Starting with polynomial:
P : t
Extension levels are: 1 4 44
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^49 - 61590049535862924641497219533608/56494332485152163715384612507*t^47 + 307852749100768046199020543858468747/564943324851521637153846125070*t^45 - 3123663287437107917876100337863411291/18831444161717387905128204169*t^43 + 31645585854122679237800228646697320273/918607032278896970981863618*t^41 - 2380711631264982745867371493961729663790/459303516139448485490931809*t^39 + 537963214392409965951508079452412224196295/918607032278896970981863618*t^37 - 23344823251379959524798027835688605429205103/459303516139448485490931809*t^35 + 3158428926537925909642707700934876483123994645/918607032278896970981863618*t^33 - 84023033586206346501506625365042490823041683640/459303516139448485490931809*t^31 + 3533469931471329402486110183919952499429498153625/459303516139448485490931809*t^29 - 117640111633089920669802609515373657262805015025750/459303516139448485490931809*t^27 + 3096852148562811384110219462735397508296135471599205/459303516139448485490931809*t^25 - 64207815356476577765735821520339351764667696082256500/459303516139448485490931809*t^23 + 1041511817189199704855112129649349139399274473042735375/459303516139448485490931809*t^21 - 13090616626066617699257040697613301317669568256314483750/459303516139448485490931809*t^19 + 125823198367911798958029713073027464512107361606441728750/459303516139448485490931809*t^17 - 908703241419267781844851394005118280169263965042090652000/459303516139448485490931809*t^15 + 9632007991160519811330377225600717806909571862343186310625/918607032278896970981863618*t^13 - 18134813288825223363929480956006184305339231150481418474375/459303516139448485490931809*t^11 + 92689299230875297371975534133246598268480133935574534603125/918607032278896970981863618*t^9 - 75071810716561620683056199132863366518569406005613710268750/459303516139448485490931809*t^7 + 138149857479073923452261846983608002763684475430027209756875/918607032278896970981863618*t^5 - 29601355885806575564973518171682031015105879875050905096875/459303516139448485490931809*t^3 + 7465654899722296102680431273677860245955743092686350728125/918607032278896970981863618*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 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: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   49 out of 49
Indefinite weights: 0 out of 49
Negative weights:   0 out of 49
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (10.122817380748711411 - 4.953134120322971955e-574j)  +/-  (3.04e-244, 3.04e-244j)
| (10.822939439609029683 - 7.2476352969085991251e-583j)  +/-  (9.03e-245, 9.03e-245j)
| (-10.822939439609029683 - 4.4763057008373536339e-596j)  +/-  (9.6e-245, 9.6e-245j)
| (-8.2844405842956046706 + 9.4224879698720536731e-596j)  +/-  (1.67e-243, 1.67e-243j)
| (-10.122817380748711411 + 5.6930576087974489647e-595j)  +/-  (3.22e-244, 3.22e-244j)
| (8.8657974839257264971 - 1.8190995103407222048e-607j)  +/-  (1.31e-243, 1.31e-243j)
| (6.1451545768340883988 - 4.0464123770689840897e-646j)  +/-  (5.33e-244, 5.33e-244j)
| (-2.8569700138728056542 + 2.3404709495112345935e-672j)  +/-  (2.86e-247, 2.86e-247j)
| (-3.2655086262251148498 - 1.7249001569765602227e-671j)  +/-  (9.96e-247, 9.96e-247j)
| (-9.4755332674305967158 + 5.7684274937509073669e-668j)  +/-  (7.31e-244, 7.31e-244j)
| (-12.54865222821579494 - 6.2581079423213320259e-674j)  +/-  (1.1e-246, 1.1e-246j)
| (6.6585233555923756536 + 5.6725848585680478952e-685j)  +/-  (1.04e-243, 1.04e-243j)
| (2.8569700138728056542 + 8.2969740714654853391e-702j)  +/-  (3.04e-247, 3.04e-247j)
| (9.4755332674305967158 - 1.1878201438453944614e-707j)  +/-  (7.22e-244, 7.22e-244j)
