Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 6 32
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P3 : 4*t^11 - 6923/82*t^9 + 97479/164*t^7 - 566685/328*t^5 + 1313235/656*t^3 - 418635/656*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^43 - 777206413554596144125804957212332944481327551817235951123089476858988125821291274138323393/528052035403059026839321983362552843795709382301566656362498161675826201194523988675382*t^41 + 257748777342921895565304658506533665318135940070984369826513302588340377995361997490047998469/1056104070806118053678643966725105687591418764603133312724996323351652402389047977350764*t^39 - 664150072640571300448298807123810410422859369507395128160284527686468028741294530795170206498275/27458705840959069395644743134852747877376887879681466130849904407142962462115247411119864*t^37 + 87998855371762678816195569241718038156930711467045969969243162733491492400835456698552506786719325/54917411681918138791289486269705495754753775759362932261699808814285924924230494822239728*t^35 - 590027830922071724814884872107452636428617032664301777700572447583504320963725630311050083389451465/7845344525988305541612783752815070822107682251337561751671401259183703560604356403177104*t^33 + 20290643762847229349319169281399405989116853273609230666904945461700248842214159447195408048908962535/7845344525988305541612783752815070822107682251337561751671401259183703560604356403177104*t^31 - 1043359537503517343845503257635176634318065054425189970341912348558553863043368603800772373393978427305/15690689051976611083225567505630141644215364502675123503342802518367407121208712806354208*t^29 + 40578006669938432189917244135968531433121747500567849544445077233479109413660512289049271538749553283925/31381378103953222166451135011260283288430729005350247006685605036734814242417425612708416*t^27 - 184641797831597437466388020908090253257706572584657649664846752597999714909573664480950956599178203901525/9655808647370222205061887695772394857978685847800076002057109242072250536128438650064128*t^25 + 4155600522008653395520313844784294346578727943538186438557599852802519412205562396187659838122392412388125/19311617294740444410123775391544789715957371695600152004114218484144501072256877300128256*t^23 - 70899266573925847782504632878863740947846331197932963744691108422061151924199442328170926654220664793993375/38623234589480888820247550783089579431914743391200304008228436968289002144513754600256512*t^21 + 909480971954310413123483631284542115865865735601785674221598315570697697432833131280143269313707329628777625/77246469178961777640495101566179158863829486782400608016456873936578004289027509200513024*t^19 - 1082171776745114105856960114141067497624189836931418626788351852227288142319621233376576891672140401756614375/19311617294740444410123775391544789715957371695600152004114218484144501072256877300128256*t^17 + 29995764576108099168897808476050643836213770632650497066970305221570521980839185986365847194205383218951724375/154492938357923555280990203132358317727658973564801216032913747873156008578055018401026048*t^15 - 