Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 6 34
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P3 : t^11 - 6923/164*t^9 + 97479/164*t^7 - 566685/164*t^5 + 1313235/164*t^3 - 418635/82*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 63617803672860193255376503302073329669785621715477162873837730021251674057501736424499613467087/74454675495315467998441464243090095879247240939292163830322529781581184407011195204105660380*t^43 + 12850315980269882203459774043746715654092756467535425355950388740045118123011033254404620445619914013/38865340608554674295186444334893030048967059770310509519428360545985378260459843896543154718360*t^41 - 20918118055079616890714391149900087304589641574203412583392726603048617989135563560025405559971680066443/272057384259882720066305110344251210342769418392173566635998523821897647823218907275802083028520*t^39 + 31158178403527736267090416059375313560017996705231088183096899083549316340023235566227866709900867589585/2591022707236978286345762955659535336597803984687367301295224036399025217363989593102876981224*t^37 - 593447225693716427926612519884031145403392080145336957873851275754490024710597624165562052370530430941535/442369730503874341571227821697969447711820192507599295343087030604711622476778711017564362648*t^35 + 143138390930528475950805883257877561526047289920444809522075167984509902335546014392734058361144573854732619/1295511353618489143172881477829767668298901992343683650647612018199512608681994796551438490612*t^33 - 1481525617062542995521121761385763836904044832105593201542167404415509649867850156058684356761646902982007577/215918558936414857195480246304961278049816998723947275107935336366585434780332466091906415102*t^31 + 2422835599756431192364902880454615918627008730993936425057924050879424950838281542538887695116643466555133719/7445467549531546799844146424309009587924724093929216383032252978158118440701119520410566038*t^29 - 44176388698958800001303095377983405122912758876072815764470650201196020823897424064188849833502967243971695220/3722733774765773399922073212154504793962362046964608191516126489079059220350559760205283019*t^27 + 4966329964224664756473594756105055532659592004453586625784685536322993022501780459392866102293093085060012003735/14890935099063093599688292848618019175849448187858432766064505956316236881402239040821132076*t^25 - 107407459036546260697641824200417939381170988036200058570464268579851783403351679220171843419174496943329039214875/14890935099063093599688292848618019175849448187858432766064505956316236881402239040821132076*t^23 + 1778216481844191100381554898366552777714812403321056155759594962457420892420218027599368550220058676073272727676225/14890935099063093599688292848618019175849448187858432766064505956316236881402239040821132076*t^21 - 22334345639859285789809488167954706500393490316605836077842821980533966475905256297113281911519389014999795330797925/14890935099063093599688292848618019175849448187858432766064505956316236881402239040821132076*t^19 + 52499124617310415565883399881349606947708246737207710457298645874830083522122165760095059281203253753539333115938375/3722733774765773399922073212154504793962362046964608191516126489079059220350559760205283019*t^17 - 