This project has retired. For details please refer to its Attic page.
Metron – HyperLogLogPlus

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
card sp p err l/m/h/std (% of actual) time l/m/h/std (ms) size l/m/h/std (b)
200 4 4 0.000 / 17.000 / 180.000 / 17.470 0.070 / 0.118 / 10.092 / 0.204 218 / 220 / 220 / 1
200 8 4 0.000 / 17.000 / 209.500 / 18.060 0.071 / 0.085 / 8.786 / 0.128 219 / 221 / 221 / 1
200 8 8 0.000 / 3.500 / 21.500 / 3.185 0.082 / 0.085 / 8.375 / 0.119 531 / 587 / 637 / 14
200 12 4 0.000 / 17.000 / 174.000 / 17.376 0.070 / 0.085 / 8.708 / 0.128 219 / 221 / 221 / 1
200 12 8 0.000 / 3.000 / 25.500 / 2.847 0.086 / 0.119 / 8.984 / 0.151 353 / 372 / 627 / 74
200 12 12 0.000 / 0.500 / 5.500 / 0.659 0.082 / 0.096 / 17.208 / 0.243 775 / 816 / 834 / 9
200 16 4 0.000 / 17.500 / 172.000 / 16.622 0.068 / 0.075 / 9.553 / 0.137 220 / 222 / 222 / 1
200 16 8 0.000 / 3.500 / 18.000 / 2.899 0.095 / 0.118 / 0.663 / 0.031 354 / 373 / 390 / 5
200 16 12 0.000 / 0.000 / 1.500 / 0.276 0.085 / 0.108 / 13.977 / 0.199 802 / 833 / 852 / 6
200 16 16 0.000 / 0.000 / 2.500 / 0.279 0.079 / 0.085 / 0.271 / 0.017 990 / 1027 / 1044 / 6
200 20 4 0.000 / 17.000 / 209.500 / 17.424 0.068 / 0.072 / 0.250 / 0.014 221 / 223 / 223 / 1
200 20 8 0.000 / 3.500 / 18.000 / 2.944 0.096 / 0.106 / 13.581 / 0.192 357 / 374 / 388 / 5
200 20 12 0.000 / 0.000 / 1.000 / 0.066 0.084 / 0.088 / 1.096 / 0.019 915 / 945 / 972 / 8
200 20 16 0.000 / 0.000 / 0.500 / 0.070 0.083 / 0.087 / 10.272 / 0.145 912 / 953 / 982 / 8
200 20 20 0.000 / 0.000 / 1.000 / 0.069 0.079 / 0.081 / 0.210 / 0.017 1028 / 1056 / 1058 / 2
200 24 4 0.000 / 17.500 / 136.000 / 16.589 0.068 / 0.071 / 0.952 / 0.025 221 / 223 / 223 / 1
200 24 8 0.000 / 3.500 / 18.000 / 2.955 0.095 / 0.106 / 10.387 / 0.148 353 / 373 / 390 / 5
200 24 12 0.000 / 0.000 / 0.500 / 0.016 0.082 / 0.083 / 0.235 / 0.014 1035 / 1048 / 1056 / 3
200 24 16 0.000 / 0.000 / 0.500 / 0.012 0.082 / 0.084 / 10.904 / 0.154 1038 / 1051 / 1059 / 3
200 24 20 0.000 / 0.000 / 0.500 / 0.010 0.082 / 0.085 / 0.410 / 0.019 1049 / 1064 / 1082 / 5
200 24 24 0.000 / 0.000 / 0.500 / 0.023 0.079 / 0.084 / 11.926 / 0.168 1247 / 1264 / 1275 / 4
200 28 4 0.000 / 17.500 / 229.000 / 17.294 0.068 / 0.072 / 0.369 / 0.015 222 / 224 / 224 / 1
200 28 8 83.000 / 83.000 / 84.000 / 0.118 0.093 / 0.098 / 10.918 / 0.157 272 / 276 / 278 / 1
200 28 12 0.000 / 0.000 / 0.500 / 0.016 0.082 / 0.083 / 10.157 / 0.143 1032 / 1067 / 1075 / 3
200 28 16 0.000 / 0.000 / 0.500 / 0.007 0.082 / 0.083 / 0.617 / 0.020 1058 / 1069 / 1077 / 3
200 28 20 0.000 / 0.000 / 0.500 / 0.010 0.082 / 0.085 / 11.619 / 0.165 1060 / 1071 / 1080 / 3
200 28 24 0.000 / 0.000 / 0.500 / 0.007 0.083 / 0.085 / 0.516 / 0.022 1065 / 1083 / 1100 / 4
200 28 28 0.000 / 0.000 / 0.500 / 0.019 0.080 / 0.087 / 11.278 / 0.160 1250 / 1267 / 1278 / 4
200 32 4 0.000 / 18.000 / 175.500 / 17.157 0.068 / 0.078 / 0.223 / 0.019 222 / 224 / 224 / 1
200 32 8 99.000 / 99.000 / 99.000 / 0.000 0.093 / 0.107 / 11.695 / 0.167 258 / 258 / 258 / 0
200 32 12 0.000 / 0.000 / 0.500 / 0.014 0.081 / 0.084 / 8.906 / 0.126 1060 / 1071 / 1075 / 2
200 32 16 0.000 / 0.000 / 0.500 / 0.010 0.082 / 0.085 / 1.458 / 0.027 1061 / 1073 / 1077 / 2
200 32 20 0.000 / 0.000 / 0.500 / 0.012 0.082 / 0.084 / 10.499 / 0.148 1065 / 1074 / 1079 / 2
200 32 24 0.000 / 0.000 / 0.500 / 0.012 0.082 / 0.085 / 0.420 / 0.020 1066 / 1075 / 1082 / 2
200 32 28 0.000 / 0.000 / 0.500 / 0.016 0.082 / 0.086 / 8.753 / 0.124 1076 / 1088 / 1102 / 4
200 32 32 0.000 / 0.000 / 0.500 / 0.010 0.080 / 0.081 / 13.248 / 0.188 1249 / 1268 / 1279 / 4
400 4 4 0.000 / 17.500 / 175.250 / 17.530 0.136 / 0.142 / 0.591 / 0.035 218 / 220 / 220 / 0
400 8 4 0.000 / 17.000 / 148.500 / 17.174 0.136 / 0.156 / 12.882 / 0.241 219 / 221 / 221 / 0
400 8 8 0.000 / 3.500 / 21.250 / 3.215 0.159 / 0.186 / 10.396 / 0.151 375 / 387 / 802 / 62
400 12 4 0.000 / 17.750 / 166.000 / 17.363 0.135 / 0.142 / 11.607 / 0.165 219 / 221 / 221 / 0
400 12 8 0.000 / 3.250 / 23.750 / 3.133 0.166 / 0.179 / 8.713 / 0.130 376 / 387 / 401 / 3
400 12 12 0.000 / 0.750 / 4.250 / 0.706 0.159 / 0.163 / 10.537 / 0.189 1334 / 1387 / 1434 / 14
400 16 4 0.000 / 17.125 / 163.250 / 17.208 0.135 / 0.138 / 12.403 / 0.178 220 / 222 / 222 / 0
400 16 8 0.000 / 3.250 / 23.500 / 3.126 0.165 / 0.179 / 9.985 / 0.147 378 / 388 / 401 / 3
400 16 12 0.000 / 0.250 / 1.500 / 0.195 0.166 / 0.173 / 10.434 / 0.150 1414 / 1446 / 1475 / 8
400 16 16 0.000 / 0.250 / 1.750 / 0.194 0.160 / 0.177 / 1.300 / 0.048 1761 / 1798 / 1825 / 8
400 20 4 0.000 / 17.750 / 270.750 / 17.592 0.135 / 0.149 / 8.814 / 0.128 221 / 223 / 223 / 0
400 20 8 0.000 / 3.500 / 23.000 / 3.103 0.165 / 0.183 / 9.271 / 0.139 379 / 389 / 398 / 3
400 20 12 0.000 / 0.000 / 0.500 / 0.066 0.164 / 0.182 / 11.093 / 0.162 1617 / 1652 / 1683 / 10
400 20 16 0.000 / 0.000 / 0.500 / 0.070 0.166 / 0.170 / 8.676 / 0.128 1624 / 1665 / 1706 / 10
400 20 20 0.000 / 0.000 / 0.750 / 0.069 0.159 / 0.162 / 12.846 / 0.183 1840 / 1853 / 1856 / 2
400 24 4 0.000 / 16.750 / 174.750 / 16.786 0.135 / 0.145 / 8.586 / 0.128 221 / 223 / 223 / 0
400 24 8 0.000 / 3.500 / 24.500 / 3.090 0.165 / 0.179 / 11.344 / 0.164 377 / 389 / 399 / 3
400 24 12 0.000 / 0.000 / 0.250 / 0.016 0.164 / 0.183 / 10.708 / 0.159 1828 / 1841 / 1852 / 4
400 24 16 0.000 / 0.000 / 0.250 / 0.017 0.164 / 0.172 / 11.180 / 0.161 1830 / 1844 / 1855 / 4
400 24 20 0.000 / 0.000 / 0.250 / 0.015 0.166 / 0.170 / 9.589 / 0.140 1843 / 1868 / 1890 / 6
400 24 24 0.000 / 0.000 / 0.250 / 0.022 0.160 / 0.162 / 9.137 / 0.134 2213 / 2232 / 2247 / 5
400 28 4 0.000 / 18.250 / 164.000 / 16.587 0.135 / 0.144 / 14.520 / 0.209 222 / 224 / 224 / 0
400 28 8 33.000 / 47.750 / 56.750 / 3.588 0.164 / 0.168 / 1.305 / 0.052 355 / 375 / 394 / 5
400 28 12 0.000 / 0.000 / 0.250 / 0.006 0.165 / 0.178 / 11.264 / 0.167 1837 / 1848 / 1854 / 3
