Replace

use Math::BigRat;  # Useless
use bignum;        # Uses M::BigInt and M::BitFloat
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with

use bignum upgrade => "Math::BigRat";
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or

use bigrat;
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I don't think they're equivalent -- the former initially creates M::BigInt objects and switches to M::BigRat when necessary, but I think the latter uses M::BitRat objects from the start -- but they have the same result here.