# How to draw this implicit function?

I want to draw an image of this implicit function $$x^2 - y^2 = \tan ( y^x)$$, but I get a lot of warning messages when I draw the image using the following method:

ContourPlot[x^2 - y^2 == Tan[y^x], {x, -10, 10}, {y, -10, 10},
PlotPoints -> 50]


What can I do to create a complete and clear image of it? (The drawing software used in the above figure is Grafeq.)

And the following method of chyanog can draw the outline of this image, but how to further improve its drawing speed?

With[{pow = Sign[#] Abs[#]^#2 &},
ContourPlot[
Cos[pow[y, x]] (x^2 - y^2) == Sin[pow[y, x]], {x, -2 Pi,
2 Pi}, {y, -2 Pi, 2 Pi}, MaxRecursion -> 1, PlotPoints -> 50]] • Everything would be much simpler if y>0. Negative y does not make much sense. Mar 13 '20 at 18:44

The equation x^2 - y^2 == Tan[y^x] is equivalent to the series of the equations ArcTan[x^2 - y^2] == y^x + k*Pi, where k∈ Integers. Therefore,
ContourPlot[Evaluate[Table[ArcTan[x^2 - y^2] == y^x + k*Pi, {k, -2, 2}]], {x, -10,   10}, {y, -10, 10}, PlotPoints -> 50]