HyperLogLogPlus

Preliminaries - Distinct Value (cardinality) Estimation

Calculating the number of distinct values (DV) in a specific finite-sized list of values using brute force (e.g. a HashSet) techniques is fairly straight forward provided that linear scaling to your number of values fits within your memory constraints. For many cases, the simple calculation serves just fine. However, in many other instances the simple linear approach simply will not scale as well as we would like, and a more robust algorithm is desirable. Enter probabilistic distinct value estimation algorithms: k-minimum-values (KMV), LogLog, HyperLogLog (HLL), and most recently HyperLogLog++ (HLLP). As data volume grows it becomes impractical to store all values in memory in order to reasonably calculate set cardinality. This is where probabilistic estimation algorithms become extremely useful. Often, we are happy to trade a handful of memory and better performance in exchange for an inexact, yet reasonably close approximation of the actual cardinality.

The Case For An Improvement

HyperLogLogPlus is an algorithm introduced by Google that builds on the DV estimation capabilities of HLL and improves on accuracy as well as scalability. HLLP not only works well with extremely large data sets (think trillion), but with smaller cardinality sets as well. HyperLogLog is simply not as accurate on the lower end of the cardinality spectrum. In addition, HLLP provides the ability to easily merge estimation sets. Although a data stream may not initially require high cardinality estimates as afforded by HLLP, it will still work accurately and efficiently on the smaller volumes without the need to rewrite code if data volume begins to surpass memory constraints. The paper describing the algorithm can be found here - https://research.google.com/pubs/pub40671.html

Performance Metrics

Overview

Below is a table detailing the performance characteristics when running HLLP over multiple data set sizes. There are three primary variables manipulated during the test: cardinality, sparse set precision, and normal set precision. Each of these values will have an impact on error rates, execution time, and total memory consumption.

Choosing p, sp

There is a tradeoff when choosing values for p and sp. A higher value for sp means a lower error rate for instances when the sparse set is being used. However, a higher value for sp also requires more memory, which means the algorithm will cut over to the dense representation more quickly. The Google paper (listed above) recommends settings of p=25, sp=14 for optimal memory use and algorithm accuracy, and these are the defaults provided by the Apache Metron implementation in Stellar. You'll notice in the tests below, memory consumption tops out around 12KB for this setting, regardless of cardinality size.

Key

card: cardinality<br>
sp: sparse precision value<br>
p: normal (dense) precision value<br>
err: error as a percent of the expected cardinality<br>
time: total time to add values to the hllp estimator and calculate a cardinality estimate<br>
size: size of the hllp set in bytes once all values have been added for the specified cardinality<br>
l=low, m=mid(based on percentile chosen), h=high, std=standard deviation<br>