400 28 16 0.000 / 0.000 / 0.250 / 0.014 0.164 / 0.167 / 8.689 / 0.130 1838 / 1850 / 1857 / 3
400 28 20 0.000 / 0.000 / 0.250 / 0.011 0.164 / 0.167 / 10.679 / 0.159 1839 / 1852 / 1863 / 3
400 28 24 0.000 / 0.000 / 0.250 / 0.011 0.166 / 0.175 / 12.887 / 0.190 1857 / 1875 / 1896 / 5
400 28 28 0.000 / 0.000 / 0.250 / 0.015 0.160 / 0.196 / 1.478 / 0.071 2217 / 2235 / 2252 / 5
400 32 4 0.000 / 17.500 / 183.750 / 19.308 0.135 / 0.142 / 9.949 / 0.148 222 / 224 / 224 / 0
400 32 8 46.500 / 56.250 / 63.250 / 2.194 0.164 / 0.181 / 1.209 / 0.063 349 / 370 / 390 / 5
400 32 12 0.000 / 0.000 / 0.250 / 0.012 0.164 / 0.171 / 11.529 / 0.170 1837 / 1848 / 1854 / 3
400 32 16 0.000 / 0.000 / 0.250 / 0.016 0.164 / 0.167 / 10.276 / 0.154 1836 / 1850 / 1856 / 3
400 32 20 0.000 / 0.000 / 0.250 / 0.015 0.164 / 0.184 / 11.611 / 0.227 1839 / 1851 / 1858 / 3
400 32 24 0.000 / 0.000 / 0.250 / 0.012 0.165 / 0.171 / 9.313 / 0.143 1842 / 1853 / 1862 / 3
400 32 28 0.000 / 0.000 / 0.250 / 0.013 0.166 / 0.180 / 10.708 / 0.162 1860 / 1877 / 1900 / 5
400 32 32 0.000 / 0.000 / 0.250 / 0.014 0.160 / 0.166 / 1.205 / 0.057 2217 / 2235 / 2249 / 5
600 4 4 0.000 / 17.333 / 219.667 / 17.222 0.202 / 0.240 / 13.390 / 0.237 218 / 220 / 220 / 0
600 8 4 0.000 / 17.417 / 231.333 / 17.340 0.202 / 0.224 / 9.662 / 0.150 220 / 221 / 221 / 0
600 8 8 0.000 / 3.500 / 24.333 / 3.240 0.234 / 0.271 / 11.443 / 0.216 382 / 392 / 403 / 3
600 12 4 0.000 / 17.167 / 188.167 / 17.324 0.202 / 0.210 / 1.320 / 0.055 219 / 221 / 221 / 0
600 12 8 0.000 / 3.500 / 23.833 / 3.243 0.235 / 0.246 / 10.821 / 0.164 382 / 392 / 403 / 3
600 12 12 0.000 / 0.667 / 4.500 / 0.694 0.240 / 0.259 / 12.004 / 0.183 2015 / 2101 / 2178 / 21
600 16 4 0.000 / 17.500 / 170.000 / 17.882 0.202 / 0.218 / 9.208 / 0.140 221 / 222 / 222 / 0
600 16 8 0.000 / 3.667 / 22.667 / 3.276 0.234 / 0.251 / 12.301 / 0.237 383 / 393 / 408 / 3
600 16 12 0.000 / 0.167 / 1.000 / 0.170 0.250 / 0.284 / 12.000 / 0.180 2199 / 2243 / 2282 / 12
600 16 16 0.000 / 0.167 / 1.167 / 0.171 0.239 / 0.291 / 21.163 / 0.333 2811 / 2859 / 2901 / 13
600 20 4 0.000 / 17.667 / 176.667 / 18.162 0.202 / 0.223 / 16.405 / 0.275 221 / 223 / 223 / 0
600 20 8 0.000 / 3.500 / 20.833 / 3.180 0.234 / 0.243 / 5.621 / 0.104 385 / 394 / 405 / 3
600 20 12 0.000 / 0.000 / 0.500 / 0.066 0.246 / 0.281 / 19.279 / 0.390 2541 / 2604 / 2663 / 15
600 20 16 0.000 / 0.000 / 0.667 / 0.071 0.248 / 0.258 / 24.627 / 0.387 2569 / 2627 / 2682 / 15
600 20 20 0.000 / 0.000 / 0.500 / 0.069 0.239 / 0.246 / 13.606 / 0.248 2938 / 2954 / 2972 / 3
600 24 4 0.000 / 17.333 / 210.333 / 18.157 0.202 / 0.218 / 11.991 / 0.180 222 / 223 / 223 / 0
600 24 8 0.000 / 3.667 / 21.167 / 3.184 0.234 / 0.258 / 11.130 / 0.238 385 / 394 / 406 / 3
600 24 12 0.000 / 0.000 / 0.167 / 0.017 0.246 / 0.272 / 12.032 / 0.191 2912 / 2935 / 2954 / 5
600 24 16 0.000 / 0.000 / 0.167 / 0.019 0.246 / 0.268 / 19.358 / 0.282 2916 / 2940 / 2959 / 6
600 24 20 0.000 / 0.000 / 0.167 / 0.015 0.248 / 0.259 / 20.293 / 0.343 2948 / 2980 / 3009 / 9
600 24 24 0.000 / 0.000 / 0.167 / 0.017 0.239 / 0.252 / 11.721 / 0.230 3586 / 3618 / 3643 / 7
600 28 4 0.000 / 17.667 / 182.667 / 17.309 0.202 / 0.210 / 11.957 / 0.177 223 / 224 / 224 / 0
600 28 8 10.333 / 28.000 / 42.833 / 3.687 0.233 / 0.238 / 10.166 / 0.210 377 / 392 / 403 / 3
600 28 12 0.000 / 0.000 / 0.333 / 0.013 0.246 / 0.252 / 9.907 / 0.158 3005 / 3024 / 3041 / 5
600 28 16 0.000 / 0.000 / 0.167 / 0.012 0.246 / 0.256 / 18.673 / 0.273 3007 / 3026 / 3045 / 5
600 28 20 0.000 / 0.000 / 0.167 / 0.011 0.246 / 0.283 / 17.762 / 0.355 3005 / 3029 / 3047 / 6
600 28 24 0.000 / 0.000 / 0.167 / 0.011 0.248 / 0.254 / 8.821 / 0.138 3035 / 3065 / 3098 / 8
600 28 28 0.000 / 0.000 / 0.167 / 0.011 0.239 / 0.242 / 12.171 / 0.177 3589 / 3621 / 3646 / 7
600 32 4 0.000 / 17.333 / 200.000 / 18.294 0.202 / 0.205 / 9.036 / 0.138 223 / 224 / 224 / 0
600 32 8 25.167 / 37.167 / 46.833 / 3.185 0.232 / 0.236 / 9.061 / 0.144 377 / 389 / 403 / 3
600 32 12 0.000 / 0.000 / 0.167 / 0.013 0.246 / 0.256 / 11.119 / 0.169 3028 / 3043 / 3055 / 4
600 32 16 0.000 / 0.000 / 0.167 / 0.010 0.246 / 0.257 / 11.557 / 0.213 3030 / 3045 / 3057 / 4
600 32 20 0.000 / 0.000 / 0.167 / 0.011 0.246 / 0.266 / 20.353 / 0.295 3030 / 3047 / 3071 / 4
600 32 24 0.000 / 0.000 / 0.167 / 0.012 0.246 / 0.270 / 11.461 / 0.183 3035 / 3050 / 3073 / 4
600 32 28 0.000 / 0.000 / 0.167 / 0.013 0.248 / 0.260 / 11.755 / 0.242 3060 / 3085 / 3108 / 7
600 32 32 0.000 / 0.000 / 0.167 / 0.012 0.239 / 0.248 / 10.380 / 0.157 3593 / 3621 / 3645 / 7
800 4 4 0.000 / 17.250 / 188.250 / 17.248 0.269 / 0.280 / 10.818 / 0.212 219 / 220 / 220 / 0
800 8 4 0.000 / 17.875 / 184.125 / 17.721 0.270 / 0.298 / 16.706 / 0.252 220 / 221 / 221 / 0
800 8 8 0.000 / 3.625 / 22.000 / 3.420 0.303 / 0.315 / 12.489 / 0.243 386 / 395 / 406 / 3
800 12 4 0.000 / 17.750 / 196.500 / 16.870 0.269 / 0.289 / 13.533 / 0.235 220 / 221 / 221 / 0
800 12 8 0.000 / 3.750 / 25.875 / 3.359 0.303 / 0.330 / 18.306 / 0.365 386 / 395 / 408 / 3
800 12 12 0.000 / 0.750 / 4.375 / 0.677 0.322 / 0.357 / 20.131 / 0.350 2449 / 2603 / 2694 / 27
800 16 4 0.000 / 17.750 / 195.250 / 17.455 0.269 / 0.274 / 10.472 / 0.205 221 / 222 / 222 / 0
800 16 8 0.000 / 3.750 / 20.375 / 3.357 0.302 / 0.308 / 10.637 / 0.165 386 / 396 / 409 / 3
800 16 12 0.000 / 0.125 / 1.375 / 0.170 0.334 / 0.344 / 10.745 / 0.221 2712 / 2836 / 2882 / 15
800 16 16 0.000 / 0.250 / 1.375 / 0.169 0.321 / 0.334 / 13.979 / 0.252 3390 / 3625 / 3668 / 19
800 20 4 0.000 / 17.750 / 220.750 / 17.953 0.269 / 0.281 / 9.422 / 0.148 222 / 223 / 223 / 0
800 20 8 0.000 / 3.750 / 21.875 / 3.305 0.302 / 0.358 / 24.073 / 0.435 387 / 397 / 408 / 3
800 20 12 0.000 / 0.000 / 0.500 / 0.067 0.331 / 0.345 / 13.461 / 0.211 3249 / 3304 / 3360 / 17
