Average Error: 0.3 → 0.2
Time: 2.7s
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 r797431 = x;
        double r797432 = y;
        double r797433 = r797432 - r797431;
        double r797434 = 6.0;
        double r797435 = r797433 * r797434;
        double r797436 = z;
        double r797437 = r797435 * r797436;
        double r797438 = r797431 + r797437;
        return r797438;
}
↓
double f(double x, double y, double z) {
        double r797439 = y;
        double r797440 = x;
        double r797441 = r797439 - r797440;
        double r797442 = 6.0;
        double r797443 = z;
        double r797444 = r797442 * r797443;
        double r797445 = fma(r797441, r797444, r797440);
        return r797445;
}

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 2020089 +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)))