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converts an expr by certain rules like
A * 1 * 1 ⟹ A + 1 - 1.
i called the result the yuuki normal form (YNF).

defines exprs the same iff they have the same YNF.
i implemented this using Perl extended regexes.
github.com/yuuki15/24/blob/1c5

it is needed to eliminate duplicate solutions to the 24 puzzle.
found that certain 19 rules can normalize an expr.

however, it didn't work for exprs whose value is 0 (or the 0 puzzle).
(due to an infinite loop.)