Starting with polynomial:
P : 2*t
Extension levels are: 1 2 18 34
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P3 : 2*t^21 - 12952203/68336*t^19 + 987853833/136672*t^17 - 9840668841/68336*t^15 + 222748598835/136672*t^13 - 5840004786525/546688*t^11 + 43360655152815/1093376*t^9 - 85340399389245/1093376*t^7 + 155352674512035/2186752*t^5 - 385274669454675/17494016*t^3 + 24027902323425/34988032*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^55 - 121893383351233469806031906700833713900180483549520718268328689787881511460859641858163839618714025825745824404870212101305980846387/108559280157203726621126636915314220836174655029261336924231678849867044296421733499469177611674318757897305685897637227526684944*t^53 + 11640873935153672807665166760691266297696297073451881819655294673493942702125716505590684728059556756387288179369945246530519619626968565/39949815097850971396574602384835633267712273050768171988117257816751072301083197927804657361096149302906208492410330499729820059392*t^51 - 40844915799036537087085243233232863307334076213881994920134762464249246854021936460969831961509652578887916559205708238245740586673848896485/878895932152721370724641252466383931889670007116899783738579671968523590623830354411702461944115284663936586833027270994056041306624*t^49 + 2244997603786177911125664385385914296609169233824938836022537190392673511912977689539267712837123984266032984189446811218197874771764411545319/439447966076360685362320626233191965944835003558449891869289835984261795311915177205851230972057642331968293416513635497028020653312*t^47 - 361654401632957063907459619279925924376545225486736120091305020807148863208999324923034794308805669064672098237791197220577919944116919270467257/878895932152721370724641252466383931889670007116899783738579671968523590623830354411702461944115284663936586833027270994056041306624*t^45 + 8055142619579273920623904638918701936941050107694209794581537613177299436062014810034407965796728355842609334986021383473610583273219688734813185/319598520782807771172596819078685066141698184406145375904938062534008578408665583422437258888769194423249667939282643997838560475136*t^43 - 367635074803916425997178313345348162895609981946790407228020196630942262379274491002276354646086177022660672965919672423760234820032914497644497415/305702932922685694165092609553524845874667828562399924778636407641225596738723601534505204154474881622238812811487746432715144802304*t^41 + 319405442357103423325339230350382663401414377088483504530692495458129872243432483794554906059227573762261131705044693105344867524639168618215898809575/7031167457221770965797130019731071455117360056935198269908637375748188724990642835293619695552922277311492694664218167952448330452992*t^39 - 19311103475103649856260850020062926725470983148646601787834881913209832181520185177984915238585640737161956150622716228766046371343251760865913401417615/14062334914443541931594260039462142910234720113870396539817274751496377449981285670587239391105844554622985389328436335904896660905984*t^37 + 3763335815628210663273254154832386690232128816332404624423678101290642460283245486242144739547605145249268644020570493952087404369855174578793261619839905/112498679315548335452754080315697143281877760910963172318538198011971019599850285364697915128846756436983883114627490687239173287247872*t^35 - 148324990035885276269343571715356532353749060692004106128927216382239896298091700852425861413041294736926575804539556594323645457169652520100656760807937075/224997358631096670905508160631394286563755521821926344637076396023942039199700570729395830257693512873967766229254981374478346574495744*t^33 + 