Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 5 32
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 32 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^41 - 176199942834421206486699614771916870411115501667208/32438330777928274825188044875952364404415805309*t^39 + 187584237899969020290619538177190256126223798751049392/227068315445497923776316314131666550830910637163*t^37 - 2419539726752346854517213879557981175768775543991283462/32438330777928274825188044875952364404415805309*t^35 + 1014372862444109274622251313680311153306611143187869747075/227068315445497923776316314131666550830910637163*t^33 - 42659143001586785381769413705340387422776873951937089567110/227068315445497923776316314131666550830910637163*t^31 + 44861816324516166699227814946221415114057252697755725639540/7829941911913721509528148763160915545893470247*t^29 - 288756503062054798911596859032768692498904077467017604141855/2237126260546777574150899646617404441683848642*t^27 + 19404942042660613332285524330923690962623229386820290549674665/8948505042187110296603598586469617766735394568*t^25 - 487704896339348363593651605805782942444730950813187129649911875/17897010084374220593207197172939235533470789136*t^23 + 2286601400774251674379777131827967383435377822647772145628525375/8948505042187110296603598586469617766735394568*t^21 - 127052858490703835125592175650133547400442931499671734957683354625/71588040337496882372828788691756942133883156544*t^19 + 1291008634798212817250066420350102292804910511533198634274114809125/143176080674993764745657577383513884267766313088*t^17 - 4710914400448852139382301032101245170751927294852139151944183710125/143176080674993764745657577383513884267766313088*t^15 + 6017867155496694368680164681595190722738502823877706120788389009375/71588040337496882372828788691756942133883156544*t^13 - 83146451051907754408246601775756965724784846286138426973698692321875/572704322699975058982630309534055537071065252352*t^11 + 739562384406692726410916872909189054645134825979516541520518266438125/4581634581599800471861042476272444296568522018816*t^9 - 987702250282296244969953762004619160717977154435061917520298480968125/9163269163199600943722084952544888593137044037632*t^7 + 178972962038164550502940748786592359286192124050123278289717294005625/4581634581599800471861042476272444296568522018816*t^5 - 240680240368651875561966582235537585048972107162411138863287136484375/36653076652798403774888339810179554372548176150528*t^3 + 26802627074204618133600274930228771410752733081173302735020759478125/73306153305596807549776679620359108745096352301056*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:
| (-7.7615893858214152556 + 4.0962252764236643529e-450j)  +/-  (1.22e-120, 1.22e-120j)
| (-6.4874087358658998326 - 1.1806407725751447348e-448j)  +/-  (4.88e-119, 4.88e-119j)
| (5.9687869796773727273 - 3.2248990280750638674e-446j)  +/-  (1.15e-118, 1.15e-118j)
| (-4.1856391591201384269 + 3.3272376532881491652e-451j)  +/-  (1.45e-118, 1.45e-118j)
| (7.7615893858214152556 - 1.9710644106286433108e-452j)  +/-  (1.24e-120, 1.24e-120j)
| (7.0659964858122524 + 4.993354682079275648e-451j)  +/-  (1.14e-119, 1.14e-119j)
| (6.4874087358658998326 + 1.5268221494901537065e-449j)  +/-  (4.73e-119, 4.73e-119j)
