Magento 1 join collection with table created by subquery

index.php

<?php

$productCollection->getSelect()->join(
                new Zend_Db_Expr("(SELECT product_id, SUM(impressions) as impressions, SUM(clicks) as clicks, SUM(cart) as cart, SUM(conversions) as conversions, round(SUM(profit), 2) as profit, round(SUM(profit)/SUM(impressions), 3) as rpi 
                                            FROM evermart_crosssells_statistics_daily" .
                                            ($dateFilter ? " WHERE $dateFilter" : "")
                                            . " GROUP BY product_id)"),
                't.product_id = e.entity_id',
                array('t.impressions','t.clicks', 't.cart', 't.conversions', 't.profit', 't.rpi')
            );