Starting with polynomial:
P : 8*t^3 - 4*t
Extension levels are: 3 4 8 16
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 8*t^3 - 4*t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : 8*t^7 - 12*t^5 + 5*t^3 - 1/2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P3 : 8*t^15 - 28*t^13 + 39*t^11 - 55/2*t^9 + 165/16*t^7 - 63/32*t^5 + 21/128*t^3 - 1/256*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^31 - 60*t^29 + 203*t^27 - 819/2*t^25 + 8775/16*t^23 - 16445/32*t^21 + 44275/128*t^19 - 43263/256*t^17 + 245157/4096*t^15 - 124355/8192*t^13 + 88179/32768*t^11 - 20995/65536*t^9 + 12597/524288*t^7 - 1071/1048576*t^5 + 85/4194304*t^3 - 1/8388608*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:
| (-0.99518472667219688624 + 5.4877938777413870482e-430j)  +/-  (2.2e-118, 2.2e-118j)
| (-0.95694033573220886494 + 3.001522727960421194e-443j)  +/-  (7.27e-118, 7.27e-118j)
| (-0.92387953251128675613 - 4.7097553998429918863e-453j)  +/-  (6.6e-118, 6.6e-118j)
| (0.99518472667219688624 - 4.8409128966758110484e-454j)  +/-  (2.43e-118, 2.43e-118j)
| (0.88192126434835502971 - 8.4093186385858844189e-460j)  +/-  (3.27e-118, 3.27e-118j)
| (0.92387953251128675613 - 1.7094035855458372614e-459j)  +/-  (5.73e-118, 5.73e-118j)
| (0.98078528040323044913 + 5.303911842488698588e-460j)  +/-  (7.09e-118, 7.09e-118j)
| (-0.88192126434835502971 - 2.6423115039676812305e-464j)  +/-  (4.17e-118, 4.17e-118j)
| (-0.98078528040323044913 - 2.7627203868076479808e-471j)  +/-  (7.15e-118, 7.15e-118j)
| (0.95694033573220886494 - 2.5859592061101226064e-476j)  +/-  (7.71e-118, 7.71e-118j)
| (0.83146961230254523708 + 1.5322078023601115968e-477j)  +/-  (1.6e-118, 1.6e-118j)
| (0.29028467725446236764 - 1.5913991460447878486e-484j)  +/-  (1.71e-124, 1.71e-124j)
| (-0.7071067811865475244 - 6.2493557925283922644e-478j)  +/-  (1.14e-119, 1.14e-119j)
| (-0.83146961230254523708 + 5.9447109819437277605e-480j)  +/-  (1.85e-118, 1.85e-118j)
| (-2.3965686021621326159e-488 + 5.2294025021769029544e-489j)  +/-  (7.6e-487, 7.6e-487j)
| (0.7071067811865475244 + 4.0136806460804422169e-484j)  +/-  (1.04e-119, 1.04e-119j)
| (0.63439328416364549822 + 8.475927321525822805e-485j)  +/-  (2.06e-120, 2.06e-120j)
| (-0.098017140329560601994 + 6.8467358689799444823e-490j)  +/-  (5.09e-127, 5.09e-127j)
| (-0.77301045336273696081 - 5.7813359736300265465e-487j)  +/-  (4.52e-119, 4.52e-119j)
| (-0.38268343236508977173 + 1.150004223063013079e-491j)  +/-  (2.43e-123, 2.43e-123j)
| (0.38268343236508977173 - 3.1705289807577521085e-494j)  +/-  (2.24e-123, 2.24e-123j)
| (0.77301045336273696081 + 1.3087890013564313328e-492j)  +/-  (4.92e-119, 4.92e-119j)
| (0.098017140329560601994 - 1.0277888875227448925e-494j)  +/-  (5.26e-127, 5.26e-127j)
| (-0.47139673682599764856 + 1.3860282944499068275e-492j)  +/-  (2.97e-122, 2.97e-122j)
| (-0.55557023301960222474 - 4.9691698402635234549e-496j)  +/-  (2.63e-121, 2.63e-121j)
| (0.19509032201612826785 - 1.2559991255782280121e-496j)  +/-  (1.02e-125, 1.02e-125j)
| (0.55557023301960222474 - 1.0464004671496056119e-495j)  +/-  (2.56e-121, 2.56e-121j)
