Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 34
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^39 - 42915193612261847582544878238169649/31479087252248108084507726170416*t^37 + 39340257054363348447395763418558876661/188874523513488648507046357022496*t^35 - 3570921378093460968383983741100202952285/188874523513488648507046357022496*t^33 + 35865924641690410601790239642531362277665/31479087252248108084507726170416*t^31 - 6076811986370637275092424936467957709945335/125916349008992432338030904681664*t^29 + 373747031723820140570255406700654936170877045/251832698017984864676061809363328*t^27 - 1416773013178170637001175069798738818763897105/41972116336330810779343634893888*t^25 + 96251371789290534307622641963877676883464458625/167888465345323243117374539575552*t^23 - 425870316780935994041361777291287158950428526375/58395987946199388910391144200192*t^21 + 8093559647569396962767066281927055438251951613625/116791975892398777820782288400384*t^19 - 56994739075220990836206258099426335082563031762375/116791975892398777820782288400384*t^17 + 293367708855621824760224984260177343607382755523875/116791975892398777820782288400384*t^15 - 4324014302290064541449472337155420056446552834966875/467167903569595111283129153601536*t^13 + 22130846018478748548288483515771569061577613877525625/934335807139190222566258307203072*t^11 - 9406293128516292234509094852066879951052844064800625/233583951784797555641564576800768*t^9 + 79475809402824538918916129246686620338666559061708125/1868671614278380445132516614406144*t^7 - 748561094051731693139081998104963914846207735664148125/29898745828454087122120265830498304*t^5 + 403370034899718385409712554880660963805900293390496875/59797491656908174244240531660996608*t^3 - 31487846715248591251022549917788619806813814078284375/59797491656908174244240531660996608*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: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-5.0379041079551277982 - 1.2967224767855484336e-974j)  +/-  (5.99e-246, 5.99e-246j)
| (-6.4887371134174706565 - 9.5620197006975941142e-977j)  +/-  (1.18e-246, 1.18e-246j)
| (-3.4013729359653467313 - 6.3578528027999331308e-976j)  +/-  (1.31e-246, 1.31e-246j)
| (-7.7624229094410100176 + 1.4310503899357828691e-979j)  +/-  (2.52e-248, 2.52e-248j)
| (2.0386185597157755942 - 2.8288587205700980628e-978j)  +/-  (1.57e-248, 1.57e-248j)
| (3.7895583624324946757 - 1.1373014818473738018e-975j)  +/-  (2.42e-246, 2.42e-246j)
| (-5.9704619631534787955 + 1.1914358352128278144e-979j)  +/-  (2.66e-246, 2.66e-246j)
| (7.067054547578547994 - 3.6558806141282846125e-990j)  +/-  (2.55e-247, 2.55e-247j)
| (6.4887371134174706565 + 5.0517807676315161715e-1007j)  +/-  (9.91e-247, 9.91e-247j)
| (-5.4905469395219612585 + 8.9736084360398105241e-1019j)  +/-  (4.9e-246, 4.9e-246j)
| (7.7624229094410100176 + 1.8203411950915778962e-1019j)  +/-  (2.82e-248, 2.82e-248j)
| (4.6059999948646292075 + 8.1889968638323611205e-1026j)  +/-  (5.55e-246, 5.55e-246j)
