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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 14 31 31 25 20 33 14

N.S.

1 1.00 1.00 2.21 2.21 1.79 1.43 2.36 1.00

time (sec)

N/A 0.005 0.004 0.046 3.267 0.490 0.051 1.610 0.058

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 14 15 14 14 26 14 14

N.S.

1 1.00 1.00 1.07 1.00 1.00 1.86 1.00 1.00

time (sec)

N/A 0.003 0.003 0.049 5.304 0.550 0.048 1.455 0.040

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

13 13 37 18 17 26 27 40 11

N.S.

1 1.00 2.85 1.38 1.31 2.00 2.08 3.08 0.85

time (sec)

N/A 0.003 0.008 0.022 4.535 0.617 0.051 1.301 0.233

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 23 15 19 23 22 21 7

N.S.

1 1.00 2.09 1.36 1.73 2.09 2.00 1.91 0.64

time (sec)

N/A 0.003 0.008 0.031 1.577 0.593 0.052 1.159 0.070

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 21 27 29 22 29 24

N.S.

1 1.00 1.00 1.40 1.80 1.93 1.47 1.93 1.60

time (sec)

N/A 0.003 0.006 0.130 2.071 0.725 0.084 0.891 0.207

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

2 2 2 3 4 4 3 4 12

N.S.

1 1.00 1.00 1.50 2.00 2.00 1.50 2.00 6.00

time (sec)

N/A 0.005 0.002 0.011 1.782 0.538 0.011 1.042 0.255

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

4 4 4 5 6 6 5 6 6

N.S.

1 1.00 1.00 1.25 1.50 1.50 1.25 1.50 1.50

time (sec)

N/A 0.004 0.002 0.000 2.306 0.884 0.030 0.988 0.208

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

6 6 6 5 27 4 7 4 4

N.S.

1 1.00 1.00 0.83 4.50 0.67 1.17 0.67 0.67

time (sec)

N/A 0.016 0.012 0.026 1.887 1.172 0.398 0.825 0.180

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

9 9 6 5 9 9 3 30 4

N.S.

1 1.00 0.67 0.56 1.00 1.00 0.33 3.33 0.44

time (sec)

N/A 0.007 0.004 0.016 2.435 1.105 0.078 1.124 0.189

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 8 9 10 10 7 8 6

N.S.

1 1.00 0.67 0.75 0.83 0.83 0.58 0.67 0.50

time (sec)

N/A 0.008 0.010 0.008 1.999 1.019 0.156 0.894 0.002

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 12 13 13 12 15 14 13

N.S.

1 1.00 1.00 1.08 1.08 1.00 1.25 1.17 1.08

time (sec)

N/A 0.016 0.016 0.033 2.900 0.773 0.156 1.020 0.198

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 16 15 15 31 15 15

N.S.

1 1.00 1.00 1.07 1.00 1.00 2.07 1.00 1.00

time (sec)

N/A 0.019 0.009 0.057 2.531 1.072 0.249 0.881 0.047

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 33 33 26 44 35 15

N.S.

1 1.00 1.00 2.20 2.20 1.73 2.93 2.33 1.00

time (sec)

N/A 0.021 0.009 0.069 2.820 1.277 0.259 0.755 0.184

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 17 18 17 21 32 17 48

N.S.

1 1.00 1.00 1.06 1.00 1.24 1.88 1.00 2.82

time (sec)

N/A 0.028 0.009 0.091 1.851 1.260 1.385 0.889 0.606

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 19 20 20 23 34 21 48

N.S.

1 1.00 1.00 1.05 1.05 1.21 1.79 1.11 2.53

time (sec)

N/A 0.031 0.009 0.138 2.238 0.788 1.419 0.836 0.491

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

18 22 22 19 18 18 34 18 58

N.S.

1 1.22 1.22 1.06 1.00 1.00 1.89 1.00 3.22

time (sec)

N/A 0.028 0.013 0.087 3.556 0.985 1.388 0.946 0.406

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

18 22 22 19 19 19 32 20 58

N.S.

