Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 6 44
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P2 : 8*t^9 - 117*t^7 + 945/2*t^5 - 2205/4*t^3 + 945/8*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^53 - 21387140945855829472998079268690365449394403568032506463415670307351/4458923152272706921798955127194800876161205722491244995776388775*t^51 + 25583416799738950832710544304540211040155121491070006004616244924570569/19322000326515063327795472217844137130031891464128728315031018025*t^49 - 3367734385487531873785904925313610687563941288494301219931894976240876763/15061251536565587824743137318524660737255628218192649763511357640*t^47 + 18249963121032385511805600172461688016712419056479805040221313107720202167055/704866571911269510197978826506954122503563400611416008932331537552*t^45 - 1710246991080873164445882005960835538855071866505279626322622630903462799412749/783185079901410566886643140563282358337292667346017787702590597280*t^43 + 217910584324680059688403825649731542683415519680976012837238736302519277443783929/1566370159802821133773286281126564716674585334692035575405181194560*t^41 - 1651248509435287176667071299789526735657203319097765273116036923728965503118795829/240980024585049405195890197096394571796090051491082396216181722240*t^39 + 1344120687891077844440448744398167684712445466673130227212962786107152796356626255/5073263675474724319913477833608306774654527399812260972972246784*t^37 - 82396994660766238957838528636637941668050697911805439302279716706212671951963061879/10146527350949448639826955667216613549309054799624521945944493568*t^35 + 4027441745451077220451790327357744673977259008094282332151570544653894793669247585289/20293054701898897279653911334433227098618109599249043891888987136*t^33 - 78689876251919795701126065722810185399752243430926356333260400571204722091019267500297/20293054701898897279653911334433227098618109599249043891888987136*t^31 + 2458350515653663949720892405553714984165184806103490879164484764197161739866911335497381/40586109403797794559307822668866454197236219198498087783777974272*t^29 - 61254070012419105101847174931111060012999353756941975999142252650457859130013783993026835/81172218807595589118615645337732908394472438396996175567555948544*t^27 + 1211568441495969153917230388098502162867689675379044467632959105529631528456369029151127215/162344437615191178237231290675465816788944876793992351135111897088*t^25 - 18889062005374854056003472173342078562986877763269002621233402265495281824209597010118473675/324688875230382356474462581350931633577889753587984702270223794176*t^23 + 9995678490668658159150081791791558810062679940498718904769513231963125451261711838352405725/28233815237424552736909789682689707267642587268520408893062938624*t^21 - 46896298486860040823579204043782879503354620767509096055982630596561065279985845992413771025/28233815237424552736909789682689707267642587268520408893062938624*t^19 + 667750327947768950272578831525539029974427334535439232689211021611809570239677382470230326625/112935260949698210947639158730758829070570349074081635572251754496*t^17 - 7069230255910502493059551944651182587513455087352086890307576402100015030375445949096719775375/451741043798792843790556634923035316282281396296326542289007017984*t^15 + 27108476322713882504337471550424276643478499623731491767756808162543712505273682330280816919875/903482087597585687581113269846070632564562792592653084578014035968*t^13 - 