\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

↓

\[1 + \mathsf{fma}\left(4, \frac{x}{y}, 3 - 4 \cdot \frac{z}{y}\right)\]

1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}

↓

1 + \mathsf{fma}\left(4, \frac{x}{y}, 3 - 4 \cdot \frac{z}{y}\right)

double f(double x, double y, double z) {
        double r272370 = 1.0;
        double r272371 = 4.0;
        double r272372 = x;
        double r272373 = y;
        double r272374 = 0.75;
        double r272375 = r272373 * r272374;
        double r272376 = r272372 + r272375;
        double r272377 = z;
        double r272378 = r272376 - r272377;
        double r272379 = r272371 * r272378;
        double r272380 = r272379 / r272373;
        double r272381 = r272370 + r272380;
        return r272381;
}

↓

double f(double x, double y, double z) {
        double r272382 = 1.0;
        double r272383 = 4.0;
        double r272384 = x;
        double r272385 = y;
        double r272386 = r272384 / r272385;
        double r272387 = 3.0;
        double r272388 = z;
        double r272389 = r272388 / r272385;
        double r272390 = r272383 * r272389;
        double r272391 = r272387 - r272390;
        double r272392 = fma(r272383, r272386, r272391);
        double r272393 = r272382 + r272392;
        return r272393;
}

Derivation

Initial program 0.2
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
Taylor expanded around 0 0.0
\[\leadsto 1 + \color{blue}{\left(\left(4 \cdot \frac{x}{y} + 3\right) - 4 \cdot \frac{z}{y}\right)}\]
Simplified0.0
\[\leadsto 1 + \color{blue}{\mathsf{fma}\left(4, \frac{x}{y}, 3 - 4 \cdot \frac{z}{y}\right)}\]
Final simplification0.0
\[\leadsto 1 + \mathsf{fma}\left(4, \frac{x}{y}, 3 - 4 \cdot \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))

Error

Derivation

Reproduce