Time series visualization of streaming telemetry (i.e., charting of key metrics such as server load over time) is increasingly prevalent in modern data platforms and applications. However, many existing systems simply plot the raw data streams as they arrive, often obscuring large-scale trends due to small-scale noise. We propose an alternative: to better prioritize end users' attention, smooth time series visualizations as much as possible to remove noise, while retaining large-scale structure to highlight significant deviations. We develop a new analytics operator called ASAP that automatically smooths streaming time series by adaptively optimizing the trade-off between noise reduction (i.e., variance) and trend retention (i.e., kurtosis). We introduce metrics to quantitatively assess the quality of smoothed plots and provide an efficient search strategy for optimizing these metrics that combines techniques from stream processing, user interface design, and signal processing via autocorrelation-based pruning, pixel-aware preaggregation, and on-demand refresh. We demonstrate that ASAP can improve users' accuracy in identifying long-term deviations in time series by up to 38.4% while reducing response times by up to 44.3%. Moreover, ASAP delivers these results several orders of magnitude faster than alternative search strategies.