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Originally raised by @KabirDubey through email, which is why I am assigning this issue to you. :)
The "analysis" part of the logical error plots are not in the gallery examples. I think there should be a paragraph or two accompanying each example that explains: what the axes of the plot mean, what we can deduce about the factor of error suppression, how the curve verifies the computation, etc.. I can work on this writing.