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

↓

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

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

↓

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

double f(double x, double y, double z) {
        double r252446 = 1.0;
        double r252447 = 4.0;
        double r252448 = x;
        double r252449 = y;
        double r252450 = 0.25;
        double r252451 = r252449 * r252450;
        double r252452 = r252448 + r252451;
        double r252453 = z;
        double r252454 = r252452 - r252453;
        double r252455 = r252447 * r252454;
        double r252456 = r252455 / r252449;
        double r252457 = r252446 + r252456;
        return r252457;
}

↓

double f(double x, double y, double z) {
        double r252458 = 4.0;
        double r252459 = x;
        double r252460 = y;
        double r252461 = r252459 / r252460;
        double r252462 = z;
        double r252463 = r252462 / r252460;
        double r252464 = r252461 - r252463;
        double r252465 = 2.0;
        double r252466 = fma(r252458, r252464, r252465);
        return r252466;
}

Derivation

Initial program 0.1
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
Simplified0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(4, 0.25 - \frac{z - x}{y}, 1\right)}\]
Taylor expanded around 0 0.0
\[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]
Simplified0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(4, \frac{x}{y} - \frac{z}{y}, 2\right)}\]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(4, \frac{x}{y} - \frac{z}{y}, 2\right)\]

Reproduce

herbie shell --seed 2019212 +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