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2.2.1 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 A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 22 12 11 11 14 11 11

N.S.

1 1.00 2.00 1.09 1.00 1.00 1.27 1.00 1.00

time (sec)

N/A 0.143 0.008 1.902 0.186 0.305 0.055 0.376 0.162

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 19 24 23 46 18 18

N.S.

1 1.00 0.92 0.76 0.96 0.92 1.84 0.72 0.72

time (sec)

N/A 0.155 0.026 0.065 0.189 0.292 0.081 0.304 0.146

Problem 3

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 24 29 22 22 22 37 25 24

N.S.

1 0.89 1.07 0.81 0.81 0.81 1.37 0.93 0.89

time (sec)

N/A 0.168 0.016 0.158 0.189 0.322 0.107 0.314 0.046

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 51 33 31 33 36 95 32 50

N.S.

1 1.11 0.72 0.67 0.72 0.78 2.07 0.70 1.09

time (sec)

N/A 0.227 0.038 0.177 0.193 0.309 0.150 0.310 0.113

Problem 5

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

42 36 44 32 34 34 60 38 32

N.S.

1 0.86 1.05 0.76 0.81 0.81 1.43 0.90 0.76

time (sec)

N/A 0.172 0.019 0.171 0.187 0.316 0.199 0.297 0.055

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 77 45 44 48 47 139 46 43

N.S.

1 1.15 0.67 0.66 0.72 0.70 2.07 0.69 0.64

time (sec)

N/A 0.291 0.038 0.215 0.190 0.305 0.308 0.316 0.170

Problem 7

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

54 46 59 42 44 44 80 50 43

N.S.

1 0.85 1.09 0.78 0.81 0.81 1.48 0.93 0.80

time (sec)

N/A 0.180 0.016 0.180 0.186 0.287 0.431 0.324 0.057

Problem 8

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

88 103 55 55 59 56 184 60 90

N.S.

1 1.17 0.62 0.62 0.67 0.64 2.09 0.68 1.02

time (sec)

N/A 0.361 0.049 0.293 0.189 0.293 0.640 0.382 0.758

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 65 45 84 0 73 0 0 34

N.S.

1 1.08 0.75 1.40 0.00 1.22 0.00 0.00 0.57

time (sec)

N/A 0.266 0.063 0.214 0.000 0.097 0.000 0.000 0.155

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 35 118 0 68 0 0 34

N.S.

1 1.00 0.85 2.88 0.00 1.66 0.00 0.00 0.83

time (sec)

N/A 0.213 0.035 0.109 0.000 0.108 0.000 0.000 0.100

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 33 72 0 60 0 0 34

N.S.

1 1.00 0.80 1.76 0.00 1.46 0.00 0.00 0.83

time (sec)

N/A 0.209 0.031 0.088 0.000 0.102 0.000 0.000 0.080

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 21 77 0 55 0 0 15

N.S.

1 1.00 1.11 4.05 0.00 2.89 0.00 0.00 0.79

time (sec)

N/A 0.157 0.022 0.160 0.000 0.104 0.000 0.000 0.071

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 21 57 0 47 0 0 15

N.S.

1 1.00 1.11 3.00 0.00 2.47 0.00 0.00 0.79

time (sec)

N/A 0.157 0.023 0.066 0.000 0.105 0.000 0.000 0.088

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 32 110 0 81 0 0 34

N.S.

1 1.00 0.86 2.97 0.00 2.19 0.00 0.00 0.92

time (sec)

N/A 0.202 0.044 0.073 0.000 0.114 0.000 0.000 0.151

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 33 72 0 97 0 0 34

N.S.

1 1.00 0.80 1.76 0.00 2.37 0.00 0.00 0.83

time (sec)

N/A 0.205 0.043 0.068 0.000 0.111 0.000 0.000 0.178

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 61 51 132 0 132 0 0 34

N.S.

1 1.02 0.85 2.20 0.00 2.20 0.00 0.00 0.57

time (sec)

N/A 0.264 0.041 0.075 0.000 0.109 0.000 0.000 0.173

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 75 55 104 0 87 0 0 42

N.S.

