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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

16 16 16 13 12 12 10 12 13

N.S.

1 1.00 1.00 0.81 0.75 0.75 0.62 0.75 0.81

time (sec)

N/A 0.119 0.000 0.014 0.188 0.238 0.015 0.276 0.021

Problem 2

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

22 22 22 16 16 16 17 16 15

N.S.

1 1.00 1.00 0.73 0.73 0.73 0.77 0.73 0.68

time (sec)

N/A 0.132 0.001 0.046 0.197 0.227 0.015 0.268 0.038

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

22 22 22 16 16 16 15 16 15

N.S.

1 1.00 1.00 0.73 0.73 0.73 0.68 0.73 0.68

time (sec)

N/A 0.134 0.001 0.047 0.186 0.230 0.015 0.278 0.030

Problem 4

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

2 2 2 3 2 2 2 3 2

N.S.

1 1.00 1.00 1.50 1.00 1.00 1.00 1.50 1.00

time (sec)

N/A 0.103 0.000 0.013 0.183 0.232 0.044 0.277 0.009

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

36 36 24 22 32 46 29 23 22

N.S.

1 1.00 0.67 0.61 0.89 1.28 0.81 0.64 0.61

time (sec)

N/A 0.147 0.015 0.086 0.199 0.231 0.051 0.266 0.133

Problem 6

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

32 32 28 25 24 33 24 34 26

N.S.

1 1.00 0.88 0.78 0.75 1.03 0.75 1.06 0.81

time (sec)

N/A 0.150 0.011 0.079 0.189 0.239 0.065 0.282 0.034

Problem 7

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

40 40 34 41 40 34 144 42 40

N.S.

1 1.00 0.85 1.02 1.00 0.85 3.60 1.05 1.00

time (sec)

N/A 0.172 0.016 0.117 0.184 0.238 0.542 0.271 0.248

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 38 35 0 120 124 34 46

N.S.

1 1.00 1.12 1.03 0.00 3.53 3.65 1.00 1.35

time (sec)

N/A 0.154 0.011 0.365 0.000 0.241 0.105 0.299 0.196

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 15 14 14 26 14 14

N.S.

1 1.00 1.00 0.94 0.88 0.88 1.62 0.88 0.88

time (sec)

N/A 0.132 0.006 0.072 0.273 0.253 0.084 0.291 0.037

Problem 10

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

19 21 16 15 14 14 22 14 14

N.S.

1 1.11 0.84 0.79 0.74 0.74 1.16 0.74 0.74

time (sec)

N/A 0.137 0.004 0.624 0.277 0.237 0.044 0.270 0.029

Problem 11

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

49 52 35 36 39 71 41 80 49

N.S.

1 1.06 0.71 0.73 0.80 1.45 0.84 1.63 1.00

time (sec)

N/A 0.183 0.023 0.112 0.272 0.253 0.082 0.278 0.128

Problem 12

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

68 68 62 69 78 81 0 81 87

N.S.

1 1.00 0.91 1.01 1.15 1.19 0.00 1.19 1.28

time (sec)

N/A 0.209 0.026 0.156 0.188 0.307 0.000 0.277 0.576

Problem 13

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

47 46 34 33 43 32 121 43 256

N.S.

1 0.98 0.72 0.70 0.91 0.68 2.57 0.91 5.45

time (sec)

N/A 0.151 0.010 0.145 0.197 0.242 0.350 0.266 0.309

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 30 41 40 30 393 40 191

N.S.

1 1.00 0.75 1.02 1.00 0.75 9.82 1.00 4.78

time (sec)

N/A 0.155 0.014 0.195 0.272 0.253 0.658 0.270 0.151

Problem 15

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 28 27 20 19 19 19 20 25

N.S.

1 1.04 1.00 0.74 0.70 0.70 0.70 0.74 0.93

time (sec)

N/A 0.144 0.004 0.095 0.280 0.234 0.057 0.274 0.045

Problem 16

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

41 45 40 33 34 34 41 35 46

N.S.

1 1.10 0.98 0.80 0.83 0.83 1.00 0.85 1.12

time (sec)

N/A 0.180 0.009 0.073 0.273 0.267 0.056 0.279 0.204

Problem 17

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

43 43 34 32 31 40 31 36 33

N.S.

