Starting with polynomial:
P : 2*t
Extension levels are: 1 4 34
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^39 - 850021374965916870649/1197449949929852181*t^37 + 4058305368660464448012727/35923498497895565430*t^35 - 153488632143528736870280003/14369399399158226172*t^33 + 51787482889596505970871491/77254835479345302*t^31 - 4565654871564628178164085335/154509670958690604*t^29 + 291872165031426753374561691115/309019341917381208*t^27 - 4591200108704901655376456436393/206012894611587472*t^25 + 322653878303028274445994591215175/824051578446349888*t^23 - 8456502998253147373070886206931075/1648103156892699776*t^21 + 164615055228194731251402018715882875/3296206313785399552*t^19 - 2356050689539866882034217681216155875/6592412627570799104*t^17 + 12193353900640574462472045582290006925/6592412627570799104*t^15 - 89074648746832008495787917246175919625/13184825255141598208*t^13 + 443509278300380644486025971929909184125/26369650510283196416*t^11 - 1431501981711177354983742283934070808125/52739301020566392832*t^9 + 11120145374060218342455763230277246670625/421914408164531142656*t^7 - 11544674399865881289867482768486791567125/843828816329062285312*t^5 + 5188336940221526480407053246696052693125/1687657632658124570624*t^3 - 624530389960994686840541252268800038125/3375315265316249141248*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
Sufficient bits for target precision reached
Positive weights:   39 out of 39
Indefinite weights: 0 out of 39
Negative weights:   0 out of 39
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-3.9128650150702067704 - 3.5553538637921801211e-455j)  +/-  (1.03e-118, 1.03e-118j)
| (6.615352279455863359 + 1.5536063948288660072e-455j)  +/-  (5.59e-119, 5.59e-119j)
| (-6.0977453025011688424 - 2.0466161419171142077e-454j)  +/-  (1.38e-118, 1.38e-118j)
| (7.8871452611138273747 + 6.3348556309377759977e-458j)  +/-  (1.32e-120, 1.32e-120j)
| (7.1928176377967678147 + 6.7737748715241169302e-457j)  +/-  (1.51e-119, 1.51e-119j)
| (-6.615352279455863359 + 4.0485934068163466931e-457j)  +/-  (5.69e-119, 5.69e-119j)
| (4.7333469423091348645 + 1.6962421777091671004e-455j)  +/-  (2.76e-118, 2.76e-118j)
| (-7.1928176377967678147 + 1.2076439013765113189e-460j)  +/-  (1.41e-119, 1.41e-119j)
| (-5.6182591695424371841 + 4.0537689223369363802e-460j)  +/-  (2.09e-118, 2.09e-118j)
| (5.1656989019817463989 + 2.3306542194021161663e-460j)  +/-  (2.76e-118, 2.76e-118j)
| (-7.8871452611138273747 - 3.0472554377972393176e-467j)  +/-  (1.25e-120, 1.25e-120j)
| (5.6182591695424371841 + 1.4876900166586003066e-465j)  +/-  (2.08e-118, 2.08e-118j)
| (-2.3857003233694352468 + 3.1021126364343434558e-473j)  +/-  (9.54e-121, 9.54e-121j)
| (3.1344534755659559621 - 3.9900782518781127067e-470j)  +/-  (1.57e-119, 1.57e-119j)