1 1.07 0.79 1.49 0.00 1.24 0.00 0.00 0.60

time (sec)

N/A 0.282 0.082 0.106 0.000 0.108 0.000 0.000 0.136

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 44 142 0 80 0 0 42

N.S.

1 1.00 0.94 3.02 0.00 1.70 0.00 0.00 0.89

time (sec)

N/A 0.211 0.059 0.074 0.000 0.119 0.000 0.000 0.106

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 40 88 0 72 0 0 42

N.S.

1 1.00 0.85 1.87 0.00 1.53 0.00 0.00 0.89

time (sec)

N/A 0.212 0.027 0.047 0.000 0.124 0.000 0.000 0.097

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 24 91 0 63 0 0 18

N.S.

1 1.00 1.14 4.33 0.00 3.00 0.00 0.00 0.86

time (sec)

N/A 0.159 0.013 0.099 0.000 0.118 0.000 0.000 0.057

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 24 69 0 55 0 0 18

N.S.

1 1.00 1.14 3.29 0.00 2.62 0.00 0.00 0.86

time (sec)

N/A 0.156 0.014 0.056 0.000 0.115 0.000 0.000 0.073

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 39 132 0 99 0 0 42

N.S.

1 1.00 0.91 3.07 0.00 2.30 0.00 0.00 0.98

time (sec)

N/A 0.215 0.057 0.047 0.000 0.090 0.000 0.000 0.141

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 43 88 0 115 0 0 42

N.S.

1 1.00 0.91 1.87 0.00 2.45 0.00 0.00 0.89

time (sec)

N/A 0.217 0.079 0.044 0.000 0.112 0.000 0.000 0.193

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 71 55 160 0 158 0 0 42

N.S.

1 1.01 0.79 2.29 0.00 2.26 0.00 0.00 0.60

time (sec)

N/A 0.286 0.207 0.048 0.000 0.104 0.000 0.000 0.185

Problem 25

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

103 109 80 108 0 105 0 0 0

N.S.

1 1.06 0.78 1.05 0.00 1.02 0.00 0.00 0.00

time (sec)

N/A 0.401 0.126 0.236 0.000 0.107 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

75 75 66 152 0 101 0 0 0

N.S.

1 1.00 0.88 2.03 0.00 1.35 0.00 0.00 0.00

time (sec)

N/A 0.299 0.088 0.136 0.000 0.106 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

75 75 62 97 0 81 0 0 0

N.S.

1 1.00 0.83 1.29 0.00 1.08 0.00 0.00 0.00

time (sec)

N/A 0.298 0.046 0.096 0.000 0.125 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 B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 42 98 0 67 0 0 36

N.S.

1 1.00 0.98 2.28 0.00 1.56 0.00 0.00 0.84

time (sec)

N/A 0.223 0.025 0.165 0.000 0.110 0.000 0.000 0.073

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 42 74 0 62 0 0 36

N.S.

1 1.00 0.98 1.72 0.00 1.44 0.00 0.00 0.84

time (sec)

N/A 0.220 0.029 0.090 0.000 0.100 0.000 0.000 0.124

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

73 73 54 141 0 108 0 0 0

N.S.

1 1.00 0.74 1.93 0.00 1.48 0.00 0.00 0.00

time (sec)

N/A 0.307 0.045 0.084 0.000 0.101 0.000 0.000 0.000

Problem 31

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

77 77 55 105 0 127 0 0 0

N.S.

1 1.00 0.71 1.36 0.00 1.65 0.00 0.00 0.00

time (sec)

N/A 0.323 0.064 0.092 0.000 0.110 0.000 0.000 0.000

Problem 32

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

105 109 68 168 0 170 0 0 0

N.S.

1 1.04 0.65 1.60 0.00 1.62 0.00 0.00 0.00

time (sec)

N/A 0.394 0.126 0.104 0.000 0.109 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

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 0.183 0.040 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

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 0.183 0.028 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 C C F F F F F F(-1)

verified

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

size

517 58 55 0 0 0 0 0 0

N.S.

