, 7 min read
Searching for Tendler-like formulas, #2
In continuation of Searching for Tendler-like formulas here we search for further Tendler-like formulas. This time we particularly watch for low error constants.
1. Order 3
$ stabregion2 -b Base3 -I3:-10:10:59000 -r600 -W89.5 -E0.14
W= 89.56934, xmin= -0.00360, parasitic=0.6994, |e|=0.136364 1.000000 3.335559 2.623882 1.477945 -6.120679 -7.546915 1
W= 89.52794, xmin= -0.00397, parasitic=0.5910, |e|=0.136364 1.000000 -9.687612 -2.527196 3.336938 -7.423275 -9.724498 2
2. Order 4
$ stabregion2 -b Base4 -I3:-10:10:2000 -r100 -W78 -E0.096
W= 78.52669, xmin= -0.93122, parasitic=0.6049, |e|=0.096000 1.000000 6.174723 9.151434 1.293058 -4.412818 -8.263781 1
W= 78.52125, xmin= -0.62438, parasitic=0.2035, |e|=0.096000 1.000000 4.588593 0.467625 9.696157 -0.059481 -9.838954 2
W= 80.46735, xmin= -0.29149, parasitic=0.3093, |e|=0.096000 1.000000 4.642505 1.606047 6.561387 -5.370817 -9.787012 3
W= 78.66516, xmin= -0.52590, parasitic=0.2016, |e|=0.096000 1.000000 -8.725426 -2.189642 8.017470 -2.111142 -8.335239 4
W= 80.08353, xmin= -0.49374, parasitic=0.2710, |e|=0.096000 1.000000 -9.096624 -2.132855 3.516639 -1.567879 -4.539268 5
W= 78.00667, xmin= -0.46577, parasitic=0.1835, |e|=0.096000 1.000000 -8.004718 -2.377983 -7.135334 2.866952 6.301039 6
W= 78.59052, xmin= -0.73024, parasitic=0.2260, |e|=0.096000 1.000000 3.683475 2.871425 -4.932404 3.618247 7.881263 7
$ stabregion2 -b Base4 -I3:-10:10:9000 -r600 -W80 -E0.096
W= 80.59363, xmin= -0.61309, parasitic=0.3071, |e|=0.096000 1.000000 -9.325420 -0.012520 -5.553564 1.195361 7.319080 1
W= 80.28302, xmin= -0.37801, parasitic=0.2860, |e|=0.096000 1.000000 -4.825342 -1.320631 4.961141 -3.047921 -6.726809 2
3. Order 5
$ stabregion2 -b Base5 -I4:-1900:1900:899000 -r900 -W74.1 -E0.08
W= 74.31418, xmin= -1.68403, parasitic=0.2051, |e|=0.078685 1.000000 -1491.817515 395.126127 -1792.630306 1110.243650 1534.486280 784.959397 -966.016786 -701.824850 1226.864835 1
$ stabregion2 -b Base5 -I4:-1900:1900:899000 -r900 -W74.1 -E0.089
W= 75.20646, xmin= -1.53885, parasitic=0.2110, |e|=0.087748 1.000000 -1252.368581 660.602768 -1231.700621 1033.954073 527.803206 -933.216358 1661.927947 1245.672615 -1554.875177 1
W= 74.33716, xmin= -1.37348, parasitic=0.1823, |e|=0.087133 1.000000 490.519477 66.562261 1860.739731 -1874.446795 -1668.188156 1420.240414 -1410.230961 -1001.645470 666.853183 2
W= 74.89894, xmin= -1.59237, parasitic=0.3850, |e|=0.081935 1.000000 -1624.672483 609.769408 755.177769 -180.897365 -346.208473 579.514095 -1030.370337 -951.801300 1012.218738 3
W= 74.74018, xmin= -0.61120, parasitic=0.3961, |e|=0.088743 1.000000 1736.941219 -1017.092362 1149.179193 -1528.840154 -1742.299332 -1839.828567 666.834218 -614.143367 -1453.277644 4
W= 75.53897, xmin= -1.36863, parasitic=0.2055, |e|=0.088627 1.000000 1712.818112 -1197.567020 -1443.226169 1087.898172 510.183732 -1455.596397 1304.210881 1870.252325 -1838.881617 5
W= 74.65602, xmin= -1.40860, parasitic=0.2517, |e|=0.085185 1.000000 -1096.204252 144.280540 757.228488 -848.965002 -1310.688236 -1108.842315 1295.166221 -46.098896 -1811.457701 6