1 1.00 0.79 0.74 0.72 0.93 0.72 0.84 0.77

time (sec)

N/A 0.280 0.025 0.089 0.274 0.228 0.057 0.302 0.043

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 90 64 22 72 61 73 72 33

N.S.

1 1.06 0.75 0.26 0.85 0.72 0.86 0.85 0.39

time (sec)

N/A 0.243 0.013 0.061 0.277 0.251 0.094 0.278 0.002

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 90 64 22 72 61 73 72 33

N.S.

1 1.06 0.75 0.26 0.85 0.72 0.86 0.85 0.39

time (sec)

N/A 0.244 0.011 0.076 0.278 0.243 0.067 0.276 0.175

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 71 73 54 53 53 70 53 47

N.S.

1 1.06 1.09 0.81 0.79 0.79 1.04 0.79 0.70

time (sec)

N/A 0.211 0.041 0.050 0.290 0.253 0.094 0.284 0.182

Problem 21

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

18 18 18 19 18 20 20 18 18

N.S.

1 1.00 1.00 1.06 1.00 1.11 1.11 1.00 1.00

time (sec)

N/A 0.127 0.005 0.076 0.203 0.242 0.017 0.277 0.220

Problem 22

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

39 39 33 36 42 53 201 76 94

N.S.

1 1.00 0.85 0.92 1.08 1.36 5.15 1.95 2.41

time (sec)

N/A 0.159 0.083 0.076 0.194 0.262 0.299 0.276 0.391

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 57 73 68 96 597 140 192

N.S.

1 1.00 0.95 1.22 1.13 1.60 9.95 2.33 3.20

time (sec)

N/A 0.177 0.056 0.086 0.202 0.249 0.479 0.274 0.603

Problem 24

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

10 10 10 11 10 10 7 11 10

N.S.

1 1.00 1.00 1.10 1.00 1.00 0.70 1.10 1.00

time (sec)

N/A 0.119 0.000 0.069 0.193 0.244 0.017 0.285 0.027

Problem 25

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

12 12 12 13 12 13 10 12 12

N.S.

1 1.00 1.00 1.08 1.00 1.08 0.83 1.00 1.00

time (sec)

N/A 0.126 0.002 0.064 0.186 0.242 0.056 0.271 0.116

Problem 26

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

18 18 18 19 18 17 14 19 18

N.S.

1 1.00 1.00 1.06 1.00 0.94 0.78 1.06 1.00

time (sec)

N/A 0.159 0.004 0.070 0.183 0.231 0.044 0.273 0.036

Problem 27

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 31 31 30 29 29 26 30 29

N.S.

1 1.00 1.00 0.97 0.94 0.94 0.84 0.97 0.94

time (sec)

N/A 0.159 0.003 0.068 0.222 0.231 0.048 0.262 0.125

Problem 28

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

18 18 18 16 18 16 10 20 15

N.S.

1 1.00 1.00 0.89 1.00 0.89 0.56 1.11 0.83

time (sec)

N/A 0.131 0.004 0.074 0.194 0.255 0.094 0.268 0.134

Problem 29

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

28 28 28 26 28 26 19 30 25

N.S.

1 1.00 1.00 0.93 1.00 0.93 0.68 1.07 0.89

time (sec)

N/A 0.153 0.004 0.074 0.181 0.241 0.079 0.275 0.053

Problem 30

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 42 35 43 45 63 37 52 45

N.S.

1 1.00 0.83 1.02 1.07 1.50 0.88 1.24 1.07

time (sec)

N/A 0.167 0.030 0.080 0.184 0.252 0.122 0.283 0.188

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 11 10 10 20 10 10

N.S.

1 1.00 1.00 1.10 1.00 1.00 2.00 1.00 1.00

time (sec)

N/A 0.125 0.002 0.112 0.267 0.245 0.045 0.274 0.041

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 19 21 18 15 23 10

N.S.

1 1.00 1.00 1.90 2.10 1.80 1.50 2.30 1.00

time (sec)

N/A 0.121 0.002 0.076 0.184 0.238 0.053 0.295 0.155

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 87 66 24 66 63 78 57 72

N.S.

