Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 4 24
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P3 : t^9 - 71/3*t^7 + 1399/9*t^5 - 2965/9*t^3 + 590/3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 27614371619222425027419982835140545895366605829633/63182519542706008820545556987124360511709738529*t^31 + 79119328926466581326024603194966773667069687784151007/947737793140590132308183354806865407675646077935*t^29 - 8728445323345597808774140034898917207923223062417069429/947737793140590132308183354806865407675646077935*t^27 + 68824339226732729335379092422906046985908141630553946573/105304199237843348034242594978540600852849564215*t^25 - 662652947579923606478401819707486712947341870037008133855/21060839847568669606848518995708120170569912843*t^23 + 454060196471565716921218623827113497118909337137050216135/429813058113646318507112632565471840215712507*t^21 - 75401507282798797245389025505980062418103463107926570376035/3008691406795524229549788427958302881509987549*t^19 + 1267274454439789951824494544368244661134284220011865762100845/3008691406795524229549788427958302881509987549*t^17 - 2143152701684930850243636579529532963913761881878808777536705/429813058113646318507112632565471840215712507*t^15 + 123301210512180682745375842388068255610914139813300760103739175/3008691406795524229549788427958302881509987549*t^13 - 686388472182978158320047396885397376264801351242077212677422525/3008691406795524229549788427958302881509987549*t^11 + 2487879770623122924450370460500087200056392599124616175535775925/3008691406795524229549788427958302881509987549*t^9 - 787431751846006787000850141789215588517281665393234723598867925/429813058113646318507112632565471840215712507*t^7 + 958912810758155454685458845297971376371982748508452052413420525/429813058113646318507112632565471840215712507*t^5 - 526768892923732411179482267280038984784449260418646917353278375/429813058113646318507112632565471840215712507*t^3 + 82289919913968510583792923260802526858906765142264139907770750/429813058113646318507112632565471840215712507*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
Positive weights:   33 out of 33
Indefinite weights: 0 out of 33
Negative weights:   0 out of 33
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (2.7726473453590291949 + 3.8227409430776966893e-457j)  +/-  (2.78e-121, 2.78e-121j)
| (-4.3778541369253002074 + 8.3116727011159169026e-456j)  +/-  (2.45e-120, 2.45e-120j)
| (-9.6244234848072835691 + 4.9577815583288710215e-457j)  +/-  (1.2e-121, 1.2e-121j)
| (-6.9934902946121200717 + 6.3374834852894589776e-455j)  +/-  (5.62e-120, 5.62e-120j)
| (8.6046483334009146125 - 6.70176356375281673e-456j)  +/-  (9.42e-121, 9.42e-121j)
| (9.6244234848072835691 - 2.2105536778094044576e-462j)  +/-  (1.27e-121, 1.27e-121j)
| (5.621751719089515406 + 3.7794213491591770948e-468j)  +/-  (7.31e-120, 7.31e-120j)
| (-7.7553593251986093245 + 1.8474434119503481409e-473j)  +/-  (2.93e-120, 2.93e-120j)
| (-8.6046483334009146125 + 3.7111879442047038864e-474j)  +/-  (8.78e-121, 8.78e-121j)
| (-5.621751719089515406 - 6.4720099805697149149e-473j)  +/-  (7.35e-120, 7.35e-120j)
| (6.9934902946121200717 - 1.8963797220386883222e-477j)  +/-  (5.76e-120, 5.76e-120j)
| (-1 + 2.4102216195818251115e-494j)  +/-  (6.7e-125, 6.7e-125j)
| (7.7553593251986093245 + 7.0325831901798100503e-489j)  +/-  (2.94e-120, 2.94e-120j)
| (4.9868837611880247335 - 2.0646349172600762448e-491j)  +/-  (4.66e-120, 4.66e-120j)
| (-3.7932353000477464006 - 2.7321138328167544914e-498j)  +/-  (1.15e-120, 1.15e-120j)
| (3.7932353000477464006 - 1.0274717074981440915e-496j)  +/-  (1.2e-120, 1.2e-120j)
| (2.0148165000730346796 + 7.1566768514095363824e-501j)  +/-  (1.23e-122, 1.23e-122j)
| (-4.9868837611880247335 + 7.5030924266985398214e-498j)  +/-  (4.83e-120, 4.83e-120j)
| (-2.0148165000730346796 + 9.7490987831316187115e-504j)  +/-  (1.21e-122, 1.21e-122j)
| (-6.2875900159861807014 + 5.9079829313915934027e-501j)  +/-  (6.9e-120, 6.9e-120j)
| (4.3778541369253002074 - 1.5351792892386807032e-502j)  +/-  (2.55e-120, 2.55e-120j)