| (-6.1451545768340883988 + 1.5383329535166065275e-719j)  +/-  (5.54e-244, 5.54e-244j)
| (11.605595682911779588 + 5.8186371445769652342e-719j)  +/-  (1.59e-245, 1.59e-245j)
| (-11.605595682911779588 + 4.3409765292398214262e-727j)  +/-  (1.66e-245, 1.66e-245j)
| (12.54865222821579494 + 1.3140919274445169686e-724j)  +/-  (1.07e-246, 1.07e-246j)
| (-0.90445270136973678237 - 7.8900042442327845592e-741j)  +/-  (2.74e-252, 2.74e-252j)
| (-3.719502367769350071 + 3.820578067059400944e-735j)  +/-  (3.33e-246, 3.33e-246j)
| (-5.1493205251355823581 + 4.3745703071567936593e-733j)  +/-  (1.08e-244, 1.08e-244j)
| (2.5716831067950223751 + 1.2591177140056792334e-733j)  +/-  (9.2e-248, 9.2e-248j)
| (-7.7254196372351785625 - 4.3343491854505103571e-733j)  +/-  (1.75e-243, 1.75e-243j)
| (-8.8657974839257264971 - 5.1395890040458981445e-734j)  +/-  (1.39e-243, 1.39e-243j)
| (4.1875950509645929844 + 1.4053516096694549835e-734j)  +/-  (1.11e-245, 1.11e-245j)
| (7.7254196372351785625 + 2.3424034354302432447e-748j)  +/-  (1.68e-243, 1.68e-243j)
| (1.3556261799742658658 - 3.6252297178435018704e-772j)  +/-  (5.31e-251, 5.31e-251j)
| (1.8029364044995615833 + 3.4434008884829394097e-770j)  +/-  (9.17e-250, 9.17e-250j)
| (-5.642552944756046402 + 1.9918768055160987e-764j)  +/-  (2.59e-244, 2.59e-244j)
| (-2.5716831067950223751 - 8.3940950116628245198e-769j)  +/-  (9.63e-248, 9.63e-248j)
| (-4.1875950509645929844 - 9.4691918501975439431e-767j)  +/-  (1.15e-245, 1.15e-245j)
| (2.232190528164185299 - 3.9960623093656146201e-769j)  +/-  (1.36e-248, 1.36e-248j)
| (3.719502367769350071 - 2.4986008313683201785e-765j)  +/-  (3.08e-246, 3.08e-246j)
| (8.2844405842956046706 + 7.4509475629084442963e-774j)  +/-  (1.75e-243, 1.75e-243j)
| (-1.8029364044995615833 + 1.93490201991236308e-798j)  +/-  (9.39e-250, 9.39e-250j)
| (-2.232190528164185299 + 1.1109027971667730618e-795j)  +/-  (1.41e-248, 1.41e-248j)
| (-2.2899095356373744015e-828 - 1.4149534328161326055e-827j)  +/-  (7.02e-826, 7.02e-826j)
| (0.90445270136973678237 + 3.9125544383895610276e-814j)  +/-  (2.51e-252, 2.51e-252j)
| (-6.6585233555923756536 + 1.2702783467841579364e-789j)  +/-  (9.36e-244, 9.36e-244j)
| (-4.6644741515193364082 - 1.4095040810297933019e-794j)  +/-  (3.38e-245, 3.38e-245j)
| (-1.3556261799742658658 + 9.3520378515616481388e-802j)  +/-  (5.37e-251, 5.37e-251j)
| (5.642552944756046402 + 1.1582106298062716709e-793j)  +/-  (2.51e-244, 2.51e-244j)
| (3.2655086262251148498 + 5.4018770735923093562e-805j)  +/-  (8.98e-247, 8.98e-247j)
| (7.1844882518581726132 - 1.5499029145263664989e-808j)  +/-  (1.4e-243, 1.4e-243j)
| (5.1493205251355823581 + 5.6050914522088844012e-819j)  +/-  (1.09e-244, 1.09e-244j)
| (-0.45232999423046289581 - 3.5018491997684022111e-830j)  +/-  (1.46e-253, 1.46e-253j)
| (-7.1844882518581726132 + 1.0210794010431869779e-821j)  +/-  (1.43e-243, 1.43e-243j)
| (4.6644741515193364082 + 2.4407854606479306784e-820j)  +/-  (3.32e-245, 3.32e-245j)
| (0.45232999423046289581 - 1.0346838012886893988e-830j)  +/-  (1.46e-253, 1.46e-253j)
-------------------------------------------------
The weights are:
| (1.4991588504618397384e-23 + 3.9155636716570964441e-596j)  +/-  (5.27e-77, 1.13e-199j)
| (1.0742301660255568066e-26 + 2.4616190996103652653e-598j)  +/-  (2.06e-78, 4.41e-201j)
| (1.0742301660255568066e-26 - 8.2280809738659413114e-600j)  +/-  (3.52e-80, 7.55e-203j)
| (2.8382983770806548469e-16 - 2.7163964743996511426e-594j)  +/-  (2.1e-75, 4.5e-198j)
| (1.4991588504618397384e-23 + 3.6677214328711187412e-598j)  +/-  (5.62e-79, 1.2e-201j)
| (2.0260865922335267653e-18 + 2.8939143092259762972e-594j)  +/-  (5.31e-77, 1.14e-199j)
| (1.2776684236960286107e-09 - 5.3272838131685817655e-590j)  +/-  (6.78e-71, 1.45e-193j)
