== alternating 1/4, 3/4 (liminf 1/4): M=100000 phases reached k=5; UI=True count_identity=True bound=True transit=True
   q'_k for the last 4 phases: [0.25, 0.75, 0.25, 0.75]
   tail (m >= 192) min of delta_A along all m: (0.24991322457480042, 99809)
   along m = 2^i: (0.25, 9)
   along m = 3^i: (0.24996189605243102, 6)
   along m = 5^i: (0.249984, 4)
   along m = 10^i: (0.25, 3)
   along m_(i+1) = 2 m_i - 1: (0.24998474214220323, 9)
   along m_(i+1) = 3 m_i - 1: (0.24994919731761836, 6)
   adversarial ratio in [1.5,4] (greedy min): (0.24991322457480042, 12)
   liminf of recent targets q'_k: 0.25
== 1/3 + (-1)^k/(k+3) (liminf 1/3): M=100000 phases reached k=5; UI=True count_identity=True bound=True transit=True
   q'_k for the last 4 phases: [0.5333333333333333, 0.2, 0.47619047619047616, 0.20833333333333334]
   tail (m >= 104) min of delta_A along all m: (0.1971326164874552, 99897)
   along m = 2^i: (0.19921875, 10)
   along m = 3^i: (0.19890260631001372, 6)
   along m = 5^i: (0.2, 5)
   along m = 10^i: (0.2, 3)
   along m_(i+1) = 2 m_i - 1: (0.19883040935672514, 10)
   along m_(i+1) = 3 m_i - 1: (0.19926873857404023, 7)
   adversarial ratio in [1.5,4] (greedy min): (0.1971326164874552, 13)
   liminf of recent targets q'_k: 0.2
== 0,1,0,1,... (liminf 0): M=100000 phases reached k=4; UI=True count_identity=True bound=True transit=True
   q'_k for the last 4 phases: [0.6666666666666666, 0.25, 0.8, 0.16666666666666666]
   tail (m >= 18) min of delta_A along all m: (0.16661845530807057, 99983)
   along m = 2^i: (0.166656494140625, 12)
   along m = 3^i: (0.16664126403495402, 8)
   along m = 5^i: (0.166656, 6)
   along m = 10^i: (0.16666, 4)
   along m_(i+1) = 2 m_i - 1: (0.16665140834325123, 12)
   along m_(i+1) = 3 m_i - 1: (0.16663844199830652, 8)
   adversarial ratio in [1.5,4] (greedy min): (0.16662856097672504, 15)
   liminf of recent targets q'_k: 0.16666666666666666
== constant 1 (liminf 1): M=100000 phases reached k=6; UI=True count_identity=True bound=True transit=True
   q'_k for the last 4 phases: [0.8, 0.8333333333333334, 0.8571428571428571, 0.875]
   tail (m >= 600) min of delta_A along all m: (0.8, 99401)
   along m = 2^i: (0.8330078125, 7)
   along m = 3^i: (0.8326474622770919, 5)
   along m = 5^i: (0.808, 4)
   along m = 10^i: (0.833, 3)
   along m_(i+1) = 2 m_i - 1: (0.8330893118594437, 7)
   along m_(i+1) = 3 m_i - 1: (0.8327239488117002, 5)
   adversarial ratio in [1.5,4] (greedy min): (0.8187311178247734, 13)
   liminf of recent targets q'_k: 0.8
== sqrt2/2 approximants from above and 1/5 alternating (liminf 1/5): M=100000 phases reached k=5; UI=True count_identity=True bound=True transit=True
   q'_k for the last 4 phases: [0.25, 0.75, 0.8, 0.2]
   tail (m >= 192) min of delta_A along all m: (0.1999907411693903, 99809)
   along m = 2^i: (0.263671875, 9)
   along m = 3^i: (0.2926383173296754, 6)
   along m = 5^i: (0.221184, 4)
   along m = 10^i: (0.2, 3)
   along m_(i+1) = 2 m_i - 1: (0.2636678517478676, 9)
   along m_(i+1) = 3 m_i - 1: (0.19999096800415472, 6)
   adversarial ratio in [1.5,4] (greedy min): (0.1999907411693903, 11)
   liminf of recent targets q'_k: 0.2