1 0.11 0.11 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.184 0.029 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 C C F F F F F F(-1)

verified

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

size

252 58 55 0 0 0 0 0 0

N.S.

1 0.23 0.22 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.183 0.030 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 C C F F F F F F(-1)

verified

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

size

271 56 53 0 0 0 0 0 0

N.S.

1 0.21 0.20 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.180 0.030 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

56 56 53 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 0.184 0.029 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 B

verified

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

size

63 63 63 0 0 0 0 0 54

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.86

time (sec)

N/A 0.185 0.034 0.000 0.000 0.000 0.000 0.000 0.337

Problem 40

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

68 68 63 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 0.200 0.030 0.000 0.000 0.000 0.000 0.000 0.000

Problem 41

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

81 81 76 0 0 0 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.245 0.059 0.000 0.000 0.000 0.000 0.000 0.000

Problem 42

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

15 15 15 14 13 13 22 24 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 1.47 1.60 0.87

time (sec)

N/A 0.178 0.003 0.065 0.184 0.315 0.144 0.296 0.035

Problem 43

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

15 15 15 14 13 13 22 13 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 1.47 0.87 0.87

time (sec)

N/A 0.177 0.003 0.053 0.191 0.330 0.099 0.303 0.026

Problem 44

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

15 15 37 14 13 13 19 13 28

N.S.

1 1.00 2.47 0.93 0.87 0.87 1.27 0.87 1.87

time (sec)

N/A 0.167 0.013 0.027 0.188 0.306 0.072 0.400 0.117

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 12 12 18 14 0 18 16

N.S.

1 1.00 1.00 1.00 1.50 1.17 0.00 1.50 1.33

time (sec)

N/A 0.160 0.007 0.056 0.184 0.331 0.000 0.319 0.138

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 11 12 12 0 12 20

N.S.

1 1.00 1.00 1.10 1.20 1.20 0.00 1.20 2.00

time (sec)

N/A 0.167 0.007 0.048 0.188 0.301 0.000 0.325 0.140

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 14 17 13 0 13 13

N.S.

1 1.00 1.00 0.93 1.13 0.87 0.00 0.87 0.87

time (sec)

N/A 0.174 0.009 0.061 0.187 0.324 0.000 0.397 0.072

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 14 13 13 0 13 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 0.00 0.87 0.87

time (sec)

N/A 0.176 0.007 0.079 0.184 0.302 0.000 0.338 0.113

Problem 49

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

61 53 47 47 46 53 88 54 45

N.S.

1 0.87 0.77 0.77 0.75 0.87 1.44 0.89 0.74

time (sec)

N/A 0.210 0.124 0.217 0.187 0.347 0.912 0.317 0.078

Problem 50

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

46 41 37 36 36 43 66 54 36

N.S.

1 0.89 0.80 0.78 0.78 0.93 1.43 1.17 0.78

time (sec)

N/A 0.205 0.063 0.132 0.192 0.315 0.450 0.319 0.041

Problem 51

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

31 29 27 26 26 33 44 26 26

N.S.

1 0.94 0.87 0.84 0.84 1.06 1.42 0.84 0.84

time (sec)

N/A 0.199 0.036 0.090 0.189 0.341 0.206 0.321 0.094

Problem 52

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

15 15 15 14 13 21 20 13 13

N.S.

1 1.00 1.00 0.93 0.87 1.40 1.33 0.87 0.87

time (sec)

N/A 0.172 0.003 0.047 0.190 0.321 0.101 0.311 0.015

Problem 53

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

14 14 23 19 18 31 0 18 14

N.S.

1 1.00 1.64 1.36 1.29 2.21 0.00 1.29 1.00

time (sec)

N/A 0.163 0.006 0.057 0.272 0.284 0.000 0.405 0.095

Problem 54

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

15 15 15 22 13 29 0 13 13

N.S.

