Average Error: 0.3 → 0.2
Time: 3.3s
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 r874669 = x;
        double r874670 = y;
        double r874671 = r874670 - r874669;
        double r874672 = 6.0;
        double r874673 = r874671 * r874672;
        double r874674 = z;
        double r874675 = r874673 * r874674;
        double r874676 = r874669 + r874675;
        return r874676;
}
↓
double f(double x, double y, double z) {
        double r874677 = y;
        double r874678 = x;
        double r874679 = r874677 - r874678;
        double r874680 = 6.0;
        double r874681 = z;
        double r874682 = r874680 * r874681;
        double r874683 = fma(r874679, r874682, r874678);
        return r874683;
}

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 2020027 +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)))