Starting with polynomial:
P : 2*t
Extension levels are: 1 4 44
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^49 - 61590049535862924641497219533608/56494332485152163715384612507*t^47 + 307852749100768046199020543858468747/1129886649703043274307692250140*t^45 - 3123663287437107917876100337863411291/75325776646869551620512816676*t^43 + 31645585854122679237800228646697320273/7348856258231175767854908944*t^41 - 1190355815632491372933685746980864831895/3674428129115587883927454472*t^39 + 537963214392409965951508079452412224196295/29395425032924703071419635776*t^37 - 23344823251379959524798027835688605429205103/29395425032924703071419635776*t^35 + 3158428926537925909642707700934876483123994645/117581700131698812285678543104*t^33 - 10502879198275793312688328170630311352880210455/14697712516462351535709817888*t^31 + 3533469931471329402486110183919952499429498153625/235163400263397624571357086208*t^29 - 58820055816544960334901304757686828631402507512875/235163400263397624571357086208*t^27 + 3096852148562811384110219462735397508296135471599205/940653601053590498285428344832*t^25 - 16051953839119144441433955380084837941166924020564125/470326800526795249142714172416*t^23 + 1041511817189199704855112129649349139399274473042735375/3762614404214361993141713379328*t^21 - 6545308313033308849628520348806650658834784128157241875/3762614404214361993141713379328*t^19 + 62911599183955899479014856536513732256053680803220864375/7525228808428723986283426758656*t^17 - 28396976294352118182651606062659946255289498907565332875/940653601053590498285428344832*t^15 + 9632007991160519811330377225600717806909571862343186310625/120403660934859583780534828138496*t^13 - 18134813288825223363929480956006184305339231150481418474375/120403660934859583780534828138496*t^11 + 92689299230875297371975534133246598268480133935574534603125/481614643739438335122139312553984*t^9 - 37535905358280810341528099566431683259284703002806855134375/240807321869719167561069656276992*t^7 + 138149857479073923452261846983608002763684475430027209756875/1926458574957753340488557250215936*t^5 - 29601355885806575564973518171682031015105879875050905096875/1926458574957753340488557250215936*t^3 + 7465654899722296102680431273677860245955743092686350728125/7705834299831013361954229000863744*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
-------------------------------------------------
The nodes are:
| (8.206395407096240315 - 3.9608869409757163347e-861j)  +/-  (1.17e-245, 1.17e-245j)
| (-4.3452804727189327921 + 7.4722851719311861591e-865j)  +/-  (3.87e-244, 3.87e-244j)
| (7.6529738701188774367 - 2.5120219860663603189e-874j)  +/-  (6.7e-245, 6.7e-245j)
| (-7.1579128146404592182 - 9.4128370828486211463e-877j)  +/-  (2.18e-244, 2.18e-244j)
| (-8.873237085323068141 + 2.2016248582111475028e-883j)  +/-  (7.54e-247, 7.54e-247j)
| (8.873237085323068141 - 8.6259717480808782782e-885j)  +/-  (7.92e-247, 7.92e-247j)
| (-4.7082870174283741447 + 8.1832448243658232563e-886j)  +/-  (6.65e-244, 6.65e-244j)
| (-8.206395407096240315 + 1.8059846531189465031e-892j)  +/-  (1.09e-245, 1.09e-245j)
| (-1.5783970593652765233 + 1.8641340248035410583e-894j)  +/-  (9.27e-249, 9.27e-249j)
| (5.4626966130007127616 + 6.5726407208318194511e-889j)  +/-  (1.28e-243, 1.28e-243j)
| (2.0201828704560856329 - 3.4192282308531281959e-897j)  +/-  (2.24e-247, 2.24e-247j)
| (-1.8184545638776486156 - 1.6118520708310750286e-897j)  +/-  (6.68e-248, 6.68e-248j)
| (4.7082870174283741447 - 1.3449472261241696993e-892j)  +/-  (7.3e-244, 7.3e-244j)
| (2.9610768574002897801 - 2.3537875706680283911e-896j)  +/-  (7.76e-246, 7.76e-246j)
| (5.8579841154924660531 + 2.8982319445398402294e-893j)  +/-  (1.22e-243, 1.22e-243j)