| (2.3857003233694352468 + 1.0853783447613925333e-474j)  +/-  (9.56e-121, 9.56e-121j)
| (-3.5193344222029184952 + 4.440556215421066521e-472j)  +/-  (4.63e-119, 4.63e-119j)
| (1.6600814928512018556 + 1.7756715953725424333e-476j)  +/-  (3.11e-122, 3.11e-122j)
| (-5.1656989019817463989 - 2.6821707660769558913e-471j)  +/-  (2.84e-118, 2.84e-118j)
| (-0.95857246461381850711 + 1.4302705870033838761e-480j)  +/-  (4.1e-124, 4.1e-124j)
| (-2.0201828704560856329 + 1.1128363345616984049e-477j)  +/-  (1.78e-121, 1.78e-121j)
| (-4.3167734742174514295 - 3.4941190405167504747e-474j)  +/-  (1.87e-118, 1.87e-118j)
| (2.0201828704560856329 - 1.5049274413847545817e-483j)  +/-  (1.92e-121, 1.92e-121j)
| (3.9128650150702067704 - 2.4933543055012542159e-480j)  +/-  (1.04e-118, 1.04e-118j)
| (-1.6600814928512018556 - 2.1970183636447473928e-494j)  +/-  (3.1e-122, 3.1e-122j)
| (-1.305730445853070471 - 1.1980750651583391405e-495j)  +/-  (3.71e-123, 3.71e-123j)
| (6.0977453025011688424 - 2.049157161940443903e-490j)  +/-  (1.38e-118, 1.38e-118j)
| (1.305730445853070471 + 2.9732018820051185498e-503j)  +/-  (3.68e-123, 3.68e-123j)
| (3.5193344222029184952 + 3.0491683619995789845e-498j)  +/-  (4.42e-119, 4.42e-119j)
| (2.7569034663838727802 + 1.0470393707361507324e-505j)  +/-  (4.45e-120, 4.45e-120j)
| (-0.62213033828822709016 - 2.3730789435161915427e-512j)  +/-  (3.29e-125, 3.29e-125j)
| (-4.7333469423091348645 + 2.3890447893716526127e-506j)  +/-  (2.71e-118, 2.71e-118j)
| (0.62213033828822709016 - 1.5512467026568064801e-516j)  +/-  (3.6e-125, 3.6e-125j)
| (0.95857246461381850711 - 1.1035457266014966155e-514j)  +/-  (3.8e-124, 3.8e-124j)
| (-3.1344534755659559621 - 6.0866620619732823789e-511j)  +/-  (1.57e-119, 1.57e-119j)
| (4.3167734742174514295 + 6.8737219120221496751e-516j)  +/-  (1.94e-118, 1.94e-118j)
| (-0.30232244036714895687 + 4.4184278527632093586e-526j)  +/-  (2.57e-126, 2.57e-126j)
| (-2.7569034663838727802 - 2.1905739919864190005e-522j)  +/-  (4.73e-120, 4.73e-120j)
| (5.0563968203724277878e-545 + 5.191300807639218243e-544j)  +/-  (2.03e-542, 2.03e-542j)
| (0.30232244036714895687 + 1.1018670736521434061e-529j)  +/-  (2.57e-126, 2.57e-126j)
-------------------------------------------------
The weights are:
| (5.0403869069842600853e-08 - 7.441109971934979732e-462j)  +/-  (3.14e-24, 2.12e-82j)
| (3.0185529438506378865e-20 - 7.4352901538249249772e-470j)  +/-  (2.93e-33, 1.98e-91j)
| (1.9900223465732893273e-17 - 1.0886158881929425529e-467j)  +/-  (1.85e-32, 1.25e-90j)
| (4.3499893387873990463e-28 - 7.1389080837452155782e-474j)  +/-  (1.27e-36, 8.59e-95j)
| (1.1890374331346980121e-23 + 1.3309193891043027424e-471j)  +/-  (7.43e-35, 5.01e-93j)
| (3.0185529438506378865e-20 + 3.1836971274641912934e-469j)  +/-  (1.23e-34, 8.31e-93j)
| (4.4510306909838208953e-11 - 8.885480378061141086e-465j)  +/-  (1.2e-30, 8.11e-89j)
