Average Error: 0.2 → 0.2
Time: 25.9s
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 r541582 = x;
        double r541583 = y;
        double r541584 = r541583 - r541582;
        double r541585 = 6.0;
        double r541586 = r541584 * r541585;
        double r541587 = z;
        double r541588 = r541586 * r541587;
        double r541589 = r541582 + r541588;
        return r541589;
}
↓
double f(double x, double y, double z) {
        double r541590 = y;
        double r541591 = x;
        double r541592 = r541590 - r541591;
        double r541593 = 6.0;
        double r541594 = z;
        double r541595 = r541593 * r541594;
        double r541596 = fma(r541592, r541595, r541591);
        return r541596;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.2
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.2

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

  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 2019323 +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)))