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 13
-------------------------------------------------
Trying to find an order 13 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^21 - 175357873392868770223885121/22322221904830692598108333440*t^20 + 13093342200490858587597836363/11719166500036113614006875056*t^19 - 229123320966736111039489489829/2421315392569444961571668400*t^18 + 173781018111036721952037276070659/32553240277878093372241319600*t^17 - 141240791513961633754320962798007/664351842405675374943700400*t^16 + 12576919914229524848470685376423941/2034577517367380835765082475*t^15 - 10896821990380721247284594781280395/81383100694695233430603299*t^14 + 355728382234134044192427972043903963/162766201389390466861206598*t^13 - 4398758476168286079084527583127419427/162766201389390466861206598*t^12 + 20609168997115831850083934139850522452/81383100694695233430603299*t^11 - 1204337321595714022552619230557322524/672587609047068044881019*t^10 + 70067770935634382515034464841319527820/7398463699517748493691209*t^9 - 273403384856197720167659823480675832092/7398463699517748493691209*t^8 + 70139033187444363620773201421643118848/672587609047068044881019*t^7 - 218754865742839604980918183884199788288/1056923385645392641955887*t^6 + 293661005406952226646725146300287675456/1056923385645392641955887*t^5 - 252128554210467865785809206521588571200/1056923385645392641955887*t^4 + 127360767357113109689832974775572590080/1056923385645392641955887*t^3 - 33151322444018766236297256903869790720/1056923385645392641955887*t^2 + 3529869979421388132487784994808343040/1056923385645392641955887*t - 93822572514457738289078395490234880/1056923385645392641955887
-------------------------------------------------
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:   21 out of 21
Indefinite weights: 0 out of 21
Negative weights:   0 out of 21
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (56.2859975308316181 - 3.7103003527027019746e-276j)  +/-  (5.44e-120, 5.44e-120j)
| (46.293744560835866962 - 1.2222877024986804238e-273j)  +/-  (4.76e-119, 4.76e-119j)
| (32.558793915003019805 + 7.2301479954292205978e-276j)  +/-  (4.82e-118, 4.82e-118j)
| (38.740016062379529441 - 4.9246277691882732522e-282j)  +/-  (1.93e-118, 1.93e-118j)
| (0.038717475587476216868 - 4.5797326546598103694e-289j)  +/-  (2.73e-127, 2.73e-127j)
| (15.740678641278004578 - 4.0332298023703519256e-292j)  +/-  (1.12e-117, 1.12e-117j)
| (2.2510866298661306893 + 3.9591332814124083931e-300j)  +/-  (1.19e-121, 1.19e-121j)
| (8.8134212035536018462 - 8.4918547531579650347e-298j)  +/-  (1.92e-118, 1.92e-118j)
| (5.5204434247143052714 - 1.5231934994734415639e-305j)  +/-  (2.32e-119, 2.32e-119j)
| (22.863131736889264106 + 2.5318022676552311828e-322j)  +/-  (1.17e-117, 1.17e-117j)
| (1.5040918147104286917 - 3.7209261005577321853e-340j)  +/-  (1.44e-122, 1.44e-122j)
| (19.018504278650323807 + 1.7561715810296850249e-344j)  +/-  (1.33e-117, 1.33e-117j)
| (13.005501928181829614 - 1.0784575358595029205e-357j)  +/-  (8.24e-118, 8.24e-118j)
| (27.336909324801565916 - 5.8169662376053411875e-366j)  +/-  (8.11e-118, 8.11e-118j)
| (0.44260785739036268374 + 2.9049812618398706217e-376j)  +/-  (6.93e-125, 6.93e-125j)
| (4.2667001702876587936 + 1.1070669314218630417e-368j)  +/-  (5.23e-120, 5.23e-120j)
| (3.1852327119162294733 - 7.5239525659308972265e-372j)  +/-  (9.53e-121, 9.53e-121j)
| (0.90370177679937991219 + 1.8540266057740408858e-377j)  +/-  (1.02e-123, 1.02e-123j)
| (10.758516010180995224 + 6.9939155865481850876e-377j)  +/-  (4.51e-118, 4.51e-118j)
| (7.0459054023934656973 - 2.6917189769841784858e-389j)  +/-  (6.87e-119, 6.87e-119j)
| (0.17027963230510099979 - 6.2133061917345308202e-398j)  +/-  (5.55e-126, 5.55e-126j)
