\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

↓

\[\mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)\]

1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}

↓

\mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)

double f(double x, double y, double z) {
        double r252280 = 1.0;
        double r252281 = 4.0;
        double r252282 = x;
        double r252283 = y;
        double r252284 = 0.25;
        double r252285 = r252283 * r252284;
        double r252286 = r252282 + r252285;
        double r252287 = z;
        double r252288 = r252286 - r252287;
        double r252289 = r252281 * r252288;
        double r252290 = r252289 / r252283;
        double r252291 = r252280 + r252290;
        return r252291;
}

↓

double f(double x, double y, double z) {
        double r252292 = 4.0;
        double r252293 = x;
        double r252294 = y;
        double r252295 = r252293 / r252294;
        double r252296 = 2.0;
        double r252297 = z;
        double r252298 = r252297 / r252294;
        double r252299 = r252292 * r252298;
        double r252300 = r252296 - r252299;
        double r252301 = fma(r252292, r252295, r252300);
        return r252301;
}

Derivation

Initial program 0.1
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
Taylor expanded around 0 0.0
\[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]
Simplified0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)}\]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(4, \frac{x}{y}, 2 - 4 \cdot \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))

Error

Derivation

Reproduce