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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

131 151 118 84 127 192 148 95 119

N.S.

1 1.15 0.90 0.64 0.97 1.47 1.13 0.73 0.91

time (sec)

N/A 0.272 0.643 3.468 0.191 0.266 0.288 0.281 9.462

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

105 119 107 73 105 169 134 83 93

N.S.

1 1.13 1.02 0.70 1.00 1.61 1.28 0.79 0.89

time (sec)

N/A 0.236 0.544 2.144 0.192 0.268 0.263 0.273 9.186

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

81 89 96 73 85 148 117 71 69

N.S.

1 1.10 1.19 0.90 1.05 1.83 1.44 0.88 0.85

time (sec)

N/A 0.199 0.428 2.430 0.193 0.279 0.256 0.271 0.089

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

60 60 83 56 63 121 102 59 55

N.S.

1 1.00 1.38 0.93 1.05 2.02 1.70 0.98 0.92

time (sec)

N/A 0.174 0.328 2.366 0.191 0.271 0.256 0.275 8.989

Problem 5

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

42 42 59 38 41 100 0 46 42

N.S.

1 1.00 1.40 0.90 0.98 2.38 0.00 1.10 1.00

time (sec)

N/A 0.167 0.094 2.040 0.195 0.275 0.000 0.270 8.961

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 70 40 44 95 0 60 0

N.S.

1 1.00 1.49 0.85 0.94 2.02 0.00 1.28 0.00

time (sec)

N/A 0.171 0.147 2.109 0.193 0.263 0.000 0.274 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 21 20 37 24 0 76 24

N.S.

1 1.00 0.91 0.87 1.61 1.04 0.00 3.30 1.04

time (sec)

N/A 0.146 0.035 2.114 0.184 0.265 0.000 0.269 9.039

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 39 29 59 38 0 107 37

N.S.

1 1.00 0.81 0.60 1.23 0.79 0.00 2.23 0.77

time (sec)

N/A 0.169 0.114 2.190 0.189 0.259 0.000 0.271 9.111

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 80 51 40 81 49 0 136 81

N.S.

1 1.08 0.69 0.54 1.09 0.66 0.00 1.84 1.09

time (sec)

N/A 0.202 0.127 2.061 0.254 0.265 0.000 0.271 9.217

Problem 10

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

100 112 62 55 103 60 0 165 103

N.S.

1 1.12 0.62 0.55 1.03 0.60 0.00 1.65 1.03

time (sec)

N/A 0.234 0.141 2.072 0.416 0.259 0.000 0.278 9.267

Problem 11

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

126 144 73 66 125 71 0 194 125

N.S.

1 1.14 0.58 0.52 0.99 0.56 0.00 1.54 0.99

time (sec)

N/A 0.266 0.148 2.169 0.213 0.261 0.000 0.269 9.357

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 156 129 95 144 214 160 106 0

N.S.

1 1.16 0.96 0.71 1.07 1.60 1.19 0.79 0.00

time (sec)

N/A 0.280 0.848 2.126 0.190 0.280 0.364 0.288 0.000

Problem 13

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

110 126 118 84 124 191 144 93 118

N.S.

1 1.15 1.07 0.76 1.13 1.74 1.31 0.85 1.07

time (sec)

N/A 0.239 0.717 2.062 0.187 0.273 0.346 0.295 9.060

Problem 14

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

89 97 107 73 102 170 257 81 87

N.S.

1 1.09 1.20 0.82 1.15 1.91 2.89 0.91 0.98

time (sec)

N/A 0.205 0.544 2.078 0.180 0.265 0.413 0.273 9.110

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 83 96 73 79 147 224 70 0

N.S.

1 1.06 1.23 0.94 1.01 1.88 2.87 0.90 0.00

time (sec)

N/A 0.202 0.477 2.035 0.185 0.275 1.108 0.282 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 68 70 59 62 126 0 58 0

N.S.

1 0.94 0.97 0.82 0.86 1.75 0.00 0.81 0.00

time (sec)

N/A 0.199 0.150 2.152 0.198 0.279 0.000 0.289 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 65 83 56 62 116 0 76 0

N.S.