W= 74.45184, xmin= -0.92923, parasitic=0.2351, |e|=0.087047 1.000000 -1581.852536 387.822554 872.573450 -1302.307854 -1811.708139 -1562.666218 1068.728308 -619.933340 -938.558801 7
W= 74.59584, xmin= -1.23390, parasitic=0.1926, |e|=0.088355 1.000000 -1767.163161 1215.328023 1345.966971 -1337.707137 -1173.589445 1710.693208 -1082.658330 -807.728682 1214.264965 8
W= 74.19220, xmin= -1.41392, parasitic=0.1600, |e|=0.080024 1.000000 1584.538390 -438.669678 -1498.637018 867.319895 954.161418 -1353.140573 1510.461700 1404.023283 -1230.044727 9
W= 74.26498, xmin= -1.25002, parasitic=0.1660, |e|=0.085538 1.000000 1808.097183 -1026.827791 -1160.187592 1094.737163 1242.728791 -1874.076961 918.040804 636.847498 -1332.949513 10
W= 75.25440, xmin= -1.14900, parasitic=0.1374, |e|=0.083791 1.000000 -872.499296 313.303682 940.672074 -649.843634 -448.661418 840.303013 -1015.153151 -853.675570 636.374128 11
4. Order 6
$ stabregion2 -b Base6 -I4:-1900:1900:1099500 -r900 -W66.1 -E0.09
W= 67.55345, xmin= -1.45207, parasitic=0.3118, |e|=0.083147 1.000000 331.108370 -484.790354 -943.081133 1775.798064 772.642075 1475.012880 -1579.506075 1323.542728 887.719731 1
W= 66.63496, xmin= -1.52131, parasitic=0.3734, |e|=0.087649 1.000000 -1426.017726 1774.952404 756.547810 -1549.081344 -412.092170 -885.455680 699.925019 -488.372693 -132.457100 2
W= 70.34158, xmin= -2.21298, parasitic=0.4175, |e|=0.089965 1.000000 -516.363044 1032.062293 878.714645 -1423.809312 -1183.216422 -1320.767055 1409.360907 -1121.281874 -1043.276621 3
Below formulas don't really get any better.
$ stabregion2 -b Base6 -I4:-1900:1900:1099500 -r900 -W66.1 -E0.09
W= 66.10921, xmin= -2.89189, parasitic=0.4068, |e|=0.088087 1.000000 777.743818 -463.908836 1003.734617 -1881.742311 64.067672 1261.830874 -1314.519519 -851.818241 636.247183 1
W= 66.41275, xmin= -2.83390, parasitic=0.2920, |e|=0.087356 1.000000 417.267233 -351.655661 623.341664 -1559.465815 -1244.346654 1345.875578 -1854.407306 1893.154591 1674.290334 2
W= 66.49257, xmin= -2.81394, parasitic=0.5255, |e|=0.086813 1.000000 1093.920090 -476.591234 -545.775038 1456.897303 1421.628310 1309.632896 -1637.645096 1675.884867 1092.694957 3
W= 67.04915, xmin= -2.64442, parasitic=0.5746, |e|=0.083940 1.000000 -684.650596 1034.047474 191.755691 -406.904827 -271.014904 1716.142605 -1815.428518 1537.632044 647.282132 4
W= 66.40144, xmin= -2.46850, parasitic=0.4717, |e|=0.085470 1.000000 -772.258784 1167.280541 -445.968061 920.404948 432.282382 1450.420341 -1351.899530 937.758821 296.142070 5
W= 68.12433, xmin= -2.09311, parasitic=0.3225, |e|=0.087345 1.000000 -1455.559408 1189.915637 790.086088 -1864.395957 -1232.425752 1142.640999 -1454.911389 1346.054102 787.678130 6
$ stabregion2 -b Base6 -I4:-1900:1900:1099500 -r900 -W66.1 -E0.09
W= 69.39934, xmin= -2.35118, parasitic=0.3066, |e|=0.084166 1.000000 -366.768582 584.012171 -886.816493 1758.921374 841.323012 -1323.201066 1507.692545 -1225.693841 -1304.468235 1
