Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 8 20
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Trying to find an order 8 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P2 : 8*t^11 - 596/3*t^9 + 1596*t^7 - 4914*t^5 + 10605/2*t^3 - 5355/4*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^31 - 3359843832175968298416364/2365356289365091915347*t^29 + 5396075807482523596875693962/49672482076666930222287*t^27 - 338615629034213939422960946901/71749140777407788098859*t^25 + 18567379275860563346158780812975/143498281554815576197718*t^23 - 96492572023781136168310663908825/40999509015661593199348*t^21 + 183450007534697194219496911709775/6307616771640245107592*t^19 - 40363279205729767325022504147850575/163998036062646372797392*t^17 + 465959432528072010082336333496199975/327996072125292745594784*t^15 - 278069518359491907958617208562638875/50460934173121960860736*t^13 + 1411180472218607278042279672274126625/100921868346243921721472*t^11 - 4488675124281877372533298302559870125/201843736692487843442944*t^9 + 1196634927084926705618126933082461625/57669639054996526697984*t^7 - 1180710553849397652456998867946623625/115339278109993053395968*t^5 + 516885121451999669467183496495431875/230678556219986106791936*t^3 - 68540125432790089255610669508669375/461357112439972213583872*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:
| (-3.5207882629582430588 + 5.3971085228554877667e-451j)  +/-  (8.02e-121, 8.02e-121j)
| (5.6660558723240047741 - 1.7709849641080783003e-451j)  +/-  (2.17e-121, 2.17e-121j)
| (-5.6660558723240047741 + 6.4085169322765409254e-456j)  +/-  (2.04e-121, 2.04e-121j)
| (-3.9983792244811185302 - 1.5801543225104820391e-455j)  +/-  (1.18e-120, 1.18e-120j)
| (6.3998847407772028793 - 2.8493567569466820524e-457j)  +/-  (2.99e-122, 2.99e-122j)
| (-2.6414479718130762063 + 6.6336317323081372995e-459j)  +/-  (2.61e-121, 2.61e-121j)
| (3.9983792244811185302 - 8.9297292996552922006e-460j)  +/-  (1.12e-120, 1.12e-120j)
| (1.2247448713915890491 + 1.1605924207433862306e-467j)  +/-  (1.54e-123, 1.54e-123j)
| (-6.3998847407772028793 + 1.7661923993834281205e-468j)  +/-  (2.76e-122, 2.76e-122j)
| (-3.0684348235062227733 + 7.4245728572978460265e-466j)  +/-  (5.29e-121, 5.29e-121j)
| (0.59841605318147530927 + 8.2683482979247072003e-471j)  +/-  (3.63e-125, 3.63e-125j)
| (2.2473897829980222564 - 7.4996663659503447624e-465j)  +/-  (1.1e-121, 1.1e-121j)
| (5.0545956009586347098 + 6.0077588935841815334e-467j)  +/-  (6.03e-121, 6.03e-121j)
| (-0.33496653021339746617 - 1.9232579353070938115e-481j)  +/-  (4.18e-126, 4.18e-126j)
| (4.5060975080215569217 - 7.5968448582639000143e-475j)  +/-  (9.19e-121, 9.19e-121j)
| (-4.5060975080215569217 - 1.1748423109641574599e-481j)  +/-  (9.05e-121, 9.05e-121j)
| (3.5207882629582430588 + 1.1817325873295945952e-484j)  +/-  (8.15e-121, 8.15e-121j)
| (0.33496653021339746617 + 1.0697829520257774587e-499j)  +/-  (3.55e-126, 3.55e-126j)
| (-1.2247448713915890491 + 1.311545097835124206e-495j)  +/-  (1.69e-123, 1.69e-123j)
| (-5.0545956009586347098 + 1.5039757936269639907e-493j)  +/-  (5.48e-121, 5.48e-121j)
| (2.6414479718130762063 - 5.2085382355101979236e-494j)  +/-  (2.66e-121, 2.66e-121j)
| (1.5704952797360713132 + 4.388767653333425021e-500j)  +/-  (9.66e-123, 9.66e-123j)
| (1.3292737075380246666e-506 + 1.9249005159684443812e-505j)  +/-  (5.98e-504, 5.98e-504j)
| (-1.5704952797360713132 + 7.1485238165462155393e-499j)  +/-  (1.06e-122, 1.06e-122j)
