Starting with polynomial:
P : 63/8*t^5 - 35/4*t^3 + 15/8*t
Extension levels are: 5 6 12
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Trying to find an order 6 Kronrod extension for:
P1 : 63/8*t^5 - 35/4*t^3 + 15/8*t
Solvable: 1
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Trying to find an order 12 Kronrod extension for:
P2 : 63/8*t^11 - 2233/104*t^9 + 71973/3380*t^7 - 6901587/746980*t^5 + 488523/298792*t^3 - 24129/298792*t
Solvable: 1
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Ending with final polynomial:
P : 63/8*t^23 - 184409473633489381237760801149041817/3933247329076320767773116754082600*t^21 + 6219722870443781394948058496724130247/51132215277992169981050517803073800*t^19 - 30567257409937313125240661237286857030839/169503293646544043487182466517189647000*t^17 + 2517471739290278643179496293192852954347/14956172968812709719457276457399086500*t^15 - 62383684937458387162828494601917017840591/607220622533796014609965424170402911900*t^13 + 895609949190308368067013767145728307815413/21719814575247318984125686326095181079500*t^11 - 694960117754649475923298591344562658042573/65159443725741956952377058978285543238500*t^9 + 857353392452625131178835238867255707468801/506795673422437442962932680942220891855000*t^7 - 1204028667427068391435001508495208560693/8044375768610118142268772713368585585000*t^5 + 4532086959759134845315673399566021327009/738473695558408845460273335087236156703000*t^3 - 18374728048950775644657398002257504809/246157898519469615153424445029078718901000*t
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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
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The nodes are:
| (0.95437314473850901745 + 3.9373457660042240066e-304j)  +/-  (7.61e-120, 7.61e-120j)
| (-0.95437314473850901745 + 1.0967683431021464089e-315j)  +/-  (7.8e-120, 7.8e-120j)
| (-0.9061798459386639928 + 2.1354015138792375021e-319j)  +/-  (3.32e-120, 3.32e-120j)
| (-1.8905676072528771126e-324 - 1.0936270401762249864e-324j)  +/-  (5.02e-323, 5.02e-323j)
| (0.99754549758686732618 + 5.4806709589920844293e-336j)  +/-  (5.31e-120, 5.31e-120j)
| (0.65311997810491663606 - 1.669373227832832758e-349j)  +/-  (3.5e-122, 3.5e-122j)
| (-0.99754549758686732618 + 1.005557555337951762e-350j)  +/-  (4.89e-120, 4.89e-120j)
| (-0.83913703080552600731 + 9.1351110391844419825e-352j)  +/-  (1.09e-120, 1.09e-120j)
| (-0.9840853600948424645 + 1.2631174577226705645e-350j)  +/-  (9.93e-120, 9.93e-120j)
| (-0.27963041316178319341 + 5.5663262974393960441e-356j)  +/-  (1.77e-125, 1.77e-125j)
| (0.83913703080552600731 - 4.332140109917547546e-350j)  +/-  (1.03e-120, 1.03e-120j)
| (0.53846931010568309104 + 8.124248157587491113e-356j)  +/-  (4.21e-123, 4.21e-123j)
| (-0.53846931010568309104 - 2.5535162229246929642e-361j)  +/-  (3.66e-123, 3.66e-123j)
| (-0.65311997810491663606 + 5.2049877674785391995e-360j)  +/-  (3.45e-122, 3.45e-122j)
| (-0.14108304540169852469 + 2.8894120334086866957e-362j)  +/-  (1.04e-126, 1.04e-126j)
| (0.75416672657084922044 - 6.5608108884495197289e-358j)  +/-  (2.44e-121, 2.44e-121j)
| (0.27963041316178319341 + 2.1846581408672727698e-364j)  +/-  (1.74e-125, 1.74e-125j)
| (0.9840853600948424645 + 5.5072765440469989865e-367j)  +/-  (1.07e-119, 1.07e-119j)
| (-0.75416672657084922044 - 8.4711203007571011323e-383j)  +/-  (2.13e-121, 2.13e-121j)
| (-0.4130159172460903685 + 1.1680094160690068064e-385j)  +/-  (3.08e-124, 3.08e-124j)
| (0.14108304540169852469 + 8.3153525005060469587e-382j)  +/-  (1.04e-126, 1.04e-126j)
| (0.9061798459386639928 - 2.593955539598118448e-387j)  +/-  (3.44e-120, 3.44e-120j)
| (0.4130159172460903685 - 1.3908830506287541206e-405j)  +/-  (3.27e-124, 3.27e-124j)
-------------------------------------------------
The weights are:
| (0.038762093615661268628 + 6.2379842048601703035e-305j)  +/-  (5.75e-41, 7.6e-98j)
| (0.038762093615661268628 - 7.9958120167040025037e-306j)  +/-  (2.65e-41, 3.5e-98j)
| (0.057677836246853514639 + 8.3934519034776508276e-306j)  +/-  (1.88e-41, 2.48e-98j)
| (0.1415024762815156672 + 1.5611493495432235376e-305j)  +/-  (1.51e-42, 1.99e-99j)
| (0.0067888161722128595953 + 1.1467955315137380398e-304j)  +/-  (1.71e-42, 2.26e-99j)
| (0.10829771463353508625 - 4.7731449932181714184e-305j)  +/-  (2.08e-42, 2.75e-99j)
| (0.0067888161722128595953 - 2.5364715651611708625e-306j)  +/-  (2.27e-42, 2.99e-99j)
| (0.076248311290396817176 - 8.4530442462308897195e-306j)  +/-  (5.51e-43, 7.28e-100j)
| (0.021011712421961465073 + 6.3560527876687142232e-306j)  +/-  (4.11e-42, 5.43e-99j)
| (0.13641553072122802237 + 1.1880044016293983673e-305j)  +/-  (1.48e-44, 1.96e-101j)
| (0.076248311290396817176 - 1.3156136868178444765e-304j)  +/-  (3.3e-45, 4.36e-102j)
| (0.12053227648303325459 + 3.4458218243671947745e-305j)  +/-  (8.12e-45, 1.07e-101j)
| (0.12053227648303325459 + 9.6000117463979777349e-306j)  +/-  (1e-44, 1.33e-101j)
| (0.10829771463353508625 - 8.9451396311055543572e-306j)  +/-  (1.15e-44, 1.52e-101j)
| (0.14024257842068333053 - 1.3539928949364727886e-305j)  +/-  (4.13e-45, 5.48e-102j)
| (0.093378762792174359548 + 7.3251299722361497269e-305j)  +/-  (3.34e-46, 4.45e-103j)
| (0.13641553072122802237 + 2.1726824014708460339e-305j)  +/-  (1.5e-46, 1.98e-103j)
| (0.021011712421961465073 - 4.146760661709283484e-304j)  +/-  (1.47e-46, 1.95e-103j)
| (0.093378762792174359548 + 8.5835751271973589036e-306j)  +/-  (9.54e-46, 1.25e-102j)
| (0.129893129061502188 - 1.0573779755152983143e-305j)  +/-  (3.97e-46, 5.17e-103j)
| (0.14024257842068333053 - 1.8237525568994498433e-305j)  +/-  (9.6e-47, 1.26e-103j)
| (0.057677836246853514639 + 3.2403803914018225188e-304j)  +/-  (3.29e-47, 4.7e-104j)
| (0.129893129061502188 - 2.6707818879759247845e-305j)  +/-  (3.82e-47, 4.8e-104j)