53816443465508379910813193877591990829973111387638887863430185999581740317489565956945247256300221978724115029350704786160928825673764898350689318292986525/5113576332524924338761549105258961058267170950498326014479009000544137254538649334758996142220307110771994687028522303965416967602176*t^31 - 1390855835049245457861333800732222790168364595145180865898867422884307838999926791403932501088767698682992175634398224642059685985418342387186065270666646875/10227152665049848677523098210517922116534341900996652028958018001088274509077298669517992284440614221543989374057044607930833935204352*t^29 + 58021946801339530200284527591495278938972660968009524788219447486649809553456607541883454231620649078441191288338154213198209221589457454885793223516420615375/40908610660199394710092392842071688466137367603986608115832072004353098036309194678071969137762456886175957496228178431723335740817408*t^27 - 971842418040719896747300869039471859894462008901552446690057566449633642267319214075643746771718230314424402955035013563875554696092783146792990413710893122125/81817221320398789420184785684143376932274735207973216231664144008706196072618389356143938275524913772351914992456356863446671481634816*t^25 + 282093517072046434806066880717011742803160908791063879952315986644287600004728234399929383550499753932183516749776667892133355622423912986560317948197716504375/3557270492191251713921077638441016388359771095998835488333223652552443307505147363310606011979344077058778912715493776671594412244992*t^23 - 1486580770925889840069999566306603805255072284882450185244247873559197147958191758033163653859600024124161801672803514488612562305202859425983544737750787478125/3557270492191251713921077638441016388359771095998835488333223652552443307505147363310606011979344077058778912715493776671594412244992*t^21 + 195345819398374626057634475254106401134424769899079269866725800439538003567090658846909781250360543571776859277319233266581555532073668475250141118047566055478125/113832655750120054845474484430112524427512675071962735626663156881678185840164715625939392383339010465880925206895800853491021191839744*t^19 - 1229489204024615683228997355515464866720552698591615751365053039112587897069497414026024051256587949720575050338158476641083381010759479698187271990184738647504375/227665311500240109690948968860225048855025350143925471253326313763356371680329431251878784766678020931761850413791601706982042383679488*t^17 + 1450820718576443552493165738505122882692716462844877662257006342290965713686444335964394910949223910026555958973469284501862610574503352489464676889612090235124375/113832655750120054845474484430112524427512675071962735626663156881678185840164715625939392383339010465880925206895800853491021191839744*t^15 - 4991593710756442000177186634381841581542706823495863461377238456344244054384862222966030634765859387540836567798503624913870214092880777668625177978208381727365625/227665311500240109690948968860225048855025350143925471253326313763356371680329431251878784766678020931761850413791601706982042383679488*t^13 + 24094955581844067220048024473680433782776481467664057687976601211862159643003245438607087225488436848149249619464397829677928124381495337224065634353060980935784375/910661246000960438763795875440900195420101400575701885013305255053425486721317725007515139066712083727047401655166406827928169534717952*t^11 - 38662875957196979217602210952456924038366229946373880921280610824710564528426774048494998453508189042781826862334736629630754096600983578250736997561407706453953125/1821322492001920877527591750881800390840202801151403770026610510106850973442635450015030278133424167454094803310332813655856339069435904*t^9 + 