What is too complicated about $y=x^{xy}$? While playing with Desmos today, I typed the equation $y=x^{xy}$ and the graph came out to be 
I clicked the Learn More option given near my equation and Desmos said: Sometimes the calculator detects that an equation is too complicated to plot perfectly in a reasonable amount of time. When this happens, the equation is plotted at lower resolution.
What is the complication?

The solution is quite simple in terms of Lambert function
$$y=x^{xy}\implies y=-\frac{W(-x \log (x))}{x \log (x)}$$ In order to stay in the real domain, you need that
$$x \log(x) \geq \frac 1e \implies x \lt \frac{1}{e W\left(\frac{1}{e}\right)}=1.32110\cdots$$
We also have
$$y'=\frac{ e^{-2 W(-x \log (x))}}{W(-x \log (x))+1}(\log (x)+1)$$ which cancels at $x=\frac 1e$ and at this point $y=e W\left(\frac{1}{e}\right)=0.756945\cdots$
I think that we have a good description of your function.
