Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 10 30
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 35/8*t^14 - 436215/27784*t^12 + 12954799/583464*t^10 - 3039465/194488*t^8 + 2679105/472328*t^6 - 8846695/8974232*t^4 + 1485/22952*t^2 - 273/390184
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^44 - 12026017565094668871888288986841923322400312513922260069510583619554397090340542655454532457889525873705/233625519930155436555004821176593861195407735922336638200224761260247676239816383598475432138425580868*t^42 + 4530409694865612769566614513536650763433105664390712679928702892594501034935713346405976201634946773297458743/16023439909929640771561560665217866563948234975969380667600615475795347122584046485485035988646056889412648*t^40 - 2779448644875068891274149160849110532849412692101949183354603205696476571340461760477074057298988297226444364735/2886889757105656945676341179850085625938007001503816750279377554889128373252225708468220650621064582909178748*t^38 + 44913429120790759982459613731918234740984951323109493005273824427922006502505413136782149248962038027094011393771605/19729004600060059566752115623095485167660339848277083671409266210112303302805710491671819926344355359601327563832*t^36 - 159334306244791519569127278554615298217518172104726407589669500807271709596896964136169319968061160138374409681538905/40162616507265121260888235375587237662737120405421206045368863356300046009283053500903347707201009124902702540658*t^34 + 49879178214894038714447026524936360488022413052660522387203234516150751386230411102702803051432553139474653924330655/9450027413474146179032525970726408861820498918922636716557379613247069649243071411977258284047296264682988833096*t^32 - 394852631528129254167959928191333572808774310360102011529934740844984013845470615883542692528971279984962234007976569/72056459027740364615123010526788867571381304256785104963750019551008906075478419516326594415860634018207789852357*t^30 + 9979810844083628351480231910158129109701492645977893215816251158239500398553723131185288399236295038350888649513247185/2218085782245225136848134410998544271327737539730602361492826688787578500062553087719966471583883864560483270237772*t^28 - 846366069596426673985587384065851783993358214374524872252624711510288630025741780183597516301168081444591575545597485/287529638439195851072906312536848331468410421816929935749070126324315731489590215074810468538651612072655238734526*t^26 + 16812923386542085023128862164782143484143486228075269931720140043972198191545641014040560864778226862875669152957848575/10926126260689442340770439876400236595799596029043337558464664800323997796604428172842797804468761258760899071911988*t^24 - 10521303200740061942591990127605038984224451146888810840537734047858973531174534409557537120786408405684577593263905025/16389189391034163511155659814600354893699394043565006337696997200485996694906642259264196706703141888141348607867982*t^22 + 5642559692192579801415151107990364932327437476189628020926328999648441215342782586524861192225377065858347137383989805/26534878061674359970442496842686288875513304641962391213414185943643994648896468419761080382281277342705040603214828*t^20 - 19347248695445590555699173711044638637918813605573655007668877394123566542279696869919271323071362162931034711742550/349143132390452104874243379509030116783069797920557779123870867679526245380216689733698426082648386088224218463353*t^18 + 6877603195436853863301056260469442018561735415409334022289823155093479162887608882260922726832179651175771061841892475/613916853730317312876522535310819308875266023496547831386514586863317560406202193501159608968383856291129314018032228*t^16 - 1850680998059633671932337746819585483057569234509792941664333540186016650245764657391380219584014560897163686324954375/1074354494028055297533914436793933790531715541118958704926400527010805730710853838627029315694671748509476299531556399*t^14 + 11789367756984429058276683163424320966725578127269526566209838571754127334913404461099124610992127722473791884198217375/60163851665571096661899208460460292269776070302661687475878429512605120919807814963113641678901617916530672773767158344*t^12 - 1431297490791047233282463418074920988721972841601968646191331877608759161215259897423881369385900044655513781527711715/90245777498356644992848812690690438404664105453992531213817644268907681379711722444670462518352426874796009160650737516*t^10 + 17310006072251814542795817734673805523121529847378614653625576830612949554999407764123696149798268198545833396801725/20054617221857032220633069486820097423258690100887229158626143170868373639935938321037880559633872638843557591255719448*t^8 - 41500591718557070950074871151951380378836893328380936931135589381021245869406543525783473260434973390948483348925/1432472658704073730045219249058578387375620721491944939901867369347740974281138451502705754259562331345968399375408532*t^6 + 4459885358122062600255073440549095164609435341010010615223345403685928988863925936414012885249430830467099334625/8594835952224442380271315494351470324253724328951669639411204216086445845686830709016234525557373988075810396252451192*t^4 - 1969959435620274234114421750169924233928078192974521674899567516691860061046964444470135440055048758276089125/529392069521070726321059287695561577943164179681805738659385766932860794843029427729260822226359992019162234551781414*t^2 + 71227272556373853876983661277545544244681966232170987544127160006579224726274985547056355961022419010325/15921566000633706054768700381821400840395915178400172591259722313770249468963291059526641269965714045689089760955832
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (-0.99444997880691468328 + 3.5564066201595316394e-886j)  +/-  (1.09e-237, 1.09e-237j)
| (0.98600624662379049835 - 4.9670204843630632273e-900j)  +/-  (4.64e-238, 4.64e-238j)
| (-0.92773572253511447459 - 5.2010357419152756857e-916j)  +/-  (1.26e-239, 1.26e-239j)
| (0.998502012978742182 - 5.3260936395658410717e-912j)  +/-  (2.04e-237, 2.04e-237j)
| (0.95280406968027788258 - 1.2850858809976882192e-929j)  +/-  (4.67e-239, 4.67e-239j)
| (0.92773572253511447459 + 3.045109029325748322e-930j)  +/-  (1.33e-239, 1.33e-239j)
| (-0.998502012978742182 - 1.0843875899514850379e-924j)  +/-  (1.96e-237, 1.96e-237j)
| (-0.95280406968027788258 - 1.8093445292443760233e-945j)  +/-  (4.66e-239, 4.66e-239j)
| (0.038542302500496519919 + 1.3935034870299811834e-965j)  +/-  (5.11e-255, 5.11e-255j)
| (-0.99981264082437336147 + 7.1791886720889409487e-944j)  +/-  (1.24e-237, 1.24e-237j)
| (0.89712440716821071821 + 3.1241143600863042122e-955j)  +/-  (3.16e-240, 3.16e-240j)
| (0.99981264082437336147 - 8.6987373671061959532e-958j)  +/-  (1.19e-237, 1.19e-237j)