W= 67.07043, xmin= -1.98584, parasitic=0.3019, |e|=0.085861 1.000000 -698.288224 1236.536907 1472.042742 -1685.730268 1204.284695 -900.003534 1743.047495 957.758375 -950.733943 2
$ stabregion2 -b Base6 -I4:-1900:1900:1099500 -r900 -W66.1 -E0.09
W= 66.22433, xmin= -1.93776, parasitic=0.4520, |e|=0.085693 1.000000 -1109.366295 1773.528426 -913.259153 1853.229863 752.930646 -1569.830832 1868.024515 -1476.688091 -468.598571 1
W= 68.08989, xmin= -2.51212, parasitic=0.4128, |e|=0.085143 1.000000 1280.640873 -1672.090745 -719.755459 1466.828140 681.221052 -1863.334099 1112.660300 -663.115698 -189.352203 2
W= 67.28186, xmin= -2.26165, parasitic=0.5384, |e|=0.083420 1.000000 -942.888268 1326.322755 -789.139652 1775.537325 1496.273632 -872.459389 1174.793850 -1361.756217 -879.110473 3
W= 66.32962, xmin= -1.86160, parasitic=0.4837, |e|=0.088438 1.000000 489.025963 -346.624518 710.923641 -1739.665606 -1169.415134 -1123.536735 1660.239406 -1584.703722 -566.135225 4
$ stabregion2 -b Base6 -I4:-1900:1900:1099500 -r900 -W66.1 -E0.09
W= 66.91742, xmin= -2.75146, parasitic=0.2836, |e|=0.087787 1.000000 -569.033533 1069.068050 724.051144 -1466.872054 -733.236224 -1368.895444 1704.712395 -1458.867723 -1621.567683 1
W= 67.45387, xmin= -1.76458, parasitic=0.3361, |e|=0.082292 1.000000 -1063.991192 1666.038072 362.224662 -450.969250 316.529548 1007.603421 -1712.275173 -941.703188 627.306638 2
W= 66.48618, xmin= -1.94415, parasitic=0.3932, |e|=0.088613 1.000000 -1026.274656 1882.488117 628.441346 -1313.531895 -321.774302 1778.007676 -1528.261739 1162.372964 398.534392 3
W= 68.06953, xmin= -2.65866, parasitic=0.2529, |e|=0.085302 1.000000 -305.201445 451.856199 1280.149981 -1866.213196 1107.241556 -979.668034 1485.078793 1313.071549 -1158.804508 4
W= 66.11887, xmin= -2.10597, parasitic=0.2568, |e|=0.078862 1.000000 -492.632733 650.274411 1592.767962 -1546.770437 725.816435 -869.915017 1839.103659 1133.129678 -1228.089256 5
W= 67.75929, xmin= -2.00557, parasitic=0.2927, |e|=0.084694 1.000000 1082.418891 -1314.032462 -898.452311 1349.638973 -558.393120 1036.462825 -1899.741000 -646.812846 974.382845 6
5. Order 7
$ stabregion2 -b Base7 -I4:-1900:1900:1099500 -r900 -W40.1 -E0.07
W= 41.94816, xmin= -6.82533, parasitic=0.5064, |e|=0.069498 1.000000 604.400265 -929.052367 520.837200 -1100.667375 -241.026895 1607.804974 -1778.079749 1469.747897 875.458526 1
W= 43.20235, xmin= -7.50878, parasitic=0.5408, |e|=0.067023 1.000000 -776.178510 1380.220808 -605.393131 1130.614447 290.072447 -1660.672501 1717.192304 -1093.818981 -1398.643812 2
W= 40.55719, xmin= -7.21602, parasitic=0.5691, |e|=0.068968 1.000000 462.612438 -710.638771 705.156252 -1195.468181 635.804851 -1838.033046 1601.028736 1552.644522 -791.168046 3
W= 40.83142, xmin= -7.97041, parasitic=0.5265, |e|=0.069279 1.000000 -1058.519862 1074.530646 -1353.715455 1678.393659 -56.256967 542.307884 -1282.895924 -291.082958 890.164289 4
W= 40.48440, xmin= -6.45767, parasitic=0.6742, |e|=0.067784 1.000000 640.563826 -1180.497876 936.083292 -1448.093006 525.906850 -1501.635942 1089.553202 410.402179 -438.353162 5