19040751254120032152139936219263690937437788984288631122529000946049514125294162655031315584476067562364176941421469675477649739897894349421046428945091510800009375/1821322492001920877527591750881800390840202801151403770026610510106850973442635450015030278133424167454094803310332813655856339069435904*t^7 - 10109781294974968729437032043261851353483696211167611311115168889637739907537730160507906215283284463786446833339146028392363400307629902178239395398914437245996875/3642644984003841755055183501763600781680405602302807540053221020213701946885270900030060556266848334908189606620665627311712678138871808*t^5 + 9055779418181189905239081950217031085062301936004521011738132575330964700314857319395318454160368315473346370112984766937329889232240948814290672280830203015296875/29141159872030734040441468014108806253443244818422460320425768161709615575082167200240484450134786679265516852965325018493701425110974464*t^3 - 459932347286399421006447732818104416420407407718219802090584646803041025992089181208924587881135423240006726947171740096507356361012674014717949773550514732640625/58282319744061468080882936028217612506886489636844920640851536323419231150164334400480968900269573358531033705930650036987402850221948928*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:   55 out of 55
Indefinite weights: 0 out of 55
Negative weights:   0 out of 55
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.7359761631918686374 + 3.98252851173668102e-887j)  +/-  (1.83e-246, 1.83e-246j)
| (6.1527401165306027767 + 2.7792307862367060299e-882j)  +/-  (8.93e-243, 8.93e-243j)
| (-8.7359761631918686374 - 2.2025747314738719463e-888j)  +/-  (1.9e-246, 1.9e-246j)
| (-7.5205079202767911349 - 1.9813949733661240791e-887j)  +/-  (2.31e-244, 2.31e-244j)
| (7.0291858603266577535 - 2.027722320083816537e-884j)  +/-  (1.04e-243, 1.04e-243j)
| (-8.0711595567782391962 - 4.6108722395195429513e-887j)  +/-  (3.02e-245, 3.02e-245j)
| (-5.7534062735008464055 + 4.3948409064110742489e-884j)  +/-  (1.98e-242, 1.98e-242j)
| (-6.5765932956022219313 - 4.5609140634875823047e-891j)  +/-  (3.46e-243, 3.46e-243j)
| (8.0711595567782391962 - 9.5545098022871856138e-895j)  +/-  (3.17e-245, 3.17e-245j)
| (5.7534062735008464055 + 1.1289119286258553914e-890j)  +/-  (2.03e-242, 2.03e-242j)
| (-4.6011958858009393032 - 5.9729008633629655219e-898j)  +/-  (2.33e-242, 2.33e-242j)
| (1.7319350879389337601 - 1.9824062547373908137e-915j)  +/-  (1.2e-247, 1.2e-247j)
| (7.5205079202767911349 + 2.7692347436516818863e-910j)  +/-  (2.24e-244, 2.24e-244j)
| (-6.1527401165306027767 + 7.4086199848524883144e-909j)  +/-  (8.39e-243, 8.39e-243j)
| (-7.0291858603266577535 + 2.9343104694016221633e-919j)  +/-  (1.16e-243, 1.16e-243j)
| (4.9270020422479671942 - 5.8719611704927520409e-932j)  +/-  (5.63e-242, 5.63e-242j)
| (0.72167284382081647552 - 5.4899715622332801202e-951j)  +/-  (1.43e-251, 1.43e-251j)
| (-5.3853563457510686316 + 3.1664079492667574019e-940j)  +/-  (4.83e-242, 4.83e-242j)
| (-0.9806480435009512337 + 7.9708446698677520044e-958j)  +/-  (2.04e-250, 2.04e-250j)
| (-1.7319350879389337601 - 1.1884561368640478459e-955j)  +/-  (1.23e-247, 1.23e-247j)
| (2.2498901573507839375 - 1.0446008740447927216e-953j)  +/-  (4.73e-246, 4.73e-246j)
| (5.3853563457510686316 - 7.1930906853725268077e-949j)  +/-  (4.87e-242, 4.87e-242j)
| (-3.6348848250778977735 + 3.3501641995363016281e-956j)  +/-  (2.03e-243, 2.03e-243j)
| (5.1310268672406262605 - 1.6942768211897500799e-956j)  +/-  (7.55e-242, 7.55e-242j)
| (-2.784698074503156652 + 4.5520579475124119114e-963j)  +/-  (7.88e-245, 7.88e-245j)
| (6.5765932956022219313 - 2.1453209774006446913e-962j)  +/-  (3.33e-243, 3.33e-243j)
| (3.3444338676496712713 + 1.1071470846681948749e-968j)  +/-  (8.24e-244, 8.24e-244j)