Table Cardinality 200-1000, step by 200

Options Used

num trials: 5000
card min: 200
card max: 1000
card step: 200
card start: 200
sp min: 4
sp max: 32
sp step: 4
error percentile: 50.0
time percentile: 50.0
size percentile: 50.0
format err as %: true
cardspperr l/m/h/std (% of actual)time l/m/h/std (ms)size l/m/h/std (b)
200440.000 / 17.000 / 180.000 / 17.4700.070 / 0.118 / 10.092 / 0.204218 / 220 / 220 / 1
200840.000 / 17.000 / 209.500 / 18.0600.071 / 0.085 / 8.786 / 0.128219 / 221 / 221 / 1
200880.000 / 3.500 / 21.500 / 3.1850.082 / 0.085 / 8.375 / 0.119531 / 587 / 637 / 14
2001240.000 / 17.000 / 174.000 / 17.3760.070 / 0.085 / 8.708 / 0.128219 / 221 / 221 / 1
2001280.000 / 3.000 / 25.500 / 2.8470.086 / 0.119 / 8.984 / 0.151353 / 372 / 627 / 74
20012120.000 / 0.500 / 5.500 / 0.6590.082 / 0.096 / 17.208 / 0.243775 / 816 / 834 / 9
2001640.000 / 17.500 / 172.000 / 16.6220.068 / 0.075 / 9.553 / 0.137220 / 222 / 222 / 1
2001680.000 / 3.500 / 18.000 / 2.8990.095 / 0.118 / 0.663 / 0.031354 / 373 / 390 / 5
20016120.000 / 0.000 / 1.500 / 0.2760.085 / 0.108 / 13.977 / 0.199802 / 833 / 852 / 6
20016160.000 / 0.000 / 2.500 / 0.2790.079 / 0.085 / 0.271 / 0.017990 / 1027 / 1044 / 6
2002040.000 / 17.000 / 209.500 / 17.4240.068 / 0.072 / 0.250 / 0.014221 / 223 / 223 / 1
2002080.000 / 3.500 / 18.000 / 2.9440.096 / 0.106 / 13.581 / 0.192357 / 374 / 388 / 5
20020120.000 / 0.000 / 1.000 / 0.0660.084 / 0.088 / 1.096 / 0.019915 / 945 / 972 / 8
20020160.000 / 0.000 / 0.500 / 0.0700.083 / 0.087 / 10.272 / 0.145912 / 953 / 982 / 8
20020200.000 / 0.000 / 1.000 / 0.0690.079 / 0.081 / 0.210 / 0.0171028 / 1056 / 1058 / 2
2002440.000 / 17.500 / 136.000 / 16.5890.068 / 0.071 / 0.952 / 0.025221 / 223 / 223 / 1
2002480.000 / 3.500 / 18.000 / 2.9550.095 / 0.106 / 10.387 / 0.148353 / 373 / 390 / 5
20024120.000 / 0.000 / 0.500 / 0.0160.082 / 0.083 / 0.235 / 0.0141035 / 1048 / 1056 / 3
20024160.000 / 0.000 / 0.500 / 0.0120.082 / 0.084 / 10.904 / 0.1541038 / 1051 / 1059 / 3
20024200.000 / 0.000 / 0.500 / 0.0100.082 / 0.085 / 0.410 / 0.0191049 / 1064 / 1082 / 5
20024240.000 / 0.000 / 0.500 / 0.0230.079 / 0.084 / 11.926 / 0.1681247 / 1264 / 1275 / 4
2002840.000 / 17.500 / 229.000 / 17.2940.068 / 0.072 / 0.369 / 0.015222 / 224 / 224 / 1
20028883.000 / 83.000 / 84.000 / 0.1180.093 / 0.098 / 10.918 / 0.157272 / 276 / 278 / 1
20028120.000 / 0.000 / 0.500 / 0.0160.082 / 0.083 / 10.157 / 0.1431032 / 1067 / 1075 / 3
20028160.000 / 0.000 / 0.500 / 0.0070.082 / 0.083 / 0.617 / 0.0201058 / 1069 / 1077 / 3
20028200.000 / 0.000 / 0.500 / 0.0100.082 / 0.085 / 11.619 / 0.1651060 / 1071 / 1080 / 3
20028240.000 / 0.000 / 0.500 / 0.0070.083 / 0.085 / 0.516 / 0.0221065 / 1083 / 1100 / 4
20028280.000 / 0.000 / 0.500 / 0.0190.080 / 0.087 / 11.278 / 0.1601250 / 1267 / 1278 / 4
2003240.000 / 18.000 / 175.500 / 17.1570.068 / 0.078 / 0.223 / 0.019222 / 224 / 224 / 1
20032899.000 / 99.000 / 99.000 / 0.0000.093 / 0.107 / 11.695 / 0.167258 / 258 / 258 / 0
20032120.000 / 0.000 / 0.500 / 0.0140.081 / 0.084 / 8.906 / 0.1261060 / 1071 / 1075 / 2
20032160.000 / 0.000 / 0.500 / 0.0100.082 / 0.085 / 1.458 / 0.0271061 / 1073 / 1077 / 2
20032200.000 / 0.000 / 0.500 / 0.0120.082 / 0.084 / 10.499 / 0.1481065 / 1074 / 1079 / 2
20032240.000 / 0.000 / 0.500 / 0.0120.082 / 0.085 / 0.420 / 0.0201066 / 1075 / 1082 / 2
20032280.000 / 0.000 / 0.500 / 0.0160.082 / 0.086 / 8.753 / 0.1241076 / 1088 / 1102 / 4
20032320.000 / 0.000 / 0.500 / 0.0100.080 / 0.081 / 13.248 / 0.1881249 / 1268 / 1279 / 4
400440.000 / 17.500 / 175.250 / 17.5300.136 / 0.142 / 0.591 / 0.035218 / 220 / 220 / 0
400840.000 / 17.000 / 148.500 / 17.1740.136 / 0.156 / 12.882 / 0.241219 / 221 / 221 / 0
400880.000 / 3.500 / 21.250 / 3.2150.159 / 0.186 / 10.396 / 0.151375 / 387 / 802 / 62
4001240.000 / 17.750 / 166.000 / 17.3630.135 / 0.142 / 11.607 / 0.165219 / 221 / 221 / 0
4001280.000 / 3.250 / 23.750 / 3.1330.166 / 0.179 / 8.713 / 0.130376 / 387 / 401 / 3
40012120.000 / 0.750 / 4.250 / 0.7060.159 / 0.163 / 10.537 / 0.1891334 / 1387 / 1434 / 14
4001640.000 / 17.125 / 163.250 / 17.2080.135 / 0.138 / 12.403 / 0.178220 / 222 / 222 / 0
4001680.000 / 3.250 / 23.500 / 3.1260.165 / 0.179 / 9.985 / 0.147378 / 388 / 401 / 3
40016120.000 / 0.250 / 1.500 / 0.1950.166 / 0.173 / 10.434 / 0.1501414 / 1446 / 1475 / 8
40016160.000 / 0.250 / 1.750 / 0.1940.160 / 0.177 / 1.300 / 0.0481761 / 1798 / 1825 / 8
4002040.000 / 17.750 / 270.750 / 17.5920.135 / 0.149 / 8.814 / 0.128221 / 223 / 223 / 0
4002080.000 / 3.500 / 23.000 / 3.1030.165 / 0.183 / 9.271 / 0.139379 / 389 / 398 / 3
40020120.000 / 0.000 / 0.500 / 0.0660.164 / 0.182 / 11.093 / 0.1621617 / 1652 / 1683 / 10
40020160.000 / 0.000 / 0.500 / 0.0700.166 / 0.170 / 8.676 / 0.1281624 / 1665 / 1706 / 10
40020200.000 / 0.000 / 0.750 / 0.0690.159 / 0.162 / 12.846 / 0.1831840 / 1853 / 1856 / 2
4002440.000 / 16.750 / 174.750 / 16.7860.135 / 0.145 / 8.586 / 0.128221 / 223 / 223 / 0
4002480.000 / 3.500 / 24.500 / 3.0900.165 / 0.179 / 11.344 / 0.164377 / 389 / 399 / 3
40024120.000 / 0.000 / 0.250 / 0.0160.164 / 0.183 / 10.708 / 0.1591828 / 1841 / 1852 / 4
40024160.000 / 0.000 / 0.250 / 0.0170.164 / 0.172 / 11.180 / 0.1611830 / 1844 / 1855 / 4
40024200.000 / 0.000 / 0.250 / 0.0150.166 / 0.170 / 9.589 / 0.1401843 / 1868 / 1890 / 6
40024240.000 / 0.000 / 0.250 / 0.0220.160 / 0.162 / 9.137 / 0.1342213 / 2232 / 2247 / 5
4002840.000 / 18.250 / 164.000 / 16.5870.135 / 0.144 / 14.520 / 0.209222 / 224 / 224 / 0
40028833.000 / 47.750 / 56.750 / 3.5880.164 / 0.168 / 1.305 / 0.052355 / 375 / 394 / 5
40028120.000 / 0.000 / 0.250 / 0.0060.165 / 0.178 / 11.264 / 0.1671837 / 1848 / 1854 / 3
40028160.000 / 0.000 / 0.250 / 0.0140.164 / 0.167 / 8.689 / 0.1301838 / 1850 / 1857 / 3
40028200.000 / 0.000 / 0.250 / 0.0110.164 / 0.167 / 10.679 / 0.1591839 / 1852 / 1863 / 3
40028240.000 / 0.000 / 0.250 / 0.0110.166 / 0.175 / 12.887 / 0.1901857 / 1875 / 1896 / 5
40028280.000 / 0.000 / 0.250 / 0.0150.160 / 0.196 / 1.478 / 0.0712217 / 2235 / 2252 / 5
4003240.000 / 17.500 / 183.750 / 19.3080.135 / 0.142 / 9.949 / 0.148222 / 224 / 224 / 0
40032846.500 / 56.250 / 63.250 / 2.1940.164 / 0.181 / 1.209 / 0.063349 / 370 / 390 / 5
40032120.000 / 0.000 / 0.250 / 0.0120.164 / 0.171 / 11.529 / 0.1701837 / 1848 / 1854 / 3
40032160.000 / 0.000 / 0.250 / 0.0160.164 / 0.167 / 10.276 / 0.1541836 / 1850 / 1856 / 3
40032200.000 / 0.000 / 0.250 / 0.0150.164 / 0.184 / 11.611 / 0.2271839 / 1851 / 1858 / 3
40032240.000 / 0.000 / 0.250 / 0.0120.165 / 0.171 / 9.313 / 0.1431842 / 1853 / 1862 / 3
40032280.000 / 0.000 / 0.250 / 0.0130.166 / 0.180 / 10.708 / 0.1621860 / 1877 / 1900 / 5
40032320.000 / 0.000 / 0.250 / 0.0140.160 / 0.166 / 1.205 / 0.0572217 / 2235 / 2249 / 5
600440.000 / 17.333 / 219.667 / 17.2220.202 / 0.240 / 13.390 / 0.237218 / 220 / 220 / 0
600840.000 / 17.417 / 231.333 / 17.3400.202 / 0.224 / 9.662 / 0.150220 / 221 / 221 / 0
600880.000 / 3.500 / 24.333 / 3.2400.234 / 0.271 / 11.443 / 0.216382 / 392 / 403 / 3
6001240.000 / 17.167 / 188.167 / 17.3240.202 / 0.210 / 1.320 / 0.055219 / 221 / 221 / 0
6001280.000 / 3.500 / 23.833 / 3.2430.235 / 0.246 / 10.821 / 0.164382 / 392 / 403 / 3
60012120.000 / 0.667 / 4.500 / 0.6940.240 / 0.259 / 12.004 / 0.1832015 / 2101 / 2178 / 21
6001640.000 / 17.500 / 170.000 / 17.8820.202 / 0.218 / 9.208 / 0.140221 / 222 / 222 / 0
6001680.000 / 3.667 / 22.667 / 3.2760.234 / 0.251 / 12.301 / 0.237383 / 393 / 408 / 3
60016120.000 / 0.167 / 1.000 / 0.1700.250 / 0.284 / 12.000 / 0.1802199 / 2243 / 2282 / 12
60016160.000 / 0.167 / 1.167 / 0.1710.239 / 0.291 / 21.163 / 0.3332811 / 2859 / 2901 / 13
6002040.000 / 17.667 / 176.667 / 18.1620.202 / 0.223 / 16.405 / 0.275221 / 223 / 223 / 0
6002080.000 / 3.500 / 20.833 / 3.1800.234 / 0.243 / 5.621 / 0.104385 / 394 / 405 / 3
60020120.000 / 0.000 / 0.500 / 0.0660.246 / 0.281 / 19.279 / 0.3902541 / 2604 / 2663 / 15
60020160.000 / 0.000 / 0.667 / 0.0710.248 / 0.258 / 24.627 / 0.3872569 / 2627 / 2682 / 15
60020200.000 / 0.000 / 0.500 / 0.0690.239 / 0.246 / 13.606 / 0.2482938 / 2954 / 2972 / 3
6002440.000 / 17.333 / 210.333 / 18.1570.202 / 0.218 / 11.991 / 0.180222 / 223 / 223 / 0
6002480.000 / 3.667 / 21.167 / 3.1840.234 / 0.258 / 11.130 / 0.238385 / 394 / 406 / 3