1 1.12 0.85 0.31 0.85 0.81 1.00 0.73 0.92

time (sec)

N/A 0.229 0.015 0.076 0.285 0.258 0.177 0.283 0.282

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 73 65 22 56 68 71 57 72

N.S.

1 0.99 0.88 0.30 0.76 0.92 0.96 0.77 0.97

time (sec)

N/A 0.216 0.013 0.073 0.274 0.240 0.140 0.298 0.355

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 110 89 29 97 300 20 104 101

N.S.

1 0.96 0.77 0.25 0.84 2.61 0.17 0.90 0.88

time (sec)

N/A 0.241 0.021 0.080 0.272 0.265 0.068 0.272 0.315

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 43 22 34 59 46 39 20

N.S.

1 1.00 1.23 0.63 0.97 1.69 1.31 1.11 0.57

time (sec)

N/A 0.140 0.013 0.076 0.270 0.261 0.183 0.288 0.162

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 43 24 41 59 48 39 18

N.S.

1 1.00 1.23 0.69 1.17 1.69 1.37 1.11 0.51

time (sec)

N/A 0.144 0.011 0.082 0.269 0.242 0.153 0.301 0.174

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 166 120 24 151 85 151 95 45

N.S.

1 0.97 0.70 0.14 0.88 0.50 0.88 0.56 0.26

time (sec)

N/A 0.332 0.036 0.075 0.281 0.257 0.234 0.300 0.121

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 75 68 35 0 151 146 74 93

N.S.

1 1.03 0.93 0.48 0.00 2.07 2.00 1.01 1.27

time (sec)

N/A 0.197 0.038 0.079 0.000 0.247 0.258 0.297 0.219

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 75 68 35 0 151 24 74 93

N.S.

1 1.03 0.93 0.48 0.00 2.07 0.33 1.01 1.27

time (sec)

N/A 0.170 0.020 0.070 0.000 0.248 0.214 0.324 0.143

Problem 41

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

72 72 83 54 75 91 158 81 67

N.S.

1 1.00 1.15 0.75 1.04 1.26 2.19 1.12 0.93

time (sec)

N/A 0.186 0.024 0.062 0.270 0.248 0.184 0.285 0.102

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 67 33 0 123 24 101 98

N.S.

1 1.00 1.00 0.49 0.00 1.84 0.36 1.51 1.46

time (sec)

N/A 0.171 0.028 0.077 0.000 0.240 0.194 0.307 0.240

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 67 33 0 123 92 51 117

N.S.

1 1.00 1.00 0.49 0.00 1.84 1.37 0.76 1.75

time (sec)

N/A 0.173 0.015 0.072 0.000 0.245 0.137 0.297 0.198

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 218 91 31 0 139 994 252 61

N.S.

1 1.11 0.46 0.16 0.00 0.71 5.07 1.29 0.31

time (sec)

N/A 0.361 0.041 0.139 0.000 0.258 0.681 0.414 0.231

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 218 91 35 0 139 24 256 132

N.S.

1 1.11 0.46 0.18 0.00 0.71 0.12 1.31 0.67

time (sec)

N/A 0.352 0.053 0.131 0.000 0.237 0.343 0.460 0.112

Problem 46

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 79 75 66 65 65 83 67 88

N.S.

1 1.08 1.03 0.90 0.89 0.89 1.14 0.92 1.21

time (sec)

N/A 0.220 0.011 0.106 0.280 0.243 0.132 0.309 0.093

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 127 122 22 112 127 14 114 140

N.S.

1 0.92 0.88 0.16 0.81 0.92 0.10 0.83 1.01

time (sec)

N/A 0.301 0.026 0.178 0.269 0.239 0.318 0.295 0.212

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 146 115 22 107 164 14 107 135

N.S.

1 1.06 0.83 0.16 0.78 1.19 0.10 0.78 0.98

time (sec)

N/A 0.325 0.019 0.218 0.266 0.256 0.138 0.277 0.130

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

339 343 209 22 0 135 14 239 288

N.S.

1 1.01 0.62 0.06 0.00 0.40 0.04 0.71 0.85

time (sec)

N/A 0.579 0.007 0.085 0.000 0.246 1.340 0.297 0.311

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 112 98 37 88 77 44 90 45

N.S.

