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Integrals 1 to 43

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 Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

152 151 97 92 178 114 0 569 113 152

N.S.

1 0.99 0.64 0.61 1.17 0.75 0.00 3.74 0.74 1.00

time (sec)

N/A 0.427 0.188 0.156 0.033 0.147 0.000 0.216 0.251 4.023

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

109 110 75 68 124 90 0 454 89 118

N.S.

1 1.01 0.69 0.62 1.14 0.83 0.00 4.17 0.82 1.08

time (sec)

N/A 0.376 0.147 0.145 0.033 0.130 0.000 0.207 0.210 3.895

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

67 72 49 44 70 66 0 330 65 83

N.S.

1 1.07 0.73 0.66 1.04 0.99 0.00 4.93 0.97 1.24

time (sec)

N/A 0.322 0.113 0.138 0.035 0.098 0.000 0.183 0.198 3.957

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B A A F A B B

verified

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

size

80 81 75 174 52 80 0 78 130 248

N.S.

1 1.01 0.94 2.18 0.65 1.00 0.00 0.98 1.62 3.10

time (sec)

N/A 0.390 0.144 0.142 0.109 0.098 0.000 0.154 0.235 5.950

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

96 99 74 138 98 85 0 157 180 584

N.S.

1 1.03 0.77 1.44 1.02 0.89 0.00 1.64 1.88 6.08

time (sec)

N/A 0.399 0.223 0.178 0.108 0.135 0.000 0.178 0.203 9.439

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

118 142 99 150 162 100 0 324 213 1004

N.S.

1 1.20 0.84 1.27 1.37 0.85 0.00 2.75 1.81 8.51

time (sec)

N/A 0.443 0.191 0.148 0.109 0.091 0.000 0.196 0.234 18.878

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

207 185 142 184 246 138 0 519 241 2314

N.S.

1 0.89 0.69 0.89 1.19 0.67 0.00 2.51 1.16 11.18

time (sec)

N/A 0.492 0.311 0.141 0.036 0.109 0.000 0.219 0.234 42.417

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

158 143 116 159 192 112 0 403 189 1681

N.S.

1 0.91 0.73 1.01 1.22 0.71 0.00 2.55 1.20 10.64

time (sec)

N/A 0.437 0.252 0.130 0.033 0.126 0.000 0.209 0.204 47.592

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

114 105 92 135 137 88 0 276 137 734

N.S.

1 0.92 0.81 1.18 1.20 0.77 0.00 2.42 1.20 6.44

time (sec)

N/A 0.331 0.183 0.132 0.033 0.094 0.000 0.177 0.210 19.515

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

104 97 74 117 105 83 0 114 125 243

N.S.

1 0.93 0.71 1.12 1.01 0.80 0.00 1.10 1.20 2.34

time (sec)

N/A 0.388 0.205 0.134 0.114 0.114 0.000 0.166 0.219 5.431

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

84 85 81 124 75 100 0 165 126 236

N.S.

1 1.01 0.96 1.48 0.89 1.19 0.00 1.96 1.50 2.81

time (sec)

N/A 0.380 0.185 0.144 0.109 0.096 0.000 0.182 0.230 5.438

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

125 118 96 129 153 96 0 172 152 1154

N.S.

1 0.94 0.77 1.03 1.22 0.77 0.00 1.38 1.22 9.23

time (sec)

N/A 0.398 0.206 0.132 0.028 0.094 0.000 0.130 0.214 37.565

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

103 98 61 57 95 55 216 108 54 108

N.S.

1 0.95 0.59 0.55 0.92 0.53 2.10 1.05 0.52 1.05

time (sec)

N/A 0.358 0.105 0.112 0.028 0.089 8.901 0.134 0.232 4.641

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

87 82 77 111 113 77 0 121 110 720

N.S.

1 0.94 0.89 1.28 1.30 0.89 0.00 1.39 1.26 8.28

time (sec)

N/A 0.342 0.162 0.125 0.031 0.093 0.000 0.133 0.208 26.012

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

65 65 43 38 54 37 202 59 35 66

N.S.

