Every mistake that people find that decreases entropy has a multiplicative effect, and some of this reduction can take place due to happenstance inside of the application: maybe you can leak a couple bytes off the stack somewhere, which lets you decrease the entropy further. That said, "search space is twice as large" is by itself "big": maybe you'd notice every day, but wouldn't notice every 12 hours, or you'd notice every week, but not notice every few days.