Unreasonable number of Chebyshev coefficients required to approximate certain Gaussians

The following function requires north of 2 million Chebyshev coefficients to represent: Fun(x -> exp(-12(x + 4.9)^2), Chebyshev(-12..12))

This is in contrast to the function's "neighbors", see as follows:

for x0 in 4.7:0.05:5.1
    fun = Fun(x -> exp(-(x + x0)^2 / (1 / 12.0)), Chebyshev(-12..12))
    @show x0, length(fun.coefficients)
end

(x0, length(fun.coefficients)) = (4.7, 144)
(x0, length(fun.coefficients)) = (4.75, 144)
(x0, length(fun.coefficients)) = (4.8, 142)
(x0, length(fun.coefficients)) = (4.85, 143)
(x0, length(fun.coefficients)) = (4.9, 2097152)
(x0, length(fun.coefficients)) = (4.95, 141)
(x0, length(fun.coefficients)) = (5.0, 142)
(x0, length(fun.coefficients)) = (5.05, 142)
(x0, length(fun.coefficients)) = (5.1, 142)

Start by reproducing the reported Fun expression on Chebyshev(-12..12) and compare its coefficient count with the neighboring x0 values in the issue. Trace the approximation path that produces 2,097,152 coefficients at x0 = 4.9; done means this case no longer requires an unreasonable coefficient count while retaining the requested approximation accuracy.