60024120.000 / 0.000 / 0.167 / 0.0170.246 / 0.272 / 12.032 / 0.1912912 / 2935 / 2954 / 5
60024160.000 / 0.000 / 0.167 / 0.0190.246 / 0.268 / 19.358 / 0.2822916 / 2940 / 2959 / 6
60024200.000 / 0.000 / 0.167 / 0.0150.248 / 0.259 / 20.293 / 0.3432948 / 2980 / 3009 / 9
60024240.000 / 0.000 / 0.167 / 0.0170.239 / 0.252 / 11.721 / 0.2303586 / 3618 / 3643 / 7
6002840.000 / 17.667 / 182.667 / 17.3090.202 / 0.210 / 11.957 / 0.177223 / 224 / 224 / 0
60028810.333 / 28.000 / 42.833 / 3.6870.233 / 0.238 / 10.166 / 0.210377 / 392 / 403 / 3
60028120.000 / 0.000 / 0.333 / 0.0130.246 / 0.252 / 9.907 / 0.1583005 / 3024 / 3041 / 5
60028160.000 / 0.000 / 0.167 / 0.0120.246 / 0.256 / 18.673 / 0.2733007 / 3026 / 3045 / 5
60028200.000 / 0.000 / 0.167 / 0.0110.246 / 0.283 / 17.762 / 0.3553005 / 3029 / 3047 / 6
60028240.000 / 0.000 / 0.167 / 0.0110.248 / 0.254 / 8.821 / 0.1383035 / 3065 / 3098 / 8
60028280.000 / 0.000 / 0.167 / 0.0110.239 / 0.242 / 12.171 / 0.1773589 / 3621 / 3646 / 7
6003240.000 / 17.333 / 200.000 / 18.2940.202 / 0.205 / 9.036 / 0.138223 / 224 / 224 / 0
60032825.167 / 37.167 / 46.833 / 3.1850.232 / 0.236 / 9.061 / 0.144377 / 389 / 403 / 3
60032120.000 / 0.000 / 0.167 / 0.0130.246 / 0.256 / 11.119 / 0.1693028 / 3043 / 3055 / 4
60032160.000 / 0.000 / 0.167 / 0.0100.246 / 0.257 / 11.557 / 0.2133030 / 3045 / 3057 / 4
60032200.000 / 0.000 / 0.167 / 0.0110.246 / 0.266 / 20.353 / 0.2953030 / 3047 / 3071 / 4
60032240.000 / 0.000 / 0.167 / 0.0120.246 / 0.270 / 11.461 / 0.1833035 / 3050 / 3073 / 4
60032280.000 / 0.000 / 0.167 / 0.0130.248 / 0.260 / 11.755 / 0.2423060 / 3085 / 3108 / 7
60032320.000 / 0.000 / 0.167 / 0.0120.239 / 0.248 / 10.380 / 0.1573593 / 3621 / 3645 / 7
800440.000 / 17.250 / 188.250 / 17.2480.269 / 0.280 / 10.818 / 0.212219 / 220 / 220 / 0
800840.000 / 17.875 / 184.125 / 17.7210.270 / 0.298 / 16.706 / 0.252220 / 221 / 221 / 0
800880.000 / 3.625 / 22.000 / 3.4200.303 / 0.315 / 12.489 / 0.243386 / 395 / 406 / 3
8001240.000 / 17.750 / 196.500 / 16.8700.269 / 0.289 / 13.533 / 0.235220 / 221 / 221 / 0
8001280.000 / 3.750 / 25.875 / 3.3590.303 / 0.330 / 18.306 / 0.365386 / 395 / 408 / 3
80012120.000 / 0.750 / 4.375 / 0.6770.322 / 0.357 / 20.131 / 0.3502449 / 2603 / 2694 / 27
8001640.000 / 17.750 / 195.250 / 17.4550.269 / 0.274 / 10.472 / 0.205221 / 222 / 222 / 0
8001680.000 / 3.750 / 20.375 / 3.3570.302 / 0.308 / 10.637 / 0.165386 / 396 / 409 / 3
80016120.000 / 0.125 / 1.375 / 0.1700.334 / 0.344 / 10.745 / 0.2212712 / 2836 / 2882 / 15
80016160.000 / 0.250 / 1.375 / 0.1690.321 / 0.334 / 13.979 / 0.2523390 / 3625 / 3668 / 19
8002040.000 / 17.750 / 220.750 / 17.9530.269 / 0.281 / 9.422 / 0.148222 / 223 / 223 / 0
8002080.000 / 3.750 / 21.875 / 3.3050.302 / 0.358 / 24.073 / 0.435387 / 397 / 408 / 3
80020120.000 / 0.000 / 0.500 / 0.0670.331 / 0.345 / 13.461 / 0.2113249 / 3304 / 3360 / 17
80020160.000 / 0.000 / 0.500 / 0.0690.333 / 0.349 / 8.271 / 0.1463190 / 3331 / 3392 / 17
80020200.000 / 0.000 / 0.375 / 0.0690.320 / 0.335 / 11.307 / 0.2393539 / 3752 / 3771 / 5
8002440.000 / 17.125 / 184.500 / 18.1840.269 / 0.283 / 1.541 / 0.079222 / 223 / 223 / 0
8002480.000 / 3.625 / 23.125 / 3.3010.302 / 0.317 / 10.845 / 0.169388 / 397 / 409 / 3
80024120.000 / 0.000 / 0.250 / 0.0170.330 / 0.352 / 10.221 / 0.2443703 / 3729 / 3749 / 6
80024160.000 / 0.000 / 0.250 / 0.0180.330 / 0.344 / 13.454 / 0.2393711 / 3734 / 3753 / 6
80024200.000 / 0.000 / 0.250 / 0.0180.333 / 0.348 / 16.987 / 0.3743751 / 3786 / 3826 / 10
80024240.000 / 0.000 / 0.250 / 0.0180.320 / 0.333 / 17.097 / 0.2884567 / 4605 / 4630 / 8
8002840.000 / 17.375 / 326.125 / 18.1210.269 / 0.274 / 9.600 / 0.149223 / 224 / 224 / 0
8002880.375 / 19.875 / 34.500 / 4.4450.302 / 0.313 / 10.025 / 0.181387 / 397 / 409 / 3
80028120.000 / 0.000 / 0.125 / 0.0110.330 / 0.343 / 11.347 / 0.2163797 / 3821 / 3839 / 6
80028160.000 / 0.000 / 0.125 / 0.0100.330 / 0.344 / 10.748 / 0.2193801 / 3823 / 3843 / 6
80028200.000 / 0.000 / 0.125 / 0.0110.330 / 0.355 / 15.268 / 0.3143802 / 3827 / 3845 / 6
80028240.000 / 0.000 / 0.125 / 0.0110.334 / 0.360 / 11.192 / 0.2433841 / 3874 / 3905 / 9
80028280.000 / 0.000 / 0.250 / 0.0110.321 / 0.334 / 1.757 / 0.0954575 / 4609 / 4635 / 8
8003240.000 / 17.125 / 161.000 / 18.3700.269 / 0.279 / 20.700 / 0.344223 / 224 / 224 / 0
80032810.500 / 27.750 / 39.500 / 3.8830.301 / 0.333 / 18.781 / 0.332385 / 395 / 406 / 3
80032120.000 / 0.000 / 0.250 / 0.0110.330 / 0.371 / 18.883 / 0.3173823 / 3840 / 3853 / 4
80032160.000 / 0.000 / 0.125 / 0.0110.330 / 0.353 / 9.319 / 0.1953824 / 3842 / 3855 / 4
80032200.000 / 0.000 / 0.125 / 0.0120.330 / 0.353 / 15.582 / 0.3053826 / 3843 / 3859 / 4
80032240.000 / 0.000 / 0.125 / 0.0130.330 / 0.349 / 11.346 / 0.2343830 / 3847 / 3862 / 5
80032280.000 / 0.000 / 0.250 / 0.0130.333 / 0.368 / 14.482 / 0.3093866 / 3894 / 3925 / 8
80032320.000 / 0.000 / 0.125 / 0.0120.320 / 0.335 / 17.771 / 0.2954576 / 4608 / 4633 / 8
1000440.000 / 17.800 / 187.500 / 18.5760.337 / 0.374 / 10.384 / 0.179219 / 220 / 220 / 0
1000840.000 / 17.600 / 181.100 / 18.0350.336 / 0.372 / 13.220 / 0.262220 / 221 / 221 / 0
1000880.000 / 3.900 / 23.100 / 3.4250.371 / 0.398 / 9.495 / 0.175386 / 398 / 409 / 3
10001240.000 / 17.600 / 178.900 / 17.5590.336 / 0.351 / 11.176 / 0.265220 / 221 / 221 / 0
10001280.000 / 3.800 / 22.700 / 3.4380.371 / 0.392 / 10.942 / 0.188387 / 398 / 411 / 3
100012120.000 / 0.800 / 4.200 / 0.6840.403 / 0.443 / 11.219 / 0.2792971 / 3242 / 3364 / 39
10001640.000 / 17.600 / 184.300 / 17.1480.336 / 0.368 / 21.656 / 0.350221 / 222 / 222 / 0
10001680.000 / 3.800 / 21.900 / 3.3500.369 / 0.385 / 15.840 / 0.277388 / 399 / 412 / 3
100016120.000 / 0.200 / 1.200 / 0.1740.422 / 0.438 / 16.035 / 0.3353428 / 3530 / 3628 / 16
100016160.000 / 0.200 / 1.200 / 0.1730.405 / 0.420 / 13.370 / 0.3054314 / 4484 / 4573 / 20
10002040.000 / 17.600 / 223.000 / 16.9680.336 / 0.372 / 17.746 / 0.392222 / 223 / 223 / 0
10002080.000 / 3.800 / 21.400 / 3.3840.369 / 0.419 / 16.486 / 0.257389 / 400 / 412 / 3
100020120.000 / 0.000 / 0.400 / 0.0680.417 / 0.446 / 12.313 / 0.2653954 / 4099 / 4158 / 18
100020160.000 / 0.000 / 0.500 / 0.0690.422 / 0.439 / 11.284 / 0.2624016 / 4134 / 4211 / 19
100020200.000 / 0.000 / 0.600 / 0.0690.404 / 0.429 / 16.987 / 0.3354517 / 4641 / 4651 / 5
10002440.000 / 17.600 / 226.700 / 17.7610.339 / 0.351 / 12.804 / 0.275222 / 223 / 223 / 0
10002480.000 / 3.800 / 24.100 / 3.4030.371 / 0.406 / 15.710 / 0.298390 / 400 / 412 / 3
100024120.000 / 0.000 / 0.200 / 0.0180.417 / 0.449 / 12.253 / 0.2944494 / 4614 / 4636 / 7
100024160.000 / 0.000 / 0.100 / 0.0180.417 / 0.434 / 11.046 / 0.2544594 / 4620 / 4641 / 7
100024200.000 / 0.000 / 0.200 / 0.0190.422 / 0.458 / 13.433 / 0.2704645 / 4682 / 4722 / 11
100024240.000 / 0.000 / 0.200 / 0.0160.405 / 0.435 / 11.470 / 0.1895635 / 5672 / 5703 / 9
10002840.000 / 17.200 / 148.500 / 17.0460.338 / 0.363 / 20.446 / 0.380224 / 224 / 224 / 0
10002880.000 / 15.100 / 30.700 / 4.7940.371 / 0.389 / 18.272 / 0.359390 / 400 / 411 / 3
100028120.000 / 0.000 / 0.100 / 0.0130.417 / 0.432 / 13.575 / 0.2644677 / 4700 / 4719 / 6
100028160.000 / 0.000 / 0.200 / 0.0130.417 / 0.435 / 18.060 / 0.3814545 / 4702 / 4723 / 6
100028200.000 / 0.000 / 0.200 / 0.0130.417 / 0.448 / 17.596 / 0.3444679 / 4707 / 4728 / 6
100028240.000 / 0.000 / 0.200 / 0.0120.421 / 0.454 / 13.807 / 0.2974733 / 4764 / 4801 / 10
100028280.000 / 0.000 / 0.200 / 0.0130.406 / 0.456 / 20.533 / 0.3535646 / 5675 / 5704 / 9
10003240.000 / 18.150 / 177.600 / 19.5370.338 / 0.352 / 12.293 / 0.252223 / 224 / 224 / 0
10003281.500 / 22.100 / 35.100 / 4.3990.371 / 0.407 / 17.782 / 0.386388 / 398 / 412 / 3
100032120.000 / 0.000 / 0.200 / 0.0110.417 / 0.435 / 11.830 / 0.2474698 / 4717 / 4730 / 5
100032160.000 / 0.000 / 0.200 / 0.0130.417 / 0.443 / 18.214 / 0.2764700 / 4719 / 4733 / 5
100032200.000 / 0.000 / 0.200 / 0.0120.417 / 0.437 / 11.208 / 0.2324703 / 4720 / 4737 / 5
100032240.000 / 0.000 / 0.200 / 0.0130.417 / 0.448 / 18.288 / 0.4054706 / 4724 / 4740 / 5
100032280.000 / 0.000 / 0.200 / 0.0110.420 / 0.437 / 13.389 / 0.2454613 / 4782 / 4814 / 9
100032320.000 / 0.000 / 0.100 / 0.0120.406 / 0.424 / 12.513 / 0.2325641 / 5675 / 5704 / 9

