Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 6 18
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Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P3 : 4*t^11 - 6923/82*t^9 + 97479/164*t^7 - 566685/328*t^5 + 1313235/656*t^3 - 418635/656*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^29 - 1739343849360700900915385139711369413654620871/2804684868715267961056838243178129357542014*t^27 + 5982798057179293696423447768778308948230504277893/145843613173193933974955588645262726592184728*t^25 - 444894871727392010877813490812968980067212146130725/291687226346387867949911177290525453184369456*t^23 + 20636133589143136862923244626466638346274168399450075/583374452692775735899822354581050906368738912*t^21 - 89557860086548338875531185093871077501902695367899625/166678415055078781685663529880300258962496832*t^19 + 28473520591687962022667037361972728427519766653631325/5208700470471211927676985308759383092578026*t^17 - 12496074056386778434148502163077088684565735481491842575/333356830110157563371327059760600517924993664*t^15 + 114783998837346305536354759434197630639156865161531801625/666713660220315126742654119521201035849987328*t^13 - 26652344991611305307564030982019675575470296695880693875/51285666170793471287896470732400079680768256*t^11 + 408530383267663189575183041312491241299789284010629351375/410285329366347770303171765859200637446146048*t^9 - 937072754814471899185380815570135204223847727610488686875/820570658732695540606343531718401274892292096*t^7 + 1165100165932814596183175323376924581360967312898482998125/1641141317465391081212687063436802549784584192*t^5 - 655318829248406657027461674460666195426726751865358063125/3282282634930782162425374126873605099569168384*t^3 + 54750150401706830323145649752298333950458786514292650625/3282282634930782162425374126873605099569168384*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:
| (3.7030184697474786934 + 4.1521319016406574264e-441j)  +/-  (4.17e-121, 4.17e-121j)
| (2.7490766116836097725 - 3.1774086048849432964e-451j)  +/-  (2.08e-121, 2.08e-121j)
| (-6.1450624638331883047 + 8.3982888582863333225e-460j)  +/-  (1.53e-122, 1.53e-122j)
| (6.1450624638331883047 - 2.6929081589192055336e-459j)  +/-  (1.44e-122, 1.44e-122j)
| (4.7799996874015418171 + 2.7070349582584496808e-458j)  +/-  (2.44e-121, 2.44e-121j)
| (5.4011491401779066141 + 7.3176984261977834056e-463j)  +/-  (9.86e-122, 9.86e-122j)
| (2.3142743884833336815 + 2.4216132228679460198e-465j)  +/-  (1.13e-121, 1.13e-121j)
| (-2.3142743884833336815 + 1.8666279742747877208e-473j)  +/-  (1.18e-121, 1.18e-121j)
| (-5.4011491401779066141 - 3.0306081107719139413e-475j)  +/-  (9.5e-122, 9.5e-122j)
| (4.2214800553941908447 - 2.1954002443903996995e-476j)  +/-  (4.04e-121, 4.04e-121j)
| (1.0278114138445907863 - 9.5061962556398280167e-484j)  +/-  (4.1e-124, 4.1e-124j)
| (1.9659765620231588295 - 3.3539562582439839364e-480j)  +/-  (6.27e-122, 6.27e-122j)
| (-2.7490766116836097725 + 7.1234135764618310192e-485j)  +/-  (2.02e-121, 2.02e-121j)
| (-0.7071067811865475244 - 2.2911638778936687714e-489j)  +/-  (4.58e-125, 4.58e-125j)
| (-4.7799996874015418171 + 5.4878603919946925699e-485j)  +/-  (2.58e-121, 2.58e-121j)
| (-4.2214800553941908447 - 2.1517074207305386716e-486j)  +/-  (4.07e-121, 4.07e-121j)
| (0.37110708725580585983 - 1.5924567085089965966e-495j)  +/-  (3.12e-126, 3.12e-126j)
| (-1.3866480207208212553 - 8.6232123801384699437e-493j)  +/-  (3.49e-123, 3.49e-123j)
| (-1.0278114138445907863 - 7.2153083573619703105e-494j)  +/-  (4.41e-124, 4.41e-124j)
