[tail] [up]

Integrals 1 to 38

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 A A B B

verified

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

size

99 119 91 76 75 75 102 69 75 91

N.S.

1 1.20 0.92 0.77 0.76 0.76 1.03 0.70 0.76 0.92

time (sec)

N/A 0.453 0.019 0.155 0.116 0.097 0.181 0.128 0.154 0.207

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

180 160 137 169 372 317 355 212 217 205

N.S.

1 0.89 0.76 0.94 2.07 1.76 1.97 1.18 1.21 1.14

time (sec)

N/A 0.446 0.272 0.086 0.114 0.109 157.609 0.136 0.166 7.667

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

148 130 117 145 308 270 298 181 177 169

N.S.

1 0.88 0.79 0.98 2.08 1.82 2.01 1.22 1.20 1.14

time (sec)

N/A 0.420 0.215 0.068 0.120 0.111 30.167 0.133 0.160 7.423

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

113 104 93 121 240 221 264 149 137 130

N.S.

1 0.92 0.82 1.07 2.12 1.96 2.34 1.32 1.21 1.15

time (sec)

N/A 0.369 0.190 0.057 0.121 0.094 9.475 0.146 0.154 7.047

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

96 97 73 102 169 181 230 0 138 90

N.S.

1 1.01 0.76 1.06 1.76 1.89 2.40 0.00 1.44 0.94

time (sec)

N/A 0.358 0.185 0.070 0.110 0.103 4.149 0.000 0.165 6.942

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

85 91 73 105 132 169 177 0 122 81

N.S.

1 1.07 0.86 1.24 1.55 1.99 2.08 0.00 1.44 0.95

time (sec)

N/A 0.371 0.188 0.063 0.115 0.087 16.008 0.000 0.155 7.811

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

77 80 70 114 80 191 102 0 134 71

N.S.

1 1.04 0.91 1.48 1.04 2.48 1.32 0.00 1.74 0.92

time (sec)

N/A 0.356 0.158 0.066 0.110 0.100 3.981 0.000 0.158 7.948

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 46 45 38 49 79 167 333 148 122

N.S.

1 1.00 0.98 0.83 1.07 1.72 3.63 7.24 3.22 2.65

time (sec)

N/A 0.345 0.064 0.064 0.040 0.095 2.060 0.530 0.160 7.091

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

74 74 63 60 84 105 231 397 188 164

N.S.

1 1.00 0.85 0.81 1.14 1.42 3.12 5.36 2.54 2.22

time (sec)

N/A 0.379 0.082 0.070 0.036 0.101 2.041 0.626 0.168 7.700

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

104 104 86 84 118 130 292 461 228 206

N.S.

1 1.00 0.83 0.81 1.13 1.25 2.81 4.43 2.19 1.98

time (sec)

N/A 0.443 0.094 0.065 0.037 0.079 2.085 0.640 0.177 8.229

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

134 134 107 108 152 153 352 525 268 248

N.S.

1 1.00 0.80 0.81 1.13 1.14 2.63 3.92 2.00 1.85

time (sec)

N/A 0.483 0.113 0.077 0.040 0.091 2.239 0.851 0.196 8.837

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

164 164 129 132 186 177 411 589 308 290

N.S.

1 1.00 0.79 0.80 1.13 1.08 2.51 3.59 1.88 1.77

time (sec)

N/A 0.553 0.114 0.076 0.038 0.072 2.287 1.042 0.212 9.270

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

192 203 146 156 223 307 1073 177 191 153

N.S.

1 1.06 0.76 0.81 1.16 1.60 5.59 0.92 0.99 0.80

time (sec)

N/A 0.682 0.260 0.066 0.131 0.121 25.408 0.136 0.347 7.393

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

167 176 136 141 206 289 585 159 174 141

N.S.

1 1.05 0.81 0.84 1.23 1.73 3.50 0.95 1.04 0.84

time (sec)

N/A 0.621 0.238 0.064 0.114 0.122 25.255 0.140 0.339 7.650

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

142 148 124 132 175 258 554 146 151 123

N.S.

1 1.04 0.87 0.93 1.23 1.82 3.90 1.03 1.06 0.87

time (sec)

N/A 0.568 0.263 0.057 0.162 0.088 8.178 0.140 0.169 7.507

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

119 121 115 117 157 240 201 129 134 111

N.S.

1 1.02 0.97 0.98 1.32 2.02 1.69 1.08 1.13 0.93

time (sec)

N/A 0.503 0.220 0.056 0.120 0.090 7.872 0.139 0.159 7.096

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

94 93 103 103 120 211 197 115 111 90

N.S.

1 0.99 1.10 1.10 1.28 2.24 2.10 1.22 1.18 0.96

time (sec)

N/A 0.439 0.248 0.050 0.111 0.087 3.905 0.136 0.159 7.277

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B F(-2) B F(-1)

verified

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

size

118 124 142 148 174 535 236 0 152 0

N.S.

1 1.05 1.20 1.25 1.47 4.53 2.00 0.00 1.29 0.00

time (sec)

N/A 0.560 0.286 0.049 0.113 0.123 4.127 0.000 0.154 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

114 114 131 139 142 465 202 136 152 0

N.S.