1 1.15 1.01 0.38 0.91 0.79 0.45 0.93 0.46

time (sec)

N/A 0.279 0.025 0.125 0.269 0.249 127.316 0.286 0.173

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

275 411 42 30 0 101 165 205 53

N.S.

1 1.49 0.15 0.11 0.00 0.37 0.60 0.75 0.19

time (sec)

N/A 0.561 0.010 0.073 0.000 0.242 0.179 0.295 0.104

Problem 52

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

49 55 260 41 40 40 46 40 52

N.S.

1 1.12 5.31 0.84 0.82 0.82 0.94 0.82 1.06

time (sec)

N/A 0.192 0.071 0.116 0.276 0.243 0.109 0.289 0.217

Problem 53

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

8 8 8 9 8 8 5 8 6

N.S.

1 1.00 1.00 1.12 1.00 1.00 0.62 1.00 0.75

time (sec)

N/A 0.131 0.002 0.017 0.177 0.240 0.046 0.301 0.023

Problem 54

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

17 17 17 14 13 13 12 13 9

N.S.

1 1.00 1.00 0.82 0.76 0.76 0.71 0.76 0.53

time (sec)

N/A 0.135 0.000 0.017 0.179 0.237 0.061 0.285 0.033

Problem 55

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

17 17 17 14 13 13 12 13 9

N.S.

1 1.00 1.00 0.82 0.76 0.76 0.71 0.76 0.53

time (sec)

N/A 0.136 0.002 0.024 0.184 0.250 0.055 0.283 0.032

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 19 19 26 25 56 0 32

N.S.

1 1.00 0.73 0.73 1.00 0.96 2.15 0.00 1.23

time (sec)

N/A 0.148 0.006 0.045 0.183 0.255 0.391 0.000 0.247

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

15 17 15 16 12 15 15 15 12

N.S.

1 1.13 1.00 1.07 0.80 1.00 1.00 1.00 0.80

time (sec)

N/A 0.150 0.000 0.017 0.189 0.242 0.038 0.289 0.032

Problem 58

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

127 172 127 104 71 103 133 103 71

N.S.

1 1.35 1.00 0.82 0.56 0.81 1.05 0.81 0.56

time (sec)

N/A 0.556 0.004 0.086 0.191 0.242 0.166 0.302 0.173

Problem 59

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

8 8 8 7 6 6 5 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.62 0.75 0.75

time (sec)

N/A 0.135 0.003 0.027 0.191 0.244 0.048 0.298 0.057

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2 2 2 9 3 2 2 3 2

N.S.

1 1.00 1.00 4.50 1.50 1.00 1.00 1.50 1.00

time (sec)

N/A 0.120 0.004 0.019 0.204 0.234 0.204 0.283 0.004

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

4 4 4 11 5 4 3 5 4

N.S.

1 1.00 1.00 2.75 1.25 1.00 0.75 1.25 1.00

time (sec)

N/A 0.139 0.004 0.029 0.205 0.241 0.207 0.281 0.014

Problem 62

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

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 0.133 0.001 0.021 0.182 0.228 0.040 0.278 0.114

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 15 6 19 14 0 17

N.S.

1 1.00 1.00 0.88 0.35 1.12 0.82 0.00 1.00

time (sec)

N/A 0.193 0.023 0.033 0.207 0.238 0.255 0.000 0.031

Problem 64

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

12 12 12 13 12 12 15 12 22

N.S.

1 1.00 1.00 1.08 1.00 1.00 1.25 1.00 1.83

time (sec)

N/A 0.143 0.003 0.053 0.177 0.261 0.420 0.279 0.161

Problem 65

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

28 46 28 25 25 25 22 24 21

N.S.

1 1.64 1.00 0.89 0.89 0.89 0.79 0.86 0.75

time (sec)

N/A 0.174 0.003 0.027 0.186 0.234 0.052 0.276 0.143

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

54 59 53 47 47 47 44 47 47

N.S.