1 1.22 1.22 1.06 1.06 1.06 1.78 1.11 3.22

time (sec)

N/A 0.029 0.011 0.166 2.702 0.647 1.436 0.944 0.379

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 19 14 13 31 61 46 26

N.S.

1 1.00 0.46 0.34 0.32 0.76 1.49 1.12 0.63

time (sec)

N/A 0.012 0.019 0.037 4.578 0.829 0.228 0.856 0.232

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

6 6 6 6 15 15 15 16 15

N.S.

1 1.00 1.00 1.00 2.50 2.50 2.50 2.67 2.50

time (sec)

N/A 0.013 0.002 0.006 1.741 0.799 0.036 0.658 0.004

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

3 3 3 4 3 3 3 4 3

N.S.

1 1.00 1.00 1.33 1.00 1.00 1.00 1.33 1.00

time (sec)

N/A 0.010 0.005 0.003 1.835 0.919 0.026 0.805 0.176

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

3 3 3 4 3 3 15 3 3

N.S.

1 1.00 1.00 1.33 1.00 1.00 5.00 1.00 1.00

time (sec)

N/A 0.015 0.011 0.004 2.087 0.901 0.052 1.030 0.336

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

9 9 7 10 7 7 7 22 7

N.S.

1 1.00 0.78 1.11 0.78 0.78 0.78 2.44 0.78

time (sec)

N/A 0.014 0.009 0.006 2.135 0.616 0.031 0.867 0.206

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

9 9 9 10 9 9 7 9 9

N.S.

1 1.00 1.00 1.11 1.00 1.00 0.78 1.00 1.00

time (sec)

N/A 0.012 0.016 0.007 3.086 0.650 0.031 0.910 0.209

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 22 22 24 22 23 24

N.S.

1 1.00 1.00 0.88 0.88 0.96 0.88 0.92 0.96

time (sec)

N/A 0.014 0.017 0.027 1.843 0.650 0.154 1.047 0.043

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 30 21 20 22 27 21 22

N.S.

1 1.00 1.00 0.70 0.67 0.73 0.90 0.70 0.73

time (sec)

N/A 0.067 0.022 0.007 2.029 0.465 2.059 0.877 0.034

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

10 10 10 11 10 10 8 11 8

N.S.

1 1.00 1.00 1.10 1.00 1.00 0.80 1.10 0.80

time (sec)

N/A 0.005 0.002 0.054 2.088 0.707 0.016 1.769 0.063

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 47 24 36 40 42 37 47

N.S.

1 1.00 1.00 0.51 0.77 0.85 0.89 0.79 1.00

time (sec)

N/A 0.019 0.022 0.054 2.110 0.723 0.037 1.589 0.132

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 30 24 23 23 27 21 21

N.S.

1 1.00 1.00 0.80 0.77 0.77 0.90 0.70 0.70

time (sec)

N/A 0.006 0.011 0.060 1.931 0.941 0.038 1.285 0.037

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 21 14 13 24 22 17 13

N.S.

1 1.00 1.00 0.67 0.62 1.14 1.05 0.81 0.62

time (sec)

N/A 0.006 0.014 0.055 4.383 0.674 0.127 1.327 0.167

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 12 11 24 26 11 11

N.S.

1 1.00 1.00 0.80 0.73 1.60 1.73 0.73 0.73

time (sec)

N/A 0.006 0.008 0.063 6.019 0.577 0.125 1.137 0.060

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 21 20 186 89 138 18 118

N.S.

1 1.00 1.00 0.95 8.86 4.24 6.57 0.86 5.62

time (sec)

N/A 0.025 0.058 0.067 6.215 0.501 0.688 1.098 1.334

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 14 11 10 10 10 10 10

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 0.71

time (sec)

N/A 0.004 0.002 0.000 3.541 0.585 0.009 0.913 0.028

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 14 11 10 10 10 10 10

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 0.71

time (sec)

N/A 0.005 0.002 0.016 2.001 0.575 0.008 0.811 0.026

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

8 8 8 7 6 6 7 6 12

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.88 0.75 1.50

time (sec)

N/A 0.010 0.001 0.023 1.972 0.561 0.008 0.760 0.030

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 11 32 14 22 15 14 11

N.S.

