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

↓

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

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

↓

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

double f(double x, double y, double z) {
        double r164664 = 1.0;
        double r164665 = 4.0;
        double r164666 = x;
        double r164667 = y;
        double r164668 = 0.25;
        double r164669 = r164667 * r164668;
        double r164670 = r164666 + r164669;
        double r164671 = z;
        double r164672 = r164670 - r164671;
        double r164673 = r164665 * r164672;
        double r164674 = r164673 / r164667;
        double r164675 = r164664 + r164674;
        return r164675;
}

↓

double f(double x, double y, double z) {
        double r164676 = x;
        double r164677 = z;
        double r164678 = -r164677;
        double r164679 = r164676 + r164678;
        double r164680 = y;
        double r164681 = r164679 / r164680;
        double r164682 = 4.0;
        double r164683 = 2.0;
        double r164684 = fma(r164681, r164682, r164683);
        return r164684;
}

Derivation

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

Error

Derivation

Reproduce