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

↓

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

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 r224621 = 1.0;
        double r224622 = 4.0;
        double r224623 = x;
        double r224624 = y;
        double r224625 = 0.25;
        double r224626 = r224624 * r224625;
        double r224627 = r224623 + r224626;
        double r224628 = z;
        double r224629 = r224627 - r224628;
        double r224630 = r224622 * r224629;
        double r224631 = r224630 / r224624;
        double r224632 = r224621 + r224631;
        return r224632;
}

↓

double f(double x, double y, double z) {
        double r224633 = 4.0;
        double r224634 = x;
        double r224635 = y;
        double r224636 = r224634 / r224635;
        double r224637 = 2.0;
        double r224638 = z;
        double r224639 = r224638 / r224635;
        double r224640 = r224633 * r224639;
        double r224641 = r224637 - r224640;
        double r224642 = fma(r224633, r224636, r224641);
        return r224642;
}

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 2020001 +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