Starting with polynomial:
P : t^5 - 10*t^3 + 15*t
Extension levels are: 5 8 18
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : t^13 - 170/3*t^11 + 3251/3*t^9 - 8652*t^7 + 29631*t^5 - 41790*t^3 + 19215*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 14560699451931256481266962557/40215459959405427123553269*t^29 + 208192419144785290304382557497/3655950905400493374868479*t^27 - 756953499128921200244292865928631/147456686517819899453028653*t^25 + 217319278577776516924500879491609781/737283432589099497265143265*t^23 - 1671619897514945905401784062267609201/147456686517819899453028653*t^21 + 16964518509749657889881901613814615919/56714110199161499789626405*t^19 - 4024742055578418935400646610482615069767/737283432589099497265143265*t^17 + 50609363231860838759829946716039534848451/737283432589099497265143265*t^15 - 6648683945405770262471749247986651105227/11342822039832299957925281*t^13 + 3413745531139248608387179413785123018943/1031165639984754541629571*t^11 - 12232006451373305981873636314656387158043/1031165639984754541629571*t^9 + 26081017691726688029653205683168621040853/1031165639984754541629571*t^7 - 29913211028780989772553228386825592222789/1031165639984754541629571*t^5 + 15504330826220252140491480150362995600035/1031165639984754541629571*t^3 - 2442872768781915414820215587646931237335/1031165639984754541629571*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:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.5450011489732884727 + 7.2481808092747136712e-428j)  +/-  (1.42e-120, 1.42e-120j)
| (-7.1136157079168271436 + 1.6220898989149000249e-428j)  +/-  (2.05e-120, 2.05e-120j)
| (8.8861430744562861899 + 1.7895231692204397861e-439j)  +/-  (8.64e-122, 8.64e-122j)
| (3.3627546290321053626 + 2.8537470302102751522e-439j)  +/-  (2.99e-121, 2.99e-121j)
| (-7.8917119609037985607 - 1.0676062951173609325e-436j)  +/-  (5.91e-121, 5.91e-121j)
| (2.370086316268142549 - 1.7700189328846464887e-444j)  +/-  (1.93e-122, 1.93e-122j)
| (-2.8569700138728056542 + 3.219609632858201315e-444j)  +/-  (8.81e-122, 8.81e-122j)
| (-8.8861430744562861899 - 7.244857384510822624e-443j)  +/-  (7.77e-122, 7.77e-122j)
| (7.1136157079168271436 - 7.2324554061644482685e-443j)  +/-  (1.94e-120, 1.94e-120j)
| (2.8569700138728056542 + 1.2902013384339343142e-444j)  +/-  (8.5e-122, 8.5e-122j)
| (3.9309600114055574643 - 1.1554187952660081512e-442j)  +/-  (7.19e-121, 7.19e-121j)
| (5.1842688974446196437 - 2.9739336821428669081e-442j)  +/-  (2.69e-120, 2.69e-120j)
| (1.3556261799742658658 + 2.7487230225182901328e-447j)  +/-  (4.57e-124, 4.57e-124j)
| (-2.370086316268142549 - 1.6529931440951103413e-444j)  +/-  (2.04e-122, 2.04e-122j)
| (-3.3627546290321053626 + 1.2704764122800715416e-442j)  +/-  (2.77e-121, 2.77e-121j)
| (1.8550647122034955328 - 6.7623972899069178674e-446j)  +/-  (3.23e-123, 3.23e-123j)
| (7.8917119609037985607 - 7.1578070576855297435e-444j)  +/-  (6.71e-121, 6.71e-121j)
| (-3.9309600114055574643 + 5.293510025425656525e-442j)  +/-  (6.31e-121, 6.31e-121j)
| (-0.9467370109606977334 - 6.5320862408331357542e-454j)  +/-  (5.87e-125, 5.87e-125j)
| (-1.3556261799742658658 - 1.5149089118975149504e-452j)  +/-  (4.45e-124, 4.45e-124j)
| (1.8239440459658021503e-458 - 2.5920498646645725766e-458j)  +/-  (9.83e-457, 9.83e-457j)
| (0.51604303696913910798 - 1.3313715699915507122e-454j)  +/-  (5.15e-126, 5.15e-126j)
| (-6.4596096547808109974 + 1.4170129378157240209e-448j)  +/-  (3.64e-120, 3.64e-120j)
