Upper bound on error function

Question

I am trying to show:

$\text{erf}(x) \leq \sqrt{1-\exp{(-\frac{4}{\pi}x^2})}$

I tried applying a chernoff bound, but that doesnt give me a bound in terms of the squareroot.

Answer 1

This has already been answered here: Proving $1-\exp(-4x^2/ \pi) \ge \text{erf}(x)^2$ (eventually found this link from a discussion on twitter)