Starting with polynomial:
P : 1/40320*t^8 - 1/630*t^7 + 7/180*t^6 - 7/15*t^5 + 35/12*t^4 - 28/3*t^3 + 14*t^2 - 8*t + 1
Extension levels are: 8 16
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : 1/40320*t^8 - 1/630*t^7 + 7/180*t^6 - 7/15*t^5 + 35/12*t^4 - 28/3*t^3 + 14*t^2 - 8*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/40320*t^24 - 155732067035034049359598960356799307/14141280335882096837844848180608194890*t^23 + 6260340637331624116817606009725167688241/2799973506504655173893279939760422588220*t^22 - 192996600347538464191787108002167308711123/699993376626163793473319984940105647055*t^21 + 1028263042706509048615056990097008604604069/44444023912772304347512379996197183940*t^20 - 9352118843280422563401795267012523862478556/6666603586915845652126856999429577591*t^19 + 141553089162577169187670365890960648756497262/2222201195638615217375618999809859197*t^18 - 4923229169993216704139591583786566038602402952/2222201195638615217375618999809859197*t^17 + 399118336413338821035599207673700083349410160307/6666603586915845652126856999429577591*t^16 - 8451908860636909156929714533564131816103617025792/6666603586915845652126856999429577591*t^15 + 46952458554684894670271428110860925148035750218880/2222201195638615217375618999809859197*t^14 - 616251569068439227950383637244178738959087481812480/2222201195638615217375618999809859197*t^13 + 6354045886781612337717268356811730274787972729137280/2222201195638615217375618999809859197*t^12 - 51180757722446397853741157994995112570770385317160960/2222201195638615217375618999809859197*t^11 + 29019771498273965612286381356918602157467355450434560/202018290512601383397783545437259927*t^10 - 138410019191496152674321351532828409766869359796940800/202018290512601383397783545437259927*t^9 + 496357555489443363895018920345673670227703082297388800/202018290512601383397783545437259927*t^8 - 1308570416587104781706639574561147927479079527302348800/202018290512601383397783545437259927*t^7 + 2460913214586330438565162951581593642294772710405529600/202018290512601383397783545437259927*t^6 - 3168594383199819189149117794284979887199889826769305600/202018290512601383397783545437259927*t^5 + 2636183725736138022188288765151596440945047458571264000/202018290512601383397783545437259927*t^4 - 1300423943961999636781612092681448137130881309425664000/202018290512601383397783545437259927*t^3 + 331244480147378606346484670498253185809046621773824000/202018290512601383397783545437259927*t^2 - 33835334957168856217297016108984754606116515381248000/202018290512601383397783545437259927*t + 759972077756134783743826706409852927404968194048000/202018290512601383397783545437259927
-------------------------------------------------
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:   24 out of 24
Indefinite weights: 0 out of 24
Negative weights:   0 out of 24
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (67.430878404170218169 - 1.1426304554684801666e-366j)  +/-  (6.73e-119, 6.73e-119j)
| (41.790082643237855188 - 1.6532400913721480931e-362j)  +/-  (1.64e-116, 1.64e-116j)
| (56.731153378376969643 + 4.6316322766461277897e-371j)  +/-  (8.92e-118, 8.92e-118j)
| (30.960461524878318026 + 6.2615774245734268672e-380j)  +/-  (8.15e-116, 8.15e-116j)
| (26.561349573980900328 - 7.8049965293289164911e-401j)  +/-  (1.27e-115, 1.27e-115j)
| (48.556528575087571936 - 1.9815703369798540833e-411j)  +/-  (5.07e-117, 5.07e-117j)
| (18.636387651897243076 - 3.5291203865477892766e-411j)  +/-  (1.59e-115, 1.59e-115j)
| (15.740678641278004578 + 1.1255227264400397196e-421j)  +/-  (4.37e-116, 4.37e-116j)
