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Integrals 1 to 33

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 B B F A F F(-1)

verified

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

size

225 244 149 252 755 430 0 163 302 0

N.S.

1 1.08 0.66 1.12 3.36 1.91 0.00 0.72 1.34 0.00

time (sec)

N/A 0.832 0.202 0.201 0.348 0.110 0.000 0.125 0.161 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

111 118 130 124 611 343 0 121 33 0

N.S.

1 1.06 1.17 1.12 5.50 3.09 0.00 1.09 0.30 0.00

time (sec)

N/A 0.376 0.118 0.162 0.296 0.113 0.000 0.119 0.159 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

91 91 105 83 464 111 0 79 13 0

N.S.

1 1.00 1.15 0.91 5.10 1.22 0.00 0.87 0.14 0.00

time (sec)

N/A 0.329 0.057 0.131 0.253 0.099 0.000 0.124 0.164 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

15 15 17 15 17 17 14 17 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.93 1.13 1.13 1.13

time (sec)

N/A 0.198 5.165 0.044 0.663 0.080 0.667 0.126 0.159 1.331

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

107 107 132 0 0 331 0 0 38 0

N.S.

1 1.00 1.23 0.00 0.00 3.09 0.00 0.00 0.36 0.00

time (sec)

N/A 0.296 0.386 0.000 0.000 0.099 0.000 0.000 0.167 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

227 246 152 244 834 467 0 167 247 0

N.S.

1 1.08 0.67 1.07 3.67 2.06 0.00 0.74 1.09 0.00

time (sec)

N/A 0.942 0.207 0.202 0.387 0.086 0.000 0.128 0.160 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

112 119 134 120 674 385 0 123 36 0

N.S.

1 1.06 1.20 1.07 6.02 3.44 0.00 1.10 0.32 0.00

time (sec)

N/A 0.418 0.122 0.164 0.312 0.087 0.000 0.123 0.160 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

91 91 109 79 512 115 0 81 14 0

N.S.

1 1.00 1.20 0.87 5.63 1.26 0.00 0.89 0.15 0.00

time (sec)

N/A 0.342 0.049 0.126 0.259 0.090 0.000 0.126 0.155 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

16 16 18 16 22 21 14 18 18 18

N.S.

1 1.00 1.12 1.00 1.38 1.31 0.88 1.12 1.12 1.12

time (sec)

N/A 0.198 6.052 0.049 0.715 0.075 0.668 0.125 0.159 1.337

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

108 108 136 0 0 371 0 0 40 0

N.S.

1 1.00 1.26 0.00 0.00 3.44 0.00 0.00 0.37 0.00

time (sec)

N/A 0.320 0.437 0.000 0.000 0.090 0.000 0.000 0.162 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

66 119 72 75 183 127 0 53 89 0

N.S.

1 1.80 1.09 1.14 2.77 1.92 0.00 0.80 1.35 0.00

time (sec)

N/A 0.689 0.102 0.216 0.151 0.096 0.000 0.128 0.163 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

52 57 75 49 123 108 0 43 21 0

N.S.

1 1.10 1.44 0.94 2.37 2.08 0.00 0.83 0.40 0.00

time (sec)

N/A 0.304 0.049 0.161 0.178 0.099 0.000 0.125 0.161 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

39 39 24 25 94 16 0 21 9 0

N.S.

1 1.00 0.62 0.64 2.41 0.41 0.00 0.54 0.23 0.00

time (sec)

N/A 0.238 0.018 0.110 0.131 0.079 0.000 0.126 0.160 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

13 13 15 11 13 13 12 13 13 13

N.S.

1 1.00 1.15 0.85 1.00 1.00 0.92 1.00 1.00 1.00

time (sec)

N/A 0.190 5.841 0.059 0.568 0.085 0.637 0.122 0.162 1.345

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

13 13 15 11 13 13 14 13 13 13

N.S.

1 1.00 1.15 0.85 1.00 1.00 1.08 1.00 1.00 1.00

time (sec)

N/A 0.435 7.464 0.057 0.383 0.095 0.453 0.119 0.189 1.336

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

268 268 176 281 294 766 0 182 372 0

N.S.

1 1.00 0.66 1.05 1.10 2.86 0.00 0.68 1.39 0.00

time (sec)

N/A 0.485 0.507 0.561 0.180 0.111 0.000 0.140 0.174 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

136 136 155 141 200 648 0 142 219 0

N.S.

