Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 18 30
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 8*t^21 - 12952203/17084*t^19 + 987853833/34168*t^17 - 9840668841/17084*t^15 + 222748598835/34168*t^13 - 5840004786525/136672*t^11 + 43360655152815/273344*t^9 - 85340399389245/273344*t^7 + 155352674512035/546688*t^5 - 385274669454675/4373504*t^3 + 24027902323425/8747008*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^51 - 9735813524578186491335971902705310046694697905039868792759436464904245417486849744177307789936586304165598127603881570799/2507417172525700799701758689152615734383887186075190402825307584136770234041411344859008392665691032482653103524900252*t^49 + 17258034866769491677124774682481380729477045106064384533750683227308943582689650412572583173229207158611868521337392561258691/20059337380205606397614069513220925875071097488601523222602460673094161872331290758872067141325528259861224828199202016*t^47 - 4640009928644267849770008366381004792299745144687973366693685047770246244074347880771259259084582020705576426926254875293344843/40118674760411212795228139026441851750142194977203046445204921346188323744662581517744134282651056519722449656398404032*t^45 + 848384635202959091385319151292894509938430883713352418641853311099788279482480116879889734325511119687048950517560732517489306965/80237349520822425590456278052883703500284389954406092890409842692376647489325163035488268565302113039444899312796808064*t^43 - 112078119889591267839489635700173066758715982781637294052732579508663330956213765525847588405912546639341341170422833036435218374585/160474699041644851180912556105767407000568779908812185780819685384753294978650326070976537130604226078889798625593616128*t^41 + 11095457956792722390771544680812057269875629609277162129164337553556394585248665964506511350538277449172458569699212053509702255574685/320949398083289702361825112211534814001137559817624371561639370769506589957300652141953074261208452157779597251187232256*t^39 - 842604074758483034723708737754546763820542637748676587636756968221792851758784191128816979888312968306537528056587517471020143419897085/641898796166579404723650224423069628002275119635248743123278741539013179914601304283906148522416904315559194502374464512*t^37 + 49843952885618999468999221432392870320118786898878608871734686535341088048181009188820718875242799629755824276096500410649559463541830755/1283797592333158809447300448846139256004550239270497486246557483078026359829202608567812297044833808631118389004748929024*t^35 - 2319492703020469270933080049223226229255710039957303867412103770549815950554185624954540612341541839668912169875051591634549006755739397075/2567595184666317618894600897692278512009100478540994972493114966156052719658405217135624594089667617262236778009497858048*t^33 + 42703400942251311175981289555662134907109166778990275487490251449387383107636869873735654035698832291810391499471543618179488402443806126975/2567595184666317618894600897692278512009100478540994972493114966156052719658405217135624594089667617262236778009497858048*t^31 - 1247401904483153963669619521986583685629171127955357608759134172270597699881080333436429348711077557267231182211059969411378178656154460740375/5135190369332635237789201795384557024018200957081989944986229932312105439316810434271249188179335234524473556018995716096*t^29 + 28900721405126153912685976319653553043744458987517440322367255342374662597096441547046137746430189724783541461511286184048089942191583222347625/10270380738665270475578403590769114048036401914163979889972459864624210878633620868542498376358670469048947112037991432192*t^27 - 529604116484368320121309780803986236428811199853720455742129303975435958574383016519321227954931773206288647485162800058070012446995212300836125/20540761477330540951156807181538228096072803828327959779944919729248421757267241737084996752717340938097894224075982864384*t^25 + 7634442398518988923054521065207635762933571061593101066106911218259252416429894838934699195600077135250993289229634655047837248332945217804228125/41081522954661081902313614363076456192145607656655919559889839458496843514534483474169993505434681876195788448151965728768*t^23 - 85861858121167712135631637845829802346328316891039495399875367699192118769324252838139129693300695998527479805128262216141072872427146882110738125/82163045909322163804627228726152912384291215313311839119779678916993687029068966948339987010869363752391576896303931457536*t^21 + 744767183841954933130509860854996632739706675387957717897774317478175576823890072307370815167204434674917531261107479107743707385899919315860201875/164326091818644327609254457452305824768582430626623678239559357833987374058137933896679974021738727504783153792607862915072*t^19 - 4905874246981576171128858020291077731735021082455751082960883968467010172669381786904264906874767864285685324421058124045164256077622581619586020625/328652183637288655218508914904611649537164861253247356479118715667974748116275867793359948043477455009566307585215725830144*t^17 + 48081890754078530637161999682934388705178681056354080015370654687462072591894434483745711750559384434221041306776133256160927674312722576670902039375/1314608734549154620874035659618446598148659445012989425916474862671898992465103471173439792173909820038265230340862903320576*t^15 - 170536309497294826250642708351998434858083139126358890956723044048787988282281146831247225585313798362892787842063409192644179897476080019147876284375/2629217469098309241748071319236893196297318890025978851832949725343797984930206942346879584347819640076530460681725806641152*t^13 + 421716267322688697091812696182390975217499876913002201212809384591989206114460152208812804396535265481341510087098765192641143938588494854550784415625/5258434938196618483496142638473786392594637780051957703665899450687595969860413884693759168695639280153060921363451613282304*t^11 - 690017943928482845146781051462633117390669849627987156629739898483210925027605328345074488465942221649089485169067405418086808901961629579962173128125/10516869876393236966992285276947572785189275560103915407331798901375191939720827769387518337391278560306121842726903226564608*t^9 + 691807491043075583409861663979702683092771663029506833163456241736020591022877947154069719533162288772566749499673998878063754651875419717797311065625/21033739752786473933984570553895145570378551120207830814663597802750383879441655538775036674782557120612243685453806453129216*t^7 - 