Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 3 8 72
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : 2*t^5 - 3*t^3 + 1*t
Solvable: 1
-------------------------------------------------
Trying to find an order 72 Kronrod extension for:
P3 : 2*t^13 - 7*t^11 + 19/2*t^9 - 25/4*t^7 + 259/128*t^5 - 73/256*t^3 + 3/256*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^85 - 43*t^83 + 446*t^81 - 5945/2*t^79 + 1831141/128*t^77 - 13560547/256*t^75 + 80384535/512*t^73 - 391820565/1024*t^71 + 25615811325/32768*t^69 - 89004181207/65536*t^67 + 132927690929/65536*t^65 - 86056018529/32768*t^63 + 3111484832911/1048576*t^61 - 6167298918865/2097152*t^59 + 10764573301519/4194304*t^57 - 16594616082417/8388608*t^55 + 724590381004479/536870912*t^53 - 876386828841381/1073741824*t^51 + 117537743465025/268435456*t^49 - 447564281106705/2147483648*t^47 + 48368073978063525/549755813888*t^45 - 36183601418599635/1099511627776*t^43 + 23947643403612915/2199023255552*t^41 - 13992539490017025/4398046511104*t^39 + 115172762172777855/140737488355328*t^37 - 51988764864122541/281474976710656*t^35 + 10253511006056829/281474976710656*t^33 - 1758390578322763/281474976710656*t^31 + 8341028974105135/9007199254740992*t^29 - 2122571584427329/18014398509481984*t^27 + 459760634073923/36028797018963968*t^25 - 83925275384405/72057594037927936*t^23 + 816426728002655/9223372036854775808*t^21 - 101842634229525/18446744073709551616*t^19 + 2560318641699/9223372036854775808*t^17 - 405953191227/36893488147419103232*t^15 + 789130130801/2361183241434822606848*t^13 - 35385125399/4722366482869645213696*t^11 + 1113061235/9444732965739290427392*t^9 - 22825561/18889465931478580854784*t^7 + 4356373/604462909807314587353088*t^5 - 24703/1208925819614629174706176*t^3 + 21/1208925819614629174706176*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-0.9993007047883985527 - 7.3091539478901395405e-1633j)  +/-  (1.77e-478, 1.77e-478j)
| (-0.95557280578614073281 - 4.3674088735266120898e-1639j)  +/-  (1.45e-479, 1.45e-479j)
| (-0.9438833303083675629 - 3.7117487136088397692e-1640j)  +/-  (7.62e-480, 7.62e-480j)
| (-0.98883082622512854507 - 1.081511902887230815e-1639j)  +/-  (1.03e-478, 1.03e-478j)
| (0.93087374864420425564 + 4.121693886820855976e-1637j)  +/-  (3.36e-480, 3.36e-480j)
| (0.9438833303083675629 + 1.8678940199946881752e-1640j)  +/-  (7.48e-480, 7.48e-480j)
| (0.9993007047883985527 - 2.2218446363024978937e-1651j)  +/-  (1.75e-478, 1.75e-478j)
| (-0.90096886790241912624 - 2.9802489187890559954e-1684j)  +/-  (5.45e-481, 5.45e-481j)
| (-0.99371220989324258353 + 1.3826473886294174567e-1680j)  +/-  (1.31e-478, 1.31e-478j)
| (0.99371220989324258353 - 1.8864564912679383877e-1685j)  +/-  (1.32e-478, 1.32e-478j)
| (0.86602540378443864676 + 1.8406796580918007722e-1712j)  +/-  (6.01e-482, 6.01e-482j)
