Average Error: 0.2 → 0.2
Time: 15.9s
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 r530894 = x;
        double r530895 = y;
        double r530896 = r530895 - r530894;
        double r530897 = 6.0;
        double r530898 = r530896 * r530897;
        double r530899 = z;
        double r530900 = r530898 * r530899;
        double r530901 = r530894 + r530900;
        return r530901;
}
↓
double f(double x, double y, double z) {
        double r530902 = y;
        double r530903 = x;
        double r530904 = r530902 - r530903;
        double r530905 = 6.0;
        double r530906 = z;
        double r530907 = r530905 * r530906;
        double r530908 = fma(r530904, r530907, r530903);
        return r530908;
}

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 2019208 +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)))