Average Error: 0.3 → 0.2
Time: 3.8s
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 r860677 = x;
        double r860678 = y;
        double r860679 = r860678 - r860677;
        double r860680 = 6.0;
        double r860681 = r860679 * r860680;
        double r860682 = z;
        double r860683 = r860681 * r860682;
        double r860684 = r860677 + r860683;
        return r860684;
}
↓
double f(double x, double y, double z) {
        double r860685 = y;
        double r860686 = x;
        double r860687 = r860685 - r860686;
        double r860688 = 6.0;
        double r860689 = z;
        double r860690 = r860688 * r860689;
        double r860691 = fma(r860687, r860690, r860686);
        return r860691;
}

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 2020065 +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)))