Starting with polynomial:
P : 2*t
Extension levels are: 1 4 10 34
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 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^15 - 1805/21*t^13 + 169685/126*t^11 - 2447225/252*t^9 + 268675/8*t^7 - 846835/16*t^5 + 1039225/32*t^3 - 327525/64*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^49 - 4175800205808505672520320090786198999805978345308978443685245435150381643997343295853489/4590629804181073661263159751716754087714196155258679218560831995805786188647872427496*t^47 + 1639633442027414667183921517477927533365639865733293557910836978694224563542005361199709720153/8676290329902229219787371930744665225779830733438903723079972472072935896544478887967440*t^45 - 3224001978586333697225100349480918863501361774349694221876997003445050706332371000278738334502641/135350129146474775828683002119616777522165359441646898080047570564337799986093870652292064*t^43 + 236744622419333190661335716380685164876887194671393693222072429147849178429133444756845441862551561/116014396411264093567442573245385809304713165235697341211469346198003828559509031987678912*t^41 - 204913304471979855280122079027876331999195528039473245799213203871201803099814802953850243949393547175/1624201549757697309944196025435401330265984313299762776960570846772053599833126447827504768*t^39 + 6316533025430263551483970362931845268601710122239858784069040298489318324671947729402795692387733947005/1082801033171798206629464016956934220177322875533175184640380564514702399888750965218336512*t^37 - 9118187731350101871789057357350193072553957422696970314921971475049982440619167281652153329663607361551/44195960537624416597120980283956498782747872470741844271035941408763363260765345519115776*t^35 + 3502705545374631251376036636993091822085826256436846332138207398476869859612758763804464314050421287821165/618743447526741832359693723975390982958470214590385819794503179722687085650714837267620864*t^33 - 25067979424138137839153374150874514976438182329410632715812941909067995730721847733387997460237504089338635/206247815842247277453231241325130327652823404863461939931501059907562361883571612422540288*t^31 + 845823351087858857131392077188279206277381522984991943535999708992932508774412080795127326786808437148569475/412495631684494554906462482650260655305646809726923879863002119815124723767143224845080576*t^29 - 3205634250434898003043614006112402984493730884283728105036220656315531643217682298473803555745498140168579975/117855894766998444258989280757217330087327659921978251389429177090035635362040921384308736*t^27 + 1330179635623195626049131204605440707400948836783403659056003712436407028024498971506436915444588391989345275/4700804919481419429133475585757956185819336862984887519806291963705125057175421365755904*t^25 - 7195269663505307303147833907171441634427250020847203123040057995535839181800642264815269256739327243315488125/3133869946320946286088983723838637457212891241989925013204194642470083371450280910503936*t^23 + 12896858368647880770186691960140958643016749497321164262734706386020166701602750824595437156586933435110866875/895391413234556081739709635382467844917968926282835718058341326420023820414365974429696*t^21 - 41202187137980680290277682657151375631564035826849532330807614040520678758496402607458993471337691028977991875/596927608823037387826473090254978563278645950855223812038894217613349213609577316286464*t^19 + 127221201665247331790886152292500751388320140206688740326828652008171602840322668239284286840539684012099044375/511652236134032046708405505932838768524553672161620410319052186525727897379637699674112*t^17 - 9447119284826398906207668212197093454781066672534450982220901963909053216580797983806318632255270726235393354625/14326262611752897307835354166119485518687502820525371488933461222720381126629855590875136*t^15 + 1709550630279463198340996190013364426054780341225152068435371517453887637624286058829132090403514989993405923125/1364405963024085457889081349154236716065476459097654427517472497401941059679033865797632*t^13 - 31426373789790618575568913313928035074200404377195029518261909575910999869788663949923167981671865478150059650625/19101683482337196410447138888159314024916670427367161985244614963627174835506474121166848*t^11 + 54245925137612520539265552783291583499632798397459586738346384885169279236529081016074534150271100401476833053125/38203366964674392820894277776318628049833340854734323970489229927254349671012948242333696*t^9 - 2716809932920654938137836567477849613175758991348831697247691029853075398392163129876923655640419236839070940625/3638415901397561221037550264411297909507937224260411806713259993071842825810756975460352*t^7 + 1521983973176400770096156310676939892621577306251042758179112904278014889618301667215480307033748794226530230625/7276831802795122442075100528822595819015874448520823613426519986143685651621513950920704*t^5 - 331693360783493209857351330325205866213699516361766042363268026742383091397561171168445125333640941475310696875/14553663605590244884150201057645191638031748897041647226853039972287371303243027901841408*t^3 + 4565967048866500492887700704482738760709333621071055677585247560936990098297633603659688510011099956590334375/29107327211180489768300402115290383276063497794083294453706079944574742606486055803682816*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:
| (-7.0881977515401369904 - 1.1849646507451288463e-677j)  +/-  (1.78e-245, 1.78e-245j)
| (7.6533788259674246294 - 4.2440939826500403481e-683j)  +/-  (3.26e-246, 3.26e-246j)
| (-7.6533788259674246294 + 1.2343860558008736543e-681j)  +/-  (3.14e-246, 3.14e-246j)
| (6.5821105466251028619 - 1.1491997336355026597e-681j)  +/-  (6.43e-245, 6.43e-245j)
| (7.0881977515401369904 - 3.9631600271110794181e-682j)  +/-  (1.76e-245, 1.76e-245j)
| (-4.8439293049236016852 + 3.9772463881886475701e-679j)  +/-  (5.48e-244, 5.48e-244j)
| (5.2504119403460895549 - 3.8712575015874239893e-688j)  +/-  (4.36e-244, 4.36e-244j)
| (2.0201828704560856329 + 1.0507886255502191449e-691j)  +/-  (1.09e-247, 1.09e-247j)
| (6.1137505186824856922 - 1.0103247713206195252e-688j)  +/-  (1.67e-244, 1.67e-244j)
| (3.3426682448651147193 + 7.8542288024483683358e-690j)  +/-  (3.12e-245, 3.12e-245j)
| (2.9876167333799223859 - 1.2481868800891958505e-689j)  +/-  (6.79e-246, 6.79e-246j)
| (1.1350535204366930296 + 5.1299175904042264776e-694j)  +/-  (6.9e-250, 6.9e-250j)
| (-2.6436261790465342931 + 7.7340716459697674608e-687j)  +/-  (1.62e-246, 1.62e-246j)
| (-6.5821105466251028619 + 1.6306506590300668272e-687j)  +/-  (6.54e-245, 6.54e-245j)
| (4.0995450260065200831 + 1.4423647059699456419e-692j)  +/-  (1.91e-243, 1.91e-243j)
| (-5.2504119403460895549 - 5.2388398291023170972e-693j)  +/-  (4.29e-244, 4.29e-244j)
| (5.6720868459012001849 + 1.7509251525853840334e-704j)  +/-  (2.95e-244, 2.95e-244j)
| (4.1771961071723433645 - 1.5012680741232966314e-702j)  +/-  (2.33e-243, 2.33e-243j)
| (-3.3426682448651147193 + 2.2221910150825806319e-710j)  +/-  (3.06e-245, 3.06e-245j)