| (-0.89712440716821071821 + 3.9539511710569072389e-979j)  +/-  (3.54e-240, 3.54e-240j)
| (-0.86113631159405257522 - 1.1664957608540907014e-981j)  +/-  (7.26e-241, 7.26e-241j)
| (0.11539569344883949077 - 1.0245969394435379132e-993j)  +/-  (1.05e-253, 1.05e-253j)
| (0.86113631159405257522 - 5.8082360913799758933e-981j)  +/-  (7.25e-241, 7.25e-241j)
| (0.81998025047725930591 + 5.1985855192829989448e-982j)  +/-  (1.4e-241, 1.4e-241j)
| (-0.98600624662379049835 - 2.3080635704378037967e-976j)  +/-  (4.23e-238, 4.23e-238j)
| (-0.81998025047725930591 + 2.270132622521162685e-992j)  +/-  (1.43e-241, 1.43e-241j)
| (-0.3399810435848562648 + 6.9274188955826922051e-1001j)  +/-  (9.16e-250, 9.16e-250j)
| (0.99444997880691468328 + 4.4963699872305563677e-989j)  +/-  (1.1e-237, 1.1e-237j)
| (0.72317255923281838433 - 1.612888863757239626e-1002j)  +/-  (3.59e-243, 3.59e-243j)
| (0.19155680515947816946 + 1.5566718032593396752e-1011j)  +/-  (2.31e-252, 2.31e-252j)
| (-0.72317255923281838433 - 7.8201994847861462377e-1001j)  +/-  (3.82e-243, 3.82e-243j)
| (-0.77390041850170683395 + 2.3939004397925538331e-999j)  +/-  (2.47e-242, 2.47e-242j)
| (-0.97222404125643132209 + 6.5133173326351496285e-1000j)  +/-  (1.57e-238, 1.57e-238j)
| (0.77390041850170683395 + 5.3122680326285199218e-1011j)  +/-  (2.44e-242, 2.44e-242j)
| (0.97222404125643132209 + 2.0446553602677095456e-1017j)  +/-  (1.53e-238, 1.53e-238j)
| (-0.2665686549642313847 + 1.5775948697152453612e-1031j)  +/-  (5.18e-251, 5.18e-251j)
| (-0.66810126170349887322 - 2.3577755789045269585e-1025j)  +/-  (4.12e-244, 4.12e-244j)
| (0.2665686549642313847 + 3.3281574920367266252e-1033j)  +/-  (5.61e-251, 5.61e-251j)
| (0.66810126170349887322 + 8.8243618060119449571e-1026j)  +/-  (4.19e-244, 4.19e-244j)
| (0.60901761613448973053 + 2.0040276860873601327e-1028j)  +/-  (4.34e-245, 4.34e-245j)
| (-0.11539569344883949077 + 2.6573432473462560698e-1037j)  +/-  (1.05e-253, 1.05e-253j)
| (-0.54627694908708365616 - 1.8031288288627355882e-1027j)  +/-  (3.51e-246, 3.51e-246j)
| (-0.60901761613448973053 + 2.2877737919508843733e-1028j)  +/-  (4.19e-245, 4.19e-245j)
| (-0.038542302500496519919 + 1.4375344324440310319e-1039j)  +/-  (4.89e-255, 4.89e-255j)
| (0.54627694908708365616 - 9.9525752290588486003e-1031j)  +/-  (3.5e-246, 3.5e-246j)
| (0.3399810435848562648 - 1.0639799041331818342e-1034j)  +/-  (9.43e-250, 9.43e-250j)
| (-0.41135322485450226221 + 2.7182921936624275077e-1032j)  +/-  (1.9e-248, 1.9e-248j)
| (-0.48025653204688832402 - 3.7786938586627834982e-1031j)  +/-  (2.62e-247, 2.62e-247j)
| (-0.19155680515947816946 - 2.3557910837946796073e-1036j)  +/-  (2.41e-252, 2.41e-252j)
| (0.41135322485450226221 + 8.8701602596386478837e-1034j)  +/-  (1.89e-248, 1.89e-248j)
| (0.48025653204688832402 + 2.4278045145500715483e-1032j)  +/-  (2.59e-247, 2.59e-247j)
-------------------------------------------------
The weights are:
| (0.0060182833054848222385 - 3.5827861192694983281e-886j)  +/-  (9.61e-68, 2.2e-181j)
| (0.011023145087972998917 + 5.44160871275609582e-889j)  +/-  (3.73e-68, 8.52e-182j)
| (0.027863384690188814883 + 2.9835903483119065724e-888j)  +/-  (2.05e-68, 4.69e-182j)
| (0.0023753141115147406701 + 1.6722562256957233174e-888j)  +/-  (2e-68, 4.57e-182j)
| (0.022254990779044248913 + 1.6355533969178037242e-889j)  +/-  (1.1e-68, 2.5e-182j)
| (0.027863384690188814883 - 1.035529558713876259e-889j)  +/-  (5.76e-69, 1.32e-182j)
