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Hello!
Very quick question here. When converting fractions a/b, for a,b nonnegative and a,b<=N, what is the smallest N (order of magnitude) such that there exist two pairs a,b, a',b' such that a/b != a'/b' but when converted into a long double you get a collision? Would be slightly helpful to know tbf.
Honestly I have no idea, but at this point you can just do $$$a/b = a'/b' \iff a \cdot b' = a' \cdot b$$$ and avoid the issue entirely. Run away from doubles.