Average Error: 0.1 → 0.0
Time: 11.3s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\mathsf{fma}\left(0.25 - \frac{z - x}{y}, 4, 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\mathsf{fma}\left(0.25 - \frac{z - x}{y}, 4, 1\right)
double f(double x, double y, double z) {
        double r11684583 = 1.0;
        double r11684584 = 4.0;
        double r11684585 = x;
        double r11684586 = y;
        double r11684587 = 0.25;
        double r11684588 = r11684586 * r11684587;
        double r11684589 = r11684585 + r11684588;
        double r11684590 = z;
        double r11684591 = r11684589 - r11684590;
        double r11684592 = r11684584 * r11684591;
        double r11684593 = r11684592 / r11684586;
        double r11684594 = r11684583 + r11684593;
        return r11684594;
}
↓
double f(double x, double y, double z) {
        double r11684595 = 0.25;
        double r11684596 = z;
        double r11684597 = x;
        double r11684598 = r11684596 - r11684597;
        double r11684599 = y;
        double r11684600 = r11684598 / r11684599;
        double r11684601 = r11684595 - r11684600;
        double r11684602 = 4.0;
        double r11684603 = 1.0;
        double r11684604 = fma(r11684601, r11684602, r11684603);
        return r11684604;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(0.25 - \frac{z - x}{y}, 4, 1\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(0.25 - \frac{z - x}{y}, 4, 1\right)\]

Reproduce

herbie shell --seed 2019192 +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)))