| (-4.1907259704348060499 + 2.5475626727905315798e-1035j)  +/-  (4.12e-246, 4.12e-246j)
| (5.9704619631534787955 - 3.3478484241140670714e-1052j)  +/-  (2.68e-246, 2.68e-246j)
| (-2.3409879419911848082 + 3.1773363665978626761e-1066j)  +/-  (5.8e-248, 5.8e-248j)
| (1.7320508075688772935 + 2.6159965032883996799e-1066j)  +/-  (2.41e-249, 2.41e-249j)
| (-4.6059999948646292075 + 1.4404866173295073632e-1063j)  +/-  (5.8e-246, 5.8e-246j)
| (2.6704389369696454828 + 2.379308714470225759e-1063j)  +/-  (1.95e-247, 1.95e-247j)
| (-1.0578116824197734103 + 3.1776536280481114561e-1076j)  +/-  (2.55e-251, 2.55e-251j)
| (5.4905469395219612585 + 1.2586223024944741294e-1071j)  +/-  (4.76e-246, 4.76e-246j)
| (3.0269251040581904721 + 8.7918390078739910842e-1083j)  +/-  (4.85e-247, 4.85e-247j)
| (2.3409879419911848082 - 2.2096866098640504103e-1085j)  +/-  (5.51e-248, 5.51e-248j)
| (5.0379041079551277982 + 1.9968703888494347211e-1086j)  +/-  (6.49e-246, 6.49e-246j)
| (-3.7895583624324946757 - 8.1893418220872687269e-1093j)  +/-  (2.49e-246, 2.49e-246j)
| (-3.0269251040581904721 + 5.1926597378375553061e-1094j)  +/-  (4.97e-247, 4.97e-247j)
| (3.4013729359653467313 + 1.8144632675688813271e-1094j)  +/-  (1.22e-246, 1.22e-246j)
| (1.4022791771909210412 - 4.7238151292359934893e-1100j)  +/-  (2.92e-250, 2.92e-250j)
| (0.35397014871372511194 + 3.4407987685276004768e-1103j)  +/-  (7.09e-254, 7.09e-254j)
| (-1.4022791771909210412 + 3.1328522765933830932e-1101j)  +/-  (2.77e-250, 2.77e-250j)
| (-1.7320508075688772935 - 3.7275966174255361444e-1099j)  +/-  (2.47e-249, 2.47e-249j)
| (-2.0386185597157755942 + 2.8676506867979492964e-1099j)  +/-  (1.67e-248, 1.67e-248j)
| (4.1907259704348060499 - 1.2305717767902252511e-1098j)  +/-  (4.68e-246, 4.68e-246j)
| (1.0578116824197734103 - 6.3134104334189641748e-1105j)  +/-  (2.22e-251, 2.22e-251j)
| (-7.067054547578547994 - 2.5647608878419632267e-1101j)  +/-  (2.55e-247, 2.55e-247j)
| (-0.7071067811865475244 - 1.1248853180100042952e-1105j)  +/-  (1.54e-252, 1.54e-252j)
| (-0.35397014871372511194 + 9.150159171094937092e-1107j)  +/-  (9.44e-254, 9.44e-254j)
| (-2.6704389369696454828 + 2.2366089532142429205e-1104j)  +/-  (1.97e-247, 1.97e-247j)
| (0.7071067811865475244 + 1.7299457672397373378e-1110j)  +/-  (1.62e-252, 1.62e-252j)
| (3.7100087627184451387e-1237 - 1.6704319093970668069e-1237j)  +/-  (1.59e-1235, 1.59e-1235j)
-------------------------------------------------
The weights are:
| (2.3641979800627171022e-12 + 1.0988592378570797766e-985j)  +/-  (2.57e-87, 3.54e-209j)
| (1.5884823282157663943e-19 - 2.3071245169519388377e-989j)  +/-  (9.27e-92, 1.28e-213j)
| (2.0351473753195190507e-06 - 5.6304124055600023742e-981j)  +/-  (2.94e-82, 4.06e-204j)
| (3.0676156230103030003e-27 - 1.4179201199182456717e-993j)  +/-  (3.57e-95, 4.92e-217j)
| (0.0026340625065102582753 - 7.302564500669231533e-980j)  +/-  (9.93e-77, 1.37e-198j)
| (1.2906360546276143602e-07 + 7.0137145134388902669e-982j)  +/-  (1.87e-86, 2.58e-208j)
