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Integrals 1 to 100

Detailed conclusion table per each integral is given by the 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 as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 21 11 10 10 12 26 10

N.S.

1 1.00 2.10 1.10 1.00 1.00 1.20 2.60 1.00

time (sec)

N/A 0.004 0.004 0.329 0.177 0.271 0.049 0.272 0.057

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 23 20 32 23 46 32 18

N.S.

1 1.00 0.92 0.80 1.28 0.92 1.84 1.28 0.72

time (sec)

N/A 0.007 0.014 0.477 0.190 0.248 0.077 0.278 1.091

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 29 23 54 38 36 54 24

N.S.

1 1.00 1.07 0.85 2.00 1.41 1.33 2.00 0.89

time (sec)

N/A 0.010 0.004 1.493 0.186 0.244 0.100 0.273 0.061

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 33 31 60 49 95 60 32

N.S.

1 1.00 0.72 0.67 1.30 1.07 2.07 1.30 0.70

time (sec)

N/A 0.016 0.041 1.428 0.188 0.244 0.145 0.286 0.089

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 44 33 82 79 58 82 31

N.S.

1 1.00 1.07 0.80 2.00 1.93 1.41 2.00 0.76

time (sec)

N/A 0.012 0.030 1.520 0.180 0.244 0.200 0.275 1.144

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 43 42 86 90 139 88 42

N.S.

1 1.00 0.64 0.63 1.28 1.34 2.07 1.31 0.63

time (sec)

N/A 0.024 0.057 1.643 0.186 0.240 0.311 0.270 0.148

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 75 116 0 326 0 0 0

N.S.

1 1.00 0.73 1.13 0.00 3.17 0.00 0.00 0.00

time (sec)

N/A 0.039 0.116 0.853 0.000 0.082 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 68 164 0 202 0 0 0

N.S.

1 1.00 0.85 2.05 0.00 2.52 0.00 0.00 0.00

time (sec)

N/A 0.027 0.064 0.749 0.000 0.077 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 83 100 0 103 0 0 0

N.S.

1 1.00 1.04 1.25 0.00 1.29 0.00 0.00 0.00

time (sec)

N/A 0.026 0.071 0.777 0.000 0.080 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 50 108 0 37 0 0 0

N.S.

1 1.00 0.93 2.00 0.00 0.69 0.00 0.00 0.00

time (sec)

N/A 0.015 0.083 0.891 0.000 0.071 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 48 87 0 24 0 0 0

N.S.

1 1.00 0.89 1.61 0.00 0.44 0.00 0.00 0.00

time (sec)

N/A 0.015 0.097 0.594 0.000 0.073 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 57 154 0 152 0 0 0

N.S.

1 1.00 0.75 2.03 0.00 2.00 0.00 0.00 0.00

time (sec)

N/A 0.025 0.049 0.875 0.000 0.073 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 86 101 0 314 0 0 0

N.S.

1 1.00 1.08 1.26 0.00 3.92 0.00 0.00 0.00

time (sec)

N/A 0.030 0.067 0.780 0.000 0.083 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 73 192 0 621 0 0 0

N.S.

1 1.00 0.71 1.86 0.00 6.03 0.00 0.00 0.00

time (sec)

N/A 0.037 0.126 0.802 0.000 0.080 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 116 76 122 0 394 0 0 0

N.S.

1 1.00 0.66 1.05 0.00 3.40 0.00 0.00 0.00

time (sec)

N/A 0.045 0.217 1.058 0.000 0.093 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 68 170 0 249 0 0 0

N.S.

1 1.00 0.77 1.93 0.00 2.83 0.00 0.00 0.00

time (sec)

N/A 0.033 0.102 0.783 0.000 0.084 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 88 106 0 115 0 0 0

N.S.

1 1.00 1.00 1.20 0.00 1.31 0.00 0.00 0.00

time (sec)

N/A 0.032 0.103 0.891 0.000 0.076 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 52 111 0 42 0 0 0

N.S.

1 1.00 0.93 1.98 0.00 0.75 0.00 0.00 0.00

time (sec)

N/A 0.017 0.052 1.246 0.000 0.072 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 54 89 0 27 0 0 0

N.S.

1 1.00 0.96 1.59 0.00 0.48 0.00 0.00 0.00

time (sec)

N/A 0.018 0.038 0.731 0.000 0.068 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 86 62 159 0 169 0 0 0

N.S.

