circuit_i	cycle_depth	circuit_depth	pure_probs	sampled_probs	e_u	u_u	m_u	y	x	numerator	denominator
0	0	1	3	[0.12499999, 0.12499999, 0.12499999, 0.625]	[0.1238, 0.126, 0.1265, 0.6237]	0.43750	0.25	0.436850	0.186850	0.18750	0.035034	0.035156
1	1	1	3	[0.12499998, 0.12499998, 0.02144662, 0.72855335]	[0.1222, 0.1303, 0.0318, 0.7157]	0.56250	0.25	0.553670	0.303670	0.31250	0.094897	0.097656
2	2	1	3	[0.21338837, 0.64016503, 0.03661165, 0.10983497]	[0.215, 0.6296, 0.0407, 0.1147]	0.46875	0.25	0.463015	0.213015	0.21875	0.046597	0.047852
3	3	1	3	[2.2204466e-16, 0.25, 0.25, 0.50000006]	[0.007, 0.2479, 0.2526, 0.4925]	0.37500	0.25	0.371375	0.121375	0.12500	0.015172	0.015625
4	4	1	3	[0.12499999, 0.12499999, 0.021446615, 0.7285534]	[0.1276, 0.1371, 0.0283, 0.707]	0.56250	0.25	0.548782	0.298782	0.31250	0.093369	0.097656