375973909499095540318372849466362542681925740137712049814804398820809881198364569594138400697319129428592401168637066940237401792697239892596444665625/42067479505572947867969141107790291140757102240415661629327195605500767758883311077550073349565114241224487370907612906258432*t^5 + 87652643580664801416519494670457667267186589859500770567060564834079049524175683711975896597890578877258027030096784837146268492444016621856638234375/84134959011145895735938282215580582281514204480831323258654391211001535517766622155100146699130228482448974741815225812516864*t^3 - 4513153757716360630224680714807480094445296893741210970925942404970631917510017947601992085464586571480353582115371779336709224663859748208097609375/168269918022291791471876564431161164563028408961662646517308782422003071035533244310200293398260456964897949483630451625033728*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:
| (6.7484187131456854645 - 7.6247445271474325317e-913j)  +/-  (6.32e-245, 6.32e-245j)
| (7.9031868700098804005 + 6.3415241161210454897e-914j)  +/-  (2.73e-246, 2.73e-246j)
| (8.7970679002358847897 - 3.9817697710370997661e-915j)  +/-  (1.06e-247, 1.06e-247j)
| (-3.6516836948838085191 - 1.5696043078709801956e-910j)  +/-  (3.48e-244, 3.48e-244j)
| (-8.7970679002358847897 - 3.5669781214414984925e-913j)  +/-  (1.18e-247, 1.18e-247j)
| (-7.9031868700098804005 + 9.9010403699484226442e-922j)  +/-  (2.42e-246, 2.42e-246j)
| (5.8112417254350818672 - 2.1899480548150714084e-930j)  +/-  (3.07e-244, 3.07e-244j)
| (-1.5220957106705343721 + 2.1222467322812644007e-934j)  +/-  (1.68e-248, 1.68e-248j)
| (6.2629903481834766705 - 4.8799377494496202605e-930j)  +/-  (1.65e-244, 1.65e-244j)
| (2.5461312372732668131 + 2.3530008676534579886e-932j)  +/-  (9.01e-246, 9.01e-246j)
| (0.93830256729624750181 + 9.2504457496543306041e-937j)  +/-  (1.07e-250, 1.07e-250j)
| (-1.7319350879389337601 - 4.2658852213400259789e-933j)  +/-  (1.17e-247, 1.17e-247j)
| (-3.0383402893009631535 - 9.3263009490797249741e-931j)  +/-  (6.67e-245, 6.67e-245j)
| (7.2829626426677222438 - 2.9232129300561436443e-936j)  +/-  (1.63e-245, 1.63e-245j)
| (-7.2829626426677222438 + 2.6913271902462126651e-941j)  +/-  (1.67e-245, 1.67e-245j)
| (3.941861650961138182 + 8.5744381498177133214e-945j)  +/-  (4.93e-244, 4.93e-244j)
| (2.2498901573507839375 + 2.871082868940188151e-947j)  +/-  (1.55e-246, 1.55e-246j)
| (-2.784698074503156652 - 8.4583332072484139152e-946j)  +/-  (2.92e-245, 2.92e-245j)
| (-0.93830256729624750181 - 3.0059229772378176783e-951j)  +/-  (1.2e-250, 1.2e-250j)
| (-4.6011958858009393032 - 2.2601968180600978956e-943j)  +/-  (6.45e-244, 6.45e-244j)
| (1.5220957106705343721 + 1.4503605313821668624e-953j)  +/-  (1.51e-248, 1.51e-248j)
| (1.9472599973887178948 - 3.1635091502045499471e-952j)  +/-  (3.2e-247, 3.2e-247j)
| (3.0383402893009631535 + 1.6365872577439893887e-949j)  +/-  (6.65e-245, 6.65e-245j)
| (-3.941861650961138182 - 1.8702929891005827598e-947j)  +/-  (4.75e-244, 4.75e-244j)
| (4.9817886992193755918 - 5.0494304222916363364e-954j)  +/-  (6.13e-244, 6.13e-244j)
| (-6.2629903481834766705 - 4.1533786574597079545e-953j)  +/-  (1.78e-244, 1.78e-244j)
| (1.7319350879389337601 - 6.9161895293458447443e-964j)  +/-  (1e-247, 1e-247j)
| (-1.9472599973887178948 - 2.1172348511539992777e-963j)  +/-  (3.31e-247, 3.31e-247j)
