Starting with polynomial:
P : t^3 - 3*t
Extension levels are: 3 10 20
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P2 : t^13 - 629/8*t^11 + 17435/8*t^9 - 105435/4*t^7 + 557865/4*t^5 - 2248785/8*t^3 + 1133055/8*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 3868363632647762340929349819043/10049566913423152616959022136*t^31 + 8430026763398522960166747363195775/130644369874500984020467287768*t^29 - 5693552740397442351951872612613544795/914510589121506888143271014376*t^27 + 117392946727225262907783260017500713685/304836863040502296047757004792*t^25 - 4909232891777820073049782510579590086655/304836863040502296047757004792*t^23 + 142672155640543737221615785127867356682415/304836863040502296047757004792*t^21 - 416814309165456309181813912986235084703475/43548123291500328006822429256*t^19 + 6008630303490478509874493928882027275380575/43548123291500328006822429256*t^17 - 60603219722255771330292820339073608766069175/43548123291500328006822429256*t^15 + 32346812700406633522862432330061087692360475/3349855637807717538986340712*t^13 - 150132604097588143758417392423343076769461425/3349855637807717538986340712*t^11 + 40584555899455401993657516550893544133046375/304532330709792503544212792*t^9 - 72460347750105257840049530972187649118992125/304532330709792503544212792*t^7 + 70489255901535674454493913527506678610924125/304532330709792503544212792*t^5 - 32179665974723661869792522467500363649815375/304532330709792503544212792*t^3 + 5000311452788290134073272393910186207099875/304532330709792503544212792*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:   33 out of 33
Indefinite weights: 0 out of 33
Negative weights:   0 out of 33
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (7.2922136383168481205 + 6.3079670027491648076e-474j)  +/-  (1.58e-120, 1.58e-120j)
| (8.1517740598597369655 + 1.5406972996011393937e-479j)  +/-  (4.96e-121, 4.96e-121j)
| (-6.525259598602038117 + 1.0963110059651522142e-480j)  +/-  (3.68e-120, 3.68e-120j)
| (6.525259598602038117 + 2.5241121354215464188e-479j)  +/-  (3.19e-120, 3.19e-120j)
| (-9.1858935929906012243 - 1.6056862915289903794e-484j)  +/-  (6.4e-122, 6.4e-122j)
| (9.1858935929906012243 + 1.8977484265778632071e-483j)  +/-  (6.09e-122, 6.09e-122j)
| (-5.8238536767427603773 + 6.1402842396844752565e-482j)  +/-  (4.88e-120, 4.88e-120j)
| (-2.6308380841127442917 + 9.7147140377618238776e-484j)  +/-  (1.65e-121, 1.65e-121j)
| (-4.6096758921816875609 - 4.0927692516328026696e-482j)  +/-  (4.17e-120, 4.17e-120j)
| (-7.2922136383168481205 + 5.8757172745345641856e-483j)  +/-  (1.55e-120, 1.55e-120j)
| (1.1876639192106980072 - 6.6110150096122734407e-486j)  +/-  (3.72e-124, 3.72e-124j)
| (-8.1517740598597369655 + 5.9645744439150220122e-484j)  +/-  (5.13e-121, 5.13e-121j)
| (4.0934966078711924231 - 5.5051652297137531675e-481j)  +/-  (2.8e-120, 2.8e-120j)
| (5.8238536767427603773 - 2.3663250498897092019e-488j)  +/-  (4.8e-120, 4.8e-120j)
| (5.1825559315457011203 + 1.4807475246643533426e-493j)  +/-  (5.82e-120, 5.82e-120j)
| (2.6308380841127442917 + 3.6504476880501305224e-501j)  +/-  (1.66e-121, 1.66e-121j)
| (-2.2419602587188745961 - 9.4966168314874873326e-507j)  +/-  (3.21e-122, 3.21e-122j)
| (-5.1825559315457011203 + 1.1710960693313229587e-504j)  +/-  (5.43e-120, 5.43e-120j)
| (-0.85995874045067267595 - 4.4984436841741241869e-509j)  +/-  (8.63e-125, 8.63e-125j)
| (-4.0934966078711924231 - 1.5148531028464170327e-504j)  +/-  (2.59e-120, 2.59e-120j)
| (3.5773982809904283695 + 1.6085954854539505947e-504j)  +/-  (1.18e-120, 1.18e-120j)
| (1.7320508075688772935 - 5.3684653555764984441e-512j)  +/-  (3.32e-123, 3.32e-123j)
| (4.6096758921816875609 - 6.2908749772927758927e-517j)  +/-  (4.54e-120, 4.54e-120j)
| (-1.1876639192106980072 + 1.3283748217788620145e-528j)  +/-  (3.55e-124, 3.55e-124j)
