Starting with polynomial:
P : -1/120*t^5 + 5/24*t^4 - 5/3*t^3 + 5*t^2 - 5*t + 1
Extension levels are: 5 25
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P1 : -1/120*t^5 + 5/24*t^4 - 5/3*t^3 + 5*t^2 - 5*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/120*t^30 + 4627841573938565857578236410272540993226431763441132217004474944057802585/697720856087799750269627896997702750475636219152408701580464258114674208*t^29 - 5143944737655869229981172716040915041140522299828402047737318345841452196415/2093162568263399250808883690993108251426908657457226104741392774344022624*t^28 + 1032392900738969370191060698003519129669147565963349687240536407486358631719105/1831517247230474344457773229618969719998545075275072841648718677551019796*t^27 - 54823732262807085887649876644032213474117085266013724789553397875789784647891785/610505749076824781485924409872989906666181691758357613882906225850339932*t^26 + 6451582272125349229451081076724453509953556502051760756904824167239700689185130857/610505749076824781485924409872989906666181691758357613882906225850339932*t^25 - 582328625475566802844299605849465034696446858774038991833131418251622002629120485625/610505749076824781485924409872989906666181691758357613882906225850339932*t^24 + 10331498762887890093346880935257372730099968925202065688359338947483255148936930615000/152626437269206195371481102468247476666545422939589403470726556462584983*t^23 - 586300846610985611195514788973049873914081254023589503535347781805369665977707031995000/152626437269206195371481102468247476666545422939589403470726556462584983*t^22 + 2447288571473562337373523430937641845515196370753246902220531412885435619492038069857500/13875130660836926851952827497113406969685947539962673042793323314780453*t^21 - 13093217404525527535459570254761942976291376016922658893550834793953959570906856716508500/1982161522976703835993261071016200995669421077137524720399046187825779*t^20 + 402075251183987215490295317436829345071654015389781568406089904750280299098519344762900000/1982161522976703835993261071016200995669421077137524720399046187825779*t^19 - 10155805179582880278532087571250794509382838812102246778627579485715903649229353100468700000/1982161522976703835993261071016200995669421077137524720399046187825779*t^18 + 211257340236894316374487018791679548290542668170209178894512552643919799445786149507850100000/1982161522976703835993261071016200995669421077137524720399046187825779*t^17 - 3617760475089774833059166415688683845970135195013551903971847525513748782933549428123750100000/1982161522976703835993261071016200995669421077137524720399046187825779*t^16 + 50908159209599583842967671688931409456030742701014328442219884898256019731351646617521047040000/1982161522976703835993261071016200995669421077137524720399046187825779*t^15 - 586694975017069028896952066934715541633005045550093543848613475550794521342652149183549184000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^14 + 5511021615645875735092295110683602964279971496651208649486859063891091383812057623487893392000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^13 - 41926190845911628670756457359922079618837922833464085262674571274988337797086116228336889936000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^12 + 256248534743986176109121954447098428879553722623714710727862491949398073682488701337721220736000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^11 - 1245623180324424647032212852923514852052177332267439920063307865537807328219585233633024480332800000/1982161522976703835993261071016200995669421077137524720399046187825779*t^10 + 4756128944067924178020114582288946035712877472471876672389613680868902027712907419793050218880000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^9 - 14046193450482049397280083403783477647447797453715854355006729939907188231950753955689903866240000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^8 + 31469686381760312793814800994018330461287326018129172883138985300368828204486565057793734840320000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^7 - 52175453954838941982089202898227183686902291383387667779911561964635826719013747208486828216320000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^6 + 61934650669086678303464673809230150681874871698039199927515556125786886006857799973694367855820800000/1982161522976703835993261071016200995669421077137524720399046187825779*t^5 - 50254713052503168928001746692495759081712113446159798133809952275638815367792242623871179704320000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^4 + 25990400709695870939493483513571371209416875612087402907308738818054795550934387408470523330560000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^3 - 7623405692180946858377564718332492222563033644087784838479592468936751640913651207844493639680000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^2 + 1012979347134088540108235161337238911037152329438434593563467069216338217917983746962655559680000000/1982161522976703835993261071016200995669421077137524720399046187825779*t - 34525359066166013663389327896199358418975949757454398692183575380452242358534211431524089856000000/1982161522976703835993261071016200995669421077137524720399046187825779
-------------------------------------------------
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:
| (97.131540108500331843 + 7.9236767676029075954e-542j)  +/-  (1.43e-244, 1.43e-244j)
| (48.214885095914880414 - 3.2303901183021002437e-537j)  +/-  (8.6e-241, 8.6e-241j)
| (60.121171005671677689 + 2.717749605930596365e-541j)  +/-  (2.25e-241, 2.25e-241j)
| (75.227195208190407316 - 4.6471466441163512845e-544j)  +/-  (1.99e-242, 1.99e-242j)
| (84.804279521226983193 - 8.8733300982372549679e-546j)  +/-  (2.73e-243, 2.73e-243j)
| (67.160367023507030623 + 3.6193637485399839714e-543j)  +/-  (7.15e-242, 7.15e-242j)
| (20.255017912970711204 - 1.796367838629779997e-543j)  +/-  (1.45e-241, 1.45e-241j)
| (23.291406349013630955 - 5.5211614322147017403e-552j)  +/-  (2.98e-241, 2.98e-241j)
| (17.476427453616492836 + 5.9310658006990197525e-568j)  +/-  (6.39e-242, 6.39e-242j)
| (8.7123004095065222155 + 1.6121014422701418029e-586j)  +/-  (5.27e-244, 5.27e-244j)
| (26.602495310635605582 - 1.2364882302526382269e-620j)  +/-  (5.5e-241, 5.5e-241j)
| (4.5707050479043936531 + 5.3647196381063106043e-652j)  +/-  (7.4e-246, 7.4e-246j)
| (30.209041936367124536 + 2.2217378117856287769e-673j)  +/-  (9.18e-241, 9.18e-241j)
| (10.565366721093465313 + 1.2350612731202120628e-689j)  +/-  (1.92e-243, 1.92e-243j)
| (12.640800844275782659 + 1.7610427647343674417e-706j)  +/-  (6.78e-243, 6.78e-243j)
| (1.2878432875819820188 - 2.1415873091048695799e-724j)  +/-  (1.16e-248, 1.16e-248j)
| (3.5964257710407220812 - 9.4203648166866515239e-721j)  +/-  (1.29e-246, 1.29e-246j)
| (2.6709868398985673142 + 2.1531578765225746821e-723j)  +/-  (1.9e-247, 1.9e-247j)
| (34.136687739995224709 - 7.4967244527337281362e-725j)  +/-  (1.13e-240, 1.13e-240j)
| (1.4134030591065167922 + 8.5484556731053305462e-752j)  +/-  (2.48e-248, 2.48e-248j)
