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

↓

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

\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)

double f(double x, double y, double z, double t) {
        double r24868133 = x;
        double r24868134 = r24868133 * r24868133;
        double r24868135 = y;
        double r24868136 = r24868135 * r24868135;
        double r24868137 = r24868134 / r24868136;
        double r24868138 = z;
        double r24868139 = r24868138 * r24868138;
        double r24868140 = t;
        double r24868141 = r24868140 * r24868140;
        double r24868142 = r24868139 / r24868141;
        double r24868143 = r24868137 + r24868142;
        return r24868143;
}

↓

double f(double x, double y, double z, double t) {
        double r24868144 = x;
        double r24868145 = y;
        double r24868146 = r24868144 / r24868145;
        double r24868147 = z;
        double r24868148 = t;
        double r24868149 = r24868147 / r24868148;
        double r24868150 = r24868149 * r24868149;
        double r24868151 = fma(r24868146, r24868146, r24868150);
        return r24868151;
}

Original	33.4
Target	0.4
Herbie	0.4

Derivation

Initial program 33.4
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
Simplified0.4
\[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z}{t} \cdot \frac{z}{t}\right)}\]
Final simplification0.4
\[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z}{t} \cdot \frac{z}{t}\right)\]

Reproduce

herbie shell --seed 2019172 +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))))

Error

Target

Derivation

Reproduce