Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 5 30
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 16*t^9 - 168*t^7 + 432*t^5 - 270*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^39 - 4054133533663046530151764713664689659180736096/845539399497391266332019985565096931719317*t^37 + 7023031957800301457157822188923678108203167577792/10992012193466086462316259812346260112351121*t^35 - 551028601925426430966690807090096301755031092114990/10992012193466086462316259812346260112351121*t^33 + 28417359252958387656608830349226950037051580644050790/10992012193466086462316259812346260112351121*t^31 - 1018637537094272337153959713516617541811907066560662185/10992012193466086462316259812346260112351121*t^29 + 52360852535354521421543673746556571828123593861406333635/21984024386932172924632519624692520224702242*t^27 - 151014182718084970298872877634976968081580988099364068985/3382157597989565065328079942260387726877268*t^25 + 1040854391549818612415399457333198011798167567474015417125/1691078798994782532664039971130193863438634*t^23 - 84521705696773165991418370592913404572374974569648610215125/13528630391958260261312319769041550907509072*t^21 + 1258263711542387363536960206931767222811528413861758925238875/27057260783916520522624639538083101815018144*t^19 - 3402052799052889226532561688833328002894648630886648439866125/13528630391958260261312319769041550907509072*t^17 + 105336772061017272862371670991159509336962047285376324149546625/108229043135666082090498558152332407260072576*t^15 - 571018262494109043336039626319764962494729314260903114789794375/216458086271332164180997116304664814520145152*t^13 + 2100722041199728944394008291122124133751396379653976519087298125/432916172542664328361994232609329629040290304*t^11 - 5008989108836112745761702006183010664472881073219548361995424375/865832345085328656723988465218659258080580608*t^9 + 14462380397535414513503124333658476281847856340206058957955751875/3463329380341314626895953860874637032322322432*t^7 - 5728439596622854641284299259043482469763140394825136645014160625/3463329380341314626895953860874637032322322432*t^5 + 2174499594116370881128893693681099296900937308817535855397540625/6926658760682629253791907721749274064644644864*t^3 - 598452682048084449352711595522475942733186027630331044574053125/27706635042730517015167630886997096258578579456*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (5.6812500504534697218 + 6.857696974276737768e-471j)  +/-  (3.88e-119, 3.88e-119j)
| (6.7953420947431972221 - 8.1639877847620796751e-478j)  +/-  (4e-120, 4e-120j)
| (-5.1923028937702425722 + 7.4380462583197928473e-482j)  +/-  (6.02e-119, 6.02e-119j)
| (3.0384026365052064709 - 1.5509050459550308525e-484j)  +/-  (6.91e-120, 6.91e-120j)
| (5.1923028937702425722 + 1.9226237615159577908e-487j)  +/-  (5.86e-119, 5.86e-119j)
| (-6.2082552986777274313 + 1.7924864535245794543e-493j)  +/-  (1.61e-119, 1.61e-119j)
| (-6.7953420947431972221 + 8.0377797571480075156e-494j)  +/-  (4.27e-120, 4.27e-120j)
| (-3.8602665808680072228 + 3.759908271666223991e-493j)  +/-  (3.45e-119, 3.45e-119j)
