Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 6 10 16
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P2 : 8*t^9 - 117*t^7 + 945/2*t^5 - 2205/4*t^3 + 945/8*t
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P3 : 8*t^19 - 23713751/51473*t^17 + 2134183615/205892*t^15 - 48885080515/411784*t^13 + 623352876985/823568*t^11 - 4536269518165/1647136*t^9 + 18427952550645/3294272*t^7 - 38805894891225/6588544*t^5 + 36681698574675/13177088*t^3 - 11110847880825/26354176*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^35 - 148158172019154347566494279532305444494687200256542484844439972024607051000023761563231/96440151552474957965152617915244855099513652762532460688601566958945283039257022569*t^33 + 2249942320220592204173182865179529289145984970438942004160704874997340053778177337020913259/17359227279445492433727471224744073917912457497255842923948282052610150947066264062420*t^31 - 220849158772970079249588044514404572697676391214019057797593782286207915104784526104267559039/34718454558890984867454942449488147835824914994511685847896564105220301894132528124840*t^29 + 14076452535407047075509904706929932084194209883569653124917820365324652269134990345424626592113/69436909117781969734909884898976295671649829989023371695793128210440603788265056249680*t^27 - 3079461704370215575368823985946098203044130613330964437033194113796741253296061531689893628203229/694369091177819697349098848989762956716498299890233716957931282104406037882650562496800*t^25 + 13621590005974628394299390435466707875960413189403142442133883552507558252569258603353414031836829/198391168907948484956885385425646559061856657111495347702266080601258867966471589284800*t^23 - 7555344735732247770778736796311822778855080357658901316591419468071013675725945354433109059803407/9884257525662913841268311017647871269985740923704394547443861666966633991212107651200*t^21 + 3219710580700670279502708780755276042659877667713327453155485017016560499238619994520958078064961/522976588659413430754937090880839749734695286968486483991738712537917142392175008000*t^19 - 94703184350745630527408004926675491861812450062856179314573920985767025554447829325616105822169860877/2645215585439313132758471805675287454158088761486604636030214408016784906219621190464000*t^17 + 157484513545995039812258087014296855688128394169414274752888698243122811598842273074780125572399172993/1058086234175725253103388722270114981663235504594641854412085763206713962487848476185600*t^15 - 23549631437656828001609343706484598645025341463453683544660303514393391646415889277922730696464830187/54260832521832064261712242167698204187858231004853428431389013497780203204505050060800*t^13 + 93354849639900358921608632783963512574570620469839157037326776142611274152386412728501470282091552853/108521665043664128523424484335396408375716462009706856862778026995560406409010100121600*t^11 - 4883263925242950190669085624551426689401578018559150322810148516683487563072259572222768280960294573/4429455716067923613200999360628424831661896408559463545419511305941241077918779596800*t^9 + 13537565622105100537332391567346142747089590000147244485599043633820513434062805161738407228679234793/16077283710172463484951775457095764203809846223660275090781929925268208356890385203200*t^7 - 916695994687218333091656821821092731491782773637716223198067748233865557741850872806864840043001917/2756105778886708025991732935502131006367402209770332872705473701474550004038351749120*t^5 + 281593491909388686402915463907712078147402844378914597860805998856747021879331968381790179022242211/5512211557773416051983465871004262012734804419540665745410947402949100008076703498240*t^3 - 4733364936815051007936085288803863817032716310637460684423752827270817573558587806396618867308523/3674807705182277367988977247336174675156536279693777163607298268632733338717802332160*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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   35 out of 35
Indefinite weights: 0 out of 35
Negative weights:   0 out of 35
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (6.3759392709822359517 - 1.4617841826127724035e-439j)  +/-  (6.42e-122, 6.42e-122j)
| (-5.0360899444730939687 - 7.0823660756481619232e-439j)  +/-  (2.29e-120, 2.29e-120j)
| (-2.9592107790638377223 + 3.3150749294778916697e-438j)  +/-  (7.96e-120, 7.96e-120j)
| (3.66777421594633786 + 7.305084220973774347e-437j)  +/-  (1.87e-119, 1.87e-119j)
| (-5.6432578578857450628 - 1.0361038371682346846e-444j)  +/-  (5.45e-121, 5.45e-121j)
| (5.0360899444730939687 + 1.0013745024660300189e-441j)  +/-  (2.27e-120, 2.27e-120j)
| (-6.3759392709822359517 + 1.0131311960501809038e-447j)  +/-  (6.44e-122, 6.44e-122j)
| (-1.2247448713915890491 - 8.6880236002857693992e-449j)  +/-  (3.95e-123, 3.95e-123j)
| (1.2247448713915890491 + 1.7685830009299372962e-448j)  +/-  (3.92e-123, 3.92e-123j)
| (-4.4995993983103888029 + 8.7134809463804699683e-445j)  +/-  (6.26e-120, 6.26e-120j)
| (1.5794121348467670857 - 3.6329884903465187573e-447j)  +/-  (7.23e-122, 7.23e-122j)
| (4.0292201405043713648 - 9.6583179884496944554e-445j)  +/-  (1.38e-119, 1.38e-119j)
| (-2.2665132620567880275 - 1.1422101804108556676e-453j)  +/-  (3.38e-120, 3.38e-120j)
| (-0.87004089535290290013 + 7.216388135300378423e-461j)  +/-  (2.45e-124, 2.45e-124j)
| (2.5705583765842967091 - 6.1860116694691436068e-455j)  +/-  (4.65e-120, 4.65e-120j)
| (5.6432578578857450628 + 6.1640049515712659581e-463j)  +/-  (5.76e-121, 5.76e-121j)
| (1.8357079751751868738 - 3.5382171362320177413e-464j)  +/-  (6.62e-121, 6.62e-121j)
| (-4.0292201405043713648 + 8.5215304671052601275e-463j)  +/-  (1.41e-119, 1.41e-119j)
| (-1.5794121348467670857 - 3.542418885153093038e-471j)  +/-  (8.07e-122, 8.07e-122j)
| (-0.17606414208200893503 + 9.2827775164364016876e-475j)  +/-  (1.18e-126, 1.18e-126j)
| (2.9592107790638377223 + 5.4364993983165312808e-467j)  +/-  (7.2e-120, 7.2e-120j)
| (0.17606414208200893503 + 7.7539926373010474896e-478j)  +/-  (7.21e-127, 7.21e-127j)
| (4.4995993983103888029 - 2.3041429313581864174e-470j)  +/-  (6.47e-120, 6.47e-120j)
| (-3.66777421594633786 - 1.4726425864354962663e-474j)  +/-  (1.88e-119, 1.88e-119j)
| (-2.0232301911005156592 - 1.5220945095250283781e-475j)  +/-  (2.12e-120, 2.12e-120j)
| (-6.3591109425209718367e-490 - 1.619908991176581805e-488j)  +/-  (5.67e-487, 5.67e-487j)
| (0.87004089535290290013 + 1.9821065751628017062e-479j)  +/-  (2.41e-124, 2.41e-124j)
| (2.2665132620567880275 - 1.0131832583415238015e-474j)  +/-  (3.43e-120, 3.43e-120j)
| (-3.3491639537131949774 - 2.1670841476246975699e-481j)  +/-  (1.41e-119, 1.41e-119j)
| (-1.8357079751751868738 - 3.5172776002875961408e-482j)  +/-  (7.17e-121, 7.17e-121j)
| (-2.5705583765842967091 + 1.5665254803949216499e-482j)  +/-  (4.65e-120, 4.65e-120j)
| (2.0232301911005156592 - 4.3464938280231449316e-488j)  +/-  (1.85e-120, 1.85e-120j)