72789580885123300648053809414523441670913041167511762404932674096295525880110722523034958006125/1806964175195171375162226539692141265129125585185306169156028071936*t^11 + 130651573221769208772288426103446639640838503378659091338860807415628036283949182037618653219625/3613928350390342750324453079384282530258251170370612338312056143872*t^9 - 146549061453340025332571041723481608957766102213267742411409360158847399217074953267743411735625/7227856700780685500648906158768565060516502340741224676624112287744*t^7 + 92286468725354381498804525099405365226876050398074235777201454593416121279082721528382175273125/14455713401561371001297812317537130121033004681482449353248224575488*t^5 - 26843873072432791996538703194732703399998216867299523842605458162179458723497844532914583355625/28911426803122742002595624635074260242066009362964898706496449150976*t^3 + 2286182671409517585669369075399265517499855929125919277204159158991536848674906872071844296875/57822853606245484005191249270148520484132018725929797412992898301952*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:   53 out of 53
Indefinite weights: 0 out of 53
Negative weights:   0 out of 53
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (7.406838529413426997 + 7.3972802352297736221e-707j)  +/-  (6.04e-244, 6.04e-244j)
| (-8.4436112896217580275 + 1.6017466308200992234e-716j)  +/-  (2.28e-245, 2.28e-245j)
| (8.4436112896217580275 + 3.6634754917025786926e-721j)  +/-  (2.59e-245, 2.59e-245j)
| (-6.5293395743442183914 - 1.4590319625008516929e-723j)  +/-  (2.79e-243, 2.79e-243j)
| (9.1037639349834164267 + 2.1133393633230382321e-732j)  +/-  (1.56e-246, 1.56e-246j)
| (6.1240531214128174748 + 3.5407314151036724826e-729j)  +/-  (4.13e-243, 4.13e-243j)
| (-7.896170797027213845 - 4.5228161407096018299e-731j)  +/-  (1.83e-244, 1.83e-244j)
| (-6.9547975644044234182 - 1.2145439650636722519e-734j)  +/-  (1.57e-243, 1.57e-243j)
| (6.5293395743442183914 - 4.4263623685662339948e-739j)  +/-  (2.95e-243, 2.95e-243j)
| (6.9547975644044234182 - 3.5749103918207186236e-737j)  +/-  (1.66e-243, 1.66e-243j)
| (1.021505258086124509 - 9.4079228166582601501e-744j)  +/-  (3.57e-250, 3.57e-250j)
| (-6.1240531214128174748 + 2.071187562360739182e-735j)  +/-  (4.08e-243, 4.08e-243j)
| (-2.3285146254673015787 - 8.4800551378343086354e-742j)  +/-  (9.21e-247, 9.21e-247j)
| (4.288413232534211384 + 1.1993841758469368665e-739j)  +/-  (1.01e-243, 1.01e-243j)
| (-9.1037639349834164267 + 7.5670036796884026346e-742j)  +/-  (1.59e-246, 1.59e-246j)
| (1.7283860285115163422 + 2.4001496918602821459e-743j)  +/-  (4.25e-248, 4.25e-248j)
| (3.2829553740981128297 - 2.2532887728151169661e-740j)  +/-  (5.41e-245, 5.41e-245j)
| (-5.7347241107361118312 + 3.5393798487671734486e-737j)  +/-  (4.3e-243, 4.3e-243j)
| (-1.2247448713915890491 + 8.9440413862014292885e-749j)  +/-  (1.95e-249, 1.95e-249j)
| (-4.288413232534211384 - 2.138049768544301423e-742j)  +/-  (9.65e-244, 9.65e-244j)
| (-7.406838529413426997 + 4.3815265715893376742e-749j)  +/-  (5.97e-244, 5.97e-244j)
| (2.0232301911005156592 - 7.8018110651898211892e-759j)  +/-  (2.2e-247, 2.2e-247j)
| (5.7347241107361118312 + 2.3874468789008913862e-753j)  +/-  (4.28e-243, 4.28e-243j)
| (-1.021505258086124509 + 2.0348502480181199455e-766j)  +/-  (3.8e-250, 3.8e-250j)
| (-2.9592107790638377223 - 1.0937195189342447242e-759j)  +/-  (1.66e-245, 1.66e-245j)
| (2.9592107790638377223 - 2.9741670731073216907e-768j)  +/-  (1.6e-245, 1.6e-245j)
| (1.2247448713915890491 + 2.9140896768752150142e-774j)  +/-  (2.05e-249, 2.05e-249j)
