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I expect to have a chimney-look plot out of the function z = 1/(x^2 + y^2), but what I got is a broken one. Is there a way to get an intact plot from ContourPlot3D without any fragment loss?

ContourPlot3D[
 1/(x^2 + y^2) - z == 0, {x, -1, 1}, {y, -1, 1}, {z, -150, 150}]

enter image description here

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Just add more PlotPoints:

ContourPlot3D[1/(x^2 + y^2) - z == 0, {x, -1, 1}, {y, -1, 1}, {z, -150, 150}, 
 PlotPoints -> 20]

Mathematica graphics

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