What is the nicest way to make a function that takes Float or Double as input?

Say I want to implement the Fermi function (the simplest example of a logistic curve) so that if it's passed a Float it returns a Float and if it's passed a Double it returns a Double. Here's what I've got:

e = 2.7182845904523536

fermiFunc :: (Floating a) => a -> a
fermiFunc x = let one = fromIntegral 1 in one/(one + e^(-x))

The problem is that ghc says e is a Double. Defining the variable one is also kinda gross. The other solution I've thought of is to just define the function for doubles:

e = 2.7182845904523536

fermiFuncDouble :: Double -> Double
fermiFuncDouble x = 1.0/(1.0 + e^(-x))

Then using Either:

fermiFunc :: (Floating a) => Either Float Double -> a
fermiFunc Right x = double2Float (fermiFuncDouble (float2Double x))
fermiFunc Left x = fermiFuncDouble x

This isn't very exciting though because I might as well have just written a separate function for the Float case that just handles the casting and calls fermiFuncDouble. Is there a nice way to write a function for both types?