| (-1.9659765620231588295 - 5.2365719657594029487e-492j)  +/-  (7.26e-122, 7.26e-122j)
| (3.2137281525534003284 + 7.6475376889855019622e-494j)  +/-  (3.27e-121, 3.27e-121j)
| (0.7071067811865475244 + 2.3499880243593364883e-501j)  +/-  (5.08e-125, 5.08e-125j)
| (-3.2137281525534003284 - 8.5834103261461008245e-497j)  +/-  (3.55e-121, 3.55e-121j)
| (-1.7320508075688772935 - 6.7762763072846414757e-499j)  +/-  (2.52e-122, 2.52e-122j)
| (-3.7030184697474786934 - 1.2182818944359089749e-499j)  +/-  (4.21e-121, 4.21e-121j)
| (-1.9549682154324799917e-510 - 3.9127086489810015036e-510j)  +/-  (1.27e-508, 1.27e-508j)
| (1.7320508075688772935 + 6.736151111973372777e-502j)  +/-  (2.56e-122, 2.56e-122j)
| (1.3866480207208212553 - 5.1140105585139696682e-508j)  +/-  (3.78e-123, 3.78e-123j)
| (-0.37110708725580585983 + 1.9920119800080848044e-511j)  +/-  (3.12e-126, 3.12e-126j)
-------------------------------------------------
The weights are:
| (3.1440382315518131469e-07 - 6.5868487154865982149e-447j)  +/-  (4.76e-33, 1.23e-93j)
| (0.00013320210015115247494 - 1.371406395608018243e-445j)  +/-  (1.07e-29, 2.78e-90j)
| (1.9228972450092079736e-17 - 9.2087853578331423384e-455j)  +/-  (9.96e-41, 2.58e-101j)
| (1.9228972450092079736e-17 + 3.7136457711219565177e-454j)  +/-  (5.49e-40, 1.42e-100j)
| (3.937957104529343396e-11 + 3.9432245207162969077e-450j)  +/-  (4.38e-37, 1.13e-97j)
| (8.0464930965423333958e-14 - 6.3428518535011561956e-452j)  +/-  (1.72e-38, 4.44e-99j)
| (0.0010945299063443786321 + 8.1620021667251361074e-445j)  +/-  (1.52e-30, 3.94e-91j)
| (0.0010945299063443786321 + 1.8837261995906585813e-445j)  +/-  (1.95e-33, 5.06e-94j)
| (8.0464930965423333958e-14 + 1.1830835865788533095e-452j)  +/-  (5.96e-42, 1.54e-102j)
| (5.5092454345164311119e-09 - 1.7556310278168082076e-448j)  +/-  (1.06e-36, 2.75e-97j)
| (0.066290413865812382999 + 1.4530276819969081406e-443j)  +/-  (1.46e-28, 3.79e-89j)
| (0.0030431473530675780833 - 3.879943907980849352e-444j)  +/-  (1.59e-31, 4.13e-92j)
| (0.00013320210015115247494 - 2.0276235085591164496e-446j)  +/-  (5.52e-36, 1.43e-96j)
| (0.1082763166861901079 - 1.2537784710804581773e-443j)  +/-  (2.03e-29, 5.27e-90j)
| (3.937957104529343396e-11 - 5.006212018308645833e-451j)  +/-  (3.7e-41, 9.6e-102j)
| (5.5092454345164311119e-09 + 1.1486244124767677313e-449j)  +/-  (2.59e-40, 6.72e-101j)
| (0.1760301943794729293 + 1.7963550188629148044e-443j)  +/-  (4.69e-31, 1.22e-91j)
| (0.030630060206135103086 - 4.3748994915660652176e-444j)  +/-  (1.58e-33, 4.1e-94j)
| (0.066290413865812382999 + 8.2166342974230951459e-444j)  +/-  (1.03e-32, 2.67e-93j)
| (0.0030431473530675780833 - 1.1888571311540368831e-444j)  +/-  (2.8e-35, 7.24e-96j)
| (8.7957259576144581017e-06 + 2.9064055118000299886e-446j)  +/-  (7.42e-38, 1.92e-98j)
| (0.1082763166861901079 - 1.8456218569992012675e-443j)  +/-  (2.3e-34, 5.95e-95j)
| (8.7957259576144581017e-06 + 2.055989833659786347e-447j)  +/-  (6.41e-39, 1.66e-99j)
| (0.0079895478296819274907 + 2.5752970730927697254e-444j)  +/-  (1.42e-35, 3.69e-96j)
| (3.1440382315518131469e-07 - 1.7626784126257191097e-448j)  +/-  (4.8e-40, 1.24e-100j)
| (0.21300694398931636134 - 1.5899159256407451982e-443j)  +/-  (1.01e-35, 2.61e-96j)
| (0.0079895478296819274907 + 7.1015462441298624116e-444j)  +/-  (3.3e-37, 8.66e-98j)
| (0.030630060206135103086 - 9.6127885534737705805e-444j)  +/-  (5.91e-37, 1.55e-97j)
| (0.1760301943794729293 + 1.4690994793328458308e-443j)  +/-  (2.74e-36, 6.64e-97j)
