Why this :$I(x)=\int_{-x}^x {0.5(\exp({-t² {\operatorname{erf}(t^2)}})}dt$ is not error function for $|x| >3$?

Question

This integral : $$I(x)=\int_{-x}^x {0.5(\exp({-t² {\operatorname{erf}(t^2)}})}dt$$ close to $x$ for $|x|<3$ and converge to $1$ for $|x|>3$ from $-\infty \to +\infty$ as shown here such that concide with error function for that large range over Real number , Now my question here is it possible to consider that distribution as Gausse distribution for $|x|>3$ since there is a concidence ?