Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 9 18
-------------------------------------------------
Trying to find an order 9 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : 4*t^11 - 1238/7*t^9 + 15354/7*t^7 - 9783*t^5 + 59445/4*t^3 - 41985/8*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^29 - 2043513178851919911531877162/2850224919301609318221683*t^27 + 22525821539178627681014146092/407174988471658474031669*t^25 - 75810174031233247115369962468215/31352474112317702500438513*t^23 + 41592892484187154753690246367848443/627049482246354050008770260*t^21 - 214420888020936329369418966738563943/179156994927529728573934360*t^19 + 2595908330326416111636630062278681479/179156994927529728573934360*t^17 - 21150010596697885735279728724273703031/179156994927529728573934360*t^15 + 183605529121517298860656872021148360473/286651191884047565718294976*t^13 - 117761403601833167872513315908748990197/52118398524372284676053632*t^11 + 64843389777761921338367830165649282337/13029599631093071169013408*t^9 - 668590035205608249624347295527423570043/104236797048744569352107264*t^7 + 1811229591549404416703024650011408191493/416947188194978277408429056*t^5 - 24566974753529111223411036510323895045/19392892474185036158531584*t^3 + 83050422651051956810709965526697173765/833894376389956554816858112*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:   29 out of 29
Indefinite weights: 0 out of 29
Negative weights:   0 out of 29
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.6358247707876598922 - 3.3420848932394089975e-461j)  +/-  (7.33e-121, 7.33e-121j)
| (3.5843494090628225013 + 1.0222124392050250467e-473j)  +/-  (4.95e-121, 4.95e-121j)
| (5.2109072187547580143 - 1.7039513604254043712e-483j)  +/-  (5.24e-121, 5.24e-121j)
| (4.094056197966554643 + 1.7599199803441426033e-492j)  +/-  (7.05e-121, 7.05e-121j)
| (-5.7602949444394278687 - 2.678962832262005687e-497j)  +/-  (3.12e-121, 3.12e-121j)
| (-6.2629248853704510994 + 4.6244228063306446303e-499j)  +/-  (6.54e-122, 6.54e-122j)
| (5.7602949444394278687 - 2.2924350398406324464e-497j)  +/-  (2.78e-121, 2.78e-121j)
| (-1.0724781581987271596 - 1.1732536622955186526e-504j)  +/-  (2.72e-124, 2.72e-124j)
| (-3.5843494090628225013 - 1.4897371753269437652e-501j)  +/-  (4.43e-121, 4.43e-121j)
| (-2.2101003296710005571 + 2.2105321341269226507e-502j)  +/-  (3.98e-122, 3.98e-122j)
| (6.2629248853704510994 + 6.4385794785332101125e-502j)  +/-  (6.94e-122, 6.94e-122j)
| (2.6430545402832988158 + 4.3082493645226076398e-501j)  +/-  (1.14e-121, 1.14e-121j)
| (-4.6358247707876598922 - 7.4073242247926793747e-506j)  +/-  (8.28e-121, 8.28e-121j)
| (-5.2109072187547580143 + 6.4251162574067046285e-506j)  +/-  (5.25e-121, 5.25e-121j)
| (-2.6430545402832988158 - 2.0436284524654126117e-505j)  +/-  (1.13e-121, 1.13e-121j)
| (1.0724781581987271596 + 2.4866038472501330413e-512j)  +/-  (2.81e-124, 2.81e-124j)
| (3.1015293948262462479 + 7.6817609551887314344e-509j)  +/-  (2.64e-121, 2.64e-121j)
| (-3.1015293948262462479 + 6.2001815512187159838e-514j)  +/-  (2.65e-121, 2.65e-121j)
| (-0.7071067811865475244 - 1.0756546376233904826e-518j)  +/-  (3.06e-125, 3.06e-125j)
| (-4.094056197966554643 + 1.2023145364375658561e-516j)  +/-  (7.26e-121, 7.26e-121j)
| (1.4341212004681264598 + 9.0378484207115170422e-518j)  +/-  (2.18e-123, 2.18e-123j)