725428369976963889982367460066222737948432574743402512025203351927054473757609505343183393842371361472267310808171625/7445467549531546799844146424309009587924724093929216383032252978158118440701119520410566038*t^15 + 3590573739930134994344709321249286093040106395679907442304184992456584485267821118683163955207451657297984370779457125/7445467549531546799844146424309009587924724093929216383032252978158118440701119520410566038*t^13 - 24603768212199835581711530175594565480133407295954428884527433434860703962018969486689648248531006765283711309882107625/14890935099063093599688292848618019175849448187858432766064505956316236881402239040821132076*t^11 + 111400171208732382939671916299837785256070340205474241615134144365908118109478864381299699284656275937348130839760585125/29781870198126187199376585697236038351698896375716865532129011912632473762804478081642264152*t^9 - 156415579995387602111693119206686034121903463440478880705991086174996357467102306628901844739584199739282191638656138125/29781870198126187199376585697236038351698896375716865532129011912632473762804478081642264152*t^7 + 124541462855582016673833688806124615238318926130525509516652385904785496112149541185247781997724301150093187337359929375/29781870198126187199376585697236038351698896375716865532129011912632473762804478081642264152*t^5 - 48432679361416675926607217107951037416435900745033859062591985543622179010955770232012193504205150369082181736532094375/29781870198126187199376585697236038351698896375716865532129011912632473762804478081642264152*t^3 + 3137452362316710645890774916760504885959036996753432480758448518634371955238148441229356333708889716192180089302346875/14890935099063093599688292848618019175849448187858432766064505956316236881402239040821132076*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:
| (-7.3087498809422795164 - 6.6441503106670260923e-853j)  +/-  (7.21e-245, 7.21e-245j)
| (0.97540703275497058911 + 2.0483804992934632519e-867j)  +/-  (1.13e-250, 1.13e-250j)
| (11.830443147042219509 - 5.1149572650129827927e-865j)  +/-  (1.19e-247, 1.19e-247j)
| (8.5580612571517520618 + 5.9545920796510161418e-861j)  +/-  (4.33e-245, 4.33e-245j)
| (-9.2386191651287192521 + 3.6119377562146430776e-860j)  +/-  (2.02e-245, 2.02e-245j)
| (-10.809209164315999772 - 2.8876855850008133166e-866j)  +/-  (1.39e-246, 1.39e-246j)
| (7.9182064912179541811 + 2.406805939463967684e-869j)  +/-  (6.06e-245, 6.06e-245j)
| (-11.830443147042219509 + 5.0956750643705562725e-870j)  +/-  (1.09e-247, 1.09e-247j)
| (5.6056544317601122842 + 2.3008315326746372345e-869j)  +/-  (2.73e-245, 2.73e-245j)
| (3.2728782272458314193 + 2.4499731849473252294e-873j)  +/-  (6.09e-247, 6.09e-247j)
| (1.961016437141193946 - 3.5705301240121225518e-875j)  +/-  (9.15e-250, 9.15e-250j)
| (-3.2728782272458314193 + 2.5729020276437552425e-871j)  +/-  (5.92e-247, 5.92e-247j)
| (-0.97540703275497058911 + 3.3615668708243801993e-875j)  +/-  (1.08e-250, 1.08e-250j)
| (-5.6056544317601122842 + 6.7304898488555801319e-870j)  +/-  (2.58e-245, 2.58e-245j)
| (-8.5580612571517520618 - 1.2853386315844346506e-878j)  +/-  (4.15e-245, 4.15e-245j)
| (-3.5757857458711647324 - 4.0131901680096570813e-884j)  +/-  (1.31e-246, 1.31e-246j)
| (7.3087498809422795164 + 1.4375700567098831798e-883j)  +/-  (7.08e-245, 7.08e-245j)