| (0.0023753141115147406701 + 8.2248229765055903655e-886j)  +/-  (8.6e-70, 1.96e-183j)
| (0.022254990779044248913 - 7.6474209362826923782e-888j)  +/-  (2.07e-71, 4.74e-185j)
| (0.077046046595346269481 + 1.8037903539096017866e-890j)  +/-  (4.11e-74, 9.38e-188j)
| (0.0005389880588407060576 - 3.5612574279997967586e-886j)  +/-  (5.97e-70, 1.36e-183j)
| (0.033331293435927850783 + 7.0929680917087585725e-890j)  +/-  (2.47e-72, 5.64e-186j)
| (0.0005389880588407060576 - 9.5763816437164489166e-889j)  +/-  (6.91e-71, 1.58e-184j)
| (0.033331293435927850783 - 1.3785561735622132646e-888j)  +/-  (7.54e-73, 1.72e-186j)
| (0.038609988317091011511 + 7.2076374726707440759e-889j)  +/-  (1.57e-73, 3.59e-187j)
| (0.076583845747493660462 - 1.7034995810758776024e-890j)  +/-  (2.03e-75, 4.64e-189j)
| (0.038609988317091011511 - 5.1782910252892172488e-890j)  +/-  (3.18e-74, 7.25e-188j)
| (0.043661375323476685929 + 3.9833052854941058981e-890j)  +/-  (5.16e-75, 1.18e-188j)
| (0.011023145087972998917 - 1.2763156881227202764e-886j)  +/-  (6.83e-73, 1.56e-186j)
| (0.043661375323476685929 - 4.1425120516081400354e-889j)  +/-  (1.27e-75, 2.91e-189j)
| (0.07246482272616650163 - 3.3018305154653559558e-890j)  +/-  (2.43e-78, 5.55e-192j)
| (0.0060182833054848222385 - 1.0761457612500705347e-888j)  +/-  (4.35e-73, 9.93e-187j)
| (0.05295262736529212453 + 2.6703830227148429084e-890j)  +/-  (1.88e-77, 4.29e-191j)
| (0.075662168851564525539 + 1.6414789355602166351e-890j)  +/-  (3.5e-78, 7.99e-192j)
| (0.05295262736529212453 - 1.6907821049806874211e-889j)  +/-  (3.94e-78, 9.01e-192j)
| (0.04845228782957575909 + 2.5665603757309271636e-889j)  +/-  (2.04e-77, 4.67e-191j)
| (0.016584250111158794655 + 2.5133454362959444388e-887j)  +/-  (9.12e-75, 2.08e-188j)
| (0.04845228782957575909 - 3.201027144993315544e-890j)  +/-  (1.95e-78, 4.45e-192j)
| (0.016584250111158794655 - 2.8404025344531517985e-889j)  +/-  (7.48e-76, 1.71e-189j)
| (0.074286453020281495599 + 2.7959480368902634727e-890j)  +/-  (2.81e-81, 6.42e-195j)
| (0.057134748460326125866 + 1.1725594539781901418e-889j)  +/-  (1.22e-79, 2.79e-193j)
| (0.074286453020281495599 - 1.6138685852730212814e-890j)  +/-  (2.27e-81, 5.19e-195j)
| (0.057134748460326125866 - 2.3016630357563110039e-890j)  +/-  (1.04e-80, 2.39e-194j)
| (0.06097328347262099761 + 2.0424231163970037462e-890j)  +/-  (1.59e-81, 3.64e-195j)
| (0.076583845747493660462 + 2.1507450327443415644e-890j)  +/-  (7.48e-83, 1.71e-196j)
| (0.064445132784477284138 + 6.3972297129455054613e-890j)  +/-  (5.98e-83, 1.37e-196j)
| (0.06097328347262099761 - 8.4968456192780023455e-890j)  +/-  (2.12e-82, 4.84e-196j)
| (0.077046046595346269481 - 1.9492484042863593205e-890j)  +/-  (1.42e-83, 3.25e-197j)
| (0.064445132784477284138 - 1.8608526730846060546e-890j)  +/-  (5.53e-84, 1.26e-197j)
| (0.07246482272616650163 + 1.6193759478607654424e-890j)  +/-  (2.3e-84, 5.26e-198j)
| (0.070208052479684812345 + 4.000159801001460316e-890j)  +/-  (3.17e-84, 7.24e-198j)
| (0.067529517446469769152 - 4.9823006681123000623e-890j)  +/-  (3.97e-84, 9.08e-198j)
| (0.075662168851564525539 - 2.4247374584942529584e-890j)  +/-  (1.31e-84, 2.98e-198j)
| (0.070208052479684812345 - 1.6591797409339878934e-890j)  +/-  (7.34e-86, 1.68e-199j)
| (0.067529517446469769152 + 1.7372042060413427097e-890j)  +/-  (7.42e-86, 1.69e-199j)