| (2.6409243395700373768 + 2.8500613765512491225e-769j)  +/-  (3.99e-246, 3.99e-246j)
| (-4.6366857340283455015 + 9.5054047347282031204e-769j)  +/-  (1.8e-243, 1.8e-243j)
| (-0.52403354748695764515 - 6.0217501845525559664e-789j)  +/-  (1.88e-252, 1.88e-252j)
| (3.6121711468114608143 - 3.69289258950979507e-780j)  +/-  (1.79e-244, 1.79e-244j)
| (7.896170797027213845 + 1.1095526660813406931e-778j)  +/-  (1.47e-244, 1.47e-244j)
| (1.4539739442300617619 - 1.9651208717283759619e-787j)  +/-  (8.15e-249, 8.15e-249j)
| (-3.2829553740981128297 + 2.2654537346545720577e-780j)  +/-  (5.51e-245, 5.51e-245j)
| (-0.78214831114433452538 + 1.2798083294973939446e-801j)  +/-  (3.22e-251, 3.22e-251j)
| (-5.3584030495306006421 - 2.4755433040504421198e-793j)  +/-  (4.38e-243, 4.38e-243j)
| (-4.9929325347797573146 + 8.3075953762967163693e-811j)  +/-  (3.34e-243, 3.34e-243j)
| (0.78214831114433452538 + 2.196544839835153924e-822j)  +/-  (3.24e-251, 3.24e-251j)
| (-3.9471515311613050754 - 1.1770632952709231007e-815j)  +/-  (4.68e-244, 4.68e-244j)
| (-2.0232301911005156592 + 2.1729159229727882792e-819j)  +/-  (2.02e-247, 2.02e-247j)
| (-0.26245596931957254635 + 1.6086382999276066646e-824j)  +/-  (1.04e-253, 1.04e-253j)
| (-3.6121711468114608143 + 6.0707760765034520952e-816j)  +/-  (1.7e-244, 1.7e-244j)
| (2.3285146254673015787 - 8.5404318641440185128e-819j)  +/-  (9.19e-247, 9.19e-247j)
| (3.9471515311613050754 + 1.9983128438094641068e-815j)  +/-  (4.49e-244, 4.49e-244j)
| (4.9929325347797573146 + 1.0802909647199211818e-813j)  +/-  (3.04e-243, 3.04e-243j)
| (1.0753299250198563482e-844 - 1.0829333705908376804e-844j)  +/-  (8.09e-843, 8.09e-843j)
| (-1.7283860285115163422 + 7.3432148572586767319e-825j)  +/-  (4.13e-248, 4.13e-248j)
| (4.6366857340283455015 + 7.47778158988171324e-823j)  +/-  (1.76e-243, 1.76e-243j)
| (0.52403354748695764515 + 1.7262543040680040409e-837j)  +/-  (1.85e-252, 1.85e-252j)
| (0.26245596931957254635 - 8.6421409772761243266e-838j)  +/-  (1.05e-253, 1.05e-253j)
| (-2.6409243395700373768 + 1.6628980800912796671e-831j)  +/-  (4.33e-246, 4.33e-246j)
| (-1.4539739442300617619 - 1.6626750242151836323e-834j)  +/-  (8.27e-249, 8.27e-249j)
| (5.3584030495306006421 + 3.786541947794203589e-836j)  +/-  (3.94e-243, 3.94e-243j)
-------------------------------------------------
The weights are:
| (3.9451829484957811788e-25 - 2.3201256852186633072e-730j)  +/-  (1.03e-82, 1.3e-202j)
| (3.6199010874508916857e-32 - 3.2933918773180986025e-736j)  +/-  (1.21e-86, 1.52e-206j)
| (3.6199010874508916857e-32 + 5.0350225903100832603e-735j)  +/-  (6.01e-86, 7.56e-206j)
| (7.1452689203298737777e-20 - 1.4808643806052356513e-729j)  +/-  (1.21e-81, 1.53e-201j)
| (4.3622791287769727541e-37 - 7.8923852051767540598e-738j)  +/-  (6.16e-88, 7.76e-208j)
| (1.1537986082285965017e-17 + 2.6472938952779096014e-727j)  +/-  (3.98e-80, 5.02e-200j)
| (2.4205935152297247253e-28 + 3.6520380356566246492e-734j)  +/-  (4.67e-86, 5.88e-206j)
| (2.4313496180947575837e-22 + 6.5000144165890008086e-731j)  +/-  (2.03e-83, 2.56e-203j)
| (7.1452689203298737777e-20 - 2.3518648810247070423e-728j)  +/-  (8.16e-82, 1.03e-201j)
| (2.4313496180947575837e-22 + 2.0650969465538879777e-729j)  +/-  (6.33e-83, 7.97e-203j)
| (0.043586679804249692702 + 3.7696210399643419188e-717j)  +/-  (8.5e-53, 1.07e-172j)
| (1.1537986082285965017e-17 + 2.5097458964152104927e-728j)  +/-  (2.45e-82, 3.09e-202j)
| (0.00077067864098288468579 - 1.5396307405456696679e-719j)  +/-  (2.8e-67, 3.52e-187j)
