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

Average Error: 33.4 → 0.4

Time: 19.1s

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 r25632067 = x;
        double r25632068 = r25632067 * r25632067;
        double r25632069 = y;
        double r25632070 = r25632069 * r25632069;
        double r25632071 = r25632068 / r25632070;
        double r25632072 = z;
        double r25632073 = r25632072 * r25632072;
        double r25632074 = t;
        double r25632075 = r25632074 * r25632074;
        double r25632076 = r25632073 / r25632075;
        double r25632077 = r25632071 + r25632076;
        return r25632077;
}

↓

double f(double x, double y, double z, double t) {
        double r25632078 = x;
        double r25632079 = y;
        double r25632080 = r25632078 / r25632079;
        double r25632081 = z;
        double r25632082 = t;
        double r25632083 = r25632081 / r25632082;
        double r25632084 = r25632083 * r25632083;
        double r25632085 = fma(r25632080, r25632080, r25632084);
        return r25632085;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	33.4
Target	0.4
Herbie	0.4

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

Derivation

1. Initial program 33.4

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

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 2019179 +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))))