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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%. 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