nlcom vs predictnl confidence intervals

I am graphing a function of estimated regression coefficients and observation specific variable values (x) by first using the “predictnl” command. The point estimates for a specific point are the same as that obtained from “nlcom”, but the “nlcom” command yields much larger standard errors and confidence intervals when comparing individual points (especially as x increases). Why is there a discrepancy?

The wider “nlcom” confidence intervals are what one may expect, and so is “predictnl” making some potentially invalid assumption when calculating the confidence intervals? Or is this an appropriate correction that I am not aware of?

In case it is helpful, an example is provided below. The regression is:
ln(y) = b0 + b1*x + b2*(x^2)

Then using the estimated coefficients, for each observation i, I am calculating:
p_i = {exp(b0 + b1*x_i + b2*(x_i^2)) - 1}*100

Using “predictnl” we get, for example:
x_i p_i (95% confidence interval)
0 -5.67 (-9.29, -2.06)
10 -5.66 (-9.28, -2.05)
20 -5.65 (-9.26, -2.03)
20000 -17.91 (-21.05, -14.76)

In contrast, using “nlcom” we get, for example:
x_i p_i (95% confidence interval)
0 -5.67 (-9.29, -2.06)
10 -5.66 (-9.27, -2.05)
20 -5.65 (-9.25, -2.04)
20000 -17.91 (-53.63, 17.82)

Notice the big difference when x_i=20000. Any thoughts would be very much appreciated. Thank you.