1 1.02 1.30 0.88 0.97 1.81 0.00 1.19 0.00

time (sec)

N/A 0.204 0.276 2.185 0.189 0.276 0.000 0.287 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 70 79 49 78 116 0 115 0

N.S.

1 1.03 1.16 0.72 1.15 1.71 0.00 1.69 0.00

time (sec)

N/A 0.205 0.174 2.131 0.192 0.282 0.000 0.282 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 21 20 73 35 0 134 26

N.S.

1 1.00 0.91 0.87 3.17 1.52 0.00 5.83 1.13

time (sec)

N/A 0.158 0.053 2.083 0.184 0.260 0.000 0.297 9.358

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 29 31 95 49 0 165 79

N.S.

1 1.00 0.60 0.65 1.98 1.02 0.00 3.44 1.65

time (sec)

N/A 0.179 0.160 2.093 0.199 0.247 0.000 0.288 9.531

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 80 40 42 117 60 0 194 101

N.S.

1 1.08 0.54 0.57 1.58 0.81 0.00 2.62 1.36

time (sec)

N/A 0.214 0.165 2.484 0.192 0.257 0.000 0.282 9.684

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 112 51 55 139 71 0 223 123

N.S.

1 1.12 0.51 0.55 1.39 0.71 0.00 2.23 1.23

time (sec)

N/A 0.246 0.184 2.495 0.198 0.257 0.000 0.278 9.869

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 144 62 66 161 82 0 252 145

N.S.

1 1.14 0.49 0.52 1.28 0.65 0.00 2.00 1.15

time (sec)

N/A 0.276 0.198 2.235 0.210 0.267 0.000 0.277 10.133

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 193 151 128 183 257 187 129 0

N.S.

1 1.18 0.93 0.79 1.12 1.58 1.15 0.79 0.00

time (sec)

N/A 0.320 1.264 2.131 0.193 0.275 0.456 0.299 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 163 140 117 163 236 172 118 0

N.S.

1 1.17 1.01 0.84 1.17 1.70 1.24 0.85 0.00

time (sec)

N/A 0.282 1.055 2.018 0.192 0.272 0.424 0.304 0.000

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

118 134 129 106 141 213 459 105 119

N.S.

1 1.14 1.09 0.90 1.19 1.81 3.89 0.89 1.01

time (sec)

N/A 0.238 0.115 2.018 0.230 0.281 0.560 0.279 9.475

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 120 118 84 118 192 415 94 0

N.S.

1 1.12 1.10 0.79 1.10 1.79 3.88 0.88 0.00

time (sec)

N/A 0.237 0.082 2.119 0.179 0.280 1.629 0.283 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 109 107 73 98 169 369 82 0

N.S.

1 1.08 1.06 0.72 0.97 1.67 3.65 0.81 0.00

time (sec)

N/A 0.229 0.088 2.130 0.194 0.286 0.596 0.282 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 105 81 64 81 148 0 70 0

N.S.

1 1.12 0.86 0.68 0.86 1.57 0.00 0.74 0.00

time (sec)

N/A 0.237 0.061 2.051 0.181 0.261 0.000 0.286 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 94 100 69 84 144 0 89 0

N.S.

1 1.02 1.09 0.75 0.91 1.57 0.00 0.97 0.00

time (sec)

N/A 0.275 0.068 2.099 0.188 0.279 0.000 0.284 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 91 101 70 99 145 0 133 0

N.S.

1 1.02 1.13 0.79 1.11 1.63 0.00 1.49 0.00

time (sec)

N/A 0.236 0.055 2.105 0.182 0.271 0.000 0.291 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 93 92 62 134 144 0 175 0

N.S.

1 1.02 1.01 0.68 1.47 1.58 0.00 1.92 0.00

time (sec)

N/A 0.240 0.223 2.074 0.190 0.268 0.000 0.297 0.000

Problem 33

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 21 20 112 46 0 192 79

N.S.

1 1.00 0.91 0.87 4.87 2.00 0.00 8.35 3.43

time (sec)

N/A 0.150 0.056 2.153 0.199 0.265 0.000 0.290 9.623

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 29 31 134 60 0 223 101

N.S.

