Starting with polynomial:
P : 2*t
Extension levels are: 1 4 42
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^47 - 6042082028238263961637701173651/6062989709009127413615092763*t^45 + 52223877439453078662870319733319555/230393608942346841717373524994*t^43 - 14398492116015867143560046342882102415/460787217884693683434747049988*t^41 + 207237263468932259836752648757147139475/70890341213029797451499546152*t^39 - 1469792988804031235541802727880437157345/7462141180318926047526268016*t^37 + 147745609997502383846464291221740937595515/14924282360637852095052536032*t^35 - 11323851931734135557003805728872894783589775/29848564721275704190105072064*t^33 + 335409429141776005417497744866680104834281475/29848564721275704190105072064*t^31 - 15478991415043210444586521556461364812281940875/59697129442551408380210144128*t^29 + 558480619033498695720799461100744730018242071225/119394258885102816760420288256*t^27 - 15752812414778707395811676122703938072271219981325/238788517770205633520840576512*t^25 + 346244620237813618703200371824213820612832693220625/477577035540411267041681153024*t^23 - 5892723240500802924927144540225297696901947771830625/955154071080822534083362306048*t^21 + 76907397856737809717236622688820071509020863840946875/1910308142161645068166724612096*t^19 - 759541446273408159992371784224450459495735936934649375/3820616284323290136333449224192*t^17 + 11152799106172287692772797742601924263831764719252231875/15282465137293160545333796896768*t^15 - 59457406625701624494136965852498445155553264857578446875/30564930274586321090667593793536*t^13 + 223033480663511672359435075630979650790966480231473715625/61129860549172642181335187587072*t^11 - 563476573862874596760432912434651623236225866268436078125/122259721098345284362670375174144*t^9 + 898893692825998097097524089690322801623793677594473778125/244519442196690568725340750348288*t^7 - 816029399917821761606448883369480451411849857192597978125/489038884393381137450681500696576*t^5 + 348029524649384212588888010645384486904261408217071609375/978077768786762274901363001393152*t^3 - 44335989471845965337836263429333145906504114639289671875/1956155537573524549802726002786304*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:   47 out of 47
Indefinite weights: 0 out of 47
Negative weights:   0 out of 47
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-6.9305269929773580707 + 8.5582263936721213456e-956j)  +/-  (7.96e-245, 7.96e-245j)
| (-8.6600529221072540559 - 5.6275848683520471965e-958j)  +/-  (2.98e-247, 2.98e-247j)
| (-7.4299150617528948146 + 2.8920314308390207256e-956j)  +/-  (2.47e-245, 2.47e-245j)
| (-5.61821557198292749 - 1.1489160788065951339e-955j)  +/-  (3.52e-244, 3.52e-244j)
| (-6.4686448389412546961 - 1.8964069933163822487e-955j)  +/-  (1.74e-244, 1.74e-244j)
| (5.61821557198292749 - 1.5446017059803119221e-953j)  +/-  (3.49e-244, 3.49e-244j)
| (7.4299150617528948146 - 8.36274841362483424e-963j)  +/-  (2.53e-245, 2.53e-245j)
| (6.4686448389412546961 - 2.1676537377059777314e-961j)  +/-  (1.84e-244, 1.84e-244j)
| (8.6600529221072540559 + 7.457959677963673498e-965j)  +/-  (3.45e-247, 3.45e-247j)
| (7.9879476427766499043 + 9.027257658723309652e-964j)  +/-  (4.33e-246, 4.33e-246j)
| (-7.9879476427766499043 + 2.5598115075911730966e-964j)  +/-  (4.44e-246, 4.44e-246j)
| (6.9305269929773580707 + 1.0228010974463590094e-962j)  +/-  (8.17e-245, 8.17e-245j)
| (-5.2188348434386563853 + 5.1021075912189703021e-962j)  +/-  (3.32e-244, 3.32e-244j)
| (4.8322150740234293752 - 9.2315642874207032913e-961j)  +/-  (2.62e-244, 2.62e-244j)
