Starting with polynomial:
P : t
Extension levels are: 1 12 14
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P2 : t^13 - 13/4*t^11 + 65/16*t^9 - 39/16*t^7 + 91/128*t^5 - 91/1024*t^3 + 13/4096*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^27 - 7*t^25 + 349/16*t^23 - 319/8*t^21 + 12145/256*t^19 - 9861/256*t^17 + 22287/1024*t^15 - 2193/256*t^13 + 75803/32768*t^11 - 13585/32768*t^9 + 48763/1048576*t^7 - 1547/524288*t^5 + 1469/16777216*t^3 - 13/16777216*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:   27 out of 27
Indefinite weights: 0 out of 27
Negative weights:   0 out of 27
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.9927088740980539928 - 4.4136136949626717484e-439j)  +/-  (2.05e-118, 2.05e-118j)
| (-0.82298386589365639458 - 2.2968559337645471001e-454j)  +/-  (8.27e-120, 8.27e-120j)
| (-0.8854560256532098959 + 4.3465537923574901361e-454j)  +/-  (2.7e-119, 2.7e-119j)
| (1 - 1.3227653973774476828e-451j)  +/-  (1.15e-118, 1.15e-118j)
| (0.93501624268541482344 - 5.615236548299900128e-462j)  +/-  (6.53e-119, 6.53e-119j)
| (0.97094181742605202716 + 4.3927514398732729355e-474j)  +/-  (1.27e-118, 1.27e-118j)
| (-0.12053668025532305335 + 1.681699300809734239e-485j)  +/-  (4.9e-127, 4.9e-127j)
| (-0.93501624268541482344 + 9.901331712461989384e-477j)  +/-  (6.98e-119, 6.98e-119j)
| (-0.97094181742605202716 + 8.0520419918177347509e-476j)  +/-  (1.65e-118, 1.65e-118j)
| (-1 - 2.9130180747639851382e-478j)  +/-  (1.08e-118, 1.08e-118j)
| (0.8854560256532098959 - 1.1290347806422194973e-485j)  +/-  (2.64e-119, 2.64e-119j)
| (-0.35460488704253562597 + 1.6135324328171406578e-495j)  +/-  (1.84e-124, 1.84e-124j)
| (-0.9927088740980539928 - 1.8873552701470973436e-491j)  +/-  (1.85e-118, 1.85e-118j)
| (-0.74851074817110109863 + 9.4702155293588730498e-496j)  +/-  (1.63e-120, 1.63e-120j)
| (0.46472317204376854566 - 1.9514951539733498873e-494j)  +/-  (3.28e-123, 3.28e-123j)
| (0.74851074817110109863 - 1.3110102684638646536e-493j)  +/-  (1.77e-120, 1.77e-120j)
| (0.82298386589365639458 - 6.579198433866808818e-497j)  +/-  (7.61e-120, 7.61e-120j)
| (0.35460488704253562597 - 1.1238020868918700199e-501j)  +/-  (1.59e-124, 1.59e-124j)
| (-0.66312265824079520238 - 1.3508992244885778437e-502j)  +/-  (2.74e-121, 2.74e-121j)
| (-0.23931566428755776715 - 3.8824831548618008097e-507j)  +/-  (1.14e-125, 1.14e-125j)
| (0.23931566428755776715 + 1.5552921377894270593e-503j)  +/-  (1.02e-125, 1.02e-125j)
| (0.66312265824079520238 - 8.268614726764793398e-504j)  +/-  (2.47e-121, 2.47e-121j)
| (0.12053668025532305335 - 4.121283409486675374e-510j)  +/-  (4.16e-127, 4.16e-127j)
| (-0.56806474673115580251 - 3.7813631204383574376e-509j)  +/-  (3.18e-122, 3.18e-122j)
| (-0.46472317204376854566 - 7.7811610015348032959e-509j)  +/-  (3.08e-123, 3.08e-123j)
| (-4.4550573877603728182e-511 + 1.0857359764545566206e-510j)  +/-  (3.17e-509, 3.17e-509j)
| (0.56806474673115580251 - 7.0409971332039804517e-511j)  +/-  (3.42e-122, 3.42e-122j)
-------------------------------------------------
The weights are:
| (0.038461538461538461538 - 5.7992846575810428083e-439j)  +/-  (1.53e-28, 4.31e-85j)
| (0.038461538461538461538 + 9.3492896206601220515e-441j)  +/-  (3.4e-29, 9.57e-86j)
| (0.038461538461538461538 - 9.0383103691062400883e-441j)  +/-  (3.19e-29, 8.99e-86j)
| (0.019230769230769230769 + 1.1641163187015859645e-438j)  +/-  (6.16e-29, 1.73e-85j)
| (0.038461538461538461538 + 2.9423926197608852419e-439j)  +/-  (4.84e-30, 1.36e-86j)
| (0.038461538461538461538 - 7.7986829106522868344e-439j)  +/-  (2.03e-29, 5.71e-86j)
| (0.038461538461538461538 - 1.5248601013433169205e-440j)  +/-  (4.95e-33, 1.39e-89j)
| (0.038461538461538461538 + 8.8059428911930618236e-441j)  +/-  (2.43e-31, 6.85e-88j)
| (0.038461538461538461538 - 8.6448355410593698247e-441j)  +/-  (4.08e-32, 1.15e-88j)
| (0.019230769230769230769 - 4.2593871861981756021e-441j)  +/-  (4.35e-33, 1.23e-89j)
| (0.038461538461538461538 - 1.5827493194311757405e-439j)  +/-  (4.53e-34, 1.27e-90j)
| (0.038461538461538461538 - 1.2599468496441405955e-440j)  +/-  (1.65e-35, 4.65e-92j)
| (0.038461538461538461538 + 8.5500581949248181277e-441j)  +/-  (7.07e-33, 1.99e-89j)
| (0.038461538461538461538 - 9.7491649365805535561e-441j)  +/-  (1.92e-34, 5.39e-91j)
| (0.038461538461538461538 + 3.2151320049510717732e-440j)  +/-  (1.29e-36, 3.63e-93j)
| (0.038461538461538461538 - 6.9515018691793299256e-440j)  +/-  (2.79e-36, 7.85e-93j)
| (0.038461538461538461538 + 1.0001730132703715361e-439j)  +/-  (9.34e-36, 2.63e-92j)
| (0.038461538461538461538 - 2.660293248855060582e-440j)  +/-  (2.2e-37, 6.2e-94j)
| (0.038461538461538461538 + 1.0251910871835502196e-440j)  +/-  (5.85e-37, 1.65e-93j)
| (0.038461538461538461538 + 1.3778489599368444144e-440j)  +/-  (1.42e-37, 4e-94j)
| (0.038461538461538461538 + 2.2531975424337586466e-440j)  +/-  (3e-38, 8.44e-95j)
| (0.038461538461538461538 + 5.1505301106600023217e-440j)  +/-  (3.96e-38, 1.12e-94j)
| (0.038461538461538461538 - 1.9463401158801321563e-440j)  +/-  (1.19e-38, 3.35e-95j)
| (0.038461538461538461538 - 1.0876296896467301991e-440j)  +/-  (6.46e-39, 1.82e-95j)
| (0.038461538461538461538 + 1.164749830583932035e-440j)  +/-  (4.52e-39, 1.27e-95j)
| (0.038461538461538461538 + 1.7100116389849209417e-440j)  +/-  (2.35e-39, 6.65e-96j)
| (0.038461538461538461538 - 3.9975678913948466672e-440j)  +/-  (1.47e-39, 4.01e-96j)