147265464134235897899469802423174862504504386477191795965819467297248642697905036033281594623785349831437800625/308985876715847110561980406264716635455317947129602432065827495746312017156110036802052096*t^13 + 3006971984395644718852183082299251292547647838098240889528272264967722200003910026065630629773948148880413125/3768120447754233055633907393472154090918511550361005269095457265198927038489146790268928*t^11 - 4271160003602439426702072053830020150646039718239549876226393880619642772320285304844713293207224019298930814375/4943774027453553768991686500235466167285087154073638913053239931940992274497760588832833536*t^9 + 5546006874667759120440300722089546048357060213623786323112067849405795840011417368378899033545017264011419196875/9887548054907107537983373000470932334570174308147277826106479863881984548995521177665667072*t^7 - 3883562376215640774853717333279210845616952494215340612311734187169969548858850228140290179216872338380026440625/19775096109814215075966746000941864669140348616294555652212959727763969097991042355331334144*t^5 + 1258960391394032296385931023512289518313691475763014050440817152138439442363151069026691754804543691231675509375/39550192219628430151933492001883729338280697232589111304425919455527938195982084710662668288*t^3 - 69055039422845262347148530517663594466461692535445577437724367582425584715847724239266453953539164559945984375/39550192219628430151933492001883729338280697232589111304425919455527938195982084710662668288*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:   43 out of 43
Indefinite weights: 0 out of 43
Negative weights:   0 out of 43
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.2234898695548983081 + 1.9547387043347606394e-975j)  +/-  (4.68e-247, 4.68e-247j)
| (0.32827242519648107189 - 2.2262721338254094518e-982j)  +/-  (1.73e-253, 1.73e-253j)
| (4.3749500805767709264 + 1.6805680338968061845e-974j)  +/-  (1.28e-245, 1.28e-245j)
| (7.9130963851673821745 + 8.0276156548633816295e-978j)  +/-  (4.52e-248, 4.52e-248j)
| (-7.9130963851673821745 - 8.5585001376010426247e-977j)  +/-  (4.48e-248, 4.48e-248j)
| (3.5901000359424915393 - 1.0584714881330191143e-973j)  +/-  (5.34e-246, 5.34e-246j)
| (6.1369813711563972393 - 8.5008224163611321159e-974j)  +/-  (6.48e-246, 6.48e-246j)
| (-6.6503390429937738661 - 5.5470587031080457642e-975j)  +/-  (2.12e-246, 2.12e-246j)
| (3.9768740262980135303 - 8.4013655409002451259e-975j)  +/-  (8.61e-246, 8.61e-246j)
| (6.6503390429937738661 - 3.5043174741420095314e-976j)  +/-  (2.21e-246, 2.21e-246j)
| (-5.2138056744628857877 + 6.3326843019387072046e-974j)  +/-  (1.72e-245, 1.72e-245j)
| (-2.0682405243504030887 - 3.1709821551417372812e-980j)  +/-  (6.48e-248, 6.48e-248j)
| (-6.1369813711563972393 - 2.4915796314329950133e-977j)  +/-  (6.85e-246, 6.85e-246j)
| (-5.6618329702201715659 + 5.9559203434507081432e-990j)  +/-  (1.19e-245, 1.19e-245j)
| (-4.7862817430976661226 + 6.995791359463712562e-1018j)  +/-  (1.78e-245, 1.78e-245j)
| (-4.3749500805767709264 - 5.543554023466804825e-1049j)  +/-  (1.46e-245, 1.46e-245j)
| (2.849426053331148482 + 7.1570970014503854927e-1065j)  +/-  (1.09e-246, 1.09e-246j)
