Starting with polynomial:
P : 2*t
Extension levels are: 1 4 12 34
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P3 : 2*t^17 - 6536/53*t^15 + 617205/212*t^13 - 7144995/212*t^11 + 172854825/848*t^9 - 269555715/424*t^7 + 3204996795/3392*t^5 - 1892565675/3392*t^3 + 1129052925/13568*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^51 - 354696408756689972035341792798958782630145129488255160445782133908844667752745790678583782583677/361947278787276079606380737395009697201726430023372024265004165160073849850080265365484966647*t^49 + 37321986895249883451351006435242722675118320856984416653385007057664987829927553050200084292749121219/169391326472445205255786185100864538290407969250938107356021949294914561729837564191046964390796*t^47 - 10232320370317224721146809214888878221154063070175806037821070009173496514466781783958634302296345184035/338782652944890410511572370201729076580815938501876214712043898589829123459675128382093928781592*t^45 + 638987315580134318602311874719572080010883069339617741700959063140321335276138979037371627195925535697055/225855101963260273674381580134486051053877292334584143141362599059886082306450085588062619187728*t^43 - 65952669946675402033554793565451275740381048501295372894087538678844184814998134728852403033214868962107991165/342848044780229095437711238644149825499785729763898729288588425372907072941191229922679055926971104*t^41 + 6750447333553301089186055254357449690277569309657451435503214077385371566169921146745701240042008937541585153665/685696089560458190875422477288299650999571459527797458577176850745814145882382459845358111853942208*t^39 - 197766103829307963551215226102760017653352691632560366792156085202205360523719100280528162412794365583267091795/509621768532484720085784078252173653660030813472907810165125864545383980588913013634602833038976*t^37 + 2523394053217598097456913507765128689886756900999495973929219978872271991570410389462236396335928403123884174705225/210983412172448674115514608396399892615252756777783833408362107921788967963809987644725572878136064*t^35 - 11160111960381113571174483775056913412210396340051286482081352546180262016466279763889397906355527526057831920922075/38360620394990668021002656072072707748227773959597060619702201440325266902510906844495558705115648*t^33 + 71795152406092846133846978118838515346907084928227981984181473784335227708334157023030038078114629045363579615037375/12786873464996889340334218690690902582742591319865686873234067146775088967503635614831852901705216*t^31 - 2203020059703572222501315036983886923939524097340230658668252787438330865855475011845440955339781571895709501618923375/25573746929993778680668437381381805165485182639731373746468134293550177935007271229663705803410432*t^29 + 53688031276435117347878917711835536445617092199030614640048881178985073030049195506079560463260779771297010893020807625/51147493859987557361336874762763610330970365279462747492936268587100355870014542459327411606820864*t^27 - 38346731162749672770576812670817877254662578513519509323176161610448756524325710856679034235414118517636347003495150375/3788703248887967211950879612056563728220027057737981295773056932377804138519595737727956415320064*t^25 + 25282469009710782895435774258476188029444273259276235159129492556476604920598775515212741206315654675281493244309015625/329452456425040627126163444526657715497393657194607069197657124554591664219095281541561427419136*t^23 - 298703427390338629770826801652916819794278231946966846478700781601851111593028188879845578051073428610462413630276520625/658904912850081254252326889053315430994787314389214138395314249109183328438190563083122854838272*t^21 + 226286306842198412192193997605824242780029209485006998835897732173593853636522764578887136018178124225982186291958268125/109817485475013542375387814842219238499131219064869023065885708184863888073031760513853809139712*t^19 - 3114133253770952543716488404596856389245548645797950527083518127730505464193940482261210374525837327739768326755381736875/439269941900054169501551259368876953996524876259476092263542832739455552292127042055415236558848*t^17 + 63504972849781442462809123110125771853169606491706965755185662594051782620480169757264963832047554590030736312583244515625/3514159535200433356012410074951015631972199010075808738108342661915644418337016336443321892470784*t^15 - 77749119371633040371441984733476231509086055001312426492522199306165984131948835035316114265440878636430042650500552571875/2342773023466955570674940049967343754648132673383872492072228441277096278891344224295547928313856*t^13 + 198202775119120067346020611038100050418432821581832124086762158018332215746161766728135670042876189141606308455467398278125/4685546046933911141349880099934687509296265346767744984144456882554192557782688448591095856627712*t^11 - 333260299449137705786273694957357432298545064688873198121098046259414702081963354388716386352714774068669298295467902340625/9371092093867822282699760199869375018592530693535489968288913765108385115565376897182191713255424*t^9 + 343799035553830506326843076746090901585877881045553832538321708972669868247874505092234407935562655509649599231626142428125/18742184187735644565399520399738750037185061387070979936577827530216770231130753794364383426510848*t^7 - 195441984601232991153874180297031047863381298236607370328457942037008319939633541146253022889590943324773095040543785703125/37484368375471289130799040799477500074370122774141959873155655060433540462261507588728766853021696*t^5 + 51560998543633382826717179703722561934567634865412661772416994527114867396403421548903382124570800130780467216865153453125/74968736750942578261598081598955000148740245548283919746311310120867080924523015177457533706043392*t^3 - 4414983813377993531404338743133537642138401133764684337047409149473624080545938214303116635706852445978240064237895078125/149937473501885156523196163197910000297480491096567839492622620241734161849046030354915067412086784*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:   51 out of 51
Indefinite weights: 0 out of 51
Negative weights:   0 out of 51
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (6.7334464080839561733 + 3.7881342685575262764e-902j)  +/-  (1.7e-244, 1.7e-244j)
| (7.2341044727109998778 - 9.7742006185248919507e-903j)  +/-  (4.57e-245, 4.57e-245j)
| (-7.2341044727109998778 + 3.3430909404552686925e-902j)  +/-  (4.37e-245, 4.37e-245j)
| (-3.8908498934873603953 + 5.1571898435223329244e-900j)  +/-  (5.54e-244, 5.54e-244j)
| (-8.4688332846750027748 + 3.7513315543413485074e-905j)  +/-  (5.04e-247, 5.04e-247j)
| (-6.2710208392810090638 - 1.7144932832460739011e-900j)  +/-  (5.16e-244, 5.16e-244j)
| (5.8362529802643323569 + 2.7745321416616493628e-906j)  +/-  (1.02e-243, 1.02e-243j)
| (8.4688332846750027748 + 2.4741894017486901333e-910j)  +/-  (5.12e-247, 5.12e-247j)
| (6.2710208392810090638 + 1.381877776695109014e-906j)  +/-  (4.71e-244, 4.71e-244j)
| (-7.7940436364285030235 + 5.5992643290254607732e-908j)  +/-  (6.91e-246, 6.91e-246j)
| (0.95857246461381850711 + 1.1009461638771074853e-913j)  +/-  (1.04e-250, 1.04e-250j)
| (-1.4758400226117297351 + 2.6200438750804982332e-911j)  +/-  (6.97e-249, 6.97e-249j)
| (-1.2280754923566695675 - 4.2992479209532794775e-912j)  +/-  (1.04e-249, 1.04e-249j)
| (-5.8362529802643323569 - 1.1146810465517914045e-904j)  +/-  (1.02e-243, 1.02e-243j)
| (-6.7334464080839561733 + 5.4236329247390697223e-917j)  +/-  (1.76e-244, 1.76e-244j)
| (2.0201828704560856329 + 6.3148092853296730116e-932j)  +/-  (2.38e-247, 2.38e-247j)
| (7.7940436364285030235 - 3.0774137051205059022e-928j)  +/-  (7.31e-246, 7.31e-246j)
