This
In[167]:= Plot[f[x, y], {x, -1, 1}, {y, -1, 1},RegionFunction -> Function[{x, y}, x^2 + y^2 <= (1/2)^2],
Contours -> Range[1/32 - 0.025, 1/32, 0.005 ], PlotRange -> {{-3/5, 3/5}, {-3/5, 3/5}}]
will do it because of
In[166]:= f[x, x] /. Last[Solve[2 x^2 == (1/2)^2, x, Reals]]
Out[166]= 1/32
because of the symmetry coincidence.
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