800 20 16 0.000 / 0.000 / 0.500 / 0.069 0.333 / 0.349 / 8.271 / 0.146 3190 / 3331 / 3392 / 17
800 20 20 0.000 / 0.000 / 0.375 / 0.069 0.320 / 0.335 / 11.307 / 0.239 3539 / 3752 / 3771 / 5
800 24 4 0.000 / 17.125 / 184.500 / 18.184 0.269 / 0.283 / 1.541 / 0.079 222 / 223 / 223 / 0
800 24 8 0.000 / 3.625 / 23.125 / 3.301 0.302 / 0.317 / 10.845 / 0.169 388 / 397 / 409 / 3
800 24 12 0.000 / 0.000 / 0.250 / 0.017 0.330 / 0.352 / 10.221 / 0.244 3703 / 3729 / 3749 / 6
800 24 16 0.000 / 0.000 / 0.250 / 0.018 0.330 / 0.344 / 13.454 / 0.239 3711 / 3734 / 3753 / 6
800 24 20 0.000 / 0.000 / 0.250 / 0.018 0.333 / 0.348 / 16.987 / 0.374 3751 / 3786 / 3826 / 10
800 24 24 0.000 / 0.000 / 0.250 / 0.018 0.320 / 0.333 / 17.097 / 0.288 4567 / 4605 / 4630 / 8
800 28 4 0.000 / 17.375 / 326.125 / 18.121 0.269 / 0.274 / 9.600 / 0.149 223 / 224 / 224 / 0
800 28 8 0.375 / 19.875 / 34.500 / 4.445 0.302 / 0.313 / 10.025 / 0.181 387 / 397 / 409 / 3
800 28 12 0.000 / 0.000 / 0.125 / 0.011 0.330 / 0.343 / 11.347 / 0.216 3797 / 3821 / 3839 / 6
800 28 16 0.000 / 0.000 / 0.125 / 0.010 0.330 / 0.344 / 10.748 / 0.219 3801 / 3823 / 3843 / 6
800 28 20 0.000 / 0.000 / 0.125 / 0.011 0.330 / 0.355 / 15.268 / 0.314 3802 / 3827 / 3845 / 6
800 28 24 0.000 / 0.000 / 0.125 / 0.011 0.334 / 0.360 / 11.192 / 0.243 3841 / 3874 / 3905 / 9
800 28 28 0.000 / 0.000 / 0.250 / 0.011 0.321 / 0.334 / 1.757 / 0.095 4575 / 4609 / 4635 / 8
800 32 4 0.000 / 17.125 / 161.000 / 18.370 0.269 / 0.279 / 20.700 / 0.344 223 / 224 / 224 / 0
800 32 8 10.500 / 27.750 / 39.500 / 3.883 0.301 / 0.333 / 18.781 / 0.332 385 / 395 / 406 / 3
800 32 12 0.000 / 0.000 / 0.250 / 0.011 0.330 / 0.371 / 18.883 / 0.317 3823 / 3840 / 3853 / 4
800 32 16 0.000 / 0.000 / 0.125 / 0.011 0.330 / 0.353 / 9.319 / 0.195 3824 / 3842 / 3855 / 4
800 32 20 0.000 / 0.000 / 0.125 / 0.012 0.330 / 0.353 / 15.582 / 0.305 3826 / 3843 / 3859 / 4
800 32 24 0.000 / 0.000 / 0.125 / 0.013 0.330 / 0.349 / 11.346 / 0.234 3830 / 3847 / 3862 / 5
800 32 28 0.000 / 0.000 / 0.250 / 0.013 0.333 / 0.368 / 14.482 / 0.309 3866 / 3894 / 3925 / 8
800 32 32 0.000 / 0.000 / 0.125 / 0.012 0.320 / 0.335 / 17.771 / 0.295 4576 / 4608 / 4633 / 8
1000 4 4 0.000 / 17.800 / 187.500 / 18.576 0.337 / 0.374 / 10.384 / 0.179 219 / 220 / 220 / 0
1000 8 4 0.000 / 17.600 / 181.100 / 18.035 0.336 / 0.372 / 13.220 / 0.262 220 / 221 / 221 / 0
1000 8 8 0.000 / 3.900 / 23.100 / 3.425 0.371 / 0.398 / 9.495 / 0.175 386 / 398 / 409 / 3
1000 12 4 0.000 / 17.600 / 178.900 / 17.559 0.336 / 0.351 / 11.176 / 0.265 220 / 221 / 221 / 0
1000 12 8 0.000 / 3.800 / 22.700 / 3.438 0.371 / 0.392 / 10.942 / 0.188 387 / 398 / 411 / 3
1000 12 12 0.000 / 0.800 / 4.200 / 0.684 0.403 / 0.443 / 11.219 / 0.279 2971 / 3242 / 3364 / 39
1000 16 4 0.000 / 17.600 / 184.300 / 17.148 0.336 / 0.368 / 21.656 / 0.350 221 / 222 / 222 / 0
1000 16 8 0.000 / 3.800 / 21.900 / 3.350 0.369 / 0.385 / 15.840 / 0.277 388 / 399 / 412 / 3
1000 16 12 0.000 / 0.200 / 1.200 / 0.174 0.422 / 0.438 / 16.035 / 0.335 3428 / 3530 / 3628 / 16
1000 16 16 0.000 / 0.200 / 1.200 / 0.173 0.405 / 0.420 / 13.370 / 0.305 4314 / 4484 / 4573 / 20
1000 20 4 0.000 / 17.600 / 223.000 / 16.968 0.336 / 0.372 / 17.746 / 0.392 222 / 223 / 223 / 0
1000 20 8 0.000 / 3.800 / 21.400 / 3.384 0.369 / 0.419 / 16.486 / 0.257 389 / 400 / 412 / 3
1000 20 12 0.000 / 0.000 / 0.400 / 0.068 0.417 / 0.446 / 12.313 / 0.265 3954 / 4099 / 4158 / 18
1000 20 16 0.000 / 0.000 / 0.500 / 0.069 0.422 / 0.439 / 11.284 / 0.262 4016 / 4134 / 4211 / 19
1000 20 20 0.000 / 0.000 / 0.600 / 0.069 0.404 / 0.429 / 16.987 / 0.335 4517 / 4641 / 4651 / 5
1000 24 4 0.000 / 17.600 / 226.700 / 17.761 0.339 / 0.351 / 12.804 / 0.275 222 / 223 / 223 / 0
1000 24 8 0.000 / 3.800 / 24.100 / 3.403 0.371 / 0.406 / 15.710 / 0.298 390 / 400 / 412 / 3
1000 24 12 0.000 / 0.000 / 0.200 / 0.018 0.417 / 0.449 / 12.253 / 0.294 4494 / 4614 / 4636 / 7
1000 24 16 0.000 / 0.000 / 0.100 / 0.018 0.417 / 0.434 / 11.046 / 0.254 4594 / 4620 / 4641 / 7
1000 24 20 0.000 / 0.000 / 0.200 / 0.019 0.422 / 0.458 / 13.433 / 0.270 4645 / 4682 / 4722 / 11
1000 24 24 0.000 / 0.000 / 0.200 / 0.016 0.405 / 0.435 / 11.470 / 0.189 5635 / 5672 / 5703 / 9
1000 28 4 0.000 / 17.200 / 148.500 / 17.046 0.338 / 0.363 / 20.446 / 0.380 224 / 224 / 224 / 0
1000 28 8 0.000 / 15.100 / 30.700 / 4.794 0.371 / 0.389 / 18.272 / 0.359 390 / 400 / 411 / 3
1000 28 12 0.000 / 0.000 / 0.100 / 0.013 0.417 / 0.432 / 13.575 / 0.264 4677 / 4700 / 4719 / 6
1000 28 16 0.000 / 0.000 / 0.200 / 0.013 0.417 / 0.435 / 18.060 / 0.381 4545 / 4702 / 4723 / 6
1000 28 20 0.000 / 0.000 / 0.200 / 0.013 0.417 / 0.448 / 17.596 / 0.344 4679 / 4707 / 4728 / 6
1000 28 24 0.000 / 0.000 / 0.200 / 0.012 0.421 / 0.454 / 13.807 / 0.297 4733 / 4764 / 4801 / 10
1000 28 28 0.000 / 0.000 / 0.200 / 0.013 0.406 / 0.456 / 20.533 / 0.353 5646 / 5675 / 5704 / 9
1000 32 4 0.000 / 18.150 / 177.600 / 19.537 0.338 / 0.352 / 12.293 / 0.252 223 / 224 / 224 / 0
1000 32 8 1.500 / 22.100 / 35.100 / 4.399 0.371 / 0.407 / 17.782 / 0.386 388 / 398 / 412 / 3
1000 32 12 0.000 / 0.000 / 0.200 / 0.011 0.417 / 0.435 / 11.830 / 0.247 4698 / 4717 / 4730 / 5
1000 32 16 0.000 / 0.000 / 0.200 / 0.013 0.417 / 0.443 / 18.214 / 0.276 4700 / 4719 / 4733 / 5
1000 32 20 0.000 / 0.000 / 0.200 / 0.012 0.417 / 0.437 / 11.208 / 0.232 4703 / 4720 / 4737 / 5
1000 32 24 0.000 / 0.000 / 0.200 / 0.013 0.417 / 0.448 / 18.288 / 0.405 4706 / 4724 / 4740 / 5
1000 32 28 0.000 / 0.000 / 0.200 / 0.011 0.420 / 0.437 / 13.389 / 0.245 4613 / 4782 / 4814 / 9
1000 32 32 0.000 / 0.000 / 0.100 / 0.012 0.406 / 0.424 / 12.513 / 0.232 5641 / 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
card sp p err l/m/h/std (% of actual) time l/m/h/std (ms) size l/m/h/std (b)
1500 4 4 0.000 / 17.600 / 254.400 / 17.627 0.501 / 0.612 / 19.629 / 0.593 220 / 220 / 220 / 0