| (2.0039512280211952451e-09 - 6.0818534196670742614e-723j)  +/-  (2.2e-77, 2.77e-197j)
| (4.3622791287769727541e-37 + 8.111629478164557031e-739j)  +/-  (3.02e-91, 3.8e-211j)
| (0.0081741407518737941915 - 3.2922858681941214695e-718j)  +/-  (8.65e-64, 1.09e-183j)
| (3.8415515864601963621e-06 + 6.0272007278145252169e-721j)  +/-  (4.19e-74, 5.28e-194j)
| (1.1253460684842212021e-15 - 3.327156705054309392e-727j)  +/-  (4.14e-82, 5.22e-202j)
| (0.025503766746266454577 - 1.8359773318252506521e-717j)  +/-  (2.27e-60, 2.86e-180j)
| (2.0039512280211952451e-09 - 1.6216671467906738555e-723j)  +/-  (3.54e-79, 4.46e-199j)
| (3.9451829484957811788e-25 - 1.9700459064507047941e-732j)  +/-  (5.57e-86, 7.01e-206j)
| (0.0028320479537871291516 + 9.9024253390736710735e-719j)  +/-  (2.01e-68, 2.53e-188j)
| (1.1253460684842212021e-15 - 2.6148951151124536385e-726j)  +/-  (5.21e-83, 6.56e-203j)
| (0.043586679804249692702 + 2.855873852995685145e-717j)  +/-  (1.62e-61, 2.04e-181j)
| (2.8503690041935876723e-05 - 1.0056400143963794811e-720j)  +/-  (6.84e-75, 8.61e-195j)
| (2.8503690041935876723e-05 - 2.3438368858528874116e-720j)  +/-  (2.9e-74, 3.65e-194j)
| (0.025503766746266454577 - 2.5634343861928675147e-717j)  +/-  (8.34e-65, 1.05e-184j)
| (0.00016649455644287775945 + 8.530262193862833651e-720j)  +/-  (4.67e-73, 5.88e-193j)
| (9.1459633162164623203e-11 + 2.4484270447988147208e-724j)  +/-  (1.99e-81, 2.51e-201j)
| (0.11178654883999354684 + 3.7713456702484652764e-717j)  +/-  (1.84e-65, 2.32e-185j)
| (4.0366663820581156418e-07 - 1.4316602032696390463e-721j)  +/-  (1.53e-77, 1.92e-197j)
| (2.4205935152297247253e-28 - 1.1421109094823881546e-732j)  +/-  (8.48e-90, 1.07e-209j)
| (0.01749750991557392718 + 1.0660081997857530672e-717j)  +/-  (5.29e-69, 6.66e-189j)
| (3.8415515864601963621e-06 + 2.325159098433997538e-721j)  +/-  (2.37e-78, 2.98e-198j)
| (0.077508868200876677527 - 3.3457901145519725781e-717j)  +/-  (1.22e-68, 1.53e-188j)
| (7.0899321307363612528e-14 + 3.5773608452963972657e-726j)  +/-  (1.4e-83, 1.76e-203j)
| (3.0324116193836960631e-12 - 3.2064093433190415127e-725j)  +/-  (7.19e-83, 9.05e-203j)
| (0.077508868200876677527 - 4.135835837844519474e-717j)  +/-  (2.38e-72, 3e-192j)
| (3.2662833129674392666e-08 + 9.4611929423635026655e-723j)  +/-  (3.49e-81, 4.4e-201j)
| (0.0028320479537871291516 + 5.6532758355177030938e-719j)  +/-  (1.53e-77, 1.92e-197j)
| (0.13805647113490656507 - 4.1858661842861046849e-717j)  +/-  (4.57e-73, 5.75e-193j)
| (4.0366663820581156418e-07 - 4.9302745309656004683e-722j)  +/-  (1.4e-80, 1.76e-200j)
| (0.00077067864098288468579 - 2.9515346541163404896e-719j)  +/-  (2.8e-78, 3.53e-198j)
| (3.2662833129674392666e-08 + 3.1049713654174703424e-722j)  +/-  (6.92e-84, 8.72e-204j)
| (3.0324116193836960631e-12 - 1.6470708421805521542e-724j)  +/-  (7.12e-88, 9.03e-208j)
| (0.14816801957086281936 + 4.4490075524018281746e-717j)  +/-  (2.27e-77, 2.47e-197j)
| (0.0081741407518737941915 - 2.0464837841026150083e-718j)  +/-  (4.26e-80, 4.99e-200j)
| (9.1459633162164623203e-11 + 1.0644788464533490369e-723j)  +/-  (7.91e-87, 9.55e-207j)
| (0.11178654883999354684 + 4.345620738500386624e-717j)  +/-  (5.04e-78, 5.31e-198j)
| (0.13805647113490656507 - 4.4934100644180197477e-717j)  +/-  (5.03e-78, 5.28e-198j)
| (0.00016649455644287775945 + 4.046124312736996165e-720j)  +/-  (1.66e-82, 1.76e-202j)
| (0.01749750991557392718 + 7.1616485270338948148e-718j)  +/-  (4.22e-80, 4.25e-200j)
| (7.0899321307363612528e-14 + 2.2293050405421526996e-725j)  +/-  (4.36e-89, 6.18e-209j)
