Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 4 22
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P3 : 4*t^9 - 142/3*t^7 + 1399/9*t^5 - 2965/18*t^3 + 295/6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^31 - 24747738563437975468285027669966887760383013/33556620219730893971779786997400739842237*t^29 + 17725417157318966622701995809882101681630819078/302009581977578045746018082976606658580133*t^27 - 38563209336510252181855187499909817888828268266835/14496459934923746195808867982877119611846384*t^25 + 6640251448466817785130490905029652852531582609451525/86978759609542477174853207897262717671078304*t^23 - 253961358105313632491565957461907925890836179010183575/173957519219084954349706415794525435342156608*t^21 + 116458771764497610811399109415608112648408076504397825/6103772604178419450866891782264050362882688*t^19 - 175144226296048893742324036140191647073942952514072925/1017295434029736575144481963710675060480448*t^17 + 4361975814607064495233822396398462498771985286596135375/4069181736118946300577927854842700241921792*t^15 - 12366749513046126558299303385104007030854306247171723625/2712787824079297533718618569895133494614528*t^13 + 70363915337526784742963560241662641666019914636387081625/5425575648158595067437237139790266989229056*t^11 - 516905761537828875556797479328819236449994876601158794625/21702302592634380269748948559161067956916224*t^9 + 42762151387960858368773252338570284822158787898373742875/1607577969824768908870292485863782811623424*t^7 - 471257905744955351842683326880370425812594563493359800625/28936403456845840359665264745548090609221632*t^5 + 260227047861899491324338498760047735475599167584956454375/57872806913691680719330529491096181218443264*t^3 - 6847833317295372070523864713987475840910366583407053125/19290935637897226906443509830365393739481088*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:
| (-5.1387919667251484694 - 1.6251847494078855104e-435j)  +/-  (6.31e-121, 6.31e-121j)
| (-4.5872564056254618022 - 2.7118379558588699188e-445j)  +/-  (1.02e-120, 1.02e-120j)
| (-6.4874119704108006612 + 3.2562808816390590148e-451j)  +/-  (3.06e-122, 3.06e-122j)
| (3.5908399493165381444 - 2.5022782036691704085e-448j)  +/-  (9.9e-121, 9.9e-121j)
| (4.5872564056254618022 - 7.5508567742186194244e-452j)  +/-  (1.08e-120, 1.08e-120j)
| (-5.7523027519292029033 - 1.8845275447558468162e-454j)  +/-  (2.02e-121, 2.02e-121j)
| (5.7523027519292029033 + 1.2434570583152839485e-457j)  +/-  (2.06e-121, 2.06e-121j)
| (-3.5908399493165381444 - 8.2377917624698315059e-462j)  +/-  (1.14e-120, 1.14e-120j)
| (-4.0750938992869966786 + 5.3146718942218904649e-473j)  +/-  (1.23e-120, 1.23e-120j)
| (6.4874119704108006612 + 1.0427410724265286048e-472j)  +/-  (3.45e-122, 3.45e-122j)
| (0.7071067811865475244 + 9.9234372523883359088e-478j)  +/-  (4.16e-125, 4.16e-125j)
| (1.4470365147572695669 - 2.8061164886140810426e-475j)  +/-  (1.23e-122, 1.23e-122j)
| (4.0750938992869966786 + 2.2362244402803175857e-473j)  +/-  (1.22e-120, 1.22e-120j)
| (-1.0672470719421885588 - 2.8568721082768721092e-480j)  +/-  (5.94e-124, 5.94e-124j)
| (-3.1278754642217910584 + 1.6640481076442755131e-476j)  +/-  (6.37e-121, 6.37e-121j)
| (-2.2514999011812653627 + 1.9943669738616856534e-478j)  +/-  (1.63e-121, 1.63e-121j)
| (0.35436610072511823316 + 2.8037058744493685e-484j)  +/-  (3.34e-126, 3.34e-126j)
| (-2.6822224032999497583 - 8.3156748844381518908e-478j)  +/-  (3.31e-121, 3.31e-121j)
| (2.9997375220104879829e-489 - 1.1255152315311704236e-489j)  +/-  (9.93e-488, 9.93e-488j)
| (2.6822224032999497583 + 1.0842109908676441052e-479j)  +/-  (3.49e-121, 3.49e-121j)
| (-1.7320508075688772935 - 2.063320926838565715e-480j)  +/-  (1.31e-121, 1.31e-121j)