| (-5.9687869796773727273 + 2.1197979598216604795e-451j)  +/-  (1.19e-118, 1.19e-118j)
| (-4.6023011139836491215 - 7.940785670897204103e-451j)  +/-  (2.39e-118, 2.39e-118j)
| (3.7822611838494062214 - 2.5193068978849616761e-452j)  +/-  (8.88e-119, 8.88e-119j)
| (3.0088734650572304465 + 1.2952160745351705647e-455j)  +/-  (1.47e-119, 1.47e-119j)
| (-5.0351265093862657074 + 2.2533680023280412013e-458j)  +/-  (2.26e-118, 2.26e-118j)
| (-7.0659964858122524 - 6.5742666189473902762e-461j)  +/-  (1.14e-119, 1.14e-119j)
| (-2.6384291054842239697 - 6.8715071267014897205e-461j)  +/-  (4.81e-120, 4.81e-120j)
| (1.3631183427052083758 + 1.1576114836374179837e-462j)  +/-  (1.84e-122, 1.84e-122j)
| (1.0520157332530725183 - 1.056512012512571809e-463j)  +/-  (2.19e-123, 2.19e-123j)
| (2.6384291054842239697 - 7.9000585825813556146e-459j)  +/-  (4.65e-120, 4.65e-120j)
| (5.4884094407174074095 - 3.4000489816038661891e-457j)  +/-  (1.95e-118, 1.95e-118j)
| (-0.73395630342256598469 - 3.678282535189120358e-475j)  +/-  (3.14e-124, 3.14e-124j)
| (-1.6506801238857845559 + 3.6316744971157151116e-474j)  +/-  (9.53e-122, 9.53e-122j)
| (-1.9492925662457627816 - 2.251506136009789281e-472j)  +/-  (3.75e-121, 3.75e-121j)
| (-2.28218870463928703 + 1.1306648658176048296e-472j)  +/-  (1.55e-120, 1.55e-120j)
| (2.28218870463928703 + 6.0878603312855984134e-469j)  +/-  (1.43e-120, 1.43e-120j)
| (-3.7822611838494062214 + 1.2620119141951627527e-471j)  +/-  (8.21e-119, 8.21e-119j)
| (-3.0088734650572304465 - 8.7149939275033614523e-473j)  +/-  (1.33e-119, 1.33e-119j)
| (1.1779198133079282237e-480 - 1.6422630104059088475e-479j)  +/-  (6.75e-478, 6.75e-478j)
| (1.6506801238857845559 - 5.5768382658136183057e-473j)  +/-  (9.5e-122, 9.5e-122j)
| (1.9492925662457627816 - 6.1208675434949496917e-472j)  +/-  (4e-121, 4e-121j)
| (-5.4884094407174074095 + 1.4083347128975603945e-471j)  +/-  (2.04e-118, 2.04e-118j)
| (-1.0520157332530725183 + 1.2941753858485024907e-475j)  +/-  (2.53e-123, 2.53e-123j)
| (5.0351265093862657074 + 7.3563702340763392458e-470j)  +/-  (2.52e-118, 2.52e-118j)
| (-3.3903050834681202432 + 2.7226316753576038327e-483j)  +/-  (3.96e-119, 3.96e-119j)
| (0.73395630342256598469 - 2.0319535655885783255e-487j)  +/-  (2.98e-124, 2.98e-124j)
| (3.3903050834681202432 - 3.8987027324332737178e-482j)  +/-  (3.94e-119, 3.94e-119j)
| (-1.3631183427052083758 - 3.6110134438394874125e-496j)  +/-  (1.86e-122, 1.86e-122j)
| (0.32393545736680206552 + 7.2605246074497356943e-499j)  +/-  (6.48e-126, 6.48e-126j)
| (4.6023011139836491215 - 1.2786351222733559077e-495j)  +/-  (2.09e-118, 2.09e-118j)
| (0.52464762327529031788 + 4.5771886209776111844e-513j)  +/-  (6.75e-125, 6.75e-125j)
| (-0.32393545736680206552 + 6.5634175888537338871e-514j)  +/-  (6.01e-126, 6.01e-126j)
| (4.1856391591201384269 + 6.9508590973632901023e-511j)  +/-  (1.41e-118, 1.41e-118j)
| (-0.52464762327529031788 + 7.0825568712657573263e-519j)  +/-  (6.82e-125, 6.82e-125j)
-------------------------------------------------
The weights are:
| (3.1083943457741465119e-27 - 3.7931507151057590398e-469j)  +/-  (6.3e-35, 7.24e-94j)
| (1.6170022592594907406e-19 - 6.077956744099644787e-465j)  +/-  (7.43e-32, 8.54e-91j)
| (9.4513278785979227609e-17 + 2.0326985543604494894e-461j)  +/-  (7.86e-32, 9.04e-91j)