1500 8 4 0.000 / 17.600 / 158.133 / 16.980 0.506 / 0.594 / 16.843 / 0.493 221 / 221 / 221 / 0
1500 8 8 0.000 / 4.000 / 23.933 / 3.590 0.533 / 0.567 / 11.059 / 0.259 392 / 404 / 416 / 3
1500 12 4 0.000 / 18.067 / 208.733 / 17.934 0.505 / 0.531 / 20.544 / 0.368 221 / 221 / 221 / 0
1500 12 8 0.000 / 4.067 / 22.133 / 3.579 0.529 / 0.576 / 22.421 / 0.453 391 / 404 / 416 / 3
1500 12 12 0.000 / 0.800 / 4.133 / 0.707 0.607 / 0.638 / 15.124 / 0.329 4338 / 4489 / 4656 / 43
1500 16 4 0.000 / 17.200 / 167.333 / 17.918 0.508 / 0.546 / 17.715 / 0.381 221 / 222 / 222 / 0
1500 16 8 0.000 / 3.933 / 23.667 / 3.605 0.530 / 0.564 / 18.635 / 0.407 393 / 405 / 417 / 3
1500 16 12 0.000 / 0.200 / 1.067 / 0.166 0.621 / 0.689 / 17.660 / 0.364 5177 / 5271 / 5341 / 21
1500 16 16 0.000 / 0.200 / 0.933 / 0.165 0.612 / 0.654 / 19.700 / 0.419 6688 / 6775 / 6855 / 23
1500 20 4 0.000 / 17.600 / 231.333 / 17.757 0.509 / 0.544 / 20.194 / 0.369 223 / 223 / 223 / 0
1500 20 8 0.000 / 3.933 / 25.600 / 3.728 0.529 / 0.570 / 15.702 / 0.372 395 / 406 / 417 / 3
1500 20 12 0.000 / 0.067 / 0.333 / 0.047 0.612 / 0.659 / 12.620 / 0.343 6097 / 6191 / 6281 / 24
1500 20 16 0.000 / 0.067 / 0.400 / 0.047 0.619 / 0.648 / 13.508 / 0.300 6163 / 6244 / 6344 / 24
1500 20 20 0.000 / 0.067 / 0.333 / 0.047 0.610 / 0.650 / 12.478 / 0.323 7019 / 7048 / 7093 / 6
1500 24 4 0.000 / 17.467 / 156.333 / 18.009 0.508 / 0.569 / 17.878 / 0.386 223 / 223 / 223 / 0
1500 24 8 0.000 / 4.067 / 27.400 / 3.599 0.529 / 0.564 / 21.583 / 0.397 394 / 406 / 416 / 3
1500 24 12 0.000 / 0.000 / 0.133 / 0.017 0.611 / 0.655 / 16.659 / 0.383 6974 / 7008 / 7039 / 8
1500 24 16 0.000 / 0.000 / 0.133 / 0.017 0.612 / 0.644 / 10.934 / 0.313 6981 / 7016 / 7048 / 9
1500 24 20 0.000 / 0.000 / 0.133 / 0.017 0.620 / 0.683 / 21.873 / 0.512 7064 / 7115 / 7167 / 14
1500 24 24 0.000 / 0.000 / 0.133 / 0.017 0.609 / 0.634 / 13.249 / 0.315 8645 / 8684 / 8722 / 11
1500 28 4 0.000 / 17.467 / 157.067 / 17.312 0.508 / 0.529 / 14.149 / 0.336 224 / 224 / 224 / 0
1500 28 8 0.000 / 8.533 / 25.933 / 4.865 0.529 / 0.561 / 15.511 / 0.380 396 / 406 / 419 / 3
1500 28 12 0.000 / 0.000 / 0.133 / 0.012 0.611 / 0.657 / 10.977 / 0.294 7178 / 7209 / 7239 / 8
1500 28 16 0.000 / 0.000 / 0.133 / 0.013 0.611 / 0.636 / 12.958 / 0.319 7177 / 7211 / 7240 / 8
1500 28 20 0.000 / 0.000 / 0.133 / 0.012 0.612 / 0.646 / 13.818 / 0.327 7185 / 7218 / 7248 / 9
1500 28 24 0.000 / 0.000 / 0.133 / 0.012 0.619 / 0.662 / 11.359 / 0.279 7258 / 7305 / 7354 / 13
1500 28 28 0.000 / 0.000 / 0.133 / 0.012 0.609 / 0.648 / 12.260 / 0.300 8643 / 8687 / 8732 / 12
1500 32 4 0.000 / 17.267 / 175.933 / 18.415 0.508 / 0.529 / 11.408 / 0.321 224 / 224 / 224 / 0
1500 32 8 0.000 / 14.667 / 29.200 / 4.897 0.529 / 0.563 / 11.784 / 0.278 393 / 404 / 416 / 3
1500 32 12 0.000 / 0.000 / 0.133 / 0.012 0.611 / 0.668 / 13.335 / 0.342 7226 / 7252 / 7273 / 6
1500 32 16 0.000 / 0.000 / 0.133 / 0.012 0.611 / 0.655 / 19.309 / 0.454 7230 / 7254 / 7276 / 6
1500 32 20 0.000 / 0.000 / 0.133 / 0.012 0.612 / 0.643 / 12.975 / 0.314 7231 / 7256 / 7277 / 6
1500 32 24 0.000 / 0.000 / 0.067 / 0.013 0.612 / 0.666 / 12.496 / 0.357 7236 / 7262 / 7286 / 7
1500 32 28 0.000 / 0.000 / 0.133 / 0.013 0.625 / 0.657 / 21.381 / 0.401 7305 / 7347 / 7383 / 11
1500 32 32 0.000 / 0.000 / 0.133 / 0.012 0.609 / 0.652 / 19.148 / 0.387 8643 / 8687 / 8724 / 12
2000 4 4 0.050 / 17.950 / 200.300 / 17.701 0.678 / 0.712 / 13.274 / 0.370 220 / 220 / 220 / 0
2000 8 4 0.050 / 17.200 / 227.450 / 17.112 0.678 / 0.706 / 12.428 / 0.357 221 / 221 / 221 / 0
2000 8 8 0.000 / 4.150 / 28.100 / 3.687 0.705 / 0.746 / 11.845 / 0.297 397 / 408 / 418 / 3
2000 12 4 0.050 / 17.075 / 166.300 / 17.289 0.679 / 0.746 / 19.810 / 0.436 221 / 221 / 221 / 0
2000 12 8 0.000 / 4.050 / 26.000 / 3.697 0.700 / 0.772 / 19.166 / 0.385 396 / 408 / 419 / 3
2000 12 12 0.050 / 0.850 / 4.150 / 0.733 0.818 / 0.904 / 20.237 / 0.460 5109 / 5354 / 5633 / 103
2000 16 4 0.050 / 17.650 / 196.200 / 17.539 0.678 / 0.747 / 17.211 / 0.435 222 / 222 / 222 / 0
2000 16 8 0.000 / 4.100 / 23.650 / 3.720 0.699 / 0.770 / 17.887 / 0.378 397 / 409 / 420 / 3
2000 16 12 0.000 / 0.200 / 1.100 / 0.163 0.835 / 0.915 / 24.825 / 0.515 6456 / 6547 / 6647 / 23
2000 16 16 0.000 / 0.200 / 1.100 / 0.167 0.820 / 0.906 / 15.149 / 0.427 8177 / 8278 / 8384 / 27
2000 20 4 0.050 / 17.650 / 184.550 / 17.468 0.678 / 0.742 / 19.468 / 0.449 223 / 223 / 223 / 0
2000 20 8 0.000 / 4.150 / 27.500 / 3.693 0.700 / 0.756 / 12.525 / 0.289 399 / 410 / 420 / 3
2000 20 12 0.000 / 0.050 / 0.350 / 0.044 0.830 / 0.921 / 19.963 / 0.553 7551 / 7643 / 7742 / 23
2000 20 16 0.000 / 0.050 / 0.300 / 0.044 0.840 / 0.916 / 16.698 / 0.448 7615 / 7702 / 7789 / 23
2000 20 20 0.000 / 0.050 / 0.300 / 0.044 0.824 / 0.909 / 23.619 / 0.600 8602 / 8633 / 8652 / 7
2000 24 4 0.050 / 17.600 / 249.350 / 17.740 0.675 / 0.754 / 18.418 / 0.431 223 / 223 / 223 / 0
2000 24 8 0.000 / 4.150 / 24.700 / 3.663 0.697 / 0.753 / 24.521 / 0.466 398 / 410 / 421 / 3
2000 24 12 0.000 / 0.000 / 0.150 / 0.017 0.825 / 0.907 / 16.320 / 0.373 8559 / 8591 / 8621 / 8
2000 24 16 0.000 / 0.000 / 0.100 / 0.017 0.826 / 0.876 / 20.177 / 0.403 8567 / 8600 / 8630 / 9
2000 24 20 0.000 / 0.000 / 0.100 / 0.017 0.836 / 0.891 / 18.865 / 0.429 8670 / 8715 / 8762 / 13
2000 24 24 0.000 / 0.000 / 0.150 / 0.017 0.823 / 0.874 / 13.270 / 0.398 10491 / 10531 / 10569 / 11
2000 28 4 0.050 / 17.600 / 206.800 / 17.750 0.675 / 0.726 / 18.063 / 0.424 224 / 224 / 224 / 0
2000 28 8 0.000 / 6.050 / 23.850 / 4.359 0.698 / 0.752 / 24.616 / 0.531 400 / 411 / 421 / 3
2000 28 12 0.000 / 0.000 / 0.100 / 0.013 0.826 / 0.879 / 16.497 / 0.458 8600 / 8623 / 8641 / 6
2000 28 16 0.000 / 0.000 / 0.100 / 0.012 0.826 / 0.898 / 16.948 / 0.417 8602 / 8626 / 8645 / 6
2000 28 20 0.000 / 0.000 / 0.150 / 0.013 0.826 / 0.876 / 21.015 / 0.435 8609 / 8634 / 8656 / 6