-------------------------------------------------
The weights are:
| (4.3413066923715983645e-24 + 1.6089478399867664947e-296j)  +/-  (2.35e-50, 1.5e-108j)
| (6.6618077437283971802e-20 + 5.4328796680117870301e-293j)  +/-  (8.33e-49, 5.33e-107j)
| (4.0959386222717913416e-14 - 1.6637088825931684299e-289j)  +/-  (9.95e-47, 6.37e-105j)
| (1.0140830688712325882e-16 - 2.0304731179231940618e-291j)  +/-  (8.71e-48, 5.58e-106j)
| (0.088291765502367940841 + 8.4361517860904690777e-282j)  +/-  (4.27e-31, 2.73e-89j)
| (4.3814981644138478482e-07 - 7.424004912006106893e-286j)  +/-  (7.69e-43, 4.92e-101j)
| (0.088543907495588157171 - 1.1561661579401770908e-281j)  +/-  (4.21e-31, 2.69e-89j)
| (0.00027610035587156871028 + 1.110098307068745511e-283j)  +/-  (1.07e-39, 6.86e-98j)
| (0.0055292437754472088286 + 1.2369850091534035017e-282j)  +/-  (3.36e-37, 2.15e-95j)
| (4.8771078399826741376e-10 - 9.4876204077372922188e-288j)  +/-  (1.28e-45, 8.17e-104j)
| (0.14743052851849149632 + 1.745392600036712822e-281j)  +/-  (6.22e-33, 3.98e-91j)
| (1.9551441953297738882e-08 + 8.734280205719925615e-287j)  +/-  (1.46e-44, 9.35e-103j)
| (5.5570497763587484438e-06 + 5.262209373553902549e-285j)  +/-  (5.7e-43, 3.65e-101j)
| (6.4710226007397948355e-12 + 1.1179893232281559938e-288j)  +/-  (5.12e-47, 3.27e-105j)
| (0.23903427808162181369 + 2.4208352745913970158e-281j)  +/-  (4.91e-36, 3.14e-94j)
| (0.016121185863798204801 - 3.1323722514695000588e-282j)  +/-  (1.57e-39, 1e-97j)
| (0.042062175704703980785 + 6.4395536786570448862e-282j)  +/-  (6.34e-39, 4.06e-97j)
| (0.21819932097758989015 - 2.1727749037051710488e-281j)  +/-  (7.97e-38, 5.11e-96j)
| (4.3751335738330929152e-05 - 2.7639524705998598854e-284j)  +/-  (1e-42, 6.43e-101j)
| (0.001447963644099146655 - 3.9204702749663487158e-283j)  +/-  (2.49e-41, 1.59e-99j)
| (0.15301376349942464023 - 2.1049108244469584961e-281j)  +/-  (1.26e-38, 8.44e-97j)
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 13
-------------------------------------------------
Trying to find an order 13 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^21 - 175357873392868770223885121/22322221904830692598108333440*t^20 + 13093342200490858587597836363/11719166500036113614006875056*t^19 - 229123320966736111039489489829/2421315392569444961571668400*t^18 + 173781018111036721952037276070659/32553240277878093372241319600*t^17 - 141240791513961633754320962798007/664351842405675374943700400*t^16 + 12576919914229524848470685376423941/2034577517367380835765082475*t^15 - 10896821990380721247284594781280395/81383100694695233430603299*t^14 + 355728382234134044192427972043903963/162766201389390466861206598*t^13 - 4398758476168286079084527583127419427/162766201389390466861206598*t^12 + 20609168997115831850083934139850522452/81383100694695233430603299*t^11 - 1204337321595714022552619230557322524/672587609047068044881019*t^10 + 70067770935634382515034464841319527820/7398463699517748493691209*t^9 - 273403384856197720167659823480675832092/7398463699517748493691209*t^8 + 70139033187444363620773201421643118848/672587609047068044881019*t^7 - 218754865742839604980918183884199788288/1056923385645392641955887*t^6 + 293661005406952226646725146300287675456/1056923385645392641955887*t^5 - 252128554210467865785809206521588571200/1056923385645392641955887*t^4 + 127360767357113109689832974775572590080/1056923385645392641955887*t^3 - 33151322444018766236297256903869790720/1056923385645392641955887*t^2 + 3529869979421388132487784994808343040/1056923385645392641955887*t - 93822572514457738289078395490234880/1056923385645392641955887
-------------------------------------------------
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:   21 out of 21
Indefinite weights: 0 out of 21
Negative weights:   0 out of 21