| (0.9806480435009512337 + 7.5286795057408349195e-976j)  +/-  (2.07e-250, 2.07e-250j)
| (3.0631438245189336159 - 1.3293184661247604621e-969j)  +/-  (2.63e-244, 2.63e-244j)
| (-2.2498901573507839375 + 1.2455632285529335804e-970j)  +/-  (4.31e-246, 4.31e-246j)
| (2.784698074503156652 + 7.9802236779286750676e-970j)  +/-  (8.18e-245, 8.18e-245j)
| (3.941861650961138182 + 1.0232274789797948936e-967j)  +/-  (4.79e-243, 4.79e-243j)
| (-5.1310268672406262605 - 1.3882691037790503275e-967j)  +/-  (7.78e-242, 7.78e-242j)
| (1.9927008072664126534 + 5.5284599002345251795e-987j)  +/-  (8.23e-247, 8.23e-247j)
| (-3.0631438245189336159 - 8.3297703853013148699e-983j)  +/-  (2.81e-244, 2.81e-244j)
| (-1.4725198510235158168 + 1.6275805169386545384e-987j)  +/-  (1.62e-248, 1.62e-248j)
| (1.4725198510235158168 + 1.3985940503589502424e-988j)  +/-  (1.58e-248, 1.58e-248j)
| (-4.2656562101516500964 - 8.5649740263303388078e-981j)  +/-  (9.39e-243, 9.39e-243j)
| (1.2247448713915890491 + 3.7228956889164027523e-1000j)  +/-  (2.05e-249, 2.05e-249j)
| (-4.9270020422479671942 - 3.4789800645903134362e-992j)  +/-  (5.6e-242, 5.6e-242j)
| (-0.72167284382081647552 + 3.5122288706191996251e-1008j)  +/-  (1.33e-251, 1.33e-251j)
| (-3.941861650961138182 - 8.2918992179342855909e-999j)  +/-  (4.63e-243, 4.63e-243j)
| (4.6011958858009393032 + 1.6934023207194976238e-999j)  +/-  (2.18e-242, 2.18e-242j)
| (2.5120230131447748102 - 1.0198647182700524969e-1004j)  +/-  (2.04e-245, 2.04e-245j)
| (3.6348848250778977735 + 9.4146540355012525067e-1003j)  +/-  (2.11e-243, 2.11e-243j)
| (-1.2247448713915890491 - 7.3389527348357558776e-1011j)  +/-  (2.13e-249, 2.13e-249j)
| (1.680447727909325991e-1035 + 1.0602356113276653284e-1036j)  +/-  (9.26e-1034, 9.26e-1034j)
| (4.2656562101516500964 + 2.0294898043879604065e-1005j)  +/-  (1e-242, 1e-242j)
| (0.45010647378563665046 + 3.3365318764262717944e-1016j)  +/-  (7.5e-253, 7.5e-253j)
| (-2.5120230131447748102 - 2.3287938075330189346e-1006j)  +/-  (1.9e-245, 1.9e-245j)
| (-0.18703245774372996923 - 1.3545988651073755966e-1016j)  +/-  (4.47e-254, 4.47e-254j)
| (-0.45010647378563665046 - 6.1609861071587001278e-1015j)  +/-  (7.5e-253, 7.5e-253j)
| (-3.3444338676496712713 + 1.1691351989539547459e-1010j)  +/-  (7.92e-244, 7.92e-244j)
| (0.18703245774372996923 + 5.3227571262613118639e-1022j)  +/-  (4.47e-254, 4.47e-254j)
| (-1.9927008072664126534 - 7.3468005462153177163e-1016j)  +/-  (8.04e-247, 8.04e-247j)
-------------------------------------------------
The weights are:
| (3.1079152159319820034e-34 - 6.3945244881687465593e-910j)  +/-  (1.16e-78, 1.1e-199j)
| (8.4120570069763657733e-18 - 2.0156104265248658314e-898j)  +/-  (1.59e-70, 1.51e-191j)
| (3.1079152159319820034e-34 + 8.1337610421301994497e-911j)  +/-  (1.02e-79, 9.66e-201j)
| (7.9675730827370706911e-26 + 6.5477070648167494911e-906j)  +/-  (1.15e-76, 1.09e-197j)
| (9.2255853976706332493e-23 + 1.4028608621295544752e-902j)  +/-  (1.88e-75, 1.78e-196j)
| (1.7094130226176608509e-29 - 4.5587451656824354558e-908j)  +/-  (3.77e-78, 3.58e-199j)
| (9.183408961733379611e-16 + 4.2056312024331148245e-898j)  +/-  (2.58e-72, 2.45e-193j)
| (4.0556903388890491108e-20 + 7.3875829160980293491e-903j)  +/-  (1.15e-74, 1.09e-195j)
| (1.7094130226176608509e-29 + 5.0584969223177049178e-907j)  +/-  (2.97e-80, 2.82e-201j)
| (9.183408961733379611e-16 + 1.844197304021380511e-897j)  +/-  (9.34e-74, 8.87e-195j)
| (1.2184187999297816757e-10 + 4.1799006440015898311e-895j)  +/-  (3.58e-70, 3.4e-191j)
| (0.007363502506066866525 + 3.7948276815437623882e-889j)  +/-  (1.98e-53, 1.88e-174j)
| (7.9675730827370706911e-26 - 1.1313992493008250406e-904j)  +/-  (1.04e-78, 9.85e-200j)
