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

↓

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

\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 r26983719 = x;
        double r26983720 = r26983719 * r26983719;
        double r26983721 = y;
        double r26983722 = r26983721 * r26983721;
        double r26983723 = r26983720 / r26983722;
        double r26983724 = z;
        double r26983725 = r26983724 * r26983724;
        double r26983726 = t;
        double r26983727 = r26983726 * r26983726;
        double r26983728 = r26983725 / r26983727;
        double r26983729 = r26983723 + r26983728;
        return r26983729;
}

↓

double f(double x, double y, double z, double t) {
        double r26983730 = x;
        double r26983731 = y;
        double r26983732 = r26983730 / r26983731;
        double r26983733 = z;
        double r26983734 = t;
        double r26983735 = r26983733 / r26983734;
        double r26983736 = r26983735 * r26983735;
        double r26983737 = fma(r26983732, r26983732, r26983736);
        return r26983737;
}

Original	33.9
Target	0.4
Herbie	0.4

Derivation

Initial program 33.9
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
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 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))))

Error

Target

Derivation

Reproduce