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

↓

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

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

↓

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

double f(double x, double y, double z) {
        double r135366 = 1.0;
        double r135367 = 4.0;
        double r135368 = x;
        double r135369 = y;
        double r135370 = 0.25;
        double r135371 = r135369 * r135370;
        double r135372 = r135368 + r135371;
        double r135373 = z;
        double r135374 = r135372 - r135373;
        double r135375 = r135367 * r135374;
        double r135376 = r135375 / r135369;
        double r135377 = r135366 + r135376;
        return r135377;
}

↓

double f(double x, double y, double z) {
        double r135378 = 4.0;
        double r135379 = x;
        double r135380 = y;
        double r135381 = r135379 / r135380;
        double r135382 = z;
        double r135383 = r135382 / r135380;
        double r135384 = r135381 - r135383;
        double r135385 = 2.0;
        double r135386 = fma(r135378, r135384, r135385);
        return r135386;
}

Derivation

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

Reproduce

herbie shell --seed 2019208 +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