Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 4 7
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P2 : 1/2*t^6 - 162/13*t^5 + 101*t^4 - 4208/13*t^3 + 5436/13*t^2 - 2928/13*t + 552/13
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^13 - 504112280487697156627091/9075455013440231194662*t^12 + 998316189656555410719133/387839957839326119430*t^11 - 2965739118746776745361636253/45377275067201155973310*t^10 + 45607911258484289158420733437/45377275067201155973310*t^9 - 49287488556967664430621524593/5041919451911239552590*t^8 + 922918877240621604852845252953/15125758355733718657770*t^7 - 3679124253775711321498662080329/15125758355733718657770*t^6 + 509555203104173268417633885977/840319908651873258765*t^5 - 459720959095965190437388662941/504191945191123955259*t^4 + 396084508837739379956824010996/504191945191123955259*t^3 - 20165652924904405596774307428/56021327243458217251*t^2 + 12744533040892287406126521992/168063981730374651753*t - 800328217570399243256211128/168063981730374651753
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 1
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   13 out of 13
Indefinite weights: 0 out of 13
Negative weights:   0 out of 13
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (12.486507079040894342 + 2.3217516362596995584e-149j)  +/-  (1.18e-57, 1.18e-57j)
| (22.500032886385026707 - 1.0076316655585728532e-155j)  +/-  (4.94e-58, 4.94e-58j)
| (16.830324996744756898 + 4.5806612309388476779e-158j)  +/-  (1.01e-57, 1.01e-57j)
| (3.4142135623730950488 + 3.3221994786004991098e-161j)  +/-  (6.65e-59, 6.65e-59j)
| (30.394595499887096545 - 3.2587599227571943537e-167j)  +/-  (1.03e-58, 1.03e-58j)
| (0.47193845768537280597 + 1.6082378507136507694e-174j)  +/-  (6.82e-61, 6.82e-61j)
| (9.1914231833294223063 + 6.0119969634738512225e-179j)  +/-  (1.2e-57, 1.2e-57j)
| (5.1643048632572456383 - 1.028981653339461434e-180j)  +/-  (3.16e-58, 3.16e-58j)
| (6.9239565457104964806 + 8.1730467104761813966e-182j)  +/-  (9.11e-58, 9.11e-58j)
| (1.0406748406401594478 - 1.2109630364634605805e-183j)  +/-  (2.61e-60, 2.61e-60j)
| (0.5857864376269049512 - 2.817159953897363032e-191j)  +/-  (1.71e-60, 1.71e-60j)
| (1.9864608100954065734 + 2.6008212876355223486e-196j)  +/-  (1.29e-59, 1.29e-59j)
| (0.10333586915048290461 - 5.9145334839812965756e-202j)  +/-  (4.19e-63, 4.19e-63j)
-------------------------------------------------
The weights are:
| (1.4360806063836109719e-05 - 2.5832093798703533326e-154j)  +/-  (2.23e-20, 7.36e-49j)
| (1.105801493940122061e-09 + 4.5930562141800100709e-158j)  +/-  (8.19e-24, 2.7e-52j)
| (2.418174482233255538e-07 - 3.7581437065021230652e-156j)  +/-  (2.65e-22, 8.74e-51j)
| (0.053789997852160894351 - 3.5715684442193436018e-152j)  +/-  (4.82e-17, 1.59e-45j)
| (6.1552089352728232106e-13 - 2.5672227794183184776e-160j)  +/-  (6.35e-26, 2.09e-54j)
| (0.25794608935243313328 - 1.5398828655958843729e-150j)  +/-  (5.41e-17, 1.76e-45j)
| (0.00028331653567148541654 + 1.3609032382147986649e-153j)  +/-  (1.51e-20, 4.96e-49j)
| (0.010224026285220476685 + 1.3919975397099440997e-152j)  +/-  (1.68e-19, 5.56e-48j)
| (0.0018108590347737448755 - 5.2924350544303309344e-153j)  +/-  (4.31e-20, 1.42e-48j)
| (0.24744442923938703477 - 4.7973890567385943707e-151j)  +/-  (7.98e-18, 2.61e-46j)
| (0.031559011676511476821 + 1.8113045361295532264e-150j)  +/-  (3.12e-17, 1.01e-45j)
| (0.16434177252477916745 + 1.1569944726141654124e-151j)  +/-  (9.6e-19, 3.2e-47j)
| (0.23258589376913351207 + 1.1860706214793724327e-151j)  +/-  (2.74e-18, 8.74e-47j)
Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 4 7
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P2 : 1/2*t^6 - 162/13*t^5 + 101*t^4 - 4208/13*t^3 + 5436/13*t^2 - 2928/13*t + 552/13
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^13 - 504112280487697156627091/9075455013440231194662*t^12 + 998316189656555410719133/387839957839326119430*t^11 - 2965739118746776745361636253/45377275067201155973310*t^10 + 45607911258484289158420733437/45377275067201155973310*t^9 - 49287488556967664430621524593/5041919451911239552590*t^8 + 922918877240621604852845252953/15125758355733718657770*t^7 - 3679124253775711321498662080329/15125758355733718657770*t^6 + 509555203104173268417633885977/840319908651873258765*t^5 - 459720959095965190437388662941/504191945191123955259*t^4 + 396084508837739379956824010996/504191945191123955259*t^3 - 20165652924904405596774307428/56021327243458217251*t^2 + 12744533040892287406126521992/168063981730374651753*t - 800328217570399243256211128/168063981730374651753
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 1
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   13 out of 13
Indefinite weights: 0 out of 13
Negative weights:   0 out of 13
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (12.486507079040894342 + 2.3217516362596995584e-149j)  +/-  (1.18e-57, 1.18e-57j)
| (22.500032886385026707 - 1.0076316655585728532e-155j)  +/-  (4.94e-58, 4.94e-58j)
| (16.830324996744756898 + 4.5806612309388476779e-158j)  +/-  (1.01e-57, 1.01e-57j)
| (3.4142135623730950488 + 3.3221994786004991098e-161j)  +/-  (6.65e-59, 6.65e-59j)
| (30.394595499887096545 - 3.2587599227571943537e-167j)  +/-  (1.03e-58, 1.03e-58j)
| (0.47193845768537280597 + 1.6082378507136507694e-174j)  +/-  (6.82e-61, 6.82e-61j)
| (9.1914231833294223063 + 6.0119969634738512225e-179j)  +/-  (1.2e-57, 1.2e-57j)
| (5.1643048632572456383 - 1.028981653339461434e-180j)  +/-  (3.16e-58, 3.16e-58j)
| (6.9239565457104964806 + 8.1730467104761813966e-182j)  +/-  (9.11e-58, 9.11e-58j)
| (1.0406748406401594478 - 1.2109630364634605805e-183j)  +/-  (2.61e-60, 2.61e-60j)
| (0.5857864376269049512 - 2.817159953897363032e-191j)  +/-  (1.71e-60, 1.71e-60j)
| (1.9864608100954065734 + 2.6008212876355223486e-196j)  +/-  (1.29e-59, 1.29e-59j)
| (0.10333586915048290461 - 5.9145334839812965756e-202j)  +/-  (4.19e-63, 4.19e-63j)
-------------------------------------------------
The weights are:
| (1.4360806063836109719e-05 - 2.5832093798703533326e-154j)  +/-  (2.23e-20, 7.36e-49j)
| (1.105801493940122061e-09 + 4.5930562141800100709e-158j)  +/-  (8.19e-24, 2.7e-52j)
| (2.418174482233255538e-07 - 3.7581437065021230652e-156j)  +/-  (2.65e-22, 8.74e-51j)
| (0.053789997852160894351 - 3.5715684442193436018e-152j)  +/-  (4.82e-17, 1.59e-45j)
| (6.1552089352728232106e-13 - 2.5672227794183184776e-160j)  +/-  (6.35e-26, 2.09e-54j)
| (0.25794608935243313328 - 1.5398828655958843729e-150j)  +/-  (5.41e-17, 1.76e-45j)
| (0.00028331653567148541654 + 1.3609032382147986649e-153j)  +/-  (1.51e-20, 4.96e-49j)
| (0.010224026285220476685 + 1.3919975397099440997e-152j)  +/-  (1.68e-19, 5.56e-48j)
| (0.0018108590347737448755 - 5.2924350544303309344e-153j)  +/-  (4.31e-20, 1.42e-48j)
| (0.24744442923938703477 - 4.7973890567385943707e-151j)  +/-  (7.98e-18, 2.61e-46j)
| (0.031559011676511476821 + 1.8113045361295532264e-150j)  +/-  (3.12e-17, 1.01e-45j)
| (0.16434177252477916745 + 1.1569944726141654124e-151j)  +/-  (9.6e-19, 3.2e-47j)
| (0.23258589376913351207 + 1.1860706214793724327e-151j)  +/-  (2.74e-18, 8.74e-47j)
