Average Error: 0.3 → 0.2
Time: 21.4s
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 r570634 = x;
        double r570635 = y;
        double r570636 = r570635 - r570634;
        double r570637 = 6.0;
        double r570638 = r570636 * r570637;
        double r570639 = z;
        double r570640 = r570638 * r570639;
        double r570641 = r570634 + r570640;
        return r570641;
}
↓
double f(double x, double y, double z) {
        double r570642 = y;
        double r570643 = x;
        double r570644 = r570642 - r570643;
        double r570645 = 6.0;
        double r570646 = z;
        double r570647 = r570645 * r570646;
        double r570648 = fma(r570644, r570647, r570643);
        return r570648;
}

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 2019325 +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)))