1 1.09 0.98 0.87 0.87 0.87 0.81 0.87 0.87

time (sec)

N/A 0.190 0.009 0.074 0.180 0.235 0.060 0.285 0.178

Problem 67

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

29 29 27 30 38 34 24 138 35

N.S.

1 1.00 0.93 1.03 1.31 1.17 0.83 4.76 1.21

time (sec)

N/A 0.154 0.010 0.096 0.173 0.248 0.133 0.299 0.237

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

46 50 46 39 44 39 42 58 66

N.S.

1 1.09 1.00 0.85 0.96 0.85 0.91 1.26 1.43

time (sec)

N/A 0.181 0.012 0.050 0.183 0.247 0.115 0.299 0.188

Problem 69

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 63 59 50 57 49 54 94 75

N.S.

1 1.07 1.00 0.85 0.97 0.83 0.92 1.59 1.27

time (sec)

N/A 0.196 0.015 0.059 0.184 0.243 0.101 0.275 0.178

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 24 23 24 23 23 36 23 23

N.S.

1 1.04 1.00 1.04 1.00 1.00 1.57 1.00 1.00

time (sec)

N/A 0.148 0.003 0.079 0.263 0.243 0.073 0.282 0.062

Problem 71

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 31 26 29 28 23 31 28 51

N.S.

1 1.15 0.96 1.07 1.04 0.85 1.15 1.04 1.89

time (sec)

N/A 0.176 0.003 0.040 0.180 0.235 0.076 0.412 0.041

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 44 37 36 36 53 36 65

N.S.

1 1.00 1.00 0.84 0.82 0.82 1.20 0.82 1.48

time (sec)

N/A 0.187 0.003 0.102 0.264 0.251 0.102 0.311 0.036

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 54 45 44 44 63 44 73

N.S.

1 1.00 1.00 0.83 0.81 0.81 1.17 0.81 1.35

time (sec)

N/A 0.192 0.005 0.153 0.258 0.243 0.119 0.350 0.127

Problem 74

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

25 27 25 32 31 31 29 33 25

N.S.

1 1.08 1.00 1.28 1.24 1.24 1.16 1.32 1.00

time (sec)

N/A 0.156 0.003 0.043 0.177 0.250 0.079 0.270 0.069

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

5 5 7 5 28 7 27 7 7

N.S.

1 1.00 1.40 1.00 5.60 1.40 5.40 1.40 1.40

time (sec)

N/A 0.155 0.039 0.050 0.263 0.252 3.797 0.275 0.584

Problem 76

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

4 4 4 5 4 4 3 4 4

N.S.

1 1.00 1.00 1.25 1.00 1.00 0.75 1.00 1.00

time (sec)

N/A 0.138 0.001 0.056 0.190 0.243 0.036 0.279 0.020

Problem 77

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

2 2 2 3 2 2 2 2 2

N.S.

1 1.00 1.00 1.50 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.134 0.004 0.043 0.185 0.252 0.043 0.278 0.027

Problem 78

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

5 5 5 6 3 11 5 6 5

N.S.

1 1.00 1.00 1.20 0.60 2.20 1.00 1.20 1.00

time (sec)

N/A 0.138 0.003 0.030 0.177 0.249 0.036 0.265 0.029

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

3 3 7 4 3 16 3 17 13

N.S.

1 1.00 2.33 1.33 1.00 5.33 1.00 5.67 4.33

time (sec)

N/A 0.142 0.000 0.036 0.185 0.251 0.058 0.276 0.192

Problem 80

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

21 21 21 26 25 37 75 26 27

N.S.

1 1.00 1.00 1.24 1.19 1.76 3.57 1.24 1.29

time (sec)

N/A 0.218 0.073 0.079 0.266 0.259 0.170 0.296 0.251

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

3 3 3 7 15 17 15 17 11

N.S.

1 1.00 1.00 2.33 5.00 5.67 5.00 5.67 3.67

time (sec)

N/A 0.140 0.002 0.116 0.175 0.254 0.066 0.278 0.129

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

5 5 17 6 15 19 15 17 5

N.S.

1 1.00 3.40 1.20 3.00 3.80 3.00 3.40 1.00

time (sec)

N/A 0.142 0.006 0.063 0.178 0.252 0.061 0.273 0.044

Problem 83

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

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 0.145 0.001 0.078 0.204 0.239 0.019 0.276 0.029

Problem 84

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

20 18 20 17 16 16 15 16 16

N.S.

