Specifying WorkingPrecision in LogLogPlot produces invalid plots

Question

I seem to have found a bug with LogLogPlot in Version 10. If I specify a working precision, the function produces total garbage. Here is a simple example. The first case, without WorkingPrecision specified works fine. The second case, with WorkingPrecision specified, produces garbage.

LogLogPlot[{1/10, 1, 2, 3}, {p, 0.1, 10000}, PlotLegends -> "Expressions"]

enter image description here

LogLogPlot[{1/10, 1, 2, 3}, {p, 0.1, 10000}, 
  PlotLegends -> "Expressions", WorkingPrecision -> 16]

enter image description here

If WorkingPrecision is not a specifiable option for LogLogPlot, why doesn't Mathematica warn me? I know it's OK to specify WorkingPrecision for normal plots. Any ideas?

confirmed (v9). The plot itself seems to become linear, and the axis labels garbage. — george2079, Feb 18 '15 at 18:32
Confirmed 10.0.2.0, even without the PlotLegends->"Expressions" option. — evanb, Feb 18 '15 at 21:13
I don't know if this has been reported as a bug to Wolfram yet, but I can confirm the same behavior in v9.0 and v10.0 (Windows 7). — Stephen Powell, Jul 24 '15 at 07:09

score 0 · Answer 1 · answered Jul 24 '15 at 07:15

With LogLogPlot[..., WorkingPrecision->_] (or indeed LogPlot[..., WorkingPrecision->_]), what is plotted is in fact the exponential of the function. As a workaround (assuming that's what you're looking for), you can use

LogLogPlot[Evaluate@Log[{1/10, 1, 2, 3}], {p, 0.1, 10000}, PlotLegends -> "Expressions", WorkingPrecision -> 16]

which produces something very similar to your first figure (but this legend is incorrect, of course).

Specifying WorkingPrecision in LogLogPlot produces invalid plots

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