Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 15 30
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 16*t^19 - 748536/667*t^17 + 226304664/7337*t^15 - 3155515020/7337*t^13 + 24226003620/7337*t^11 - 9496214910/667*t^9 + 1965071745/58*t^7 - 112008278655/2668*t^5 + 250467132825/10672*t^3 - 83438061525/21344*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^49 - 8592445836680086373465447652611370960567447151287783355867959395577337443182657718599891278944768657414700846356/1137420755529850221718542737587247161471537838960260415721652995168689140649544237870882606666156878678875877*t^47 + 1853588024995569620980131042444321748496927664341266295337087617456537243764736315165412646736504447838994642698534/1137420755529850221718542737587247161471537838960260415721652995168689140649544237870882606666156878678875877*t^45 - 2670434258537623899275254407600794195462315744702849309534489702376081179237291588853121671375532990089581295848361360/12511628310828352438903970113459718776186916228562864572938182946855580547144986616579708673327725665467634647*t^43 + 645973171963149764776540274611000448354029431893863672605440174786777155288261147295880984663931689374586067623611652345/33960133986534099477025061736533522392507344048956346697975067998608004342250677959287780684746683949126436899*t^41 - 166446750333940275765704890107801965599547798334590687991146978445545398665651923724869839057527014621207505102708949098705/135840535946136397908100246946134089570029376195825386791900271994432017369002711837151122738986735796505747596*t^39 + 273210773745804578955625398740076707663938395138482095228886040338791425568826310281483633119815062133119231801019962317328535/4618578222168637528875408396168559045380998790658063150924609247810688590546092202463138173125549017081195418264*t^37 - 10115086299084423035282479542008728064312451457649898256446710285777744227915268206538525381429956187687003070334721487391365315/4618578222168637528875408396168559045380998790658063150924609247810688590546092202463138173125549017081195418264*t^35 + 25345196538138814330549762568421965773909479784950994510430105820954435838980590381367898591852938477271192652667021488201149575/401615497579881524250035512710309482207043373100701143558661673722668573090964539344620710706569479746190905936*t^33 - 2398896644188816254838542148157557760913185923577980231233935283305228781633115027418068815588639103358844698994214457800944049575/1679482989879504555954693962243112380138545014784750236699857908294795851107669891804777517500199642574980152096*t^31 + 2955654381124324765901818457587218363967089796775462186957040182774980547638418024892006541635572415628075386806963461518407393625/115826413095138245238254756016766371044037587226534499082748821261710058697080682193432932241393078798274493248*t^29 - 41739575227623123124891450248330424060324314802131895839732841937670506475712362520455428407197531116207272368399949275032046380625/115826413095138245238254756016766371044037587226534499082748821261710058697080682193432932241393078798274493248*t^27 + 919307951689787560893993762847050662203309971731892813286658332257791419037865169568676787053895841074866138089999195441817421125/228905954733474792960977778689261602853829223767854741270254587473735293867748383781488008382199760470898208*t^25 - 1416448126282522970684006663864629938821597467281389284353157699248157348656704349759651061737459697543311478841496250126486045659375/40287448033091563561132089049310042102273943383142434463564807395377411720723715545541889475267157842878084608*t^23 + 19331858313198078731062017767763864957599010506942246529094989748859605953552775966256501984763150584384037516329794883235864807703125/80574896066183127122264178098620084204547886766284868927129614790754823441447431091083778950534315685756169216*t^21 - 2676103536715282786940233049820631086398174163293411017431513175018096142687040796347236461476347221438643435697058964848356470086875/2120392001741661240059583634174212742224944388586443919134989862914600616880195555028520498698271465414636032*t^19 + 5029161016706303737884851787711643400947986979315548925689018599024411514532621142855443808740694611095926007543440073167973217520625/997831530231369995322157004317276584576444418158326550181171700195106172649503790601656705269774807253946368*t^17 - 59753000415919973478858880827643471098056769887181347067590473370376609741615197584584859086569191162970700013955487439650330210695625/3991326120925479981288628017269106338305777672633306200724686800780424690598015162406626821079099229015785472*t^15 + 256897599669911717503789602777219416777434396984505723286502101867323928036320383893208320188183028518345020645157290410114268050534375/7982652241850959962577256034538212676611555345266612401449373601560849381196030324813253642158198458031570944*t^13 - 192571578444022914887642692605008941166190954495149651451502038984483307769406499283541201818326568447743921147898879381139276681759375/3991326120925479981288628017269106338305777672633306200724686800780424690598015162406626821079099229015785472*t^11 + 69570340687228094119923886110440384623796006755928124357937047013892353545594183043961216880048408847061504672106428795109243674634375/1451391316700174538650410188097856850293010062775747709354431563920154432944732786329682480392399719642103808*t^9 - 170372374403137084303215068694561738547948379726239041336866949587355289913305173043713943918330983463763185677279607654985444333315625/5805565266800698154601640752391427401172040251102990837417726255680617731778931145318729921569598878568415232*t^7 + 115398443097450904539018295729776429018940596106809540331967086064043622318724341880459350814353749153556202760417558459133593492384375/11611130533601396309203281504782854802344080502205981674835452511361235463557862290637459843139197757136830464*t^5 - 18129358188232164699096264494462024647148279258054150092654441852341768620837777004440793542583284927104122337518068016890092634390625/11611130533601396309203281504782854802344080502205981674835452511361235463557862290637459843139197757136830464*t^3 + 1799858646221399258936722232789998753982341018292155311023827971840575675200939272649617863287288332958701518330910651862082747765625/23222261067202792618406563009565709604688161004411963349670905022722470927115724581274919686278395514273660928*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
Positive weights:   49 out of 49
Indefinite weights: 0 out of 49
Negative weights:   0 out of 49
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.6982778556672322738 + 7.1465708064408581511e-883j)  +/-  (3.97e-244, 3.97e-244j)
| (1.3498998593245308008 - 2.3974157519684023258e-898j)  +/-  (1.27e-249, 1.27e-249j)
| (6.6335554260225075874 - 3.2988637133645247676e-892j)  +/-  (7.34e-245, 7.34e-245j)
| (-6.1492385830111995694 - 1.5642354407991453515e-897j)  +/-  (1.77e-244, 1.77e-244j)
| (7.7797468609329591265 - 5.0817107326542361602e-896j)  +/-  (2.8e-246, 2.8e-246j)
| (-6.6335554260225075874 - 1.4558923512074239015e-897j)  +/-  (6.43e-245, 6.43e-245j)
| (4.0676787766194897745 + 2.2335687940229969918e-894j)  +/-  (7.07e-244, 7.07e-244j)
| (-7.7797468609329591265 - 8.053227548961782455e-907j)  +/-  (2.88e-246, 2.88e-246j)
| (-4.5547551618451053272 + 7.2678144808859903524e-903j)  +/-  (2.52e-243, 2.52e-243j)
| (3.7200412771956876814 - 1.3960722266025832107e-905j)  +/-  (2.48e-244, 2.48e-244j)
| (-7.1658022358554662112 - 9.6423976057317321156e-916j)  +/-  (1.77e-245, 1.77e-245j)
| (-3.7200412771956876814 - 4.2705054249414881509e-915j)  +/-  (2.38e-244, 2.38e-244j)
