Table 1 The three-dimensional convex hull of models found by the machine-learning algorithm

5393157

1

2

\({\sum} {rf(r)}\)

1800.1

1

4

\({\sum} {r^{ - 3.20}f(r)}\)

105.30

1

8

\({\sum} {(649.17r^{ - 9.83} - 0.09)f(r)}\)

54.144

1

10

\({\sum} {(r^{10.20 - 5.49r} - 0.07)f(r)}\)

26.906

2

13

\({\sum} {r^{10.20 - 5.49r}f(r)} + 33.77\left( {{\sum} {f(r)} } \right)^{ - 1}\)

8.1584

2

15

\({\sum} {r^{10.21 - 5.48r}f(r)} + 1.19\left( {{\sum} {0.33^rf(r)} } \right)^{ - 1}\)

7.8230^b

2

21

\({\sum} {(r^{10.21 - 5.47r} - 0.21^r)f(r)} + 0.97\left( {{\sum} {0.33^rf(r)} } \right)^{ - 1}\)

7.8229

2

25

\(0.999{\sum} {(r^{10.21 - 5.46r} - 0.21^r)f(r)} + 0.97\left( {{\sum} {0.33^rf(r)} } \right)^{ - 1} + 5.76\)

7.4131

4

19

\({\sum} {r^{10.21 - 5.48r}f(r)} + \left( {3.07{\sum} {f(r)} } \right)\left( {{\sum} {0.31^rf(r)} } \right)^{ - 1}\left( {{\sum} {rf(r)} } \right)^{ - 1}\)

4.7294^b

3

28

\(7.33{\sum} {r^{3.98 - 3.94r}f(r)} + \left( {27.32 - {\sum} {(11.13 + 0.03r^{11.74 - 2.93r})f(r)} } \right)\left( {{\sum} {f(r)} } \right)^{ - 1}\)

4.2932

4

29

\(6.76{\sum} {r^{4.00 - 3.88r}f(r)} + 17.25\left( {{\sum} {f(r)} } \right)\left( {{\sum} {r^{11.68 - 3.07r}f(r)} } \right)^{ - 1} + 25.30\left( {{\sum} {f(r)} } \right)^{ - 1}\)