Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 6 18
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Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P3 : t^11 - 6923/164*t^9 + 97479/164*t^7 - 566685/164*t^5 + 1313235/164*t^3 - 418635/82*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 1739343849360700900915385139711369413654620871/5609369737430535922113676486356258715084028*t^27 + 5982798057179293696423447768778308948230504277893/145843613173193933974955588645262726592184728*t^25 - 444894871727392010877813490812968980067212146130725/145843613173193933974955588645262726592184728*t^23 + 20636133589143136862923244626466638346274168399450075/145843613173193933974955588645262726592184728*t^21 - 89557860086548338875531185093871077501902695367899625/20834801881884847710707941235037532370312104*t^19 + 227788164733503696181336298895781827420158133229050600/2604350235235605963838492654379691546289013*t^17 - 12496074056386778434148502163077088684565735481491842575/10417400940942423855353970617518766185156052*t^15 + 114783998837346305536354759434197630639156865161531801625/10417400940942423855353970617518766185156052*t^13 - 26652344991611305307564030982019675575470296695880693875/400669266959323994436691177596875622506002*t^11 + 408530383267663189575183041312491241299789284010629351375/1602677067837295977746764710387502490024008*t^9 - 937072754814471899185380815570135204223847727610488686875/1602677067837295977746764710387502490024008*t^7 + 1165100165932814596183175323376924581360967312898482998125/1602677067837295977746764710387502490024008*t^5 - 655318829248406657027461674460666195426726751865358063125/1602677067837295977746764710387502490024008*t^3 + 54750150401706830323145649752298333950458786514292650625/801338533918647988873382355193751245012004*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: 1
  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:
| (3.887781428245635466 - 2.7402332268862361852e-410j)  +/-  (3.1e-121, 3.1e-121j)
| (8.6904306779827217861 + 1.6049422071195137199e-413j)  +/-  (1.98e-122, 1.98e-122j)
| (-8.6904306779827217861 - 3.5672995486849674113e-410j)  +/-  (1.99e-122, 1.99e-122j)
| (-7.6383783664393766285 + 3.9410023832216364974e-414j)  +/-  (1.34e-121, 1.34e-121j)
| (5.9700743476259892559 - 4.0082721075305616499e-418j)  +/-  (5.61e-121, 5.61e-121j)
| (-2.4494897427831780982 - 1.141709714412248704e-418j)  +/-  (3.65e-122, 3.65e-122j)
| (-5.1162268016735536685e-426 + 2.1697110040613066337e-425j)  +/-  (6.46e-424, 6.46e-424j)
| (-5.9700743476259892559 - 3.108856366780297142e-424j)  +/-  (5.36e-121, 5.36e-121j)
| (-3.887781428245635466 + 9.0990753625076574893e-437j)  +/-  (2.87e-121, 2.87e-121j)
| (7.6383783664393766285 - 1.4863835276831082195e-446j)  +/-  (1.22e-121, 1.22e-121j)
| (5.2368589416349489402 + 5.4141875808265636006e-446j)  +/-  (6.52e-121, 6.52e-121j)
| (-5.2368589416349489402 + 2.5608764160633130161e-449j)  +/-  (6.18e-121, 6.18e-121j)
| (-2.7803107173207814961 + 1.2944380011289791264e-457j)  +/-  (9.46e-122, 9.46e-122j)
| (-6.759940386062415194 - 2.3026060597005878691e-460j)  +/-  (3.64e-121, 3.64e-121j)
| (6.759940386062415194 + 2.6387092186561707824e-466j)  +/-  (3.52e-121, 3.52e-121j)
| (3.2728782272458314193 + 1.5823600157759341739e-465j)  +/-  (1.7e-121, 1.7e-121j)
| (2.7803107173207814961 - 6.3380457592575471771e-467j)  +/-  (9.21e-122, 9.21e-122j)
| (2.4494897427831780982 - 5.8348876445174246441e-468j)  +/-  (3.69e-122, 3.69e-122j)