1 0.90 1.00 0.85 0.80 0.80 0.75 0.80 0.80

time (sec)

N/A 0.210 0.003 0.327 0.194 0.246 0.184 0.283 0.164

Problem 85

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

13 13 15 11 11 11 8 11 10

N.S.

1 1.00 1.15 0.85 0.85 0.85 0.62 0.85 0.77

time (sec)

N/A 0.162 0.001 0.151 0.173 0.238 0.020 0.271 0.034

Problem 86

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

44 44 44 0 0 0 0 0 35

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.80

time (sec)

N/A 0.168 0.018 0.000 0.000 0.000 0.000 0.000 0.313

Problem 87

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

19 19 19 16 15 18 17 15 15

N.S.

1 1.00 1.00 0.84 0.79 0.95 0.89 0.79 0.79

time (sec)

N/A 0.183 0.004 0.154 0.179 0.258 0.204 0.280 0.046

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

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 0.155 0.001 0.079 0.173 0.242 0.018 0.294 0.026

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

11 11 11 11 9 10 8 9 9

N.S.

1 1.00 1.00 1.00 0.82 0.91 0.73 0.82 0.82

time (sec)

N/A 0.168 0.000 0.143 0.190 0.244 0.022 0.289 0.030

Problem 90

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

2 2 2 3 2 7 5 2 2

N.S.

1 1.00 1.00 1.50 1.00 3.50 2.50 1.00 1.00

time (sec)

N/A 0.155 0.001 0.132 0.176 0.242 0.038 0.282 0.023

Problem 91

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 12 11 10 20 6 6

N.S.

1 1.00 1.00 0.80 0.73 0.67 1.33 0.40 0.40

time (sec)

N/A 0.160 0.018 0.167 0.182 0.244 0.149 0.300 0.028

Problem 92

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

8 8 8 9 8 8 7 8 8

N.S.

1 1.00 1.00 1.12 1.00 1.00 0.88 1.00 1.00

time (sec)

N/A 0.179 0.002 0.050 0.173 0.246 0.068 0.300 0.021

Problem 93

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

17 17 15 17 15 15 17 15 15

N.S.

1 1.00 0.88 1.00 0.88 0.88 1.00 0.88 0.88

time (sec)

N/A 0.242 0.005 0.086 0.184 0.247 0.098 0.279 0.027

Problem 94

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

25 25 25 20 19 19 36 19 19

N.S.

1 1.00 1.00 0.80 0.76 0.76 1.44 0.76 0.76

time (sec)

N/A 0.164 0.002 0.100 0.208 0.243 0.097 0.283 0.056

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 46 29 19 26 29 56 26 28

N.S.

1 1.12 0.71 0.46 0.63 0.71 1.37 0.63 0.68

time (sec)

N/A 0.219 0.017 0.181 0.184 0.258 0.132 0.264 0.160

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

33 32 31 23 23 23 39 23 25

N.S.

1 0.97 0.94 0.70 0.70 0.70 1.18 0.70 0.76

time (sec)

N/A 0.243 0.003 0.223 0.182 0.268 0.145 0.266 0.068

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

7 7 7 8 7 7 7 7 7

N.S.

1 1.00 1.00 1.14 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.176 0.007 0.078 0.193 0.246 0.064 0.298 0.020

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

16 17 14 15 14 14 17 14 14

N.S.

1 1.06 0.88 0.94 0.88 0.88 1.06 0.88 0.88

time (sec)

N/A 0.233 0.011 0.097 0.178 0.248 0.124 0.288 0.025

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

25 25 25 20 19 19 36 19 19

N.S.

1 1.00 1.00 0.80 0.76 0.76 1.44 0.76 0.76

time (sec)

N/A 0.159 0.010 0.104 0.213 0.245 0.090 0.268 0.145

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

41 46 29 27 26 29 56 26 28

N.S.

1 1.12 0.71 0.66 0.63 0.71 1.37 0.63 0.68

time (sec)

N/A 0.219 0.027 0.184 0.202 0.245 0.146 0.266 0.066

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