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

↓

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

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 r289760 = 1.0;
        double r289761 = 4.0;
        double r289762 = x;
        double r289763 = y;
        double r289764 = 0.25;
        double r289765 = r289763 * r289764;
        double r289766 = r289762 + r289765;
        double r289767 = z;
        double r289768 = r289766 - r289767;
        double r289769 = r289761 * r289768;
        double r289770 = r289769 / r289763;
        double r289771 = r289760 + r289770;
        return r289771;
}

↓

double f(double x, double y, double z) {
        double r289772 = 4.0;
        double r289773 = x;
        double r289774 = y;
        double r289775 = r289773 / r289774;
        double r289776 = 2.0;
        double r289777 = z;
        double r289778 = r289777 / r289774;
        double r289779 = r289772 * r289778;
        double r289780 = r289776 - r289779;
        double r289781 = fma(r289772, r289775, r289780);
        return r289781;
}

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 2019362 +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