| (1 + 1.909974357380735015e-512j)  +/-  (8.15e-125, 8.15e-125j)
| (-3.2403133007037706958 - 4.2451752232016289291e-508j)  +/-  (5.94e-121, 5.94e-121j)
| (-1.5093152835436173382 - 5.0122596928634486293e-513j)  +/-  (9.67e-124, 9.67e-124j)
| (6.2875900159861807014 + 4.6603940810950072734e-514j)  +/-  (6.9e-120, 6.9e-120j)
| (-2.7726473453590291949 + 5.9662202684716757196e-519j)  +/-  (2.88e-121, 2.88e-121j)
| (3.2403133007037706958 + 8.0787052854207987565e-520j)  +/-  (5.91e-121, 5.91e-121j)
| (2.4494897427831780982 + 2.6740591142800580324e-521j)  +/-  (9.63e-122, 9.63e-122j)
| (-2.4494897427831780982 + 3.4530706405572926873e-522j)  +/-  (9.94e-122, 9.94e-122j)
| (-0.4972798256499026162 + 1.5054654959107395858e-525j)  +/-  (4.54e-126, 4.54e-126j)
| (-2.126716754507160936e-536 - 7.2471710027548510647e-536j)  +/-  (2.49e-534, 2.49e-534j)
| (0.4972798256499026162 - 1.147150303871797151e-525j)  +/-  (4.54e-126, 4.54e-126j)
| (1.5093152835436173382 - 6.147484667702926342e-524j)  +/-  (8.88e-124, 8.88e-124j)
-------------------------------------------------
The weights are:
| (0.0032234803455836095835 - 7.720544253131438862e-459j)  +/-  (3.37e-20, 1.3e-79j)
| (1.6410031680570402352e-05 + 4.3941206534107734438e-460j)  +/-  (6.76e-27, 2.61e-86j)
| (3.6015197569257242615e-21 + 1.6078157593007625816e-470j)  +/-  (4.23e-38, 1.63e-97j)
| (6.982908399039081586e-12 - 2.9882223418857676964e-465j)  +/-  (1.2e-33, 4.62e-93j)
| (3.0431306826563765944e-17 + 8.1331832788108838498e-469j)  +/-  (6.67e-38, 2.57e-97j)
| (3.6015197569257242615e-21 - 5.2990503438893331148e-471j)  +/-  (1.71e-39, 6.6e-99j)
| (3.552690311451739055e-08 + 1.8506614946930288433e-463j)  +/-  (4.81e-33, 1.85e-92j)
| (2.7705125884558277957e-14 + 1.7810641041443007856e-466j)  +/-  (2.47e-36, 9.51e-96j)
| (3.0431306826563765944e-17 - 2.9345417087320748118e-468j)  +/-  (8.22e-38, 3.17e-97j)
| (3.552690311451739055e-08 - 1.6973066525717013048e-462j)  +/-  (1.81e-33, 6.97e-93j)
| (6.982908399039081586e-12 + 9.9010594642013119531e-466j)  +/-  (3.5e-37, 1.35e-96j)
| (0.12252971860201025046 - 2.6490637465019893056e-458j)  +/-  (1.24e-21, 4.77e-81j)
| (2.7705125884558277957e-14 - 3.9234233680456155652e-467j)  +/-  (3.13e-38, 1.21e-97j)
| (9.8633121575157149857e-07 - 1.6357485555397180282e-462j)  +/-  (2.26e-34, 8.73e-94j)
| (0.00017116329603379650867 - 1.4790464691045319628e-459j)  +/-  (1.08e-32, 4.18e-92j)
| (0.00017116329603379650867 - 6.3094090759297416572e-461j)  +/-  (8.59e-33, 3.31e-92j)
| (0.025764933047617364995 - 1.2381646672430955323e-458j)  +/-  (1.04e-28, 4.01e-88j)
| (9.8633121575157149857e-07 + 3.0841933595021436273e-461j)  +/-  (1.34e-34, 5.16e-94j)
| (0.025764933047617364995 - 2.3741620035127244109e-458j)  +/-  (2.51e-30, 9.68e-90j)
| (7.1002163806943008581e-10 + 9.2211947236424505124e-464j)  +/-  (1.2e-36, 4.64e-96j)
| (1.6410031680570402352e-05 + 1.1500654871363589678e-461j)  +/-  (1.22e-34, 4.72e-94j)
| (0.12252971860201025046 - 1.8462522215803904092e-458j)  +/-  (6.15e-31, 2.37e-90j)
| (0.0011055237196887973011 + 4.5141774782575047211e-459j)  +/-  (5.43e-33, 2.1e-92j)
| (0.065258581664804101401 + 2.4281526148774408462e-458j)  +/-  (1.55e-30, 5.97e-90j)
| (7.1002163806943008581e-10 - 1.6010631899659086721e-464j)  +/-  (7.09e-38, 2.73e-97j)
| (0.0032234803455836095835 - 1.4924412597442299952e-458j)  +/-  (7.25e-33, 2.8e-92j)
| (0.0011055237196887973011 + 1.0840173986305305908e-460j)  +/-  (5.49e-34, 2.11e-93j)
| (0.0069158210646804893695 + 1.3776206338160197008e-458j)  +/-  (3.91e-33, 1.5e-92j)
| (0.0069158210646804893695 + 2.3541701628583697368e-458j)  +/-  (1.24e-32, 4.79e-92j)
| (0.17603205236374696963 + 2.7878120257634140753e-458j)  +/-  (1.87e-32, 7.26e-92j)
| (0.19796258657800580447 - 2.6847782304341906921e-458j)  +/-  (9.19e-33, 3.56e-92j)
| (0.17603205236374696963 + 2.3264567826474841262e-458j)  +/-  (3.22e-33, 1.25e-92j)
| (0.065258581664804101401 + 1.4267923680704135049e-458j)  +/-  (1.76e-33, 6.62e-93j)
