Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 6 34
-------------------------------------------------
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 34 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^45 - 63617803672860193255376503302073329669785621715477162873837730021251674057501736424499613467087/37227337747657733999220732121545047939623620469646081915161264890790592203505597602052830190*t^43 + 12850315980269882203459774043746715654092756467535425355950388740045118123011033254404620445619914013/38865340608554674295186444334893030048967059770310509519428360545985378260459843896543154718360*t^41 - 20918118055079616890714391149900087304589641574203412583392726603048617989135563560025405559971680066443/544114768519765440132610220688502420685538836784347133271997047643795295646437814551604166057040*t^39 + 31158178403527736267090416059375313560017996705231088183096899083549316340023235566227866709900867589585/10364090828947913145383051822638141346391215938749469205180896145596100869455958372411507924896*t^37 - 593447225693716427926612519884031145403392080145336957873851275754490024710597624165562052370530430941535/3538957844030994732569822573583755581694561540060794362744696244837692979814229688140514901184*t^35 + 143138390930528475950805883257877561526047289920444809522075167984509902335546014392734058361144573854732619/20728181657895826290766103645276282692782431877498938410361792291192201738911916744823015849792*t^33 - 1481525617062542995521121761385763836904044832105593201542167404415509649867850156058684356761646902982007577/6909393885965275430255367881758760897594143959166312803453930763730733912970638914941005283264*t^31 + 2422835599756431192364902880454615918627008730993936425057924050879424950838281542538887695116643466555133719/476509923170018995190025371155776613627182342011469848514064190602119580204871649306276226432*t^29 - 11044097174739700000325773844495851280728189719018203941117662550299005205974356016047212458375741810992923805/119127480792504748797506342788944153406795585502867462128516047650529895051217912326569056608*t^27 + 4966329964224664756473594756105055532659592004453586625784685536322993022501780459392866102293093085060012003735/3812079385360151961520202969246212909017458736091758788112513524816956641638973194450209811456*t^25 - 107407459036546260697641824200417939381170988036200058570464268579851783403351679220171843419174496943329039214875/7624158770720303923040405938492425818034917472183517576225027049633913283277946388900419622912*t^23 + 1778216481844191100381554898366552777714812403321056155759594962457420892420218027599368550220058676073272727676225/15248317541440607846080811876984851636069834944367035152450054099267826566555892777800839245824*t^21 - 22334345639859285789809488167954706500393490316605836077842821980533966475905256297113281911519389014999795330797925/30496635082881215692161623753969703272139669888734070304900108198535653133111785555601678491648*t^19 + 52499124617310415565883399881349606947708246737207710457298645874830083522122165760095059281203253753539333115938375/15248317541440607846080811876984851636069834944367035152450054099267826566555892777800839245824*t^17 - 