circuit_i cycle_depth circuit_depth pure_probs sampled_probs e_u u_u m_u y x numerator denominator
0 0 1 3 [0.12499998, 0.37499994, 0.12499999, 0.37499994] [0.1286, 0.377, 0.1305, 0.3639] 0.31250 0.25 0.310225 0.060225 0.06250 0.003764 0.003906
1 1 1 3 [0.46338835, 0.28661165, 0.03661164, 0.21338831] [0.4566, 0.2877, 0.043, 0.2127] 0.34375 0.25 0.341003 0.091003 0.09375 0.008532 0.008789
2 2 1 3 [0.21338834, 0.036611646, 0.28661165, 0.4633883] [0.2061, 0.0478, 0.2934, 0.4527] 0.34375 0.25 0.339597 0.089597 0.09375 0.008400 0.008789
3 3 1 3 [0.72855335, 0.021446612, 0.12499998, 0.12499999] [0.7099, 0.0327, 0.1302, 0.1272] 0.56250 0.25 0.550076 0.300076 0.31250 0.093774 0.097656
4 4 1 3 [0.12500001, 0.37500003, 0.12499999, 0.37500003] [0.1344, 0.3685, 0.1304, 0.3667] 0.31250 0.25 0.308800 0.058800 0.06250 0.003675 0.003906