1 1.00 0.60 0.65 2.79 1.25 0.00 4.65 2.10

time (sec)

N/A 0.175 0.187 2.103 0.185 0.262 0.000 0.292 9.800

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 80 40 42 156 71 0 252 123

N.S.

1 1.08 0.54 0.57 2.11 0.96 0.00 3.41 1.66

time (sec)

N/A 0.207 0.201 2.171 0.204 0.266 0.000 0.287 10.103

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 112 51 55 178 82 0 281 145

N.S.

1 1.12 0.51 0.55 1.78 0.82 0.00 2.81 1.45

time (sec)

N/A 0.240 0.222 2.299 0.190 0.265 0.000 0.286 10.385

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 144 69 66 200 93 0 310 167

N.S.

1 1.14 0.55 0.52 1.59 0.74 0.00 2.46 1.33

time (sec)

N/A 0.276 0.106 2.384 0.193 0.267 0.000 0.293 10.705

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 176 80 77 222 104 0 339 189

N.S.

1 1.16 0.53 0.51 1.46 0.68 0.00 2.23 1.24

time (sec)

N/A 0.314 0.109 2.688 0.198 0.242 0.000 0.278 11.041

Problem 39

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

50 54 54 32 49 42 27 29 42

N.S.

1 1.08 1.08 0.64 0.98 0.84 0.54 0.58 0.84

time (sec)

N/A 0.182 0.098 2.592 0.274 0.258 0.301 0.272 0.084

Problem 40

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 59 75 38 49 43 34 32 44

N.S.

1 1.13 1.44 0.73 0.94 0.83 0.65 0.62 0.85

time (sec)

N/A 0.201 0.096 2.104 0.271 0.251 0.284 0.274 9.108

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

48 53 53 37 46 37 37 38 33

N.S.

1 1.10 1.10 0.77 0.96 0.77 0.77 0.79 0.69

time (sec)

N/A 0.181 0.093 2.101 0.198 0.253 0.214 0.261 9.105

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 141 119 73 110 170 143 87 0

N.S.

1 1.10 0.93 0.57 0.86 1.33 1.12 0.68 0.00

time (sec)

N/A 0.285 0.466 2.157 0.200 0.264 0.285 0.269 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 109 108 73 88 147 129 75 0

N.S.

1 1.07 1.06 0.72 0.86 1.44 1.26 0.74 0.00

time (sec)

N/A 0.248 0.374 2.255 0.185 0.271 0.290 0.285 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 77 97 59 66 126 116 63 0

N.S.

1 1.01 1.28 0.78 0.87 1.66 1.53 0.83 0.00

time (sec)

N/A 0.204 0.284 2.068 0.193 0.266 0.318 0.296 0.000

Problem 45

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 47 78 39 45 98 99 50 46

N.S.

1 1.00 1.66 0.83 0.96 2.09 2.11 1.06 0.98

time (sec)

N/A 0.177 0.211 2.015 0.231 0.278 0.292 0.278 0.090

Problem 46

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

28 28 55 23 27 62 75 59 28

N.S.

1 1.00 1.96 0.82 0.96 2.21 2.68 2.11 1.00

time (sec)

N/A 0.150 0.059 1.972 0.200 0.259 0.315 0.278 9.047

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

21 21 21 18 19 19 0 23 19

N.S.

1 1.00 1.00 0.86 0.90 0.90 0.00 1.10 0.90

time (sec)

N/A 0.147 0.030 1.959 0.194 0.248 0.000 0.270 8.978

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

48 48 29 24 40 27 0 49 25

N.S.

1 1.00 0.60 0.50 0.83 0.56 0.00 1.02 0.52

time (sec)

N/A 0.168 0.102 1.865 0.191 0.258 0.000 0.270 9.058

Problem 49

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

74 80 40 37 62 38 0 78 38

N.S.

1 1.08 0.54 0.50 0.84 0.51 0.00 1.05 0.51

time (sec)

N/A 0.200 0.113 1.889 0.197 0.252 0.000 0.265 9.046

Problem 50

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

100 112 51 48 84 49 0 107 84

N.S.

