Human cognitive performance is critical to productivity, learning, and accident avoidance. Cognitive performance varies throughout each day and is in part driven by intrinsic, near 24-hour circadian rhythms. Prior research on the impact of sleep and circadian rhythms on cognitive performance has typically been restricted to small-scale laboratory-based studies that do not capture the variability of real-world conditions, such as environmental factors, motivation, and sleep patterns in real-world settings. Given these limitations, leading sleep researchers have called for larger in situ monitoring of sleep and performance [39]. We present the largest study to date on the impact of objectively measured real-world sleep on performance enabled through a reframing of everyday interactions with a web search engine as a series of performance tasks. Our analysis includes 3 million nights of sleep and 75 million interaction tasks. We measure cognitive performance through the speed of keystroke and click interactions on a web search engine and correlate them to wearable device-defined sleep measures over time. We demonstrate that real-world performance varies throughout the day and is influenced by both circadian rhythms, chronotype (morning/evening preference), and prior sleep duration and timing. We develop a statistical model that operationalizes a large body of work on sleep and performance and demonstrates that our estimates of circadian rhythms, homeostatic sleep drive, and sleep inertia align with expectations from laboratory-based sleep studies. Further, we quantify the impact of insufficient sleep on real-world performance and show that two consecutive nights with less than six hours of sleep are associated with decreases in performance which last for a period of six days. This work demonstrates the feasibility of using online interactions for large-scale physiological sensing.