Optimization, Mathematics.
it will take more than $n²$ steps for typical case to resemble worst case. Expanding $E_1(x)$ at $0$ and at $\infty$, we get the following small-x and large-x approximations. $$L_\text{small}(x)\approx -\log(x)$$ $$L_\text{large}(x)\approx \frac{1}{x e^{x}}$$ Initial decay is logarithmic and this