| (-4.2438566526426439137 + 3.1942821780825175749e-935j)  +/-  (1.91e-243, 1.91e-243j)
| (-2.0201828704560856329 + 2.7820292308445839176e-960j)  +/-  (2.16e-247, 2.16e-247j)
| (-4.5523894302597057925 - 3.6306564071477779542e-954j)  +/-  (7.32e-243, 7.32e-243j)
| (5.0318538452090480302 + 4.1186505388695666193e-970j)  +/-  (3.7e-243, 3.7e-243j)
| (1.2280754923566695675 + 1.0523406088816034701e-978j)  +/-  (1.06e-249, 1.06e-249j)
| (2.8936367492419226221 + 2.4742531997451854909e-975j)  +/-  (1.94e-245, 1.94e-245j)
| (-3.5446014948410696673 - 2.863976048229844635e-971j)  +/-  (1.89e-244, 1.89e-244j)
| (4.5523894302597057925 + 8.5278301516036534394e-973j)  +/-  (7.12e-243, 7.12e-243j)
| (-0.95857246461381850711 - 2.8348894883408232051e-994j)  +/-  (1.03e-250, 1.03e-250j)
| (0.67937564139520684118 + 7.4670814034891825993e-995j)  +/-  (1.01e-251, 1.01e-251j)
| (-5.0318538452090480302 + 7.6321766767320872555e-985j)  +/-  (3.33e-243, 3.33e-243j)
| (4.6990084695455690955 + 1.4049639676934637987e-1001j)  +/-  (7.44e-243, 7.44e-243j)
| (-2.8936367492419226221 - 6.3571156255562862938e-1004j)  +/-  (1.79e-245, 1.79e-245j)
| (-4.6990084695455690955 - 1.1102981112682844914e-1003j)  +/-  (8.08e-243, 8.08e-243j)
| (2.5950369655393867119 - 7.1751389455912017244e-1019j)  +/-  (5.13e-246, 5.13e-246j)
| (3.2107875901386318771 + 3.243655351325747412e-1018j)  +/-  (5.86e-245, 5.86e-245j)
| (4.2438566526426439137 + 8.3256945433201479688e-1016j)  +/-  (1.84e-243, 1.84e-243j)
| (-3.2107875901386318771 - 3.2258494401658919277e-1019j)  +/-  (5.82e-245, 5.82e-245j)
| (3.5446014948410696673 + 3.8131655914504747901e-1019j)  +/-  (1.69e-244, 1.69e-244j)
| (5.4234690793123793386 + 8.9552894805893712559e-1018j)  +/-  (1.9e-243, 1.9e-243j)
| (1.4758400226117297351 - 2.2678030363527447819e-1024j)  +/-  (7.52e-249, 7.52e-249j)
| (2.3074857757913967309 + 4.1088182811967632097e-1022j)  +/-  (1.14e-246, 1.14e-246j)
| (-2.5950369655393867119 + 8.3058446779331002676e-1022j)  +/-  (5.57e-246, 5.57e-246j)
| (-0.67937564139520684118 - 4.4821445282785063647e-1027j)  +/-  (9.47e-252, 9.47e-252j)
| (2.5290976114481494249e-1044 - 2.2941896715087988e-1044j)  +/-  (1.74e-1042, 1.74e-1042j)
| (-2.3074857757913967309 - 3.801633553700636044e-1022j)  +/-  (1.16e-246, 1.16e-246j)
| (1.7372317047927888894 + 1.2334151605941016397e-1023j)  +/-  (4.25e-248, 4.25e-248j)
| (3.8908498934873603953 - 2.0777803368504489334e-1022j)  +/-  (5.34e-244, 5.34e-244j)
| (-1.7372317047927888894 - 1.7004464405769219443e-1027j)  +/-  (3.86e-248, 3.86e-248j)
| (-0.46851498816181809435 + 4.6795070664493214491e-1031j)  +/-  (1.31e-252, 1.31e-252j)
| (-5.4234690793123793386 - 1.0921880131393116618e-1028j)  +/-  (1.93e-243, 1.93e-243j)
| (0.46851498816181809435 - 9.922760164004453774e-1044j)  +/-  (1.28e-252, 1.28e-252j)
| (0.27949930703826081571 - 1.4151571660543991216e-1044j)  +/-  (1.26e-253, 1.26e-253j)
| (-0.27949930703826081571 - 1.6936662290518466961e-1045j)  +/-  (1.26e-253, 1.26e-253j)
-------------------------------------------------
The weights are:
| (5.5124467537038658614e-21 + 5.5221528600540919445e-917j)  +/-  (2.1e-78, 1.46e-199j)
| (5.549515044188048608e-24 - 8.2328184228854100887e-919j)  +/-  (5.6e-80, 3.89e-201j)
| (5.549515044188048608e-24 + 2.740606642564663349e-918j)  +/-  (1.02e-81, 7.09e-203j)
| (5.2737396090219674513e-08 + 1.2183816584100448676e-906j)  +/-  (2.17e-69, 1.5e-190j)
| (3.1235510775836419166e-32 + 3.4446445136768628845e-923j)  +/-  (1.7e-85, 1.18e-206j)
| (2.1043298951962875868e-18 + 1.0082821485729345553e-914j)  +/-  (4.65e-79, 3.23e-200j)
| (3.8462674852894204921e-16 + 7.503346468972381107e-914j)  +/-  (2.13e-78, 1.48e-199j)
| (3.1235510775836419166e-32 - 1.2756496473883406701e-923j)  +/-  (8.94e-87, 6.21e-208j)
