Starting with polynomial:
P : 2*t
Extension levels are: 1 2 6 48
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P3 : 2*t^9 - 117/4*t^7 + 945/8*t^5 - 2205/16*t^3 + 945/32*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^57 - 3445309416318978752482380285423175684680230898320616164332576236328329645492111/2086443512219264068464527187610771334446467196183835399274787270753245826892*t^55 + 10138760996665475777651974223260404601490204267670064776108445962791803415841737595/16312194731896064535268121648593303160217834442891804030693791389525376464792*t^53 - 357479866206088125745663792919257043314431330569546126710975509937786248439744777452375/2512077988711993938431290733883368686673546504205337820726843873986907975577968*t^51 + 111946466668427568121412449480891470409706597999696155717245105422848644050111110555466835/5024155977423987876862581467766737373347093008410675641453687747973815951155936*t^49 - 1823804120383677035056697190782731423430317015601519103320404834670435105254721508009948315/717736568203426839551797352538105339049584715487239377350526821139116564450848*t^47 + 13690226780967820671252072484509533909940914059536638990299030803867615390604356981156567465/62411875495950159961025856742443942526050844824977337160915375751227527343552*t^45 - 3879040525920347242250180595693778102862846616561422402987326022155797665919381606475242525/263897993640381226050849288551560010680976088054872461568352540174323582848*t^43 + 37318840334008495138083660444329567644825959283179961894744600548731877482090187401462521425/47981453389160222918336234282101820123813834191794993012427734577149742336*t^41 - 614217772231924154354635817928893928205081501550844362487238648149283194388354157945940388425/18683043797549113348732692994800708720777068180875926482715224083137952768*t^39 + 4723052119204925559916560298715766712978877245521589260516401642797076082807943474146229557522525/4222367898246099616813588616824960170895617408877959385093640642789177325568*t^37 - 259905904477336457223734050958910161414424160952104348292291193819579381780099052120639529135975325/8444735796492199233627177233649920341791234817755918770187281285578354651136*t^35 + 11590483233134510706189489927067585274695267015328999029863833982540095553623321875463810526650693625/16889471592984398467254354467299840683582469635511837540374562571156709302272*t^33 - 9519413233061789005007757218405494075999127924766172964329668781700322477534928907038696908307327125/767703254226563566693379748513629121981021347068719888198843753234395877376*t^31 + 3060295541777628487054375696514166696075238602423304580432264960449387820967054293523677251337459722875/16889471592984398467254354467299840683582469635511837540374562571156709302272*t^29 - 72046243981629632179879462179736839387467951132267620361071698083627466559162158318968663124356924370375/33778943185968796934508708934599681367164939271023675080749125142313418604544*t^27 + 339565221757632824225744768141168344272916442565321888954771377709294969353528554414673296737988466391375/16889471592984398467254354467299840683582469635511837540374562571156709302272*t^25 - 81370256598334771320115887069734274724131886384110392177344562127511467133990725224201422988490563971528125/540463090975500750952139342953594901874639028336378801291986002277014697672704*t^23 + 87108522121628032042632011912088495513693402484805314822727579399705351230869931138544956625429977365571875/98266016541000136536752607809744527613570732424796145689452000414002672304128*t^21 - 796080139399540441096243672245198471916858669213432748244213493767515166787477785634040380944350830430896875/196532033082000273073505215619489055227141464849592291378904000828005344608256*t^19 + 5555135932996416622110180432032978034262679536175837055235649623261634529330212606342221145042876592507834375/393064066164000546147010431238978110454282929699184582757808001656010689216512*t^17 - 14501049703044417580049649939951398961796555624298392738504706443139743053752837710396784648529762641416884375/393064066164000546147010431238978110454282929699184582757808001656010689216512*t^15 + 55195926366374273905353696895509207345343285459499023451942899771036009543465043247666184559171720587062046875/786128132328001092294020862477956220908565859398369165515616003312021378433024*t^13 - 148089609018298518626019153469185370195172927395691946651279118535695813934209931031835385331408875748143859375/1572256264656002184588041724955912441817131718796738331031232006624042756866048*t^11 + 267380197561656994923117264725803663445939142974133950566425544976420729208585318127201344893965706210178328125/3144512529312004369176083449911824883634263437593476662062464013248085513732096*t^9 - 606790859032922964504297423217200773294476802486215954803695492565021651804712387835769592573555574500435078125/12578050117248017476704333799647299534537053750373906648249856052992342054928384*t^7 + 387098726435022551935484127224463974876460085979683037957358341987519057862951686310376837785100789712292890625/25156100234496034953408667599294599069074107500747813296499712105984684109856768*t^5 - 112908884982232061108478784068197790842846807991973388337287591228719701506063245957714964756079563013541640625/50312200468992069906817335198589198138148215001495626592999424211969368219713536*t^3 + 9280949664014822815275080621085192296701322762874262974406334052744228269010467911047446515113602805835078125/100624400937984139813634670397178396276296430002991253185998848423938736439427072*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:
| (-7.6718667570255576976 + 8.4966787879818320063e-911j)  +/-  (4.05e-243, 4.05e-243j)
| (8.6910789208978074313 + 2.1133967955684188637e-921j)  +/-  (1.74e-244, 1.74e-244j)
| (9.338917696216259821 - 1.0977467503297705981e-922j)  +/-  (1.27e-245, 1.27e-245j)
| (4.2598503084754328815 + 2.7114878423674389317e-921j)  +/-  (3.6e-243, 3.6e-243j)
| (-9.338917696216259821 + 6.9944035680875129971e-920j)  +/-  (1.34e-245, 1.34e-245j)
| (-12.839109552126825044 + 2.5955339242629993237e-931j)  +/-  (5.57e-249, 5.57e-249j)
| (8.1531264891502383408 - 1.2943223442004449104e-923j)  +/-  (1.1e-243, 1.1e-243j)
| (-7.2270056591305955343 - 5.9581525791872177473e-930j)  +/-  (9.36e-243, 9.36e-243j)
