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

↓

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

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 r216184 = 1.0;
        double r216185 = 4.0;
        double r216186 = x;
        double r216187 = y;
        double r216188 = 0.25;
        double r216189 = r216187 * r216188;
        double r216190 = r216186 + r216189;
        double r216191 = z;
        double r216192 = r216190 - r216191;
        double r216193 = r216185 * r216192;
        double r216194 = r216193 / r216187;
        double r216195 = r216184 + r216194;
        return r216195;
}

↓

double f(double x, double y, double z) {
        double r216196 = 4.0;
        double r216197 = x;
        double r216198 = y;
        double r216199 = r216197 / r216198;
        double r216200 = 2.0;
        double r216201 = z;
        double r216202 = r216201 / r216198;
        double r216203 = r216196 * r216202;
        double r216204 = r216200 - r216203;
        double r216205 = fma(r216196, r216199, r216204);
        return r216205;
}

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 2020036 +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