| (35.998480342138149954 - 2.3156922600578193295e-427j)  +/-  (3.98e-116, 3.98e-116j)
| (3.1617198047822179495 + 1.3826117235600216837e-433j)  +/-  (1.89e-120, 1.89e-120j)
| (10.758516010180995224 + 1.0593526978532663704e-428j)  +/-  (4.5e-117, 4.5e-117j)
| (13.085368962847679983 - 1.1662262880130091611e-432j)  +/-  (1.37e-116, 1.37e-116j)
| (8.757223774642053442 - 5.9084048049133301652e-441j)  +/-  (1.32e-117, 1.32e-117j)
| (20.803655896421769172 - 7.0335212359403476474e-454j)  +/-  (2.99e-115, 2.99e-115j)
| (5.5625508432875171519 + 1.4170440723674735109e-471j)  +/-  (7.47e-119, 7.47e-119j)
| (0.90370177679937991219 - 1.4578049635808230126e-478j)  +/-  (1.72e-123, 1.72e-123j)
| (1.5062581091273780094 + 4.4346027146482665493e-478j)  +/-  (2.54e-122, 2.54e-122j)
| (4.2667001702876587936 + 2.5929545985207327257e-475j)  +/-  (1.25e-119, 1.25e-119j)
| (22.863131736889264106 - 6.096247446533644252e-470j)  +/-  (2.71e-115, 2.71e-115j)
| (0.45478661578111528379 - 3.3884597188242083847e-488j)  +/-  (1.2e-124, 1.2e-124j)
| (0.17027963230510099979 + 2.3672034747291413416e-489j)  +/-  (7.05e-126, 7.05e-126j)
| (2.2510866298661306893 + 5.1503930299831173415e-485j)  +/-  (2.39e-121, 2.39e-121j)
| (0.030584800965448165655 - 1.4682406249931653847e-490j)  +/-  (1.52e-127, 1.52e-127j)
| (7.0459054023934656973 + 2.08779376524028492e-480j)  +/-  (3.53e-118, 3.53e-118j)
-------------------------------------------------
The weights are:
| (6.684262989519956123e-29 + 1.403363445538993702e-387j)  +/-  (3.31e-46, 4.45e-103j)
| (4.4189535941494613228e-18 + 4.4711035322865293732e-380j)  +/-  (6.4e-42, 8.6e-99j)
| (2.1026084332598313133e-24 - 8.7287642629720144833e-385j)  +/-  (8.81e-45, 1.18e-101j)
| (1.6857969370453231219e-13 + 6.151102535065212232e-378j)  +/-  (4.94e-40, 6.64e-97j)
| (1.1922167521232907513e-11 - 9.8583371724072260297e-377j)  +/-  (3.8e-39, 5.11e-96j)
| (6.020013946795968042e-21 + 2.0167225638147738293e-382j)  +/-  (8.43e-44, 1.13e-100j)
| (2.3137880445142197953e-08 + 1.7930721910396381456e-374j)  +/-  (1.14e-37, 1.53e-94j)
| (4.0973438579613378673e-07 - 5.2677873197266244532e-374j)  +/-  (5.74e-37, 7.72e-94j)
| (1.2516900779087012512e-15 - 4.3890133840124927325e-379j)  +/-  (8.85e-42, 1.19e-98j)
| (0.042595542499335069997 + 8.6086750481820513706e-371j)  +/-  (1.03e-29, 1.39e-86j)
| (4.59518325470426326e-05 - 7.4205755568169218951e-373j)  +/-  (4.89e-36, 6.56e-93j)
| (5.1746500190465612016e-06 + 1.9622764896403284142e-373j)  +/-  (9.28e-37, 1.25e-93j)
| (0.00029062093265967955517 + 2.5714309050775645445e-372j)  +/-  (8.14e-36, 1.09e-92j)
| (1.2779260591731081016e-09 - 7.4557324691402652476e-375j)  +/-  (3.02e-39, 4.06e-96j)
| (0.0053255343174616054608 + 1.9469587816614911828e-371j)  +/-  (1.75e-35, 2.32e-92j)
| (0.21434138523014712454 - 2.4725303783297906144e-370j)  +/-  (8.03e-33, 1.09e-89j)
| (0.14926372077834598955 + 2.0625725783848358035e-370j)  +/-  (5.46e-33, 7.28e-90j)
| (0.016874493201424381968 - 4.3437627764910041711e-371j)  +/-  (6.37e-35, 8.49e-92j)
| (3.699254107642452785e-10 + 1.7099429437589064336e-375j)  +/-  (3.94e-40, 5.35e-97j)
| (0.23247743172625426391 + 2.5499461086868152871e-370j)  +/-  (1.61e-33, 2.28e-90j)
| (0.17393668524906630596 - 2.014517721070299326e-370j)  +/-  (5.53e-34, 7.83e-91j)
| (0.086456190563778570415 - 1.4609835004683378502e-370j)  +/-  (1.17e-34, 1.55e-91j)
| (0.077004839654630467659 + 7.7113569156875819065e-371j)  +/-  (1.84e-34, 2.69e-91j)
| (0.0013819948321207372535 - 7.666003642012495545e-372j)  +/-  (2.11e-36, 2.72e-93j)