| (4.8439293049236016852 - 3.1289216502076964918e-723j)  +/-  (5.84e-244, 5.84e-244j)
| (-6.1137505186824856922 - 1.6629002932732715264e-729j)  +/-  (1.5e-244, 1.5e-244j)
| (-1.1350535204366930296 - 2.6202396439990635184e-739j)  +/-  (7.88e-250, 7.88e-250j)
| (-8.3336579354624078501 + 4.3692342665274510315e-743j)  +/-  (2.32e-247, 2.32e-247j)
| (8.3336579354624078501 + 1.5960536304237028321e-745j)  +/-  (2.53e-247, 2.53e-247j)
| (-2.0201828704560856329 - 1.177057573388753927e-740j)  +/-  (1.06e-247, 1.06e-247j)
| (-4.1771961071723433645 + 2.016808388367878823e-766j)  +/-  (2.39e-243, 2.39e-243j)
| (0.83683758159104843976 - 4.2678527971627037285e-795j)  +/-  (6.87e-251, 6.87e-251j)
| (-3.7077866046649300639 - 4.1176454278411356155e-812j)  +/-  (1.28e-244, 1.28e-244j)
| (-0.95857246461381850711 + 2.1336513064538545757e-831j)  +/-  (2.67e-250, 2.67e-250j)
| (-1.4594230210196350585 - 1.5084077381793758452e-829j)  +/-  (3.98e-249, 3.98e-249j)
| (0.085837652865014043082 + 2.2309252273714028522e-838j)  +/-  (1.31e-254, 1.31e-254j)
| (4.4459982154151086254 + 7.2171003373950464265e-839j)  +/-  (1.05e-243, 1.05e-243j)
| (-4.4459982154151086254 - 1.4095620881352577686e-864j)  +/-  (1.05e-243, 1.05e-243j)
| (3.7077866046649300639 - 1.1712939819129187621e-881j)  +/-  (1.29e-244, 1.29e-244j)
| (-1.7491988858051629888 + 1.056402204532122855e-881j)  +/-  (2.64e-248, 2.64e-248j)
| (-2.3167663863001497656 - 1.0397463806768407026e-887j)  +/-  (4.76e-247, 4.76e-247j)
| (2.3167663863001497656 + 2.1316187877070747955e-897j)  +/-  (4.88e-247, 4.88e-247j)
| (0.95857246461381850711 + 9.6006601353613489082e-904j)  +/-  (2.94e-250, 2.94e-250j)
| (-4.0995450260065200831 + 3.6395669328237099748e-907j)  +/-  (1.84e-243, 1.84e-243j)
| (-2.9876167333799223859 - 1.4477801410634873981e-919j)  +/-  (6.98e-246, 6.98e-246j)
| (-0.83683758159104843976 + 8.3132097880769708967e-926j)  +/-  (6.62e-251, 6.62e-251j)
| (-5.6720868459012001849 - 3.6090324398435920696e-918j)  +/-  (2.9e-244, 2.9e-244j)
| (1.4594230210196350585 - 3.9797130370069427459e-930j)  +/-  (4.14e-249, 4.14e-249j)
| (1.7491988858051629888 + 3.1848107117256015661e-929j)  +/-  (2.38e-248, 2.38e-248j)
| (2.6436261790465342931 - 3.3927382665265385836e-927j)  +/-  (1.78e-246, 1.78e-246j)
| (-0.48488888867740967968 + 3.9913132143300828768e-934j)  +/-  (5.95e-253, 5.95e-253j)
| (1.5340611931581797998e-938 + 1.2997505435222127656e-937j)  +/-  (6.41e-936, 6.41e-936j)
| (-0.085837652865014043082 + 6.6972503414825671253e-935j)  +/-  (1.31e-254, 1.31e-254j)
| (0.48488888867740967968 - 4.3063220526309524307e-934j)  +/-  (5.76e-253, 5.76e-253j)
-------------------------------------------------
The weights are:
| (4.530589604758706341e-23 + 1.0539000893814643822e-697j)  +/-  (2.93e-82, 6.96e-204j)
| (1.2489663588786341328e-26 + 1.7586643635928889004e-700j)  +/-  (2.13e-84, 5.07e-206j)
| (1.2489663588786341328e-26 - 7.8935334512289582393e-700j)  +/-  (3.35e-84, 7.96e-206j)
| (4.1837765224601522531e-20 + 1.2244093923182508403e-696j)  +/-  (1.01e-81, 2.41e-203j)
| (4.530589604758706341e-23 - 2.0691738813660166287e-698j)  +/-  (4.05e-83, 9.63e-205j)
| (1.4582059842458575606e-11 + 4.4178518978111629821e-689j)  +/-  (5.04e-78, 1.2e-199j)
| (2.4866799910709027194e-13 - 2.8667329946080740772e-692j)  +/-  (9.37e-79, 2.23e-200j)
| (0.0026529744299036493949 - 9.8060670132069491484e-685j)  +/-  (4.12e-63, 9.8e-185j)
| (1.4965859962240128032e-17 - 4.6170936220463247531e-695j)  +/-  (6.09e-81, 1.45e-202j)
