No search result is displayed when the search block is not visible on the search page

I've set visibility of the search block only on the front page <front>. When i enter some keywords into the search block, no result is displayed. I need to enter the search keywords again on the search page, then result is displayed normally.

When i set visibility of the search block also on the search page, for ex.:

<front>.
search
search/*

the result is displayed correct.

I'd like to save area on the page and display navigation/search and other block on the front page only, but the search module in this case doesn't works correctly.