pairs,epsilon,theoretical_lower,lp_lower,constructive_value
1,0.0,1.0,1.0,1.0
1,0.0625,0.9375,0.9375,0.9375
1,0.125,0.875,0.875,0.875
1,0.1875,0.8125,0.8125,0.8125
1,0.25,0.75,0.75,0.75
1,0.3125,0.6875,0.6875,0.6875
1,0.375,0.625,0.625,0.625
1,0.4375,0.5625,0.5625,0.5625
1,0.5,0.5,0.5,0.5
1,0.5625,0.4375,0.4375,0.43750000000000006
1,0.625,0.375,0.375,0.37500000000000006
1,0.6875,0.3125,0.3125,0.31250000000000006
1,0.75,0.25,0.25,0.25000000000000006
1,0.8125,0.1875,0.1875,0.18750000000000006
1,0.875,0.125,0.125,0.12500000000000006
1,0.9375,0.0625,0.0625,0.06250000000000006
1,1.0,0.0,0.0,6.123233995736766e-17
2,0.0,1.0,1.0,1.0
2,0.0625,0.8125,0.8125,0.8125
2,0.125,0.625,0.625,0.625
2,0.1875,0.4375,0.4375,0.4375
2,0.25,0.25,0.25,0.25
2,0.3125,0.0625,0.0625,0.0625
2,0.375,-0.125,-0.125,-0.125
2,0.4375,-0.3125,-0.3125,-0.3125
2,0.5,-0.5,-0.5,-0.49999999999999994
2,0.5625,-0.5625,-0.5625,-0.5625
2,0.625,-0.625,-0.625,-0.625
2,0.6875,-0.6875,-0.6875,-0.6875
2,0.75,-0.75,-0.75,-0.75
2,0.8125,-0.8125,-0.8125,-0.8125
2,0.875,-0.875,-0.875,-0.875
2,0.9375,-0.9375,-0.9375,-0.9375
2,1.0,-1.0,-1.0,-1.0
3,0.0,1.0,1.0,1.0
3,0.0625,0.5625,0.5625,0.5625
3,0.125,0.125,0.125,0.125
3,0.1875,-0.3125,-0.3125,-0.3125
3,0.25,-0.75,-0.75,-0.75
3,0.3125,-0.9375,-0.9375,-0.9375
3,0.3333333333333333,-1.0,-1.0,-1.0
3,0.375,-1.0,-1.0,-1.0
3,0.4375,-1.0,-1.0,-1.0
3,0.5,-1.0,-1.0,-1.0
3,0.5625,-1.0,-1.0,-1.0
3,0.625,-1.0,-1.0,-1.0
3,0.6875,-1.0,-1.0,-1.0
3,0.75,-1.0,-1.0,-1.0
3,0.8125,-1.0,-1.0,-1.0
3,0.875,-1.0,-1.0,-1.0
3,0.9375,-1.0,-1.0,-1.0
3,1.0,-1.0,-1.0,-1.0
4,0.0,1.0,1.0,1.0
4,0.0625,0.0625,0.0625,0.0625
4,0.125,-0.875,-0.875,-0.875
4,0.14285714285714285,-1.0,-1.0000000000000002,-1.0
4,0.1875,-1.0,-1.0,-1.0
4,0.25,-1.0,-1.0,-1.0
4,0.3125,-1.0,-1.0,-1.0
4,0.375,-1.0,-1.0,-1.0
4,0.4375,-1.0,-1.0,-1.0
4,0.5,-1.0,-1.0,-1.0
4,0.5625,-1.0,-1.0,-1.0
4,0.625,-1.0,-1.0,-1.0
4,0.6875,-1.0,-1.0,-1.0
4,0.75,-1.0,-1.0,-1.0
4,0.8125,-1.0,-1.0,-1.0
4,0.875,-1.0,-1.0,-1.0
4,0.9375,-1.0,-1.0,-1.0
4,1.0,-1.0,-1.0,-1.0
5,0.0,1.0,1.0,1.0
5,0.0625,-0.9375,-0.9375,-0.9375
5,0.06666666666666667,-1.0,-1.0000000000000007,-1.0
5,0.125,-1.0,-1.0,-1.0
5,0.1875,-1.0,-1.0,-1.0
5,0.25,-1.0,-1.0,-1.0
5,0.3125,-1.0,-1.0,-1.0
5,0.375,-1.0,-1.0,-1.0
5,0.4375,-1.0,-1.0,-1.0
5,0.5,-1.0,-1.0,-1.0
5,0.5625,-1.0,-1.0,-1.0
5,0.625,-1.0,-1.0,-1.0
5,0.6875,-1.0,-1.0,-1.0
5,0.75,-1.0,-1.0,-1.0
5,0.8125,-1.0,-1.0,-1.0
5,0.875,-1.0,-1.0,-1.0
5,0.9375,-1.0,-1.0,-1.0
5,1.0,-1.0,-1.0,-1.0