Average Error: 0.3 → 0.2
Time: 2.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[\mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
\mathsf{fma}\left(y - x, 6 \cdot z, x\right)
double f(double x, double y, double z) {
        double r858977 = x;
        double r858978 = y;
        double r858979 = r858978 - r858977;
        double r858980 = 6.0;
        double r858981 = r858979 * r858980;
        double r858982 = z;
        double r858983 = r858981 * r858982;
        double r858984 = r858977 + r858983;
        return r858984;
}
↓
double f(double x, double y, double z) {
        double r858985 = y;
        double r858986 = x;
        double r858987 = r858985 - r858986;
        double r858988 = 6.0;
        double r858989 = z;
        double r858990 = r858988 * r858989;
        double r858991 = fma(r858987, r858990, r858986);
        return r858991;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.3
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.3

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6 z) (- x y)))

  (+ x (* (* (- y x) 6) z)))