| (8.4120570069763657733e-18 + 1.3147837911166636678e-900j)  +/-  (1.52e-74, 1.45e-195j)
| (9.2255853976706332493e-23 - 4.0451013399105816315e-904j)  +/-  (4.53e-77, 4.3e-198j)
| (4.7221075288203024036e-12 - 5.70390436395554702e-895j)  +/-  (3.25e-73, 3.09e-194j)
| (0.089596580245203732072 + 2.3642388157673966817e-888j)  +/-  (3.87e-57, 3.68e-178j)
| (4.8614041256994343986e-14 - 5.0964446690651705521e-897j)  +/-  (2.81e-73, 2.67e-194j)
| (0.053883997518187667704 - 1.3525264176057773818e-888j)  +/-  (1.23e-57, 1.17e-178j)
| (0.007363502506066866525 + 2.282717830331479243e-889j)  +/-  (4.89e-58, 4.65e-179j)
| (0.00092087173582228059112 + 8.357773890899128834e-890j)  +/-  (3.14e-62, 2.98e-183j)
| (4.8614041256994343986e-14 - 2.8265472254481091886e-896j)  +/-  (1.53e-74, 1.45e-195j)
| (3.0734978549119129415e-07 - 7.1509066005218235066e-893j)  +/-  (1.44e-70, 1.37e-191j)
| (3.3401021039472045797e-13 + 2.0570999202560404916e-895j)  +/-  (6.26e-74, 5.95e-195j)
| (6.6933036565050689264e-05 + 4.6807091141587073241e-891j)  +/-  (9.38e-68, 8.91e-189j)
| (4.0556903388890491108e-20 - 1.4683093796852526079e-900j)  +/-  (2.33e-78, 2.21e-199j)
| (2.2256284995529897392e-06 + 9.3549058227106839389e-892j)  +/-  (7.82e-71, 7.43e-192j)
| (0.053883997518187667704 - 1.7966448497959651273e-888j)  +/-  (6.01e-61, 5.71e-182j)
| (1.3273738370625508983e-05 - 3.3587750115234485128e-891j)  +/-  (6.84e-70, 6.5e-191j)
| (0.00092087173582228059112 + 4.2786380223884461734e-890j)  +/-  (3.08e-68, 2.92e-189j)
| (6.6933036565050689264e-05 + 1.0889751552227245645e-890j)  +/-  (4.41e-69, 4.19e-190j)
| (3.1823940331000509012e-08 + 4.6967402611072958469e-893j)  +/-  (1.69e-73, 1.6e-194j)
| (3.3401021039472045797e-13 + 3.6977524405546463707e-896j)  +/-  (1.13e-77, 1.07e-198j)
| (0.0027499733954459287637 - 1.8636861972299685033e-889j)  +/-  (3.77e-67, 3.58e-188j)
| (1.3273738370625508983e-05 - 1.312550245933099995e-891j)  +/-  (7.62e-73, 7.24e-194j)
| (0.016427167852147293363 - 4.7657033591743751754e-889j)  +/-  (4.97e-67, 4.72e-188j)
| (0.016427167852147293363 - 7.3243500929167564828e-889j)  +/-  (3.96e-66, 3.76e-187j)
| (2.3377218348760768252e-09 - 2.2830345160307394549e-894j)  +/-  (1.44e-76, 1.37e-197j)
| (0.030506260633063376485 + 1.2523869655809425205e-888j)  +/-  (1.89e-67, 1.8e-188j)
| (4.7221075288203024036e-12 - 1.088665028617778372e-895j)  +/-  (8.97e-78, 8.53e-199j)
| (0.089596580245203732072 + 1.9195549518480289157e-888j)  +/-  (1.65e-68, 1.57e-189j)
| (3.1823940331000509012e-08 + 1.3267682284479572407e-893j)  +/-  (5.54e-76, 5.27e-197j)
| (1.2184187999297816757e-10 + 1.9312884377440026505e-894j)  +/-  (1.48e-78, 1.41e-199j)
| (0.00027440900060555322327 - 3.2274848577159092868e-890j)  +/-  (5.12e-73, 4.87e-194j)
| (3.0734978549119129415e-07 - 2.249965550553360525e-892j)  +/-  (2.12e-76, 2.02e-197j)
| (0.030506260633063376485 + 8.7737227419821915855e-889j)  +/-  (1.85e-72, 1.76e-193j)
| (0.081983712889257715777 - 7.9835678569613668983e-888j)  +/-  (5.77e-72, 5.54e-193j)
| (2.3377218348760768252e-09 - 9.1981612697297935818e-894j)  +/-  (3.47e-78, 3.3e-199j)
| (0.12569939310665851262 - 3.3956229114237327495e-888j)  +/-  (9.86e-72, 9.38e-193j)
| (0.00027440900060555322327 - 1.5184210640701536104e-890j)  +/-  (3.84e-76, 3.63e-197j)
| (0.13150321352033950594 + 5.7887544864033618455e-888j)  +/-  (1.31e-72, 1.26e-193j)
| (0.12569939310665851262 - 2.9826099042064298695e-888j)  +/-  (6.02e-73, 5.72e-194j)
| (2.2256284995529897392e-06 + 3.3089290029803414858e-892j)  +/-  (5.44e-78, 5.26e-199j)
| (0.13150321352033950594 + 6.1089099142343316751e-888j)  +/-  (1.03e-73, 1.5e-194j)
| (0.0027499733954459287637 - 1.0345076277921493954e-889j)  +/-  (2.34e-75, 2.14e-196j)