Table Cardinality 1500-5000, step by 500

Options Used

num trials: 5000
card min: 1500
card max: 5000
card step: 500
card start: 1500
sp min: 4
sp max: 32
sp step: 4
error percentile: 50.0
time percentile: 50.0
size percentile: 50.0
format err as %: true
cardspperr l/m/h/std (% of actual)time l/m/h/std (ms)size l/m/h/std (b)
1500440.000 / 17.600 / 254.400 / 17.6270.501 / 0.612 / 19.629 / 0.593220 / 220 / 220 / 0
1500840.000 / 17.600 / 158.133 / 16.9800.506 / 0.594 / 16.843 / 0.493221 / 221 / 221 / 0
1500880.000 / 4.000 / 23.933 / 3.5900.533 / 0.567 / 11.059 / 0.259392 / 404 / 416 / 3
15001240.000 / 18.067 / 208.733 / 17.9340.505 / 0.531 / 20.544 / 0.368221 / 221 / 221 / 0
15001280.000 / 4.067 / 22.133 / 3.5790.529 / 0.576 / 22.421 / 0.453391 / 404 / 416 / 3
150012120.000 / 0.800 / 4.133 / 0.7070.607 / 0.638 / 15.124 / 0.3294338 / 4489 / 4656 / 43
15001640.000 / 17.200 / 167.333 / 17.9180.508 / 0.546 / 17.715 / 0.381221 / 222 / 222 / 0
15001680.000 / 3.933 / 23.667 / 3.6050.530 / 0.564 / 18.635 / 0.407393 / 405 / 417 / 3
150016120.000 / 0.200 / 1.067 / 0.1660.621 / 0.689 / 17.660 / 0.3645177 / 5271 / 5341 / 21
150016160.000 / 0.200 / 0.933 / 0.1650.612 / 0.654 / 19.700 / 0.4196688 / 6775 / 6855 / 23
15002040.000 / 17.600 / 231.333 / 17.7570.509 / 0.544 / 20.194 / 0.369223 / 223 / 223 / 0
15002080.000 / 3.933 / 25.600 / 3.7280.529 / 0.570 / 15.702 / 0.372395 / 406 / 417 / 3
150020120.000 / 0.067 / 0.333 / 0.0470.612 / 0.659 / 12.620 / 0.3436097 / 6191 / 6281 / 24
150020160.000 / 0.067 / 0.400 / 0.0470.619 / 0.648 / 13.508 / 0.3006163 / 6244 / 6344 / 24
150020200.000 / 0.067 / 0.333 / 0.0470.610 / 0.650 / 12.478 / 0.3237019 / 7048 / 7093 / 6
15002440.000 / 17.467 / 156.333 / 18.0090.508 / 0.569 / 17.878 / 0.386223 / 223 / 223 / 0
15002480.000 / 4.067 / 27.400 / 3.5990.529 / 0.564 / 21.583 / 0.397394 / 406 / 416 / 3
150024120.000 / 0.000 / 0.133 / 0.0170.611 / 0.655 / 16.659 / 0.3836974 / 7008 / 7039 / 8
150024160.000 / 0.000 / 0.133 / 0.0170.612 / 0.644 / 10.934 / 0.3136981 / 7016 / 7048 / 9
150024200.000 / 0.000 / 0.133 / 0.0170.620 / 0.683 / 21.873 / 0.5127064 / 7115 / 7167 / 14
150024240.000 / 0.000 / 0.133 / 0.0170.609 / 0.634 / 13.249 / 0.3158645 / 8684 / 8722 / 11
15002840.000 / 17.467 / 157.067 / 17.3120.508 / 0.529 / 14.149 / 0.336224 / 224 / 224 / 0
15002880.000 / 8.533 / 25.933 / 4.8650.529 / 0.561 / 15.511 / 0.380396 / 406 / 419 / 3
150028120.000 / 0.000 / 0.133 / 0.0120.611 / 0.657 / 10.977 / 0.2947178 / 7209 / 7239 / 8
150028160.000 / 0.000 / 0.133 / 0.0130.611 / 0.636 / 12.958 / 0.3197177 / 7211 / 7240 / 8
150028200.000 / 0.000 / 0.133 / 0.0120.612 / 0.646 / 13.818 / 0.3277185 / 7218 / 7248 / 9
150028240.000 / 0.000 / 0.133 / 0.0120.619 / 0.662 / 11.359 / 0.2797258 / 7305 / 7354 / 13
150028280.000 / 0.000 / 0.133 / 0.0120.609 / 0.648 / 12.260 / 0.3008643 / 8687 / 8732 / 12
15003240.000 / 17.267 / 175.933 / 18.4150.508 / 0.529 / 11.408 / 0.321224 / 224 / 224 / 0
15003280.000 / 14.667 / 29.200 / 4.8970.529 / 0.563 / 11.784 / 0.278393 / 404 / 416 / 3
150032120.000 / 0.000 / 0.133 / 0.0120.611 / 0.668 / 13.335 / 0.3427226 / 7252 / 7273 / 6
150032160.000 / 0.000 / 0.133 / 0.0120.611 / 0.655 / 19.309 / 0.4547230 / 7254 / 7276 / 6
150032200.000 / 0.000 / 0.133 / 0.0120.612 / 0.643 / 12.975 / 0.3147231 / 7256 / 7277 / 6
150032240.000 / 0.000 / 0.067 / 0.0130.612 / 0.666 / 12.496 / 0.3577236 / 7262 / 7286 / 7
150032280.000 / 0.000 / 0.133 / 0.0130.625 / 0.657 / 21.381 / 0.4017305 / 7347 / 7383 / 11
150032320.000 / 0.000 / 0.133 / 0.0120.609 / 0.652 / 19.148 / 0.3878643 / 8687 / 8724 / 12
2000440.050 / 17.950 / 200.300 / 17.7010.678 / 0.712 / 13.274 / 0.370220 / 220 / 220 / 0
2000840.050 / 17.200 / 227.450 / 17.1120.678 / 0.706 / 12.428 / 0.357221 / 221 / 221 / 0
2000880.000 / 4.150 / 28.100 / 3.6870.705 / 0.746 / 11.845 / 0.297397 / 408 / 418 / 3
20001240.050 / 17.075 / 166.300 / 17.2890.679 / 0.746 / 19.810 / 0.436221 / 221 / 221 / 0
20001280.000 / 4.050 / 26.000 / 3.6970.700 / 0.772 / 19.166 / 0.385396 / 408 / 419 / 3
200012120.050 / 0.850 / 4.150 / 0.7330.818 / 0.904 / 20.237 / 0.4605109 / 5354 / 5633 / 103
20001640.050 / 17.650 / 196.200 / 17.5390.678 / 0.747 / 17.211 / 0.435222 / 222 / 222 / 0
20001680.000 / 4.100 / 23.650 / 3.7200.699 / 0.770 / 17.887 / 0.378397 / 409 / 420 / 3
200016120.000 / 0.200 / 1.100 / 0.1630.835 / 0.915 / 24.825 / 0.5156456 / 6547 / 6647 / 23
200016160.000 / 0.200 / 1.100 / 0.1670.820 / 0.906 / 15.149 / 0.4278177 / 8278 / 8384 / 27
20002040.050 / 17.650 / 184.550 / 17.4680.678 / 0.742 / 19.468 / 0.449223 / 223 / 223 / 0
20002080.000 / 4.150 / 27.500 / 3.6930.700 / 0.756 / 12.525 / 0.289399 / 410 / 420 / 3
200020120.000 / 0.050 / 0.350 / 0.0440.830 / 0.921 / 19.963 / 0.5537551 / 7643 / 7742 / 23
200020160.000 / 0.050 / 0.300 / 0.0440.840 / 0.916 / 16.698 / 0.4487615 / 7702 / 7789 / 23
200020200.000 / 0.050 / 0.300 / 0.0440.824 / 0.909 / 23.619 / 0.6008602 / 8633 / 8652 / 7
20002440.050 / 17.600 / 249.350 / 17.7400.675 / 0.754 / 18.418 / 0.431223 / 223 / 223 / 0
20002480.000 / 4.150 / 24.700 / 3.6630.697 / 0.753 / 24.521 / 0.466398 / 410 / 421 / 3
200024120.000 / 0.000 / 0.150 / 0.0170.825 / 0.907 / 16.320 / 0.3738559 / 8591 / 8621 / 8
200024160.000 / 0.000 / 0.100 / 0.0170.826 / 0.876 / 20.177 / 0.4038567 / 8600 / 8630 / 9
200024200.000 / 0.000 / 0.100 / 0.0170.836 / 0.891 / 18.865 / 0.4298670 / 8715 / 8762 / 13
200024240.000 / 0.000 / 0.150 / 0.0170.823 / 0.874 / 13.270 / 0.39810491 / 10531 / 10569 / 11
20002840.050 / 17.600 / 206.800 / 17.7500.675 / 0.726 / 18.063 / 0.424224 / 224 / 224 / 0
20002880.000 / 6.050 / 23.850 / 4.3590.698 / 0.752 / 24.616 / 0.531400 / 411 / 421 / 3
200028120.000 / 0.000 / 0.100 / 0.0130.826 / 0.879 / 16.497 / 0.4588600 / 8623 / 8641 / 6
200028160.000 / 0.000 / 0.100 / 0.0120.826 / 0.898 / 16.948 / 0.4178602 / 8626 / 8645 / 6
200028200.000 / 0.000 / 0.150 / 0.0130.826 / 0.876 / 21.015 / 0.4358609 / 8634 / 8656 / 6
200028240.000 / 0.000 / 0.100 / 0.0120.836 / 0.878 / 19.773 / 0.4628704 / 8746 / 8791 / 12
200028280.000 / 0.000 / 0.100 / 0.0120.823 / 0.877 / 14.429 / 0.36610489 / 10535 / 10573 / 11
20003240.050 / 18.300 / 180.850 / 18.6350.676 / 0.723 / 18.331 / 0.431224 / 224 / 224 / 0
20003280.000 / 10.900 / 26.400 / 5.1220.698 / 0.742 / 18.170 / 0.443397 / 409 / 420 / 3
200032120.000 / 0.000 / 0.100 / 0.0130.825 / 0.869 / 12.927 / 0.3768603 / 8623 / 8642 / 6
200032160.000 / 0.000 / 0.100 / 0.0120.826 / 0.876 / 12.052 / 0.3768601 / 8625 / 8644 / 6
200032200.000 / 0.000 / 0.100 / 0.0120.824 / 0.883 / 19.872 / 0.4928602 / 8627 / 8644 / 6
200032240.000 / 0.000 / 0.100 / 0.0120.826 / 0.879 / 21.842 / 0.5098610 / 8635 / 8654 / 6
