How to reduce the size of an .eps file?

There are two reasons why eps files produced by Mathematica (such as p01.eps linked in your question) are often excessively large. The first is specific to Mathematica, but the second seems to be common to a few applications that generate postscript images.

1: Some methods for exporting images (such as right-clicking on the image) will include a large amount of data as comments, in case the file should be loaded back into Mathematica. Use the the Export command to avoid this.

2: Mathematica shades regions in a truly absurd way, using a huge number of small polygons where a few larger ones would do instead. A utility called polygone deals with this by merging shapes that share a common edge.

A version of your file p01.eps that has been processed by polygone 4 (and had the excess comments removed) is available here (409Kb).

EDIT

Prompted by @Bernard's answer, I should point out that the best reduction is usually achieved by converting to pdf after processing with polygone. Converting the file produced by polygone using epstopdf results in a 123Kb image. Not bad when starting from 4.6Mb.

EDIT 03/07/2014

Version 4 of polygone is now available.

You also can convert it to .pdf with Ghostscript and its Windows interface GsView. You'll still have a vector format, and as .pdf is more or less a compressed .ps format, you'll get a rather considerable size reduction — in the case of your file and 600dpi resolution, it is only 660 Kb. Unfortunately I don't know where I could upload the resulting file.