Operator script does not commute

Hi, I have the given script:

syms f(x,y)
n = 2;
m = 2
res = exp(-i.*(x+y))
for k=1:m
  res = simplify(diff(res,x) - x*res);
end
for k=1:n
  res = simplify(diff(res,y) - y*res);
end
res = (-1)^(n+m)*res

which should do the following operation (image),

however it does not generate a commutation in the operations. How can this be modified to respect order of commutation?