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The colored curves represent different quantile contours of the empirical error distribution. The orange and green curves are the contours corresponding to +/- one standard deviation from the mean error, and which define the 68% confidence bounds. The red and blue curves are the contours at +/- two standard deviations and define the 95.4% confidence bounds. The brown and purple curves are the contours at +/- three standard deviations and define the 99.7% confidence bounds. The mean (gray) and median (black) overlap each other and hug the axis close to zero.
### Introduction to Detailed Accuracy Measurements
-Measuring the error properties of these stochastic algorithms is tricky and requires a great deal of thought into the design of the program that measures it. Getting smooth-looking plots requires many tens of thousands of trials, which even with fast CPUs requires a lot of time.
+Measuring the error properties of these stochastic algorithms is tricky and requires a great deal of thought into the design of the program that measures it. Getting smooth-looking plots requires many tens of thousands of trials, which even with fast CPUs requires a lot of time. The code used to produce the data for the plots in this paper can be found at <https://github.com/DataSketches/sketches-misc/tree/master/src/main/java/com/yahoo/sketches/performance>
For accuracy purposes, the *HllSketch* sketch is configured with one parameter, *Log_2(K)* which we abreviate as *LgK*. This defines the number of bins of the final HyperLogLog-Array (HLL-Array)\[6\] mode, and defines the bounds[7] on the accuracy of the sketch as well as its ultimate size. Thus, specifying a *LgK = 12*, means that the final HyperLogLog mode of the sketch will have *k = 2<sup>12</sup> = 4096* bins. A sketch with *LgK = 21* will ultimately have *k =2,097,152* bins, which is a very large sketch.