2000 28 24 0.000 / 0.000 / 0.100 / 0.012 0.836 / 0.878 / 19.773 / 0.462 8704 / 8746 / 8791 / 12
2000 28 28 0.000 / 0.000 / 0.100 / 0.012 0.823 / 0.877 / 14.429 / 0.366 10489 / 10535 / 10573 / 11
2000 32 4 0.050 / 18.300 / 180.850 / 18.635 0.676 / 0.723 / 18.331 / 0.431 224 / 224 / 224 / 0
2000 32 8 0.000 / 10.900 / 26.400 / 5.122 0.698 / 0.742 / 18.170 / 0.443 397 / 409 / 420 / 3
2000 32 12 0.000 / 0.000 / 0.100 / 0.013 0.825 / 0.869 / 12.927 / 0.376 8603 / 8623 / 8642 / 6
2000 32 16 0.000 / 0.000 / 0.100 / 0.012 0.826 / 0.876 / 12.052 / 0.376 8601 / 8625 / 8644 / 6
2000 32 20 0.000 / 0.000 / 0.100 / 0.012 0.824 / 0.883 / 19.872 / 0.492 8602 / 8627 / 8644 / 6
2000 32 24 0.000 / 0.000 / 0.100 / 0.012 0.826 / 0.879 / 21.842 / 0.509 8610 / 8635 / 8654 / 6
2000 32 28 0.000 / 0.000 / 0.150 / 0.012 0.836 / 0.894 / 18.071 / 0.448 8707 / 8748 / 8791 / 12
2000 32 32 0.000 / 0.000 / 0.100 / 0.012 0.823 / 0.870 / 13.917 / 0.398 10491 / 10535 / 10575 / 11
2500 4 4 0.000 / 17.480 / 215.840 / 18.035 0.844 / 0.896 / 17.723 / 0.444 220 / 220 / 220 / 0
2500 8 4 0.000 / 17.960 / 369.960 / 18.503 0.844 / 0.897 / 20.260 / 0.542 221 / 221 / 221 / 0
2500 8 8 0.000 / 4.080 / 23.280 / 3.639 0.874 / 0.928 / 21.505 / 0.472 399 / 412 / 420 / 3
2500 12 4 0.000 / 17.520 / 204.760 / 17.973 0.845 / 0.963 / 21.008 / 0.499 221 / 221 / 221 / 0
2500 12 8 0.000 / 4.080 / 30.120 / 3.683 0.869 / 0.946 / 18.277 / 0.488 400 / 412 / 421 / 3
2500 12 12 0.000 / 0.880 / 4.600 / 0.747 1.025 / 1.134 / 20.157 / 0.532 6140 / 6934 / 7154 / 78
2500 16 4 0.000 / 17.240 / 173.400 / 17.729 0.845 / 0.902 / 15.768 / 0.421 222 / 222 / 222 / 0
2500 16 8 0.000 / 4.160 / 25.520 / 3.846 0.868 / 0.929 / 11.497 / 0.362 401 / 413 / 422 / 3
2500 16 12 0.000 / 0.200 / 1.080 / 0.164 1.048 / 1.156 / 20.371 / 0.514 8704 / 8924 / 9057 / 33
2500 16 16 0.000 / 0.200 / 1.000 / 0.166 1.031 / 1.108 / 13.336 / 0.432 11159 / 11486 / 11633 / 42
2500 20 4 0.000 / 17.600 / 154.600 / 17.373 0.845 / 0.951 / 14.707 / 0.424 223 / 223 / 223 / 0
2500 20 8 0.000 / 4.200 / 23.720 / 3.781 0.868 / 0.932 / 20.062 / 0.477 397 / 414 / 424 / 3
2500 20 12 0.000 / 0.040 / 0.320 / 0.044 1.032 / 1.119 / 17.855 / 0.560 10273 / 10533 / 10639 / 33
2500 20 16 0.000 / 0.040 / 0.320 / 0.043 1.045 / 1.107 / 16.834 / 0.461 10370 / 10621 / 10730 / 33
2500 20 20 0.000 / 0.040 / 0.400 / 0.044 1.028 / 1.087 / 22.330 / 0.536 11718 / 11995 / 12020 / 12
2500 24 4 0.000 / 17.480 / 156.160 / 17.171 0.844 / 0.890 / 18.096 / 0.406 223 / 223 / 223 / 0
2500 24 8 0.000 / 4.140 / 22.280 / 3.716 0.868 / 0.915 / 19.031 / 0.458 403 / 414 / 423 / 3
2500 24 12 0.000 / 0.000 / 0.160 / 0.017 1.030 / 1.088 / 22.283 / 0.500 11894 / 11934 / 11971 / 11
2500 24 16 0.000 / 0.000 / 0.120 / 0.017 1.032 / 1.090 / 18.220 / 0.547 11896 / 11947 / 11990 / 12
2500 24 20 0.000 / 0.000 / 0.120 / 0.018 1.043 / 1.101 / 17.194 / 0.516 12056 / 12115 / 12187 / 18
2500 24 24 0.000 / 0.000 / 0.120 / 0.018 1.027 / 1.098 / 21.530 / 0.547 14736 / 14798 / 14849 / 15
2500 28 4 0.000 / 17.720 / 199.480 / 17.641 0.845 / 0.900 / 20.585 / 0.511 224 / 224 / 224 / 0
2500 28 8 0.000 / 5.200 / 22.920 / 4.106 0.869 / 0.914 / 12.212 / 0.359 403 / 414 / 425 / 3
2500 28 12 0.000 / 0.000 / 0.080 / 0.012 1.031 / 1.085 / 17.978 / 0.500 12267 / 12329 / 12367 / 11
2500 28 16 0.000 / 0.000 / 0.120 / 0.013 1.030 / 1.094 / 18.134 / 0.519 11986 / 12331 / 12372 / 13
2500 28 20 0.000 / 0.000 / 0.120 / 0.011 1.031 / 1.086 / 20.068 / 0.550 12296 / 12341 / 12382 / 12
2500 28 24 0.000 / 0.000 / 0.080 / 0.012 1.043 / 1.121 / 21.095 / 0.587 12117 / 12486 / 12547 / 17
2500 28 28 0.000 / 0.000 / 0.080 / 0.012 1.028 / 1.097 / 20.162 / 0.573 14747 / 14802 / 14864 / 15
2500 32 4 0.000 / 18.200 / 187.680 / 18.797 0.844 / 0.889 / 20.143 / 0.460 224 / 224 / 224 / 0
2500 32 8 0.000 / 8.680 / 25.600 / 4.951 0.868 / 0.923 / 20.998 / 0.525 402 / 413 / 422 / 3
2500 32 12 0.000 / 0.000 / 0.080 / 0.012 1.030 / 1.130 / 24.624 / 0.666 12378 / 12414 / 12443 / 8
2500 32 16 0.000 / 0.000 / 0.080 / 0.012 1.030 / 1.090 / 17.364 / 0.532 12381 / 12416 / 12443 / 8
2500 32 20 0.000 / 0.000 / 0.120 / 0.012 1.029 / 1.152 / 27.049 / 0.647 12386 / 12418 / 12444 / 8
2500 32 24 0.000 / 0.000 / 0.080 / 0.013 1.031 / 1.083 / 26.018 / 0.575 12390 / 12427 / 12460 / 9
2500 32 28 0.000 / 0.000 / 0.120 / 0.013 1.042 / 1.102 / 18.739 / 0.486 12513 / 12568 / 12621 / 14
2500 32 32 0.000 / 0.000 / 0.120 / 0.012 1.027 / 1.088 / 16.996 / 0.499 14742 / 14802 / 14851 / 15
3000 4 4 0.000 / 17.833 / 186.867 / 17.498 1.013 / 1.080 / 18.433 / 0.461 220 / 220 / 220 / 0
3000 8 4 0.033 / 17.600 / 201.567 / 17.855 1.013 / 1.074 / 19.563 / 0.528 221 / 221 / 221 / 0
3000 8 8 0.000 / 4.300 / 26.467 / 3.786 1.042 / 1.101 / 13.911 / 0.435 403 / 414 / 422 / 3
3000 12 4 0.000 / 17.467 / 212.600 / 18.720 1.014 / 1.070 / 21.257 / 0.509 221 / 221 / 221 / 0
3000 12 8 0.000 / 4.167 / 30.600 / 3.794 1.039 / 1.104 / 20.074 / 0.553 405 / 414 / 422 / 3
3000 12 12 0.000 / 0.833 / 4.833 / 0.745 1.233 / 1.322 / 20.558 / 0.638 7453 / 7706 / 7923 / 67
3000 16 4 0.000 / 18.117 / 152.933 / 17.161 1.013 / 1.101 / 21.535 / 0.564 222 / 222 / 222 / 0
3000 16 8 0.000 / 4.200 / 25.633 / 3.817 1.037 / 1.100 / 18.806 / 0.554 405 / 415 / 423 / 3
3000 16 12 0.000 / 0.200 / 1.033 / 0.169 1.258 / 1.331 / 22.352 / 0.682 10292 / 10439 / 10570 / 37
3000 16 16 0.000 / 0.200 / 0.967 / 0.166 1.238 / 1.317 / 18.279 / 0.589 13313 / 13458 / 13612 / 43
3000 20 4 0.000 / 17.467 / 164.967 / 17.757 1.013 / 1.113 / 19.652 / 0.508 223 / 223 / 223 / 0
3000 20 8 0.000 / 4.167 / 24.267 / 3.743 1.038 / 1.092 / 18.642 / 0.554 405 / 416 / 425 / 3
3000 20 12 0.000 / 0.033 / 0.400 / 0.045 1.240 / 1.303 / 14.404 / 0.517 12293 / 12419 / 12571 / 35