725428369976963889982367460066222737948432574743402512025203351927054473757609505343183393842371361472267310808171625/60993270165762431384323247507939406544279339777468140609800216397071306266223571111203356983296*t^15 + 3590573739930134994344709321249286093040106395679907442304184992456584485267821118683163955207451657297984370779457125/121986540331524862768646495015878813088558679554936281219600432794142612532447142222406713966592*t^13 - 24603768212199835581711530175594565480133407295954428884527433434860703962018969486689648248531006765283711309882107625/487946161326099451074585980063515252354234718219745124878401731176570450129788568889626855866368*t^11 + 111400171208732382939671916299837785256070340205474241615134144365908118109478864381299699284656275937348130839760585125/1951784645304397804298343920254061009416938872878980499513606924706281800519154275558507423465472*t^9 - 156415579995387602111693119206686034121903463440478880705991086174996357467102306628901844739584199739282191638656138125/3903569290608795608596687840508122018833877745757960999027213849412563601038308551117014846930944*t^7 + 124541462855582016673833688806124615238318926130525509516652385904785496112149541185247781997724301150093187337359929375/7807138581217591217193375681016244037667755491515921998054427698825127202076617102234029693861888*t^5 - 48432679361416675926607217107951037416435900745033859062591985543622179010955770232012193504205150369082181736532094375/15614277162435182434386751362032488075335510983031843996108855397650254404153234204468059387723776*t^3 + 3137452362316710645890774916760504885959036996753432480758448518634371955238148441229356333708889716192180089302346875/15614277162435182434386751362032488075335510983031843996108855397650254404153234204468059387723776*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:
| (4.3532212075783708415 + 7.1600912075921773883e-902j)  +/-  (3.59e-245, 3.59e-245j)
| (7.6432650993516178761 + 1.5694965986366089322e-911j)  +/-  (9.62e-247, 9.62e-247j)
| (-6.0514631487418737701 + 3.9327528587577213781e-911j)  +/-  (3e-245, 3e-245j)
| (-8.36538657371547339 - 5.0441962832083346668e-921j)  +/-  (8.64e-248, 8.64e-248j)
| (-7.6432650993516178761 + 2.0193122572147437872e-924j)  +/-  (1.06e-246, 1.06e-246j)
| (6.5326902604625176551 - 6.5474557143939429079e-933j)  +/-  (1.54e-245, 1.54e-245j)
| (-5.1680666028106577124 + 1.1083177885001633585e-950j)  +/-  (5.24e-245, 5.24e-245j)
| (7.0550687958749555725 + 8.4015660776961548971e-961j)  +/-  (5.24e-246, 5.24e-246j)
| (8.36538657371547339 - 3.3858208389095340967e-965j)  +/-  (8.01e-248, 8.01e-248j)
| (0.34608705131651273919 - 3.2156890822316269625e-968j)  +/-  (1.47e-253, 1.47e-253j)
| (-1.03964189180334253 - 2.1909031259411176888e-968j)  +/-  (7.03e-251, 7.03e-251j)
| (4.7538844398427718096 + 2.5167585242401659843e-961j)  +/-  (4.53e-245, 4.53e-245j)
| (-4.7538844398427718096 - 8.5776271529847805139e-971j)  +/-  (4.58e-245, 4.58e-245j)
| (-7.0550687958749555725 + 7.8406502618422991481e-979j)  +/-  (5.8e-246, 5.8e-246j)
| (-4.3532212075783708415 + 5.1967227289747969474e-982j)  +/-  (3.37e-245, 3.37e-245j)
| (1.3866480207208212553 - 3.7317053055749761107e-991j)  +/-  (6.98e-250, 6.98e-250j)
| (1.7320508075688772935 + 2.0366029856841102191e-990j)  +/-  (6.93e-249, 6.93e-249j)
