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This would allows users for a much quicker comparison of found items with given expression and without it. This would also allow for keeping history of searches less cluttered as not every expression a user might need to have remembered [because now users either have to click some item with it in order for it to be added to the history thus be available for later - or manually copy it, remove it and then paste it again if needed for re-comparison]
This could also be done in form of a button, but as there are none for now I reckon this would require a lot of new code writing - while adding another tick to Filter and coping it to Search Edit would be probably much easier. [Some buttons idea related suggestions I have made here viewtopic.php?t=11806 and here viewtopic.php?t=13053]