200032280.000 / 0.000 / 0.150 / 0.0120.836 / 0.894 / 18.071 / 0.4488707 / 8748 / 8791 / 12
200032320.000 / 0.000 / 0.100 / 0.0120.823 / 0.870 / 13.917 / 0.39810491 / 10535 / 10575 / 11
2500440.000 / 17.480 / 215.840 / 18.0350.844 / 0.896 / 17.723 / 0.444220 / 220 / 220 / 0
2500840.000 / 17.960 / 369.960 / 18.5030.844 / 0.897 / 20.260 / 0.542221 / 221 / 221 / 0
2500880.000 / 4.080 / 23.280 / 3.6390.874 / 0.928 / 21.505 / 0.472399 / 412 / 420 / 3
25001240.000 / 17.520 / 204.760 / 17.9730.845 / 0.963 / 21.008 / 0.499221 / 221 / 221 / 0
25001280.000 / 4.080 / 30.120 / 3.6830.869 / 0.946 / 18.277 / 0.488400 / 412 / 421 / 3
250012120.000 / 0.880 / 4.600 / 0.7471.025 / 1.134 / 20.157 / 0.5326140 / 6934 / 7154 / 78
25001640.000 / 17.240 / 173.400 / 17.7290.845 / 0.902 / 15.768 / 0.421222 / 222 / 222 / 0
25001680.000 / 4.160 / 25.520 / 3.8460.868 / 0.929 / 11.497 / 0.362401 / 413 / 422 / 3
250016120.000 / 0.200 / 1.080 / 0.1641.048 / 1.156 / 20.371 / 0.5148704 / 8924 / 9057 / 33
250016160.000 / 0.200 / 1.000 / 0.1661.031 / 1.108 / 13.336 / 0.43211159 / 11486 / 11633 / 42
25002040.000 / 17.600 / 154.600 / 17.3730.845 / 0.951 / 14.707 / 0.424223 / 223 / 223 / 0
25002080.000 / 4.200 / 23.720 / 3.7810.868 / 0.932 / 20.062 / 0.477397 / 414 / 424 / 3
250020120.000 / 0.040 / 0.320 / 0.0441.032 / 1.119 / 17.855 / 0.56010273 / 10533 / 10639 / 33
250020160.000 / 0.040 / 0.320 / 0.0431.045 / 1.107 / 16.834 / 0.46110370 / 10621 / 10730 / 33
250020200.000 / 0.040 / 0.400 / 0.0441.028 / 1.087 / 22.330 / 0.53611718 / 11995 / 12020 / 12
25002440.000 / 17.480 / 156.160 / 17.1710.844 / 0.890 / 18.096 / 0.406223 / 223 / 223 / 0
25002480.000 / 4.140 / 22.280 / 3.7160.868 / 0.915 / 19.031 / 0.458403 / 414 / 423 / 3
250024120.000 / 0.000 / 0.160 / 0.0171.030 / 1.088 / 22.283 / 0.50011894 / 11934 / 11971 / 11
250024160.000 / 0.000 / 0.120 / 0.0171.032 / 1.090 / 18.220 / 0.54711896 / 11947 / 11990 / 12
250024200.000 / 0.000 / 0.120 / 0.0181.043 / 1.101 / 17.194 / 0.51612056 / 12115 / 12187 / 18
250024240.000 / 0.000 / 0.120 / 0.0181.027 / 1.098 / 21.530 / 0.54714736 / 14798 / 14849 / 15
25002840.000 / 17.720 / 199.480 / 17.6410.845 / 0.900 / 20.585 / 0.511224 / 224 / 224 / 0
25002880.000 / 5.200 / 22.920 / 4.1060.869 / 0.914 / 12.212 / 0.359403 / 414 / 425 / 3
250028120.000 / 0.000 / 0.080 / 0.0121.031 / 1.085 / 17.978 / 0.50012267 / 12329 / 12367 / 11
250028160.000 / 0.000 / 0.120 / 0.0131.030 / 1.094 / 18.134 / 0.51911986 / 12331 / 12372 / 13
250028200.000 / 0.000 / 0.120 / 0.0111.031 / 1.086 / 20.068 / 0.55012296 / 12341 / 12382 / 12
250028240.000 / 0.000 / 0.080 / 0.0121.043 / 1.121 / 21.095 / 0.58712117 / 12486 / 12547 / 17
250028280.000 / 0.000 / 0.080 / 0.0121.028 / 1.097 / 20.162 / 0.57314747 / 14802 / 14864 / 15
25003240.000 / 18.200 / 187.680 / 18.7970.844 / 0.889 / 20.143 / 0.460224 / 224 / 224 / 0
25003280.000 / 8.680 / 25.600 / 4.9510.868 / 0.923 / 20.998 / 0.525402 / 413 / 422 / 3
250032120.000 / 0.000 / 0.080 / 0.0121.030 / 1.130 / 24.624 / 0.66612378 / 12414 / 12443 / 8
250032160.000 / 0.000 / 0.080 / 0.0121.030 / 1.090 / 17.364 / 0.53212381 / 12416 / 12443 / 8
250032200.000 / 0.000 / 0.120 / 0.0121.029 / 1.152 / 27.049 / 0.64712386 / 12418 / 12444 / 8
250032240.000 / 0.000 / 0.080 / 0.0131.031 / 1.083 / 26.018 / 0.57512390 / 12427 / 12460 / 9
250032280.000 / 0.000 / 0.120 / 0.0131.042 / 1.102 / 18.739 / 0.48612513 / 12568 / 12621 / 14
250032320.000 / 0.000 / 0.120 / 0.0121.027 / 1.088 / 16.996 / 0.49914742 / 14802 / 14851 / 15
3000440.000 / 17.833 / 186.867 / 17.4981.013 / 1.080 / 18.433 / 0.461220 / 220 / 220 / 0
3000840.033 / 17.600 / 201.567 / 17.8551.013 / 1.074 / 19.563 / 0.528221 / 221 / 221 / 0
3000880.000 / 4.300 / 26.467 / 3.7861.042 / 1.101 / 13.911 / 0.435403 / 414 / 422 / 3
30001240.000 / 17.467 / 212.600 / 18.7201.014 / 1.070 / 21.257 / 0.509221 / 221 / 221 / 0
30001280.000 / 4.167 / 30.600 / 3.7941.039 / 1.104 / 20.074 / 0.553405 / 414 / 422 / 3
300012120.000 / 0.833 / 4.833 / 0.7451.233 / 1.322 / 20.558 / 0.6387453 / 7706 / 7923 / 67
30001640.000 / 18.117 / 152.933 / 17.1611.013 / 1.101 / 21.535 / 0.564222 / 222 / 222 / 0
30001680.000 / 4.200 / 25.633 / 3.8171.037 / 1.100 / 18.806 / 0.554405 / 415 / 423 / 3
300016120.000 / 0.200 / 1.033 / 0.1691.258 / 1.331 / 22.352 / 0.68210292 / 10439 / 10570 / 37
300016160.000 / 0.200 / 0.967 / 0.1661.238 / 1.317 / 18.279 / 0.58913313 / 13458 / 13612 / 43
30002040.000 / 17.467 / 164.967 / 17.7571.013 / 1.113 / 19.652 / 0.508223 / 223 / 223 / 0
30002080.000 / 4.167 / 24.267 / 3.7431.038 / 1.092 / 18.642 / 0.554405 / 416 / 425 / 3
300020120.000 / 0.033 / 0.400 / 0.0451.240 / 1.303 / 14.404 / 0.51712293 / 12419 / 12571 / 35
300020160.000 / 0.033 / 0.300 / 0.0451.256 / 1.327 / 17.597 / 0.53712406 / 12522 / 12655 / 35
300020200.000 / 0.033 / 0.333 / 0.0441.237 / 1.308 / 20.509 / 0.55814100 / 14156 / 14250 / 11
30002440.000 / 17.417 / 215.733 / 18.1491.013 / 1.091 / 21.116 / 0.517223 / 223 / 223 / 0
30002480.000 / 4.233 / 21.767 / 3.7731.036 / 1.092 / 11.990 / 0.434406 / 416 / 426 / 3
300024120.000 / 0.000 / 0.100 / 0.0171.239 / 1.343 / 19.689 / 0.54114036 / 14088 / 14126 / 12
300024160.000 / 0.000 / 0.133 / 0.0171.239 / 1.311 / 14.029 / 0.53214050 / 14102 / 14146 / 13
300024200.000 / 0.000 / 0.133 / 0.0171.255 / 1.327 / 25.879 / 0.61114218 / 14302 / 14381 / 20
300024240.000 / 0.000 / 0.133 / 0.0171.233 / 1.299 / 20.804 / 0.61517434 / 17491 / 17548 / 17
30002840.000 / 17.467 / 160.633 / 17.6031.014 / 1.069 / 15.224 / 0.466224 / 224 / 224 / 0
30002880.000 / 4.733 / 22.600 / 3.9371.037 / 1.099 / 17.982 / 0.528407 / 417 / 426 / 3
300028120.000 / 0.000 / 0.100 / 0.0131.239 / 1.301 / 20.579 / 0.68814494 / 14534 / 14579 / 12
300028160.000 / 0.000 / 0.100 / 0.0121.237 / 1.299 / 16.532 / 0.49914490 / 14536 / 14575 / 12
300028200.000 / 0.000 / 0.100 / 0.0131.239 / 1.337 / 19.234 / 0.59114503 / 14548 / 14594 / 13
300028240.000 / 0.000 / 0.100 / 0.0121.254 / 1.328 / 17.902 / 0.58014666 / 14722 / 14789 / 18
300028280.000 / 0.000 / 0.100 / 0.0131.234 / 1.300 / 20.500 / 0.55217439 / 17495 / 17558 / 17
30003240.000 / 17.600 / 205.500 / 18.2331.012 / 1.059 / 11.735 / 0.414224 / 224 / 224 / 0
30003280.000 / 7.450 / 23.967 / 4.7861.038 / 1.102 / 15.705 / 0.478405 / 416 / 424 / 3
300032120.000 / 0.000 / 0.133 / 0.0131.238 / 1.335 / 18.066 / 0.60014599 / 14630 / 14661 / 9
300032160.000 / 0.000 / 0.100 / 0.0121.238 / 1.324 / 20.202 / 0.64214596 / 14632 / 14662 / 9
300032200.000 / 0.000 / 0.100 / 0.0131.238 / 1.313 / 17.383 / 0.51314601 / 14634 / 14663 / 9
300032240.000 / 0.000 / 0.100 / 0.0121.239 / 1.300 / 19.292 / 0.56014607 / 14646 / 14677 / 10
300032280.000 / 0.000 / 0.100 / 0.0121.254 / 1.332 / 20.109 / 0.57814761 / 14815 / 14872 / 16