3000 20 16 0.000 / 0.033 / 0.300 / 0.045 1.256 / 1.327 / 17.597 / 0.537 12406 / 12522 / 12655 / 35
3000 20 20 0.000 / 0.033 / 0.333 / 0.044 1.237 / 1.308 / 20.509 / 0.558 14100 / 14156 / 14250 / 11
3000 24 4 0.000 / 17.417 / 215.733 / 18.149 1.013 / 1.091 / 21.116 / 0.517 223 / 223 / 223 / 0
3000 24 8 0.000 / 4.233 / 21.767 / 3.773 1.036 / 1.092 / 11.990 / 0.434 406 / 416 / 426 / 3
3000 24 12 0.000 / 0.000 / 0.100 / 0.017 1.239 / 1.343 / 19.689 / 0.541 14036 / 14088 / 14126 / 12
3000 24 16 0.000 / 0.000 / 0.133 / 0.017 1.239 / 1.311 / 14.029 / 0.532 14050 / 14102 / 14146 / 13
3000 24 20 0.000 / 0.000 / 0.133 / 0.017 1.255 / 1.327 / 25.879 / 0.611 14218 / 14302 / 14381 / 20
3000 24 24 0.000 / 0.000 / 0.133 / 0.017 1.233 / 1.299 / 20.804 / 0.615 17434 / 17491 / 17548 / 17
3000 28 4 0.000 / 17.467 / 160.633 / 17.603 1.014 / 1.069 / 15.224 / 0.466 224 / 224 / 224 / 0
3000 28 8 0.000 / 4.733 / 22.600 / 3.937 1.037 / 1.099 / 17.982 / 0.528 407 / 417 / 426 / 3
3000 28 12 0.000 / 0.000 / 0.100 / 0.013 1.239 / 1.301 / 20.579 / 0.688 14494 / 14534 / 14579 / 12
3000 28 16 0.000 / 0.000 / 0.100 / 0.012 1.237 / 1.299 / 16.532 / 0.499 14490 / 14536 / 14575 / 12
3000 28 20 0.000 / 0.000 / 0.100 / 0.013 1.239 / 1.337 / 19.234 / 0.591 14503 / 14548 / 14594 / 13
3000 28 24 0.000 / 0.000 / 0.100 / 0.012 1.254 / 1.328 / 17.902 / 0.580 14666 / 14722 / 14789 / 18
3000 28 28 0.000 / 0.000 / 0.100 / 0.013 1.234 / 1.300 / 20.500 / 0.552 17439 / 17495 / 17558 / 17
3000 32 4 0.000 / 17.600 / 205.500 / 18.233 1.012 / 1.059 / 11.735 / 0.414 224 / 224 / 224 / 0
3000 32 8 0.000 / 7.450 / 23.967 / 4.786 1.038 / 1.102 / 15.705 / 0.478 405 / 416 / 424 / 3
3000 32 12 0.000 / 0.000 / 0.133 / 0.013 1.238 / 1.335 / 18.066 / 0.600 14599 / 14630 / 14661 / 9
3000 32 16 0.000 / 0.000 / 0.100 / 0.012 1.238 / 1.324 / 20.202 / 0.642 14596 / 14632 / 14662 / 9
3000 32 20 0.000 / 0.000 / 0.100 / 0.013 1.238 / 1.313 / 17.383 / 0.513 14601 / 14634 / 14663 / 9
3000 32 24 0.000 / 0.000 / 0.100 / 0.012 1.239 / 1.300 / 19.292 / 0.560 14607 / 14646 / 14677 / 10
3000 32 28 0.000 / 0.000 / 0.100 / 0.012 1.254 / 1.332 / 20.109 / 0.578 14761 / 14815 / 14872 / 16
3000 32 32 0.000 / 0.000 / 0.067 / 0.012 1.234 / 1.304 / 18.132 / 0.537 17436 / 17495 / 17546 / 17
3500 4 4 0.057 / 17.843 / 154.429 / 17.131 1.183 / 1.241 / 18.127 / 0.543 220 / 220 / 220 / 0
3500 8 4 0.000 / 18.057 / 187.514 / 17.697 1.182 / 1.250 / 20.428 / 0.564 221 / 221 / 221 / 0
3500 8 8 0.000 / 4.314 / 28.257 / 3.833 1.213 / 1.299 / 20.333 / 0.672 405 / 416 / 424 / 2
3500 12 4 0.057 / 17.571 / 161.857 / 17.664 1.181 / 1.252 / 20.923 / 0.569 221 / 221 / 221 / 0
3500 12 8 0.000 / 4.229 / 24.943 / 3.759 1.208 / 1.275 / 22.113 / 0.543 406 / 416 / 424 / 3
3500 12 12 0.000 / 0.871 / 4.657 / 0.786 1.442 / 1.523 / 18.288 / 0.590 8126 / 8383 / 8643 / 70
3500 16 4 0.000 / 18.114 / 163.343 / 17.771 1.183 / 1.253 / 20.723 / 0.585 222 / 222 / 222 / 0
3500 16 8 0.000 / 4.286 / 30.143 / 3.812 1.207 / 1.298 / 20.047 / 0.593 406 / 418 / 424 / 2
3500 16 12 0.000 / 1.057 / 5.457 / 0.698 1.528 / 1.659 / 22.643 / 0.768 2763 / 2824 / 2893 / 18
3500 16 16 0.000 / 0.200 / 1.029 / 0.166 1.450 / 1.558 / 20.879 / 0.642 15119 / 15300 / 15466 / 46
3500 20 4 0.057 / 18.029 / 156.029 / 17.445 1.183 / 1.247 / 13.857 / 0.462 223 / 223 / 223 / 0
3500 20 8 0.000 / 4.314 / 26.371 / 3.859 1.206 / 1.311 / 22.816 / 0.630 408 / 419 / 426 / 3
3500 20 12 0.000 / 1.057 / 4.771 / 0.694 1.537 / 1.636 / 23.911 / 0.753 2760 / 2824 / 2883 / 18
3500 20 16 0.000 / 0.057 / 0.343 / 0.042 1.472 / 1.571 / 20.930 / 0.676 14140 / 14282 / 14406 / 38
3500 20 20 0.000 / 0.057 / 0.257 / 0.043 1.447 / 1.526 / 15.232 / 0.536 16096 / 16146 / 16234 / 13
3500 24 4 0.057 / 17.029 / 212.571 / 17.691 1.183 / 1.254 / 17.746 / 0.583 223 / 223 / 223 / 0
3500 24 8 0.000 / 4.271 / 23.257 / 3.762 1.207 / 1.268 / 15.615 / 0.492 409 / 418 / 426 / 2
3500 24 12 0.000 / 1.057 / 6.229 / 0.706 1.533 / 1.653 / 22.778 / 0.677 2760 / 2824 / 2888 / 18
3500 24 16 0.000 / 0.000 / 0.114 / 0.017 1.451 / 1.588 / 18.966 / 0.697 16029 / 16088 / 16131 / 13
3500 24 20 0.000 / 0.000 / 0.114 / 0.017 1.469 / 1.573 / 16.584 / 0.477 16233 / 16316 / 16395 / 22
3500 24 24 0.000 / 0.000 / 0.114 / 0.017 1.443 / 1.545 / 14.326 / 0.523 19883 / 19959 / 20026 / 18
3500 28 4 0.029 / 17.371 / 256.857 / 18.779 1.182 / 1.254 / 13.532 / 0.445 224 / 224 / 224 / 0
3500 28 8 0.000 / 4.543 / 28.200 / 3.934 1.208 / 1.317 / 22.788 / 0.594 408 / 419 / 427 / 3
3500 28 12 84.371 / 84.371 / 84.514 / 0.021 1.511 / 1.626 / 15.627 / 0.572 1188 / 1204 / 1220 / 4
3500 28 16 0.000 / 0.000 / 0.086 / 0.012 1.449 / 1.530 / 13.406 / 0.526 16477 / 16528 / 16572 / 12
3500 28 20 0.000 / 0.000 / 0.114 / 0.012 1.451 / 1.539 / 16.128 / 0.543 16495 / 16542 / 16587 / 13
3500 28 24 0.000 / 0.000 / 0.086 / 0.012 1.469 / 1.551 / 15.112 / 0.554 16679 / 16744 / 16813 / 19
3500 28 28 0.000 / 0.000 / 0.086 / 0.012 1.445 / 1.545 / 15.241 / 0.543 19879 / 19962 / 20018 / 17
3500 32 4 0.057 / 17.371 / 188.286 / 17.775 1.183 / 1.258 / 13.408 / 0.468 224 / 224 / 224 / 0
3500 32 8 0.000 / 6.400 / 25.629 / 4.553 1.207 / 1.271 / 12.497 / 0.443 409 / 418 / 427 / 3
3500 32 12 99.086 / 99.086 / 99.086 / 0.000 1.506 / 1.646 / 14.954 / 0.571 920 / 920 / 920 / 0
3500 32 16 0.000 / 0.000 / 0.086 / 0.012 1.449 / 1.537 / 15.306 / 0.511 16582 / 16624 / 16657 / 10
3500 32 20 0.000 / 0.000 / 0.114 / 0.013 1.450 / 1.558 / 15.277 / 0.547 16587 / 16626 / 16657 / 10
3500 32 24 0.000 / 0.000 / 0.086 / 0.013 1.451 / 1.555 / 20.496 / 0.661 16604 / 16639 / 16678 / 10
3500 32 28 0.000 / 0.000 / 0.114 / 0.012 1.468 / 1.554 / 15.893 / 0.489 16768 / 16836 / 16895 / 17
3500 32 32 0.000 / 0.000 / 0.086 / 0.012 1.445 / 1.548 / 20.310 / 0.537 19889 / 19962 / 20025 / 17
4000 4 4 0.025 / 17.950 / 203.200 / 17.860 1.351 / 1.431 / 14.530 / 0.524 220 / 220 / 220 / 0