W= 40.18680, xmin= -7.65083, parasitic=0.6002, |e|=0.066508 1.000000 -1465.482996 1674.200029 -884.223738 1673.487634 508.354938 1725.926060 -1793.674594 747.162553 1254.954011 6
$ stabregion2 -b Base7 -I4:-1900:1900:1099500 -r900 -W40.1 -E0.07
W= 41.42166, xmin= -9.82521, parasitic=0.4210, |e|=0.066272 1.000000 1236.188284 -1808.160341 1126.292246 -1679.801885 909.605818 -1191.758587 1887.441802 1295.949128 -1612.483830 1
W= 40.36240, xmin= -9.58647, parasitic=0.5251, |e|=0.065729 1.000000 -968.693470 1188.004256 610.692301 -1216.555984 -719.153902 -1784.007621 1864.718312 -1357.790974 -1577.915290 2
W= 40.45280, xmin= -7.13364, parasitic=0.6838, |e|=0.067193 1.000000 -780.795789 506.937029 671.842933 -1257.171471 -191.646258 644.053859 -1137.012644 246.705772 498.893610 3
W= 46.81597, xmin= -6.51908, parasitic=0.4308, |e|=0.068767 1.000000 681.091183 -1233.682610 -890.294075 1855.390968 514.351326 -953.372885 1424.568886 -1322.828240 -647.160123 4
6. Order 8
$ stabregion2 -b Base8 -I4:-1900:1900:1099500 -r1400 -E0.05
W= 0.00000, xmin=-23.85777, parasitic=0.6766, |e|=0.048399 1.000000 1887.256462 -1035.917921 -1007.169342 1231.223647 822.188747 1682.595870 -1709.029070 -474.801023 1536.391356 1
W= 0.00000, xmin=-513.58927, parasitic=0.6778, |e|=0.044933 1.000000 1475.503275 -832.927478 93.207109 1278.271777 -1129.167000 -720.790624 -1547.021667 -1111.843338 1404.176119 2
W= 0.00000, xmin=-176.02952, parasitic=0.7454, |e|=0.040882 1.000000 -585.347260 -721.840790 -249.374842 20.963422 1171.825122 -1048.687503 -1505.200219 1128.745873 -1843.950602 3
W= 0.00000, xmin=-111.39488, parasitic=0.7305, |e|=0.040882 1.000000 1180.692065 9.269570 -238.044717 -87.989443 730.150525 -848.945749 -583.824082 1490.722406 -1510.606463 4
W= 0.00000, xmin=-42.44942, parasitic=0.7074, |e|=0.048062 1.000000 1884.500963 -231.040531 -1116.089647 1442.308622 1433.176484 -763.342553 1087.766794 755.733718 -1812.126287 5
W= 0.00000, xmin=-31.13149, parasitic=0.7322, |e|=0.048026 1.000000 1464.863516 -1305.078037 1317.524158 -1419.509962 -549.927224 978.144408 -1274.578366 -1040.095413 1859.378833 6
W= 0.00000, xmin=-122.87497, parasitic=0.6960, |e|=0.049351 1.000000 -396.471382 454.988598 -1226.771985 -265.654099 1435.930816 -356.245894 -615.321618 1655.269703 -1133.700838 7
W= 0.00000, xmin=-187.37440, parasitic=0.6242, |e|=0.040882 1.000000 936.734284 829.835423 685.155070 1005.491085 -1306.343359 -305.727304 43.252381 1877.639396 -1025.981211 8
W= 0.00000, xmin=-41.74583, parasitic=0.7208, |e|=0.049830 1.000000 1475.927015 -1557.606702 -465.305102 645.924265 345.597859 -878.147686 -116.514129 997.536019 -1570.976615 9
W= 0.00000, xmin=-48.46757, parasitic=0.6751, |e|=0.048326 1.000000 -639.841356 649.520124 1591.607647 -1858.621137 -1325.482235 -785.060208 68.735301 1313.552262 -1836.762112 10
W= 0.02785, xmin=-23.54848, parasitic=0.6394, |e|=0.048973 1.000000 -1149.074731 1262.745407 1614.956209 -1762.078435 -268.729817 1205.705699 -1187.735828 -1074.378044 1251.230795 11
W= 0.14471, xmin=-23.69321, parasitic=0.6383, |e|=0.049722 1.000000 1755.807518 -1772.726701 -1255.350352 1814.943391 1303.016747 -1289.925655 1196.057832 -266.187408 -1428.783815 12