| (-8.622010765216335462 + 9.9853043523919484224e-918j)  +/-  (1.4e-247, 1.4e-247j)
| (8.622010765216335462 + 3.0861985332102088567e-913j)  +/-  (1.36e-247, 1.36e-247j)
| (3.3862181400001748776 + 4.1826771898056375593e-912j)  +/-  (8.73e-245, 8.73e-245j)
| (1.6506801238857845559 - 2.7108547109294941595e-925j)  +/-  (1.47e-248, 1.47e-248j)
| (-2.7676033562166682643 - 6.7278767862048002883e-923j)  +/-  (8.52e-246, 8.52e-246j)
| (-2.4709524457860414546 + 3.9428733139825516758e-922j)  +/-  (2.28e-246, 2.28e-246j)
| (-1.0392484373427345816 - 1.2461545882805139377e-926j)  +/-  (1.06e-250, 1.06e-250j)
| (-4.8759532376325231043 + 1.0564100533803364376e-918j)  +/-  (1.36e-243, 1.36e-243j)
| (5.2737165329917782175 + 1.2096186932079339378e-931j)  +/-  (6.36e-244, 6.36e-244j)
| (2.4709524457860414546 - 1.5150223203761342616e-947j)  +/-  (2.27e-246, 2.27e-246j)
| (2.1888080617024303415 - 3.3739208494545500983e-948j)  +/-  (5.21e-247, 5.21e-247j)
| (-5.6982778556672322738 + 7.817831977386598432e-946j)  +/-  (3.69e-244, 3.69e-244j)
| (7.1658022358554662112 + 5.3575338278558014933e-945j)  +/-  (1.82e-245, 1.82e-245j)
| (-5.2737165329917782175 - 6.2078268000816480239e-948j)  +/-  (6.6e-244, 6.6e-244j)
| (0.74548618799551030927 - 2.9947935577342084473e-955j)  +/-  (1.3e-251, 1.3e-251j)
| (3.0706922130670027239 - 1.2901400716868031522e-946j)  +/-  (2.69e-245, 2.69e-245j)
| (-4.3843844334492092276 + 1.1452164437985993374e-947j)  +/-  (2.25e-243, 2.25e-243j)
| (-0.2953349042979468064 + 2.6027590861593617203e-960j)  +/-  (1.24e-253, 1.24e-253j)
| (-1.3498998593245308008 + 7.0015835641596274294e-954j)  +/-  (1.2e-249, 1.2e-249j)
| (2.7676033562166682643 - 6.0317870888003550713e-950j)  +/-  (8.02e-246, 8.02e-246j)
| (-1.6506801238857845559 + 2.6541998415122188718e-953j)  +/-  (1.34e-248, 1.34e-248j)
| (4.8759532376325231043 + 4.9857166144812411364e-946j)  +/-  (1.31e-243, 1.31e-243j)
| (-1.9256587142851324209 + 2.6982609851658826526e-962j)  +/-  (1.11e-247, 1.11e-247j)
| (-4.0676787766194897745 - 2.7912630914780663764e-958j)  +/-  (6.83e-244, 6.83e-244j)
| (6.1492385830111995694 + 7.1900640096619188639e-957j)  +/-  (1.82e-244, 1.82e-244j)
| (0.2953349042979468064 - 1.2682283834068512164e-978j)  +/-  (1.44e-253, 1.44e-253j)
| (4.3843844334492092276 - 6.2809198358343875575e-968j)  +/-  (2.31e-243, 2.31e-243j)
| (-2.2859793536195462783e-1010 - 6.2615443531704988143e-1010j)  +/-  (3.27e-1008, 3.27e-1008j)
| (-0.74548618799551030927 - 7.0937297783214749487e-998j)  +/-  (1.1e-251, 1.1e-251j)
| (-3.3862181400001748776 + 4.4396461053941458664e-992j)  +/-  (8.53e-245, 8.53e-245j)
| (1.0392484373427345816 - 5.3287612531805632231e-997j)  +/-  (1.23e-250, 1.23e-250j)
| (1.9256587142851324209 - 1.9990846636481486119e-994j)  +/-  (1.09e-247, 1.09e-247j)
| (-3.0706922130670027239 + 5.4713808182607017663e-994j)  +/-  (2.7e-245, 2.7e-245j)
| (-0.52464762327529031788 - 1.6172294625267108745e-1000j)  +/-  (1.78e-252, 1.78e-252j)
| (-2.1888080617024303415 + 2.7703809596333440077e-1001j)  +/-  (5.62e-247, 5.62e-247j)
| (4.5547551618451053272 + 2.9981777976021364055e-1004j)  +/-  (2.59e-243, 2.59e-243j)
| (0.52464762327529031788 + 2.5663098263892106494e-1021j)  +/-  (1.68e-252, 1.68e-252j)
-------------------------------------------------
The weights are:
| (1.9510612024955082095e-15 - 1.0728819992917365616e-896j)  +/-  (1.69e-81, 1.06e-201j)
| (0.028179867528516411097 - 4.5868514034540773099e-889j)  +/-  (1.17e-52, 7.32e-173j)
| (2.2076695379063066529e-20 + 1.0729962073948814008e-900j)  +/-  (8.92e-85, 5.57e-205j)
| (9.9487669801525543295e-18 + 3.7208031496908959962e-900j)  +/-  (7.96e-85, 4.97e-205j)
| (1.9847316096610543596e-27 + 4.0425978245831889202e-905j)  +/-  (6.46e-89, 4.04e-209j)
| (2.2076695379063066529e-20 - 8.1378758751846758095e-902j)  +/-  (1.53e-86, 9.55e-207j)
