Average Error: 0.3 → 0.2
Time: 4.7s
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 r871711 = x;
        double r871712 = y;
        double r871713 = r871712 - r871711;
        double r871714 = 6.0;
        double r871715 = r871713 * r871714;
        double r871716 = z;
        double r871717 = r871715 * r871716;
        double r871718 = r871711 + r871717;
        return r871718;
}
↓
double f(double x, double y, double z) {
        double r871719 = y;
        double r871720 = x;
        double r871721 = r871719 - r871720;
        double r871722 = 6.0;
        double r871723 = z;
        double r871724 = r871722 * r871723;
        double r871725 = fma(r871721, r871724, r871720);
        return r871725;
}

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 2020035 +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)))