1 1.12 0.51 0.48 0.84 0.49 0.00 1.07 0.84

time (sec)

N/A 0.236 0.133 1.970 0.191 0.255 0.000 0.281 9.046

Problem 51

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

126 144 62 59 106 60 0 136 106

N.S.

1 1.14 0.49 0.47 0.84 0.48 0.00 1.08 0.84

time (sec)

N/A 0.269 0.137 1.883 0.198 0.238 0.000 0.283 8.990

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 97 97 73 91 182 0 100 0

N.S.

1 1.00 1.00 0.75 0.94 1.88 0.00 1.03 0.00

time (sec)

N/A 0.275 0.394 1.871 0.236 0.265 0.000 0.281 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 71 80 58 66 152 0 87 0

N.S.

1 1.03 1.16 0.84 0.96 2.20 0.00 1.26 0.00

time (sec)

N/A 0.207 0.304 1.895 0.193 0.254 0.000 0.294 0.000

Problem 54

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

48 48 73 39 45 126 0 67 46

N.S.

1 1.00 1.52 0.81 0.94 2.62 0.00 1.40 0.96

time (sec)

N/A 0.177 0.169 1.917 0.194 0.237 0.000 0.303 8.986

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

19 19 17 16 17 23 0 32 15

N.S.

1 1.00 0.89 0.84 0.89 1.21 0.00 1.68 0.79

time (sec)

N/A 0.145 0.033 2.095 0.192 0.228 0.000 0.274 0.033

Problem 56

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

24 24 22 21 35 35 0 24 24

N.S.

1 1.00 0.92 0.88 1.46 1.46 0.00 1.00 1.00

time (sec)

N/A 0.145 0.099 1.875 0.188 0.236 0.000 0.265 0.039

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 40 35 57 50 0 0 45

N.S.

1 1.00 0.78 0.69 1.12 0.98 0.00 0.00 0.88

time (sec)

N/A 0.170 0.140 1.851 0.191 0.242 0.000 0.000 9.048

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 83 49 46 79 59 0 0 54

N.S.

1 1.08 0.64 0.60 1.03 0.77 0.00 0.00 0.70

time (sec)

N/A 0.202 0.159 1.907 0.185 0.257 0.000 0.000 9.076

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 115 62 59 101 72 0 0 102

N.S.

1 1.12 0.60 0.57 0.98 0.70 0.00 0.00 0.99

time (sec)

N/A 0.234 0.177 1.864 0.205 0.237 0.000 0.000 9.144

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 128 109 98 190 248 0 157 0

N.S.

1 1.05 0.89 0.80 1.56 2.03 0.00 1.29 0.00

time (sec)

N/A 0.310 0.509 1.918 0.199 0.259 0.000 0.298 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 102 96 82 162 221 0 144 0

N.S.

1 1.09 1.02 0.87 1.72 2.35 0.00 1.53 0.00

time (sec)

N/A 0.248 0.067 1.910 0.190 0.253 0.000 0.288 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 76 84 73 140 193 0 124 0

N.S.

1 1.07 1.18 1.03 1.97 2.72 0.00 1.75 0.00

time (sec)

N/A 0.203 0.078 1.974 0.188 0.255 0.000 0.296 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 21 25 74 35 0 85 24

N.S.

1 1.00 0.91 1.09 3.22 1.52 0.00 3.70 1.04

time (sec)

N/A 0.147 0.014 1.915 0.197 0.250 0.000 0.301 9.179

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

51 51 29 29 54 44 0 60 31

N.S.

1 1.00 0.57 0.57 1.06 0.86 0.00 1.18 0.61

time (sec)

N/A 0.172 0.013 1.923 0.206 0.244 0.000 0.288 9.194

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 38 39 52 59 0 0 45

N.S.

1 1.00 0.79 0.81 1.08 1.23 0.00 0.00 0.94

time (sec)

N/A 0.164 0.014 2.103 0.180 0.251 0.000 0.000 9.178

Problem 66

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

54 54 48 47 72 72 0 50 43

N.S.

