141.92% attack speed between items and runes (purely for demonstrative purposes, please never stack Maladies). You're just under the hardcap, not at it, so your calculation doesn't work for getting there. And it certainly doesn't allow for Rapid Fire.
going to make a practice game to confirm this.
EDIT: confirmed. attached is a screenshot of the stat box of an in-game level 18 Tristana. no attack speed runes or masteries, four daggers (+15% attack speed each) and two recurve bows (+40% attack speed each) make +140% attack speed. the top box shows her without Rapid Fire (1.887 AS) and the bottom with (2.477 AS).