| (1 + 1.2854198719445769801e-1727j)  +/-  (9.47e-479, 9.47e-479j)
| (-0.93087374864420425564 + 4.2307234859406949978e-1763j)  +/-  (3.4e-480, 3.4e-480j)
| (-0.88411539350460978945 + 5.9815889545928852918e-1768j)  +/-  (1.92e-481, 1.92e-481j)
| (0.99720379718118014823 - 8.0325799665740659529e-1766j)  +/-  (1.6e-478, 1.6e-478j)
| (0.84672419922828416835 + 5.4860888835664462252e-1788j)  +/-  (1.85e-482, 1.85e-482j)
| (0.88411539350460978945 + 3.3172396532700268335e-1784j)  +/-  (1.96e-481, 1.96e-481j)
| (0.97492791218182360702 - 9.4685960974742678585e-1786j)  +/-  (4.42e-479, 4.42e-479j)
| (-0.80459777976666832735 + 8.76482316558411449e-1809j)  +/-  (1.18e-483, 1.18e-483j)
| (0.98883082622512854507 - 1.4427054801970631686e-1800j)  +/-  (1.04e-478, 1.04e-478j)
| (0.95557280578614073281 - 1.2933998734034518679e-1816j)  +/-  (1.48e-479, 1.48e-479j)
| (0.78183148246802980871 + 2.4929635309307492123e-1833j)  +/-  (2.7e-484, 2.7e-484j)
| (-1 + 3.1678152692402003214e-1823j)  +/-  (1.61e-478, 1.61e-478j)
| (-0.82623877431599487195 - 1.5092918254709355531e-1833j)  +/-  (4.78e-483, 4.78e-483j)
| (-0.78183148246802980871 - 3.4816403631983063857e-1835j)  +/-  (2.65e-484, 2.65e-484j)
| (-0.98256647323328823615 - 4.8169619681628325337e-1828j)  +/-  (7.04e-479, 7.04e-479j)
| (0.75797172314545298179 - 5.1095585409934800193e-1837j)  +/-  (5.54e-485, 5.54e-485j)
| (0.82623877431599487195 + 4.6205908769179165567e-1835j)  +/-  (4.84e-483, 4.84e-483j)
| (-0.7071067811865475244 + 1.5017599280513729066e-1838j)  +/-  (1.97e-486, 1.97e-486j)
| (-0.65228741127812115437 - 2.1101981164486030137e-1840j)  +/-  (3.48e-488, 3.48e-488j)
| (-0.91656225586997618582 + 5.094595436072679495e-1832j)  +/-  (1.43e-480, 1.43e-480j)
| (0.80459777976666832735 + 1.3880415433791031282e-1835j)  +/-  (1.22e-483, 1.22e-483j)
| (0.68017273777091939019 - 5.0097145153125758194e-1840j)  +/-  (2.18e-487, 2.18e-487j)
| (-0.99720379718118014823 + 3.0713088530498665698e-1828j)  +/-  (1.61e-478, 1.61e-478j)
| (-0.73305187182982632852 + 6.5336737542098495063e-1839j)  +/-  (1.03e-485, 1.03e-485j)
| (-0.75797172314545298179 - 6.2700028976390967216e-1839j)  +/-  (5.79e-485, 5.79e-485j)
| (-0.96592582628906828675 - 1.9426479616741689311e-1831j)  +/-  (2.65e-479, 2.65e-479j)
| (0.59382018557350161165 - 6.1291751084012016925e-1843j)  +/-  (4.87e-490, 4.87e-490j)
| (0.91656225586997618582 - 4.0947059595363960719e-1830j)  +/-  (1.39e-480, 1.39e-480j)
| (-0.86602540378443864676 + 5.6072763902768263501e-1843j)  +/-  (6.1e-482, 6.1e-482j)
| (-0.59382018557350161165 - 6.1131231003842577707e-1852j)  +/-  (4.78e-490, 4.78e-490j)
| (0.96592582628906828675 + 3.31676443310684129e-1838j)  +/-  (2.67e-479, 2.67e-479j)
| (0.7071067811865475244 - 9.5562637605522495016e-1868j)  +/-  (1.98e-486, 1.98e-486j)
| (0.62348980185873353053 + 2.4824428505105245053e-1870j)  +/-  (4.02e-489, 4.02e-489j)