| (-1.8550647122034955328 - 2.4658045606942880369e-462j)  +/-  (3.08e-123, 3.08e-123j)
| (-4.5450011489732884727 - 1.0429508938022660464e-458j)  +/-  (1.41e-120, 1.41e-120j)
| (5.8291542710901158007 - 2.2992668227042248873e-467j)  +/-  (3.43e-120, 3.43e-120j)
| (0.9467370109606977334 + 3.8475641576550868061e-476j)  +/-  (6.26e-125, 6.26e-125j)
| (6.4596096547808109974 - 2.9912271098561841485e-471j)  +/-  (3.53e-120, 3.53e-120j)
| (-5.1842688974446196437 + 1.5792394018029583991e-475j)  +/-  (2.62e-120, 2.62e-120j)
| (-0.51604303696913910798 + 6.2356884186990937213e-492j)  +/-  (5.15e-126, 5.15e-126j)
| (-5.8291542710901158007 + 5.880366443597831133e-493j)  +/-  (3.62e-120, 3.62e-120j)
-------------------------------------------------
The weights are:
| (8.2097150069527193094e-06 - 1.8116053978018071796e-432j)  +/-  (4.47e-32, 2.41e-91j)
| (2.8716270238524123759e-12 - 5.7737858785980656585e-438j)  +/-  (2.4e-38, 1.3e-97j)
| (3.3177961699321545724e-18 + 2.8258834417178986251e-441j)  +/-  (1.72e-41, 9.29e-101j)
| (0.00075046701771312638609 - 1.6108912190107356278e-431j)  +/-  (3.2e-29, 1.73e-88j)
| (1.0353126064146174029e-14 + 1.4685194166418579054e-439j)  +/-  (5.78e-40, 3.12e-99j)
| (0.012052477087118081332 - 8.4088515449947260404e-431j)  +/-  (2.04e-26, 1.1e-85j)
| (0.0032529807987924527137 + 9.3422786309984493692e-432j)  +/-  (7.3e-30, 3.94e-89j)
| (3.3177961699321545724e-18 - 9.1781828279558369969e-442j)  +/-  (7.79e-42, 4.21e-101j)
| (2.8716270238524123759e-12 + 2.7183238525923976347e-437j)  +/-  (1.53e-39, 8.26e-99j)
| (0.0032529807987924527137 + 4.1008591760477230035e-431j)  +/-  (3.22e-29, 1.74e-88j)
| (0.00010474510405421269945 + 6.0365963080793355322e-432j)  +/-  (1.93e-32, 1.04e-91j)
| (3.7575093070999641843e-07 - 1.3151111811574023013e-433j)  +/-  (7.64e-36, 4.13e-95j)
| (0.073271003559178610325 - 3.1622617876087244667e-430j)  +/-  (4.51e-26, 2.44e-85j)
| (0.012052477087118081332 - 2.6425614934938736106e-431j)  +/-  (1.57e-31, 8.47e-91j)
| (0.00075046701771312638609 - 2.405151249687057543e-432j)  +/-  (1.1e-34, 5.93e-94j)
| (0.037166144911795968764 + 1.6171496947117580126e-430j)  +/-  (3.12e-29, 1.68e-88j)
| (1.0353126064146174029e-14 - 5.4003868519126742338e-439j)  +/-  (6.26e-42, 3.38e-101j)
| (0.00010474510405421269945 + 4.3656044591110407801e-433j)  +/-  (1.04e-36, 5.61e-96j)
| (0.097804961185288988799 + 2.9159591204559957702e-430j)  +/-  (6.9e-29, 3.73e-88j)
| (0.073271003559178610325 - 1.7085091447687572309e-430j)  +/-  (1.06e-30, 5.7e-90j)
| (0.21135949920373546605 + 3.4563604460383385445e-430j)  +/-  (2.11e-29, 1.14e-88j)
| (0.1699088743761760496 - 4.1803639474761584659e-430j)  +/-  (1.03e-29, 5.58e-89j)
| (2.1743789160486536259e-10 + 9.7204369996910715304e-437j)  +/-  (9.49e-42, 5.13e-101j)
| (0.037166144911795968764 + 6.7926917736383733239e-431j)  +/-  (7.57e-33, 4.09e-92j)
| (8.2097150069527193094e-06 - 6.5308012593165948744e-434j)  +/-  (1.09e-38, 5.88e-98j)
| (1.067175723856318507e-08 + 8.1686450482725876438e-435j)  +/-  (2.55e-40, 1.38e-99j)
| (0.097804961185288988799 + 4.451710922103991045e-430j)  +/-  (1.19e-33, 6.43e-93j)
| (2.1743789160486536259e-10 - 5.6509906373945548561e-436j)  +/-  (2.06e-41, 1.11e-100j)
| (3.7575093070999641843e-07 + 8.6116482425181648062e-435j)  +/-  (6.16e-41, 3.33e-100j)
| (0.1699088743761760496 - 3.3273418465993562015e-430j)  +/-  (6.94e-36, 3.63e-95j)
| (1.067175723856318507e-08 - 1.0056311384464586489e-435j)  +/-  (6.76e-42, 3.66e-101j)