W= 0.00000, xmin=-179.25813, parasitic=0.7192, |e|=0.040882 1.000000 707.567714 1291.548005 493.649594 -172.511800 -1352.259319 479.847960 488.736186 -1738.382843 886.413860 13
W= 0.00000, xmin=-74.92529, parasitic=0.7264, |e|=0.045020 1.000000 -1520.719189 876.351998 -1129.515740 832.168443 1507.417644 175.605164 72.244941 -446.362741 529.810811 14
W= 0.00000, xmin=-45.04340, parasitic=0.6982, |e|=0.049245 1.000000 1054.501705 -1195.716079 -328.786365 387.184316 287.952548 -738.145733 271.656352 1087.269981 -1820.330214 15
W= 0.00000, xmin=-257.95909, parasitic=0.6958, |e|=0.040882 1.000000 1774.058735 1050.777827 -1885.341121 -808.716280 1599.936578 -237.165686 -964.458272 1866.747880 -761.720810 16
W= 0.00000, xmin=-245.11378, parasitic=0.6810, |e|=0.047281 1.000000 -890.338809 782.113738 982.470328 391.431984 -1694.916969 96.729519 878.703770 -409.121653 -194.516133 17
W= 0.00000, xmin=-188.19747, parasitic=0.7437, |e|=0.040882 1.000000 1613.225604 572.352618 -314.824608 -705.546246 1818.295876 1684.336705 1586.817791 -732.380468 1169.107483 18
W= 0.00000, xmin=-35.54136, parasitic=0.6592, |e|=0.049764 1.000000 200.262601 -163.361730 -1441.139532 1757.722424 185.357370 -250.035159 441.624109 325.011823 -555.213909 19
W= 0.00000, xmin=-194.26458, parasitic=0.7466, |e|=0.045204 1.000000 1412.355014 -849.032482 -345.758821 -1384.854380 1793.222670 -975.180725 -1587.901451 381.241703 124.431518 20
W= 0.00000, xmin=-190.15261, parasitic=0.6549, |e|=0.040882 1.000000 1650.638868 120.878463 340.728352 944.620954 -1826.707751 801.091257 723.157884 -894.558731 1355.555690 21
W= 0.00000, xmin=-52.97417, parasitic=0.7485, |e|=0.047320 1.000000 1851.725143 723.872535 -371.232556 457.549074 1072.883990 350.161394 -461.711870 -79.557471 1162.292805 22
W= 0.00000, xmin=-51.22602, parasitic=0.7270, |e|=0.048297 1.000000 1684.304709 -1703.525632 526.510580 -36.263800 -1181.625893 -362.550077 418.453136 559.019841 -1254.580573 23
W= 0.00000, xmin=-85.44861, parasitic=0.7042, |e|=0.047948 1.000000 678.890110 -655.756404 1251.044723 134.716159 -1679.169324 -412.232047 -137.371602 1392.412048 -1211.229781 24
W= 0.00000, xmin=-45.20671, parasitic=0.7251, |e|=0.047838 1.000000 -1733.036218 718.344552 892.946576 -1160.408085 -1280.002521 -623.396178 638.184774 533.721161 -1804.260148 25
W= 0.00000, xmin=-121.39983, parasitic=0.7379, |e|=0.044937 1.000000 -1877.143577 1060.523019 -370.771386 -10.185957 533.260376 334.704346 720.977849 -1319.530974 873.569898 26
W= 0.00000, xmin=-48.43030, parasitic=0.7110, |e|=0.047750 1.000000 -862.094807 810.401745 579.690995 -395.415089 -470.515753 427.136262 -497.433835 -891.840080 1277.174692 27
W= 0.00000, xmin=-190.44704, parasitic=0.5666, |e|=0.040882 1.000000 313.952344 61.170909 213.642056 204.374189 -865.133420 751.703233 1415.395593 -1165.514410 659.051952 28
W= 0.00000, xmin=-37.26504, parasitic=0.7364, |e|=0.046796 1.000000 1128.694962 -919.091451 -1086.702152 485.713689 1313.404502 991.436045 -1098.628630 -1364.271296 1893.178776 29
Checking on solution #12.
