  Full binary trees naturally represent commutative non-associative products.
There are many important examples of these products: finite-precision
floating-point addition and NAND gates, among others. Balance in such a tree is
highly desirable for efficiency in calculation. The best balance is attained
with a divide-and-conquer approach. However, this may not be the optimal
solution, since the success of many calculations is dependent on the grouping
and ordering of the calculation, for reasons ranging from the avoidance of
rounding error, to calculating with varying precision, to the placement of
calculation within a heterogeneous system.
  We introduce a new class of computational trees having near-best balance in
terms of the Colless index from mathematical phylogenetics. These trees are
easily constructed from the binary decomposition of the number of terms in the
problem. They also permit much more flexibility than the optimally balanced
divide-and-conquer trees. This gives needed freedom in the grouping and
ordering of calculation, and allows intelligent efficiency trade-offs.
