Maple has a dedicated command for Horner's rule: 
convert(x^2 - x - 6, horner, x)
\[ -6 + (-1 + x)*x \]

An example from https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/05Interpolation/horner/ 
xpts := [3.5, 4.7, 5.1,  6.9, 8.3];
coefflist := [5.3, 3.2, 2.1, -1.8, 1.7];
s := xpts[-1];
x := 5.5235423;
for i from -2 to -nops( xpts ) by -1 do
    s := s*(x - xpts[i]) + coefflist[i];
end do:
xpts := [3.5, 4.7, 5.1, 6.9, 8.3] coefflist := [5.3, 3.2, 2.1, -1.8, 1.7] s := 8.3 x := 5.5235423 s := -13.22459891 s := -3.501177039 s := 0.316632609 s := 5.940719478

 

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