1 1.00 0.72 1.85 0.00 1.97 0.00 0.00 0.00

time (sec)

N/A 0.030 0.059 0.746 0.000 0.074 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 90 84 114 0 347 0 0 0

N.S.

1 1.00 0.93 1.27 0.00 3.86 0.00 0.00 0.00

time (sec)

N/A 0.028 0.081 0.875 0.000 0.086 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 118 79 205 0 675 0 0 0

N.S.

1 1.00 0.67 1.74 0.00 5.72 0.00 0.00 0.00

time (sec)

N/A 0.046 0.134 0.934 0.000 0.084 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 65 122 0 104 0 0 0

N.S.

1 1.00 0.71 1.34 0.00 1.14 0.00 0.00 0.00

time (sec)

N/A 0.031 0.134 0.849 0.000 0.085 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F F(-1) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 55 169 0 94 0 0 0

N.S.

1 1.00 0.89 2.73 0.00 1.52 0.00 0.00 0.00

time (sec)

N/A 0.016 0.053 0.868 0.000 0.079 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 94 104 0 79 0 0 0

N.S.

1 1.00 1.52 1.68 0.00 1.27 0.00 0.00 0.00

time (sec)

N/A 0.017 0.107 1.084 0.000 0.077 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 28 91 0 53 0 0 0

N.S.

1 1.00 0.93 3.03 0.00 1.77 0.00 0.00 0.00

time (sec)

N/A 0.007 0.025 1.485 0.000 0.076 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 28 68 0 20 0 0 0

N.S.

1 1.00 0.93 2.27 0.00 0.67 0.00 0.00 0.00

time (sec)

N/A 0.008 0.031 0.641 0.000 0.074 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 50 159 0 87 0 0 0

N.S.

1 1.00 0.86 2.74 0.00 1.50 0.00 0.00 0.00

time (sec)

N/A 0.015 0.081 0.973 0.000 0.082 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 83 112 0 132 0 0 0

N.S.

1 1.00 1.34 1.81 0.00 2.13 0.00 0.00 0.00

time (sec)

N/A 0.018 0.074 0.934 0.000 0.086 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 80 204 0 178 0 0 0

N.S.

1 1.00 0.88 2.24 0.00 1.96 0.00 0.00 0.00

time (sec)

N/A 0.026 0.100 0.977 0.000 0.076 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

60 60 57 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.012 0.044 0.000 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

60 60 57 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.013 0.029 0.000 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

60 60 57 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.012 0.031 0.000 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

60 60 57 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.012 0.033 0.000 0.000 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

58 58 55 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.012 0.032 0.000 0.000 0.000 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

58 58 55 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.012 0.029 0.000 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

70 70 65 0 0 0 0 0 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.016 0.033 0.000 0.000 0.000 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

72 72 67 0 0 0 0 0 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.013 0.031 0.000 0.000 0.000 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

72 72 67 0 0 0 0 0 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.012 0.033 0.000 0.000 0.000 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 134 51 59 67 58 50 50

N.S.

1 1.00 2.91 1.11 1.28 1.46 1.26 1.09 1.09

time (sec)

N/A 0.045 0.148 3.487 0.189 0.246 0.092 0.279 1.262

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 41 39 45 55 41 38 38

N.S.

1 1.00 1.14 1.08 1.25 1.53 1.14 1.06 1.06

time (sec)

N/A 0.032 0.100 2.369 0.191 0.239 0.078 0.259 1.165

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 79 25 33 37 20 26 24

N.S.

1 1.00 3.59 1.14 1.50 1.68 0.91 1.18 1.09

time (sec)

N/A 0.041 0.086 1.780 0.187 0.254 0.061 0.261 1.144

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 43 13 12 16 8 10 12

N.S.

1 1.00 3.07 0.93 0.86 1.14 0.57 0.71 0.86

time (sec)

N/A 0.020 0.052 1.029 0.184 0.244 0.040 0.260 1.177

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 30 21 29 33 0 24 35

N.S.

1 1.00 1.58 1.11 1.53 1.74 0.00 1.26 1.84

time (sec)

N/A 0.028 0.017 1.635 0.183 0.241 0.000 0.274 0.193

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 36 35 51 77 0 44 51

N.S.

1 1.00 1.57 1.52 2.22 3.35 0.00 1.91 2.22

time (sec)

N/A 0.042 0.034 2.717 0.182 0.250 0.000 0.269 1.405

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 49 53 75 126 0 51 70

N.S.

