Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 8 12
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Trying to find an order 8 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
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Trying to find an order 12 Kronrod extension for:
P2 : 35/8*t^12 - 87219/8284*t^10 + 102069/11336*t^8 - 891429/269230*t^6 + 24664563/47599864*t^4 - 792603/23799932*t^2 + 30429/47599864
Solvable: 1
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Ending with final polynomial:
P : 35/8*t^24 - 47566502905086455908758187661243346/2044168929494834254367149915397081*t^22 + 48257244675469401318457266530042046993/903522666836716740430280262605509802*t^20 - 148362548501874249167326911132777756553/2139922105665908069440137464065681110*t^18 + 205082996656420196464236260429316302616347/3657269540056747951211157601919186729064*t^16 - 416435757303908941260548137290693671841796/14171919467719898310943235707436848575123*t^14 + 25194149765865608476111468507908340488937699/2501888859878243586431901996043659036915945*t^12 - 620308978578415036294579693286961131542429/277987651097582620714655777338184337435105*t^10 + 3446464492298603748105035890107767560028621/11119506043903304828586231093527373497404200*t^8 - 403214254477978889877992914908492397969394/15845296112562209380735379308276507233800985*t^6 + 197263241835746715539716791113605022839447/179580022609038372981667632160467081983077830*t^4 - 3394425870324322590701767699385159202433/179580022609038372981667632160467081983077830*t^2 + 32246346427533396033929944065917341621/622544078377999693003114458156285884208003144
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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
-------------------------------------------------
The nodes are:
| (0.99546177155001729373 - 1.0048978788227544064e-440j)  +/-  (3.87e-121, 3.87e-121j)
| (-0.35241611849142175407 + 7.9697775425423993553e-443j)  +/-  (5.35e-123, 5.35e-123j)
| (-0.92849639635025196002 + 5.4433550749218428602e-444j)  +/-  (7.29e-121, 7.29e-121j)
| (0.057798702582244333721 + 9.6216179912851580989e-448j)  +/-  (2.21e-127, 2.21e-127j)
| (0.39829549941770898999 - 1.7509192388768551787e-455j)  +/-  (3.01e-123, 3.01e-123j)
| (0.5471825721852412894 + 1.5674389493776511971e-460j)  +/-  (6.77e-123, 6.77e-123j)
| (0.92849639635025196002 + 4.1035061268625657534e-462j)  +/-  (7.26e-121, 7.26e-121j)
| (-0.86113631159405257522 + 1.325242072706655151e-461j)  +/-  (3.71e-121, 3.71e-121j)
| (-0.057798702582244333721 - 2.9801426864597952611e-465j)  +/-  (2.21e-127, 2.21e-127j)
| (-0.6674742407002819824 - 2.0447862118340279982e-468j)  +/-  (3.05e-122, 3.05e-122j)
| (0.86113631159405257522 + 8.8954602831273962883e-467j)  +/-  (3.23e-121, 3.23e-121j)
| (0.9732162594524303742 - 1.648994028897925142e-467j)  +/-  (9.56e-121, 9.56e-121j)
| (-0.9732162594524303742 - 1.1162347555827610833e-466j)  +/-  (9.48e-121, 9.48e-121j)
| (-0.39829549941770898999 - 7.9469062348878738884e-471j)  +/-  (3.11e-123, 3.11e-123j)