| (-5.3853563457510686316 - 2.3600063299910748258e-959j)  +/-  (4.49e-244, 4.49e-244j)
| (-0.72167284382081647552 - 6.0103313532615408619e-973j)  +/-  (1.42e-251, 1.42e-251j)
| (-4.2509732848408059244 + 3.5611489350613214721e-965j)  +/-  (6e-244, 6e-244j)
| (5.3853563457510686316 - 4.0513838832167811314e-973j)  +/-  (4.81e-244, 4.81e-244j)
| (1.2247448713915890491 + 2.6512002169104922413e-985j)  +/-  (1.12e-249, 1.12e-249j)
| (2.784698074503156652 - 8.9141355320868772505e-981j)  +/-  (3.13e-245, 3.13e-245j)
| (-4.9817886992193755918 + 1.0581900036472938706e-978j)  +/-  (6e-244, 6e-244j)
| (-1.2247448713915890491 + 2.251548824738429417e-994j)  +/-  (1.21e-249, 1.21e-249j)
| (3.6516836948838085191 + 6.489906436503745656e-988j)  +/-  (3.11e-244, 3.11e-244j)
| (3.3444338676496712713 - 5.3399080992316873179e-992j)  +/-  (1.45e-244, 1.45e-244j)
| (0.18703245774372996923 - 1.6038502662397689411e-1010j)  +/-  (3.39e-254, 3.39e-254j)
| (-5.8112417254350818672 + 1.7260735316759084386e-1005j)  +/-  (3.04e-244, 3.04e-244j)
| (-0.18703245774372996923 - 2.6808780553802053367e-1032j)  +/-  (4.41e-254, 4.41e-254j)
| (-6.7484187131456854645 - 2.1412191433041026839e-1026j)  +/-  (6.28e-245, 6.28e-245j)
| (0.72167284382081647552 - 6.8673790418880911399e-1040j)  +/-  (1.51e-251, 1.51e-251j)
| (1.1640896392515723284e-1058 - 2.12850315028196934e-1058j)  +/-  (1.24e-1056, 1.24e-1056j)
| (4.2509732848408059244 - 9.7882450655226468915e-1031j)  +/-  (6.23e-244, 6.23e-244j)
| (-0.4775455879581033022 - 7.0801187640997854158e-1041j)  +/-  (8.83e-253, 8.83e-253j)
| (-2.5461312372732668131 - 6.5070389445272374491e-1033j)  +/-  (9.43e-246, 9.43e-246j)
| (4.6011958858009393032 - 7.1193615473997908496e-1034j)  +/-  (7.09e-244, 7.09e-244j)
| (0.4775455879581033022 - 5.4655059680774835891e-1041j)  +/-  (9.29e-253, 9.29e-253j)
| (-3.3444338676496712713 - 2.732870957141830476e-1036j)  +/-  (1.49e-244, 1.49e-244j)
| (-2.2498901573507839375 - 2.4563654147493499134e-1043j)  +/-  (1.58e-246, 1.58e-246j)
-------------------------------------------------
The weights are:
| (4.7607096909435052009e-21 - 5.3811518829303682157e-928j)  +/-  (7.29e-86, 2.72e-207j)
| (2.9110598580061749005e-28 - 3.2036065352513050934e-932j)  +/-  (1.67e-89, 6.25e-211j)
| (2.074472933464108285e-34 + 1.6119282428635742696e-935j)  +/-  (4.69e-92, 1.75e-213j)
| (2.7104128495753970183e-07 - 2.4065656394243661728e-916j)  +/-  (5.63e-76, 2.1e-197j)
| (2.074472933464108285e-34 - 3.8998874955492706847e-935j)  +/-  (1.01e-94, 3.78e-216j)
| (2.9110598580061749005e-28 + 8.706808833679214427e-932j)  +/-  (1.9e-92, 7.08e-214j)
| (5.3267230992755353111e-16 - 8.7060460178589318907e-925j)  +/-  (1.7e-85, 6.35e-207j)
| (0.01525909557028719232 - 3.1215201090065759304e-913j)  +/-  (2.66e-62, 9.93e-184j)
| (2.428676645942021273e-18 + 2.6102051738098176261e-926j)  +/-  (1.31e-86, 4.9e-208j)
| (0.0002341039955487718371 - 2.5645763107907728047e-915j)  +/-  (1.24e-72, 4.63e-194j)
| (0.059630382576086227827 - 4.9020227564091535807e-913j)  +/-  (4.11e-63, 1.53e-184j)
| (0.0045604231086941333481 + 2.388943007917695187e-913j)  +/-  (1.71e-65, 6.37e-187j)
| (1.595644773841111451e-05 - 2.4274963952460917544e-915j)  +/-  (4.57e-76, 1.71e-197j)
| (2.9519584611342843553e-24 + 6.4694384061407837256e-930j)  +/-  (9.75e-90, 3.64e-211j)
