2D contour plot in Wolfram Alpha shows an artifact

Questions
,
1

If I give this query:

x**y / y ** x with x=2.6..2.8, y=2.6..2.8

I observe what appears to be an artifact in the 2d contour plot (roughly at centre of the plot.)

The 3d plot does not show the weird crinkle that the 2d plot shows. At first I thought a floating point precision issue, but if that were the case, it would show in the 3d plot as well?

Is this is a bug?

wa.png
wa.png809×677 35.9 KB

2

The glitch is due to numerical instability around a stationary point of the function. In Mathematica it can be eliminated, for example, by increasing the PlotPoints:

ContourPlot[x^y/y^x, {x, 2.6, 2.8}, {y, 2.6, 2.8},
 PlotPoints -> 50]

I don’t know what to do in Wolfram Alpha.

The 3D plot avoids the critical contour entirely.