1 1.00 1.00 1.47 0.87 1.93 0.00 0.87 0.87

time (sec)

N/A 0.182 0.005 0.082 0.240 0.273 0.000 0.340 0.072

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 29 56 42 26 39 0 26 25

N.S.

1 0.94 1.81 1.35 0.84 1.26 0.00 0.84 0.81

time (sec)

N/A 0.204 0.113 0.149 0.238 0.289 0.000 0.333 0.076

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 41 77 60 36 51 0 36 35

N.S.

1 0.89 1.67 1.30 0.78 1.11 0.00 0.78 0.76

time (sec)

N/A 0.208 0.096 0.233 0.196 0.283 0.000 0.375 0.088

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 53 98 77 46 61 0 46 45

N.S.

1 0.87 1.61 1.26 0.75 1.00 0.00 0.75 0.74

time (sec)

N/A 0.217 0.104 0.301 0.191 0.267 0.000 0.352 0.083

Problem 58

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

88 103 52 55 48 57 189 60 89

N.S.

1 1.17 0.59 0.62 0.55 0.65 2.15 0.68 1.01

time (sec)

N/A 0.401 0.120 0.356 0.192 0.306 0.646 0.304 0.763

Problem 59

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 77 40 44 37 47 136 46 43

N.S.

1 1.15 0.60 0.66 0.55 0.70 2.03 0.69 0.64

time (sec)

N/A 0.315 0.057 0.266 0.194 0.287 0.321 0.311 0.167

Problem 60

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 51 23 19 24 36 92 18 50

N.S.

1 1.11 0.50 0.41 0.52 0.78 2.00 0.39 1.09

time (sec)

N/A 0.249 0.055 0.088 0.193 0.303 0.161 0.314 0.116

Problem 61

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 19 24 23 46 18 18

N.S.

1 1.00 0.92 0.76 0.96 0.92 1.84 0.72 0.72

time (sec)

N/A 0.167 0.013 0.000 0.196 0.305 0.083 0.302 0.001

Problem 62

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

23 20 23 28 34 36 3160 36 27

N.S.

1 0.87 1.00 1.22 1.48 1.57 137.39 1.57 1.17

time (sec)

N/A 0.173 0.011 0.099 0.200 0.317 18.822 0.311 0.125

Problem 63

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

34 34 34 48 46 61 0 48 69

N.S.

1 1.00 1.00 1.41 1.35 1.79 0.00 1.41 2.03

time (sec)

N/A 0.239 0.013 0.106 0.191 0.303 0.000 0.334 0.550

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 60 55 66 65 71 0 82 125

N.S.

1 1.09 1.00 1.20 1.18 1.29 0.00 1.49 2.27

time (sec)

N/A 0.319 0.015 0.181 0.192 0.304 0.000 0.349 5.676

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 86 76 84 91 84 0 73 177

N.S.

1 1.13 1.00 1.11 1.20 1.11 0.00 0.96 2.33

time (sec)

N/A 0.407 0.015 0.256 0.185 0.292 0.000 0.356 7.172

Problem 66

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

31 30 48 26 36 26 44 27 25

N.S.

1 0.97 1.55 0.84 1.16 0.84 1.42 0.87 0.81

time (sec)

N/A 0.203 0.097 0.187 0.197 0.302 0.627 0.318 0.104

Problem 67

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

31 30 27 26 26 26 46 27 26

N.S.

1 0.97 0.87 0.84 0.84 0.84 1.48 0.87 0.84

time (sec)

N/A 0.204 0.073 0.150 0.188 0.288 0.454 0.315 0.053

Problem 68

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

31 29 35 26 26 26 44 26 37

N.S.

1 0.94 1.13 0.84 0.84 0.84 1.42 0.84 1.19

time (sec)

N/A 0.199 0.040 0.103 0.190 0.314 0.305 0.292 0.241

Problem 69

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

31 30 27 26 26 26 46 27 26

N.S.

1 0.97 0.87 0.84 0.84 0.84 1.48 0.87 0.84

time (sec)

N/A 0.201 0.036 0.089 0.194 0.290 0.208 0.314 0.076

Problem 70

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

15 15 15 14 13 24 20 13 13

N.S.

