Starting with polynomial:
P : t^3 - 3*t
Extension levels are: 3 8 22
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : t^11 - 149/3*t^9 + 798*t^7 - 4914*t^5 + 10605*t^3 - 5355*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 352128240105506857881621355/758389759703712471637608*t^31 + 70469647556337902667730560547/758389759703712471637608*t^29 - 8039357930764015329357528671065/758389759703712471637608*t^27 + 1359038320071302874875649124548321/1769576105975329100487752*t^25 - 65922238821787426099292192900244675/1769576105975329100487752*t^23 + 18482114929426498463347114783251525/14870387445170832777208*t^21 - 429077620177517363177396668029902775/14870387445170832777208*t^19 + 6936712950789970049921300085433237875/14870387445170832777208*t^17 - 77426987547450717866864174174110413675/14870387445170832777208*t^15 + 586081965505491221704912161226985281875/14870387445170832777208*t^13 - 2922217798003982663649174612142715813625/14870387445170832777208*t^11 + 9182700087608075206309809999665351275125/14870387445170832777208*t^9 - 17016829873838637297785909480870397804375/14870387445170832777208*t^7 + 16805397874703921635412245469979708588375/14870387445170832777208*t^5 - 7519902533241770412199803266118369298125/14870387445170832777208*t^3 + 1079540107983915478600492013258658245625/14870387445170832777208*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:
| (8.9233983751305992145 - 9.1750031740443493898e-263j)  +/-  (3e-121, 3e-121j)
| (7.1112823957983282511 + 1.105762813203792607e-278j)  +/-  (2.73e-120, 2.73e-120j)
| (-8.9233983751305992145 - 2.6835584714067917449e-294j)  +/-  (2.91e-121, 2.91e-121j)
| (7.9453460270375925591 - 1.2633522408697541733e-294j)  +/-  (1.32e-120, 1.32e-120j)
| (-7.1112823957983282511 - 8.5526276436370553163e-307j)  +/-  (2.6e-120, 2.6e-120j)
| (-7.9453460270375925591 + 1.9989507276364070425e-305j)  +/-  (1.25e-120, 1.25e-120j)
| (-5.6480028169844754977 - 7.080254551327993151e-306j)  +/-  (3.1e-120, 3.1e-120j)
| (10.648699222697209052 - 2.3467575851443139587e-305j)  +/-  (2.14e-122, 2.14e-122j)
| (-2.6840395601585691766 - 3.8410776311210135494e-310j)  +/-  (7.16e-122, 7.16e-122j)
| (-10.648699222697209052 + 1.2598378636271328813e-314j)  +/-  (2.33e-122, 2.33e-122j)
| (4.9791465117195582423 + 1.0166666706401115841e-319j)  +/-  (2.37e-120, 2.37e-120j)
| (-4.9791465117195582423 + 1.2157465006296539928e-334j)  +/-  (2.36e-120, 2.36e-120j)
| (-0.84628809835102169611 - 2.6114839854455393008e-338j)  +/-  (5.23e-125, 5.23e-125j)
| (5.6480028169844754977 + 1.3725715140535885476e-348j)  +/-  (3.3e-120, 3.3e-120j)
| (-3.1741311888752791267 - 9.2560437989716456984e-361j)  +/-  (2.31e-121, 2.31e-121j)
| (2.2305884602206900985 + 5.7600723543110314775e-361j)  +/-  (1.75e-122, 1.75e-122j)
| (-4.3415155382340913607 - 1.0129741737172616333e-358j)  +/-  (1.2e-120, 1.2e-120j)
| (2.6840395601585691766 - 3.8135807907037589262e-361j)  +/-  (7.19e-122, 7.19e-122j)
| (-1.2191599794012175106 + 1.4406074027940488605e-362j)  +/-  (3.27e-124, 3.27e-124j)
| (-6.3543175590465458287 - 1.8589765769432700502e-358j)  +/-  (3.35e-120, 3.35e-120j)
| (0.84628809835102169611 - 1.2792106334075875618e-363j)  +/-  (5.86e-125, 5.86e-125j)
| (6.3543175590465458287 - 5.3841862305453417636e-358j)  +/-  (3.47e-120, 3.47e-120j)
| (4.3415155382340913607 + 1.2565685608869336912e-362j)  +/-  (1.01e-120, 1.01e-120j)
| (-1.7320508075688772935 - 3.1291070892468714062e-368j)  +/-  (2.4e-123, 2.4e-123j)
| (-2.2305884602206900985 + 3.52657341310178123e-367j)  +/-  (1.86e-122, 1.86e-122j)
| (-3.7355715460409572598 - 3.4389229189924033698e-366j)  +/-  (4.98e-121, 4.98e-121j)