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (56.2859975308316181 - 3.7103003527027019746e-276j)  +/-  (5.44e-120, 5.44e-120j)
| (46.293744560835866962 - 1.2222877024986804238e-273j)  +/-  (4.76e-119, 4.76e-119j)
| (32.558793915003019805 + 7.2301479954292205978e-276j)  +/-  (4.82e-118, 4.82e-118j)
| (38.740016062379529441 - 4.9246277691882732522e-282j)  +/-  (1.93e-118, 1.93e-118j)
| (0.038717475587476216868 - 4.5797326546598103694e-289j)  +/-  (2.73e-127, 2.73e-127j)
| (15.740678641278004578 - 4.0332298023703519256e-292j)  +/-  (1.12e-117, 1.12e-117j)
| (2.2510866298661306893 + 3.9591332814124083931e-300j)  +/-  (1.19e-121, 1.19e-121j)
| (8.8134212035536018462 - 8.4918547531579650347e-298j)  +/-  (1.92e-118, 1.92e-118j)
| (5.5204434247143052714 - 1.5231934994734415639e-305j)  +/-  (2.32e-119, 2.32e-119j)
| (22.863131736889264106 + 2.5318022676552311828e-322j)  +/-  (1.17e-117, 1.17e-117j)
| (1.5040918147104286917 - 3.7209261005577321853e-340j)  +/-  (1.44e-122, 1.44e-122j)
| (19.018504278650323807 + 1.7561715810296850249e-344j)  +/-  (1.33e-117, 1.33e-117j)
| (13.005501928181829614 - 1.0784575358595029205e-357j)  +/-  (8.24e-118, 8.24e-118j)
| (27.336909324801565916 - 5.8169662376053411875e-366j)  +/-  (8.11e-118, 8.11e-118j)
| (0.44260785739036268374 + 2.9049812618398706217e-376j)  +/-  (6.93e-125, 6.93e-125j)
| (4.2667001702876587936 + 1.1070669314218630417e-368j)  +/-  (5.23e-120, 5.23e-120j)
| (3.1852327119162294733 - 7.5239525659308972265e-372j)  +/-  (9.53e-121, 9.53e-121j)
| (0.90370177679937991219 + 1.8540266057740408858e-377j)  +/-  (1.02e-123, 1.02e-123j)
| (10.758516010180995224 + 6.9939155865481850876e-377j)  +/-  (4.51e-118, 4.51e-118j)
| (7.0459054023934656973 - 2.6917189769841784858e-389j)  +/-  (6.87e-119, 6.87e-119j)
| (0.17027963230510099979 - 6.2133061917345308202e-398j)  +/-  (5.55e-126, 5.55e-126j)
-------------------------------------------------
The weights are:
| (4.3413066923715983645e-24 + 1.6089478399867664947e-296j)  +/-  (2.35e-50, 1.5e-108j)
| (6.6618077437283971802e-20 + 5.4328796680117870301e-293j)  +/-  (8.33e-49, 5.33e-107j)
| (4.0959386222717913416e-14 - 1.6637088825931684299e-289j)  +/-  (9.95e-47, 6.37e-105j)
| (1.0140830688712325882e-16 - 2.0304731179231940618e-291j)  +/-  (8.71e-48, 5.58e-106j)
| (0.088291765502367940841 + 8.4361517860904690777e-282j)  +/-  (4.27e-31, 2.73e-89j)
| (4.3814981644138478482e-07 - 7.424004912006106893e-286j)  +/-  (7.69e-43, 4.92e-101j)
| (0.088543907495588157171 - 1.1561661579401770908e-281j)  +/-  (4.21e-31, 2.69e-89j)
| (0.00027610035587156871028 + 1.110098307068745511e-283j)  +/-  (1.07e-39, 6.86e-98j)
| (0.0055292437754472088286 + 1.2369850091534035017e-282j)  +/-  (3.36e-37, 2.15e-95j)
| (4.8771078399826741376e-10 - 9.4876204077372922188e-288j)  +/-  (1.28e-45, 8.17e-104j)
| (0.14743052851849149632 + 1.745392600036712822e-281j)  +/-  (6.22e-33, 3.98e-91j)
| (1.9551441953297738882e-08 + 8.734280205719925615e-287j)  +/-  (1.46e-44, 9.35e-103j)
| (5.5570497763587484438e-06 + 5.262209373553902549e-285j)  +/-  (5.7e-43, 3.65e-101j)
| (6.4710226007397948355e-12 + 1.1179893232281559938e-288j)  +/-  (5.12e-47, 3.27e-105j)
| (0.23903427808162181369 + 2.4208352745913970158e-281j)  +/-  (4.91e-36, 3.14e-94j)
| (0.016121185863798204801 - 3.1323722514695000588e-282j)  +/-  (1.57e-39, 1e-97j)
| (0.042062175704703980785 + 6.4395536786570448862e-282j)  +/-  (6.34e-39, 4.06e-97j)
| (0.21819932097758989015 - 2.1727749037051710488e-281j)  +/-  (7.97e-38, 5.11e-96j)
| (4.3751335738330929152e-05 - 2.7639524705998598854e-284j)  +/-  (1e-42, 6.43e-101j)
| (0.001447963644099146655 - 3.9204702749663487158e-283j)  +/-  (2.49e-41, 1.59e-99j)
| (0.15301376349942464023 - 2.1049108244469584961e-281j)  +/-  (1.26e-38, 8.44e-97j)
