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Thank you all for your quick replies. By checking your comments, I went back to the initial functions that formed the problematic final expression and was indeed a formatting error. The problematic function in full form is the following: I assume that the \.08 character is what is causing the problem as when I rewritten the Cos[y] factor the problem was ...


Based on the reference to $MinMachineNumber from Michael E2 I found the practical solution to the FixedPoint never-ending search: SetSystemOptions["CatchMachineUnderflow" -> False]; FixedPoint[Sin[0.5 #] &, 1.] 0. SetSystemOptions["CatchMachineUnderflow" -> True]; (* the default *) FixedPoint[Sin[0.5 #] &, 1.] (* will never stop *) ...


According to $MinMachineNumber, MachinePrecision computations are automatically converted to arbitrary precision numbers (of precision $MachinePrecision) when a computation results in a value less than $MinMachineNumber. Precision[$MinMachineNumber] Precision[$MinMachineNumber/2.] (* MachinePrecision 15.9546 *)

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