| (2.3142743884833336815 + 1.7729679817093742603e-988j)  +/-  (3.94e-247, 3.94e-247j)
| (-1.3866480207208212553 + 2.4488847150946380106e-991j)  +/-  (6.98e-250, 6.98e-250j)
| (5.1680666028106577124 + 1.3785559511888551772e-987j)  +/-  (5.14e-245, 5.14e-245j)
| (-2.3142743884833336815 + 1.0143197808076404613e-987j)  +/-  (4.16e-247, 4.16e-247j)
| (3.5841185066507565327 + 1.7863862615658564241e-988j)  +/-  (9.93e-246, 9.93e-246j)
| (-1.7320508075688772935 + 4.054505499376863741e-990j)  +/-  (7.28e-249, 7.28e-249j)
| (-3.2137281525534003284 + 7.056532521431224115e-986j)  +/-  (4.26e-246, 4.26e-246j)
| (5.599017504775554169 + 2.6212352558778470486e-990j)  +/-  (4.79e-245, 4.79e-245j)
| (-5.599017504775554169 - 4.115693539957715356e-995j)  +/-  (4.41e-245, 4.41e-245j)
| (1.03964189180334253 - 5.9020651630333304601e-1007j)  +/-  (7.69e-251, 7.69e-251j)
| (6.0514631487418737701 + 2.0536315399406936373e-1000j)  +/-  (3.05e-245, 3.05e-245j)
| (2.8550584860587026855 - 4.8026259155014639646e-1003j)  +/-  (1.76e-246, 1.76e-246j)
| (-0.7071067811865475244 + 2.4056347531526161826e-1006j)  +/-  (8.06e-251, 8.06e-251j)
| (-3.5841185066507565327 - 1.5639694883383506337e-1000j)  +/-  (1.03e-245, 1.03e-245j)
| (0.68971692727808858226 - 3.2446134956216761338e-1013j)  +/-  (6.11e-251, 6.11e-251j)
| (3.2137281525534003284 - 1.2597581714296897206e-1007j)  +/-  (4.65e-246, 4.65e-246j)
| (-2.0646129850830634044 + 1.5705793942112069307e-1008j)  +/-  (8.04e-248, 8.04e-248j)
| (-2.8550584860587026855 + 3.3401643241802047129e-1006j)  +/-  (1.72e-246, 1.72e-246j)
| (-2.5284623489756973133 - 1.0647734132192462141e-1008j)  +/-  (8.89e-247, 8.89e-247j)
| (2.0646129850830634044 + 8.3717088018364580399e-1013j)  +/-  (8.15e-248, 8.15e-248j)
| (-6.5326902604625176551 - 1.1362725464355831204e-1009j)  +/-  (1.46e-245, 1.46e-245j)
| (-3.9637962616859981184 - 1.4911740534953708269e-1022j)  +/-  (1.92e-245, 1.92e-245j)
| (3.9637962616859981184 - 1.7109103315808530732e-1029j)  +/-  (2.05e-245, 2.05e-245j)
| (-0.68971692727808858226 + 3.6560314948863892593e-1034j)  +/-  (6.42e-251, 6.42e-251j)
| (1.3407361033072830186e-1044 + 2.3169038704698023266e-1044j)  +/-  (1.2e-1042, 1.2e-1042j)
| (2.5284623489756973133 - 2.4171704264370097236e-1033j)  +/-  (9.64e-247, 9.64e-247j)
| (0.7071067811865475244 + 3.0671189611040668749e-1037j)  +/-  (8.75e-251, 8.75e-251j)
| (-0.34608705131651273919 + 1.1045417011590657409e-1039j)  +/-  (1.47e-253, 1.47e-253j)
-------------------------------------------------
The weights are:
| (1.3110323500506065767e-09 - 5.0759789461369730647e-910j)  +/-  (2.86e-80, 3.27e-201j)
| (1.5268819047428511327e-26 - 1.1820413972682753643e-920j)  +/-  (3.9e-91, 4.46e-212j)
| (3.275100739272883336e-17 - 3.6394533236265723495e-916j)  +/-  (1.29e-87, 1.47e-208j)
| (1.9434132558668411004e-31 - 9.3329861234044340154e-924j)  +/-  (4.89e-94, 5.59e-215j)
| (1.5268819047428511327e-26 + 3.2417559437122192205e-921j)  +/-  (3.02e-92, 3.45e-213j)
| (8.2345796403700302971e-20 - 6.631588107371773274e-917j)  +/-  (3.32e-90, 3.79e-211j)
| (5.9858722829497922928e-13 - 9.982403105460478632e-914j)  +/-  (1.2e-86, 1.37e-207j)
| (7.4949632235920746903e-23 + 1.2572732294824770497e-918j)  +/-  (1.6e-91, 1.83e-212j)