300032320.000 / 0.000 / 0.067 / 0.0121.234 / 1.304 / 18.132 / 0.53717436 / 17495 / 17546 / 17
3500440.057 / 17.843 / 154.429 / 17.1311.183 / 1.241 / 18.127 / 0.543220 / 220 / 220 / 0
3500840.000 / 18.057 / 187.514 / 17.6971.182 / 1.250 / 20.428 / 0.564221 / 221 / 221 / 0
3500880.000 / 4.314 / 28.257 / 3.8331.213 / 1.299 / 20.333 / 0.672405 / 416 / 424 / 2
35001240.057 / 17.571 / 161.857 / 17.6641.181 / 1.252 / 20.923 / 0.569221 / 221 / 221 / 0
35001280.000 / 4.229 / 24.943 / 3.7591.208 / 1.275 / 22.113 / 0.543406 / 416 / 424 / 3
350012120.000 / 0.871 / 4.657 / 0.7861.442 / 1.523 / 18.288 / 0.5908126 / 8383 / 8643 / 70
35001640.000 / 18.114 / 163.343 / 17.7711.183 / 1.253 / 20.723 / 0.585222 / 222 / 222 / 0
35001680.000 / 4.286 / 30.143 / 3.8121.207 / 1.298 / 20.047 / 0.593406 / 418 / 424 / 2
350016120.000 / 1.057 / 5.457 / 0.6981.528 / 1.659 / 22.643 / 0.7682763 / 2824 / 2893 / 18
350016160.000 / 0.200 / 1.029 / 0.1661.450 / 1.558 / 20.879 / 0.64215119 / 15300 / 15466 / 46
35002040.057 / 18.029 / 156.029 / 17.4451.183 / 1.247 / 13.857 / 0.462223 / 223 / 223 / 0
35002080.000 / 4.314 / 26.371 / 3.8591.206 / 1.311 / 22.816 / 0.630408 / 419 / 426 / 3
350020120.000 / 1.057 / 4.771 / 0.6941.537 / 1.636 / 23.911 / 0.7532760 / 2824 / 2883 / 18
350020160.000 / 0.057 / 0.343 / 0.0421.472 / 1.571 / 20.930 / 0.67614140 / 14282 / 14406 / 38
350020200.000 / 0.057 / 0.257 / 0.0431.447 / 1.526 / 15.232 / 0.53616096 / 16146 / 16234 / 13
35002440.057 / 17.029 / 212.571 / 17.6911.183 / 1.254 / 17.746 / 0.583223 / 223 / 223 / 0
35002480.000 / 4.271 / 23.257 / 3.7621.207 / 1.268 / 15.615 / 0.492409 / 418 / 426 / 2
350024120.000 / 1.057 / 6.229 / 0.7061.533 / 1.653 / 22.778 / 0.6772760 / 2824 / 2888 / 18
350024160.000 / 0.000 / 0.114 / 0.0171.451 / 1.588 / 18.966 / 0.69716029 / 16088 / 16131 / 13
350024200.000 / 0.000 / 0.114 / 0.0171.469 / 1.573 / 16.584 / 0.47716233 / 16316 / 16395 / 22
350024240.000 / 0.000 / 0.114 / 0.0171.443 / 1.545 / 14.326 / 0.52319883 / 19959 / 20026 / 18
35002840.029 / 17.371 / 256.857 / 18.7791.182 / 1.254 / 13.532 / 0.445224 / 224 / 224 / 0
35002880.000 / 4.543 / 28.200 / 3.9341.208 / 1.317 / 22.788 / 0.594408 / 419 / 427 / 3
3500281284.371 / 84.371 / 84.514 / 0.0211.511 / 1.626 / 15.627 / 0.5721188 / 1204 / 1220 / 4
350028160.000 / 0.000 / 0.086 / 0.0121.449 / 1.530 / 13.406 / 0.52616477 / 16528 / 16572 / 12
350028200.000 / 0.000 / 0.114 / 0.0121.451 / 1.539 / 16.128 / 0.54316495 / 16542 / 16587 / 13
350028240.000 / 0.000 / 0.086 / 0.0121.469 / 1.551 / 15.112 / 0.55416679 / 16744 / 16813 / 19
350028280.000 / 0.000 / 0.086 / 0.0121.445 / 1.545 / 15.241 / 0.54319879 / 19962 / 20018 / 17
35003240.057 / 17.371 / 188.286 / 17.7751.183 / 1.258 / 13.408 / 0.468224 / 224 / 224 / 0
35003280.000 / 6.400 / 25.629 / 4.5531.207 / 1.271 / 12.497 / 0.443409 / 418 / 427 / 3
3500321299.086 / 99.086 / 99.086 / 0.0001.506 / 1.646 / 14.954 / 0.571920 / 920 / 920 / 0
350032160.000 / 0.000 / 0.086 / 0.0121.449 / 1.537 / 15.306 / 0.51116582 / 16624 / 16657 / 10
350032200.000 / 0.000 / 0.114 / 0.0131.450 / 1.558 / 15.277 / 0.54716587 / 16626 / 16657 / 10
350032240.000 / 0.000 / 0.086 / 0.0131.451 / 1.555 / 20.496 / 0.66116604 / 16639 / 16678 / 10
350032280.000 / 0.000 / 0.114 / 0.0121.468 / 1.554 / 15.893 / 0.48916768 / 16836 / 16895 / 17
350032320.000 / 0.000 / 0.086 / 0.0121.445 / 1.548 / 20.310 / 0.53719889 / 19962 / 20025 / 17
4000440.025 / 17.950 / 203.200 / 17.8601.351 / 1.431 / 14.530 / 0.524220 / 220 / 220 / 0
4000840.050 / 17.175 / 216.800 / 17.7341.351 / 1.421 / 19.692 / 0.620221 / 221 / 221 / 0
4000880.000 / 4.325 / 24.925 / 3.8171.382 / 1.475 / 19.092 / 0.560408 / 418 / 424 / 2
40001240.025 / 17.538 / 175.650 / 18.0661.352 / 1.437 / 19.980 / 0.590221 / 221 / 221 / 0
40001280.000 / 4.400 / 29.450 / 3.8631.378 / 1.477 / 22.190 / 0.643410 / 418 / 424 / 2
400012120.025 / 0.900 / 5.775 / 0.7991.648 / 1.764 / 19.034 / 0.7208718 / 8981 / 9265 / 70
40001640.050 / 17.575 / 176.200 / 17.0051.350 / 1.429 / 18.900 / 0.549222 / 222 / 222 / 0
40001680.000 / 4.250 / 26.400 / 3.8281.376 / 1.451 / 18.224 / 0.601410 / 419 / 425 / 2
400016120.275 / 0.950 / 4.275 / 0.6151.697 / 1.867 / 21.027 / 0.7592813 / 2882 / 2951 / 17
400016160.000 / 0.200 / 1.075 / 0.1681.660 / 1.801 / 17.255 / 0.65016124 / 17130 / 17352 / 55
40002040.050 / 18.325 / 148.475 / 17.1871.351 / 1.479 / 18.402 / 0.524223 / 223 / 223 / 0
40002080.000 / 4.350 / 25.750 / 3.8711.375 / 1.446 / 24.560 / 0.671410 / 420 / 426 / 2
400020120.275 / 0.975 / 4.400 / 0.6351.680 / 1.805 / 23.306 / 0.7292821 / 2883 / 2951 / 17
400020160.000 / 0.050 / 0.325 / 0.0421.684 / 1.783 / 20.501 / 0.69915888 / 16038 / 16188 / 39
400020200.000 / 0.050 / 0.325 / 0.0421.658 / 1.759 / 19.013 / 0.68918077 / 18134 / 18240 / 14
40002440.000 / 17.625 / 164.300 / 17.2921.351 / 1.427 / 19.917 / 0.579223 / 223 / 223 / 0
40002480.000 / 4.125 / 26.750 / 3.9051.375 / 1.442 / 18.641 / 0.557410 / 420 / 426 / 2
400024120.275 / 0.975 / 4.275 / 0.6101.703 / 1.810 / 22.554 / 0.8262825 / 2883 / 2942 / 16
400024160.000 / 0.000 / 0.100 / 0.0171.659 / 1.752 / 17.914 / 0.61218021 / 18073 / 18152 / 14
400024200.000 / 0.000 / 0.125 / 0.0171.681 / 1.789 / 20.884 / 0.74318241 / 18331 / 18404 / 22
400024240.000 / 0.000 / 0.150 / 0.0171.653 / 1.725 / 16.967 / 0.60422355 / 22426 / 22594 / 19
40002840.050 / 18.125 / 167.050 / 17.3291.348 / 1.501 / 23.889 / 0.758224 / 224 / 224 / 0
40002880.000 / 4.475 / 23.700 / 3.8351.374 / 1.588 / 21.053 / 0.732411 / 421 / 427 / 2
4000281267.225 / 75.800 / 76.550 / 0.2611.691 / 1.936 / 17.278 / 0.6671620 / 1704 / 2001 / 23
400028160.000 / 0.000 / 0.100 / 0.0121.707 / 1.932 / 16.598 / 0.57718470 / 18520 / 18569 / 13
400028200.000 / 0.000 / 0.075 / 0.0121.732 / 1.984 / 20.429 / 0.75218482 / 18536 / 18582 / 14
400028240.000 / 0.000 / 0.075 / 0.0121.739 / 1.993 / 21.507 / 0.67018690 / 18766 / 18838 / 20
400028280.000 / 0.000 / 0.100 / 0.0121.658 / 1.939 / 14.211 / 0.59422364 / 22431 / 22489 / 18
40003240.000 / 17.950 / 206.150 / 18.0201.386 / 1.567 / 14.368 / 0.550224 / 224 / 224 / 0
40003280.000 / 5.925 / 22.650 / 4.3661.395 / 1.594 / 16.171 / 0.515412 / 421 / 427 / 2
4000321288.250 / 88.675 / 89.125 / 0.1271.732 / 1.985 / 23.129 / 0.7741408 / 1486 / 1563 / 22
400032160.000 / 0.000 / 0.100 / 0.0121.709 / 1.935 / 28.713 / 0.67518577 / 18616 / 18647 / 10
400032200.000 / 0.000 / 0.100 / 0.0121.711 / 1.925 / 20.065 / 0.65318583 / 18618 / 18653 / 10
400032240.000 / 0.000 / 0.100 / 0.0131.699 / 1.917 / 20.723 / 0.61718589 / 18633 / 18664 / 10
400032280.000 / 0.000 / 0.075 / 0.0121.734 / 1.977 / 27.269 / 0.75318792 / 18858 / 18921 / 18