| (4.4561276555810791919 + 1.1340304350627910499e-968j)  +/-  (1.72e-244, 1.72e-244j)
| (4.0888774863754493962 - 8.7632307769824630606e-977j)  +/-  (8.77e-245, 8.77e-245j)
| (2.6863287382718186034 - 1.5305834241321673497e-984j)  +/-  (1.07e-246, 1.07e-246j)
| (-4.4561276555810791919 + 5.0849448592224445626e-991j)  +/-  (1.66e-244, 1.66e-244j)
| (-4.8322150740234293752 - 1.8656171893575756651e-992j)  +/-  (2.65e-244, 2.65e-244j)
| (-2.6863287382718186034 - 1.2429627253429293353e-992j)  +/-  (1.06e-246, 1.06e-246j)
| (-6.0333840573827062251 + 1.4827347212682359313e-994j)  +/-  (2.78e-244, 2.78e-244j)
| (0.95857246461381850711 - 3.1207956988176527737e-1001j)  +/-  (4.13e-251, 4.13e-251j)
| (5.2188348434386563853 - 7.4681149304271863496e-993j)  +/-  (3.31e-244, 3.31e-244j)
| (-3.3759289780279881732 - 2.9519147031958072076e-1006j)  +/-  (1.37e-245, 1.37e-245j)
| (-1.2367109497576824164 - 5.2350515280643117244e-1014j)  +/-  (6.58e-250, 6.58e-250j)
| (-4.0888774863754493962 - 2.0275105170628894731e-1010j)  +/-  (8.69e-245, 8.69e-245j)
| (0.64495882275284201358 - 4.2890240606809660405e-1015j)  +/-  (2.04e-252, 2.04e-252j)
| (4.0493976404027007402e-1015 + 7.9397990301313453973e-1015j)  +/-  (4.19e-1013, 4.19e-1013j)
| (-3.028464551774431644 + 1.2447880536073287928e-1009j)  +/-  (4.33e-246, 4.33e-246j)
| (-0.64495882275284201358 + 1.5880512972956492488e-1018j)  +/-  (1.95e-252, 1.95e-252j)
| (6.0333840573827062251 - 2.8381161339817827012e-1011j)  +/-  (2.97e-244, 2.97e-244j)
| (2.3496634583833435155 - 5.664627482006874265e-1022j)  +/-  (2.65e-247, 2.65e-247j)
| (0.32346479464420107477 + 2.740073831929449704e-1041j)  +/-  (1.01e-253, 1.01e-253j)
| (2.0201828704560856329 - 1.3426863594127765892e-1032j)  +/-  (5.42e-248, 5.42e-248j)
| (-2.3496634583833435155 + 4.5538457646737462238e-1038j)  +/-  (2.47e-247, 2.47e-247j)
| (1.2367109497576824164 - 1.260872799188591404e-1043j)  +/-  (6.13e-250, 6.13e-250j)
| (3.7291504046610640534 + 5.8491617412525182603e-1053j)  +/-  (4.07e-245, 4.07e-245j)
| (1.7062245074049517026 - 1.9104010850432879257e-1074j)  +/-  (1.23e-248, 1.23e-248j)
| (-3.7291504046610640534 + 2.0836840998595978977e-1072j)  +/-  (3.84e-245, 3.84e-245j)
| (1.4458788358072834206 + 6.121421590987130536e-1076j)  +/-  (3.03e-249, 3.03e-249j)
| (-1.7062245074049517026 - 2.7173334794412647394e-1078j)  +/-  (1.24e-248, 1.24e-248j)
| (-2.0201828704560856329 + 1.4755702032242082002e-1075j)  +/-  (5.56e-248, 5.56e-248j)
| (3.3759289780279881732 - 1.1831654562917767587e-1077j)  +/-  (1.35e-245, 1.35e-245j)
| (-1.4458788358072834206 - 4.6987140198631665381e-1088j)  +/-  (3.1e-249, 3.1e-249j)
| (3.028464551774431644 + 8.670448607847230083e-1087j)  +/-  (4.23e-246, 4.23e-246j)
| (-0.32346479464420107477 + 5.1592235756001977244e-1093j)  +/-  (1.01e-253, 1.01e-253j)
| (-0.95857246461381850711 + 6.7160191193127281234e-1091j)  +/-  (4.13e-251, 4.13e-251j)
-------------------------------------------------
The weights are:
| (3.7237601014019463774e-22 - 1.1000271012832244275e-972j)  +/-  (4.51e-73, 8.91e-196j)
| (1.1758416090148482335e-33 + 1.0463461526754746818e-978j)  +/-  (4.22e-78, 8.35e-201j)
| (3.1327039947964453807e-25 + 2.6100548816772389193e-974j)  +/-  (1.01e-74, 2e-197j)
| (4.4922260439109058812e-15 + 3.0720948131599154556e-969j)  +/-  (1.12e-70, 2.22e-193j)
| (1.6967060051581689336e-19 + 2.8769120434707814598e-971j)  +/-  (1.82e-72, 3.6e-195j)
| (4.4922260439109058812e-15 + 4.1600349137841298798e-967j)  +/-  (1e-74, 1.98e-197j)
| (3.1327039947964453807e-25 - 1.7836348028307853654e-973j)  +/-  (2.37e-80, 4.68e-203j)