| (-0.99546177155001729373 + 2.9115369252746650623e-472j)  +/-  (4.17e-121, 4.17e-121j)
| (0.6674742407002819824 - 8.9301489091253866611e-476j)  +/-  (2.88e-122, 2.88e-122j)
| (0.35241611849142175407 + 1.6640195020240511774e-480j)  +/-  (5.57e-123, 5.57e-123j)
| (-0.18035397587349104032 - 1.4716704090612077924e-490j)  +/-  (4.3e-126, 4.3e-126j)
| (-0.77313202939632075478 + 1.3754519149552483527e-490j)  +/-  (1.21e-121, 1.21e-121j)
| (-0.3399810435848562648 + 4.1969243371356384282e-492j)  +/-  (3.34e-123, 3.34e-123j)
| (0.3399810435848562648 - 9.159879600980043054e-498j)  +/-  (3.74e-123, 3.74e-123j)
| (0.77313202939632075478 - 1.9255545642796748106e-504j)  +/-  (1.21e-121, 1.21e-121j)
| (0.18035397587349104032 + 1.4178214590486807859e-506j)  +/-  (4e-126, 4e-126j)
| (-0.5471825721852412894 + 2.2846265327015573573e-508j)  +/-  (7.02e-123, 7.02e-123j)
-------------------------------------------------
The weights are:
| (0.012117785377486384994 + 1.1208834134142432471e-440j)  +/-  (2.51e-38, 2.12e-97j)
| (-0.92954809608525266793 - 1.1221417085539626838e-438j)  +/-  (1.12e-38, 9.45e-98j)
| (0.056254139110973177282 - 3.7251317595034691055e-442j)  +/-  (3.47e-39, 2.93e-98j)
| (0.11702003844014279383 - 9.8650869632743707865e-440j)  +/-  (6.53e-39, 5.5e-98j)
| (0.29686270122283916758 - 4.5866285883786440034e-439j)  +/-  (2.02e-39, 1.71e-98j)
| (0.12726578957850912081 + 3.5419310171462521064e-440j)  +/-  (1.22e-39, 1.03e-98j)
| (0.056254139110973177282 + 1.0761538118189024089e-440j)  +/-  (1.04e-40, 8.81e-100j)
| (0.078118878876939026912 + 6.8118099341962255267e-442j)  +/-  (4.14e-41, 3.49e-100j)
| (0.11702003844014279383 + 8.781964242976874637e-440j)  +/-  (3.99e-40, 3.37e-99j)
| (0.11337965578019151787 + 3.2588445419062406774e-441j)  +/-  (1.36e-41, 1.15e-100j)
| (0.078118878876939026912 - 9.5280844073157391432e-441j)  +/-  (3.37e-41, 2.84e-100j)
| (0.033160678502632064583 - 1.7247321445157263165e-440j)  +/-  (5.3e-41, 4.47e-100j)
| (0.033160678502632064583 + 1.9850584757225903139e-442j)  +/-  (9.09e-43, 7.67e-102j)
| (0.29686270122283916758 + 1.9603466246676221816e-439j)  +/-  (7.71e-42, 6.49e-101j)
| (0.012117785377486384994 - 6.1926606634788675535e-443j)  +/-  (3.37e-43, 2.84e-102j)
| (0.11337965578019151787 - 1.6570704982059402779e-440j)  +/-  (8.18e-43, 6.9e-102j)
| (-0.92954809608525266793 + 2.3439666324340883236e-438j)  +/-  (3.21e-42, 2.71e-101j)
| (0.12914967466081907727 - 7.9182018356435980989e-440j)  +/-  (7.71e-43, 6.47e-102j)
| (0.097380982940762291238 - 1.3771597047362912189e-441j)  +/-  (2.98e-44, 2.49e-103j)
| (0.86883777159395804556 + 9.7303918256467736785e-439j)  +/-  (4.46e-42, 3.76e-101j)
| (0.86883777159395804556 - 1.9735644388722130043e-438j)  +/-  (1.18e-42, 9.95e-102j)
| (0.097380982940762291238 + 1.101008939363674251e-440j)  +/-  (2.99e-45, 2.52e-104j)
| (0.12914967466081907727 + 1.1423310427328823066e-439j)  +/-  (6.13e-44, 5.23e-103j)
| (0.12726578957850912081 - 1.0271922793840119908e-440j)  +/-  (8.39e-45, 6.61e-104j)