| (-4.5448979391212497356 + 4.6318598529006441905e-470j)  +/-  (4.91e-121, 4.91e-121j)
| (1.4535448410208861999 + 1.0883749970029242364e-473j)  +/-  (6.32e-124, 6.32e-124j)
| (1 + 3.0990092513524488178e-474j)  +/-  (6.29e-125, 6.29e-125j)
| (-1.961016437141193946 - 1.0568321679998600725e-473j)  +/-  (5.52e-123, 5.52e-123j)
| (1.961016437141193946 + 8.3379193974081010572e-473j)  +/-  (5.12e-123, 5.12e-123j)
| (4.5448979391212497356 + 1.1246227190049501205e-471j)  +/-  (5.24e-121, 5.24e-121j)
| (-1.4535448410208861999 + 5.6813941304818140159e-474j)  +/-  (5.87e-124, 5.87e-124j)
| (-0.52482467588993622704 + 5.9718571557349136331e-476j)  +/-  (4.41e-126, 4.41e-126j)
| (0.52482467588993622704 - 3.9601266406811353614e-476j)  +/-  (4.41e-126, 4.41e-126j)
| (-3.2728782272458314193 - 1.9343013451440953576e-474j)  +/-  (1.62e-121, 1.62e-121j)
| (-1 + 6.7402431929085930322e-481j)  +/-  (6.42e-125, 6.42e-125j)
-------------------------------------------------
The weights are:
| (0.00013320210015115247494 + 1.2571143789039395286e-413j)  +/-  (6.87e-33, 7.47e-94j)
| (1.9228972450092079736e-17 - 5.2685002262661199077e-423j)  +/-  (8.1e-43, 8.81e-104j)
| (1.9228972450092079736e-17 + 2.0082686663084661509e-423j)  +/-  (1.58e-43, 1.72e-104j)
| (8.0464930965423333958e-14 - 2.6064548106449577697e-421j)  +/-  (4.25e-42, 4.62e-103j)
| (5.5092454345164311119e-09 + 1.2196078717021513254e-417j)  +/-  (9.41e-40, 1.02e-100j)
| (0.0079895478296819274907 - 6.1620985525329903182e-413j)  +/-  (3.05e-31, 3.32e-92j)
| (0.21300694398931636134 + 4.225065335483330842e-412j)  +/-  (3.05e-31, 3.32e-92j)
| (5.5092454345164311119e-09 - 2.575935298739582432e-418j)  +/-  (4.22e-40, 4.59e-101j)
| (0.00013320210015115247494 + 4.6940487695516898688e-415j)  +/-  (2.75e-36, 2.98e-97j)
| (8.0464930965423333958e-14 + 8.0125091055324098002e-421j)  +/-  (1.89e-43, 2.05e-104j)
| (3.1440382315518131469e-07 - 2.6998132708995675596e-416j)  +/-  (1.29e-39, 1.4e-100j)
| (3.1440382315518131469e-07 + 3.9913741207289624089e-417j)  +/-  (1.6e-39, 1.74e-100j)
| (0.0030431473530675780833 + 2.819884393491035485e-413j)  +/-  (8.39e-35, 9.12e-96j)
| (3.937957104529343396e-11 + 1.112622804181836864e-419j)  +/-  (8.48e-42, 9.21e-103j)
| (3.937957104529343396e-11 - 4.1253793545302469076e-419j)  +/-  (1.02e-42, 1.11e-103j)
| (0.0010945299063443786321 - 5.1430658936093450881e-413j)  +/-  (4.03e-38, 4.38e-99j)
| (0.0030431473530675780833 + 1.697902999083921963e-412j)  +/-  (1.19e-37, 1.29e-98j)
| (0.0079895478296819274907 - 2.7151538579319668249e-412j)  +/-  (2.17e-37, 2.35e-98j)
| (8.7957259576144581017e-06 - 4.7048272582205083771e-416j)  +/-  (3.12e-41, 3.41e-102j)
| (0.066290413865812382999 - 4.4552921599999027986e-412j)  +/-  (1.36e-36, 1.47e-97j)
| (0.1082763166861901079 + 5.3421294982073376968e-412j)  +/-  (1.94e-36, 2.09e-97j)
| (0.030630060206135103086 + 1.0621626978112885671e-412j)  +/-  (3.15e-38, 3.41e-99j)
| (0.030630060206135103086 + 3.2243118709306040297e-412j)  +/-  (2.31e-37, 2.5e-98j)
| (8.7957259576144581017e-06 + 6.0379784921764268652e-415j)  +/-  (2.94e-41, 3.17e-102j)
| (0.066290413865812382999 - 2.0304110995718268161e-412j)  +/-  (5.07e-38, 5.32e-99j)
| (0.1760301943794729293 - 3.7843786597063239651e-412j)  +/-  (1.25e-37, 1.31e-98j)
| (0.1760301943794729293 - 4.9655863491805719701e-412j)  +/-  (1.9e-37, 2.08e-98j)
| (0.0010945299063443786321 - 4.4163223850048409053e-414j)  +/-  (3.48e-40, 4.12e-101j)
| (0.1082763166861901079 + 3.1561887149076550995e-412j)  +/-  (6.08e-38, 6.04e-99j)