4000 8 4 0.050 / 17.175 / 216.800 / 17.734 1.351 / 1.421 / 19.692 / 0.620 221 / 221 / 221 / 0
4000 8 8 0.000 / 4.325 / 24.925 / 3.817 1.382 / 1.475 / 19.092 / 0.560 408 / 418 / 424 / 2
4000 12 4 0.025 / 17.538 / 175.650 / 18.066 1.352 / 1.437 / 19.980 / 0.590 221 / 221 / 221 / 0
4000 12 8 0.000 / 4.400 / 29.450 / 3.863 1.378 / 1.477 / 22.190 / 0.643 410 / 418 / 424 / 2
4000 12 12 0.025 / 0.900 / 5.775 / 0.799 1.648 / 1.764 / 19.034 / 0.720 8718 / 8981 / 9265 / 70
4000 16 4 0.050 / 17.575 / 176.200 / 17.005 1.350 / 1.429 / 18.900 / 0.549 222 / 222 / 222 / 0
4000 16 8 0.000 / 4.250 / 26.400 / 3.828 1.376 / 1.451 / 18.224 / 0.601 410 / 419 / 425 / 2
4000 16 12 0.275 / 0.950 / 4.275 / 0.615 1.697 / 1.867 / 21.027 / 0.759 2813 / 2882 / 2951 / 17
4000 16 16 0.000 / 0.200 / 1.075 / 0.168 1.660 / 1.801 / 17.255 / 0.650 16124 / 17130 / 17352 / 55
4000 20 4 0.050 / 18.325 / 148.475 / 17.187 1.351 / 1.479 / 18.402 / 0.524 223 / 223 / 223 / 0
4000 20 8 0.000 / 4.350 / 25.750 / 3.871 1.375 / 1.446 / 24.560 / 0.671 410 / 420 / 426 / 2
4000 20 12 0.275 / 0.975 / 4.400 / 0.635 1.680 / 1.805 / 23.306 / 0.729 2821 / 2883 / 2951 / 17
4000 20 16 0.000 / 0.050 / 0.325 / 0.042 1.684 / 1.783 / 20.501 / 0.699 15888 / 16038 / 16188 / 39
4000 20 20 0.000 / 0.050 / 0.325 / 0.042 1.658 / 1.759 / 19.013 / 0.689 18077 / 18134 / 18240 / 14
4000 24 4 0.000 / 17.625 / 164.300 / 17.292 1.351 / 1.427 / 19.917 / 0.579 223 / 223 / 223 / 0
4000 24 8 0.000 / 4.125 / 26.750 / 3.905 1.375 / 1.442 / 18.641 / 0.557 410 / 420 / 426 / 2
4000 24 12 0.275 / 0.975 / 4.275 / 0.610 1.703 / 1.810 / 22.554 / 0.826 2825 / 2883 / 2942 / 16
4000 24 16 0.000 / 0.000 / 0.100 / 0.017 1.659 / 1.752 / 17.914 / 0.612 18021 / 18073 / 18152 / 14
4000 24 20 0.000 / 0.000 / 0.125 / 0.017 1.681 / 1.789 / 20.884 / 0.743 18241 / 18331 / 18404 / 22
4000 24 24 0.000 / 0.000 / 0.150 / 0.017 1.653 / 1.725 / 16.967 / 0.604 22355 / 22426 / 22594 / 19
4000 28 4 0.050 / 18.125 / 167.050 / 17.329 1.348 / 1.501 / 23.889 / 0.758 224 / 224 / 224 / 0
4000 28 8 0.000 / 4.475 / 23.700 / 3.835 1.374 / 1.588 / 21.053 / 0.732 411 / 421 / 427 / 2
4000 28 12 67.225 / 75.800 / 76.550 / 0.261 1.691 / 1.936 / 17.278 / 0.667 1620 / 1704 / 2001 / 23
4000 28 16 0.000 / 0.000 / 0.100 / 0.012 1.707 / 1.932 / 16.598 / 0.577 18470 / 18520 / 18569 / 13
4000 28 20 0.000 / 0.000 / 0.075 / 0.012 1.732 / 1.984 / 20.429 / 0.752 18482 / 18536 / 18582 / 14
4000 28 24 0.000 / 0.000 / 0.075 / 0.012 1.739 / 1.993 / 21.507 / 0.670 18690 / 18766 / 18838 / 20
4000 28 28 0.000 / 0.000 / 0.100 / 0.012 1.658 / 1.939 / 14.211 / 0.594 22364 / 22431 / 22489 / 18
4000 32 4 0.000 / 17.950 / 206.150 / 18.020 1.386 / 1.567 / 14.368 / 0.550 224 / 224 / 224 / 0
4000 32 8 0.000 / 5.925 / 22.650 / 4.366 1.395 / 1.594 / 16.171 / 0.515 412 / 421 / 427 / 2
4000 32 12 88.250 / 88.675 / 89.125 / 0.127 1.732 / 1.985 / 23.129 / 0.774 1408 / 1486 / 1563 / 22
4000 32 16 0.000 / 0.000 / 0.100 / 0.012 1.709 / 1.935 / 28.713 / 0.675 18577 / 18616 / 18647 / 10
4000 32 20 0.000 / 0.000 / 0.100 / 0.012 1.711 / 1.925 / 20.065 / 0.653 18583 / 18618 / 18653 / 10
4000 32 24 0.000 / 0.000 / 0.100 / 0.013 1.699 / 1.917 / 20.723 / 0.617 18589 / 18633 / 18664 / 10
4000 32 28 0.000 / 0.000 / 0.075 / 0.012 1.734 / 1.977 / 27.269 / 0.753 18792 / 18858 / 18921 / 18
4000 32 32 0.000 / 0.000 / 0.100 / 0.012 1.704 / 1.921 / 14.253 / 0.553 22343 / 22431 / 22575 / 19
4500 4 4 0.044 / 17.911 / 173.911 / 18.150 1.550 / 1.758 / 15.086 / 0.501 220 / 220 / 220 / 0
4500 8 4 0.044 / 17.800 / 206.000 / 17.391 1.551 / 1.768 / 13.653 / 0.545 221 / 221 / 221 / 0
4500 8 8 0.000 / 4.222 / 26.378 / 3.844 1.595 / 1.838 / 20.724 / 0.697 411 / 419 / 424 / 2
4500 12 4 0.000 / 17.689 / 172.667 / 17.123 1.561 / 1.751 / 15.085 / 0.578 221 / 221 / 221 / 0
4500 12 8 0.000 / 4.300 / 24.644 / 3.826 1.588 / 1.791 / 20.054 / 0.593 410 / 419 / 424 / 2
4500 12 12 0.022 / 0.911 / 4.956 / 0.805 1.915 / 2.172 / 19.644 / 0.615 9234 / 9507 / 9768 / 70
4500 16 4 0.000 / 18.244 / 258.444 / 17.967 1.526 / 1.758 / 15.643 / 0.552 222 / 222 / 222 / 0
4500 16 8 0.000 / 4.200 / 26.978 / 3.931 1.563 / 1.786 / 15.151 / 0.572 413 / 420 / 425 / 2
4500 16 12 0.133 / 0.933 / 5.044 / 0.687 1.972 / 2.210 / 22.173 / 0.741 2864 / 2927 / 2980 / 15
4500 16 16 0.000 / 0.200 / 0.978 / 0.166 1.947 / 2.221 / 21.386 / 0.766 17912 / 18092 / 18533 / 55
4500 20 4 0.044 / 17.478 / 185.133 / 17.498 1.561 / 1.765 / 13.399 / 0.524 223 / 223 / 223 / 0
4500 20 8 0.000 / 4.333 / 29.822 / 3.854 1.590 / 1.787 / 17.447 / 0.612 412 / 421 / 426 / 2
4500 20 12 0.133 / 0.911 / 4.778 / 0.683 1.953 / 2.210 / 24.534 / 0.768 2875 / 2928 / 2982 / 15
4500 20 16 0.000 / 0.044 / 0.311 / 0.042 1.987 / 2.216 / 14.466 / 0.611 16982 / 17116 / 17239 / 36
4500 20 20 0.000 / 0.044 / 0.244 / 0.042 1.944 / 2.176 / 20.109 / 0.655 19151 / 19206 / 19254 / 15
4500 24 4 0.044 / 17.644 / 191.756 / 18.124 1.562 / 1.747 / 15.134 / 0.531 223 / 223 / 223 / 0
4500 24 8 0.000 / 4.178 / 28.111 / 3.838 1.553 / 1.804 / 23.164 / 0.670 413 / 421 / 426 / 2
4500 24 12 0.133 / 0.933 / 4.156 / 0.663 1.951 / 2.182 / 18.935 / 0.663 2869 / 2928 / 2982 / 16
4500 24 16 0.000 / 0.022 / 0.067 / 0.012 1.943 / 2.170 / 17.937 / 0.713 19107 / 19153 / 19196 / 13
4500 24 20 0.000 / 0.022 / 0.089 / 0.011 1.977 / 2.262 / 24.969 / 0.761 19338 / 19410 / 19500 / 20
4500 24 24 0.000 / 0.022 / 0.089 / 0.012 1.929 / 2.189 / 18.456 / 0.712 23435 / 23497 / 23550 / 17
4500 28 4 0.044 / 17.133 / 288.400 / 17.897 1.563 / 1.759 / 19.175 / 0.641 224 / 224 / 224 / 0
4500 28 8 0.000 / 4.378 / 24.867 / 3.803 1.572 / 1.769 / 21.643 / 0.634 415 / 422 / 427 / 2
4500 28 12 66.089 / 67.400 / 68.667 / 0.359 1.930 / 2.183 / 28.176 / 0.759 2026 / 2113 / 2214 / 27
4500 28 16 0.000 / 0.000 / 0.089 / 0.012 1.954 / 2.170 / 20.834 / 0.751 19176 / 19211 / 19240 / 9
