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Re: Machine-precision Exp function
Daniel Lichtblau kindly pointed out a very simple solution: with SetSystemOptions["CatchMachineUnderflow" -> False] the default behavior of switching to arbitrary-precision numbers can be suppressed. After the above command, we get In := Exp[-1`*^6] Out = 0.` and the execution speed is identical to that of the compiled command. There are some hints in this direction in the help file under $MinMachineNumber, but they seem outdated (Version 188.8.131.52) as they invoke the command Developer`SetSystemOption["CatchMachineUnderflow" -> False] which no longer exists. Roman.