| (0.52403354748695764515 + 5.7055244568112514085e-500j)  +/-  (1.65e-125, 1.65e-125j)
| (3.3491639537131949774 + 8.5758154125083632811e-500j)  +/-  (1.55e-119, 1.55e-119j)
| (-0.52403354748695764515 - 2.1901424087615722477e-509j)  +/-  (1.65e-125, 1.65e-125j)
-------------------------------------------------
The weights are:
| (1.0541326582333341189e-18 - 1.5540400793167614981e-452j)  +/-  (1.74e-45, 6.47e-104j)
| (3.0972223576063161713e-12 + 1.5260476883342704423e-448j)  +/-  (2.56e-42, 9.56e-101j)
| (3.5729348198975100228e-05 + 5.1456798168787267984e-442j)  +/-  (2.8e-35, 1.05e-93j)
| (2.4676421345798078671e-07 - 1.2002638188351930158e-442j)  +/-  (6.02e-39, 2.25e-97j)
| (5.4500412650636899171e-15 - 1.7565322505499722022e-450j)  +/-  (2.8e-44, 1.04e-102j)
| (3.0972223576063161713e-12 - 6.8252559883866739561e-448j)  +/-  (9.44e-44, 3.52e-102j)
| (1.0541326582333341189e-18 + 5.8170395897939717191e-453j)  +/-  (1.54e-46, 5.75e-105j)
| (0.045273685465150515865 - 4.5607511303864637295e-440j)  +/-  (1.16e-27, 4.33e-86j)
| (0.045273685465150515865 - 1.4276173649774888874e-439j)  +/-  (3.84e-28, 1.43e-86j)
| (4.6011760348656187011e-10 - 9.4526840129668225375e-447j)  +/-  (1.2e-41, 4.47e-100j)
| (0.015673473751851151542 + 1.5072145208851751586e-439j)  +/-  (4.23e-31, 1.58e-89j)
| (2.1394194479561106307e-08 - 3.9470877616227286433e-444j)  +/-  (2.17e-41, 8.09e-100j)
| (0.00081895392750226490906 + 2.291774464227212442e-441j)  +/-  (5.47e-36, 2.04e-94j)
| (0.092364726716986305928 + 9.0741046106334841769e-440j)  +/-  (5.91e-30, 2.21e-88j)
| (0.000275242141167851575 + 6.8946539944458806191e-441j)  +/-  (2.33e-37, 8.69e-96j)
| (5.4500412650636899171e-15 + 5.5442158891131329125e-450j)  +/-  (3.14e-46, 1.17e-104j)
| (0.0031554462691875638051 - 1.7504649071920701026e-439j)  +/-  (2.25e-34, 8.38e-93j)
| (2.1394194479561106307e-08 + 3.739814551881461933e-445j)  +/-  (2.06e-42, 7.7e-101j)
| (0.015673473751851151542 + 2.8348770297828697757e-440j)  +/-  (2.08e-35, 7.77e-94j)
| (0.19176011588804442959 + 7.3891225160493158087e-439j)  +/-  (1.73e-32, 6.46e-91j)
| (3.5729348198975100228e-05 - 1.1232773189400353527e-441j)  +/-  (2.53e-39, 9.43e-98j)
| (0.19176011588804442959 + 8.5366545616499706728e-439j)  +/-  (1.11e-32, 4.13e-91j)
| (4.6011760348656187011e-10 + 5.4271050498686350574e-446j)  +/-  (2.38e-43, 8.86e-102j)
| (2.4676421345798078671e-07 - 6.1446036179469999188e-444j)  +/-  (6.54e-42, 2.44e-100j)
| (0.0023113452403522101207 + 3.8655910625763213784e-441j)  +/-  (6.31e-38, 2.35e-96j)
| (0.0005148945080687842938 - 1.2532267995328795866e-438j)  +/-  (4.68e-34, 1.75e-92j)
| (0.092364726716986305928 + 1.9311478859008283106e-439j)  +/-  (7.16e-36, 2.67e-94j)
| (0.00081895392750226490906 - 3.6199459442988051812e-440j)  +/-  (1e-38, 3.75e-97j)
| (2.7342206801187829817e-06 + 5.7262616319553630256e-443j)  +/-  (1.45e-41, 5.4e-100j)
| (0.0031554462691875638051 - 1.7280140589129667852e-440j)  +/-  (5.35e-38, 2e-96j)
| (0.000275242141167851575 - 1.6896707239526181648e-441j)  +/-  (6.98e-40, 2.6e-98j)
| (0.0023113452403522101207 + 1.1932524990981285658e-439j)  +/-  (2.57e-39, 9.61e-98j)
| (0.14807083115521600615 - 3.1339410245877827208e-439j)  +/-  (4.03e-38, 1.51e-96j)
| (2.7342206801187829817e-06 + 3.4573517714697244745e-442j)  +/-  (5.98e-43, 2.24e-101j)
| (0.14807083115521600615 - 2.0233971167183615129e-439j)  +/-  (2.53e-38, 8.83e-97j)
