\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

↓

\[1 + \mathsf{fma}\left(4, \frac{x}{y}, 3 - 4 \cdot \frac{z}{y}\right)\]

1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}

↓

1 + \mathsf{fma}\left(4, \frac{x}{y}, 3 - 4 \cdot \frac{z}{y}\right)

double f(double x, double y, double z) {
        double r190003 = 1.0;
        double r190004 = 4.0;
        double r190005 = x;
        double r190006 = y;
        double r190007 = 0.75;
        double r190008 = r190006 * r190007;
        double r190009 = r190005 + r190008;
        double r190010 = z;
        double r190011 = r190009 - r190010;
        double r190012 = r190004 * r190011;
        double r190013 = r190012 / r190006;
        double r190014 = r190003 + r190013;
        return r190014;
}

↓

double f(double x, double y, double z) {
        double r190015 = 1.0;
        double r190016 = 4.0;
        double r190017 = x;
        double r190018 = y;
        double r190019 = r190017 / r190018;
        double r190020 = 3.0;
        double r190021 = z;
        double r190022 = r190021 / r190018;
        double r190023 = r190016 * r190022;
        double r190024 = r190020 - r190023;
        double r190025 = fma(r190016, r190019, r190024);
        double r190026 = r190015 + r190025;
        return r190026;
}

Derivation

Initial program 0.2
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
Taylor expanded around 0 0.0
\[\leadsto 1 + \color{blue}{\left(\left(4 \cdot \frac{x}{y} + 3\right) - 4 \cdot \frac{z}{y}\right)}\]
Simplified0.0
\[\leadsto 1 + \color{blue}{\mathsf{fma}\left(4, \frac{x}{y}, 3 - 4 \cdot \frac{z}{y}\right)}\]
Final simplification0.0
\[\leadsto 1 + \mathsf{fma}\left(4, \frac{x}{y}, 3 - 4 \cdot \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))

Error

Derivation

Reproduce