| (4.9417428707257606067 + 7.7947117130271955452e-941j)  +/-  (1.36e-242, 1.36e-242j)
| (7.6718667570255576976 - 1.3454056830158289964e-941j)  +/-  (3.94e-243, 3.94e-243j)
| (1.4222124432587378379 + 9.926301426072201696e-950j)  +/-  (1.11e-248, 1.11e-248j)
| (5.6540788789860757282 - 3.6100823668971613217e-943j)  +/-  (2.52e-242, 2.52e-242j)
| (-1.0880931745211194127 - 1.6596704760705769456e-951j)  +/-  (1.05e-249, 1.05e-249j)
| (-2.6439252186531036965 + 2.2049396594471707136e-947j)  +/-  (6.86e-246, 6.86e-246j)
| (-5.2934907412057409403 + 2.5353110947968563352e-944j)  +/-  (2.04e-242, 2.04e-242j)
| (6.0251497814179606518 + 7.4707377388126641345e-959j)  +/-  (2.99e-242, 2.99e-242j)
| (2.9592107790638377223 - 7.2697005277659699557e-963j)  +/-  (3.07e-245, 3.07e-245j)
| (3.9278150777591513469 + 2.0223327630093057364e-961j)  +/-  (1.52e-243, 1.52e-243j)
| (12.839109552126825044 + 1.0264451225790115632e-966j)  +/-  (5.95e-249, 5.95e-249j)
| (1.7184492469788673279 - 2.4289440384668476777e-965j)  +/-  (4.55e-248, 4.55e-248j)
| (6.4088504148849924307 - 2.5481263611707876189e-959j)  +/-  (2.75e-242, 2.75e-242j)
| (3.2780242666494460012 - 5.1963053537324066199e-962j)  +/-  (1.3e-244, 1.3e-244j)
| (4.5975426972068125834 - 3.3380632870768267011e-960j)  +/-  (7.07e-243, 7.07e-243j)
| (-1.2247448713915890491 + 8.1877650153653153609e-966j)  +/-  (4.49e-249, 4.49e-249j)
| (-3.6007338497515305637 - 6.4265847498576461827e-959j)  +/-  (4.65e-244, 4.65e-244j)
| (5.2934907412057409403 + 2.3841621645500274223e-962j)  +/-  (2.2e-242, 2.2e-242j)
| (-6.0251497814179606518 - 6.4450117594356172975e-961j)  +/-  (2.79e-242, 2.79e-242j)
| (2.6439252186531036965 - 3.3564179075396591118e-976j)  +/-  (7.06e-246, 7.06e-246j)
| (2.0232301911005156592 + 7.2995555686673789814e-977j)  +/-  (2.57e-247, 2.57e-247j)
| (-6.8080905816685400933 - 2.8303583653483943171e-970j)  +/-  (1.66e-242, 1.66e-242j)
| (2.3319330725422100784 - 1.0131594335697680052e-980j)  +/-  (1.26e-246, 1.26e-246j)
| (-8.6910789208978074313 - 1.442535926139921302e-977j)  +/-  (1.72e-244, 1.72e-244j)
| (-4.2598503084754328815 + 6.8050626018812791387e-975j)  +/-  (3.35e-243, 3.35e-243j)
| (-4.5975426972068125834 + 1.4259427044055865721e-976j)  +/-  (8.01e-243, 8.01e-243j)
| (-2.3319330725422100784 - 1.9856285038932923449e-983j)  +/-  (1.32e-246, 1.32e-246j)
| (-1.4222124432587378379 - 3.4617327014285253514e-986j)  +/-  (1.06e-248, 1.06e-248j)
| (3.6007338497515305637 + 6.102610484105508697e-981j)  +/-  (4.58e-244, 4.58e-244j)
| (1.2247448713915890491 + 1.9216876648559013186e-985j)  +/-  (4.65e-249, 4.65e-249j)
| (-3.9278150777591513469 + 1.0441921524371608918e-978j)  +/-  (1.31e-243, 1.31e-243j)
| (6.8080905816685400933 + 7.1911574321374723953e-979j)  +/-  (1.68e-242, 1.68e-242j)
| (-0.8075687085372603334 + 1.03866878268247899e-987j)  +/-  (3.63e-251, 3.63e-251j)
| (-2.9592107790638377223 - 6.0470106453631926712e-981j)  +/-  (3.49e-245, 3.49e-245j)
| (-3.2780242666494460012 - 1.4477285572380682651e-981j)  +/-  (1.37e-244, 1.37e-244j)
| (1.0880931745211194127 + 1.2735752754389629256e-986j)  +/-  (1.19e-249, 1.19e-249j)