| (2.2514999011812653627 + 3.7555858431811793619e-480j)  +/-  (1.62e-121, 1.62e-121j)
| (-0.35436610072511823316 - 3.4418772646240499401e-485j)  +/-  (2.78e-126, 2.78e-126j)
| (1.7320508075688772935 + 1.6337885624687872714e-479j)  +/-  (1.4e-121, 1.4e-121j)
| (-1.4470365147572695669 - 1.4760849057082605032e-486j)  +/-  (1.15e-122, 1.15e-122j)
| (5.1387919667251484694 + 2.3323212284426074433e-483j)  +/-  (6.92e-121, 6.92e-121j)
| (1.0672470719421885588 + 1.0308254753460973817e-485j)  +/-  (6.26e-124, 6.26e-124j)
| (-1.8278922080946851907 + 1.3154563701720731777e-483j)  +/-  (1.63e-121, 1.63e-121j)
| (1.8278922080946851907 - 7.5896255785733906637e-487j)  +/-  (1.86e-121, 1.86e-121j)
| (-0.7071067811865475244 + 2.9700550503539632967e-498j)  +/-  (4.16e-125, 4.16e-125j)
| (3.1278754642217910584 + 4.2995054653218026099e-501j)  +/-  (6.28e-121, 6.28e-121j)
-------------------------------------------------
The weights are:
| (1.107298272793138206e-12 - 1.0725641450612504017e-446j)  +/-  (1.38e-39, 2.32e-99j)
| (2.1693830043083160367e-10 + 7.400901582090787925e-446j)  +/-  (2.55e-38, 4.29e-98j)
| (2.5159656893958528703e-19 + 2.4055551236795093299e-451j)  +/-  (3.21e-43, 5.4e-103j)
| (6.702307382730135383e-07 + 7.6177593491825813107e-445j)  +/-  (6.7e-38, 1.13e-97j)
| (2.1693830043083160367e-10 + 4.1968333501134670994e-447j)  +/-  (4.56e-41, 7.66e-101j)
| (1.5825983794900687586e-15 - 6.909098947301418808e-449j)  +/-  (5.93e-42, 9.97e-102j)
| (1.5825983794900687586e-15 + 3.8919932531681131954e-450j)  +/-  (2.13e-44, 3.58e-104j)
| (6.702307382730135383e-07 + 4.2960139770631616241e-444j)  +/-  (4.15e-38, 6.98e-98j)
| (1.720090924247798943e-08 - 5.705768487590788315e-445j)  +/-  (7.37e-39, 1.24e-98j)
| (2.5159656893958528703e-19 - 2.7904032781437810083e-452j)  +/-  (1.17e-46, 1.97e-106j)
| (0.12119239473004141413 + 1.6816034338893959108e-440j)  +/-  (2.42e-31, 4.07e-91j)
| (0.027367232687845008481 + 1.1162622060360423014e-440j)  +/-  (4.94e-33, 8.31e-93j)
| (1.720090924247798943e-08 - 6.5870307139542922069e-446j)  +/-  (6.37e-41, 1.07e-100j)
| (0.066518934083366788933 - 1.8819666920630580697e-440j)  +/-  (2.31e-31, 3.88e-91j)
| (1.4432178432527784587e-05 - 2.910192443189201773e-443j)  +/-  (2.29e-38, 3.86e-98j)
| (0.0015038277755032682481 - 1.2315786486802887208e-441j)  +/-  (2.98e-37, 5.02e-97j)
| (0.17566890006964331197 - 2.1167690120132345304e-440j)  +/-  (3.87e-33, 6.52e-93j)
| (0.00018549033180804305006 + 1.8377967700862701013e-442j)  +/-  (6.49e-38, 1.09e-97j)
| (0.20039492208663630603 + 2.3875022531984003473e-440j)  +/-  (2.26e-33, 3.8e-93j)
| (0.00018549033180804305006 + 5.7724936918459981932e-443j)  +/-  (1.5e-40, 2.52e-100j)
| (-0.001774816167263117299 - 3.2727232370887672057e-440j)  +/-  (3.82e-37, 6.45e-97j)
| (0.0015038277755032682481 - 4.8116195208979726381e-442j)  +/-  (1.29e-39, 2.18e-99j)
| (0.17566890006964331197 - 2.4303327296688201023e-440j)  +/-  (2.55e-36, 4.3e-96j)
| (-0.001774816167263117299 - 1.6227006384997657742e-440j)  +/-  (2.09e-38, 3.52e-98j)
| (0.027367232687845008481 + 1.9913321788607765701e-440j)  +/-  (1.11e-37, 1.85e-97j)
| (1.107298272793138206e-12 - 1.7509604150154702943e-448j)  +/-  (1.37e-46, 2.28e-106j)
| (0.066518934083366788933 - 1.2346863805461745822e-440j)  +/-  (5.31e-38, 9.03e-98j)
| (0.009125455617609904643 + 2.2467717300028407572e-440j)  +/-  (1.09e-38, 1.91e-98j)
| (0.009125455617609904643 + 1.0677728161266134745e-440j)  +/-  (5.54e-39, 9.53e-99j)
| (0.12119239473004141413 + 2.2182269263962589777e-440j)  +/-  (9.47e-39, 2.06e-98j)
| (1.4432178432527784587e-05 - 7.0792179116067005045e-444j)  +/-  (2.38e-42, 3.8e-102j)