| (5.7026649233089534662 - 1.8588870123490922888e-748j)  +/-  (3.28e-245, 3.28e-245j)
| (7.0858100058588375569 + 2.2999594106054543018e-748j)  +/-  (1.31e-244, 1.31e-244j)
| (53.857121341163716054 + 2.802467939036232293e-743j)  +/-  (5.57e-241, 5.57e-241j)
| (38.417516251998946919 + 7.189180058902035567e-762j)  +/-  (1.4e-240, 1.4e-240j)
| (0.2635603197181409102 - 5.3270596259836754529e-788j)  +/-  (6.02e-253, 6.02e-253j)
| (0.65089203797330341492 + 2.0697942515822193277e-786j)  +/-  (3.24e-251, 3.24e-251j)
| (1.7855334698380066541 - 1.8653058744204614068e-782j)  +/-  (3.58e-248, 3.58e-248j)
| (0.049956528299559189867 + 8.0460526354550570166e-789j)  +/-  (8.98e-255, 8.98e-255j)
| (43.09242799906276827 - 4.8110846598003185832e-775j)  +/-  (1.28e-240, 1.28e-240j)
| (14.941943396732370296 - 9.1980293537111227944e-783j)  +/-  (2.21e-242, 2.21e-242j)
-------------------------------------------------
The weights are:
| (9.6443634102741122323e-42 - 5.4472620918649990493e-570j)  +/-  (1.59e-100, 3.97e-219j)
| (6.1713308308900255624e-21 + 1.068346227442594237e-557j)  +/-  (3.2e-92, 7.99e-211j)
| (5.1353781595494025261e-26 - 3.3458330557864212869e-561j)  +/-  (5.5e-95, 1.37e-213j)
| (1.8588454087057982738e-32 - 6.2660778745021663922e-565j)  +/-  (4.27e-98, 1.07e-216j)
| (1.5704720627996152281e-36 + 3.5628109171028089599e-567j)  +/-  (8.16e-100, 2.04e-218j)
| (5.1003808727563119977e-29 + 5.5646450770960351212e-563j)  +/-  (8.42e-97, 2.1e-215j)
| (4.63977577818576497e-09 + 2.3227866280196386608e-552j)  +/-  (2.22e-87, 5.54e-206j)
| (2.4311737264490843366e-10 + 1.0095489933480627333e-552j)  +/-  (8.29e-89, 2.07e-207j)
| (6.824441064631282062e-08 - 3.2753832524074741537e-552j)  +/-  (9.46e-87, 2.36e-205j)
| (0.00028654289069694864148 + 1.5213261978620064451e-549j)  +/-  (2.16e-82, 5.39e-201j)
| (9.6634063996606922875e-12 - 1.32226077181654265e-553j)  +/-  (1.46e-90, 3.64e-209j)
| (0.010626222812547478129 - 4.395928291887794323e-548j)  +/-  (3.6e-79, 8.99e-198j)
| (2.8565301728293362793e-13 + 1.9147405278878685564e-554j)  +/-  (3.33e-92, 8.3e-211j)
| (5.0663724070515868759e-05 - 3.9480004809969478057e-550j)  +/-  (5.61e-85, 1.4e-203j)
| (7.0807714742435809509e-06 + 8.9358415167301542938e-551j)  +/-  (3.42e-86, 8.52e-205j)
| (0.39576211571110390805 + 1.6292847576817451116e-546j)  +/-  (4.22e-75, 1.05e-193j)
| (0.025898687686259149207 + 8.64570652956977352e-548j)  +/-  (4.92e-80, 1.23e-198j)
| (0.062263778459983634118 - 1.6125402238050837035e-547j)  +/-  (5.45e-79, 1.36e-197j)
| (6.1266565188297121222e-15 - 2.7140690600180649775e-555j)  +/-  (2.08e-94, 5.19e-213j)
| (-0.26599941269623694843 - 2.0813189314450382292e-546j)  +/-  (1.36e-77, 3.39e-196j)
| (0.0041847180619746289059 + 1.723854813137812558e-548j)  +/-  (3.94e-83, 9.82e-202j)
| (0.0012626578954212046217 - 5.3968896954014438872e-549j)  +/-  (3.34e-84, 8.34e-203j)
| (2.4177546627634935584e-23 + 1.833304709038641464e-559j)  +/-  (2.07e-99, 5.15e-218j)
| (9.2428931031263486626e-17 + 3.7695466240680179638e-556j)  +/-  (1.99e-96, 4.97e-215j)
| (0.23004859505694120895 + 5.0671038423082580719e-548j)  +/-  (2.89e-84, 7.21e-203j)
| (0.24936277684442344678 - 1.3467123601998594378e-547j)  +/-  (4.94e-84, 1.23e-202j)
| (0.16425781601751039757 + 6.5473488911771332922e-547j)  +/-  (3.86e-84, 9.63e-203j)
| (0.12198690030416396952 - 1.2988070371258427497e-548j)  +/-  (2.79e-85, 6.95e-204j)
| (9.4269145515568457143e-19 - 5.8698082712859875235e-557j)  +/-  (1.35e-97, 3.37e-216j)
| (7.8332240713790519105e-07 - 1.3691872224216724462e-551j)  +/-  (2.12e-90, 5.28e-209j)
