Hence my use of $x*$x rather than $x**2. I doubt there's much difference on modern processors.

Oh yes it does make a difference. $x*$x does a multiplication of two numbers, while $x**2 goes the long route of exp(log($x)*2), as ** is a very generic power raising operator. Not only will it take longer (maybe negligible these days, like you say), but most of all: its result will be less precise: both log and exp have quite large margins of error.