Talk:Common subexpression elimination

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This problem seems much more complicated than the article suggests. For example,

$x^{3}+3x^{2}y+3xy^{2}+y^{3}-x^{2}-2xy+2xc-y^{2}+2yc-c^{2}$

takes 19 multiplications and 9 additions to evaluate, but it can be rewritten as

$(x+y)^{3}+(x+y-c)^{2}$

which only requires 3 multiplications and 3 additions. How does subexpression elimination know how to do this?