| (2.2101003296710005571 - 5.0337926119995785752e-519j)  +/-  (3.77e-122, 3.77e-122j)
| (5.7340279623452268838e-525 - 4.5499442938928824968e-525j)  +/-  (2.12e-523, 2.12e-523j)
| (-1.4341212004681264598 - 2.7584829157684450123e-520j)  +/-  (2.12e-123, 2.12e-123j)
| (-1.8072511045821133892 - 9.0965360231715734525e-522j)  +/-  (1.08e-122, 1.08e-122j)
| (1.8072511045821133892 + 1.5933151969020292414e-523j)  +/-  (9.84e-123, 9.84e-123j)
| (0.34648717248448133544 + 1.9193807905453141722e-526j)  +/-  (2.22e-126, 2.22e-126j)
| (0.7071067811865475244 - 1.2441686741479528865e-527j)  +/-  (3.3e-125, 3.3e-125j)
| (-0.34648717248448133544 - 1.8710609159515157452e-530j)  +/-  (2.78e-126, 2.78e-126j)
-------------------------------------------------
The weights are:
| (1.4651807012365342102e-10 + 2.3010113872705566899e-470j)  +/-  (1.74e-32, 6.26e-93j)
| (7.3604860149091675773e-07 + 4.647785830244930814e-469j)  +/-  (7.01e-30, 2.53e-90j)
| (5.3141913765609518586e-13 + 5.5163098375428159036e-472j)  +/-  (1.69e-34, 6.1e-95j)
| (1.5561200081563432617e-08 - 1.0420984941110904844e-469j)  +/-  (2.43e-31, 8.78e-92j)
| (1.0591795842534912471e-15 + 1.6910517065760240334e-474j)  +/-  (6.62e-39, 2.39e-99j)
| (3.3559369409544793223e-18 - 5.6402908583494221865e-476j)  +/-  (6.15e-40, 2.22e-100j)
| (1.0591795842534912471e-15 - 1.5634363986082079655e-473j)  +/-  (3.42e-37, 1.23e-97j)
| (0.064861888077064088239 + 2.5449345092251513546e-466j)  +/-  (1.1e-23, 3.97e-84j)
| (7.3604860149091675773e-07 + 5.9451687767118673068e-470j)  +/-  (3.54e-35, 1.28e-95j)
| (0.0017868039638507563832 - 1.1561956540823310191e-467j)  +/-  (4.35e-31, 1.57e-91j)
| (3.3559369409544793223e-18 + 3.7780169457674884117e-475j)  +/-  (4.16e-39, 1.5e-99j)
| (0.00023288668402424852538 + 8.982481984137324457e-468j)  +/-  (3.65e-32, 1.32e-92j)
| (1.4651807012365342102e-10 + 5.2814316000899205214e-472j)  +/-  (6.9e-38, 2.49e-98j)
| (5.3141913765609518586e-13 - 3.2217114962109536684e-473j)  +/-  (7.23e-39, 2.61e-99j)
| (0.00023288668402424852538 + 2.4591728931494325828e-468j)  +/-  (2.26e-34, 8.16e-95j)
| (0.064861888077064088239 + 4.076857710592074807e-466j)  +/-  (7.05e-31, 2.54e-91j)
| (1.7631979696833869749e-05 - 2.1487718404847622119e-468j)  +/-  (4.28e-35, 1.54e-95j)
| (1.7631979696833869749e-05 - 4.2609535874759080175e-469j)  +/-  (1.58e-35, 5.69e-96j)
| (0.12512343130845383693 - 4.4542576588024540181e-466j)  +/-  (1.35e-31, 4.86e-92j)
| (1.5561200081563432617e-08 - 6.4671696658314717773e-471j)  +/-  (2.34e-37, 8.44e-98j)
| (0.026201340903880275248 - 2.2720515065776019817e-466j)  +/-  (1.26e-33, 4.54e-94j)
| (0.0017868039638507563832 - 3.2630371014477726952e-467j)  +/-  (4.1e-35, 1.48e-95j)
| (0.1932067827872110356 - 8.0866694794421888445e-466j)  +/-  (3.76e-33, 1.35e-93j)
| (0.026201340903880275248 - 1.1984349539581990854e-466j)  +/-  (7.07e-34, 2.55e-94j)
| (0.0083216262077528910262 + 4.2999848572880372544e-467j)  +/-  (1.64e-34, 5.9e-95j)
| (0.0083216262077528910262 + 9.7947347206425644217e-467j)  +/-  (3.1e-35, 1.13e-95j)
| (0.17685024772481942771 + 7.7309776977157051302e-466j)  +/-  (3.01e-34, 1.09e-94j)
| (0.12512343130845383693 - 6.0576487925035797519e-466j)  +/-  (1.97e-34, 7.15e-95j)
| (0.17685024772481942771 + 6.6556999417234717088e-466j)  +/-  (2.26e-34, 7.7e-95j)