| (0.98256647323328823615 + 9.9657758305184882156e-1862j)  +/-  (6.81e-479, 6.81e-479j)
| (-0.56332005806362202775 + 3.9921759950021855932e-1878j)  +/-  (5.71e-491, 5.71e-491j)
| (-0.68017273777091939019 - 1.3362146861251117647e-1875j)  +/-  (2.32e-487, 2.32e-487j)
| (0.90096886790241912624 + 9.4982752360294546849e-1870j)  +/-  (5.46e-481, 5.46e-481j)
| (0.46726862827306198914 + 4.3830115435665768484e-1883j)  +/-  (3.77e-494, 3.77e-494j)
| (0.33027906195516708177 - 2.0421978361856099221e-1887j)  +/-  (8.91e-499, 8.91e-499j)
| (-0.62348980185873353053 - 2.1773193112501562938e-1876j)  +/-  (3.95e-489, 3.95e-489j)
| (-0.46726862827306198914 - 3.3723637960293098767e-1882j)  +/-  (3.82e-494, 3.82e-494j)
| (-0.074730093586424254291 + 4.0791621934325312417e-1896j)  +/-  (6.51e-508, 6.51e-508j)
| (0.65228741127812115437 - 5.3400799241183280937e-1877j)  +/-  (3.32e-488, 3.32e-488j)
| (0.56332005806362202775 - 1.9455159274340735632e-1879j)  +/-  (5.51e-491, 5.51e-491j)
| (-0.97492791218182360702 - 5.5284112020190852637e-1872j)  +/-  (4.45e-479, 4.45e-479j)
| (-0.5 + 7.2177206727843184505e-1888j)  +/-  (3.77e-493, 3.77e-493j)
| (-0.84672419922828416835 + 1.6364869620649490625e-1886j)  +/-  (1.82e-482, 1.82e-482j)
| (0.53203207651533656356 + 1.6404361302158920653e-1894j)  +/-  (6.11e-492, 6.11e-492j)
| (0.43388373911755812048 + 3.7238382017035865036e-1899j)  +/-  (3.07e-495, 3.07e-495j)
| (0.73305187182982632852 - 1.7539382394089726615e-1900j)  +/-  (1.07e-485, 1.07e-485j)
| (-0.43388373911755812048 - 1.0693318290325789848e-1908j)  +/-  (3.1e-495, 3.1e-495j)
| (-0.39989202431974097188 - 4.9778602339556082284e-1911j)  +/-  (2.4e-496, 2.4e-496j)
| (-0.037391194276325621096 + 4.9475206927040668277e-1923j)  +/-  (1.29e-509, 1.29e-509j)
| (0.39989202431974097188 - 3.7581945124554690788e-1912j)  +/-  (2.39e-496, 2.39e-496j)
| (0.5 - 2.5394824712904620512e-1907j)  +/-  (3.95e-493, 3.95e-493j)
| (-2.904475142065017519e-1973 + 4.459517301678034858e-1973j)  +/-  (4.52e-1971, 4.52e-1971j)
| (-0.36534102436639501454 - 1.0259787561995732639e-1910j)  +/-  (1.64e-497, 1.64e-497j)
| (-0.53203207651533656356 - 1.4444603573420364596e-1908j)  +/-  (6.09e-492, 6.09e-492j)
| (0.14904226617617444693 - 2.7643336555238160917e-1922j)  +/-  (3.4e-505, 3.4e-505j)
| (0.36534102436639501454 + 1.0729041010786311719e-1914j)  +/-  (1.65e-497, 1.65e-497j)
| (0.11196447610330785847 + 1.1353191412248856502e-1923j)  +/-  (1.86e-506, 1.86e-506j)
| (-0.25881904510252076235 - 6.6926271906949352537e-1919j)  +/-  (3.34e-501, 3.34e-501j)
| (-0.33027906195516708177 + 1.1057458002398888522e-1915j)  +/-  (8.55e-499, 8.55e-499j)
| (0.037391194276325621096 - 4.9044335376437623329e-1926j)  +/-  (1.38e-509, 1.38e-509j)
| (0.29475517441090421683 + 7.4563475158787711894e-1918j)  +/-  (4.87e-500, 4.87e-500j)
