Average Error: 0.3 → 0.2
Time: 23.7s
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 r517306 = x;
        double r517307 = y;
        double r517308 = r517307 - r517306;
        double r517309 = 6.0;
        double r517310 = r517308 * r517309;
        double r517311 = z;
        double r517312 = r517310 * r517311;
        double r517313 = r517306 + r517312;
        return r517313;
}
↓
double f(double x, double y, double z) {
        double r517314 = y;
        double r517315 = x;
        double r517316 = r517314 - r517315;
        double r517317 = 6.0;
        double r517318 = z;
        double r517319 = r517317 * r517318;
        double r517320 = fma(r517316, r517319, r517315);
        return r517320;
}

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)))