Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 5 18
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : 4*t^7 - 106/3*t^5 + 215/3*t^3 - 55/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^25 - 2485846480284814814/3917479702543341*t^23 + 32172829350933064699091/795248379616298223*t^21 - 727510583935616176487947/530165586410865482*t^19 + 14548556139364493604290931/530165586410865482*t^17 - 32533326815945525412952593/96393742983793724*t^15 + 781460072458071965705337975/302951763663351704*t^13 - 7327676586560574966719136165/605903527326703408*t^11 + 7396791576953884479287819685/220328555391528512*t^9 - 22826622339241546445089698735/440657110783057024*t^7 + 35276920329102940997326533105/881314221566114048*t^5 - 22803484244302509213359763675/1762628443132228096*t^3 + 1038885630882372447020428725/881314221566114048*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:   25 out of 25
Indefinite weights: 0 out of 25
Negative weights:   0 out of 25
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (3.5109928828725703281 - 4.0103074550262394865e-441j)  +/-  (3.85e-122, 3.85e-122j)
| (-7.3892390014428395509 + 3.8802020604929454574e-441j)  +/-  (6.26e-124, 6.26e-124j)
| (7.3892390014428395509 + 7.892422830144674562e-444j)  +/-  (7.35e-124, 7.35e-124j)
| (-4.7185686155888635677 - 1.1104878086341743311e-440j)  +/-  (2.85e-122, 2.85e-122j)
| (1.5054482028623358456 + 1.0253127995009778447e-449j)  +/-  (6.67e-124, 6.67e-124j)
| (1.9736338515940706855 - 6.2151347121645127293e-449j)  +/-  (2.81e-123, 2.81e-123j)
| (4.7185686155888635677 + 6.9720985259970003767e-447j)  +/-  (3.06e-122, 3.06e-122j)
| (-1.5054482028623358456 - 2.6868398533186556019e-448j)  +/-  (6.04e-124, 6.04e-124j)
| (4.0853639714567934518 - 9.2481290048836896313e-450j)  +/-  (3.73e-122, 3.73e-122j)
| (-2.973823341468389919 - 5.0706119260687913709e-449j)  +/-  (2.24e-122, 2.24e-122j)
| (1.0708183122728702925 - 3.0184429801466391513e-463j)  +/-  (1.21e-124, 1.21e-124j)
| (5.467276719221541494 - 1.1797250130794599394e-462j)  +/-  (9.7e-123, 9.7e-123j)
| (-1.0708183122728702925 - 7.5068069176049570732e-462j)  +/-  (1.22e-124, 1.22e-124j)
| (-5.467276719221541494 + 1.4920021844818790167e-463j)  +/-  (9.95e-123, 9.95e-123j)
| (-4.0853639714567934518 - 6.763015234561381188e-479j)  +/-  (4.16e-122, 4.16e-122j)
| (0.38098935784659668481 - 1.5464251586383236833e-490j)  +/-  (2.73e-126, 2.73e-126j)
| (2.4631197782145911371 - 7.2683618884740512928e-489j)  +/-  (8.82e-123, 8.82e-123j)
| (-0.38098935784659668481 + 3.6584410002971453804e-491j)  +/-  (2.73e-126, 2.73e-126j)
| (-0.7071067811865475244 - 1.6028819501441672463e-490j)  +/-  (2.42e-125, 2.42e-125j)
| (-5.0115630141056786033e-491 - 8.1657794091060689732e-491j)  +/-  (2.4e-489, 2.4e-489j)
| (2.973823341468389919 + 3.7556039566930718023e-490j)  +/-  (2.44e-122, 2.44e-122j)
| (0.7071067811865475244 + 1.0758240500943695267e-492j)  +/-  (2.37e-125, 2.37e-125j)
| (-3.5109928828725703281 + 2.4998085421543949827e-489j)  +/-  (3.53e-122, 3.53e-122j)
| (-2.4631197782145911371 - 1.5664723845216634005e-497j)  +/-  (8.78e-123, 8.78e-123j)
| (-1.9736338515940706855 - 2.3731961292909678838e-507j)  +/-  (2.77e-123, 2.77e-123j)
-------------------------------------------------
The weights are:
| (1.3831431377728153432e-06 + 2.2229934522820309258e-446j)  +/-  (6.16e-44, 5.11e-104j)
| (4.2507598271756792681e-22 + 1.0565640796103243979e-455j)  +/-  (3.32e-52, 2.76e-112j)
| (4.2507598271756792681e-22 - 2.6351327376861965959e-455j)  +/-  (3.45e-52, 2.86e-112j)
| (8.1586684735675977154e-11 - 1.3114535367369928951e-450j)  +/-  (6.29e-48, 5.22e-108j)
| (0.026632764296295897338 + 1.9914399572087892038e-444j)  +/-  (1.67e-37, 1.39e-97j)
| (0.005501569358053536854 - 6.7914408954710053631e-445j)  +/-  (6.37e-40, 5.29e-100j)
| (8.1586684735675977154e-11 - 2.2089479313610394832e-449j)  +/-  (5.71e-48, 4.74e-108j)
| (0.026632764296295897338 + 7.6212223931416681249e-445j)  +/-  (1.15e-40, 9.52e-101j)
| (1.9062269455788019053e-08 + 8.7959403460636822419e-448j)  +/-  (1.24e-46, 1.03e-106j)
| (4.2552200572767041804e-05 - 5.5999384474816669827e-447j)  +/-  (2.16e-46, 1.79e-106j)
| (0.072924849260167711552 - 5.4285588069625708239e-444j)  +/-  (4.1e-40, 3.41e-100j)
| (5.0237764582012856781e-14 + 2.8557414373347651502e-451j)  +/-  (6.86e-50, 5.69e-110j)
| (0.072924849260167711552 - 2.8075744915733438373e-444j)  +/-  (2.27e-40, 1.89e-100j)
| (5.0237764582012856781e-14 - 8.710792690871136403e-452j)  +/-  (1.52e-51, 1.26e-111j)
| (1.9062269455788019053e-08 - 3.9202395669163981431e-449j)  +/-  (3.4e-49, 2.82e-109j)
| (0.17213165699513021684 - 1.3442178516478668895e-443j)  +/-  (1.42e-41, 1.18e-101j)
| (0.0006534294454865725315 + 2.2173274608087309071e-445j)  +/-  (3.51e-45, 2.91e-105j)
| (0.17213165699513021684 - 1.0703630927522912972e-443j)  +/-  (4.87e-42, 4.04e-102j)
| (0.11049493902123724926 + 7.079184195894777444e-444j)  +/-  (2.86e-42, 2.38e-102j)
| (0.22323367427202379496 + 1.2357674058870206004e-443j)  +/-  (2.55e-42, 2.12e-102j)
| (4.2552200572767041804e-05 - 7.7234549485031306073e-446j)  +/-  (3.29e-46, 2.73e-106j)
| (0.11049493902123724926 + 1.085132825376232909e-443j)  +/-  (1.52e-43, 1.26e-103j)
| (1.3831431377728153432e-06 + 6.3323204110657943957e-448j)  +/-  (1.74e-48, 1.44e-108j)
| (0.0006534294454865725315 + 3.5555599033975323643e-446j)  +/-  (2.89e-47, 2.41e-107j)
| (0.005501569358053536854 - 1.7879608586845181527e-445j)  +/-  (1.48e-46, 1.22e-106j)
