Despite of the complaints, the recently closed section can't be disabled, the big search field on top takes much space. In my case (I use 125% default page zoom) more than a half of screen is occupied by information which is actually not 'history'.
*btw, after using the small one search field and if there was no matches and thus page is scrolled top, the big one field is still not in focus. So need to select it again to delete/chsnge the phrase.