| (-3.9768740262980135303 + 2.4411309218349653491e-1077j)  +/-  (8.67e-246, 8.67e-246j)
| (5.2138056744628857877 - 2.4091541573702532339e-1085j)  +/-  (1.7e-245, 1.7e-245j)
| (1.3866480207208212553 - 1.982771590826618108e-1091j)  +/-  (4.25e-250, 4.25e-250j)
| (1.7320508075688772935 + 1.5707633643868404352e-1090j)  +/-  (5.35e-249, 5.35e-249j)
| (4.7862817430976661226 - 2.7335272912376259091e-1087j)  +/-  (1.7e-245, 1.7e-245j)
| (-1.7320508075688772935 - 1.8092065071622012367e-1089j)  +/-  (5.04e-249, 5.04e-249j)
| (-1.0425854342497595253 + 3.1580377013969575081e-1093j)  +/-  (4.22e-251, 4.22e-251j)
| (-2.849426053331148482 - 6.2115825864561413424e-1088j)  +/-  (1.16e-246, 1.16e-246j)
| (-0.32827242519648107189 - 9.2612291890008478738e-1099j)  +/-  (1.73e-253, 1.73e-253j)
| (0.50057407627422777969 - 1.9954071090704078689e-1098j)  +/-  (1.15e-252, 1.15e-252j)
| (2.3142743884833336815 + 6.1666091606459370779e-1093j)  +/-  (3.21e-247, 3.21e-247j)
| (-2.5162914461052164783 - 7.8125165763817648982e-1091j)  +/-  (6.18e-247, 6.18e-247j)
| (2.0682405243504030887 - 7.6749367623348450152e-1096j)  +/-  (6.39e-248, 6.39e-248j)
| (-3.5901000359424915393 - 1.0718295267514055589e-1092j)  +/-  (5.11e-246, 5.11e-246j)
| (3.2137281525534003284 + 1.7254860288141533986e-1096j)  +/-  (2.51e-246, 2.51e-246j)
| (1.0425854342497595253 + 1.0635188736215839595e-1102j)  +/-  (4.22e-251, 4.22e-251j)
| (7.2234898695548983081 + 1.0599084102611118088e-1097j)  +/-  (4.82e-247, 4.82e-247j)
| (-1.3866480207208212553 + 2.958549016419783297e-1101j)  +/-  (4.5e-250, 4.5e-250j)
| (5.6618329702201715659 - 1.7810631106520018016e-1097j)  +/-  (1.24e-245, 1.24e-245j)
| (-3.2137281525534003284 + 3.0620177245565028167e-1098j)  +/-  (2.34e-246, 2.34e-246j)
| (0.7071067811865475244 + 3.6105495136160638108e-1105j)  +/-  (4.97e-252, 4.97e-252j)
| (-2.3142743884833336815 + 1.2360030301845034101e-1100j)  +/-  (3.15e-247, 3.15e-247j)
| (-0.50057407627422777969 + 2.2509876986511901909e-1105j)  +/-  (1.2e-252, 1.2e-252j)
| (-0.7071067811865475244 - 1.0293757099034186688e-1104j)  +/-  (4.97e-252, 4.97e-252j)
| (2.5162914461052164783 - 1.2863748089011014673e-1103j)  +/-  (5.77e-247, 5.77e-247j)
| (5.9124563589535328631e-1238 + 3.7554911228129564278e-1238j)  +/-  (3.01e-1236, 3.01e-1236j)
-------------------------------------------------
The weights are:
| (7.5866178838425793837e-24 + 4.4035667307502502292e-991j)  +/-  (1.31e-91, 6.91e-214j)
| (0.15553898369041559496 - 1.5643543941526517765e-975j)  +/-  (1.34e-77, 7.05e-200j)
| (1.1108456558316799546e-09 - 1.1087141977962485269e-981j)  +/-  (6.17e-83, 3.25e-205j)
| (2.8680305969316895827e-28 + 4.3130010196977966061e-993j)  +/-  (5.64e-94, 2.97e-216j)
| (2.8680305969316895827e-28 - 1.6123422788211971515e-993j)  +/-  (6.61e-94, 3.48e-216j)
| (5.4377654475689170919e-07 + 2.964958723709038121e-979j)  +/-  (2.2e-80, 1.16e-202j)
| (1.2207332485464347084e-17 - 5.4428222062309810922e-987j)  +/-  (1.07e-89, 5.65e-212j)
| (1.8828566986133637754e-20 - 3.4995967215797927297e-989j)  +/-  (8.89e-92, 4.68e-214j)