1 1.00 0.66 0.58 0.83 0.57 3.11 0.91 0.54 1.02

time (sec)

N/A 0.306 0.082 0.122 0.032 0.092 6.542 0.127 0.207 4.708

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

47 47 58 91 74 55 0 69 69 293

N.S.

1 1.00 1.23 1.94 1.57 1.17 0.00 1.47 1.47 6.23

time (sec)

N/A 0.268 0.120 0.109 0.035 0.117 0.000 0.135 0.234 15.841

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

46 46 45 62 29 48 162 45 61 77

N.S.

1 1.00 0.98 1.35 0.63 1.04 3.52 0.98 1.33 1.67

time (sec)

N/A 0.324 0.087 0.108 0.111 0.092 16.297 0.129 0.221 6.016

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C A A C A B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

33 33 48 77 44 56 148 56 52 61

N.S.

1 1.00 1.45 2.33 1.33 1.70 4.48 1.70 1.58 1.85

time (sec)

N/A 0.296 0.094 0.123 0.106 0.105 15.637 0.134 0.221 5.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

60 60 55 71 45 57 0 114 110 297

N.S.

1 1.00 0.92 1.18 0.75 0.95 0.00 1.90 1.83 4.95

time (sec)

N/A 0.327 0.112 0.121 0.102 0.117 0.000 0.141 0.219 12.153

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C B B B

verified

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

size

62 62 42 37 54 52 146 105 75 53

N.S.

1 1.00 0.68 0.60 0.87 0.84 2.35 1.69 1.21 0.85

time (sec)

N/A 0.322 0.109 0.115 0.103 0.091 20.733 0.136 0.225 4.933

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

99 94 78 94 85 78 0 268 156 650

N.S.

1 0.95 0.79 0.95 0.86 0.79 0.00 2.71 1.58 6.57

time (sec)

N/A 0.378 0.218 0.116 0.106 0.094 0.000 0.147 0.198 25.835

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

164 148 119 160 196 115 0 203 189 1682

N.S.

1 0.90 0.73 0.98 1.20 0.70 0.00 1.24 1.15 10.26

time (sec)

N/A 0.453 0.276 0.134 0.033 0.132 0.000 0.150 0.201 48.106

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

118 110 74 68 124 66 240 124 65 130

N.S.

1 0.93 0.63 0.58 1.05 0.56 2.03 1.05 0.55 1.10

time (sec)

N/A 0.391 0.135 0.129 0.034 0.109 10.110 0.140 0.236 5.283

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

118 107 92 136 142 90 0 140 137 1048

N.S.

1 0.91 0.78 1.15 1.20 0.76 0.00 1.19 1.16 8.88

time (sec)

N/A 0.397 0.208 0.144 0.033 0.116 0.000 0.141 0.203 28.947

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

72 72 48 43 69 42 223 65 40 76

N.S.

1 1.00 0.67 0.60 0.96 0.58 3.10 0.90 0.56 1.06

time (sec)

N/A 0.323 0.105 0.134 0.038 0.103 5.170 0.129 0.210 4.982

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

68 68 68 111 89 63 0 79 86 417

N.S.

1 1.00 1.00 1.63 1.31 0.93 0.00 1.16 1.26 6.13

time (sec)

N/A 0.312 0.141 0.131 0.036 0.090 0.000 0.139 0.198 13.340

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B A A C A B B

verified

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

size

56 56 54 108 37 61 178 55 85 108

N.S.

1 1.00 0.96 1.93 0.66 1.09 3.18 0.98 1.52 1.93

time (sec)

N/A 0.365 0.105 0.125 0.110 0.089 27.746 0.138 0.193 6.300

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C A A C A B B

verified

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

size

57 57 57 97 55 68 165 64 66 77

N.S.

1 1.00 1.00 1.70 0.96 1.19 2.89 1.12 1.16 1.35

time (sec)

N/A 0.338 0.122 0.147 0.103 0.093 26.508 0.137 0.223 5.204

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

76 76 70 123 60 73 0 141 158 457

N.S.