| (-7.6529738701188774367 - 8.9668534277232694745e-897j)  +/-  (6.78e-245, 6.78e-245j)
| (-3.2982813032086903325 + 1.3387178504373987129e-896j)  +/-  (2.42e-245, 2.42e-245j)
| (-3.9898874504411230848 + 7.5783850778893385759e-908j)  +/-  (1.72e-244, 1.72e-244j)
| (-0.95857246461381850711 - 1.9327647903916316025e-927j)  +/-  (3.82e-251, 3.82e-251j)
| (0.95857246461381850711 - 1.1972393989951482522e-926j)  +/-  (3.79e-251, 3.79e-251j)
| (-5.0802003622439982026 + 4.2276606205645534899e-924j)  +/-  (1.01e-243, 1.01e-243j)
| (-6.2690655215105122789 - 2.4341986069627570863e-936j)  +/-  (9.05e-244, 9.05e-244j)
| (-2.3882968416543099199e-957 - 2.0581310391736470129e-957j)  +/-  (1.54e-955, 1.54e-955j)
| (-1.27486855766973223 - 3.5776934946636684873e-944j)  +/-  (6.26e-250, 6.26e-250j)
| (4.3452804727189327921 + 6.920335957799355233e-937j)  +/-  (3.6e-244, 3.6e-244j)
| (1.5783970593652765233 - 9.5252463631925616528e-949j)  +/-  (1.07e-248, 1.07e-248j)
| (3.2982813032086903325 + 2.9338998620203513738e-943j)  +/-  (2.62e-245, 2.62e-245j)
| (7.1579128146404592182 - 7.265634196323890052e-944j)  +/-  (2.26e-244, 2.26e-244j)
| (6.7002138287588986581 - 1.1449880834814887667e-948j)  +/-  (5.19e-244, 5.19e-244j)
| (3.6411194618264442261 + 1.994596765538132369e-956j)  +/-  (7.07e-245, 7.07e-245j)
| (6.2690655215105122789 - 3.8354499469809643583e-956j)  +/-  (8.76e-244, 8.76e-244j)
| (-0.63954463840103227937 - 6.3991966310112919488e-967j)  +/-  (1.99e-252, 1.99e-252j)
| (2.309063293626945693 + 6.3797996344431330944e-962j)  +/-  (7.12e-247, 7.12e-247j)
| (-2.0201828704560856329 - 4.8331272035101441382e-962j)  +/-  (2.08e-247, 2.08e-247j)
| (-5.4626966130007127616 - 1.1854048525397107197e-957j)  +/-  (1.25e-243, 1.25e-243j)
| (-2.6300853468891272379 + 1.5230259274858378211e-966j)  +/-  (2.34e-246, 2.34e-246j)
| (-3.6411194618264442261 - 6.9196021755518369912e-965j)  +/-  (7.1e-245, 7.1e-245j)
| (2.6300853468891272379 - 8.0888035531302700824e-968j)  +/-  (2.35e-246, 2.35e-246j)
| (-6.7002138287588986581 - 7.3089040435878961508e-964j)  +/-  (5.46e-244, 5.46e-244j)
| (-2.309063293626945693 + 1.6365819350879580143e-976j)  +/-  (6.48e-247, 6.48e-247j)
| (-5.8579841154924660531 + 3.5827850235869606733e-972j)  +/-  (1.2e-243, 1.2e-243j)
| (1.8184545638776486156 - 5.8981228999488605497e-979j)  +/-  (6.73e-248, 6.73e-248j)
| (1.27486855766973223 - 3.5035159720282486373e-981j)  +/-  (5.61e-250, 5.61e-250j)
| (0.31984560625443223103 - 3.3868757870361095268e-986j)  +/-  (7.97e-254, 7.97e-254j)
| (5.0802003622439982026 - 4.915699876872021808e-977j)  +/-  (9.58e-244, 9.58e-244j)
| (-0.31984560625443223103 + 2.4675438659281388002e-994j)  +/-  (7.97e-254, 7.97e-254j)
| (-2.9610768574002897801 - 2.0542328744846761573e-986j)  +/-  (7.74e-246, 7.74e-246j)
| (3.9898874504411230848 - 1.059035030112984549e-989j)  +/-  (1.76e-244, 1.76e-244j)
| (0.63954463840103227937 + 2.7181079132314307186e-999j)  +/-  (2.04e-252, 2.04e-252j)
-------------------------------------------------
The weights are:
| (1.8991654423021864049e-30 - 7.0955160218371453439e-886j)  +/-  (9.58e-83, 5.96e-204j)
| (1.2776684236960286107e-09 + 4.684433055788854808e-873j)  +/-  (1.56e-70, 9.69e-192j)
| (1.0742301660255568066e-26 + 6.4715215086450520889e-884j)  +/-  (2.16e-81, 1.34e-202j)
| (1.4991588504618397384e-23 + 1.1894676709520154429e-881j)  +/-  (3.35e-81, 2.09e-202j)
| (2.7779046834954628315e-35 - 6.3854462878090810259e-888j)  +/-  (4.63e-86, 2.88e-207j)
| (2.7779046834954628315e-35 + 2.1873482548858785817e-888j)  +/-  (5.04e-86, 3.14e-207j)
| (4.8856373464525989362e-11 + 4.2421814699911090283e-874j)  +/-  (6.22e-74, 3.87e-195j)