| (2.9943924920534081433e-08 + 2.1011432184381781995e-980j)  +/-  (1.73e-82, 9.11e-205j)
| (1.8828566986133637754e-20 + 1.1865664095515467183e-988j)  +/-  (3.28e-91, 1.73e-213j)
| (3.8552666147553833134e-13 + 8.1678853764715031697e-985j)  +/-  (2.3e-89, 1.21e-211j)
| (0.002492529641159706201 - 1.4524377560226175336e-977j)  +/-  (1.32e-77, 6.97e-200j)
| (1.2207332485464347084e-17 + 1.3934034061988482554e-987j)  +/-  (1.6e-91, 8.44e-214j)
| (3.1080720643274200065e-15 - 3.382782491854959009e-986j)  +/-  (1.33e-90, 6.99e-213j)
| (2.6573266358750340883e-11 - 9.8546856959098913256e-984j)  +/-  (2.58e-89, 1.36e-211j)
| (1.1108456558316799546e-09 + 1.0444304527586038123e-982j)  +/-  (6.48e-89, 3.41e-211j)
| (5.97582288912229944e-05 + 3.8520380989516993755e-978j)  +/-  (2.58e-86, 1.36e-208j)
| (2.9943924920534081433e-08 - 9.5606192654311493527e-982j)  +/-  (1.51e-88, 7.98e-211j)
| (3.8552666147553833134e-13 - 3.4715148007031988711e-984j)  +/-  (1.2e-93, 6.34e-216j)
| (0.028492078760360070538 - 1.2170347729548852842e-976j)  +/-  (1.61e-80, 8.47e-203j)
| (0.0096692100294743085842 + 6.991942953588565959e-977j)  +/-  (9.14e-83, 4.82e-205j)
| (2.6573266358750340883e-11 + 5.960171331310589057e-983j)  +/-  (2.42e-92, 1.28e-214j)
| (0.0096692100294743085842 + 2.4352801128669641251e-977j)  +/-  (1.52e-83, 8.01e-206j)
| (0.065066805538170161206 + 1.4548636384693177598e-976j)  +/-  (5.13e-80, 2.7e-202j)
| (5.97582288912229944e-05 + 4.3929228185044765262e-979j)  +/-  (3.61e-88, 1.9e-210j)
| (0.15553898369041559496 - 1.3018318077717738698e-975j)  +/-  (2.21e-80, 1.16e-202j)
| (0.033684050042526229432 + 1.7767561511750761562e-975j)  +/-  (3.98e-80, 2.1e-202j)
| (0.00043080566507499020554 + 4.3537580022478148041e-977j)  +/-  (1.29e-86, 6.81e-209j)
| (0.00029061128595811491371 - 3.5251036390019728024e-978j)  +/-  (1.67e-87, 8.81e-210j)
| (0.002492529641159706201 - 5.4183657123296554239e-977j)  +/-  (9.02e-86, 4.75e-208j)
| (5.4377654475689170919e-07 + 7.7396524645041479883e-981j)  +/-  (2.08e-90, 1.1e-212j)
| (6.8458490611804894508e-06 - 1.0671012126259232435e-978j)  +/-  (1.28e-89, 6.73e-212j)
| (0.065066805538170161206 + 2.6486323027253617479e-976j)  +/-  (2.89e-85, 1.52e-207j)
| (7.5866178838425793837e-24 - 1.3212009220650657601e-990j)  +/-  (2.12e-101, 1.11e-223j)
| (0.028492078760360070538 - 5.3795875871892714838e-977j)  +/-  (8.58e-87, 4.51e-209j)
| (3.1080720643274200065e-15 + 1.6086590953026047895e-985j)  +/-  (1.46e-96, 7.71e-219j)
| (6.8458490611804894508e-06 - 5.8142593357379986145e-980j)  +/-  (9.98e-91, 5.24e-213j)
| (0.10981366573047444022 - 8.7444672386198906424e-976j)  +/-  (9.3e-87, 4.87e-209j)
| (0.00043080566507499020554 + 9.3662226681391063758e-978j)  +/-  (1.27e-88, 6.68e-211j)
| (0.033684050042526229432 + 1.3412651290786187629e-975j)  +/-  (2.89e-87, 1.5e-209j)
| (0.10981366573047444022 - 5.8625302848483021619e-976j)  +/-  (1.32e-87, 7.06e-210j)
| (0.00029061128595811491371 - 2.0157982954238606518e-977j)  +/-  (3.21e-90, 2.18e-212j)
| (0.18890816136031346736 + 9.1574010057292168127e-976j)  +/-  (1.24e-87, 5.42e-210j)
