Average Error: 0.2 → 0.0
Time: 11.2s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4, 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4, 1\right)
double f(double x, double y, double z) {
        double r328700 = 1.0;
        double r328701 = 4.0;
        double r328702 = x;
        double r328703 = y;
        double r328704 = 0.75;
        double r328705 = r328703 * r328704;
        double r328706 = r328702 + r328705;
        double r328707 = z;
        double r328708 = r328706 - r328707;
        double r328709 = r328701 * r328708;
        double r328710 = r328709 / r328703;
        double r328711 = r328700 + r328710;
        return r328711;
}
↓
double f(double x, double y, double z) {
        double r328712 = 0.75;
        double r328713 = x;
        double r328714 = z;
        double r328715 = r328713 - r328714;
        double r328716 = y;
        double r328717 = r328715 / r328716;
        double r328718 = r328712 + r328717;
        double r328719 = 4.0;
        double r328720 = 1.0;
        double r328721 = fma(r328718, r328719, r328720);
        return r328721;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.2

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4, 1\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4, 1\right)\]

Reproduce

herbie shell --seed 2020042 +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)))