Starting with polynomial:
P : 2*t^2 - 1
Extension levels are: 2 3
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Trying to find an order 3 Kronrod extension for:
P1 : 2*t^2 - 1
Solvable: 1
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Ending with final polynomial:
P : 2*t^5 - 3*t^3 + 1*t
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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: 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:   5 out of 5
Indefinite weights: 0 out of 5
Negative weights:   0 out of 5
Extension rule has valid weights: 1
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The nodes are:
| (1 + 8.8108147574137676194e-86j)  +/-  (3.04e-63, 3.04e-63j)
| (-0.7071067811865475244 - 3.041490152750504832e-89j)  +/-  (2.37e-63, 2.37e-63j)
| (-1 - 7.178996849044423115e-97j)  +/-  (3.04e-63, 3.04e-63j)
| (5.0758836746312984465e-116 + 0j)  +/-  (2.54e-115, 2.54e-115j)
| (0.7071067811865475244 + 1.7610509143420669137e-132j)  +/-  (4.25e-63, 4.25e-63j)
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The weights are:
| (0.125 - 6.0572124377662449827e-86j)  +/-  (8.74e-29, 3.91e-60j)
| (0.25 + 1.2908516119732504846e-86j)  +/-  (3.69e-29, 1.67e-60j)
| (0.125 - 5.5197395950388420331e-87j)  +/-  (2.03e-29, 9.21e-61j)
| (0.25 - 2.2016283602154284019e-86j)  +/-  (1.9e-29, 8.64e-61j)
| (0.25 + 7.5199631455123071033e-86j)  +/-  (1.11e-29, 4.55e-61j)