400032320.000 / 0.000 / 0.100 / 0.0121.704 / 1.921 / 14.253 / 0.55322343 / 22431 / 22575 / 19
4500440.044 / 17.911 / 173.911 / 18.1501.550 / 1.758 / 15.086 / 0.501220 / 220 / 220 / 0
4500840.044 / 17.800 / 206.000 / 17.3911.551 / 1.768 / 13.653 / 0.545221 / 221 / 221 / 0
4500880.000 / 4.222 / 26.378 / 3.8441.595 / 1.838 / 20.724 / 0.697411 / 419 / 424 / 2
45001240.000 / 17.689 / 172.667 / 17.1231.561 / 1.751 / 15.085 / 0.578221 / 221 / 221 / 0
45001280.000 / 4.300 / 24.644 / 3.8261.588 / 1.791 / 20.054 / 0.593410 / 419 / 424 / 2
450012120.022 / 0.911 / 4.956 / 0.8051.915 / 2.172 / 19.644 / 0.6159234 / 9507 / 9768 / 70
45001640.000 / 18.244 / 258.444 / 17.9671.526 / 1.758 / 15.643 / 0.552222 / 222 / 222 / 0
45001680.000 / 4.200 / 26.978 / 3.9311.563 / 1.786 / 15.151 / 0.572413 / 420 / 425 / 2
450016120.133 / 0.933 / 5.044 / 0.6871.972 / 2.210 / 22.173 / 0.7412864 / 2927 / 2980 / 15
450016160.000 / 0.200 / 0.978 / 0.1661.947 / 2.221 / 21.386 / 0.76617912 / 18092 / 18533 / 55
45002040.044 / 17.478 / 185.133 / 17.4981.561 / 1.765 / 13.399 / 0.524223 / 223 / 223 / 0
45002080.000 / 4.333 / 29.822 / 3.8541.590 / 1.787 / 17.447 / 0.612412 / 421 / 426 / 2
450020120.133 / 0.911 / 4.778 / 0.6831.953 / 2.210 / 24.534 / 0.7682875 / 2928 / 2982 / 15
450020160.000 / 0.044 / 0.311 / 0.0421.987 / 2.216 / 14.466 / 0.61116982 / 17116 / 17239 / 36
450020200.000 / 0.044 / 0.244 / 0.0421.944 / 2.176 / 20.109 / 0.65519151 / 19206 / 19254 / 15
45002440.044 / 17.644 / 191.756 / 18.1241.562 / 1.747 / 15.134 / 0.531223 / 223 / 223 / 0
45002480.000 / 4.178 / 28.111 / 3.8381.553 / 1.804 / 23.164 / 0.670413 / 421 / 426 / 2
450024120.133 / 0.933 / 4.156 / 0.6631.951 / 2.182 / 18.935 / 0.6632869 / 2928 / 2982 / 16
450024160.000 / 0.022 / 0.067 / 0.0121.943 / 2.170 / 17.937 / 0.71319107 / 19153 / 19196 / 13
450024200.000 / 0.022 / 0.089 / 0.0111.977 / 2.262 / 24.969 / 0.76119338 / 19410 / 19500 / 20
450024240.000 / 0.022 / 0.089 / 0.0121.929 / 2.189 / 18.456 / 0.71223435 / 23497 / 23550 / 17
45002840.044 / 17.133 / 288.400 / 17.8971.563 / 1.759 / 19.175 / 0.641224 / 224 / 224 / 0
45002880.000 / 4.378 / 24.867 / 3.8031.572 / 1.769 / 21.643 / 0.634415 / 422 / 427 / 2
4500281266.089 / 67.400 / 68.667 / 0.3591.930 / 2.183 / 28.176 / 0.7592026 / 2113 / 2214 / 27
450028160.000 / 0.000 / 0.089 / 0.0121.954 / 2.170 / 20.834 / 0.75119176 / 19211 / 19240 / 9
450028200.000 / 0.000 / 0.089 / 0.0121.942 / 2.170 / 21.282 / 0.70819191 / 19228 / 19261 / 10
450028240.000 / 0.000 / 0.067 / 0.0121.982 / 2.234 / 29.563 / 0.90519410 / 19480 / 19557 / 18
450028280.000 / 0.000 / 0.089 / 0.0121.944 / 2.180 / 21.368 / 0.74923437 / 23501 / 23562 / 17
45003240.044 / 17.778 / 204.511 / 18.4881.564 / 1.801 / 23.871 / 0.680224 / 224 / 224 / 0
45003280.000 / 5.489 / 22.289 / 4.2251.588 / 1.786 / 19.144 / 0.592413 / 422 / 427 / 2
4500321277.822 / 78.800 / 79.689 / 0.2421.926 / 2.172 / 21.370 / 0.7261838 / 1948 / 2039 / 26
450032160.000 / 0.000 / 0.089 / 0.0121.955 / 2.213 / 24.360 / 0.72519171 / 19210 / 19238 / 9
450032200.000 / 0.000 / 0.089 / 0.0121.949 / 2.186 / 17.274 / 0.66019179 / 19212 / 19241 / 9
450032240.000 / 0.000 / 0.089 / 0.0121.889 / 2.182 / 28.660 / 0.82519192 / 19228 / 19262 / 10
450032280.000 / 0.000 / 0.089 / 0.0121.903 / 2.039 / 21.219 / 0.70019423 / 19482 / 19549 / 18
450032320.000 / 0.000 / 0.089 / 0.0121.870 / 2.004 / 20.273 / 0.74223437 / 23501 / 23566 / 17
5000440.000 / 17.720 / 192.140 / 17.7401.684 / 1.829 / 14.606 / 0.612220 / 220 / 220 / 0
5000840.060 / 17.700 / 186.580 / 17.2791.683 / 1.818 / 15.426 / 0.599221 / 221 / 221 / 0
5000880.000 / 4.300 / 27.780 / 3.7831.715 / 1.913 / 20.698 / 0.741412 / 420 / 424 / 2
50001240.000 / 17.040 / 206.400 / 18.5931.683 / 1.809 / 17.501 / 0.622221 / 221 / 221 / 0
50001280.000 / 4.300 / 25.740 / 3.8051.710 / 1.811 / 19.765 / 0.670413 / 421 / 424 / 2
500012120.020 / 0.920 / 5.200 / 0.8422.066 / 2.203 / 25.912 / 0.8409696 / 9977 / 10220 / 71
50001640.000 / 17.700 / 190.640 / 16.7541.682 / 1.765 / 21.803 / 0.664222 / 222 / 222 / 0
50001680.000 / 4.300 / 30.580 / 3.8611.709 / 1.813 / 20.311 / 0.618414 / 422 / 425 / 2
500016120.000 / 0.880 / 5.140 / 0.7472.037 / 2.178 / 23.255 / 0.7402911 / 2962 / 3013 / 14
500016160.000 / 0.200 / 1.120 / 0.1712.094 / 2.204 / 20.890 / 0.78420566 / 21208 / 21872 / 88
50002040.000 / 17.620 / 127.520 / 17.2571.687 / 1.927 / 26.894 / 0.816223 / 223 / 223 / 0
50002080.000 / 4.330 / 28.580 / 3.8611.710 / 1.909 / 18.186 / 0.643415 / 423 / 426 / 2
500020120.000 / 0.900 / 5.340 / 0.7432.055 / 2.302 / 22.473 / 0.7632905 / 2963 / 3013 / 14
500020160.000 / 0.040 / 0.320 / 0.0432.137 / 2.410 / 24.675 / 0.86419509 / 19910 / 20058 / 42
500020200.000 / 0.040 / 0.280 / 0.0422.097 / 2.369 / 25.517 / 0.83021768 / 22416 / 22538 / 26
50002440.040 / 17.450 / 201.900 / 17.5041.686 / 1.861 / 18.820 / 0.618223 / 223 / 223 / 0
50002480.000 / 4.200 / 28.260 / 3.8391.713 / 1.923 / 19.929 / 0.679415 / 422 / 426 / 2
500024120.000 / 0.900 / 4.780 / 0.7662.047 / 2.287 / 15.684 / 0.6992912 / 2963 / 3016 / 14
500024160.000 / 0.020 / 0.100 / 0.0122.102 / 2.375 / 21.730 / 0.81822296 / 22351 / 22415 / 15
500024200.000 / 0.020 / 0.080 / 0.0122.128 / 2.397 / 24.851 / 0.84522577 / 22658 / 22745 / 23
500024240.000 / 0.020 / 0.080 / 0.0122.092 / 2.377 / 22.543 / 0.80027480 / 27560 / 27624 / 20
50002840.000 / 17.860 / 158.380 / 17.5341.686 / 1.875 / 17.770 / 0.647224 / 224 / 224 / 0
50002880.000 / 4.380 / 22.440 / 3.8861.712 / 1.969 / 22.211 / 0.772416 / 423 / 427 / 2
5000281259.020 / 60.660 / 62.740 / 0.4632.037 / 2.288 / 20.272 / 0.6522300 / 2388 / 2487 / 26
500028160.000 / 0.000 / 0.100 / 0.0122.099 / 2.378 / 23.672 / 0.86822667 / 22723 / 22765 / 13
500028200.000 / 0.000 / 0.080 / 0.0122.100 / 2.389 / 21.719 / 0.83822687 / 22742 / 22788 / 14
500028240.000 / 0.000 / 0.080 / 0.0122.132 / 2.393 / 23.989 / 0.76322950 / 23027 / 23106 / 21
500028280.000 / 0.000 / 0.080 / 0.0122.094 / 2.386 / 24.741 / 0.89227502 / 27565 / 27637 / 20
50003240.000 / 18.060 / 189.520 / 18.3781.686 / 1.919 / 26.851 / 0.838224 / 224 / 224 / 0
50003280.000 / 5.280 / 26.500 / 4.1571.714 / 1.930 / 21.178 / 0.750416 / 423 / 427 / 2
5000321269.800 / 70.920 / 72.440 / 0.3412.034 / 2.293 / 21.420 / 0.7542160 / 2261 / 2356 / 27
500032160.000 / 0.000 / 0.080 / 0.0122.099 / 2.387 / 25.364 / 0.79421966 / 22798 / 22832 / 16
500032200.000 / 0.000 / 0.080 / 0.0122.095 / 2.410 / 41.338 / 1.02222759 / 22800 / 22839 / 11
500032240.000 / 0.000 / 0.100 / 0.0122.100 / 2.277 / 23.671 / 0.74222773 / 22818 / 22856 / 11
500032280.000 / 0.000 / 0.100 / 0.0122.125 / 2.435 / 20.889 / 0.96122274 / 23099 / 23169 / 23
500032320.000 / 0.000 / 0.060 / 0.0122.088 / 2.280 / 16.157 / 0.70527494 / 27565 / 27640 / 19