| (-1.8979025739610826354 + 1.9654797080141484952e-501j)  +/-  (3.96e-122, 3.96e-122j)
| (1.8979025739610826354 - 9.0080765809144584032e-502j)  +/-  (4.34e-122, 4.34e-122j)
| (0.87931959764697797308 - 6.1667437547720406864e-509j)  +/-  (2.17e-124, 2.17e-124j)
| (3.0684348235062227733 - 3.8228887820212562516e-511j)  +/-  (5.48e-121, 5.48e-121j)
| (-2.2473897829980222564 + 4.6090833423444218866e-515j)  +/-  (1.14e-121, 1.14e-121j)
| (-0.87931959764697797308 - 1.833098812391496532e-520j)  +/-  (2.27e-124, 2.27e-124j)
| (-0.59841605318147530927 + 8.920220277200873969e-521j)  +/-  (4e-125, 4e-125j)
-------------------------------------------------
The weights are:
| (1.0838265985708568313e-06 + 2.9110170520478434309e-456j)  +/-  (4.67e-38, 1.53e-97j)
| (4.226469169022273101e-15 + 3.6826435792797678298e-463j)  +/-  (5.15e-45, 1.69e-104j)
| (4.226469169022273101e-15 - 1.556007831158657331e-462j)  +/-  (7.51e-45, 2.47e-104j)
| (3.1609310509441943207e-08 + 1.0948732967057736521e-457j)  +/-  (4.44e-40, 1.46e-99j)
| (7.7644167578883331338e-19 - 2.4810826275957775542e-465j)  +/-  (4.4e-47, 1.45e-106j)
| (0.00021715076230543381016 + 4.2317714170473068275e-455j)  +/-  (2.47e-36, 8.12e-96j)
| (3.1609310509441943207e-08 - 6.9615859659080370499e-459j)  +/-  (3.16e-42, 1.04e-101j)
| (0.044481385621128847499 + 1.3385921821042182813e-453j)  +/-  (1.58e-30, 5.2e-90j)
| (7.7644167578883331338e-19 + 8.574768490825077722e-465j)  +/-  (3.09e-47, 1.02e-106j)
| (2.0232543534503754413e-05 - 1.1381763509920896686e-455j)  +/-  (4.56e-38, 1.5e-97j)
| (0.095370664742481130158 + 7.3395450026998150917e-453j)  +/-  (1.06e-31, 3.47e-91j)
| (0.0013471469565227679705 - 3.7566881227922455582e-455j)  +/-  (1.63e-37, 5.37e-97j)
| (2.6008512932958704308e-12 - 1.7113377183433606765e-461j)  +/-  (5.73e-45, 1.88e-104j)
| (0.15446510655576585012 - 1.081724989609428628e-452j)  +/-  (5.32e-34, 1.75e-93j)
| (4.5065599115684821853e-10 + 4.268043793692729069e-460j)  +/-  (7.36e-44, 2.42e-103j)
| (4.5065599115684821853e-10 - 3.4715604723193640661e-459j)  +/-  (4.49e-44, 1.48e-103j)
| (1.0838265985708568313e-06 + 8.3133195322278731373e-458j)  +/-  (1.42e-42, 4.66e-102j)
| (0.15446510655576585012 - 8.9381520733873762942e-453j)  +/-  (1.68e-35, 5.52e-95j)
| (0.044481385621128847499 + 2.766185389977493413e-453j)  +/-  (6.92e-37, 2.27e-96j)
| (2.6008512932958704308e-12 + 9.5376872032488701291e-461j)  +/-  (1.47e-45, 4.84e-105j)
| (0.00021715076230543381016 + 6.0412942335773796724e-456j)  +/-  (4.33e-41, 1.42e-100j)
| (0.016004991112877288561 - 5.0004478983363261261e-454j)  +/-  (1.74e-38, 5.73e-98j)
| (0.1965496921139127001 + 9.0495272764630471354e-453j)  +/-  (4.95e-36, 1.63e-95j)
| (0.016004991112877288561 - 1.3050918821064861407e-453j)  +/-  (4.11e-39, 1.35e-98j)
| (0.0050719932375344830764 + 5.4782684609407550953e-454j)  +/-  (4.64e-40, 1.53e-99j)
| (0.0050719932375344830764 + 1.6411813676438823623e-454j)  +/-  (5.14e-40, 1.69e-99j)
| (0.084745366521723195011 - 3.6845362251265476339e-453j)  +/-  (2.59e-38, 8.5e-98j)
| (2.0232543534503754413e-05 - 7.818024610518925969e-457j)  +/-  (8.84e-43, 2.91e-102j)
| (0.0013471469565227679705 - 1.7011009540467747288e-454j)  +/-  (3.23e-41, 1.06e-100j)
| (0.084745366521723195011 - 6.136917107716182293e-453j)  +/-  (1.05e-39, 3.51e-99j)
| (0.095370664742481130158 + 1.0344584966044168954e-452j)  +/-  (2.3e-39, 7.23e-99j)
