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

↓

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

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 r246378 = 1.0;
        double r246379 = 4.0;
        double r246380 = x;
        double r246381 = y;
        double r246382 = 0.25;
        double r246383 = r246381 * r246382;
        double r246384 = r246380 + r246383;
        double r246385 = z;
        double r246386 = r246384 - r246385;
        double r246387 = r246379 * r246386;
        double r246388 = r246387 / r246381;
        double r246389 = r246378 + r246388;
        return r246389;
}

↓

double f(double x, double y, double z) {
        double r246390 = 4.0;
        double r246391 = x;
        double r246392 = y;
        double r246393 = r246391 / r246392;
        double r246394 = 2.0;
        double r246395 = z;
        double r246396 = r246395 / r246392;
        double r246397 = r246390 * r246396;
        double r246398 = r246394 - r246397;
        double r246399 = fma(r246390, r246393, r246398);
        return r246399;
}

Derivation

Initial program 0.2
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
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 2020021 +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