| (-2.9198036845560688454 - 8.1533922726756619266e-887j)  +/-  (1.32e-247, 1.32e-247j)
| (6.1563844717675145008 + 6.852327938879484298e-883j)  +/-  (4.39e-245, 4.39e-245j)
| (9.2386191651287192521 + 6.7937981055909248537e-889j)  +/-  (2.07e-245, 2.07e-245j)
| (-5.0687090012579039552 + 3.7501611581601152934e-889j)  +/-  (1.42e-245, 1.42e-245j)
| (4.5448979391212497356 + 1.1284320460172469938e-898j)  +/-  (5.79e-246, 5.79e-246j)
| (10.809209164315999772 - 1.2223719261924042612e-902j)  +/-  (1.5e-246, 1.5e-246j)
| (-2.4494897427831780982 - 2.7462805596718022971e-901j)  +/-  (9.66e-249, 9.66e-249j)
| (-6.7230078487800717878 - 2.0932336023621886929e-906j)  +/-  (6.21e-245, 6.21e-245j)
| (1 + 3.0364211495707005698e-928j)  +/-  (1.36e-250, 1.36e-250j)
| (3.5757857458711647324 + 2.6205306875526839911e-923j)  +/-  (1.38e-246, 1.38e-246j)
| (-6.1563844717675145008 - 5.9654001534016552347e-925j)  +/-  (4.62e-245, 4.62e-245j)
| (2.9198036845560688454 + 9.1741948346848075274e-935j)  +/-  (1.21e-247, 1.21e-247j)
| (-1.4702756633995088851 - 3.8953999615809665896e-938j)  +/-  (1.02e-250, 1.02e-250j)
| (9.9773739746015830635 + 7.7940358333291412955e-934j)  +/-  (7.47e-246, 7.47e-246j)
| (-4.5448979391212497356 - 6.9758926306774983855e-932j)  +/-  (5.4e-246, 5.4e-246j)
| (0.48944100173352563561 + 1.562742242804641459e-945j)  +/-  (2.4e-253, 2.4e-253j)
| (1.4702756633995088851 - 3.4856131414115917946e-943j)  +/-  (1.12e-250, 1.12e-250j)
| (-1.961016437141193946 + 1.2679605816152656238e-941j)  +/-  (9.08e-250, 9.08e-250j)
| (-4.0376624323526134512 + 9.5333989372437449496e-938j)  +/-  (2.28e-246, 2.28e-246j)
| (2.4494897427831780982 - 7.3172820379228169322e-942j)  +/-  (1e-248, 1e-248j)
| (6.7230078487800717878 - 1.5043556795017455722e-938j)  +/-  (6.62e-245, 6.62e-245j)
| (-1 - 3.8815452256361787396e-951j)  +/-  (1.39e-250, 1.39e-250j)
| (-0.48944100173352563561 - 9.559868002317719107e-954j)  +/-  (2.4e-253, 2.4e-253j)
| (5.0687090012579039552 + 1.1394036533660935538e-945j)  +/-  (1.41e-245, 1.41e-245j)
| (-7.9182064912179541811 + 6.9423353113362155168e-959j)  +/-  (6.21e-245, 6.21e-245j)
| (-9.9773739746015830635 + 1.0876231164582507874e-976j)  +/-  (7.28e-246, 7.28e-246j)
| (4.0376624323526134512 - 1.417444954484743303e-985j)  +/-  (2.47e-246, 2.47e-246j)
| (-1.7347124576704870739e-1112 - 2.2357714546276309432e-1112j)  +/-  (1.27e-1110, 1.27e-1110j)
-------------------------------------------------
The weights are:
| (5.9858722829497922928e-13 - 1.6780941144100729007e-864j)  +/-  (4.94e-88, 3.31e-209j)
| (0.10114167732072151862 - 8.3095181265713642696e-857j)  +/-  (7.35e-71, 4.92e-192j)
| (1.9434132558668411004e-31 - 2.5952109835433983127e-876j)  +/-  (1.19e-97, 7.99e-219j)
| (3.275100739272883336e-17 - 9.9864587814955761366e-869j)  +/-  (1.33e-91, 8.89e-213j)
| (8.2345796403700302971e-20 - 3.1338373707987128311e-869j)  +/-  (3.09e-93, 2.07e-214j)
| (1.5268819047428511327e-26 - 4.648849071228183792e-873j)  +/-  (1.48e-96, 9.95e-218j)
| (6.0383547416032166474e-15 + 1.9001503614040925201e-867j)  +/-  (1.57e-91, 1.05e-212j)
| (1.9434132558668411004e-31 + 1.0984876920164552989e-875j)  +/-  (1.39e-98, 9.3e-220j)
