Average Error: 0.3 → 0.2
Time: 4.0s
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 r965615 = x;
        double r965616 = y;
        double r965617 = r965616 - r965615;
        double r965618 = 6.0;
        double r965619 = r965617 * r965618;
        double r965620 = z;
        double r965621 = r965619 * r965620;
        double r965622 = r965615 + r965621;
        return r965622;
}
↓
double f(double x, double y, double z) {
        double r965623 = y;
        double r965624 = x;
        double r965625 = r965623 - r965624;
        double r965626 = 6.0;
        double r965627 = z;
        double r965628 = r965626 * r965627;
        double r965629 = fma(r965625, r965628, r965624);
        return r965629;
}

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 2020057 +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)))