Finite-precision arithmetic computations face an inherent tradeo between accuracy and e ciency. The points in this tradeo space are determined, among other factors, by di erent data types but also evaluation orders. To put it simply, the shorter a precision's bit-length, the larger the roundo error will be, but the faster the program will run. Similarly, the fewer arithmetic operations the program performs, the faster it will run; however, the e ect on the roundo error is less clear-cut. Manually optimizing the e ciency of nite-precision programs while ensuring that results remain accurate enough is challenging. The unintuitive and discrete nature of nite-precision makes estimation of roundo errors di cult; furthermore the space of possible data types and evaluation orders is prohibitively large.We present the rst fully automated and sound technique and tool for optimizing the performance of oating-point and xedpoint arithmetic kernels. Our technique combines rewriting and mixed-precision tuning. Rewriting searches through di erent evaluation orders to nd one which minimizes the roundo error at no additional runtime cost. Mixed-precision tuning assigns di erent nite precisions to di erent variables and operations and thus provides ner-grained control than uniform precision. We show that when these two techniques are designed and applied together, they can provide higher performance improvements than each alone.

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In this work, we provide a simple method to represent the contact line dynamics of an evaporating sessile droplet. As a droplet evaporates, two distinct contact line dynamics are observed. They are collectively known as modes of evaporation, namely Constant Contact Radius (CCR) and Constant Contact Angle (CCA). Another intermediate mode—Stick-Slide (SS) or mixed mode is also commonly observed. In this article, we are able to provide a graphical representation to these modes (named as MOE plot), which is visually more comprehensive especially for comparative studies. In addition, the method facilitates quantitative estimation for mode of evaporation (named as MOE fraction or MOEf), which doesn’t exist in literature. Thus, various substrates can now be compared based on mode of evaporation (or contact line dynamics), which are governed by fluid property and surface characteristics.