| (1.2829236375428639672e-08 + 7.3851207367795285905e-893j)  +/-  (1.41e-77, 8.79e-198j)
| (1.9847316096610543596e-27 - 6.2431567298779613031e-906j)  +/-  (1.39e-90, 8.67e-211j)
| (1.1755821160754055742e-10 + 1.4489397861274949108e-894j)  +/-  (1.76e-81, 1.1e-201j)
| (1.8880199060069557601e-07 - 2.6227788701753713968e-892j)  +/-  (1.86e-77, 1.16e-197j)
| (1.5946035017535067465e-23 + 1.0781522147686123559e-903j)  +/-  (9.75e-89, 6.09e-209j)
| (1.8880199060069557601e-07 - 5.5089204671306838389e-893j)  +/-  (4.01e-79, 2.5e-199j)
| (3.5760135871354914433e-33 + 5.1641889842120295349e-909j)  +/-  (1.61e-93, 1.01e-213j)
| (3.5760135871354914433e-33 - 2.5293923570687578719e-908j)  +/-  (8.66e-95, 5.41e-215j)
| (1.9176696830898245607e-06 + 1.0323598799838675649e-891j)  +/-  (1.1e-77, 6.85e-198j)
| (0.010706994522439346215 + 2.9072640732887127773e-889j)  +/-  (3.99e-68, 2.49e-188j)
| (7.9754421648914016928e-05 + 4.2332639565110053709e-891j)  +/-  (4.01e-76, 2.5e-196j)
| (0.00036732310439957852444 - 1.4192442158835662999e-890j)  +/-  (8.94e-75, 5.58e-195j)
| (0.059136595703659589249 + 5.7547159554181291104e-889j)  +/-  (8.14e-65, 5.08e-185j)
| (1.0119626572508382207e-11 - 8.3923315941513660501e-896j)  +/-  (8.07e-84, 5.03e-204j)
| (1.9405194422170844753e-13 + 8.5109820316046908614e-896j)  +/-  (3.08e-86, 1.92e-206j)
| (0.00036732310439957852444 - 3.5924895630722993378e-890j)  +/-  (3.73e-76, 2.33e-196j)
| (0.0012673058116489018084 + 9.1964019937085343132e-890j)  +/-  (1e-74, 6.25e-195j)
| (1.9510612024955082095e-15 - 1.2234746515058472609e-898j)  +/-  (4.92e-87, 3.07e-207j)
| (1.5946035017535067465e-23 - 9.4509070043173466411e-903j)  +/-  (9.95e-93, 6.22e-213j)
| (1.9405194422170844753e-13 + 3.2933244943962635386e-897j)  +/-  (5.6e-86, 3.49e-206j)
| (0.086336444016420826952 - 1.7745575454364418032e-888j)  +/-  (1.95e-71, 1.22e-191j)
| (1.3948841145122088046e-05 - 3.7759383019940205945e-891j)  +/-  (4.18e-80, 2.62e-200j)
| (5.9648960664489060885e-10 - 4.1046943408388618417e-894j)  +/-  (6.98e-84, 4.35e-204j)
| (0.14200731260910030394 - 2.2132382818496051263e-888j)  +/-  (1.48e-72, 9.26e-193j)
| (0.028179867528516411097 - 2.8298610681479619482e-889j)  +/-  (6.13e-75, 3.83e-195j)
| (7.9754421648914016928e-05 + 1.2228689945937937996e-890j)  +/-  (2.59e-79, 1.63e-199j)
| (0.010706994522439346215 + 1.6012386384469479948e-889j)  +/-  (3.11e-77, 1.94e-197j)
| (1.0119626572508382207e-11 - 1.0791657186132466804e-894j)  +/-  (4.04e-87, 2.54e-207j)
| (0.0036343328836384089585 - 8.9712620011439469892e-890j)  +/-  (7.67e-79, 4.73e-199j)
| (1.2829236375428639672e-08 + 1.23307644497744735e-893j)  +/-  (3.67e-84, 2.27e-204j)
| (9.9487669801525543295e-18 - 9.7751919000553587094e-899j)  +/-  (5.29e-91, 3.3e-211j)
| (0.14200731260910030394 - 2.4551977183703771735e-888j)  +/-  (1.88e-77, 1.13e-197j)
| (5.9648960664489060885e-10 - 3.1498937578872214665e-893j)  +/-  (8.92e-86, 5.46e-206j)
| (0.17174079056733817571 + 2.0079258532460725724e-888j)  +/-  (2.22e-77, 1.32e-197j)
| (0.086336444016420826952 - 1.3639564958859197789e-888j)  +/-  (7.54e-78, 4.49e-198j)
| (1.9176696830898245607e-06 + 2.6274189486424577767e-892j)  +/-  (5.63e-84, 3.35e-204j)
| (0.059136595703659589249 + 8.3220230167099592989e-889j)  +/-  (1.82e-79, 1.09e-199j)
| (0.0036343328836384089585 - 1.8129667978684044445e-889j)  +/-  (8.18e-81, 4.9e-201j)
| (1.3948841145122088046e-05 - 1.1314443081783709309e-891j)  +/-  (1.32e-83, 7.82e-204j)
| (0.082397605248439985548 + 2.2052758160850515374e-888j)  +/-  (6.11e-80, 3.45e-200j)
| (0.0012673058116489018084 + 4.0920683953674179794e-890j)  +/-  (5.38e-82, 3.18e-202j)
| (1.1755821160754055742e-10 + 1.2991458377223190106e-893j)  +/-  (3.94e-87, 2.87e-207j)
| (0.082397605248439985548 + 2.6525411455987358364e-888j)  +/-  (3.27e-80, 1.58e-200j)