| (0.18591160716291458111 - 5.6852175195490295026e-1921j)  +/-  (7.7e-504, 7.7e-504j)
| (-0.11196447610330785847 - 3.2805875948855177516e-1924j)  +/-  (1.74e-506, 1.74e-506j)
| (-0.29475517441090421683 - 7.6919189904292017369e-1917j)  +/-  (4.86e-500, 4.86e-500j)
| (-0.14904226617617444693 - 3.4882270351377297305e-1922j)  +/-  (3.42e-505, 3.42e-505j)
| (0.22252093395631440429 - 1.2403640282615496076e-1919j)  +/-  (1.43e-502, 1.43e-502j)
| (0.25881904510252076235 + 2.1872146076762883387e-1918j)  +/-  (3.36e-501, 3.36e-501j)
| (0.074730093586424254291 + 1.0054578923836025546e-1924j)  +/-  (6.62e-508, 6.62e-508j)
| (-0.18591160716291458111 + 2.2116015585225730766e-1921j)  +/-  (7.18e-504, 7.18e-504j)
| (-0.22252093395631440429 + 2.9363181521127291635e-1919j)  +/-  (1.43e-502, 1.43e-502j)
-------------------------------------------------
The weights are:
| (0.011904761904761904762 + 3.1096774942251650822e-1632j)  +/-  (4.99e-129, 2.96e-359j)
| (0.011904761904761904762 + 1.9898875733161235527e-1633j)  +/-  (2.47e-129, 1.46e-359j)
| (0.011904761904761904762 - 1.5701452819065732583e-1633j)  +/-  (1.52e-129, 8.98e-360j)
| (0.011904761904761904762 + 8.3108632577568288774e-1633j)  +/-  (1.01e-130, 5.96e-361j)
| (0.011904761904761904762 + 4.5098012625422495867e-1635j)  +/-  (4.49e-130, 2.66e-360j)
| (0.011904761904761904762 - 4.5156073505485996945e-1635j)  +/-  (3.96e-130, 2.34e-360j)
| (0.011904761904761904762 - 4.3608951514983775512e-1635j)  +/-  (2.1e-131, 1.24e-361j)
| (0.011904761904761904762 + 8.8489525918184234472e-1634j)  +/-  (3.12e-132, 1.85e-362j)
| (0.011904761904761904762 - 1.5570157390997377121e-1632j)  +/-  (1.07e-131, 6.31e-362j)
| (0.011904761904761904762 - 4.373740477416068917e-1635j)  +/-  (5.99e-132, 3.55e-362j)
| (0.011904761904761904762 + 4.657233284753256178e-1635j)  +/-  (1.42e-133, 8.39e-364j)
| (0.005952380952380952381 + 2.1796499284232485753e-1635j)  +/-  (1.06e-131, 6.26e-362j)
| (0.011904761904761904762 + 1.2716248991970664342e-1633j)  +/-  (9.62e-133, 5.7e-363j)
| (0.011904761904761904762 - 7.5542042460302783313e-1634j)  +/-  (4.6e-134, 2.73e-364j)
| (0.011904761904761904762 + 4.3656943616109627415e-1635j)  +/-  (7.28e-132, 4.31e-362j)
| (0.011904761904761904762 - 4.7077412540131678138e-1635j)  +/-  (3.25e-135, 1.92e-365j)
| (0.011904761904761904762 - 4.6095019610507479112e-1635j)  +/-  (1.13e-134, 6.68e-365j)
| (0.011904761904761904762 + 4.4186080821978091342e-1635j)  +/-  (1.78e-134, 1.05e-364j)
| (0.011904761904761904762 - 4.4690192886537540633e-1634j)  +/-  (4.5e-139, 2.66e-369j)
| (0.011904761904761904762 + 4.3851171790282175162e-1635j)  +/-  (1.24e-133, 7.32e-364j)
| (0.011904761904761904762 + 4.4709626359416047513e-1635j)  +/-  (9.45e-135, 5.59e-365j)
| (0.011904761904761904762 + 4.8820105719727994434e-1635j)  +/-  (3.87e-139, 2.29e-369j)