1 1.00 1.00 2.91 1.27 2.00 1.36 1.27 1.00

time (sec)

N/A 0.011 0.006 0.027 3.748 0.548 0.025 0.680 0.072

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

7 7 6 15 9 18 12 9 6

N.S.

1 1.00 0.86 2.14 1.29 2.57 1.71 1.29 0.86

time (sec)

N/A 0.019 0.008 0.021 2.136 0.517 0.014 0.977 0.201

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 28 18 12 23 19 18 10

N.S.

1 1.00 2.00 1.29 0.86 1.64 1.36 1.29 0.71

time (sec)

N/A 0.006 0.011 0.013 3.842 0.575 0.014 1.040 0.170

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 26 19 12 20 17 22 18

N.S.

1 1.00 1.62 1.19 0.75 1.25 1.06 1.38 1.12

time (sec)

N/A 0.010 0.013 0.027 2.554 0.665 0.047 0.848 0.270

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

10 10 10 11 12 19 10 12 12

N.S.

1 1.00 1.00 1.10 1.20 1.90 1.00 1.20 1.20

time (sec)

N/A 0.021 0.013 0.033 2.729 0.678 0.138 1.418 0.267

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 12 15 14 25 10 14 14

N.S.

1 1.00 0.86 1.07 1.00 1.79 0.71 1.00 1.00

time (sec)

N/A 0.048 0.009 0.040 2.157 0.613 0.644 1.049 0.275

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 25 19 28 24 29 12 12

N.S.

1 1.00 2.27 1.73 2.55 2.18 2.64 1.09 1.09

time (sec)

N/A 0.017 0.028 0.027 2.975 0.494 0.229 1.295 0.235

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 21 17 23 14 8 12 10

N.S.

1 1.00 1.31 1.06 1.44 0.88 0.50 0.75 0.62

time (sec)

N/A 0.020 0.017 0.024 2.278 0.553 0.197 1.115 0.166

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 33 29 18 22 19 18 18

N.S.

1 1.00 1.32 1.16 0.72 0.88 0.76 0.72 0.72

time (sec)

N/A 0.018 0.020 0.016 3.130 0.664 0.035 1.238 0.216

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 21 14 13 13 12 15 8

N.S.

1 1.00 1.00 0.67 0.62 0.62 0.57 0.71 0.38

time (sec)

N/A 0.003 0.003 0.080 6.091 0.749 0.030 1.344 0.257

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 14 11 10 10 10 10 10

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 0.71

time (sec)

N/A 0.012 0.005 0.013 2.143 0.598 0.034 1.677 0.063

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 47 29 35 45 42 44 34

N.S.

1 1.00 0.92 0.57 0.69 0.88 0.82 0.86 0.67

time (sec)

N/A 0.011 0.018 0.100 3.044 0.672 0.040 1.483 0.122

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 33 47 25 25 29 25 25

N.S.

1 1.00 1.00 1.42 0.76 0.76 0.88 0.76 0.76

time (sec)

N/A 0.008 0.015 0.094 3.517 0.944 0.042 1.077 0.203

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 29 19 18 68 73 18 19

N.S.

1 1.00 1.00 0.66 0.62 2.34 2.52 0.62 0.66

time (sec)

N/A 0.010 0.017 0.054 3.559 0.748 0.434 1.315 0.205

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 20 23 22 19 37 19 20

N.S.

1 1.00 0.74 0.85 0.81 0.70 1.37 0.70 0.74

time (sec)

N/A 0.007 0.011 0.048 2.112 0.792 0.145 1.131 0.042

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 22 19 18 25 29 10 18

N.S.

1 1.00 1.00 0.86 0.82 1.14 1.32 0.45 0.82

time (sec)

N/A 0.007 0.090 0.053 4.489 0.971 0.453 1.052 0.094

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 22 41 12 26 22 20 24

N.S.