| (1.8991654423021864049e-30 + 2.3068110453070383351e-885j)  +/-  (2.47e-84, 1.54e-205j)
| (0.01337909870064659675 - 1.5245999954281063039e-869j)  +/-  (9.24e-57, 5.75e-178j)
| (2.404230500376047618e-14 - 2.4719098408524869169e-877j)  +/-  (2.18e-78, 1.36e-199j)
| (0.0023813751281237155234 - 3.4643747154387193887e-870j)  +/-  (1.15e-62, 7.17e-184j)
| (0.003886186075548725695 + 1.5684506172910466135e-869j)  +/-  (2.79e-60, 1.74e-181j)
| (4.8856373464525989362e-11 - 1.7009165022735842375e-875j)  +/-  (1.9e-76, 1.18e-197j)
| (2.9356458062936151475e-05 + 5.6955061809693758272e-872j)  +/-  (1.15e-69, 7.18e-191j)
| (2.8382983770806548469e-16 + 2.2078995723127621405e-878j)  +/-  (9.77e-80, 6.08e-201j)
| (1.0742301660255568066e-26 - 2.3475088876147842725e-883j)  +/-  (8.75e-85, 5.44e-206j)
| (3.6173023921382073967e-06 - 1.0034363890024328228e-871j)  +/-  (2.58e-72, 1.6e-193j)
| (2.4225418860931792205e-08 - 1.4464641226468547474e-872j)  +/-  (1.14e-74, 7.06e-196j)
| (0.071639830618902989943 - 1.2615388081007511722e-869j)  +/-  (1.61e-62, 1e-183j)
| (0.071639830618902989943 - 8.0553935549415151269e-870j)  +/-  (3.83e-63, 2.38e-184j)
| (1.3157566987108921876e-12 - 2.8798531414002006225e-875j)  +/-  (1.09e-78, 6.76e-200j)
| (2.0260865922335267653e-18 + 8.5194022391293138077e-879j)  +/-  (1.18e-82, 7.32e-204j)
| (0.18046203697446641236 + 1.1586171404054498568e-869j)  +/-  (4.69e-63, 2.92e-184j)
| (0.034774909665411690674 + 1.312644058265689551e-869j)  +/-  (6.1e-63, 3.79e-184j)
| (1.2776684236960286107e-09 + 1.0985579329819395126e-874j)  +/-  (5.77e-79, 3.59e-200j)
| (0.01337909870064659675 - 7.1212321059629578708e-870j)  +/-  (2.01e-67, 1.25e-188j)
| (3.6173023921382073967e-06 - 1.3744845605764507369e-872j)  +/-  (7.85e-76, 4.88e-197j)
| (1.4991588504618397384e-23 - 2.9083260976057751971e-882j)  +/-  (3.19e-87, 1.98e-208j)
| (7.9650440260047511088e-21 + 8.0491774420268204492e-881j)  +/-  (2.47e-86, 1.53e-207j)
| (3.4070134102139214689e-07 + 3.0649292787355038474e-873j)  +/-  (6.35e-79, 3.95e-200j)
| (2.0260865922335267653e-18 - 1.5440820361214772217e-879j)  +/-  (3.05e-85, 1.9e-206j)
| (0.11975121830997262537 + 1.2506311088786869841e-869j)  +/-  (2.7e-70, 1.68e-191j)
| (0.00085186250174896475405 + 9.0195403956410215588e-871j)  +/-  (3.26e-75, 2.03e-196j)
| (0.0023813751281237155234 - 9.4844900990192132705e-870j)  +/-  (3e-75, 1.86e-196j)
| (2.404230500376047618e-14 + 2.1696939101603597825e-876j)  +/-  (1.09e-85, 6.79e-207j)
| (0.00018283029409514498466 - 9.1785683276545119845e-871j)  +/-  (7.42e-79, 4.62e-200j)
| (3.4070134102139214689e-07 + 3.4761631996931830034e-872j)  +/-  (3.44e-81, 2.14e-202j)
| (0.00018283029409514498466 - 2.2569455907409010178e-871j)  +/-  (3.39e-79, 2.11e-200j)
| (7.9650440260047511088e-21 - 3.7753809828398424487e-880j)  +/-  (1.3e-89, 8.07e-211j)
| (0.00085186250174896475405 + 2.9475819379355105111e-870j)  +/-  (4.98e-79, 3.09e-200j)
| (2.8382983770806548469e-16 - 1.4892453216691987169e-877j)  +/-  (3.28e-87, 2.04e-208j)
| (0.003886186075548725695 + 6.4298663829124844028e-870j)  +/-  (8.01e-79, 4.97e-200j)
| (0.034774909665411690674 + 7.1712623230062973087e-870j)  +/-  (1.14e-78, 7.06e-200j)
| (0.16288833020323650142 - 1.055731354131736695e-869j)  +/-  (1.25e-78, 7.53e-200j)
| (1.3157566987108921876e-12 + 2.2454619572877960016e-876j)  +/-  (1.37e-86, 8.51e-208j)
| (0.16288833020323650142 - 1.2235002012474881686e-869j)  +/-  (6.19e-79, 3.61e-200j)
| (2.9356458062936151475e-05 + 3.0063097272617388347e-871j)  +/-  (1.22e-81, 7.25e-203j)
| (2.4225418860931792205e-08 - 6.1673911709319834088e-874j)  +/-  (2.95e-84, 1.88e-205j)
| (0.11975121830997262537 + 9.2972320463875923534e-870j)  +/-  (2.49e-79, 1.4e-200j)
