Could somebody who knows about numerical evaluation of symbolic functions please have a look at #17130. The problem is that there is some coercion going on *after* calling _eval_().

Look at the difference between the following two (the second has false precision):

sage: bessel_Y._eval_(RealField(200)(1), 1.0)
-0.781212821300289

sage: bessel_Y(RealField(200)(1), 1.0)
-0.78121282130028868451177004317287355661392211914062500000000

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