| (2.9519584611342843553e-24 - 1.9480765667865329698e-929j)  +/-  (9.94e-93, 3.71e-214j)
| (2.9352133582791399263e-08 + 9.37426650500060602e-919j)  +/-  (5.25e-81, 1.96e-202j)
| (0.0011074186723208135608 + 7.5713731563614768918e-915j)  +/-  (3.1e-72, 1.16e-193j)
| (5.3973663664538140098e-05 + 7.0599648594562204186e-915j)  +/-  (1.05e-75, 3.91e-197j)
| (0.059630382576086227827 - 8.2923195922900144547e-913j)  +/-  (6.01e-67, 2.24e-188j)
| (1.3246306853272420702e-10 - 6.6957349788312290498e-920j)  +/-  (2.78e-85, 1.04e-206j)
| (0.01525909557028719232 - 1.2848534964100358415e-913j)  +/-  (4.36e-68, 1.63e-189j)
| (0.0035647706979407086475 - 3.2300668229923511508e-914j)  +/-  (5.67e-71, 2.12e-192j)
| (1.595644773841111451e-05 - 2.2255334643966753667e-916j)  +/-  (1.1e-77, 4.1e-199j)
| (2.9352133582791399263e-08 - 2.4531168705264807753e-917j)  +/-  (1.93e-82, 7.2e-204j)
| (3.6896821441630342768e-12 - 4.5102471269130840948e-922j)  +/-  (6.77e-86, 2.53e-207j)
| (2.428676645942021273e-18 - 9.91062449013287944e-926j)  +/-  (7.83e-92, 2.92e-213j)
| (0.0045604231086941333481 + 8.5187448775001864848e-914j)  +/-  (7.77e-72, 2.9e-193j)
| (0.0035647706979407086475 - 1.0610609128190524412e-913j)  +/-  (1.44e-74, 5.36e-196j)
| (5.9354813129114302791e-14 - 1.1483851568543225887e-922j)  +/-  (3.09e-89, 1.15e-210j)
| (0.068400525111042686805 + 1.2529620504349968065e-912j)  +/-  (3.71e-72, 1.38e-193j)
| (2.645967631815739773e-09 + 1.3770356872810996976e-918j)  +/-  (1.17e-84, 4.37e-206j)
| (5.9354813129114302791e-14 + 2.2030611627284660076e-923j)  +/-  (2.02e-88, 7.55e-210j)
| (0.038253894029551883991 + 2.0703853129802346452e-913j)  +/-  (2.49e-73, 9.29e-195j)
| (5.3973663664538140098e-05 + 9.5098180125110281019e-916j)  +/-  (1.35e-79, 5.04e-201j)
| (3.6896821441630342768e-12 + 2.927529797435679664e-921j)  +/-  (4.99e-88, 1.86e-209j)
| (0.038253894029551883991 + 4.1600100394324801861e-913j)  +/-  (5.35e-75, 2e-196j)
| (2.7104128495753970183e-07 - 5.8250789680427558685e-918j)  +/-  (6.26e-84, 2.34e-205j)
| (2.4546108889058243115e-06 + 3.4833723950672064579e-917j)  +/-  (9.93e-83, 3.71e-204j)
| (0.15159798903730785507 + 2.0066741189399378455e-912j)  +/-  (1.13e-76, 4.22e-198j)
| (5.3267230992755353111e-16 + 3.814910815216109772e-924j)  +/-  (6.62e-92, 2.47e-213j)
| (0.15159798903730785507 + 2.2233270402345888958e-912j)  +/-  (1.6e-77, 5.97e-199j)
| (4.7607096909435052009e-21 + 1.8073101207701461051e-927j)  +/-  (4.47e-95, 1.67e-216j)
| (0.068400525111042686805 + 8.3944484685885830514e-913j)  +/-  (5.68e-78, 2.12e-199j)
| (0.060974643513244777393 - 2.897712430540492356e-912j)  +/-  (1.35e-77, 5.03e-199j)
| (2.645967631815739773e-09 - 1.0442581929092868697e-919j)  +/-  (2.25e-87, 8.4e-209j)
| (0.12683138754670667007 - 1.4144649163035395269e-912j)  +/-  (9.8e-79, 3.64e-200j)
| (0.0002341039955487718371 - 1.4377231239966428449e-914j)  +/-  (5.67e-84, 2.11e-205j)
| (1.3246306853272420702e-10 + 7.703572716365620579e-921j)  +/-  (8.79e-89, 3.29e-210j)
| (0.12683138754670667007 - 1.0872988749077541119e-912j)  +/-  (5.97e-80, 2.23e-201j)
| (2.4546108889058243115e-06 + 7.9316935705703246932e-916j)  +/-  (5.67e-86, 2.14e-207j)
| (0.0011074186723208135608 + 3.187562943543905446e-914j)  +/-  (1.42e-83, 5.18e-205j)
