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Hm, does this kind of approach also work for the "recover the algebraic expression that generated an approximated float" problem?

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If by "this kind of approach" you mean lattice tools, then I think the answer is yes. See the link below for an example in the Wikipedia page on the LLL. Also the second link may be helpful

https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%...

https://eprint.iacr.org/2023/032.pdf

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