1 1.00 1.00 0.93 0.87 1.60 1.33 0.87 0.87

time (sec)

N/A 0.175 0.002 0.054 0.185 0.316 0.145 0.328 0.085

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 25 25 25 25 25 0 29 25

N.S.

1 0.89 0.89 0.89 0.89 0.89 0.00 1.04 0.89

time (sec)

N/A 0.192 0.014 0.132 0.189 0.318 0.000 0.307 0.165

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-2) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 22 21 33 19 22 0 23 20

N.S.

1 1.05 1.00 1.57 0.90 1.05 0.00 1.10 0.95

time (sec)

N/A 0.192 0.066 0.066 0.184 0.328 0.000 0.304 0.236

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 25 23 31 34 0 42 27

N.S.

1 1.00 0.93 0.85 1.15 1.26 0.00 1.56 1.00

time (sec)

N/A 0.215 0.019 0.125 0.189 0.320 0.000 0.362 0.117

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 25 27 24 25 25 0 25 23

N.S.

1 0.93 1.00 0.89 0.93 0.93 0.00 0.93 0.85

time (sec)

N/A 0.187 0.070 0.094 0.190 0.295 0.000 0.306 0.192

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 26 39 25 0 25 13

N.S.

1 1.00 1.00 1.73 2.60 1.67 0.00 1.67 0.87

time (sec)

N/A 0.181 0.004 0.093 0.183 0.306 0.000 0.335 0.110

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 29 31 26 25 25 0 25 25

N.S.

1 0.94 1.00 0.84 0.81 0.81 0.00 0.81 0.81

time (sec)

N/A 0.199 0.106 0.155 0.191 0.303 0.000 0.424 0.282

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 29 31 26 49 25 0 25 25

N.S.

1 0.94 1.00 0.84 1.58 0.81 0.00 0.81 0.81

time (sec)

N/A 0.200 0.017 0.166 0.186 0.289 0.000 0.356 0.126

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 29 31 26 25 25 0 25 25

N.S.

1 0.94 1.00 0.84 0.81 0.81 0.00 0.81 0.81

time (sec)

N/A 0.204 0.086 0.208 0.186 0.299 0.000 0.349 0.379

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 29 31 26 59 25 0 25 35

N.S.

1 0.94 1.00 0.84 1.90 0.81 0.00 0.81 1.13

time (sec)

N/A 0.202 0.017 0.274 0.183 0.310 0.000 0.416 0.151

Problem 80

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

61 53 47 47 46 63 88 82 45

N.S.

1 0.87 0.77 0.77 0.75 1.03 1.44 1.34 0.74

time (sec)

N/A 0.212 0.135 0.283 0.187 0.319 1.831 0.327 0.111

Problem 81

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

46 41 37 36 36 53 66 68 36

N.S.

1 0.89 0.80 0.78 0.78 1.15 1.43 1.48 0.78

time (sec)

N/A 0.206 0.067 0.210 0.189 0.337 0.933 0.324 0.113

Problem 82

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

31 29 27 26 26 41 44 26 26

N.S.

1 0.94 0.87 0.84 0.84 1.32 1.42 0.84 0.84

time (sec)

N/A 0.201 0.042 0.128 0.187 0.299 0.459 0.322 0.034

Problem 83

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

15 15 15 14 13 31 20 13 13

N.S.

1 1.00 1.00 0.93 0.87 2.07 1.33 0.87 0.87

time (sec)

N/A 0.172 0.002 0.073 0.189 0.341 0.204 0.307 0.085

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 49 31 42 41 42 0 41 38

N.S.

1 1.22 0.78 1.05 1.02 1.05 0.00 1.02 0.95

time (sec)

N/A 0.205 0.154 0.117 0.276 0.290 0.000 0.328 0.189

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 38 28 29 46 0 29 24

N.S.

