So, in mid-March I applied the intelligent sorting logic to lump together, and thus identify algebraically equivalent duplicate expressions, and also those expressions which are not (apparently) algebraic equivalents, but appear to produce the exact same solutions. Of these groups of effectively equivalent expressions, my program then eliminated all but the preferred (briefest and 'best-looking') expression. This produced a list of 1315 algebracic expressions, to which I began to refer as my master...
