Average Error: 0.3 → 0.2
Time: 17.6s
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 r930360 = x;
        double r930361 = y;
        double r930362 = r930361 - r930360;
        double r930363 = 6.0;
        double r930364 = r930362 * r930363;
        double r930365 = z;
        double r930366 = r930364 * r930365;
        double r930367 = r930360 + r930366;
        return r930367;
}
↓
double f(double x, double y, double z) {
        double r930368 = y;
        double r930369 = x;
        double r930370 = r930368 - r930369;
        double r930371 = 6.0;
        double r930372 = z;
        double r930373 = r930371 * r930372;
        double r930374 = fma(r930370, r930373, r930369);
        return r930374;
}

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 2020042 +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)))