$ echo 1 1755.807518 -1772.726701 -1255.350352 1814.943391 1303.016747 -1289.925655 1196.057832 -266.187408 -1428.783815 | stabregion2 -b Base8 -l- -r64000 -d
Base8, p=8, k=8, l=9, cpLen=18
-2283.00000000 -105.00000000 15.00000000 -5.00000000 3.00000000 -3.00000000 5.00000000 -15.00000000 105.00000000
6720.00000000 -1338.00000000 -240.00000000 60.00000000 -32.00000000 30.00000000 -48.00000000 140.00000000 -960.00000000
-11760.00000000 2940.00000000 -798.00000000 -420.00000000 168.00000000 -140.00000000 210.00000000 -588.00000000 3920.00000000
15680.00000000 -2940.00000000 1680.00000000 -378.00000000 -672.00000000 420.00000000 -560.00000000 1470.00000000 -9408.00000000
-14700.00000000 2450.00000000 -1050.00000000 1050.00000000 0.00000000 -1050.00000000 1050.00000000 -2450.00000000 14700.00000000
9408.00000000 -1470.00000000 560.00000000 -420.00000000 672.00000000 378.00000000 -1680.00000000 2940.00000000 -15680.00000000
-3920.00000000 588.00000000 -210.00000000 140.00000000 -168.00000000 420.00000000 798.00000000 -2940.00000000 11760.00000000
960.00000000 -140.00000000 48.00000000 -30.00000000 32.00000000 -60.00000000 240.00000000 1338.00000000 -6720.00000000
-105.00000000 15.00000000 -5.00000000 3.00000000 -3.00000000 5.00000000 -15.00000000 105.00000000 2283.00000000
840.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 840.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 840.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 840.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 840.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 840.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 840.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 840.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 840.00000000
fname=-, l=4, il=10
1.00000000
1755.80751800 -1772.72670100
-1255.35035200 1814.94339100 1303.01674700
-1289.92565500 1196.05783200 -266.18740800 -1428.78381500
fm based on LinearCombination, l=4, colLen=24
LinearCombination, p=8, k=8, l=4
105.0000 0.0000 0.0000 0.0000
-960.0000 210950.6899 0.0000 0.0000
3920.0000 -1933756.9554 -152520.8541 0.0000
-9408.0000 7925128.7707 1396683.6088 -150427.6468
14700.0000 -19124545.3798 -5714526.5769 1375690.2064
-15680.0000 30153550.9321 13748613.5181 -5615660.1944
11760.0000 -32742878.3832 -21532093.8980 13442801.3215
-6720.0000 25860112.9126 22830758.9539 -20671522.5895
2283.0000 -14170934.8469 -19059046.3450 23649558.8599
0.0000 3822372.2600 11177072.6419 -19498442.4828
0.0000 0.0000 -2694941.0488 10290467.8318
0.0000 0.0000 0.0000 -2822465.3060
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
840.0000 -1489090.4288 1094534.0675 -1200178.4046
0.0000 1474878.3151 1524552.4484 -223597.4227
0.0000 0.0000 -1054494.2957 1004688.5789
0.0000 0.0000 0.0000 -1083537.5502
rho_0 0.000000000 -0.000000001 0.000000004 0.000000001 <-----
rho_1 0.000000000 -0.000000000 -0.000000000 0.000000000 <-----
rho_2 0.000000000 -0.000000000 -0.000000000 0.000000000 <-----
rho_3 0.000000000 -0.000000000 -0.000000000 0.000000000 <-----
rho_4 0.000000000 0.000000000 -0.000000000 0.000000000 <-----
rho_5 0.000000000 -0.000000000 -0.000000000 0.000000000 <-----
rho_6 0.000000000 -0.000000000 -0.000000000 0.000000000 <-----
rho_7 0.000000000 -0.000000000 -0.000000000 0.000000000 <-----
rho_8 0.000000000 -0.000000000 -0.000000000 0.000000000 <-----
rho_9 -0.040881881 -0.048283413 -0.049721675 -0.047069863 <-----
. . .
63999 -0.00000000 -0.00002454, -23.69333 0.00317
63999 -0.26987232 0.00009273, -23.69333 0.00317
7. Order 9
Surprisingly, there is a 4-stage cyclic formula of order 9. However, its Widlund-δ-distance is enormous.
