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I have a really complex function that takes a few hours to plot as a function of a parameter. Few days later I realised that I named the axes wrong. Is there an easy way to edit the AxesLabels without running the plot again? (it takes too long!!) I tried Show[%, AxesLabel-> {newname, newname2}] but it doesn't change anything...

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Very straightforward:

plot = Plot[Sin[x], {x, 0, 2 Pi}];

plot /. (AxesLabel -> _) -> (AxesLabel -> {"x", "y"})
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You can copy and paste your graphic, add /. {"oldName1" -> "newName1", "oldName2" -> "newName2"} after it, and evaluate :

enter image description here

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Is this what you want?

g = Plot[Sin[x], {x, 0, 2 \[Pi]}]
Graphics[Line@Cases[g, Line[x__] :> x, \[Infinity]], PlotLabel -> "New labels", Options[g]]
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