| (2.6384291054842239697 - 2.0306147351509664955e-496j)  +/-  (2.52e-120, 2.52e-120j)
| (-4.2875587399760920162 - 8.284916867422916327e-494j)  +/-  (5.7e-119, 5.7e-119j)
| (4.7300328893488555147 + 3.8671163011146403844e-498j)  +/-  (6.94e-119, 6.94e-119j)
| (-3.4447880879663715265 + 4.2515304777882917931e-506j)  +/-  (1.74e-119, 1.74e-119j)
| (1.6506801238857845559 + 2.9357789848879698118e-511j)  +/-  (8.48e-121, 8.48e-121j)
| (-4.7300328893488555147 + 2.2976795217009388548e-508j)  +/-  (6.65e-119, 6.65e-119j)
| (2.2403576384084485833 + 1.0696711890516363272e-510j)  +/-  (7.91e-121, 7.91e-121j)
| (-7.5001896510094169925 + 2.2835943687572976015e-511j)  +/-  (4.79e-121, 4.79e-121j)
| (7.5001896510094169925 + 9.2176252358380544137e-511j)  +/-  (4.61e-121, 4.61e-121j)
| (-1.5845339300529355491 - 7.2419246456889750017e-515j)  +/-  (4.89e-121, 4.89e-121j)
| (-1.1293857510265105724 + 2.3659186732501871148e-517j)  +/-  (2.61e-123, 2.61e-123j)
| (-2.6384291054842239697 - 1.4867278621602465598e-514j)  +/-  (2.43e-120, 2.43e-120j)
| (1.1293857510265105724 + 2.8886848790626800696e-522j)  +/-  (2.86e-123, 2.86e-123j)
| (1.5845339300529355491 - 9.9844331751529497904e-520j)  +/-  (4.39e-121, 4.39e-121j)
| (6.2082552986777274313 + 5.7008082150718928415e-519j)  +/-  (1.55e-119, 1.55e-119j)
| (-1.6506801238857845559 - 1.9105194039683391374e-524j)  +/-  (8.34e-121, 8.34e-121j)
| (-2.2403576384084485833 + 4.0235601714659565811e-525j)  +/-  (8.19e-121, 8.19e-121j)
| (4.2875587399760920162 + 6.1272707910455623028e-522j)  +/-  (5.05e-119, 5.05e-119j)
| (1.8007534752684395135 + 1.7160541726672213532e-529j)  +/-  (6.33e-121, 6.33e-121j)
| (3.8602665808680072228 - 2.6964384331040278306e-527j)  +/-  (3.52e-119, 3.52e-119j)
| (-1.8007534752684395135 - 5.5851246942601090141e-534j)  +/-  (5.85e-121, 5.85e-121j)
| (-0.73395630342256598469 - 3.5196142389482839634e-538j)  +/-  (2.23e-124, 2.23e-124j)
| (-5.6812500504534697218 + 3.0890472963553070414e-533j)  +/-  (3.95e-119, 3.95e-119j)
| (3.4447880879663715265 - 3.2341931563588161206e-534j)  +/-  (1.81e-119, 1.81e-119j)
| (0.52464762327529031788 - 1.9689895916407223657e-539j)  +/-  (7.7e-125, 7.7e-125j)
| (-3.0384026365052064709 + 2.9082853787284762351e-539j)  +/-  (7.11e-120, 7.11e-120j)
| (-0.39677551259507194687 - 2.1553687879651422886e-545j)  +/-  (1.84e-125, 1.84e-125j)
| (-0.52464762327529031788 + 4.3633464603345389404e-545j)  +/-  (8.33e-125, 8.33e-125j)
| (0.39677551259507194687 + 2.4997489436982680557e-544j)  +/-  (1.84e-125, 1.84e-125j)
| (0.73395630342256598469 + 1.9336644168808080001e-543j)  +/-  (2.33e-124, 2.33e-124j)
| (-2.6505248156648052582e-607 - 6.3795279904663641458e-608j)  +/-  (1.06e-605, 1.06e-605j)
-------------------------------------------------
The weights are:
| (2.7391003267531170491e-15 - 1.2062989170579644825e-484j)  +/-  (5.27e-30, 9.75e-89j)
| (3.1384867207094217919e-21 + 8.5490226344744662281e-489j)  +/-  (3.23e-33, 5.98e-92j)
| (5.2335703237283023214e-13 + 3.4941509924279180447e-485j)  +/-  (1.96e-30, 3.62e-89j)
| (2.2235034755781654552e-05 - 1.0503751598611939846e-479j)  +/-  (1.19e-21, 2.2e-80j)
