Average Error: 0.4 → 0.2
Time: 5.2s
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 r247741 = x;
        double r247742 = y;
        double r247743 = r247742 - r247741;
        double r247744 = 6.0;
        double r247745 = r247743 * r247744;
        double r247746 = 2.0;
        double r247747 = 3.0;
        double r247748 = r247746 / r247747;
        double r247749 = z;
        double r247750 = r247748 - r247749;
        double r247751 = r247745 * r247750;
        double r247752 = r247741 + r247751;
        return r247752;
}
↓
double f(double x, double y, double z) {
        double r247753 = y;
        double r247754 = x;
        double r247755 = r247753 - r247754;
        double r247756 = 6.0;
        double r247757 = 2.0;
        double r247758 = 3.0;
        double r247759 = r247757 / r247758;
        double r247760 = z;
        double r247761 = r247759 - r247760;
        double r247762 = r247756 * r247761;
        double r247763 = fma(r247755, r247762, r247754);
        return r247763;
}

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 2020039 +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))))