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Have a look at real or complex ball fields, which keep track of approximation error.

sage: x = exp(12*pi*i*i)
sage: RBF(x)
[+/- 67.1]
sage: 5 + RBF(x)  # not accurate enough
[+/- 72.1]
sage: 5 + RealBallField(80)(x)  # more precision
[5.00000 +/- 1.75e-6]