1 1.00 0.89 0.87 1.33 1.33 0.00 0.93 0.80

time (sec)

N/A 0.168 0.015 2.048 0.187 0.246 0.000 0.282 0.044

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 86 64 63 96 83 0 0 67

N.S.

1 1.08 0.80 0.79 1.20 1.04 0.00 0.00 0.84

time (sec)

N/A 0.198 0.187 2.141 0.186 0.251 0.000 0.000 9.346

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 118 73 75 118 94 0 0 121

N.S.

1 1.11 0.69 0.71 1.11 0.89 0.00 0.00 1.14

time (sec)

N/A 0.229 0.201 2.114 0.187 0.243 0.000 0.000 9.485

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

26 28 47 23 22 32 17 22 22

N.S.

1 1.08 1.81 0.88 0.85 1.23 0.65 0.85 0.85

time (sec)

N/A 0.156 0.017 2.414 0.273 0.254 0.272 0.269 9.210

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

28 28 46 26 29 27 29 28 23

N.S.

1 1.00 1.64 0.93 1.04 0.96 1.04 1.00 0.82

time (sec)

N/A 0.159 0.007 2.115 0.176 0.240 0.258 0.279 0.136

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 51 53 25 36 35 26 23 0

N.S.

1 1.11 1.15 0.54 0.78 0.76 0.57 0.50 0.00

time (sec)

N/A 0.193 0.079 2.351 0.273 0.255 0.264 0.277 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 154 64 64 64 71 0 70 0

N.S.

1 1.13 0.47 0.47 0.47 0.52 0.00 0.51 0.00

time (sec)

N/A 0.276 0.053 2.112 0.193 0.240 0.000 0.279 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 120 53 53 53 60 0 58 0

N.S.

1 1.11 0.49 0.49 0.49 0.56 0.00 0.54 0.00

time (sec)

N/A 0.248 0.043 1.991 0.199 0.249 0.000 0.271 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 86 42 42 42 49 0 46 0

N.S.

1 1.08 0.52 0.52 0.52 0.61 0.00 0.58 0.00

time (sec)

N/A 0.207 0.039 2.071 0.199 0.250 0.000 0.277 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 52 41 31 30 37 0 34 0

N.S.

1 1.00 0.79 0.60 0.58 0.71 0.00 0.65 0.00

time (sec)

N/A 0.176 0.029 2.017 0.197 0.245 0.000 0.276 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 23 23 12 24 0 21 0

N.S.

1 1.00 0.92 0.92 0.48 0.96 0.00 0.84 0.00

time (sec)

N/A 0.149 0.010 1.992 0.194 0.252 0.000 0.277 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 60 48 0 111 0 61 0

N.S.

1 1.00 1.13 0.91 0.00 2.09 0.00 1.15 0.00

time (sec)

N/A 0.185 0.055 2.022 0.000 0.249 0.000 0.268 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 68 53 0 126 0 41 0

N.S.

1 1.00 1.26 0.98 0.00 2.33 0.00 0.76 0.00

time (sec)

N/A 0.181 0.083 2.022 0.000 0.259 0.000 0.291 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 84 81 70 0 148 0 66 0

N.S.

1 0.98 0.94 0.81 0.00 1.72 0.00 0.77 0.00

time (sec)

N/A 0.215 0.143 2.113 0.000 0.270 0.000 0.278 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 118 93 82 0 174 0 84 0

N.S.

1 1.04 0.82 0.72 0.00 1.53 0.00 0.74 0.00

time (sec)

N/A 0.251 0.174 2.103 0.000 0.257 0.000 0.287 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 152 105 93 0 196 0 99 0

N.S.

1 1.07 0.74 0.65 0.00 1.38 0.00 0.70 0.00

time (sec)

N/A 0.278 0.188 1.993 0.000 0.262 0.000 0.293 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 188 75 77 168 93 0 182 0

N.S.

1 1.15 0.46 0.47 1.02 0.57 0.00 1.11 0.00

time (sec)

N/A 0.316 0.060 2.020 0.195 0.244 0.000 0.270 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 154 64 66 147 82 0 158 0

N.S.