4500 28 20 0.000 / 0.000 / 0.089 / 0.012 1.942 / 2.170 / 21.282 / 0.708 19191 / 19228 / 19261 / 10
4500 28 24 0.000 / 0.000 / 0.067 / 0.012 1.982 / 2.234 / 29.563 / 0.905 19410 / 19480 / 19557 / 18
4500 28 28 0.000 / 0.000 / 0.089 / 0.012 1.944 / 2.180 / 21.368 / 0.749 23437 / 23501 / 23562 / 17
4500 32 4 0.044 / 17.778 / 204.511 / 18.488 1.564 / 1.801 / 23.871 / 0.680 224 / 224 / 224 / 0
4500 32 8 0.000 / 5.489 / 22.289 / 4.225 1.588 / 1.786 / 19.144 / 0.592 413 / 422 / 427 / 2
4500 32 12 77.822 / 78.800 / 79.689 / 0.242 1.926 / 2.172 / 21.370 / 0.726 1838 / 1948 / 2039 / 26
4500 32 16 0.000 / 0.000 / 0.089 / 0.012 1.955 / 2.213 / 24.360 / 0.725 19171 / 19210 / 19238 / 9
4500 32 20 0.000 / 0.000 / 0.089 / 0.012 1.949 / 2.186 / 17.274 / 0.660 19179 / 19212 / 19241 / 9
4500 32 24 0.000 / 0.000 / 0.089 / 0.012 1.889 / 2.182 / 28.660 / 0.825 19192 / 19228 / 19262 / 10
4500 32 28 0.000 / 0.000 / 0.089 / 0.012 1.903 / 2.039 / 21.219 / 0.700 19423 / 19482 / 19549 / 18
4500 32 32 0.000 / 0.000 / 0.089 / 0.012 1.870 / 2.004 / 20.273 / 0.742 23437 / 23501 / 23566 / 17
5000 4 4 0.000 / 17.720 / 192.140 / 17.740 1.684 / 1.829 / 14.606 / 0.612 220 / 220 / 220 / 0
5000 8 4 0.060 / 17.700 / 186.580 / 17.279 1.683 / 1.818 / 15.426 / 0.599 221 / 221 / 221 / 0
5000 8 8 0.000 / 4.300 / 27.780 / 3.783 1.715 / 1.913 / 20.698 / 0.741 412 / 420 / 424 / 2
5000 12 4 0.000 / 17.040 / 206.400 / 18.593 1.683 / 1.809 / 17.501 / 0.622 221 / 221 / 221 / 0
5000 12 8 0.000 / 4.300 / 25.740 / 3.805 1.710 / 1.811 / 19.765 / 0.670 413 / 421 / 424 / 2
5000 12 12 0.020 / 0.920 / 5.200 / 0.842 2.066 / 2.203 / 25.912 / 0.840 9696 / 9977 / 10220 / 71
5000 16 4 0.000 / 17.700 / 190.640 / 16.754 1.682 / 1.765 / 21.803 / 0.664 222 / 222 / 222 / 0
5000 16 8 0.000 / 4.300 / 30.580 / 3.861 1.709 / 1.813 / 20.311 / 0.618 414 / 422 / 425 / 2
5000 16 12 0.000 / 0.880 / 5.140 / 0.747 2.037 / 2.178 / 23.255 / 0.740 2911 / 2962 / 3013 / 14
5000 16 16 0.000 / 0.200 / 1.120 / 0.171 2.094 / 2.204 / 20.890 / 0.784 20566 / 21208 / 21872 / 88
5000 20 4 0.000 / 17.620 / 127.520 / 17.257 1.687 / 1.927 / 26.894 / 0.816 223 / 223 / 223 / 0
5000 20 8 0.000 / 4.330 / 28.580 / 3.861 1.710 / 1.909 / 18.186 / 0.643 415 / 423 / 426 / 2
5000 20 12 0.000 / 0.900 / 5.340 / 0.743 2.055 / 2.302 / 22.473 / 0.763 2905 / 2963 / 3013 / 14
5000 20 16 0.000 / 0.040 / 0.320 / 0.043 2.137 / 2.410 / 24.675 / 0.864 19509 / 19910 / 20058 / 42
5000 20 20 0.000 / 0.040 / 0.280 / 0.042 2.097 / 2.369 / 25.517 / 0.830 21768 / 22416 / 22538 / 26
5000 24 4 0.040 / 17.450 / 201.900 / 17.504 1.686 / 1.861 / 18.820 / 0.618 223 / 223 / 223 / 0
5000 24 8 0.000 / 4.200 / 28.260 / 3.839 1.713 / 1.923 / 19.929 / 0.679 415 / 422 / 426 / 2
5000 24 12 0.000 / 0.900 / 4.780 / 0.766 2.047 / 2.287 / 15.684 / 0.699 2912 / 2963 / 3016 / 14
5000 24 16 0.000 / 0.020 / 0.100 / 0.012 2.102 / 2.375 / 21.730 / 0.818 22296 / 22351 / 22415 / 15
5000 24 20 0.000 / 0.020 / 0.080 / 0.012 2.128 / 2.397 / 24.851 / 0.845 22577 / 22658 / 22745 / 23
5000 24 24 0.000 / 0.020 / 0.080 / 0.012 2.092 / 2.377 / 22.543 / 0.800 27480 / 27560 / 27624 / 20
5000 28 4 0.000 / 17.860 / 158.380 / 17.534 1.686 / 1.875 / 17.770 / 0.647 224 / 224 / 224 / 0
5000 28 8 0.000 / 4.380 / 22.440 / 3.886 1.712 / 1.969 / 22.211 / 0.772 416 / 423 / 427 / 2
5000 28 12 59.020 / 60.660 / 62.740 / 0.463 2.037 / 2.288 / 20.272 / 0.652 2300 / 2388 / 2487 / 26
5000 28 16 0.000 / 0.000 / 0.100 / 0.012 2.099 / 2.378 / 23.672 / 0.868 22667 / 22723 / 22765 / 13
5000 28 20 0.000 / 0.000 / 0.080 / 0.012 2.100 / 2.389 / 21.719 / 0.838 22687 / 22742 / 22788 / 14
5000 28 24 0.000 / 0.000 / 0.080 / 0.012 2.132 / 2.393 / 23.989 / 0.763 22950 / 23027 / 23106 / 21
5000 28 28 0.000 / 0.000 / 0.080 / 0.012 2.094 / 2.386 / 24.741 / 0.892 27502 / 27565 / 27637 / 20
5000 32 4 0.000 / 18.060 / 189.520 / 18.378 1.686 / 1.919 / 26.851 / 0.838 224 / 224 / 224 / 0
5000 32 8 0.000 / 5.280 / 26.500 / 4.157 1.714 / 1.930 / 21.178 / 0.750 416 / 423 / 427 / 2
5000 32 12 69.800 / 70.920 / 72.440 / 0.341 2.034 / 2.293 / 21.420 / 0.754 2160 / 2261 / 2356 / 27
5000 32 16 0.000 / 0.000 / 0.080 / 0.012 2.099 / 2.387 / 25.364 / 0.794 21966 / 22798 / 22832 / 16
5000 32 20 0.000 / 0.000 / 0.080 / 0.012 2.095 / 2.410 / 41.338 / 1.022 22759 / 22800 / 22839 / 11
5000 32 24 0.000 / 0.000 / 0.100 / 0.012 2.100 / 2.277 / 23.671 / 0.742 22773 / 22818 / 22856 / 11
5000 32 28 0.000 / 0.000 / 0.100 / 0.012 2.125 / 2.435 / 20.889 / 0.961 22274 / 23099 / 23169 / 23
5000 32 32 0.000 / 0.000 / 0.060 / 0.012 2.088 / 2.280 / 16.157 / 0.705 27494 / 27565 / 27640 / 19

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

card sp p err l/m/h/std (% of actual) time l/m/h/std (ms) size l/m/h/std (b)
55000 25 12 0.000 / 1.031 / 5.431 / 0.928 19.336 / 22.410 / 83.150 / 3.282 3467 / 3501 / 3538 / 10
55000 25 14 0.000 / 0.470 / 2.525 / 0.428 21.031 / 24.079 / 58.355 / 3.192 11981 / 12073 / 12166 / 25
55000 25 16 0.000 / 0.140 / 0.751 / 0.124 25.372 / 29.282 / 99.309 / 3.888 41546 / 41834 / 42083 / 74
60000 25 12 0.002 / 1.080 / 5.500 / 0.936 21.866 / 25.060 / 83.602 / 3.563 3486 / 3519 / 3552 / 9
60000 25 14 0.002 / 0.483 / 2.762 / 0.432 23.089 / 26.556 / 56.951 / 3.455 12056 / 12141 / 12233 / 25
60000 25 16 0.000 / 0.145 / 1.552 / 0.135 27.680 / 31.433 / 99.324 / 3.967 42217 / 42469 / 42714 / 70
65000 25 12 0.000 / 1.053 / 5.968 / 0.927 23.661 / 26.901 / 59.004 / 3.475 3499 / 3534 / 3565 / 9
65000 25 14 0.000 / 0.483 / 2.517 / 0.431 24.753 / 28.293 / 60.108 / 3.483 12120 / 12206 / 12299 / 25
65000 25 16 0.000 / 0.158 / 1.455 / 0.158 29.270 / 33.727 / 75.299 / 4.108 42757 / 43002 / 43219 / 66
100000 25 14 0.001 / 0.520 / 2.814 / 0.451 35.787 / 41.099 / 197.958 / 7.919 12510 / 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)