$ stabregion2 -b Base9 -I4:-1900:1900:1099500 -r19500 -E0.05
W= 0.00232, xmin=-376.86583, parasitic=0.6895, |e|=0.035349 1.000000 1285.147501 630.706237 258.664447 -133.593623 -1256.384007 -794.490164 -1351.699759 1475.827104 -1330.879604 1
Searching for 5-stage cyclic formulas.
$ stabregion2 -b Base9 -I5:-1900:1900:2099500 -r19500 -E0.05
W= 0.00000, xmin=-77.99213, parasitic=0.6481, |e|=0.046158 1.000000 -635.929995 1197.438115 -1705.402704 1736.138997 1799.824913 -1885.217062 -364.365106 -1868.833292 332.614681 1836.415456 -906.179706 -372.683443 -1753.289873 1211.838718 1
W= 0.00000, xmin=-95.71107, parasitic=0.7170, |e|=0.043922 1.000000 653.266267 -695.552005 742.248596 -399.821459 -1568.054703 -475.082850 803.267298 -299.222882 -1712.011932 -686.161477 -393.089533 855.504204 -383.521770 715.098937 2
W= 0.00000, xmin=-87.09916, parasitic=0.6843, |e|=0.041257 1.000000 1641.882781 -219.270218 1728.848482 -1441.475710 221.042597 -1587.316427 336.948242 -1017.479202 965.230519 -873.485619 1476.915671 1711.232141 -1769.201903 514.970838 3
W= 0.00000, xmin=-93.20954, parasitic=0.7077, |e|=0.042560 1.000000 -1169.995357 924.058730 1330.388072 -1361.477472 1654.715396 1147.463239 -590.188946 -1684.961322 648.748375 1250.070060 -212.286528 1149.045875 1747.626462 -1779.754762 4
$ stabregion2 -b Base9 -I5:-1900:1900:3099500 -r19500 -E0.05
W= 0.00653, xmin=-107.73419, parasitic=0.6960, |e|=0.046719 1.000000 643.245487 -693.833660 -974.151372 -268.060978 933.196601 1544.408832 -332.586678 -549.165176 -1113.060631 684.484908 -1666.867528 -1640.142136 802.315914 1769.222144 1
W= 0.00000, xmin=-135.67292, parasitic=0.7267, |e|=0.046149 1.000000 -513.538976 966.289438 1752.519109 -1480.794223 -544.351124 -563.548812 52.359850 340.471937 -1183.335764 -1607.926942 -1864.386294 985.420325 862.198047 51.540752 2
W= 0.00000, xmin=-65.54811, parasitic=0.6881, |e|=0.044826 1.000000 -292.575450 145.999624 483.071129 -1020.184032 -1018.950959 1710.799227 -1197.581726 1761.169695 1487.822194 1209.704241 -205.105418 -1365.861210 727.377200 331.206604 3
W= 0.00634, xmin=-126.43438, parasitic=0.6879, |e|=0.044570 1.000000 1544.033244 -17.007798 877.011835 774.025823 -706.931386 1472.441772 -1471.650435 -929.256095 -965.274164 -556.778211 1034.080630 535.852385 -501.857101 -476.703132 4
W= 0.00000, xmin=-132.67919, parasitic=0.7149, |e|=0.042009 1.000000 514.659729 -469.198973 1547.803775 510.306623 573.495462 1629.600035 -793.678072 -263.161259 -1013.882639 824.641169 -1551.997124 -1830.889100 1781.564551 -432.675743 5
W= 0.00000, xmin=-96.34673, parasitic=0.6749, |e|=0.047176 1.000000 -1799.701667 -880.734083 1851.738765 -828.255398 -1699.556379 -1860.835088 665.213522 716.054189 643.126991 802.133831 -1887.182379 -634.294542 1459.233782 187.714336 6
Details on the surprising 4-stage formula.