| (0.47139673682599764856 + 5.3511310874217398562e-498j)  +/-  (2.64e-122, 2.64e-122j)
| (-0.29028467725446236764 + 4.189889433394995631e-498j)  +/-  (1.5e-124, 1.5e-124j)
| (-0.63439328416364549822 + 6.891862506149390454e-498j)  +/-  (1.95e-120, 1.95e-120j)
| (-0.19509032201612826785 + 5.5008115210995093999e-505j)  +/-  (8.95e-126, 8.95e-126j)
-------------------------------------------------
The weights are:
| (0.0003002299936995242324 + 2.5600165548062659959e-431j)  +/-  (3.4e-26, 1.69e-82j)
| (0.0026332873077727306706 + 3.778577096078166003e-431j)  +/-  (1.89e-26, 9.41e-83j)
| (0.0045764565439601949312 - 3.5221347475784879389e-431j)  +/-  (1.39e-26, 6.92e-83j)
| (0.0003002299936995242324 + 8.2778617737035364607e-434j)  +/-  (3.44e-28, 1.72e-84j)
| (0.0069442151090687152384 + 2.0301688526682360833e-432j)  +/-  (2.63e-28, 1.31e-84j)
| (0.0045764565439601949312 - 1.3086925090450777639e-432j)  +/-  (2.49e-28, 1.24e-84j)
| (0.0011893823045111444355 - 3.3032307705171613437e-433j)  +/-  (1.42e-28, 7.09e-85j)
| (0.0069442151090687152384 + 3.3645820443233874602e-431j)  +/-  (3.3e-29, 1.64e-85j)
| (0.0011893823045111444355 - 4.532872172353670519e-431j)  +/-  (1.34e-28, 6.67e-85j)
| (0.0026332873077727306706 + 7.4026701691596922784e-433j)  +/-  (6.7e-29, 3.34e-85j)
| (0.0096455713692954723167 - 2.8978064638901658068e-432j)  +/-  (4.43e-30, 2.21e-86j)
| (0.028616712692227269329 + 1.2216752902386291627e-431j)  +/-  (1.73e-32, 8.62e-89j)
| (0.015625 - 2.9765131515069787511e-431j)  +/-  (1.15e-31, 5.74e-88j)
| (0.0096455713692954723167 - 3.2332327843734754374e-431j)  +/-  (1.2e-30, 5.97e-87j)
| (0.03125 - 1.7232334267516972071e-431j)  +/-  (5.79e-33, 2.89e-89j)
| (0.015625 - 5.0371384068978866008e-432j)  +/-  (3.65e-32, 1.82e-88j)
| (0.018673286281502004185 + 6.2884467912268382568e-432j)  +/-  (1.33e-32, 6.61e-89j)
| (0.030949770006300475768 + 1.8931352508005542395e-431j)  +/-  (8.02e-34, 4e-90j)
| (0.012576713718497995815 + 3.1064988541832782412e-431j)  +/-  (8.78e-33, 4.38e-89j)
| (0.026673543456039805069 - 2.3898546800839653801e-431j)  +/-  (1.01e-34, 5.06e-91j)
| (0.026673543456039805069 - 1.0623578715833518133e-431j)  +/-  (2.35e-34, 1.17e-90j)
| (0.012576713718497995815 + 3.9033254544399160939e-432j)  +/-  (3.44e-33, 1.71e-89j)
| (0.030949770006300475768 + 1.553655948502110765e-431j)  +/-  (1.23e-34, 6.15e-91j)
| (0.024305784890931284762 + 2.546548223782790196e-431j)  +/-  (1.34e-35, 6.68e-92j)
| (0.021604428630704527683 - 2.6969231652626243438e-431j)  +/-  (1.09e-35, 5.45e-92j)
| (0.030060617695488855565 - 1.3859525488014671617e-431j)  +/-  (2.3e-35, 1.14e-91j)
| (0.021604428630704527683 - 7.6453504424226204895e-432j)  +/-  (7.37e-36, 3.67e-92j)
| (0.024305784890931284762 + 9.0949695491172767535e-432j)  +/-  (5.53e-36, 2.76e-92j)
| (0.028616712692227269329 + 2.2278707576091016068e-431j)  +/-  (4.35e-37, 2.19e-93j)
| (0.018673286281502004185 + 2.8402876027337139178e-431j)  +/-  (2.89e-37, 1.53e-93j)
| (0.030060617695488855565 - 2.0618376130420595342e-431j)  +/-  (4.41e-37, 2.17e-93j)