| (2.1043298951962875868e-18 - 2.3686757743933196021e-915j)  +/-  (1.74e-79, 1.21e-200j)
| (1.409579495580142068e-27 - 1.8420640325482782058e-920j)  +/-  (1.02e-84, 7.1e-206j)
| (0.063213397666095293719 + 6.3358013757642160325e-903j)  +/-  (2.61e-54, 1.81e-175j)
| (0.015870992332698221218 + 3.6379479433592833588e-903j)  +/-  (3.61e-57, 2.51e-178j)
| (0.031901246150458237378 - 6.3851590301814690855e-903j)  +/-  (2.6e-54, 1.81e-175j)
| (3.8462674852894204921e-16 - 3.7487579085253428767e-913j)  +/-  (6.79e-80, 4.72e-201j)
| (5.5124467537038658614e-21 - 2.0656361117362421204e-916j)  +/-  (6.02e-82, 4.18e-203j)
| (0.0027387190696952555119 + 2.0474091019846476436e-904j)  +/-  (1.22e-65, 8.48e-187j)
| (1.409579495580142068e-27 + 6.1516149182145057364e-921j)  +/-  (1.76e-86, 1.22e-207j)
| (2.9891721772791405995e-09 + 1.821844880882171255e-907j)  +/-  (6.5e-76, 4.51e-197j)
| (0.0027387190696952555119 + 6.4692497309211915026e-904j)  +/-  (1.14e-66, 7.93e-188j)
| (1.1178502165276802732e-10 - 3.8054637717376605561e-908j)  +/-  (4e-77, 2.77e-198j)
| (2.1525602153085794323e-12 + 5.0503402760425942716e-911j)  +/-  (2.91e-81, 2.02e-202j)
| (0.031901246150458237378 - 3.3215229400606519731e-903j)  +/-  (7.13e-63, 4.95e-184j)
| (4.0090377949882109638e-05 - 4.4953562404540670424e-906j)  +/-  (8.89e-75, 6.17e-196j)
| (6.7182307293422415479e-07 - 3.8841783220938416199e-906j)  +/-  (2.23e-75, 1.55e-196j)
| (1.1178502165276802732e-10 + 2.982149964544275085e-909j)  +/-  (1.24e-80, 8.59e-202j)
| (0.063213397666095293719 + 1.047801097442004569e-902j)  +/-  (8.33e-65, 5.79e-186j)
| (0.094418664361639046157 - 1.5004582968190393114e-902j)  +/-  (1.98e-64, 1.38e-185j)
| (2.1525602153085794323e-12 - 3.9483853798532096424e-910j)  +/-  (3.14e-80, 2.18e-201j)
| (3.3213460167422355427e-11 - 1.1580282236599250827e-909j)  +/-  (5.07e-81, 3.52e-202j)
| (4.0090377949882109638e-05 - 3.0581896757206535212e-905j)  +/-  (3.56e-75, 2.47e-196j)
| (3.3213460167422355427e-11 + 1.2306224705410902018e-908j)  +/-  (1.04e-78, 7.25e-200j)
| (0.00019522417507380207787 + 1.8477540916013161213e-905j)  +/-  (4.86e-76, 3.38e-197j)
| (6.1331370578829731268e-06 + 9.3808911967958664733e-907j)  +/-  (1.53e-78, 1.06e-199j)
| (2.9891721772791405995e-09 - 7.9070352350684262283e-909j)  +/-  (1.52e-81, 1.05e-202j)
| (6.1331370578829731268e-06 + 9.7953493599243490222e-906j)  +/-  (2.67e-78, 1.85e-199j)
| (6.7182307293422415479e-07 - 1.8089237347739076888e-907j)  +/-  (3.26e-80, 2.26e-201j)
| (3.8200379943266041062e-14 - 1.9761039105127767648e-912j)  +/-  (7.91e-85, 5.49e-206j)
| (0.015870992332698221218 + 1.6371221268025441484e-903j)  +/-  (2.72e-75, 1.89e-196j)
| (0.00078718039097882611209 - 6.4345951706422961467e-905j)  +/-  (3.25e-77, 2.26e-198j)
| (0.00019522417507380207787 + 9.2479781744246271401e-905j)  +/-  (3.03e-79, 2.11e-200j)
| (0.094418664361639046157 - 2.135264864484460807e-902j)  +/-  (8.76e-76, 6.08e-197j)
| (0.16451100553401834115 + 2.3779941792781969906e-902j)  +/-  (4.97e-76, 3.45e-197j)
| (0.00078718039097882611209 - 2.518805859862604166e-904j)  +/-  (9.46e-79, 6.57e-200j)
| (0.0075864292541468357784 - 6.2599219267366404527e-904j)  +/-  (2.89e-77, 2.01e-198j)
| (5.2737396090219674513e-08 + 3.4954792070090535091e-908j)  +/-  (6.68e-82, 4.64e-203j)
| (0.0075864292541468357784 - 1.6358591565487047934e-903j)  +/-  (4.11e-78, 2.84e-199j)
| (0.070498432303402575472 + 3.5021676662396312968e-902j)  +/-  (4.39e-77, 3.05e-198j)
| (3.8200379943266041062e-14 + 1.2004893457845313804e-911j)  +/-  (1.66e-87, 1.18e-208j)
| (0.070498432303402575472 + 2.7494124537064602601e-902j)  +/-  (1.51e-77, 1.07e-198j)
| (0.13048726031696414004 - 2.8159789814910499157e-902j)  +/-  (1.06e-77, 7.61e-199j)
| (0.13048726031696414004 - 3.2518461803236955444e-902j)  +/-  (9.1e-78, 5.88e-199j)
