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

↓

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

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 r218473 = 1.0;
        double r218474 = 4.0;
        double r218475 = x;
        double r218476 = y;
        double r218477 = 0.25;
        double r218478 = r218476 * r218477;
        double r218479 = r218475 + r218478;
        double r218480 = z;
        double r218481 = r218479 - r218480;
        double r218482 = r218474 * r218481;
        double r218483 = r218482 / r218476;
        double r218484 = r218473 + r218483;
        return r218484;
}

↓

double f(double x, double y, double z) {
        double r218485 = 4.0;
        double r218486 = x;
        double r218487 = y;
        double r218488 = r218486 / r218487;
        double r218489 = 2.0;
        double r218490 = z;
        double r218491 = r218490 / r218487;
        double r218492 = r218485 * r218491;
        double r218493 = r218489 - r218492;
        double r218494 = fma(r218485, r218488, r218493);
        return r218494;
}

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 2019353 +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