Average Error: 0.3 → 0.2
Time: 5.4s
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 r810764 = x;
        double r810765 = y;
        double r810766 = r810765 - r810764;
        double r810767 = 6.0;
        double r810768 = r810766 * r810767;
        double r810769 = z;
        double r810770 = r810768 * r810769;
        double r810771 = r810764 + r810770;
        return r810771;
}
↓
double f(double x, double y, double z) {
        double r810772 = y;
        double r810773 = x;
        double r810774 = r810772 - r810773;
        double r810775 = 6.0;
        double r810776 = z;
        double r810777 = r810775 * r810776;
        double r810778 = fma(r810774, r810777, r810773);
        return r810778;
}

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 2020036 +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)))