As is well known, Mathematica changed how it handles numbers smaller than $MinMachineNumber in recent versions.
I'm running Mathematica 12 on a Mac, and I cannot figure out why it's treating these differently:
Exp[-N[2695, $MachinePrecision]] Exp[-N[2695.0, $MachinePrecision]]
The top line returns 3.77... times 10^-1171 while the bottom line gives the "too small to represent as a normalized machine number" error and returns zero.
Since both numbers are set to MachinePrecision I'd think that the fact that the bottom one has the added .0 is irrelevant, but obviously my understanding is wrong.
N[Precision[-N[2695, $MachinePrecision]]] N[Precision[-N[2695.0, $MachinePrecision]]]
confirms both exponents have the same precision.
I'd greatly appreciate it if someone could explain why Mathematica is treating these differently to me.