| (0.005952380952380952381 - 6.2215310671479279734e-1632j)  +/-  (3.45e-137, 2.04e-367j)
| (0.011904761904761904762 + 5.0278635745844413192e-1634j)  +/-  (8.86e-140, 5.24e-370j)
| (0.011904761904761904762 + 4.0011658255632720378e-1634j)  +/-  (1.15e-140, 6.83e-371j)
| (0.011904761904761904762 - 5.1997422302560001582e-1633j)  +/-  (4.02e-138, 2.38e-368j)
| (0.011904761904761904762 - 4.9487959778051447909e-1635j)  +/-  (5.17e-141, 3.06e-371j)
| (0.011904761904761904762 + 4.7617761222564436144e-1635j)  +/-  (2.01e-139, 1.19e-369j)
| (0.011904761904761904762 - 2.977912492084627167e-1634j)  +/-  (6.46e-143, 3.82e-373j)
| (0.011904761904761904762 - 2.507471516558873403e-1634j)  +/-  (6.15e-144, 3.64e-374j)
| (0.011904761904761904762 - 1.0516683274398525087e-1633j)  +/-  (4.11e-139, 2.43e-369j)
| (0.011904761904761904762 - 4.8197617667729303592e-1635j)  +/-  (1.4e-140, 8.27e-371j)
| (0.011904761904761904762 + 5.1790529471205448038e-1635j)  +/-  (1.72e-144, 1.02e-374j)
| (0.011904761904761904762 + 4.1496219247232830061e-1632j)  +/-  (2.65e-138, 1.57e-368j)
| (0.011904761904761904762 + 3.2681038141366651063e-1634j)  +/-  (2.55e-143, 1.51e-373j)
| (0.011904761904761904762 - 3.6055746316836484926e-1634j)  +/-  (8.6e-143, 5.09e-373j)
| (0.011904761904761904762 - 2.607164347789745235e-1633j)  +/-  (4.98e-140, 2.95e-370j)
| (0.011904761904761904762 - 5.4603824385323424239e-1635j)  +/-  (9.99e-149, 5.91e-379j)
| (0.011904761904761904762 - 4.5074709847770289056e-1635j)  +/-  (7.02e-143, 4.16e-373j)
| (0.011904761904761904762 + 6.5288383712653058492e-1634j)  +/-  (3.76e-143, 2.22e-373j)
| (0.011904761904761904762 - 2.145907451588127984e-1634j)  +/-  (1.45e-149, 8.57e-380j)
| (0.011904761904761904762 - 4.4416549059470223965e-1635j)  +/-  (3.12e-142, 1.85e-372j)
| (0.011904761904761904762 - 5.0970400821203586533e-1635j)  +/-  (1.95e-147, 1.15e-377j)
| (0.011904761904761904762 + 5.360382742890812278e-1635j)  +/-  (2.24e-149, 1.33e-379j)
| (0.011904761904761904762 - 4.3999762350564332266e-1635j)  +/-  (2.96e-142, 1.75e-372j)
| (0.011904761904761904762 + 1.9957821783480528505e-1634j)  +/-  (5.19e-151, 3.07e-381j)
| (0.011904761904761904762 + 2.7265770073760833058e-1634j)  +/-  (7.56e-148, 4.48e-378j)
| (0.011904761904761904762 + 4.5626147077852870649e-1635j)  +/-  (4.47e-144, 2.65e-374j)
| (0.011904761904761904762 - 5.9320864194666472397e-1635j)  +/-  (2.59e-154, 1.53e-384j)
| (0.011904761904761904762 - 6.5436327968191381325e-1635j)  +/-  (3.28e-156, 1.94e-386j)
| (0.011904761904761904762 + 2.3153262472788472923e-1634j)  +/-  (6.96e-150, 4.12e-380j)
| (0.011904761904761904762 - 1.6354616598947756266e-1634j)  +/-  (1.12e-154, 6.62e-385j)
| (0.011904761904761904762 + 9.4107647551009335309e-1635j)  +/-  (2.05e-158, 1.21e-388j)
