Transformation of an expression:

It is well known that the interval evaluation of an expression is
sensitive to the manner with which the expression is written. For
example in term of interval analysis is not equivalent to
as the interval evaluation of these two forms will usually
be different. Unfortunately there is usually no known rule to determine
which form will lead to the best interval evaluation of an
expression (except if there is exactly one and only one occurrence of
each variable in the expression). Hence
ALIAS-Maple uses a set of heuristics to transform an
expression into a form that leads usually to a good interval
evaluation. The procedure `MinimalCout` takes as argument an
expression and returns a mathematical equivalent of this expression
but in a form that may be better for the interval evaluation.

Among the heuristics that are used in this procedure we use a
conversion into Horner form. For a multivariate expression there are
different Horner form according to the ordering of the variable.
`MinimalCout` will consider all possible ordering of the variable to
produce the best form but this may be computer intensive if there is a
large number of variables. Hence all the ordering will be tested only
if the number of variables does not exceed ``ALIAS/mincout`` with
a default value of 8. Reducing the value of ``ALIAS/mincout`` will
allow to reduce the computation time for calculating the best form for
the expression as the possible expense of getting a less sharper
interval evaluation. If the use of `MinimalCout` has to be avoided
it is sufficient to set ``ALIAS/mincout`` to a negative value.

`MinimalCout` accepts an optional second argument which is a list
of variables. The procedure will try find an expression that is the
best with respect to this list.