TITLE: Why does this function start swinging up and down so weirdly
QUESTION [12 upvotes]: Please have a look at the function: $$f(x) = \left(x + \frac{1}{x^x}\right)^x - x^x$$
You may see the plot on Wolfram Alpha.
Why does it have such a weird behaviour from $x = 13$? It starts swinging up and down so weirdly!

REPLY [3 votes]: As others have said this is a floating point error. If I plot it in mathematica I find:

Which clearly resembles the output by WolframAlpha (although they are not the same). If I increase the precision of the calculations and replot the same equation I find the following:

Note the change in scale.
Even with this increased precision you will still find erroneous weird behavior after some time and you will have to increase the working precision again (ad infinitum).