| (0.0023813751281237155234 + 3.7709422317104825806e-586j)  +/-  (8.65e-58, 1.85e-180j)
| (0.00085186250174896475405 - 9.9500663083062561449e-587j)  +/-  (3.24e-60, 6.94e-183j)
| (7.9650440260047511088e-21 - 1.006889988182514331e-596j)  +/-  (1.6e-78, 3.42e-201j)
| (2.7779046834954628315e-35 - 2.8305833114151248143e-604j)  +/-  (3.52e-85, 7.54e-208j)
| (4.8856373464525989362e-11 + 9.8662278691678685391e-591j)  +/-  (4.46e-74, 9.55e-197j)
| (0.0023813751281237155234 + 6.736451507118313555e-586j)  +/-  (5.2e-62, 1.11e-184j)
| (7.9650440260047511088e-21 - 3.0486431919079579892e-595j)  +/-  (1.24e-79, 2.66e-202j)
| (1.2776684236960286107e-09 - 1.3025679368445332137e-590j)  +/-  (1.45e-74, 3.1e-197j)
| (1.8991654423021864049e-30 - 1.3332470831417309186e-600j)  +/-  (1.04e-84, 2.23e-207j)
| (1.8991654423021864049e-30 + 9.0982707324066052981e-602j)  +/-  (9.89e-85, 2.12e-207j)
| (2.7779046834954628315e-35 + 2.6454184870059629655e-603j)  +/-  (4.25e-87, 9.1e-210j)
| (0.11975121830997262537 - 9.3282037960158985381e-586j)  +/-  (5.84e-63, 1.25e-185j)
| (0.00018283029409514498466 + 2.5243051847340498169e-587j)  +/-  (1.67e-68, 3.57e-191j)
| (3.4070134102139214689e-07 - 3.5574148703629063263e-589j)  +/-  (2.33e-73, 5e-196j)
| (0.003886186075548725695 - 1.1649204500894287921e-585j)  +/-  (3.08e-66, 6.6e-189j)
| (2.404230500376047618e-14 + 3.014950975214158417e-593j)  +/-  (1.06e-78, 2.28e-201j)
| (2.0260865922335267653e-18 + 1.9157310273917246168e-595j)  +/-  (3.65e-80, 7.82e-203j)
| (2.9356458062936151475e-05 - 1.5561768622955371709e-587j)  +/-  (4.55e-74, 9.75e-197j)
| (2.404230500376047618e-14 + 2.2445820577447255278e-592j)  +/-  (1.13e-80, 2.42e-203j)
| (0.071639830618902989943 + 1.0816337407268942231e-585j)  +/-  (5.76e-63, 1.23e-185j)
| (0.034774909665411690674 - 1.0751989318766866611e-585j)  +/-  (1.36e-65, 2.92e-188j)
| (2.4225418860931792205e-08 + 7.2372670128586057498e-590j)  +/-  (5.22e-76, 1.12e-198j)
| (0.003886186075548725695 - 6.929355547087721955e-586j)  +/-  (2.54e-69, 5.44e-192j)
| (2.9356458062936151475e-05 - 6.4542204539799477023e-588j)  +/-  (2.99e-73, 6.4e-196j)
| (0.01337909870064659675 + 1.1865814938477702812e-585j)  +/-  (5.66e-69, 1.21e-191j)
| (0.00018283029409514498466 + 5.4568984095243167367e-587j)  +/-  (2.36e-74, 5.05e-197j)
| (2.8382983770806548469e-16 - 2.7198673708579378891e-593j)  +/-  (1.75e-82, 3.75e-205j)
| (0.034774909665411690674 - 7.5010161203064471753e-586j)  +/-  (1.15e-69, 2.47e-192j)
| (0.01337909870064659675 + 7.5781997608993175307e-586j)  +/-  (2.23e-70, 4.79e-193j)
| (0.18046203697446641236 - 1.1038720932322542051e-585j)  +/-  (1.82e-68, 3.91e-191j)
| (0.11975121830997262537 - 1.1158662758250768766e-585j)  +/-  (5.34e-69, 1.14e-191j)
| (4.8856373464525989362e-11 + 2.0367570621919056678e-591j)  +/-  (1.57e-79, 3.36e-202j)
| (3.6173023921382073967e-06 + 1.576920434245371705e-588j)  +/-  (1.79e-75, 3.84e-198j)
| (0.071639830618902989943 + 8.2614770582687225079e-586j)  +/-  (1.87e-70, 4.02e-193j)
| (2.4225418860931792205e-08 + 2.5466843806390843286e-589j)  +/-  (1.95e-80, 4.17e-203j)
| (0.00085186250174896475405 - 1.9426678350889580238e-586j)  +/-  (6.07e-76, 1.3e-198j)
| (1.3157566987108921876e-12 - 1.5987187953486122683e-591j)  +/-  (1.04e-82, 2.24e-205j)
| (3.4070134102139214689e-07 - 1.092376894287257047e-588j)  +/-  (3.18e-80, 6.8e-203j)
| (0.16288833020323650142 + 1.0336958980321904151e-585j)  +/-  (8.99e-76, 1.66e-198j)
| (1.3157566987108921876e-12 - 2.7142075750917868837e-592j)  +/-  (2.89e-83, 6.12e-206j)
| (3.6173023921382073967e-06 + 4.2720622733248916646e-588j)  +/-  (1.39e-79, 2.99e-202j)
| (0.16288833020323650142 + 1.1303966414189485622e-585j)  +/-  (6.99e-76, 1.17e-198j)