| (9.2568057470925125536e-17 + 8.5463681369279409364e-988j)  +/-  (9.18e-91, 1.27e-212j)
| (7.1564955686511235933e-23 + 9.8565753796673984859e-992j)  +/-  (8.57e-97, 1.18e-218j)
| (1.5884823282157663943e-19 - 8.0160952568500971726e-990j)  +/-  (1.26e-95, 1.74e-217j)
| (2.120856980873003087e-14 - 2.1760134990502257803e-986j)  +/-  (2.79e-91, 3.85e-213j)
| (3.0676156230103030003e-27 - 3.5220910028495029648e-994j)  +/-  (7.59e-99, 1.05e-220j)
| (1.4593475485928267437e-10 - 2.9414086527085817697e-984j)  +/-  (7.22e-92, 9.96e-214j)
| (5.4304234232227991115e-09 + 4.3012031355986567548e-983j)  +/-  (5.88e-90, 8.11e-212j)
| (9.2568057470925125536e-17 + 3.3239991265868961146e-988j)  +/-  (4.21e-95, 5.81e-217j)
| (0.00073685883773214424839 + 7.7633029106677414899e-980j)  +/-  (1.49e-85, 2.06e-207j)
| (0.0089458612864657720744 + 9.5257079722269674201e-980j)  +/-  (1.08e-82, 1.5e-204j)
| (1.4593475485928267437e-10 - 3.0914140198644689993e-984j)  +/-  (6.36e-91, 8.78e-213j)
| (0.00015554384474828760935 - 1.8474412275088664862e-980j)  +/-  (2.23e-87, 3.08e-209j)
| (0.0642231702730168224 + 2.67199349409699749e-979j)  +/-  (1.38e-80, 1.9e-202j)
| (2.120856980873003087e-14 - 8.8787081238318555938e-987j)  +/-  (1.18e-94, 1.63e-216j)
| (2.1700829521746146731e-05 + 5.9859551499642104162e-981j)  +/-  (3.37e-89, 4.65e-211j)
| (0.00073685883773214424839 + 5.5327275399772932602e-980j)  +/-  (3.82e-87, 5.27e-209j)
| (2.3641979800627171022e-12 + 1.7603822101352121507e-985j)  +/-  (6.09e-94, 8.41e-216j)
| (1.2906360546276143602e-07 - 5.938372020575045652e-982j)  +/-  (2.61e-92, 3.61e-214j)
| (2.1700829521746146731e-05 + 1.656649096634240402e-980j)  +/-  (2.61e-91, 3.6e-213j)
| (2.0351473753195190507e-06 - 2.2655526380339403545e-981j)  +/-  (8.63e-91, 1.19e-212j)
| (0.026770461161271274424 - 1.5115169280496477415e-979j)  +/-  (2.59e-87, 3.58e-209j)
| (0.17606613969416888786 + 2.7908669038988438888e-979j)  +/-  (1.24e-86, 1.71e-208j)
| (0.026770461161271274424 - 2.3417345210710769454e-979j)  +/-  (2.17e-88, 2.99e-210j)
| (0.0089458612864657720744 + 1.9418347744414224848e-979j)  +/-  (1.32e-89, 1.83e-211j)
| (0.0026340625065102582753 - 1.3922737420692195646e-979j)  +/-  (3.63e-90, 5.01e-212j)
| (5.4304234232227991115e-09 + 5.166763711308760856e-983j)  +/-  (1.03e-93, 1.41e-215j)
| (0.0642231702730168224 + 1.9836473443374039573e-979j)  +/-  (2.55e-89, 3.49e-211j)
| (7.1564955686511235933e-23 + 3.278152813504199186e-991j)  +/-  (4.61e-102, 6.33e-224j)
| (0.12055772182343694821 - 2.930819442735840251e-979j)  +/-  (3.72e-90, 5.04e-212j)
| (0.17606613969416888786 + 3.0608582592270675407e-979j)  +/-  (2.35e-90, 3.16e-212j)
| (0.00015554384474828760935 - 3.4711417221905153487e-980j)  +/-  (5.2e-92, 7.33e-214j)
| (0.12055772182343694821 - 2.4256320666530936746e-979j)  +/-  (9.85e-91, 1.45e-212j)
| (0.19977261990680679822 - 3.0158123587679084548e-979j)  +/-  (1.32e-90, 1.66e-212j)
