Let's say you have an N×N-bit multiplier but you don't need all the bits of the result. You can generate a few extra bits (columns in the compressor tree) and faithfully round the result. But if you Booth encoded the multiplicand to half the rows in your circuit you end up with a multiplier where A×B ≠ B×A. That's hard to explain to a compiler, being commutative is important.
Lots of rounding strategies I never heard of - AND arrays, CCT, VCT, statistical predict, etc.
https://arxiv.org/abs/2404.14069
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