1 1.00 1.32 1.43 2.03 3.41 0.00 1.38 1.89

time (sec)

N/A 0.053 0.152 3.497 0.185 0.245 0.000 0.260 1.446

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 53 71 103 174 0 58 85

N.S.

1 1.00 1.13 1.51 2.19 3.70 0.00 1.23 1.81

time (sec)

N/A 0.051 0.201 4.335 0.182 0.257 0.000 0.276 1.486

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 147 52 71 89 70 50 97

N.S.

1 1.00 2.53 0.90 1.22 1.53 1.21 0.86 1.67

time (sec)

N/A 0.070 0.146 3.043 0.187 0.246 0.102 0.259 1.296

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 45 38 59 74 54 38 79

N.S.

1 1.00 1.02 0.86 1.34 1.68 1.23 0.86 1.80

time (sec)

N/A 0.097 0.104 2.362 0.187 0.250 0.088 0.263 1.339

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 55 26 40 50 41 22 71

N.S.

1 1.00 1.72 0.81 1.25 1.56 1.28 0.69 2.22

time (sec)

N/A 0.044 0.112 1.661 0.179 0.242 0.069 0.262 1.301

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 22 23 81 32 37 20 25

N.S.

1 1.00 0.71 0.74 2.61 1.03 1.19 0.65 0.81

time (sec)

N/A 0.021 0.009 1.400 0.184 0.229 0.062 0.260 1.296

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 68 36 55 78 0 34 41

N.S.

1 1.00 2.00 1.06 1.62 2.29 0.00 1.00 1.21

time (sec)

N/A 0.057 0.717 2.332 0.181 0.251 0.000 0.267 0.311

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 88 58 79 130 0 46 85

N.S.

1 1.00 2.10 1.38 1.88 3.10 0.00 1.10 2.02

time (sec)

N/A 0.080 1.267 3.171 0.186 0.255 0.000 0.295 1.483

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 140 72 105 174 0 59 79

N.S.

1 1.00 2.41 1.24 1.81 3.00 0.00 1.02 1.36

time (sec)

N/A 0.092 1.158 4.161 0.192 0.266 0.000 0.258 1.582

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 143 88 127 226 0 84 189

N.S.

1 1.00 2.23 1.38 1.98 3.53 0.00 1.31 2.95

time (sec)

N/A 0.095 2.331 5.817 0.188 0.276 0.000 0.278 1.950

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 42 18 20 16 15 15 17

N.S.

1 1.00 1.56 0.67 0.74 0.59 0.56 0.56 0.63

time (sec)

N/A 0.009 0.188 0.862 0.180 0.254 0.059 0.266 0.210

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 61 28 94 50 61 25 29

N.S.

1 1.00 1.03 0.47 1.59 0.85 1.03 0.42 0.49

time (sec)

N/A 0.020 0.278 0.945 0.187 0.246 0.099 0.255 1.318

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 81 40 211 85 109 36 40

N.S.

1 1.00 0.92 0.45 2.40 0.97 1.24 0.41 0.45

time (sec)

N/A 0.032 0.295 0.984 0.195 0.240 0.152 0.265 1.508

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 87 51 372 120 155 47 53

N.S.

1 1.00 0.74 0.44 3.18 1.03 1.32 0.40 0.45

time (sec)

N/A 0.042 0.184 1.061 0.193 0.238 0.214 0.271 1.891

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 42 18 20 16 17 15 17

N.S.

1 1.00 1.56 0.67 0.74 0.59 0.63 0.56 0.63

time (sec)

N/A 0.009 0.190 0.968 0.192 0.262 0.059 0.261 0.162

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 59 28 94 50 61 25 29

N.S.

1 1.00 1.00 0.47 1.59 0.85 1.03 0.42 0.49

time (sec)

N/A 0.020 0.184 0.963 0.210 0.237 0.101 0.276 1.362

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 81 40 211 85 109 36 40

N.S.

1 1.00 0.92 0.45 2.40 0.97 1.24 0.41 0.45

time (sec)

N/A 0.031 0.338 0.956 0.224 0.237 0.156 0.260 1.421

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 87 51 372 120 155 47 52

N.S.

1 1.00 0.74 0.44 3.18 1.03 1.32 0.40 0.44

time (sec)

N/A 0.043 0.189 1.137 0.226 0.231 0.216 0.275 1.678

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F A F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 75 108 0 76 0 0 0

N.S.

