circuit_i	cycle_depth	circuit_depth	pure_probs	sampled_probs	e_u	u_u	m_u	y	x	numerator	denominator
0	0	1	3	[0.25, 0.49999997, 4.4408918e-16, 0.24999994]	[0.2485, 0.491, 0.0068, 0.2537]	0.375000	0.25	0.371050	0.121050	0.125000	0.015131	0.015625
1	1	1	3	[0.64016503, 0.109834954, 0.21338834, 0.036611...	[0.6315, 0.1176, 0.2118, 0.0391]	0.468750	0.25	0.463808	0.213808	0.218750	0.046770	0.047852
2	2	1	3	[0.010723308, 0.13572334, 0.48927668, 0.36427674]	[0.0183, 0.1355, 0.4858, 0.3604]	0.390625	0.25	0.387563	0.137563	0.140625	0.019345	0.019775
3	3	1	3	[0.12499999, 0.12499999, 0.72855335, 0.021446602]	[0.1263, 0.1263, 0.7127, 0.0347]	0.562500	0.25	0.551559	0.301559	0.312500	0.094237	0.097656
4	4	1	3	[0.18750001, 0.062499985, 0.062499993, 0.68749...	[0.1829, 0.073, 0.072, 0.6721]	0.515625	0.25	0.505425	0.255425	0.265625	0.067847	0.070557