1 1.00 1.36 1.00 1.04 1.64 0.00 1.04 0.86

time (sec)

N/A 0.229 0.010 0.102 0.273 0.303 0.000 0.341 0.130

Problem 86

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

15 15 15 22 13 39 0 13 13

N.S.

1 1.00 1.00 1.47 0.87 2.60 0.00 0.87 0.87

time (sec)

N/A 0.184 0.005 0.127 0.193 0.305 0.000 0.353 0.144

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 29 77 42 26 49 0 26 25

N.S.

1 0.94 2.48 1.35 0.84 1.58 0.00 0.84 0.81

time (sec)

N/A 0.203 0.110 0.206 0.189 0.282 0.000 0.416 0.133

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 41 98 60 36 61 0 36 35

N.S.

1 0.89 2.13 1.30 0.78 1.33 0.00 0.78 0.76

time (sec)

N/A 0.205 0.102 0.260 0.196 0.309 0.000 0.364 0.168

Problem 89

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

111 131 62 66 48 66 231 74 109

N.S.

1 1.18 0.56 0.59 0.43 0.59 2.08 0.67 0.98

time (sec)

N/A 0.507 0.131 0.326 0.192 0.314 1.295 0.325 1.760

Problem 90

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

90 105 33 31 33 56 189 32 90

N.S.

1 1.17 0.37 0.34 0.37 0.62 2.10 0.36 1.00

time (sec)

N/A 0.414 0.063 0.216 0.186 0.329 0.660 0.329 1.325

Problem 91

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

69 79 40 42 37 46 136 46 43

N.S.

1 1.14 0.58 0.61 0.54 0.67 1.97 0.67 0.62

time (sec)

N/A 0.337 0.042 0.137 0.190 0.312 0.332 0.315 0.285

Problem 92

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 51 33 31 33 36 95 32 50

N.S.

1 1.11 0.72 0.67 0.72 0.78 2.07 0.70 1.09

time (sec)

N/A 0.223 0.023 0.000 0.200 0.324 0.166 0.312 0.002

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 32 38 38 46 48 0 48 53

N.S.

1 0.84 1.00 1.00 1.21 1.26 0.00 1.26 1.39

time (sec)

N/A 0.198 0.012 0.120 0.261 0.295 0.000 0.310 0.338

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 51 53 58 56 74 0 58 98

N.S.

1 1.04 1.08 1.18 1.14 1.51 0.00 1.18 2.00

time (sec)

N/A 0.195 0.014 0.149 0.269 0.326 0.000 0.341 3.884

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 60 73 76 71 74 0 63 126

N.S.

1 1.09 1.33 1.38 1.29 1.35 0.00 1.15 2.29

time (sec)

N/A 0.318 0.017 0.168 0.250 0.306 0.000 0.362 6.588

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 88 99 94 91 84 0 73 177

N.S.

1 1.13 1.27 1.21 1.17 1.08 0.00 0.94 2.27

time (sec)

N/A 0.436 0.019 0.250 0.238 0.314 0.000 0.338 7.168

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 114 120 112 111 94 0 107 229

N.S.

1 1.15 1.21 1.13 1.12 0.95 0.00 1.08 2.31

time (sec)

N/A 0.547 0.020 0.391 0.216 0.310 0.000 0.369 7.379

Problem 98

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

46 44 68 47 46 36 65 85 35

N.S.

1 0.96 1.48 1.02 1.00 0.78 1.41 1.85 0.76

time (sec)

N/A 0.217 0.236 0.362 0.228 0.286 2.628 0.341 0.146

Problem 99

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

46 42 37 37 36 36 68 82 36

N.S.

1 0.91 0.80 0.80 0.78 0.78 1.48 1.78 0.78

time (sec)

N/A 0.207 0.178 0.250 0.229 0.324 1.856 0.406 0.134

Problem 100

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

46 44 50 36 36 36 65 43 36

N.S.

1 0.96 1.09 0.78 0.78 0.78 1.41 0.93 0.78

time (sec)

N/A 0.224 0.049 0.220 0.197 0.299 1.252 0.361 0.211

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