1 1.00 1.32 1.89 0.00 1.33 0.00 0.00 0.00

time (sec)

N/A 0.041 0.252 4.206 0.000 0.276 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F A F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 76 108 0 76 0 0 0

N.S.

1 1.00 1.33 1.89 0.00 1.33 0.00 0.00 0.00

time (sec)

N/A 0.040 0.278 4.369 0.000 0.275 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A F(-1) F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

104 104 145 0 0 101 0 0 0

N.S.

1 1.00 1.39 0.00 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.037 6.041 0.000 0.000 0.261 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F A F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

69 69 113 0 0 63 0 0 0

N.S.

1 1.00 1.64 0.00 0.00 0.91 0.00 0.00 0.00

time (sec)

N/A 0.023 5.357 0.000 0.000 0.251 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 74 89 0 27 0 0 53

N.S.

1 1.00 2.39 2.87 0.00 0.87 0.00 0.00 1.71

time (sec)

N/A 0.011 0.033 2.191 0.000 0.243 0.000 0.000 1.528

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 52 84 160 0 93 0 0 0

N.S.

1 1.00 1.62 3.08 0.00 1.79 0.00 0.00 0.00

time (sec)

N/A 0.017 0.169 6.702 0.000 0.243 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F B F F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

87 87 156 0 0 235 0 0 0

N.S.

1 1.00 1.79 0.00 0.00 2.70 0.00 0.00 0.00

time (sec)

N/A 0.032 0.283 0.000 0.000 0.276 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F B F(-1) F F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

122 122 210 0 0 348 0 0 0

N.S.

1 1.00 1.72 0.00 0.00 2.85 0.00 0.00 0.00

time (sec)

N/A 0.048 0.259 0.000 0.000 0.296 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 108 105 201 158 799 0 156 199

N.S.

1 1.00 0.97 1.86 1.46 7.40 0.00 1.44 1.84

time (sec)

N/A 0.225 1.643 0.670 0.270 0.295 0.000 0.280 1.539

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 82 152 118 459 0 117 159

N.S.

1 1.00 1.00 1.85 1.44 5.60 0.00 1.43 1.94

time (sec)

N/A 0.132 0.926 0.579 0.274 0.304 0.000 0.271 1.353

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 61 92 84 238 1253 86 129

N.S.

1 1.00 1.07 1.61 1.47 4.18 21.98 1.51 2.26

time (sec)

N/A 0.080 0.253 0.534 0.275 0.346 110.085 0.279 1.268

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 52 63 65 134 170 67 99

N.S.

1 1.00 1.11 1.34 1.38 2.85 3.62 1.43 2.11

time (sec)

N/A 0.042 0.029 0.405 0.269 0.258 14.053 0.276 1.276

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 67 49 83 156 0 82 287

N.S.

1 1.00 1.34 0.98 1.66 3.12 0.00 1.64 5.74

time (sec)

N/A 0.053 0.238 0.536 0.273 0.292 0.000 0.269 1.382

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 90 73 100 345 0 98 292

N.S.

1 1.00 1.53 1.24 1.69 5.85 0.00 1.66 4.95

time (sec)

N/A 0.082 0.709 0.679 0.277 0.293 0.000 0.273 1.435

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 81 136 108 154 929 0 137 617

N.S.

1 1.00 1.68 1.33 1.90 11.47 0.00 1.69 7.62

time (sec)

N/A 0.220 0.655 0.820 0.271 0.315 0.000 0.272 1.773

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 109 211 151 194 1676 0 171 694

N.S.

1 1.00 1.94 1.39 1.78 15.38 0.00 1.57 6.37

time (sec)

N/A 0.336 0.999 0.879 0.277 0.326 0.000 0.286 1.638

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 162 118 218 256 1769 0 235 305

N.S.

1 1.00 0.73 1.35 1.58 10.92 0.00 1.45 1.88

time (sec)

N/A 0.277 1.024 0.803 0.283 0.296 0.000 0.277 1.609

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 115 95 161 208 1053 0 184 274

N.S.

1 1.00 0.83 1.40 1.81 9.16 0.00 1.60 2.38

time (sec)

N/A 0.157 0.429 0.684 0.276 0.280 0.000 0.282 1.543

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 83 86 127 149 521 0 131 228

N.S.

1 1.00 1.04 1.53 1.80 6.28 0.00 1.58 2.75

time (sec)

N/A 0.091 0.202 0.530 0.277 0.286 0.000 0.280 1.551

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 68 97 117 341 0 99 142

N.S.