1 1.00 1.15 1.22 1.25 4.08 1.77 1.19 1.33 0.00

time (sec)

N/A 0.543 0.299 0.066 0.124 0.109 3.119 15.579 0.161 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

111 109 138 131 160 493 182 207 150 88

N.S.

1 0.98 1.24 1.18 1.44 4.44 1.64 1.86 1.35 0.79

time (sec)

N/A 0.498 0.394 0.065 0.112 0.109 3.492 45.656 0.161 8.262

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

111 115 138 125 155 510 187 227 225 82

N.S.

1 1.04 1.24 1.13 1.40 4.59 1.68 2.05 2.03 0.74

time (sec)

N/A 0.498 0.420 0.067 0.108 0.099 4.686 67.550 0.180 8.032

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

111 118 148 122 181 558 221 305 175 85

N.S.

1 1.06 1.33 1.10 1.63 5.03 1.99 2.75 1.58 0.77

time (sec)

N/A 0.513 0.554 0.075 0.110 0.098 5.983 0.211 0.165 9.014

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

93 97 123 117 132 211 245 248 164 68

N.S.

1 1.04 1.32 1.26 1.42 2.27 2.63 2.67 1.76 0.73

time (sec)

N/A 0.400 0.529 0.086 0.121 0.119 1.844 81.232 0.171 8.842

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

118 124 117 126 174 240 275 405 188 0

N.S.

1 1.05 0.99 1.07 1.47 2.03 2.33 3.43 1.59 0.00

time (sec)

N/A 0.450 0.790 0.069 0.112 0.099 1.894 171.602 0.179 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

138 152 136 141 192 259 303 405 204 0

N.S.

1 1.10 0.99 1.02 1.39 1.88 2.20 2.93 1.48 0.00

time (sec)

N/A 0.511 0.750 0.076 0.110 0.109 1.748 171.451 0.185 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

163 180 137 150 229 288 333 0 228 0

N.S.

1 1.10 0.84 0.92 1.40 1.77 2.04 0.00 1.40 0.00

time (sec)

N/A 0.587 0.857 0.090 0.117 0.127 1.818 0.000 0.194 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

185 207 145 165 246 307 360 0 244 0

N.S.

1 1.12 0.78 0.89 1.33 1.66 1.95 0.00 1.32 0.00

time (sec)

N/A 0.616 0.859 0.091 0.112 0.148 1.892 0.000 0.219 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

168 162 130 0 0 0 860 0 1301 0

N.S.

1 0.96 0.77 0.00 0.00 0.00 5.12 0.00 7.74 0.00

time (sec)

N/A 0.695 0.397 0.000 0.000 0.000 27.658 0.000 0.164 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F(-2) C F F F(-1)

verified

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

size

314 305 206 0 0 0 342 0 0 0

N.S.

1 0.97 0.66 0.00 0.00 0.00 1.09 0.00 0.00 0.00

time (sec)

N/A 0.916 0.799 0.000 0.000 0.000 20.085 0.000 0.338 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

60 45 45 0 0 66 162 0 249 0

N.S.

1 0.75 0.75 0.00 0.00 1.10 2.70 0.00 4.15 0.00

time (sec)

N/A 0.543 0.718 0.000 0.000 0.093 136.234 0.000 0.164 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

280 273 178 0 0 0 304 0 0 0

N.S.

1 0.98 0.64 0.00 0.00 0.00 1.09 0.00 0.00 0.00

time (sec)

N/A 0.794 0.260 0.000 0.000 0.000 107.754 0.000 0.404 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F F F(-1) F(-2) F F(-1)

verified

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

size

306 297 204 0 0 0 0 0 0 0

N.S.

1 0.97 0.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.833 0.336 0.000 0.000 0.000 0.000 0.000 0.579 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 24 21 20 20 0 0 18 20

N.S.

1 1.00 1.00 0.88 0.83 0.83 0.00 0.00 0.75 0.83

time (sec)

N/A 0.363 5.766 3.506 0.079 0.104 0.000 0.000 0.213 7.113

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C F(-1) F F(-2) F F F F(-1)

verified

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

size

103 103 93 0 0 0 0 0 149 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 1.45 0.00

time (sec)

N/A 0.590 10.221 0.000 0.000 0.000 0.000 0.000 0.159 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

28 28 28 0 0 61 0 228 246 95

N.S.

1 1.00 1.00 0.00 0.00 2.18 0.00 8.14 8.79 3.39

time (sec)

N/A 0.444 0.342 0.000 0.000 0.083 0.000 0.186 0.162 6.481

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

45 45 46 138 77 119 0 237 73 124

N.S.

1 1.00 1.02 3.07 1.71 2.64 0.00 5.27 1.62 2.76

time (sec)

N/A 0.528 1.409 0.206 0.148 0.089 0.000 0.184 0.195 6.565

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

31 31 31 52 59 54 0 111 51 76

N.S.

1 1.00 1.00 1.68 1.90 1.74 0.00 3.58 1.65 2.45

time (sec)

N/A 0.594 0.736 0.038 0.130 0.109 0.000 0.214 0.206 6.480

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

45 45 41 103 92 88 0 155 62 106

N.S.

1 1.00 0.91 2.29 2.04 1.96 0.00 3.44 1.38 2.36

time (sec)

N/A 1.044 2.203 0.227 0.154 0.121 0.000 0.298 0.163 6.861

[front] [up]