| (3.2559545086675320418e-08 + 2.3634089477415617157e-863j)  +/-  (1.42e-86, 9.5e-208j)
| (0.00048465810598787816219 - 1.4226701673425783611e-859j)  +/-  (1.8e-78, 1.2e-199j)
| (0.028604770488232885238 + 8.6145358740690872754e-859j)  +/-  (7.11e-71, 4.77e-192j)
| (0.00048465810598787816219 - 3.7300905281433606298e-859j)  +/-  (1.02e-79, 6.87e-201j)
| (0.10114167732072151862 - 1.0869039256346556305e-856j)  +/-  (2.33e-72, 1.56e-193j)
| (3.2559545086675320418e-08 + 1.7921496241152608025e-862j)  +/-  (7.88e-88, 5.28e-209j)
| (3.275100739272883336e-17 + 1.2683247504300815418e-867j)  +/-  (1.62e-93, 1.09e-214j)
| (0.00026898326958376729382 + 1.5569751559889436362e-859j)  +/-  (2.22e-81, 1.49e-202j)
| (5.9858722829497922928e-13 - 2.7207823427540707612e-866j)  +/-  (2.83e-92, 1.9e-213j)
| (0.0024834805245399828083 + 5.2926947472587538976e-859j)  +/-  (1.16e-79, 7.76e-201j)
| (1.3110323500506065767e-09 - 2.9171406592522822766e-864j)  +/-  (3.86e-90, 2.59e-211j)
| (8.2345796403700302971e-20 + 3.6548991273543332616e-870j)  +/-  (9.36e-97, 6.28e-218j)
| (5.5801400262190778183e-07 - 9.4424478924221173654e-862j)  +/-  (1.62e-88, 1.09e-209j)
| (6.7421916176645130564e-06 + 1.1555518848110693537e-861j)  +/-  (6e-88, 4.02e-209j)
| (1.5268819047428511327e-26 + 8.9817549708048184911e-874j)  +/-  (2.01e-100, 1.35e-221j)
| (0.0096273482698659046016 - 7.6929327208378536491e-859j)  +/-  (1.24e-81, 8.32e-203j)
| (3.5171270572439187699e-11 + 7.4142829750310256296e-864j)  +/-  (8.39e-93, 5.62e-214j)
| (0.020045370389989751864 + 8.1462692493700209888e-857j)  +/-  (9.69e-76, 6.49e-197j)
| (0.00026898326958376729382 + 5.3398074269460199574e-860j)  +/-  (1.2e-86, 8.04e-208j)
| (1.3110323500506065767e-09 - 3.4086141914872754391e-863j)  +/-  (1.06e-91, 7.09e-213j)
| (0.0024834805245399828083 + 2.2710300469252054549e-859j)  +/-  (2.33e-85, 1.56e-206j)
| (0.066417071051861062386 - 4.1156154882587609893e-858j)  +/-  (1.44e-81, 9.69e-203j)
| (7.4949632235920746903e-23 - 8.2229754327247626456e-872j)  +/-  (1.95e-99, 1.31e-220j)
| (6.7421916176645130564e-06 + 4.9559474834045327792e-861j)  +/-  (3.88e-89, 2.6e-210j)
| (0.17324171837841105272 + 6.3408852532090547863e-858j)  +/-  (3.32e-81, 2.23e-202j)
| (0.066417071051861062386 - 2.7370822419900265258e-858j)  +/-  (2.32e-83, 1.55e-204j)
| (0.028604770488232885238 + 1.4932444805195795711e-858j)  +/-  (2.55e-84, 1.71e-205j)
| (5.6897810456996002867e-05 - 2.7177573830781785465e-860j)  +/-  (4.29e-88, 2.88e-209j)
| (0.0096273482698659046016 - 3.830809937323791075e-859j)  +/-  (2.99e-86, 2e-207j)
| (3.5171270572439187699e-11 + 3.095020071378998263e-865j)  +/-  (2.17e-94, 1.46e-215j)
| (0.020045370389989751864 + 1.0728799672884354936e-856j)  +/-  (1.47e-83, 9.86e-205j)
| (0.17324171837841105272 + 7.2510916346536623541e-858j)  +/-  (9.76e-85, 6.53e-206j)
| (5.5801400262190778183e-07 - 1.7088700914900463563e-862j)  +/-  (6.97e-92, 4.67e-213j)
| (6.0383547416032166474e-15 - 4.747426819077404211e-866j)  +/-  (1.75e-97, 1.17e-218j)
| (7.4949632235920746903e-23 + 5.3264666371893420141e-871j)  +/-  (6.05e-102, 4.03e-223j)
| (5.6897810456996002867e-05 - 7.8350952011776741681e-861j)  +/-  (6.95e-91, 4.8e-212j)
| (0.19524138055675109632 - 5.3270658711842931654e-858j)  +/-  (1.29e-87, 7.07e-209j)