1 1.13 0.47 0.49 1.08 0.60 0.00 1.16 0.00

time (sec)

N/A 0.288 0.053 2.024 0.207 0.248 0.000 0.280 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 120 53 55 124 71 0 134 0

N.S.

1 1.11 0.49 0.51 1.15 0.66 0.00 1.24 0.00

time (sec)

N/A 0.250 0.047 2.007 0.200 0.248 0.000 0.275 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 86 42 44 102 60 0 110 0

N.S.

1 1.08 0.52 0.55 1.28 0.75 0.00 1.38 0.00

time (sec)

N/A 0.213 0.046 1.977 0.203 0.246 0.000 0.262 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 52 31 33 77 48 0 86 0

N.S.

1 1.00 0.60 0.63 1.48 0.92 0.00 1.65 0.00

time (sec)

N/A 0.177 0.035 2.086 0.190 0.253 0.000 0.265 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 23 25 49 35 0 60 0

N.S.

1 1.00 0.92 1.00 1.96 1.40 0.00 2.40 0.00

time (sec)

N/A 0.150 0.013 2.396 0.231 0.245 0.000 0.276 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 78 70 61 0 129 0 77 0

N.S.

1 1.03 0.92 0.80 0.00 1.70 0.00 1.01 0.00

time (sec)

N/A 0.221 0.079 2.061 0.000 0.264 0.000 0.269 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 79 69 68 0 135 0 56 0

N.S.

1 1.05 0.92 0.91 0.00 1.80 0.00 0.75 0.00

time (sec)

N/A 0.207 0.110 2.129 0.000 0.266 0.000 0.293 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 82 82 68 0 153 0 64 0

N.S.

1 0.99 0.99 0.82 0.00 1.84 0.00 0.77 0.00

time (sec)

N/A 0.206 0.168 2.063 0.000 0.257 0.000 0.299 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 112 94 82 0 174 0 84 0

N.S.

1 1.01 0.85 0.74 0.00 1.57 0.00 0.76 0.00

time (sec)

N/A 0.248 0.193 1.959 0.000 0.257 0.000 0.290 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 146 104 93 0 196 0 99 0

N.S.

1 1.05 0.75 0.67 0.00 1.41 0.00 0.71 0.00

time (sec)

N/A 0.279 0.224 2.039 0.000 0.266 0.000 0.298 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 180 116 104 0 218 0 114 0

N.S.

1 1.08 0.69 0.62 0.00 1.31 0.00 0.68 0.00

time (sec)

N/A 0.317 0.269 2.043 0.000 0.263 0.000 0.311 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 120 53 48 53 49 0 61 0

N.S.

1 1.11 0.49 0.44 0.49 0.45 0.00 0.56 0.00

time (sec)

N/A 0.235 0.045 1.982 0.200 0.258 0.000 0.268 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 86 42 37 42 38 0 49 0

N.S.

1 1.08 0.52 0.46 0.52 0.48 0.00 0.61 0.00

time (sec)

N/A 0.207 0.039 2.006 0.187 0.249 0.000 0.285 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 52 30 26 30 26 0 34 0

N.S.

1 1.00 0.58 0.50 0.58 0.50 0.00 0.65 0.00

time (sec)

N/A 0.175 0.029 2.067 0.191 0.250 0.000 0.259 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 21 18 12 19 0 21 0

N.S.

1 1.00 0.91 0.78 0.52 0.83 0.00 0.91 0.00

time (sec)

N/A 0.143 0.008 2.039 0.194 0.242 0.000 0.266 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 48 37 0 71 0 39 0

N.S.

1 1.00 1.50 1.16 0.00 2.22 0.00 1.22 0.00

time (sec)

N/A 0.151 0.037 2.031 0.000 0.257 0.000 0.268 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 63 52 0 126 0 47 0

N.S.

1 1.00 1.12 0.93 0.00 2.25 0.00 0.84 0.00

time (sec)

N/A 0.185 0.088 2.057 0.000 0.262 0.000 0.286 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 90 83 71 0 152 0 69 0

N.S.

1 1.01 0.93 0.80 0.00 1.71 0.00 0.78 0.00

time (sec)

N/A 0.216 0.125 2.028 0.000 0.260 0.000 0.278 0.000

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