| (5.2335703237283023214e-13 + 7.7705402416479060967e-484j)  +/-  (6.69e-29, 1.24e-87j)
| (5.6821220426538584002e-18 + 4.9621700862594217977e-488j)  +/-  (9.22e-34, 1.71e-92j)
| (3.1384867207094217919e-21 - 7.6338137534157326501e-490j)  +/-  (2.04e-35, 3.77e-94j)
| (8.0147642229863236369e-08 - 5.6790270701682175368e-482j)  +/-  (6.1e-28, 1.13e-86j)
| (0.00021277785009109738498 + 5.8510097296045267332e-479j)  +/-  (3.14e-23, 5.81e-82j)
| (2.5436169243214942947e-09 + 6.0725891480778199781e-483j)  +/-  (2.48e-29, 4.59e-88j)
| (4.891952067227788694e-11 - 5.7568073629172561794e-483j)  +/-  (3.93e-31, 7.27e-90j)
| (1.626155254523507092e-06 + 4.5063195887713579376e-481j)  +/-  (1.97e-27, 3.65e-86j)
| (-0.043913954511369437534 - 4.3030058568590693926e-476j)  +/-  (3.6e-20, 6.66e-79j)
| (4.891952067227788694e-11 - 5.259653396299068281e-484j)  +/-  (9.07e-31, 1.68e-89j)
| (0.0014941463608262759853 - 3.6376563975164300318e-478j)  +/-  (1.45e-23, 2.68e-82j)
| (1.7005097898217682497e-25 + 3.5389464806957823148e-492j)  +/-  (5.99e-39, 1.11e-97j)
| (1.7005097898217682497e-25 - 2.5645936587681569129e-491j)  +/-  (1.07e-39, 1.97e-98j)
| (0.055448411244771658465 + 2.1828434307918381773e-476j)  +/-  (9.96e-23, 1.84e-81j)
| (0.062159473891466594766 - 8.2807134359485241489e-477j)  +/-  (3.54e-20, 6.56e-79j)
| (0.00021277785009109738498 + 2.1399352834240770554e-479j)  +/-  (4.43e-27, 8.2e-86j)
| (0.062159473891466594766 - 1.2389851645145832409e-476j)  +/-  (3.38e-21, 6.25e-80j)
| (0.055448411244771658465 + 3.8714102615071969286e-476j)  +/-  (1.53e-22, 2.84e-81j)
| (5.6821220426538584002e-18 - 1.119490708870519862e-486j)  +/-  (1.01e-36, 1.87e-95j)
| (-0.043913954511369437534 - 2.3654843394890508343e-476j)  +/-  (8.11e-24, 1.5e-82j)
| (0.0014941463608262759853 - 1.5800813161008358873e-478j)  +/-  (1.31e-26, 2.41e-85j)
| (2.5436169243214942947e-09 + 4.3436074819238316686e-482j)  +/-  (1.22e-32, 2.25e-91j)
| (0.015162546756262970036 + 9.1078705001539917459e-477j)  +/-  (1.85e-25, 3.43e-84j)
| (8.0147642229863236369e-08 - 2.9756739769665336566e-481j)  +/-  (4.81e-32, 8.9e-91j)
| (0.015162546756262970036 + 4.723742801462297161e-477j)  +/-  (8.16e-27, 1.51e-85j)
| (0.13661685852411881259 + 3.521023061825432457e-476j)  +/-  (1.07e-26, 1.98e-85j)
| (2.7391003267531170491e-15 - 1.6531502577631780543e-486j)  +/-  (4.26e-37, 7.88e-96j)
| (1.626155254523507092e-06 + 1.8388349606523092081e-480j)  +/-  (2.42e-31, 4.48e-90j)
| (-0.056648950697857063551 - 1.1640769885044185061e-475j)  +/-  (1.59e-27, 2.94e-86j)
| (2.2235034755781654552e-05 - 3.1835915709640180869e-480j)  +/-  (4.04e-31, 7.44e-90j)
| (0.22090004471416629781 + 8.412178250548288139e-476j)  +/-  (9.8e-28, 1.8e-86j)
| (-0.056648950697857063551 - 9.6725446347719135398e-476j)  +/-  (9.75e-28, 1.79e-86j)
| (0.22090004471416629781 + 9.6754055826303889122e-476j)  +/-  (3.18e-28, 5.96e-87j)
| (0.13661685852411881259 + 4.5657465820561267367e-476j)  +/-  (1.28e-28, 2.44e-87j)
| (0.21708940387361542441 - 3.5175500111864223595e-476j)  +/-  (1.09e-28, 1.94e-87j)
