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

↓

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

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 r242013 = 1.0;
        double r242014 = 4.0;
        double r242015 = x;
        double r242016 = y;
        double r242017 = 0.25;
        double r242018 = r242016 * r242017;
        double r242019 = r242015 + r242018;
        double r242020 = z;
        double r242021 = r242019 - r242020;
        double r242022 = r242014 * r242021;
        double r242023 = r242022 / r242016;
        double r242024 = r242013 + r242023;
        return r242024;
}

↓

double f(double x, double y, double z) {
        double r242025 = 4.0;
        double r242026 = x;
        double r242027 = y;
        double r242028 = r242026 / r242027;
        double r242029 = 2.0;
        double r242030 = z;
        double r242031 = r242030 / r242027;
        double r242032 = r242025 * r242031;
        double r242033 = r242029 - r242032;
        double r242034 = fma(r242025, r242028, r242033);
        return r242034;
}

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 2020034 +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