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

↓

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

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 r297116 = 1.0;
        double r297117 = 4.0;
        double r297118 = x;
        double r297119 = y;
        double r297120 = 0.25;
        double r297121 = r297119 * r297120;
        double r297122 = r297118 + r297121;
        double r297123 = z;
        double r297124 = r297122 - r297123;
        double r297125 = r297117 * r297124;
        double r297126 = r297125 / r297119;
        double r297127 = r297116 + r297126;
        return r297127;
}

↓

double f(double x, double y, double z) {
        double r297128 = 4.0;
        double r297129 = x;
        double r297130 = y;
        double r297131 = r297129 / r297130;
        double r297132 = 2.0;
        double r297133 = z;
        double r297134 = r297133 / r297130;
        double r297135 = r297128 * r297134;
        double r297136 = r297132 - r297135;
        double r297137 = fma(r297128, r297131, r297136);
        return r297137;
}

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 2020064 +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