| (1.1890374331346980121e-23 - 4.8543520047450198654e-471j)  +/-  (1.74e-36, 1.17e-94j)
| (5.1298442427271611874e-15 + 2.4038509633140459245e-466j)  +/-  (8.38e-33, 5.65e-91j)
| (6.4197631553082042852e-13 + 3.5203409356820533432e-466j)  +/-  (2.17e-32, 1.47e-90j)
| (4.3499893387873990463e-28 + 2.2501477396689891669e-473j)  +/-  (7.36e-39, 4.97e-97j)
| (5.1298442427271611874e-15 - 3.5253094552427666941e-467j)  +/-  (1.47e-33, 9.94e-92j)
| (0.00070110970191212535038 - 2.200861199480494899e-460j)  +/-  (1.6e-25, 1.08e-83j)
| (1.1628474935098572038e-05 - 5.1033096154275952932e-462j)  +/-  (1.29e-28, 8.7e-87j)
| (0.00070110970191212535038 - 5.5577950546884502371e-461j)  +/-  (4.35e-26, 2.93e-84j)
| (9.1680571493548539831e-07 + 2.1453670824616211538e-461j)  +/-  (8.16e-30, 5.5e-88j)
| (0.012813273095241408152 - 3.6676655342263466425e-460j)  +/-  (1.1e-23, 7.44e-82j)
| (6.4197631553082042852e-13 - 3.9476332724085053657e-465j)  +/-  (1.13e-33, 7.6e-92j)
| (0.077122863369598148969 - 2.5733560451369919935e-459j)  +/-  (8.1e-25, 5.46e-83j)
| (0.0034568571640740576121 + 4.5941419597969797425e-460j)  +/-  (1.95e-26, 1.32e-84j)
| (1.8669155742433244597e-09 - 7.7901359749437380197e-463j)  +/-  (5.3e-32, 3.57e-90j)
| (0.0034568571640740576121 + 1.512501056940138514e-460j)  +/-  (7.83e-27, 5.28e-85j)
| (5.0403869069842600853e-08 - 2.6587664199147899894e-463j)  +/-  (6.75e-33, 4.55e-91j)
| (0.012813273095241408152 - 8.8560002806291910932e-460j)  +/-  (8.24e-27, 5.56e-85j)
| (0.036012043599063422527 + 1.5727441044964806828e-459j)  +/-  (6.95e-26, 4.69e-84j)
| (1.9900223465732893273e-17 + 2.0832810523197339568e-468j)  +/-  (1.82e-37, 1.23e-95j)
| (0.036012043599063422527 + 8.0008069435759443403e-460j)  +/-  (5.55e-27, 3.74e-85j)
| (9.1680571493548539831e-07 + 1.252370055898793856e-462j)  +/-  (3.51e-32, 2.37e-90j)
| (0.0001056115368677351552 + 1.8017495078219028804e-461j)  +/-  (1.66e-30, 1.12e-88j)
| (0.12611791649368110969 + 3.8452725778694452293e-459j)  +/-  (5.86e-28, 3.95e-86j)
| (4.4510306909838208953e-11 + 5.4371642581996123179e-464j)  +/-  (2.89e-35, 1.95e-93j)
| (0.12611791649368110969 + 2.8130235727303932833e-459j)  +/-  (9.95e-29, 6.71e-87j)
| (0.077122863369598148969 - 1.5807604494820644045e-459j)  +/-  (1.11e-28, 7.48e-87j)
| (1.1628474935098572038e-05 - 4.3074594041511908363e-461j)  +/-  (6.23e-33, 4.2e-91j)
| (1.8669155742433244597e-09 + 5.1031087962101371146e-464j)  +/-  (5.63e-35, 3.8e-93j)
| (0.15956538897466822011 - 5.0304278615795122298e-459j)  +/-  (3.04e-30, 2.05e-88j)
| (0.0001056115368677351552 + 9.8612213173691008379e-461j)  +/-  (2.26e-32, 1.52e-90j)
| (0.16818467693660332258 + 5.3137003991565142921e-459j)  +/-  (1.35e-30, 9.07e-89j)
| (0.15956538897466822011 - 4.3256756055897679466e-459j)  +/-  (8.98e-31, 6.04e-89j)
