>> While “independently” is a much better name than “perform”, I think it is still not quite right.  If the evaluations are truly independent then they could be evaluated in parallel (at least in some interpretation of “independent”).  Why not simply call it “out-of-order”?

"in-any-order" would be more precise, as in-order execution is also a
permitted strategy.

I also slightly prefer "independently", as it sounds more natural since
it's one word. The thesaurus doesn't give any other good one-word names.

IMHO the following language suggested by Göran is the right thing:

   Although the order of evaluation is otherwise unspecified, the effect
   of any concurrent evaluation of the operator and operand expressions
   is constrained to be consistent with some sequential order of
   evaluation. The order of evaluation may be chosen differently for each
   procedure call.

> Each expression can evaluate to zero or more than one value.  An
> expression standing for a procedure argument must evaluate to exactly
> one value.

Yes, to account for Scheme implementations like Chibi that emulate
multiple values using a list.