1 1.00 1.14 1.04 1.47 4.76 0.00 1.04 1.61 0.00

time (sec)

N/A 0.304 0.261 0.487 0.169 0.105 0.000 0.134 0.173 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

110 110 140 94 96 128 0 94 15 0

N.S.

1 1.00 1.27 0.85 0.87 1.16 0.00 0.85 0.14 0.00

time (sec)

N/A 0.261 0.093 0.441 0.118 0.087 0.000 0.126 0.188 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

17 17 19 17 51 19 15 19 65 19

N.S.

1 1.00 1.12 1.00 3.00 1.12 0.88 1.12 3.82 1.12

time (sec)

N/A 0.218 11.569 0.106 0.258 0.079 0.844 0.139 0.164 1.357

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

268 268 181 273 322 843 0 186 310 0

N.S.

1 1.00 0.68 1.02 1.20 3.15 0.00 0.69 1.16 0.00

time (sec)

N/A 0.479 0.493 0.539 0.192 0.132 0.000 0.135 0.164 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

136 136 159 137 216 730 0 144 176 0

N.S.

1 1.00 1.17 1.01 1.59 5.37 0.00 1.06 1.29 0.00

time (sec)

N/A 0.299 0.267 0.490 0.166 0.085 0.000 0.127 0.165 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

110 110 144 90 96 132 0 96 16 0

N.S.

1 1.00 1.31 0.82 0.87 1.20 0.00 0.87 0.15 0.00

time (sec)

N/A 0.260 0.102 0.439 0.130 0.087 0.000 0.128 0.168 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

18 18 20 18 51 22 15 20 69 20

N.S.

1 1.00 1.11 1.00 2.83 1.22 0.83 1.11 3.83 1.11

time (sec)

N/A 0.219 13.012 0.108 0.244 0.096 0.870 0.135 0.163 1.345

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

68 68 99 77 113 268 0 61 105 0

N.S.

1 1.00 1.46 1.13 1.66 3.94 0.00 0.90 1.54 0.00

time (sec)

N/A 0.292 0.144 0.615 0.158 0.118 0.000 0.119 0.161 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

75 75 88 75 121 307 0 70 123 0

N.S.

1 1.00 1.17 1.00 1.61 4.09 0.00 0.93 1.64 0.00

time (sec)

N/A 0.258 0.146 0.539 0.178 0.095 0.000 0.134 0.168 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

56 56 48 49 45 41 0 42 11 0

N.S.

1 1.00 0.86 0.88 0.80 0.73 0.00 0.75 0.20 0.00

time (sec)

N/A 0.234 0.051 0.477 0.117 0.082 0.000 0.129 0.163 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

15 15 17 13 43 15 14 15 54 15

N.S.

1 1.00 1.13 0.87 2.87 1.00 0.93 1.00 3.60 1.00

time (sec)

N/A 0.215 12.817 0.153 0.217 0.090 0.719 0.128 0.165 1.342

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

261 269 194 460 536 634 0 227 554 0

N.S.

1 1.03 0.74 1.76 2.05 2.43 0.00 0.87 2.12 0.00

time (sec)

N/A 0.901 0.375 0.284 0.258 0.108 0.000 0.123 0.187 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

128 127 146 200 254 413 0 139 53 0

N.S.

1 0.99 1.14 1.56 1.98 3.23 0.00 1.09 0.41 0.00

time (sec)

N/A 0.398 0.171 0.210 0.151 0.091 0.000 0.125 0.190 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

19 19 21 19 21 21 17 21 21 21

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.89 1.11 1.11 1.11

time (sec)

N/A 0.187 2.854 0.060 0.618 0.077 0.583 0.126 0.178 1.328

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

311 311 240 528 601 1142 0 263 732 0

N.S.

1 1.00 0.77 1.70 1.93 3.67 0.00 0.85 2.35 0.00

time (sec)

N/A 0.616 0.886 0.878 0.323 0.102 0.000 0.136 0.207 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

160 160 177 231 299 777 0 165 352 0

N.S.

1 1.00 1.11 1.44 1.87 4.86 0.00 1.03 2.20 0.00

time (sec)

N/A 0.354 0.445 0.673 0.268 0.111 0.000 0.128 0.197 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

21 21 23 21 72 23 19 23 23 23

N.S.

1 1.00 1.10 1.00 3.43 1.10 0.90 1.10 1.10 1.10

time (sec)

N/A 0.234 5.979 0.104 0.257 0.096 4.959 0.154 0.190 1.382

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