949945 = z;
        double r25949946 = r25949945 * r25949945;
        double r25949947 = t;
        double r25949948 = r25949947 * r25949947;
        double r25949949 = r25949946 / r25949948;
        double r25949950 = r25949944 + r25949949;
        return r25949950;
}

↓

double f(double x, double y, double z, double t) {
        double r25949951 = z;
        double r25949952 = t;
        double r25949953 = r25949951 / r25949952;
        double r25949954 = x;
        double r25949955 = y;
        double r25949956 = r25949954 / r25949955;
        double r25949957 = r25949956 * r25949956;
        double r25949958 = fma(r25949953, r25949953, r25949957);
        return r25949958;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	33.7
Target	0.4
Herbie	0.4

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

Derivation

1. Initial program 33.7

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

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 2019169 +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))))