| (1.6967060051581689336e-19 - 3.7282003479262732284e-970j)  +/-  (6.68e-78, 1.32e-200j)
| (1.1758416090148482335e-33 - 4.7502965336077482566e-978j)  +/-  (2.8e-84, 5.53e-207j)
| (6.5833349762053062922e-29 + 1.7027955768668359331e-975j)  +/-  (2.43e-82, 4.79e-205j)
| (6.5833349762053062922e-29 - 3.091085414791311299e-976j)  +/-  (4.53e-82, 8.96e-205j)
| (3.7237601014019463774e-22 + 9.8048489976243545856e-972j)  +/-  (1.27e-79, 2.5e-202j)
| (3.2869926125040005956e-13 - 5.1103670197757503877e-968j)  +/-  (3.74e-76, 7.39e-199j)
| (1.5541046331493630956e-11 + 7.1698601220825739048e-966j)  +/-  (6.77e-76, 1.34e-198j)
| (4.9828166853307267506e-10 - 3.2768281280239577769e-965j)  +/-  (2.87e-75, 5.67e-198j)
| (1.1239619716755752628e-08 + 1.4311886778674949784e-964j)  +/-  (1.07e-74, 2.11e-197j)
| (0.00014068118327174643177 + 2.2970179501171197055e-962j)  +/-  (6.23e-71, 1.23e-193j)
| (4.9828166853307267506e-10 - 3.5372188739852191492e-966j)  +/-  (6.26e-78, 1.24e-200j)
| (1.5541046331493630956e-11 + 4.8584508331182069267e-967j)  +/-  (1.84e-78, 3.64e-201j)
| (0.00014068118327174643177 + 7.9579840163051166826e-963j)  +/-  (2.61e-74, 5.15e-197j)
| (3.7160972558973831821e-17 - 5.6181703067435502585e-970j)  +/-  (3.64e-81, 7.19e-204j)
| (0.068505641787363872837 + 1.6033101773804017296e-960j)  +/-  (4.14e-68, 8.19e-191j)
| (3.2869926125040005956e-13 - 1.7387957901903844078e-966j)  +/-  (3e-80, 5.92e-203j)
| (2.2191319251198704206e-06 + 5.1639444212559967471e-964j)  +/-  (6.86e-77, 1.36e-199j)
| (0.029155605598868900478 - 1.1971329587681560521e-960j)  +/-  (2.15e-69, 4.25e-192j)
| (1.1239619716755752628e-08 + 2.1499544369441992182e-965j)  +/-  (3.52e-78, 6.95e-201j)
| (0.11883187986015956987 - 1.3899253566888323803e-960j)  +/-  (2.42e-68, 4.78e-191j)
| (0.1826364553410499092 - 1.2105986390761232139e-960j)  +/-  (1.13e-68, 2.23e-191j)
| (2.0219510304902156373e-05 - 2.1219079324633913126e-963j)  +/-  (3.31e-76, 6.55e-199j)
| (0.11883187986015956987 - 1.0997800134513005734e-960j)  +/-  (3.39e-69, 6.71e-192j)
| (3.7160972558973831821e-17 + 1.3077463959176087033e-968j)  +/-  (4.47e-83, 8.83e-206j)
| (0.00075326600935467513981 - 6.9189046248162254809e-962j)  +/-  (3.42e-76, 6.77e-199j)
| (0.1640950637155770124 + 1.2855553979050918882e-960j)  +/-  (4.24e-70, 8.37e-193j)
| (0.0030899253554689836762 + 2.0512667890489994232e-961j)  +/-  (1.85e-75, 3.66e-198j)
| (0.00075326600935467513981 - 2.79484567327865905e-962j)  +/-  (8.4e-77, 1.66e-199j)
| (0.029155605598868900478 - 1.8861226606199846627e-960j)  +/-  (4.76e-73, 9.4e-196j)
| (1.8353984674361813653e-07 - 5.7692146551065706807e-964j)  +/-  (5.43e-80, 1.07e-202j)
| (0.0091481797567925240216 - 6.2104263626626598732e-961j)  +/-  (3.09e-75, 6.1e-198j)
| (1.8353984674361813653e-07 - 1.1243198057464729546e-964j)  +/-  (1.86e-79, 3.67e-202j)
| (0.014938895126765334457 + 1.4779042406422289101e-960j)  +/-  (1.26e-74, 2.49e-197j)
| (0.0091481797567925240216 - 3.2834775908651962477e-961j)  +/-  (4.68e-77, 9.24e-200j)
| (0.0030899253554689836762 + 9.5419469725699762139e-962j)  +/-  (2.04e-77, 4.03e-200j)
| (2.2191319251198704206e-06 + 2.1316909522694663743e-963j)  +/-  (1.92e-80, 3.8e-203j)
| (0.014938895126765334457 + 8.656391007790906447e-961j)  +/-  (2.34e-77, 4.54e-200j)
| (2.0219510304902156373e-05 - 7.2506230200143858039e-963j)  +/-  (8.37e-80, 1.66e-202j)
| (0.1640950637155770124 + 1.14357954020923235e-960j)  +/-  (2.79e-77, 5.73e-200j)
| (0.068505641787363872837 + 1.1299039469046946867e-960j)  +/-  (1.51e-77, 2.83e-200j)
