Average Error: 0.4 → 0.3
Time: 4.9s
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 r244657 = x;
        double r244658 = y;
        double r244659 = r244658 - r244657;
        double r244660 = 6.0;
        double r244661 = r244659 * r244660;
        double r244662 = 2.0;
        double r244663 = 3.0;
        double r244664 = r244662 / r244663;
        double r244665 = z;
        double r244666 = r244664 - r244665;
        double r244667 = r244661 * r244666;
        double r244668 = r244657 + r244667;
        return r244668;
}
↓
double f(double x, double y, double z) {
        double r244669 = y;
        double r244670 = x;
        double r244671 = r244669 - r244670;
        double r244672 = 6.0;
        double r244673 = 2.0;
        double r244674 = 3.0;
        double r244675 = r244673 / r244674;
        double r244676 = z;
        double r244677 = r244675 - r244676;
        double r244678 = r244672 * r244677;
        double r244679 = fma(r244671, r244678, r244670);
        return r244679;
}

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. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 +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))))