| (0.50989496927010096937 - 1.5095868487296557308e-370j)  +/-  (6.18e-126, 6.18e-126j)
| (2.1245438700432462678e-375 + 4.2712963275058548716e-376j)  +/-  (7.15e-374, 7.15e-374j)
| (3.1741311888752791267 + 5.6255336564887094878e-366j)  +/-  (1.94e-121, 1.94e-121j)
| (-0.50989496927010096937 + 2.1314521449027673356e-373j)  +/-  (6.18e-126, 6.18e-126j)
| (3.7355715460409572598 + 3.1973016938259000047e-371j)  +/-  (5.09e-121, 5.09e-121j)
| (1.7320508075688772935 + 4.0141943051299026352e-374j)  +/-  (2.3e-123, 2.3e-123j)
| (1.2191599794012175106 + 8.2181848229035306827e-377j)  +/-  (3.29e-124, 3.29e-124j)
-------------------------------------------------
The weights are:
| (2.2532600409556452825e-18 + 9.736082496696776646e-280j)  +/-  (8.48e-40, 2.33e-99j)
| (3.2882458717461010791e-12 + 2.7447261254718423165e-277j)  +/-  (6.2e-37, 1.7e-96j)
| (2.2532600409556452825e-18 + 1.1583965636528635134e-281j)  +/-  (1.71e-41, 4.69e-101j)
| (6.9386506509674883113e-15 - 1.6100064211708149558e-278j)  +/-  (1.57e-38, 4.31e-98j)
| (3.2882458717461010791e-12 + 3.1018778246449603177e-278j)  +/-  (6.38e-39, 1.75e-98j)
| (6.9386506509674883113e-15 - 9.3348415455762822854e-280j)  +/-  (3.29e-40, 9.04e-100j)
| (3.2380576304824185664e-08 + 8.2293444997369348849e-276j)  +/-  (4.97e-37, 1.37e-96j)
| (7.1524931741472861586e-25 + 7.952851307556051281e-284j)  +/-  (2.3e-45, 6.32e-105j)
| (0.0049470716575257833299 - 1.2587515792370686622e-271j)  +/-  (1.94e-30, 5.32e-90j)
| (7.1524931741472861586e-25 - 7.0105215002708141319e-285j)  +/-  (2.69e-45, 7.39e-105j)
| (1.0767777891957212781e-06 - 2.98915008470470919e-274j)  +/-  (1.5e-37, 4.11e-97j)
| (1.0767777891957212781e-06 - 8.4804335375777567922e-275j)  +/-  (1.45e-36, 3.99e-96j)
| (0.073276471131867835117 - 5.3657499597704745846e-270j)  +/-  (1.1e-29, 3.02e-89j)
| (3.2380576304824185664e-08 + 3.661025916566049396e-275j)  +/-  (1.03e-38, 2.82e-98j)
| (0.0013716592979159211342 + 3.0243243366385352893e-272j)  +/-  (1.78e-33, 4.88e-93j)
| (0.015619214998466684729 + 5.8238720735198308929e-271j)  +/-  (1.37e-32, 3.75e-92j)
| (2.0051537142955281079e-05 + 7.1058486766340812015e-274j)  +/-  (4.92e-36, 1.35e-95j)
| (0.0049470716575257833299 - 2.3417279347488142125e-271j)  +/-  (2.88e-34, 7.91e-94j)
| (0.091914678696995344431 + 2.6425159736606133225e-270j)  +/-  (1.08e-29, 2.95e-89j)
| (4.9616042432182768124e-10 - 6.0748764195916727913e-277j)  +/-  (3.25e-39, 8.93e-99j)
| (0.073276471131867835117 - 6.4901546476043609601e-270j)  +/-  (1.55e-31, 4.25e-91j)
| (4.9616042432182768124e-10 - 3.6125853142761108809e-276j)  +/-  (2.23e-40, 6.12e-100j)
| (2.0051537142955281079e-05 + 2.0571995036169258503e-273j)  +/-  (5.37e-38, 1.47e-97j)
| (0.046161234573278374041 - 8.7574177278447121106e-271j)  +/-  (4.14e-33, 1.14e-92j)
| (0.015619214998466684729 + 3.4945413987117518003e-271j)  +/-  (3.84e-34, 1.05e-93j)
| (0.0002186070312512650027 - 5.0654860181339562956e-273j)  +/-  (2.51e-36, 6.89e-96j)
| (0.16073228852266358482 + 6.3502046306025673842e-270j)  +/-  (2.29e-33, 6.29e-93j)
| (0.21147522579014228094 - 4.7567181369239545773e-270j)  +/-  (3.15e-33, 8.64e-93j)
| (0.0013716592979159211342 + 6.3637420019535679448e-272j)  +/-  (1.59e-37, 4.36e-97j)
| (0.16073228852266358482 + 5.6637132268550494853e-270j)  +/-  (2.74e-34, 7.53e-94j)
| (0.0002186070312512650027 - 1.2360442484338577125e-272j)  +/-  (2.58e-38, 7.08e-98j)
| (0.046161234573278374041 - 1.2975901761672020102e-270j)  +/-  (2.62e-36, 7.24e-96j)
| (0.091914678696995344431 + 3.4788477574229642622e-270j)  +/-  (6.94e-36, 1.86e-95j)