1 1.00 1.13 1.62 1.95 5.68 0.00 1.65 2.37

time (sec)

N/A 0.053 0.144 0.454 0.275 0.261 0.000 0.281 1.408

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 85 100 115 162 672 0 142 1001

N.S.

1 1.00 1.18 1.35 1.91 7.91 0.00 1.67 11.78

time (sec)

N/A 0.144 0.400 0.727 0.272 0.369 0.000 0.285 3.669

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 115 128 141 251 1740 0 205 1017

N.S.

1 1.00 1.11 1.23 2.18 15.13 0.00 1.78 8.84

time (sec)

N/A 0.255 0.803 0.803 0.288 0.397 0.000 0.285 4.355

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 158 174 175 363 3754 0 203 977

N.S.

1 1.00 1.10 1.11 2.30 23.76 0.00 1.28 6.18

time (sec)

N/A 0.462 0.959 0.969 0.290 0.514 0.000 0.270 4.444

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 198 232 219 477 6430 0 236 975

N.S.

1 1.00 1.17 1.11 2.41 32.47 0.00 1.19 4.92

time (sec)

N/A 0.598 1.111 1.023 0.284 0.538 0.000 0.300 4.181

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 81 36 19 28 31 32 39

N.S.

1 1.00 1.11 0.49 0.26 0.38 0.42 0.44 0.53

time (sec)

N/A 0.019 0.128 2.055 0.271 0.279 0.171 0.270 0.345

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 102 142 74 79 103 75 67 106

N.S.

1 1.00 1.39 0.73 0.77 1.01 0.74 0.66 1.04

time (sec)

N/A 0.033 0.385 1.168 0.269 0.292 0.211 0.271 1.776

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 131 204 100 124 193 138 89 147

N.S.

1 1.00 1.56 0.76 0.95 1.47 1.05 0.68 1.12

time (sec)

N/A 0.057 0.566 1.778 0.277 0.316 0.263 0.275 1.830

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 160 265 123 167 283 197 111 237

N.S.

1 1.00 1.66 0.77 1.04 1.77 1.23 0.69 1.48

time (sec)

N/A 0.086 0.574 2.047 0.274 0.291 0.326 0.276 2.076

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 171 32 36 26 31 28 32

N.S.

1 1.00 4.62 0.86 0.97 0.70 0.84 0.76 0.86

time (sec)

N/A 0.010 0.127 1.754 0.264 0.295 0.118 0.268 1.342

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 183 73 64 103 82 65 102

N.S.

1 1.00 2.77 1.11 0.97 1.56 1.24 0.98 1.55

time (sec)

N/A 0.025 0.374 1.071 0.273 0.296 0.155 0.267 1.780

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 95 277 96 108 193 141 87 143

N.S.

1 1.00 2.92 1.01 1.14 2.03 1.48 0.92 1.51

time (sec)

N/A 0.048 0.750 1.342 0.273 0.291 0.205 0.272 2.269

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 124 308 119 152 283 202 109 232

N.S.

1 1.00 2.48 0.96 1.23 2.28 1.63 0.88 1.87

time (sec)

N/A 0.068 1.522 1.323 0.276 0.311 0.258 0.274 2.839

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 183 138 155 272 223 314 269 160

N.S.

1 1.00 0.75 0.85 1.49 1.22 1.72 1.47 0.87

time (sec)

N/A 0.179 0.938 4.184 0.199 0.273 0.272 0.283 0.621

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 137 108 119 182 146 240 200 114

N.S.

1 1.00 0.79 0.87 1.33 1.07 1.75 1.46 0.83

time (sec)

N/A 0.106 0.480 2.837 0.195 0.291 0.188 0.274 0.381

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 92 71 77 115 91 128 135 75

N.S.

1 1.00 0.77 0.84 1.25 0.99 1.39 1.47 0.82

time (sec)

N/A 0.050 0.252 2.133 0.203 0.279 0.135 0.293 1.212

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 52 48 48 55 46 78 76 41

N.S.

1 1.00 0.92 0.92 1.06 0.88 1.50 1.46 0.79

time (sec)

N/A 0.012 0.143 0.787 0.197 0.283 0.099 0.270 1.234

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 26 16 15 17 17 31 15

N.S.

1 1.00 1.73 1.07 1.00 1.13 1.13 2.07 1.00

time (sec)

N/A 0.007 0.037 0.589 0.187 0.276 0.066 0.270 1.150

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