Starting with polynomial:
P : 1/40320*t^8 - 1/630*t^7 + 7/180*t^6 - 7/15*t^5 + 35/12*t^4 - 28/3*t^3 + 14*t^2 - 8*t + 1
Extension levels are: 8 16
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P1 : 1/40320*t^8 - 1/630*t^7 + 7/180*t^6 - 7/15*t^5 + 35/12*t^4 - 28/3*t^3 + 14*t^2 - 8*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/40320*t^24 - 155732067035034049359598960356799307/14141280335882096837844848180608194890*t^23 + 6260340637331624116817606009725167688241/2799973506504655173893279939760422588220*t^22 - 192996600347538464191787108002167308711123/699993376626163793473319984940105647055*t^21 + 1028263042706509048615056990097008604604069/44444023912772304347512379996197183940*t^20 - 9352118843280422563401795267012523862478556/6666603586915845652126856999429577591*t^19 + 141553089162577169187670365890960648756497262/2222201195638615217375618999809859197*t^18 - 4923229169993216704139591583786566038602402952/2222201195638615217375618999809859197*t^17 + 399118336413338821035599207673700083349410160307/6666603586915845652126856999429577591*t^16 - 8451908860636909156929714533564131816103617025792/6666603586915845652126856999429577591*t^15 + 46952458554684894670271428110860925148035750218880/2222201195638615217375618999809859197*t^14 - 616251569068439227950383637244178738959087481812480/2222201195638615217375618999809859197*t^13 + 6354045886781612337717268356811730274787972729137280/2222201195638615217375618999809859197*t^12 - 51180757722446397853741157994995112570770385317160960/2222201195638615217375618999809859197*t^11 + 29019771498273965612286381356918602157467355450434560/202018290512601383397783545437259927*t^10 - 138410019191496152674321351532828409766869359796940800/202018290512601383397783545437259927*t^9 + 496357555489443363895018920345673670227703082297388800/202018290512601383397783545437259927*t^8 - 1308570416587104781706639574561147927479079527302348800/202018290512601383397783545437259927*t^7 + 2460913214586330438565162951581593642294772710405529600/202018290512601383397783545437259927*t^6 - 3168594383199819189149117794284979887199889826769305600/202018290512601383397783545437259927*t^5 + 2636183725736138022188288765151596440945047458571264000/202018290512601383397783545437259927*t^4 - 1300423943961999636781612092681448137130881309425664000/202018290512601383397783545437259927*t^3 + 331244480147378606346484670498253185809046621773824000/202018290512601383397783545437259927*t^2 - 33835334957168856217297016108984754606116515381248000/202018290512601383397783545437259927*t + 759972077756134783743826706409852927404968194048000/202018290512601383397783545437259927
-------------------------------------------------
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:   24 out of 24
Indefinite weights: 0 out of 24
Negative weights:   0 out of 24
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (67.430878404170218169 - 1.1426304554684801666e-366j)  +/-  (6.73e-119, 6.73e-119j)
| (41.790082643237855188 - 1.6532400913721480931e-362j)  +/-  (1.64e-116, 1.64e-116j)
| (56.731153378376969643 + 4.6316322766461277897e-371j)  +/-  (8.92e-118, 8.92e-118j)
| (30.960461524878318026 + 6.2615774245734268672e-380j)  +/-  (8.15e-116, 8.15e-116j)
| (26.561349573980900328 - 7.8049965293289164911e-401j)  +/-  (1.27e-115, 1.27e-115j)
| (48.556528575087571936 - 1.9815703369798540833e-411j)  +/-  (5.07e-117, 5.07e-117j)
| (18.636387651897243076 - 3.5291203865477892766e-411j)  +/-  (1.59e-115, 1.59e-115j)
| (15.740678641278004578 + 1.1255227264400397196e-421j)  +/-  (4.37e-116, 4.37e-116j)
