In reply to Ian Wakeling.

You are correct. In the original version of this post I had written the following:
"The most extreme example of this phenomenon is seen when computing a quadratic form such as y = x′*A*x, where x is a column vector and x′ is its transpose. It is always more efficient to compute a quadratic form as
y = x′*(A*x)"

As Ian points out, this statement is incorrect. I have no idea what I was thinking when I wrote it. Sorry for the confusion.