Table 3 Numerical results for the comparisons

\(\, f_{1} (x)\)

Best

4.77e−29

3.21e−30

3.38e−41

3.85e−54

5.11e−38

1.89e−19

1.45e−150

0.00

SD

1.13e−28

1.91e−30

8.50e−41

1.75e−53

1.91e−37

1.49e−19

5.73e−150

0.00

Rank

7

6

4

3

5

8

2

1

\(\, f_{2} (x)\)

Best

2.03e−20

1.32e−17

6.9e−23

2.61e−29

6.29e−27

1.01e−13

5.15e−84

3.95e−323

SD

2.89e−20

7.86e−18

6.89e−23

6.6e−29

8.68e−27

6.51e−14

1.44e−83

5.13e−322

Rank

6

7

5

3

4

8

2

1

\(\, f_{3} (x)\)

Best

18.60

0.77

2.89e−7

47.5

1.44

395

1.0e−10

0.00

SD

30.71

0.86

2.97e−7

56.4

1.55

142

2.13e−10

0.00

Rank

6

4

3

7

5

8

2

1

\(\, f_{5} (x)\)

Best

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

SD

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

Rank

1

1

1

1

1

1

1

1

\(\, f_{6} (x)\)

Best

1.49e−2

2.55e−3

5.54e−2

1.1e−2

1.08e−2

3.92e−3

4.66e−3

5.88e−001

SD

5.66e−3

6.25e−4

2.08e−2

3.94e−3

3.24e−3

1.14e−3

1.7e−3

2.73e−001

Rank

6

1

7

5

4

2

3

8

\(\, f_{7} (x)\)

Best

34.90

29.98

2.39

28.1

34.09

2.57e−11

5.8e−15

0.00

SD

7.25

10.92

3.71

6.42

8.07

6.64e–11

1.01e−14

0.00

Rank

8

6

4

5

7

3

2

1

\(\, f_{8} (x)\)

Best

30.40

21.33

35.91

1.83

32.8

0.167

4.14e−16

0.00

SD

9.23

9.46

9.49

2.65

6.49

0.397

1.45e−15

0.00

Rank

6

5

8

4

7

3

2

1

\(\, f_{9} (x)\)

Best

1.85e−14

7.69e−15

2.06e−10

8.52e−15

1.14e−14

2.01e−12

1.11e−14

3.55e−015

SD

4.80e−15

9.33e−16

9.45e−10

1.79e−15

3.48e−15

9.22e−13

3.55e−15

0.00e+000

Rank

6

2

8

3

5

7

4

1

\(\, f_{10} (x)\)

Best

1.10e−2

9.04e−4

1.07e−2

1.31e−2

1.31e−2

6.45e−13

1.67e−2

0.00

SD

1.60e−2

2.78e−3

1.14e−2

1.73e−2

1.35e−2

2.07e−12

2.41e−2

0.00

Rank

5

3

4

7

6

2

8

1

\(\, f_{12} (x)\)

Best

2.18e−30

1.22e−31

7.07e−30

2.05e−32

3.46e−3

1.59e−21

3.76e−31

9.72e−002

SD

5.14e−30

4.85e−32

4.05e−30

8.12e−33

1.89e−2

1.93e−21

1.2e−30

1.97e−002

Rank

4

2

5

1

7

6

3

8

AR

5.5

3.7

4.9

3.9

5.1

4.8

2.9

2.4

FR

8

3

6

4

7

5

2

1