Average Error: 0.2 → 0.0
Time: 10.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\mathsf{fma}\left(4, 0.75 - \frac{z - x}{y}, 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\mathsf{fma}\left(4, 0.75 - \frac{z - x}{y}, 1\right)
double f(double x, double y, double z) {
        double r199693 = 1.0;
        double r199694 = 4.0;
        double r199695 = x;
        double r199696 = y;
        double r199697 = 0.75;
        double r199698 = r199696 * r199697;
        double r199699 = r199695 + r199698;
        double r199700 = z;
        double r199701 = r199699 - r199700;
        double r199702 = r199694 * r199701;
        double r199703 = r199702 / r199696;
        double r199704 = r199693 + r199703;
        return r199704;
}
↓
double f(double x, double y, double z) {
        double r199705 = 4.0;
        double r199706 = 0.75;
        double r199707 = z;
        double r199708 = x;
        double r199709 = r199707 - r199708;
        double r199710 = y;
        double r199711 = r199709 / r199710;
        double r199712 = r199706 - r199711;
        double r199713 = 1.0;
        double r199714 = fma(r199705, r199712, r199713);
        return r199714;
}

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

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

  3. Final simplification0.0

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

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, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))