1 1.00 1.00 1.86 0.55 1.18 1.00 0.91 1.09

time (sec)

N/A 0.009 0.019 0.055 4.408 1.088 0.451 0.792 0.258

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 53 37 34 25 22 43 21

N.S.

1 1.00 2.30 1.61 1.48 1.09 0.96 1.87 0.91

time (sec)

N/A 0.010 0.038 0.052 2.025 0.928 0.466 0.706 0.445

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 49 35 12 40 7 37 26

N.S.

1 1.00 2.33 1.67 0.57 1.90 0.33 1.76 1.24

time (sec)

N/A 0.009 0.027 0.053 1.959 0.743 0.432 0.880 0.094

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 21 7 8 30 0 26 6

N.S.

1 1.00 1.75 0.58 0.67 2.50 0.00 2.17 0.50

time (sec)

N/A 0.005 0.060 0.099 3.025 0.755 0.000 0.703 0.182

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 33 15 16 38 0 53 26

N.S.

1 1.00 1.74 0.79 0.84 2.00 0.00 2.79 1.37

time (sec)

N/A 0.009 0.064 0.226 3.865 0.693 0.000 0.766 0.294

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

8 8 38 7 6 16 0 25 6

N.S.

1 1.00 4.75 0.88 0.75 2.00 0.00 3.12 0.75

time (sec)

N/A 0.002 0.030 0.075 2.435 0.672 0.000 0.695 0.156

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 36 22 21 43 0 21 40

N.S.

1 1.00 1.33 0.81 0.78 1.59 0.00 0.78 1.48

time (sec)

N/A 0.008 0.093 0.096 2.730 0.625 0.000 0.701 0.315

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 34 25 33 39 0 71 28

N.S.

1 1.00 1.06 0.78 1.03 1.22 0.00 2.22 0.88

time (sec)

N/A 0.008 0.073 0.106 1.574 0.577 0.000 0.976 0.338

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 23 21 22 17 17 0 28 19

N.S.

1 1.10 1.00 1.05 0.81 0.81 0.00 1.33 0.90

time (sec)

N/A 0.004 0.102 0.090 3.862 0.499 0.000 0.917 0.221

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 54 23 33 39 22 31 22

N.S.

1 1.00 1.93 0.82 1.18 1.39 0.79 1.11 0.79

time (sec)

N/A 0.097 0.049 0.069 3.470 0.886 0.302 0.979 0.278

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 48 17 14 13 31 0 46 26

N.S.

1 1.30 0.46 0.38 0.35 0.84 0.00 1.24 0.70

time (sec)

N/A 0.018 0.036 0.039 1.879 1.279 0.000 0.795 0.236

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 21 11 47 32 27 11 10

N.S.

1 1.00 1.50 0.79 3.36 2.29 1.93 0.79 0.71

time (sec)

N/A 0.025 0.015 0.077 2.320 0.971 0.691 0.950 0.215

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 23 4 15 45 15 17 3

N.S.

1 1.00 2.09 0.36 1.36 4.09 1.36 1.55 0.27

time (sec)

N/A 0.023 0.007 0.020 2.214 0.893 0.053 1.308 0.352

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

18 19 19 15 14 14 0 14 14

N.S.

1 1.06 1.06 0.83 0.78 0.78 0.00 0.78 0.78

time (sec)

N/A 0.034 0.013 0.037 1.517 0.875 0.000 1.534 0.315

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

18 18 18 15 14 15 17 14 14

N.S.

1 1.00 1.00 0.83 0.78 0.83 0.94 0.78 0.78

time (sec)

N/A 0.033 0.015 0.065 2.255 0.795 1.039 1.161 0.304

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 17 16 15 15 0 15 37

N.S.

1 1.00 1.00 0.94 0.88 0.88 0.00 0.88 2.18

time (sec)

N/A 0.010 0.021 0.041 2.479 0.612 0.000 1.075 0.293

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 20 0 18 16 7 16 16

N.S.

