circuit_i	cycle_depth	circuit_depth	pure_probs	sampled_probs	e_u	u_u	m_u	y	x	numerator	denominator
0	0	1	3	[0.1357233, 0.010723307, 0.3642766, 0.4892766]	[0.1371, 0.0183, 0.363, 0.4816]	0.390625	0.25	0.386672	0.136672	0.140625	0.019219	0.019775
1	1	1	3	[0.37500003, 0.37500003, 0.12500001, 0.12499998]	[0.3719, 0.3679, 0.1264, 0.1338]	0.312500	0.25	0.309950	0.059950	0.062500	0.003747	0.003906
2	2	1	3	[0.37499994, 0.12499998, 0.37499994, 0.12499998]	[0.3786, 0.1224, 0.3738, 0.1252]	0.312500	0.25	0.313100	0.063100	0.062500	0.003944	0.003906
3	3	1	3	[0.021446606, 0.12499998, 0.72855335, 0.124999...	[0.0329, 0.1223, 0.7077, 0.1371]	0.562500	0.25	0.548728	0.298728	0.312500	0.093352	0.097656
4	4	1	3	[0.21338831, 0.03661164, 0.28661165, 0.4633883]	[0.2119, 0.0416, 0.2907, 0.4558]	0.343750	0.25	0.341270	0.091270	0.093750	0.008557	0.008789