| (0.011904761904761904762 - 5.2667246627037182135e-1635j)  +/-  (1.19e-150, 7.05e-381j)
| (0.011904761904761904762 + 5.5671104649990096877e-1635j)  +/-  (6.17e-153, 3.65e-383j)
| (0.011904761904761904762 + 3.570116711197746338e-1633j)  +/-  (3.33e-147, 1.97e-377j)
| (0.011904761904761904762 + 1.7426765080501459667e-1634j)  +/-  (5.51e-155, 3.26e-385j)
| (0.011904761904761904762 - 5.702924996006732486e-1634j)  +/-  (1.97e-148, 1.16e-378j)
| (0.011904761904761904762 - 5.6809888466217845986e-1635j)  +/-  (8.88e-155, 5.26e-385j)
| (0.011904761904761904762 + 6.0703653512563280021e-1635j)  +/-  (4.62e-157, 2.74e-387j)
| (0.011904761904761904762 + 5.0203824486184950168e-1635j)  +/-  (2.33e-151, 1.38e-381j)
| (0.011904761904761904762 + 1.5388933517968344594e-1634j)  +/-  (8.52e-158, 5.04e-388j)
| (0.011904761904761904762 - 1.4516216873774307246e-1634j)  +/-  (7.01e-159, 4.15e-389j)
| (0.011904761904761904762 - 9.0454248902966870263e-1635j)  +/-  (1.42e-162, 8.39e-393j)
| (0.011904761904761904762 - 6.2179247694287655836e-1635j)  +/-  (3.51e-159, 2.08e-389j)
| (0.011904761904761904762 + 5.8024790344172133011e-1635j)  +/-  (6.54e-157, 3.87e-387j)
| (0.011904761904761904762 + 8.7069296798532334665e-1635j)  +/-  (2.18e-163, 1.29e-393j)
| (0.011904761904761904762 + 1.3725048660182549037e-1634j)  +/-  (2.23e-161, 1.32e-391j)
| (0.011904761904761904762 - 1.8621431038981332509e-1634j)  +/-  (4.84e-158, 2.87e-388j)
| (0.011904761904761904762 + 7.5766973351199349848e-1635j)  +/-  (1.59e-164, 9.4e-395j)
| (0.011904761904761904762 + 6.3754345645532498971e-1635j)  +/-  (1.59e-161, 9.41e-392j)
| (0.011904761904761904762 - 7.829546083298242131e-1635j)  +/-  (1.07e-164, 6.31e-395j)
| (0.011904761904761904762 - 1.1750543732953988496e-1634j)  +/-  (3.28e-165, 1.94e-395j)
| (0.011904761904761904762 - 1.3005718531706612077e-1634j)  +/-  (7.61e-164, 4.5e-394j)
| (0.011904761904761904762 - 8.3928488520051152571e-1635j)  +/-  (2.51e-165, 1.49e-395j)
| (0.011904761904761904762 + 6.7233339203509909387e-1635j)  +/-  (9.11e-165, 5.39e-395j)
| (0.011904761904761904762 - 7.3409524351830900328e-1635j)  +/-  (1.15e-165, 6.82e-396j)
| (0.011904761904761904762 - 9.8056969183813835554e-1635j)  +/-  (1.1e-166, 6.49e-397j)
| (0.011904761904761904762 + 1.2349926392086742706e-1634j)  +/-  (3.16e-166, 1.87e-396j)
| (0.011904761904761904762 + 1.0233337164542813256e-1634j)  +/-  (3.02e-167, 1.79e-397j)
| (0.011904761904761904762 + 7.1209424200203527775e-1635j)  +/-  (5.29e-167, 3.13e-397j)
| (0.011904761904761904762 - 6.9154381852416361714e-1635j)  +/-  (6.33e-167, 3.75e-397j)
| (0.011904761904761904762 + 8.1010267365319109045e-1635j)  +/-  (1.74e-167, 1.03e-397j)
| (0.011904761904761904762 - 1.0697229938801407622e-1634j)  +/-  (1.09e-168, 6.44e-399j)
| (0.011904761904761904762 + 1.1201420821530737475e-1634j)  +/-  (1.07e-168, 6.3e-399j)
