Starting with polynomial:
P : t
Extension levels are: 1 2 18 22
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P3 : t^21 - 492974097/95285320*t^19 + 1092720951/95285320*t^17 - 62676676797/4406946050*t^15 + 104814789093/9695281310*t^13 - 239868945099/46239033940*t^11 + 190151996979/121902907660*t^9 - 17182210131/60951453830*t^7 + 42668603943/1523786345750*t^5 - 107290416779/84113006285400*t^3 + 479989951/28037668761800*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 88186444764315217611843095555521587690799414053147879926410892410827896054407913547944858522059749780552782483/8129593605284088567884799856518750526623724600943891295414455184024596607033838892923784410690794859007026680*t^41 + 8012264149779481236318049782373213159109936363964618512260306206509746539568623881306840719228975038012478824521/146332684895113594221926397417337509479227042816990043317460193312442738926609100072628119392434307462126480240*t^39 - 1638479810486437760498107329226996319982472287865658552941291157541814339008261387213423326857624870028020445441/9596436265719962754716903056436525790023751478604451617770342347678804218866601741735626404679314739628996400*t^37 + 867996566660490583575845876696447463343943066324233895236633559381262670835637739741794459491396748725930559726633467/2356913017443335378935235286402247263254458027710420016925107890517370991549849724515941444537296728304411774234800*t^35 - 3756941176802135826528008773478659716728222357477828553864269087375545687785015287309834629667060726247900952933813680251/6444271572293567593084720320081024467190339139365830410276629994252595765095599116771487097653876714529922673112790160*t^33 + 151914677784456496098243684931116622638883338679496865684991855224783214660616518555488852911320016300994157031556556546963/216615401259595147049370485304541708794875263343683254018162176397717934922190706675114304941592810472494446216677651060*t^31 - 307795225452439297277127615199942551311993912944050911764792478382922986446278298847679174575046610709402184607842139859784097/469964582016664219519339055810566506723126631829229181145146241870365004808444527704779445401829279159630934490164154107820*t^29 + 33318685285176206700201806009128596640655497570725186906356091905229715355317819067171377536472623655378675771690035852390571553/69279261659353087532592222882419717801426425898963956875706902896407255019175874342687314796304143738186973963636267545204500*t^27 - 1931833409951959689969177808013171404429517591432333701013128395956437968418468816614016223360718719814636083565671139737845774656911/6909878918273047273956982014181101443655371005949715576804568641436211411985092119002461434125977144374899689646099506824924227750*t^25 + 11031948203331092399844940285494290007042384222080530865837767925317611456286978657710056864657811958546750212624064552385949817198324219/85581890749535730628757763317719181064306978271929845293578376634389710270456639334377845944681242363026657612130386675809689527343960*t^23 - 453804740241924698961932761216667816560801109190611761445676069564725453303467840695264454458966687785861806365471661963140297206955163/9649247814796585693588752975395014519409703519237484399349662214489038814576172305202513212628025115359674734455378895651350403598840*t^21 + 365680012087117870586125462655994560267105292704574942799114729605288334158405250500563413696136216720560352266635459959258896891975639/27109791479666597901035067883252659840246309887381503788649050983564442383809246000330870454526356276486705206327016897306174943444360*t^19 - 420759514422391430296571837823320681353174235599795397612006945905541638137056108308801362587552553565989587091756597324206181965597/139885404951840030449097357498723734985791072690307037093132358016328392073319122808724821746782024130478355037807104733261996612200*t^17 + 1399294096324799470310836557644350347217319657030480017739059706585826754656423597487240925098520368864503936035879706270925656995809/2727765396560880593757398471225112832222925917460987223316080981318403645429722894770134024062249470544327923237238542298608933937900*t^15 - 6308164446426024289129195136421625030497533582231975208047988823145360401473041021457518913164396081652940835971613028817792043531/96497220026099817614885804240645017185113502686364345926957406292619755209899801666357631272780142069668966949809307841419716307060*t^13 + 240093880966180187919444829822334962377523078641911908410762488225583944029231476256174594177848904501085373376842337193523844461509/39853351870779224674947837151386392097451876609468474867833408798851958901688618088205701715658198674773283350271244138506342834815780*t^11 - 8329672436450669111527808781280720208195208531618492550916744901571608878124415731309168913321065895702071909758453985667631243563/21738191929515940731789729355301668416791932696073713564272768435737432128193791684475837299449926549876336372875224075548914273535880*t^9 + 221721652019643817699415474866257500798028284676440849186995745581351547821795414284439533956262952377541370624516259750010322113/14127546117714762320450348218330224757244232989062581142399493113372335345367034428066057783709595870988813994950355269224661267916400*t^7 - 16993699496896892386539037154573750890468337544403823501118881112510742009351802340405909532129235092413286421839444916350792363/45842445565645861407175619728867464008200674393080620441663661327065333059456295389030677298159709050759620922389928322586145746912400*t^5 + 29731237943723201170363927581221467729466965216672635474582269668469866125233819191731458813886057645472702316712362070193492051/7178926975580141896363702049540644863684225609956425161164529363818431157110855857922204064891810437348956636446262775316990423966481840*t^3 - 232019873271156359790595157336686293162060178708399486327569234244649345848079926911391178311675499171024198664550178091449981/16750829609686997758181971448928171348596526423231658709383901848909672699925330335151809484747557687147565485041279809072977655921790960*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:
| (-0.96863851499355040942 + 1.6586175795240476319e-921j)  +/-  (3.57e-240, 3.57e-240j)
| (-0.9990130266325466666 - 1.0683406474459699208e-922j)  +/-  (1.44e-240, 1.44e-240j)
| (-0.92316618973895636051 + 2.0674466404930027788e-931j)  +/-  (1.31e-240, 1.31e-240j)
| (0.9990130266325466666 + 1.1732036162251656168e-927j)  +/-  (1.46e-240, 1.46e-240j)
| (0.8930681618696741024 - 1.9402528370394612577e-940j)  +/-  (5.47e-241, 5.47e-241j)
| (0.96863851499355040942 - 5.5153279253316980353e-954j)  +/-  (3.76e-240, 3.76e-240j)
| (-0.81860060849733478918 - 2.5998412438534793645e-967j)  +/-  (5.71e-242, 5.71e-242j)
| (-0.8930681618696741024 - 3.9869669531410738339e-965j)  +/-  (5.33e-241, 5.33e-241j)
| (-0.9940396115810441603 + 1.6127927096729429469e-963j)  +/-  (3.67e-240, 3.67e-240j)