| (-8.1531264891502383408 + 1.040402322769504144e-977j)  +/-  (1.08e-243, 1.08e-243j)
| (7.2270056591305955343 + 2.8843426812837361373e-987j)  +/-  (9.49e-243, 9.49e-243j)
| (-2.0232301911005156592 - 2.5022567076519843511e-991j)  +/-  (2.7e-247, 2.7e-247j)
| (-6.4088504148849924307 + 1.8061499681647657239e-984j)  +/-  (2.75e-242, 2.75e-242j)
| (-1.7184492469788673279 - 2.0150310229182538138e-1007j)  +/-  (4.38e-248, 4.38e-248j)
| (0.52403354748695764515 - 9.7323995508731687032e-1015j)  +/-  (1.46e-252, 1.46e-252j)
| (-1.0987012653168872065e-1019 - 1.2260340365495166714e-1018j)  +/-  (7.02e-1017, 7.02e-1017j)
| (-0.25378798851972746021 + 5.7402671022632040456e-1017j)  +/-  (1.07e-253, 1.07e-253j)
| (-4.9417428707257606067 + 3.5943712907224941222e-1011j)  +/-  (1.41e-242, 1.41e-242j)
| (0.8075687085372603334 + 9.1898962774616158312e-1036j)  +/-  (3.59e-251, 3.59e-251j)
| (0.25378798851972746021 - 8.1504958281811022901e-1038j)  +/-  (1.07e-253, 1.07e-253j)
| (-5.6540788789860757282 + 6.6114223210083098169e-1036j)  +/-  (2.52e-242, 2.52e-242j)
| (-0.52403354748695764515 + 2.2706260610427383516e-1051j)  +/-  (1.59e-252, 1.59e-252j)
-------------------------------------------------
The weights are:
| (7.1355535383953730654e-27 + 4.8491155336118058149e-936j)  +/-  (7.51e-72, 3.52e-192j)
| (5.120845172988965739e-34 + 7.2907569859401098158e-942j)  +/-  (3.37e-75, 1.58e-195j)
| (5.5931124993285098118e-39 - 1.9985945294807559678e-944j)  +/-  (4.7e-77, 2.2e-197j)
| (2.4847236593978411138e-09 - 1.9108849784779811075e-928j)  +/-  (1.08e-59, 5.05e-180j)
| (5.5931124993285098118e-39 + 2.063255113041460578e-943j)  +/-  (1.93e-78, 9.05e-199j)
| (7.0267784762670823298e-60 - 6.255344229982010241e-954j)  +/-  (1.82e-86, 8.54e-207j)
| (3.8505819571380051745e-30 - 7.5597079232233051154e-940j)  +/-  (2.1e-74, 9.86e-195j)
| (5.0403492754266237402e-24 - 4.2187483531543946993e-935j)  +/-  (7.57e-73, 3.55e-193j)
| (4.8629961692566978514e-12 - 3.947470726025349896e-930j)  +/-  (9.2e-65, 4.31e-185j)
| (7.1355535383953730654e-27 + 3.8876807371318164783e-938j)  +/-  (1.18e-73, 5.54e-194j)
| (0.021249872629442584094 + 4.8424815907430522111e-923j)  +/-  (1.51e-42, 7.09e-163j)
| (2.6949230168070300283e-15 - 6.1562999552479095043e-932j)  +/-  (4.83e-68, 2.26e-188j)
| (0.044287804431831448077 + 2.1435418323252969199e-922j)  +/-  (3.94e-39, 1.85e-159j)
| (0.0001629122575401157744 + 4.459349210272027679e-925j)  +/-  (1.07e-56, 5e-177j)
| (1.3595700483012870662e-13 + 3.0690071704962945571e-930j)  +/-  (3.74e-70, 1.76e-190j)
| (3.6458019152488792945e-17 + 5.8600004383908758746e-933j)  +/-  (1.06e-69, 4.98e-190j)
| (2.8144633575311547367e-05 - 6.1464329018448638096e-926j)  +/-  (1.01e-58, 4.74e-179j)
| (3.7071345736305715258e-08 + 9.035350391775589992e-928j)  +/-  (8.38e-63, 3.93e-183j)
| (7.0267784762670823298e-60 + 1.564075546243391414e-954j)  +/-  (2.15e-90, 1.01e-210j)
| (0.0088950047860863563571 - 9.825232593669101245e-924j)  +/-  (7.91e-52, 3.71e-172j)
| (3.2030195604502990555e-19 - 4.5229411738266639296e-934j)  +/-  (1.29e-71, 6.04e-192j)
| (3.8978495618129875938e-06 + 1.6054837368215350998e-926j)  +/-  (2.98e-61, 1.4e-181j)