| (5.6906799934198153987e-09 + 2.2916226984266132406e-458j)  +/-  (7.23e-26, 8.32e-85j)
| (3.1083943457741465119e-27 + 3.2866199525751662369e-468j)  +/-  (9.27e-37, 1.07e-95j)
| (7.2671491329445348769e-23 - 1.2087900307746049028e-465j)  +/-  (3.5e-35, 4.03e-94j)
| (1.6170022592594907406e-19 + 1.7179237279795453536e-463j)  +/-  (8.86e-34, 1.02e-92j)
| (9.4513278785979227609e-17 + 2.0149876155127915448e-463j)  +/-  (1.64e-33, 1.89e-92j)
| (1.5138846345654348765e-10 - 1.2542345761030790542e-459j)  +/-  (4.83e-30, 5.56e-89j)
| (1.3736928446203805774e-07 - 3.5558595398931124852e-457j)  +/-  (5.69e-29, 6.54e-88j)
| (2.4831614829444715379e-05 - 1.0243971303975366005e-455j)  +/-  (3.46e-26, 3.98e-85j)
| (2.4354568761543435709e-12 + 4.5179561473900506888e-461j)  +/-  (1.03e-31, 1.19e-90j)
| (7.2671491329445348769e-23 + 8.7229767245903378154e-467j)  +/-  (6.59e-37, 7.58e-96j)
| (0.00019478321521039066669 + 2.1015192998834391855e-455j)  +/-  (8.08e-26, 9.3e-85j)
| (0.026201426192731200064 + 5.3072308078278359737e-453j)  +/-  (3.17e-19, 3.65e-78j)
| (0.059919017325907034098 - 1.1423144892290654684e-452j)  +/-  (4.39e-17, 5.05e-76j)
| (0.00019478321521039066669 + 4.7699455784874140068e-455j)  +/-  (3.81e-26, 4.39e-85j)
| (2.1737312615922585931e-14 - 1.3683309240663994101e-460j)  +/-  (1.47e-34, 1.69e-93j)
| (0.098777676671402692222 + 2.6102505283590467336e-452j)  +/-  (6e-18, 6.91e-77j)
| (0.010536930733881088354 - 1.4247170282210484795e-453j)  +/-  (1.12e-22, 1.29e-81j)
| (0.0039943484647062218957 + 4.3743766000976295224e-454j)  +/-  (2.46e-24, 2.83e-83j)
| (0.0010702746121257658474 - 1.0185675407643276199e-454j)  +/-  (7.6e-26, 8.74e-85j)
| (0.0010702746121257658474 - 2.0661302414222136032e-454j)  +/-  (9.94e-28, 1.14e-86j)
| (1.3736928446203805774e-07 - 1.2870926088338003033e-457j)  +/-  (3.6e-31, 4.14e-90j)
| (2.4831614829444715379e-05 - 4.039178252391468265e-456j)  +/-  (3.47e-29, 4e-88j)
| (0.18811494987237931992 - 3.5456645059528968763e-452j)  +/-  (2.2e-22, 2.53e-81j)
| (0.010536930733881088354 - 2.3662497569058430061e-453j)  +/-  (9.09e-26, 1.05e-84j)
| (0.0039943484647062218957 + 7.983196574071630579e-454j)  +/-  (7.18e-27, 8.26e-86j)
| (2.1737312615922585931e-14 - 4.0335862493399029713e-462j)  +/-  (1.31e-35, 1.51e-94j)
| (0.059919017325907034098 - 8.2864323818906708626e-453j)  +/-  (3.5e-25, 4.03e-84j)
| (2.4354568761543435709e-12 + 1.0736860241693164609e-459j)  +/-  (4.81e-37, 5.53e-96j)
| (2.2226504950203328663e-06 + 7.2681053016772798031e-457j)  +/-  (3.02e-31, 3.48e-90j)
| (0.098777676671402692222 + 3.263504056764048404e-452j)  +/-  (1.34e-26, 1.54e-85j)
| (2.2226504950203328663e-06 + 2.0126030044123148771e-456j)  +/-  (4.62e-33, 5.32e-92j)
| (0.026201426192731200064 + 3.4961921243897734359e-453j)  +/-  (2.93e-28, 3.36e-87j)
| (0.15129547827269653592 + 5.1392634366888440901e-452j)  +/-  (6.62e-28, 7.58e-87j)
| (1.5138846345654348765e-10 - 8.5104338926358861708e-459j)  +/-  (1.35e-36, 1.55e-95j)
| (0.053925392096014738148 - 5.8046950003738468834e-452j)  +/-  (3.36e-28, 3.88e-87j)
| (0.15129547827269653592 + 4.6577938842856432511e-452j)  +/-  (1.96e-28, 2.24e-87j)
| (5.6906799934198153987e-09 + 6.085769658205313078e-458j)  +/-  (8.88e-36, 1.02e-94j)
| (0.053925392096014738148 - 4.9491452035310185143e-452j)  +/-  (1.81e-28, 2.04e-87j)