| (-0.55300446288863479767 + 1.3907118970881515388e-529j)  +/-  (9.39e-126, 9.39e-126j)
| (-3.5773982809904283695 + 8.6435768683931038925e-525j)  +/-  (1.29e-120, 1.29e-120j)
| (0.55300446288863479767 + 4.0983471088708645575e-529j)  +/-  (9.78e-126, 9.78e-126j)
| (3.0590181841417991132 + 7.1120771976785556456e-527j)  +/-  (4.96e-121, 4.96e-121j)
| (-3.0590181841417991132 + 2.9802026812604132804e-535j)  +/-  (4.17e-121, 4.17e-121j)
| (-1.7320508075688772935 - 3.2785922231419097894e-539j)  +/-  (3.26e-123, 3.26e-123j)
| (-4.2371080792005404329e-542 + 2.4299302280818421898e-542j)  +/-  (1.61e-540, 1.61e-540j)
| (2.2419602587188745961 - 1.8372363058752642189e-538j)  +/-  (3.32e-122, 3.32e-122j)
| (0.85995874045067267595 + 2.0135072887707961325e-544j)  +/-  (8.18e-125, 8.18e-125j)
-------------------------------------------------
The weights are:
| (9.1261616919179749675e-13 - 2.6614929725958717437e-485j)  +/-  (1.72e-33, 2.9e-93j)
| (1.3707281068125487991e-15 - 1.1910709192594049209e-487j)  +/-  (3.44e-35, 5.79e-95j)
| (1.6572302740173285848e-10 + 1.2615727343708885051e-485j)  +/-  (4.98e-34, 8.38e-94j)
| (1.6572302740173285848e-10 + 2.2725496539566502018e-484j)  +/-  (1.07e-32, 1.8e-92j)
| (2.258952335436588882e-19 - 3.5581440585422620094e-491j)  +/-  (4.09e-39, 6.87e-99j)
| (2.258952335436588882e-19 + 3.0961882477114148683e-490j)  +/-  (1.08e-37, 1.81e-97j)
| (1.1565547781149712628e-08 - 2.6513787201431732105e-484j)  +/-  (3.48e-33, 5.86e-93j)
| (0.0045481617363706090372 - 2.3660527147971459985e-479j)  +/-  (1.51e-25, 2.54e-85j)
| (5.213319043301180724e-06 - 3.9429083932027548853e-482j)  +/-  (2.83e-31, 4.76e-91j)
| (9.1261616919179749675e-13 - 3.9470553622726345487e-487j)  +/-  (2.54e-36, 4.27e-96j)
| (0.10340927155443487085 + 4.2412773027379069699e-478j)  +/-  (7.03e-21, 1.18e-80j)
| (1.3707281068125487991e-15 + 6.6290024585948992298e-489j)  +/-  (4.95e-38, 8.32e-98j)
| (4.649761900231882578e-05 + 9.062067182516457459e-481j)  +/-  (3.92e-33, 6.59e-93j)
| (1.1565547781149712628e-08 - 2.3682223936526106978e-483j)  +/-  (5.77e-36, 9.71e-96j)
| (3.5736203533697133397e-07 + 2.3328946015905424101e-482j)  +/-  (3.09e-35, 5.2e-95j)
| (0.0045481617363706090372 - 5.0368567589533174301e-479j)  +/-  (4.51e-31, 7.58e-91j)
| (0.014721994268910193954 + 4.6873219272441792857e-479j)  +/-  (6.18e-30, 1.04e-89j)
| (3.5736203533697133397e-07 + 3.9453954053722782321e-483j)  +/-  (1.22e-35, 2.05e-95j)
| (0.036089113730312813099 - 5.9941504914046848589e-478j)  +/-  (1.09e-27, 1.83e-87j)
| (4.649761900231882578e-05 + 2.5457542433271284937e-481j)  +/-  (2.4e-34, 4.04e-94j)
| (0.0003487362361618940415 - 3.901741647284397865e-480j)  +/-  (3.25e-34, 5.45e-94j)
| (0.048313760304841967277 - 1.4807736982718350141e-478j)  +/-  (3.06e-31, 5.13e-91j)
| (5.213319043301180724e-06 - 1.7492310997697665317e-481j)  +/-  (1.71e-35, 2.88e-95j)
| (0.10340927155443487085 + 3.0532319744835923389e-478j)  +/-  (1.26e-30, 2.12e-90j)
| (0.17829413386947098476 + 5.3767852457607153454e-478j)  +/-  (6.86e-30, 1.16e-89j)
| (0.0003487362361618940415 - 1.333412855208414e-480j)  +/-  (8.32e-35, 1.4e-94j)
| (0.17829413386947098476 + 6.2592047417443666641e-478j)  +/-  (1.26e-31, 2.1e-91j)
| (0.0018317554889132691844 + 1.6815897271287335606e-479j)  +/-  (2.27e-34, 3.72e-94j)
| (0.0018317554889132691844 + 6.8768559290627455429e-480j)  +/-  (3.72e-34, 6.29e-94j)
| (0.048313760304841967277 - 9.1235275424217235234e-479j)  +/-  (7.39e-33, 1.26e-92j)
| (0.2247819855566352903 - 3.7539245983094241964e-478j)  +/-  (3.06e-32, 5.25e-92j)
| (0.014721994268910193954 + 8.8490652917098467372e-479j)  +/-  (9.06e-34, 1.43e-93j)
| (0.036089113730312813099 - 7.5969343207842377516e-478j)  +/-  (1.55e-32, 2.7e-92j)