| (1.2707401944062951187e-10 + 2.3946191376283392256e-929j)  +/-  (1.44e-65, 6.77e-186j)
| (0.009518792255735045361 - 2.009842210289256478e-922j)  +/-  (1.81e-51, 8.48e-172j)
| (4.2884436472249330474e-07 - 1.0228198391211040649e-926j)  +/-  (3.63e-69, 1.7e-189j)
| (1.3595700483012870662e-13 + 5.3719778888783419085e-931j)  +/-  (4.85e-68, 2.27e-188j)
| (3.6458019152488792945e-17 + 5.016484566149503522e-932j)  +/-  (5.98e-78, 2.81e-198j)
| (0.0001629122575401157744 + 2.2174298680462207211e-925j)  +/-  (1.4e-60, 6.58e-181j)
| (0.002888842897927851089 + 2.6545528466578827224e-924j)  +/-  (4.38e-58, 2.05e-178j)
| (1.7090781812089176488e-21 + 4.6837658369027867578e-934j)  +/-  (4.18e-80, 1.96e-200j)
| (0.00076147907018862231467 - 7.689540844596934881e-925j)  +/-  (2.9e-60, 1.36e-180j)
| (5.120845172988965739e-34 - 1.1858558843506575753e-940j)  +/-  (1.01e-85, 4.72e-206j)
| (2.4847236593978411138e-09 - 5.5184025057887321432e-928j)  +/-  (5.89e-74, 2.76e-194j)
| (1.2707401944062951187e-10 + 1.1000874254423751781e-928j)  +/-  (4.35e-75, 2.04e-195j)
| (0.00076147907018862231467 - 1.4183633131122798673e-924j)  +/-  (1.07e-67, 5.02e-188j)
| (0.021249872629442584094 + 6.9939106534413268869e-923j)  +/-  (1.46e-62, 6.86e-183j)
| (4.2884436472249330474e-07 - 3.9130609884631603904e-927j)  +/-  (3.96e-68, 1.86e-188j)
| (0.009518792255735045361 - 1.465600365020132064e-922j)  +/-  (3.55e-61, 1.67e-181j)
| (3.7071345736305715258e-08 + 2.4919369644127331508e-927j)  +/-  (2.8e-73, 1.31e-193j)
| (1.7090781812089176488e-21 + 2.7363616720316282188e-935j)  +/-  (6.65e-79, 3.12e-199j)
| (0.084278269059837066176 - 1.3818349692782402566e-922j)  +/-  (4.77e-63, 2.24e-183j)
| (2.8144633575311547367e-05 - 1.3502434681217284727e-925j)  +/-  (5.72e-71, 2.68e-191j)
| (3.8978495618129875938e-06 + 3.8553113800859142155e-926j)  +/-  (6.43e-72, 3.01e-192j)
| (0.044287804431831448077 + 1.6198322030211000775e-922j)  +/-  (3.64e-65, 1.7e-185j)
| (3.8505819571380051745e-30 + 2.5222070192582115975e-938j)  +/-  (1.17e-86, 5.49e-207j)
| (5.0403492754266237402e-24 - 1.2368273641725311866e-936j)  +/-  (2.26e-81, 1.04e-201j)
| (0.002888842897927851089 + 4.5009361604335907835e-924j)  +/-  (4.57e-70, 2.08e-190j)
| (3.2030195604502990555e-19 - 5.1658189084950103266e-933j)  +/-  (8.14e-82, 3.81e-202j)
| (0.0088950047860863563571 - 1.5349396893832435657e-923j)  +/-  (1.65e-69, 7.16e-190j)
| (0.11935634832607001675 + 1.2540061553614497671e-922j)  +/-  (4.45e-69, 1.92e-189j)
| (0.14082668136727415816 + 1.7357466181155571964e-922j)  +/-  (3.06e-69, 1.33e-189j)
| (0.13815482258605686788 - 1.6487992921002120401e-922j)  +/-  (2.24e-69, 9.78e-190j)
| (4.8629961692566978514e-12 - 1.9553411789764694717e-929j)  +/-  (2.47e-78, 1.16e-198j)
| (0.084278269059837066176 - 1.1230214532374051888e-922j)  +/-  (6.75e-70, 2.76e-190j)
| (0.13815482258605686788 - 1.5450479095528211199e-922j)  +/-  (7.43e-70, 3.02e-190j)
| (2.6949230168070300283e-15 - 4.2130223485000381157e-931j)  +/-  (2.58e-80, 1.27e-200j)
| (0.11935634832607001675 + 1.4343005240630370614e-922j)  +/-  (3.84e-70, 1.47e-190j)