$ echo 1 1285.147501 630.706237 258.664447 -133.593623 -1256.384007 -794.490164 -1351.699759 1475.827104 -1330.879604 | stabregion2 -b Base9 -l- -r360100 -d
Base9, p=9, k=9, l=10, cpLen=20
-7129.00000000 -280.00000000 35.00000000 -10.00000000 5.00000000 -4.00000000 5.00000000 -10.00000000 35.00000000 -280.00000000
22680.00000000 -4329.00000000 -630.00000000 135.00000000 -60.00000000 45.00000000 -54.00000000 105.00000000 -360.00000000 2835.00000000
-45360.00000000 10080.00000000 -2754.00000000 -1080.00000000 360.00000000 -240.00000000 270.00000000 -504.00000000 1680.00000000 -12960.00000000
70560.00000000 -11760.00000000 5880.00000000 -1554.00000000 -1680.00000000 840.00000000 -840.00000000 1470.00000000 -4704.00000000 35280.00000000
-79380.00000000 11760.00000000 -4410.00000000 3780.00000000 -504.00000000 -2520.00000000 1890.00000000 -2940.00000000 8820.00000000 -63504.00000000
63504.00000000 -8820.00000000 2940.00000000 -1890.00000000 2520.00000000 504.00000000 -3780.00000000 4410.00000000 -11760.00000000 79380.00000000
-35280.00000000 4704.00000000 -1470.00000000 840.00000000 -840.00000000 1680.00000000 1554.00000000 -5880.00000000 11760.00000000 -70560.00000000
12960.00000000 -1680.00000000 504.00000000 -270.00000000 240.00000000 -360.00000000 1080.00000000 2754.00000000 -10080.00000000 45360.00000000
-2835.00000000 360.00000000 -105.00000000 54.00000000 -45.00000000 60.00000000 -135.00000000 630.00000000 4329.00000000 -22680.00000000
280.00000000 -35.00000000 10.00000000 -5.00000000 4.00000000 -5.00000000 10.00000000 -35.00000000 280.00000000 7129.00000000
2520.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 2520.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 2520.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 2520.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 2520.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 2520.00000000 0.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 2520.00000000 0.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 2520.00000000 0.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 2520.00000000 0.00000000
0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 2520.00000000
fname=-, l=4, il=10
1.00000000
1285.14750100 630.70623700
258.66444700 -133.59362300 -1256.38400700
-794.49016400 -1351.69975900 1475.82710400 -1330.87960400
fm based on LinearCombination, l=4, colLen=26
LinearCombination, p=9, k=9, l=4
-280.0000 0.0000 0.0000 0.0000
2835.0000 -337766.5820 0.0000 0.0000
-12960.0000 3416338.9200 -64537.9819 0.0000
35280.0000 -15595925.1348 649487.0908 153735.0853
-63504.0000 42373161.6964 -2943510.9802 -1538938.3572
79380.0000 -76049177.8932 7907221.6025 6922582.5768
-70560.0000 94597903.2823 -13910753.8166 -18383812.6093
45360.0000 -83262902.3234 16563191.3385 31677017.3630
-22680.0000 51936771.7764 -12434886.4256 -35631517.6207
7129.0000 -26416818.0227 9619561.4805 29417186.5299
0.0000 9338414.2810 -7236358.3763 -19785862.3962
0.0000 0.0000 1850586.0685 13276968.4849
0.0000 0.0000 0.0000 -6107359.0564
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
2520.0000 1589379.7172 -3166087.6976 -3353816.6021
0.0000 3238571.7025 -336655.9300 3719084.3021
0.0000 0.0000 651834.4064 -3406283.3927
0.0000 0.0000 0.0000 -2002115.2133
rho_0 0.000000000 -0.000000002 -0.000000005 0.000000014 <-----
rho_1 0.000000000 -0.000000000 -0.000000000 -0.000000000 <-----
rho_2 0.000000000 0.000000000 -0.000000000 -0.000000000 <-----
rho_3 0.000000000 0.000000000 -0.000000000 -0.000000000 <-----
rho_4 0.000000000 0.000000000 -0.000000000 -0.000000000 <-----
rho_5 0.000000000 0.000000000 -0.000000000 -0.000000000 <-----
rho_6 0.000000000 0.000000000 -0.000000000 -0.000000000 <-----
rho_7 0.000000000 0.000000000 -0.000000000 -0.000000000 <-----
rho_8 0.000000000 0.000000000 -0.000000000 -0.000000000 <-----
rho_9 0.000000000 0.000000000 -0.000000000 0.000000000 <-----
rho_10 -0.035348576 -0.032789014 -0.032492071 -0.024239692 <-----
. . .
360099 1.58070137 0.00004958, -376.86584 0.00077
360099 -0.00000000 -0.00000436, -376.86584 0.00077
360099 0.15016818 -0.00000836, -376.86584 0.00077