Very cool. <nitpick>...but there's still a comparison; it's just hidden in the abs() function: (roughly:) abs(x) := x >= 0 ? x : x.</nitpick>
[OT] Reminds me of a programming assignment where we were supposed to put the square roots of the integers from 1100 inclusive into two groups with roughly equal sums. I used the fact that sqrt(x) + sqrt(x+3) is very close to sqrt(x+1) + sqrt(x+2) and managed to outperform all the other submissions by several orders of magnitude in both speed and "difference in sum". (Yea math!)
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