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

↓

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

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 r226162 = 1.0;
        double r226163 = 4.0;
        double r226164 = x;
        double r226165 = y;
        double r226166 = 0.25;
        double r226167 = r226165 * r226166;
        double r226168 = r226164 + r226167;
        double r226169 = z;
        double r226170 = r226168 - r226169;
        double r226171 = r226163 * r226170;
        double r226172 = r226171 / r226165;
        double r226173 = r226162 + r226172;
        return r226173;
}

↓

double f(double x, double y, double z) {
        double r226174 = 4.0;
        double r226175 = x;
        double r226176 = y;
        double r226177 = r226175 / r226176;
        double r226178 = 2.0;
        double r226179 = z;
        double r226180 = r226179 / r226176;
        double r226181 = r226174 * r226180;
        double r226182 = r226178 - r226181;
        double r226183 = fma(r226174, r226177, r226182);
        return r226183;
}

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 2020039 +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