1 1.00 1.00 0.00 0.90 0.80 0.35 0.80 0.80

time (sec)

N/A 0.017 0.025 0.007 1.210 0.638 0.342 0.761 0.341

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 12 13 12 12 15 12 12

N.S.

1 1.00 1.00 1.08 1.00 1.00 1.25 1.00 1.00

time (sec)

N/A 0.017 0.005 0.138 0.286 0.700 0.878 0.736 0.232

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 42 38 0 38 0 15 -1

N.S.

1 1.00 1.00 0.90 0.00 0.90 0.00 0.36 -0.02

time (sec)

N/A 0.022 0.029 0.071 0.000 0.644 0.000 1.167 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

8 8 8 7 6 6 7 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.88 0.75 0.75

time (sec)

N/A 0.017 0.006 0.054 2.500 0.623 0.479 0.824 0.349

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 28 23 17 22 22 22 17

N.S.

1 1.00 1.00 0.82 0.61 0.79 0.79 0.79 0.61

time (sec)

N/A 0.007 0.002 0.000 1.671 0.573 0.034 0.835 0.034

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 17 14 13 11 15 13 9

N.S.

1 1.00 1.00 0.82 0.76 0.65 0.88 0.76 0.53

time (sec)

N/A 0.005 0.002 0.008 0.428 0.656 0.034 0.778 0.166

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 38 38 53 28 28 26 70 40

N.S.

1 1.06 1.06 1.47 0.78 0.78 0.72 1.94 1.11

time (sec)

N/A 0.020 0.006 0.030 0.852 0.935 0.042 0.878 0.345

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 23 17 15 18 17 15 21

N.S.

1 1.00 1.21 0.89 0.79 0.95 0.89 0.79 1.11

time (sec)

N/A 0.007 0.002 0.011 0.681 0.737 0.011 0.816 0.002

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 30 26 18 25 31 22 26

N.S.

1 1.00 0.88 0.76 0.53 0.74 0.91 0.65 0.76

time (sec)

N/A 0.023 0.012 0.021 0.780 0.811 0.009 0.828 0.022

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 71 26 42 69 46 38 33

N.S.

1 1.00 2.73 1.00 1.62 2.65 1.77 1.46 1.27

time (sec)

N/A 0.009 0.006 0.076 0.590 0.818 0.056 0.783 0.291

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 14 18 11 17 17 11 11

N.S.

1 1.00 0.61 0.78 0.48 0.74 0.74 0.48 0.48

time (sec)

N/A 0.007 0.010 0.025 1.632 0.656 0.163 0.888 0.023

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 22 22 19 21 26 19 19

N.S.

1 1.00 0.81 0.81 0.70 0.78 0.96 0.70 0.70

time (sec)

N/A 0.007 0.027 0.024 0.610 0.801 0.087 0.791 0.036

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 20 32 24 20 104 329 20

N.S.

1 1.00 0.65 1.03 0.77 0.65 3.35 10.61 0.65

time (sec)

N/A 0.008 0.015 0.033 0.960 0.997 0.268 0.752 0.026

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 17 14 10 13 15 13 13

N.S.

1 1.00 1.00 0.82 0.59 0.76 0.88 0.76 0.76

time (sec)

N/A 0.003 0.003 0.016 0.587 0.644 0.106 0.832 0.195

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 12 67 94 22 15 12 35

N.S.

1 1.00 1.00 5.58 7.83 1.83 1.25 1.00 2.92

time (sec)

N/A 0.017 0.013 0.119 1.127 0.628 20.405 0.650 0.428

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 20 107 21 19 23 13

N.S.

1 1.00 1.00 1.33 7.13 1.40 1.27 1.53 0.87

time (sec)

N/A 0.014 0.014 0.006 1.412 0.492 0.055 0.587 0.023

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 22 21 33 39 22 38 20

N.S.

1 1.00 1.00 0.95 1.50 1.77 1.00 1.73 0.91

time (sec)

N/A 0.011 0.003 0.001 0.917 0.490 0.965 0.805 0.021

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 24 23 23 22 23 22

N.S.