Higher Cardinalities - sp=25, p=12,14,16

cardspperr l/m/h/std (% of actual)time l/m/h/std (ms)size l/m/h/std (b)
5500025120.000 / 1.031 / 5.431 / 0.92819.336 / 22.410 / 83.150 / 3.2823467 / 3501 / 3538 / 10
5500025140.000 / 0.470 / 2.525 / 0.42821.031 / 24.079 / 58.355 / 3.19211981 / 12073 / 12166 / 25
5500025160.000 / 0.140 / 0.751 / 0.12425.372 / 29.282 / 99.309 / 3.88841546 / 41834 / 42083 / 74
6000025120.002 / 1.080 / 5.500 / 0.93621.866 / 25.060 / 83.602 / 3.5633486 / 3519 / 3552 / 9
6000025140.002 / 0.483 / 2.762 / 0.43223.089 / 26.556 / 56.951 / 3.45512056 / 12141 / 12233 / 25
6000025160.000 / 0.145 / 1.552 / 0.13527.680 / 31.433 / 99.324 / 3.96742217 / 42469 / 42714 / 70
6500025120.000 / 1.053 / 5.968 / 0.92723.661 / 26.901 / 59.004 / 3.4753499 / 3534 / 3565 / 9
6500025140.000 / 0.483 / 2.517 / 0.43124.753 / 28.293 / 60.108 / 3.48312120 / 12206 / 12299 / 25
6500025160.000 / 0.158 / 1.455 / 0.15829.270 / 33.727 / 75.299 / 4.10842757 / 43002 / 43219 / 66
10000025140.001 / 0.520 / 2.814 / 0.45135.787 / 41.099 / 197.958 / 7.91912510 / 12598 / 12685 / 26

HLLPMeasurement tool usage

usage: HLLPMeasurement
 -cd,--chart_delim <CHART_DELIM>                    Column delimiter for
                                                    the chart. Default is
                                                    pipe '|'
 -cmn,--card_min <CARD_MIN>                         Lowest cardinality to
                                                    start running trials
                                                    from. Default 100
 -cmx,--card_max <CARD_MAX>                         Max cardinality to run
                                                    trials up to. Default
                                                    1000
 -cp,--chart_padding <CHART_PADDING>                Amount of padding to
                                                    use for each column.
                                                    Default 20
 -cs,--card_step <CARD_STEP>                        Quantity to increment
                                                    cardinality by for
                                                    each successive
                                                    measurement up until
                                                    the cardinality high
                                                    value. Default 100
 -efp,--error_format_percent <ERR_FORMAT_PERCENT>   Format error in
                                                    percent instead of
                                                    absolute terms.
                                                    Default true.
 -ep,--error_percentile <ERR_PERCENTILE>            What percentile to
                                                    calculate between
                                                    min/max for error.
                                                    Default is the median
                                                    (50th percentile)
 -h,--help                                          This screen
 -nt,--num_trials <NUM_TRIALS>                      Number of trials to
                                                    run. Default 1000
 -pmn,--p_min <P_MIN>                               Minimum sparse
                                                    precision to get
                                                    measurements for.
                                                    Default 4
 -pmx,--p_max <P_MAX>                               Maximum sparse
                                                    precision to get
                                                    measurements for.
                                                    Default 32
 -ps,--p_step <P_STEP>                              Increment precision
                                                    values by this step
                                                    amount when running
                                                    trials. Default 4
 -spmn,--sp_min <SP_MIN>                            Minimum sparse
                                                    precision to get
                                                    measurements for.
                                                    Default 4
 -spmx,--sp_max <SP_MAX>                            Maximum sparse
                                                    precision to get
                                                    measurements for.
                                                    Default 32
 -sps,--sp_step <SP_STEP>                           Increment precision
                                                    values by this step
                                                    amount when running
                                                    trials. Default 4
 -spt,--size_percentile <SIZE_PERCENTILE>           What percentile to
                                                    calculate between
                                                    min/max for size.
                                                    Default is the median
                                                    (50th percentile)
 -tp,--time_percentile <ERR_PERCENTILE>             What percentile to
                                                    calculate between
                                                    min/max for time.
                                                    Default is the median
                                                    (50th percentile)