| (2.851498307768635382e-06 - 2.3005390070177867306e-687j)  +/-  (3.78e-72, 8.98e-194j)
| (2.6245963505469648698e-05 + 1.0642555029649269874e-686j)  +/-  (2.08e-70, 4.95e-192j)
| (0.054707230286753891117 + 4.6901587066554191265e-683j)  +/-  (6.31e-57, 1.5e-178j)
| (0.00017535886446495442451 - 1.7380826708351967178e-685j)  +/-  (8.73e-72, 2.07e-193j)
| (4.1837765224601522531e-20 - 7.9715607884455783356e-696j)  +/-  (2.02e-86, 4.8e-208j)
| (1.4329728326309641296e-08 - 4.2698332014085803327e-688j)  +/-  (2.91e-76, 6.91e-198j)
| (2.4866799910709027194e-13 + 7.1028274422411910316e-691j)  +/-  (3.73e-83, 8.88e-205j)
| (2.5900107144391477366e-15 + 1.2744313486468395159e-693j)  +/-  (2.16e-81, 5.14e-203j)
| (-2.3400176278323144142e-09 + 3.1000026554106979275e-688j)  +/-  (9.98e-77, 2.37e-198j)
| (2.851498307768635382e-06 - 1.25347580837948225e-686j)  +/-  (2.55e-78, 6.07e-200j)
| (1.4582059842458575606e-11 + 5.9971808073718419985e-691j)  +/-  (1.89e-79, 4.49e-201j)
| (1.4965859962240128032e-17 + 3.9654492687704379362e-694j)  +/-  (9.7e-87, 2.31e-208j)
| (0.054707230286753891117 + 7.5591330902466386808e-683j)  +/-  (1.27e-66, 3.01e-188j)
| (3.0502733597216691066e-31 + 1.594848606243041602e-702j)  +/-  (1.44e-93, 3.42e-215j)
| (3.0502733597216691066e-31 - 4.2056075765853358954e-703j)  +/-  (3.55e-92, 8.45e-214j)
| (0.0026529744299036493949 - 2.3826570010959835885e-684j)  +/-  (2.87e-74, 6.81e-196j)
| (-2.3400176278323144142e-09 + 4.1891678571428133964e-687j)  +/-  (2.46e-82, 5.86e-204j)
| (0.10860998309139234292 + 1.2330723902486466977e-682j)  +/-  (2.25e-70, 5.36e-192j)
| (2.2402668488413015487e-07 + 4.2530173967654882137e-687j)  +/-  (2.31e-81, 5.48e-203j)
| (-0.021246493800255972969 - 1.9873087083760530946e-682j)  +/-  (2.06e-71, 4.9e-193j)
| (0.020588370853858037139 - 1.5784956169466202102e-683j)  +/-  (1.84e-73, 4.38e-195j)
| (0.4946767192480765545 + 6.476170277193149516e-682j)  +/-  (4.94e-72, 1.18e-193j)
| (5.896196922031808051e-10 - 1.7368709351353799255e-689j)  +/-  (7.35e-82, 1.75e-203j)
| (5.896196922031808051e-10 - 4.0490136352962579982e-688j)  +/-  (1.67e-83, 3.96e-205j)
| (2.2402668488413015487e-07 + 5.6559829470437835451e-688j)  +/-  (9.86e-81, 2.34e-202j)
| (0.0072385614421953669122 + 6.3033236189108557447e-684j)  +/-  (4.11e-76, 9.76e-198j)
| (0.00082725733396639530179 + 6.8643821830542308826e-685j)  +/-  (2.07e-78, 4.93e-200j)
| (0.00082725733396639530179 + 2.4238745154696488735e-685j)  +/-  (1.3e-79, 3.08e-201j)
| (-0.021246493800255972969 - 1.330960587822130307e-682j)  +/-  (1.36e-75, 3.24e-197j)
| (1.4329728326309641296e-08 - 5.1238645224534158669e-687j)  +/-  (1.82e-82, 4.33e-204j)
| (2.6245963505469648698e-05 + 4.4868665480382285728e-686j)  +/-  (6.9e-81, 1.64e-202j)
| (0.10860998309139234292 + 1.7478054074138342849e-682j)  +/-  (5.94e-77, 1.41e-198j)
| (2.5900107144391477366e-15 - 1.6132684955420737007e-692j)  +/-  (3.5e-88, 8.32e-210j)
| (0.020588370853858037139 - 8.4781083621735888886e-684j)  +/-  (1.86e-79, 4.41e-201j)
| (0.0072385614421953669122 + 2.9598014512934012414e-684j)  +/-  (3.38e-80, 8.05e-202j)
| (0.00017535886446495442451 - 5.1107892738632093873e-686j)  +/-  (5.53e-82, 1.32e-203j)
| (0.15556061556413915484 - 8.9133521718859241711e-683j)  +/-  (3.25e-79, 7.72e-201j)
| (-0.64763982279431243907 - 1.2276747379893233792e-681j)  +/-  (3.05e-79, 7.25e-201j)
| (0.4946767192480765545 + 6.7097208271916359929e-682j)  +/-  (1.64e-79, 3.9e-201j)
| (0.15556061556413915484 - 7.2919391226580117738e-683j)  +/-  (1.47e-80, 3.41e-202j)