1 1.00 1.00 0.96 0.92 0.92 0.88 0.92 0.88

time (sec)

N/A 0.023 0.006 0.001 1.414 0.497 0.061 0.685 0.049

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 23 20 24 19 19 19 19

N.S.

1 1.00 1.00 0.87 1.04 0.83 0.83 0.83 0.83

time (sec)

N/A 0.039 0.012 0.079 0.919 0.467 0.111 0.590 0.220

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 57 49 45 78 30 63 0 -1

N.S.

1 1.50 1.29 1.18 2.05 0.79 1.66 0.00 -0.03

time (sec)

N/A 0.024 0.038 0.008 1.306 0.516 4.691 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 22 21 21 22 21 21

N.S.

1 1.00 1.00 0.88 0.84 0.84 0.88 0.84 0.84

time (sec)

N/A 0.006 0.002 0.040 0.564 0.441 0.007 0.581 0.043

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 39 30 29 29 34 29 29

N.S.

1 1.00 1.00 0.77 0.74 0.74 0.87 0.74 0.74

time (sec)

N/A 0.010 0.001 0.084 0.755 0.465 0.010 0.582 0.032

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 23 29 23 27 75 23 23

N.S.

1 1.00 1.00 1.26 1.00 1.17 3.26 1.00 1.00

time (sec)

N/A 0.006 0.034 0.077 0.284 0.438 26.079 0.566 0.725

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 27 23 22 22 20 23 20

N.S.

1 1.00 0.90 0.77 0.73 0.73 0.67 0.77 0.67

time (sec)

N/A 0.009 0.006 0.052 0.905 0.395 0.017 0.479 0.035

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 35 27 26 32 34 26 32

N.S.

1 1.00 0.85 0.66 0.63 0.78 0.83 0.63 0.78

time (sec)

N/A 0.009 0.008 0.061 1.038 0.416 0.029 0.496 0.041

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 21 16 15 15 14 17 8

N.S.

1 1.00 1.00 0.76 0.71 0.71 0.67 0.81 0.38

time (sec)

N/A 0.004 0.003 0.081 2.573 0.402 0.031 1.087 0.089

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 32 29 28 28 36 28 30

N.S.

1 1.00 0.97 0.88 0.85 0.85 1.09 0.85 0.91

time (sec)

N/A 0.012 0.007 0.173 2.082 0.416 0.035 0.964 0.044

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 22 21 21 22 21 21

N.S.

1 1.00 1.00 0.88 0.84 0.84 0.88 0.84 0.84

time (sec)

N/A 0.012 0.004 0.079 2.369 0.403 0.033 0.817 0.040

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 47 39 38 38 46 38 40

N.S.

1 1.00 1.00 0.83 0.81 0.81 0.98 0.81 0.85

time (sec)

N/A 0.044 0.013 0.122 4.697 0.389 0.037 0.667 0.197

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 18 17 17 17 20 17

N.S.

1 1.00 1.00 0.72 0.68 0.68 0.68 0.80 0.68

time (sec)

N/A 0.027 0.004 0.015 1.616 0.382 0.047 0.785 0.227

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 29 30 25 25 26 28 25

N.S.

1 1.00 0.88 0.91 0.76 0.76 0.79 0.85 0.76

time (sec)

N/A 0.038 0.011 0.020 1.626 0.399 0.114 0.678 0.088

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 61 37 26 25 25 29 29 29

N.S.

1 1.65 1.00 0.70 0.68 0.68 0.78 0.78 0.78

time (sec)

N/A 0.027 0.005 0.019 1.446 0.787 0.071 0.602 0.061

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 69 26 43 51 60 59 25

N.S.

1 1.00 2.23 0.84 1.39 1.65 1.94 1.90 0.81

time (sec)

N/A 0.008 0.013 0.020 2.718 1.022 0.302 0.478 0.083

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 41 26 25 25 26 29 15

N.S.

1 1.00 1.00 0.63 0.61 0.61 0.63 0.71 0.37

time (sec)

N/A 0.015 0.006 0.082 1.294 0.940 0.066 0.538 0.246

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