| (35.998480342138149954 - 2.3156922600578193295e-427j)  +/-  (3.98e-116, 3.98e-116j)
| (3.1617198047822179495 + 1.3826117235600216837e-433j)  +/-  (1.89e-120, 1.89e-120j)
| (10.758516010180995224 + 1.0593526978532663704e-428j)  +/-  (4.5e-117, 4.5e-117j)
| (13.085368962847679983 - 1.1662262880130091611e-432j)  +/-  (1.37e-116, 1.37e-116j)
| (8.757223774642053442 - 5.9084048049133301652e-441j)  +/-  (1.32e-117, 1.32e-117j)
| (20.803655896421769172 - 7.0335212359403476474e-454j)  +/-  (2.99e-115, 2.99e-115j)
| (5.5625508432875171519 + 1.4170440723674735109e-471j)  +/-  (7.47e-119, 7.47e-119j)
| (0.90370177679937991219 - 1.4578049635808230126e-478j)  +/-  (1.72e-123, 1.72e-123j)
| (1.5062581091273780094 + 4.4346027146482665493e-478j)  +/-  (2.54e-122, 2.54e-122j)
| (4.2667001702876587936 + 2.5929545985207327257e-475j)  +/-  (1.25e-119, 1.25e-119j)
| (22.863131736889264106 - 6.096247446533644252e-470j)  +/-  (2.71e-115, 2.71e-115j)
| (0.45478661578111528379 - 3.3884597188242083847e-488j)  +/-  (1.2e-124, 1.2e-124j)
| (0.17027963230510099979 + 2.3672034747291413416e-489j)  +/-  (7.05e-126, 7.05e-126j)
| (2.2510866298661306893 + 5.1503930299831173415e-485j)  +/-  (2.39e-121, 2.39e-121j)
| (0.030584800965448165655 - 1.4682406249931653847e-490j)  +/-  (1.52e-127, 1.52e-127j)
| (7.0459054023934656973 + 2.08779376524028492e-480j)  +/-  (3.53e-118, 3.53e-118j)
-------------------------------------------------
The weights are:
| (6.684262989519956123e-29 + 1.403363445538993702e-387j)  +/-  (3.31e-46, 4.45e-103j)
| (4.4189535941494613228e-18 + 4.4711035322865293732e-380j)  +/-  (6.4e-42, 8.6e-99j)
| (2.1026084332598313133e-24 - 8.7287642629720144833e-385j)  +/-  (8.81e-45, 1.18e-101j)
| (1.6857969370453231219e-13 + 6.151102535065212232e-378j)  +/-  (4.94e-40, 6.64e-97j)
| (1.1922167521232907513e-11 - 9.8583371724072260297e-377j)  +/-  (3.8e-39, 5.11e-96j)
| (6.020013946795968042e-21 + 2.0167225638147738293e-382j)  +/-  (8.43e-44, 1.13e-100j)
| (2.3137880445142197953e-08 + 1.7930721910396381456e-374j)  +/-  (1.14e-37, 1.53e-94j)
| (4.0973438579613378673e-07 - 5.2677873197266244532e-374j)  +/-  (5.74e-37, 7.72e-94j)
| (1.2516900779087012512e-15 - 4.3890133840124927325e-379j)  +/-  (8.85e-42, 1.19e-98j)
| (0.042595542499335069997 + 8.6086750481820513706e-371j)  +/-  (1.03e-29, 1.39e-86j)
| (4.59518325470426326e-05 - 7.4205755568169218951e-373j)  +/-  (4.89e-36, 6.56e-93j)
| (5.1746500190465612016e-06 + 1.9622764896403284142e-373j)  +/-  (9.28e-37, 1.25e-93j)
| (0.00029062093265967955517 + 2.5714309050775645445e-372j)  +/-  (8.14e-36, 1.09e-92j)
| (1.2779260591731081016e-09 - 7.4557324691402652476e-375j)  +/-  (3.02e-39, 4.06e-96j)
| (0.0053255343174616054608 + 1.9469587816614911828e-371j)  +/-  (1.75e-35, 2.32e-92j)
| (0.21434138523014712454 - 2.4725303783297906144e-370j)  +/-  (8.03e-33, 1.09e-89j)
| (0.14926372077834598955 + 2.0625725783848358035e-370j)  +/-  (5.46e-33, 7.28e-90j)
| (0.016874493201424381968 - 4.3437627764910041711e-371j)  +/-  (6.37e-35, 8.49e-92j)
| (3.699254107642452785e-10 + 1.7099429437589064336e-375j)  +/-  (3.94e-40, 5.35e-97j)
| (0.23247743172625426391 + 2.5499461086868152871e-370j)  +/-  (1.61e-33, 2.28e-90j)
| (0.17393668524906630596 - 2.014517721070299326e-370j)  +/-  (5.53e-34, 7.83e-91j)
| (0.086456190563778570415 - 1.4609835004683378502e-370j)  +/-  (1.17e-34, 1.55e-91j)
| (0.077004839654630467659 + 7.7113569156875819065e-371j)  +/-  (1.84e-34, 2.69e-91j)
| (0.0013819948321207372535 - 7.666003642012495545e-372j)  +/-  (2.11e-36, 2.72e-93j)