| (1.9434132558668411004e-31 + 2.9585667363933907669e-923j)  +/-  (2.62e-95, 2.99e-216j)
| (0.17324171837841105272 + 2.9489932224080816598e-905j)  +/-  (1.7e-64, 1.94e-185j)
| (0.066417071051861062386 - 1.0648260454412550388e-905j)  +/-  (1.7e-64, 1.94e-185j)
| (3.5171270572439187699e-11 - 2.5903590036300388567e-911j)  +/-  (4.75e-86, 5.43e-207j)
| (3.5171270572439187699e-11 + 1.1396174056803709548e-912j)  +/-  (9.74e-87, 1.11e-207j)
| (7.4949632235920746903e-23 - 2.9776247289398446679e-919j)  +/-  (4.64e-93, 5.3e-214j)
| (1.3110323500506065767e-09 - 1.0781798988422865278e-911j)  +/-  (5.4e-86, 6.17e-207j)
| (0.028604770488232885238 + 6.4329400519670535025e-906j)  +/-  (2.89e-72, 3.3e-193j)
| (0.0096273482698659046016 - 3.4082444023813223513e-906j)  +/-  (2.53e-75, 2.89e-196j)
| (0.00048465810598787816219 - 1.7644717994973944309e-906j)  +/-  (2.04e-79, 2.33e-200j)
| (0.028604770488232885238 + 3.3247773967973974226e-906j)  +/-  (3.24e-74, 3.71e-195j)
| (5.9858722829497922928e-13 + 1.1664216741344753283e-912j)  +/-  (2.14e-89, 2.44e-210j)
| (0.00048465810598787816219 - 5.395825330715267437e-907j)  +/-  (1.82e-81, 2.08e-202j)
| (5.5801400262190778183e-07 - 6.5723412646507877357e-909j)  +/-  (7.69e-86, 8.78e-207j)
| (0.0096273482698659046016 - 1.4680673799428405945e-906j)  +/-  (1.55e-78, 1.77e-199j)
| (6.7421916176645130564e-06 + 4.3259803641881350433e-909j)  +/-  (1.42e-85, 1.62e-206j)
| (6.0383547416032166474e-15 - 5.5503188958015919039e-914j)  +/-  (4.96e-91, 5.66e-212j)
| (6.0383547416032166474e-15 + 6.9477500775961076462e-915j)  +/-  (4.74e-92, 5.41e-213j)
| (0.066417071051861062386 - 1.7330084903607500296e-905j)  +/-  (2.08e-77, 2.37e-198j)
| (3.275100739272883336e-17 + 2.229797895395635327e-915j)  +/-  (2.83e-92, 3.24e-213j)
| (5.6897810456996002867e-05 - 1.4181029282455930199e-907j)  +/-  (2.67e-85, 3.05e-206j)
| (0.020045370389989751864 + 3.1965365916368382828e-904j)  +/-  (2.96e-79, 3.38e-200j)
| (5.5801400262190778183e-07 - 6.3683873943229113095e-910j)  +/-  (4.15e-88, 4.74e-209j)
| (0.10114167732072151862 - 4.4904653964837031437e-904j)  +/-  (1.99e-79, 2.27e-200j)
| (6.7421916176645130564e-06 + 2.8727225852242690557e-908j)  +/-  (2.31e-86, 2.64e-207j)
| (0.0024834805245399828083 + 8.6499283999291709952e-907j)  +/-  (1.08e-83, 1.24e-204j)
| (5.6897810456996002867e-05 - 2.9473730663493982421e-908j)  +/-  (1.41e-86, 1.61e-207j)
| (0.00026898326958376729382 + 2.018388221451338526e-907j)  +/-  (1.62e-85, 1.86e-206j)
| (0.0024834805245399828083 + 2.4256579043763153253e-906j)  +/-  (9.62e-86, 1.1e-206j)
| (8.2345796403700302971e-20 + 1.327710692304832866e-917j)  +/-  (6.39e-97, 7.3e-218j)
| (3.2559545086675320418e-08 + 8.7702008946959741139e-911j)  +/-  (5.91e-90, 6.74e-211j)
| (3.2559545086675320418e-08 + 1.8730673219481323557e-909j)  +/-  (9.82e-91, 1.11e-211j)
| (0.10114167732072151862 - 3.2621536811742744064e-904j)  +/-  (4.51e-84, 5.07e-205j)
| (0.19524138055675109632 - 2.1373927496872244162e-905j)  +/-  (1.04e-85, 1.2e-206j)
| (0.00026898326958376729382 + 7.6119148395030351584e-907j)  +/-  (8.22e-88, 9.87e-209j)
| (0.020045370389989751864 + 4.4363729960555757962e-904j)  +/-  (1.06e-84, 1.36e-205j)
| (0.17324171837841105272 + 2.5146278594786863001e-905j)  +/-  (8.15e-86, 8.19e-207j)