1 1.00 0.92 1.62 0.79 0.96 0.00 1.86 2.08 6.01

time (sec)

N/A 0.363 0.132 0.134 0.107 0.090 0.000 0.140 0.231 10.091

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

75 75 54 49 75 67 170 126 93 79

N.S.

1 1.00 0.72 0.65 1.00 0.89 2.27 1.68 1.24 1.05

time (sec)

N/A 0.349 0.122 0.132 0.117 0.092 31.008 0.141 0.221 4.995

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

123 115 101 151 114 100 0 325 214 1005

N.S.

1 0.93 0.82 1.23 0.93 0.81 0.00 2.64 1.74 8.17

time (sec)

N/A 0.418 0.205 0.155 0.110 0.134 0.000 0.145 0.242 23.034

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

169 141 137 275 196 190 0 214 331 0

N.S.

1 0.83 0.81 1.63 1.16 1.12 0.00 1.27 1.96 0.00

time (sec)

N/A 0.463 0.284 0.161 0.030 0.104 0.000 0.164 0.262 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

123 103 72 68 123 80 226 200 73 90

N.S.

1 0.84 0.59 0.55 1.00 0.65 1.84 1.63 0.59 0.73

time (sec)

N/A 0.401 0.141 0.155 0.036 0.089 59.109 0.159 0.205 5.241

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

120 133 108 251 138 159 0 147 285 0

N.S.

1 1.11 0.90 2.09 1.15 1.32 0.00 1.22 2.38 0.00

time (sec)

N/A 0.447 0.199 0.145 0.033 0.088 0.000 0.160 0.231 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C B B B

verified

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

size

76 73 45 42 69 56 201 152 48 67

N.S.

1 0.96 0.59 0.55 0.91 0.74 2.64 2.00 0.63 0.88

time (sec)

N/A 0.334 0.109 0.138 0.026 0.091 54.360 0.149 0.210 5.220

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

63 63 71 160 76 129 182 113 192 0

N.S.

1 1.00 1.13 2.54 1.21 2.05 2.89 1.79 3.05 0.00

time (sec)

N/A 0.299 0.201 0.128 0.027 0.093 177.218 0.143 0.247 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

65 65 70 188 58 101 172 115 206 0

N.S.

1 1.00 1.08 2.89 0.89 1.55 2.65 1.77 3.17 0.00

time (sec)

N/A 0.375 0.173 0.132 0.110 0.097 177.654 0.165 0.233 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C B B B

verified

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

size

67 66 51 48 71 103 165 219 137 73

N.S.

1 0.99 0.76 0.72 1.06 1.54 2.46 3.27 2.04 1.09

time (sec)

N/A 0.358 0.119 0.128 0.105 0.095 57.483 0.182 0.221 4.955

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

117 105 93 239 104 138 0 211 400 0

N.S.

1 0.90 0.79 2.04 0.89 1.18 0.00 1.80 3.42 0.00

time (sec)

N/A 0.422 0.231 0.155 0.112 0.095 0.000 0.208 0.226 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C B B B

verified

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

size

119 106 77 73 125 132 165 242 176 104

N.S.

1 0.89 0.65 0.61 1.05 1.11 1.39 2.03 1.48 0.87

time (sec)

N/A 0.393 0.166 0.163 0.105 0.079 70.645 0.215 0.216 5.311

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

166 146 122 267 162 165 0 402 447 0

N.S.

1 0.88 0.73 1.61 0.98 0.99 0.00 2.42 2.69 0.00

time (sec)

N/A 0.471 0.304 0.175 0.109 0.100 0.000 0.251 0.246 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

40 40 40 53 23 39 148 40 48 72

N.S.

1 1.00 1.00 1.32 0.58 0.98 3.70 1.00 1.20 1.80

time (sec)

N/A 0.315 0.071 0.109 0.105 0.081 25.457 0.128 0.216 5.916

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A A A C F B B

verified

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

size

53 53 244 66 79 65 1867 0 54 96

N.S.

1 1.00 4.60 1.25 1.49 1.23 35.23 0.00 1.02 1.81

time (sec)

N/A 0.357 10.220 0.199 0.119 0.126 63.551 0.000 0.381 5.484

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