I have a problem with understanding how calculation with BigFloat works in Julia. I want to calcualate an integral using DoubleExponentialFormulas QuadDE function.

I thought this part would work:

setprecision(BigFloat, 426)
f_int(a,b) = quadde(x->f(x), BigFloat(a), BigFloat(b))[1]

But from what I found it should be like:

setprecision(BigFloat, 426)
qde = QuadDE(BigFloat; h0=one(BigFloat)/8, maxlevel=10)
f_int(a,b) = qde(x->f(x), BigFloat(a), BigFloat(b))[1]

And all arguments of f should also be BigFloats, for example f(x) = BigFloat(x)^BigFloat(2) + BigFloat(5)

Why it should be like this?