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

↓

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

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 r211121 = 1.0;
        double r211122 = 4.0;
        double r211123 = x;
        double r211124 = y;
        double r211125 = 0.25;
        double r211126 = r211124 * r211125;
        double r211127 = r211123 + r211126;
        double r211128 = z;
        double r211129 = r211127 - r211128;
        double r211130 = r211122 * r211129;
        double r211131 = r211130 / r211124;
        double r211132 = r211121 + r211131;
        return r211132;
}

↓

double f(double x, double y, double z) {
        double r211133 = 4.0;
        double r211134 = x;
        double r211135 = y;
        double r211136 = r211134 / r211135;
        double r211137 = 2.0;
        double r211138 = z;
        double r211139 = r211138 / r211135;
        double r211140 = r211133 * r211139;
        double r211141 = r211137 - r211140;
        double r211142 = fma(r211133, r211136, r211141);
        return r211142;
}

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 2020020 +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