| (0.94835757651647283262 - 8.1996815963554008148e-976j)  +/-  (2.3e-240, 2.3e-240j)
| (0.85815313192946415361 + 5.0477174312483149078e-995j)  +/-  (1.79e-241, 1.79e-241j)
| (0.9940396115810441603 - 5.8314026492907128393e-1004j)  +/-  (3.63e-240, 3.63e-240j)
| (-0.94835757651647283262 + 3.3778202653436761093e-1015j)  +/-  (2.47e-240, 2.47e-240j)
| (-0.85815313192946415361 - 1.5060626157010432883e-1018j)  +/-  (1.84e-241, 1.84e-241j)
| (-0.074149897046529985022 + 2.1881184076833184311e-1031j)  +/-  (2.35e-254, 2.35e-254j)
| (0.81860060849733478918 - 7.7736525851073966295e-1017j)  +/-  (5.18e-242, 5.18e-242j)
| (0.92316618973895636051 - 3.2334604986441837824e-1024j)  +/-  (1.3e-240, 1.3e-240j)
| (-0.29239730601748887918 - 2.3234913558948176892e-1039j)  +/-  (1.8e-250, 1.8e-250j)
| (-0.72632446049439515791 + 5.8597611908821965596e-1031j)  +/-  (2.44e-243, 2.44e-243j)
| (-0.98393195261383823874 + 4.2109072671889546636e-1030j)  +/-  (4.38e-240, 4.38e-240j)
| (0.49574951572269775249 - 1.0992740227457832848e-1040j)  +/-  (5.76e-247, 5.76e-247j)
| (0.77459666924148337704 - 8.768875597998400394e-1036j)  +/-  (1.2e-242, 1.2e-242j)
| (0.43027365915780572809 - 2.6717119168467390868e-1047j)  +/-  (4.4e-248, 4.4e-248j)
| (-0.61794311282460414893 + 1.1295440714394751558e-1045j)  +/-  (5.76e-245, 5.76e-245j)
| (-0.77459666924148337704 + 3.4727506765299104856e-1044j)  +/-  (1.3e-242, 1.3e-242j)
| (0.98393195261383823874 + 7.1936747151164991474e-1043j)  +/-  (4.09e-240, 4.09e-240j)
| (0.67401253888417823604 + 1.7878589963277574168e-1047j)  +/-  (4.4e-244, 4.4e-244j)
| (0.72632446049439515791 - 2.3909325295922330053e-1049j)  +/-  (2.41e-243, 2.41e-243j)
| (1.9319555100764141806e-1072 + 7.6431917973646831122e-1072j)  +/-  (3.39e-1070, 3.39e-1070j)
| (-0.67401253888417823604 - 9.5031992922090630532e-1052j)  +/-  (4.56e-244, 4.56e-244j)
| (-0.36236130384595011635 - 1.3252863192844942282e-1058j)  +/-  (3.29e-249, 3.29e-249j)
| (0.074149897046529985022 - 8.5665215734884102184e-1063j)  +/-  (2.13e-254, 2.13e-254j)
| (0.61794311282460414893 - 1.1333651616900133508e-1053j)  +/-  (5.7e-245, 5.7e-245j)
| (0.14788136810434884046 - 8.1998936132585258595e-1063j)  +/-  (5.07e-253, 5.07e-253j)
| (-0.43027365915780572809 - 3.9950080514400815756e-1057j)  +/-  (4.58e-248, 4.58e-248j)
| (-0.55841853871864983226 - 1.9144428806713849065e-1056j)  +/-  (6.56e-246, 6.56e-246j)
| (0.22077021219003756334 + 1.4064456869938082575e-1062j)  +/-  (9.46e-252, 9.46e-252j)
| (0.55841853871864983226 - 2.7433359270129880718e-1058j)  +/-  (5.87e-246, 5.87e-246j)
| (0.29239730601748887918 + 1.8254287549469766265e-1063j)  +/-  (2.01e-250, 2.01e-250j)
| (-0.14788136810434884046 + 8.4179351495935509417e-1066j)  +/-  (4.63e-253, 4.63e-253j)
| (-0.49574951572269775249 - 1.3541651419574723474e-1060j)  +/-  (5.51e-247, 5.51e-247j)
| (-0.22077021219003756334 + 1.5200462638321207756e-1064j)  +/-  (9.19e-252, 9.19e-252j)
| (0.36236130384595011635 - 6.5086490388809980358e-1062j)  +/-  (3.24e-249, 3.24e-249j)
-------------------------------------------------
The weights are:
| (0.017813952893785077277 + 2.2827631259382100993e-922j)  +/-  (8.3e-78, 6.21e-193j)
| (0.0026617889964950861575 + 4.5369092705110516949e-923j)  +/-  (2.59e-78, 1.94e-193j)
| (0.027649021313224054814 + 9.5531999697151920968e-922j)  +/-  (2.43e-78, 1.82e-193j)
| (0.0026617889964950861575 - 2.5815877876435075144e-924j)  +/-  (2.4e-79, 1.8e-194j)
