Average Error: 0.4 → 0.2
Time: 15.6s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)
double f(double x, double y, double z) {
        double r185723 = x;
        double r185724 = y;
        double r185725 = r185724 - r185723;
        double r185726 = 6.0;
        double r185727 = r185725 * r185726;
        double r185728 = 2.0;
        double r185729 = 3.0;
        double r185730 = r185728 / r185729;
        double r185731 = z;
        double r185732 = r185730 - r185731;
        double r185733 = r185727 * r185732;
        double r185734 = r185723 + r185733;
        return r185734;
}
↓
double f(double x, double y, double z) {
        double r185735 = y;
        double r185736 = x;
        double r185737 = r185735 - r185736;
        double r185738 = 6.0;
        double r185739 = 2.0;
        double r185740 = 3.0;
        double r185741 = r185739 / r185740;
        double r185742 = z;
        double r185743 = r185741 - r185742;
        double r185744 = r185738 * r185743;
        double r185745 = fma(r185737, r185744, r185736);
        return r185745;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.4

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)}\]

  3. Final simplification0.2

    \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)\]

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6) (- (/ 2 3) z))))