| (0.032531813429758549638 - 2.6402626363729624684e-923j)  +/-  (1.18e-79, 8.83e-195j)
| (0.017813952893785077277 + 1.6142346694816888714e-923j)  +/-  (7.99e-80, 5.98e-195j)
| (0.041807558748801225577 - 3.6869811668136003408e-922j)  +/-  (2.31e-79, 1.73e-194j)
| (0.032531813429758549638 - 6.4057237788354608196e-922j)  +/-  (8.79e-79, 6.58e-194j)
| (0.007472563950188274285 - 3.8186757235759662504e-922j)  +/-  (1.37e-78, 1.02e-193j)
| (0.022736637760304238617 - 2.0036472620874310142e-923j)  +/-  (2.21e-80, 1.66e-195j)
| (0.037266423512152878636 + 2.8954660521269100636e-923j)  +/-  (3.38e-81, 2.53e-196j)
| (0.007472563950188274285 + 7.5037292063603695688e-924j)  +/-  (1.47e-80, 1.1e-195j)
| (0.022736637760304238617 - 1.8318938096004456914e-921j)  +/-  (2.5e-79, 1.87e-194j)
| (0.037266423512152878636 + 4.7339566248703724344e-922j)  +/-  (3.9e-80, 2.92e-195j)
| (0.074010973440796506113 - 6.8578631020094663263e-923j)  +/-  (3.11e-84, 2.33e-199j)
| (0.041807558748801225577 - 3.1217400502662206386e-923j)  +/-  (2.99e-82, 2.23e-197j)
| (0.027649021313224054814 + 2.3468525204905284326e-923j)  +/-  (5.23e-81, 3.92e-196j)
| (0.070860908095510444666 + 9.0953028389395432324e-923j)  +/-  (1.33e-84, 9.93e-200j)
| (0.050335499902022833397 - 2.4390238515078516342e-922j)  +/-  (4.53e-83, 3.39e-198j)
| (0.012734248983796552195 + 1.3573189861121390761e-921j)  +/-  (2.9e-80, 2.17e-195j)
| (0.06413179469971093787 - 4.2079561851735965319e-923j)  +/-  (1.77e-85, 1.33e-200j)
| (0.046170935878571123623 + 3.3230050558904802676e-923j)  +/-  (9.23e-84, 6.91e-199j)
| (0.066757780967964901355 + 4.4081226598813137306e-923j)  +/-  (4.53e-86, 3.39e-201j)
| (0.057847719023109082579 - 1.7354075539828338496e-922j)  +/-  (4.03e-85, 3.01e-200j)
| (0.046170935878571123623 + 2.9655412629414019696e-922j)  +/-  (5.09e-83, 3.81e-198j)
| (0.012734248983796552195 - 1.1972284851050916466e-923j)  +/-  (1.16e-82, 8.68e-198j)
| (0.054240530437645388052 + 3.6779646728967375478e-923j)  +/-  (1.26e-85, 9.42e-201j)
| (0.050335499902022833397 - 3.5052872440370302381e-923j)  +/-  (5.92e-85, 4.43e-200j)
| (0.074219237735797928649 + 6.3323427814634075727e-923j)  +/-  (2.66e-88, 1.99e-203j)
| (0.054240530437645388052 + 2.041947751543424764e-922j)  +/-  (3.98e-86, 2.98e-201j)
| (0.069002567701666013858 - 1.0152535056418066147e-922j)  +/-  (3.32e-88, 2.49e-203j)
| (0.074010973440796506113 - 5.8840723181113890921e-923j)  +/-  (7.81e-89, 5.85e-204j)
| (0.057847719023109082579 - 3.849062330056743903e-923j)  +/-  (7.82e-88, 5.85e-203j)
| (0.073381036795249722082 + 5.5000218839627770234e-923j)  +/-  (2.28e-89, 1.71e-204j)
| (0.066757780967964901355 + 1.1433619572634571203e-922j)  +/-  (1.99e-89, 1.49e-204j)
| (0.061150108261918899481 + 1.4937595872837328503e-922j)  +/-  (4.97e-89, 3.72e-204j)
| (0.072326516339429245402 - 5.169545343360045302e-923j)  +/-  (2.44e-90, 1.83e-205j)
| (0.061150108261918899481 + 4.0239037094201231181e-923j)  +/-  (8.2e-90, 6.13e-205j)
| (0.070860908095510444666 + 4.8827633215144787215e-923j)  +/-  (9.01e-91, 6.77e-206j)
| (0.073381036795249722082 + 7.4781124070838005896e-923j)  +/-  (2.65e-91, 2.01e-206j)
| (0.06413179469971093787 - 1.3001465012934567044e-922j)  +/-  (2.56e-91, 1.93e-206j)
| (0.072326516339429245402 - 8.2151239529578082776e-923j)  +/-  (1.66e-91, 1.26e-206j)
| (0.069002567701666013858 - 4.63112670621423131e-923j)  +/-  (1.19e-91, 8.41e-207j)
