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Integrals 1 to 86

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 B B B

verified

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

size

42 34 37 37 35 51 60 127 215 230

N.S.

1 0.81 0.88 0.88 0.83 1.21 1.43 3.02 5.12 5.48

time (sec)

N/A 0.272 0.012 0.559 0.039 0.117 0.642 0.172 0.240 0.989

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

45 36 40 149 38 56 0 60 56 58

N.S.

1 0.80 0.89 3.31 0.84 1.24 0.00 1.33 1.24 1.29

time (sec)

N/A 0.282 0.023 11.860 0.024 0.123 0.000 0.133 0.206 1.682

Problem 3

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

40 40 42 36 39 38 34 38 39 39

N.S.

1 1.00 1.05 0.90 0.98 0.95 0.85 0.95 0.98 0.98

time (sec)

N/A 0.247 0.130 0.549 0.816 0.145 4.228 0.245 0.630 1.212

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

488 486 0 1640 0 0 0 0 150 0

N.S.

1 1.00 0.00 3.36 0.00 0.00 0.00 0.00 0.31 0.00

time (sec)

N/A 1.119 0.000 0.789 0.000 0.000 0.000 0.000 0.220 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

321 323 0 903 0 0 0 0 108 0

N.S.

1 1.01 0.00 2.81 0.00 0.00 0.00 0.00 0.34 0.00

time (sec)

N/A 0.789 0.000 0.443 0.000 0.000 0.000 0.000 0.217 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

98 93 93 363 0 0 0 0 64 0

N.S.

1 0.95 0.95 3.70 0.00 0.00 0.00 0.00 0.65 0.00

time (sec)

N/A 0.333 0.028 0.278 0.000 0.000 0.000 0.000 0.202 0.000

Problem 7

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

40 40 42 36 39 48 61 38 63 39

N.S.

1 1.00 1.05 0.90 0.98 1.20 1.52 0.95 1.58 0.98

time (sec)

N/A 0.244 0.193 0.348 0.326 0.095 3.139 0.213 0.243 0.945

Problem 8

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

40 40 42 36 163 91 126 38 123 39

N.S.

1 1.00 1.05 0.90 4.08 2.28 3.15 0.95 3.08 0.98

time (sec)

N/A 0.240 0.883 0.369 0.404 0.089 6.808 0.324 0.238 1.768

Problem 9

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 Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 18 20 17 15 48 30 21 21

N.S.

1 1.00 1.12 1.25 1.06 0.94 3.00 1.88 1.31 1.31

time (sec)

N/A 0.163 0.007 0.278 0.031 0.100 0.073 0.125 0.197 0.118

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

403 519 371 8038 0 1965 0 0 17 0

N.S.

1 1.29 0.92 19.95 0.00 4.88 0.00 0.00 0.04 0.00

time (sec)

N/A 1.551 2.260 42.097 0.000 0.193 0.000 0.000 0.205 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

305 396 281 7646 0 1545 0 0 15 0

N.S.

1 1.30 0.92 25.07 0.00 5.07 0.00 0.00 0.05 0.00

time (sec)

N/A 1.097 2.074 5.346 0.000 0.175 0.000 0.000 0.250 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

198 277 549 1138 433 1101 0 0 13 0

N.S.

1 1.40 2.77 5.75 2.19 5.56 0.00 0.00 0.07 0.00

time (sec)

N/A 0.677 0.526 4.681 0.203 0.150 0.000 0.000 0.202 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A F(-1) 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 0 17 14 17 17 17

N.S.

1 1.00 1.13 1.00 0.00 1.13 0.93 1.13 1.13 1.13

time (sec)

N/A 0.298 0.299 0.325 0.000 0.091 54.617 0.912 0.194 0.893

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

154 198 136 1448 310 321 0 0 24 0

N.S.

1 1.29 0.88 9.40 2.01 2.08 0.00 0.00 0.16 0.00

time (sec)

N/A 0.804 0.170 3.227 0.094 0.130 0.000 0.000 0.227 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

123 155 110 1413 218 270 0 0 22 0

N.S.

1 1.26 0.89 11.49 1.77 2.20 0.00 0.00 0.18 0.00

time (sec)

N/A 0.635 0.077 2.254 0.054 0.106 0.000 0.000 0.223 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

85 107 967 562 455 199 0 0 20 0

N.S.

1 1.26 11.38 6.61 5.35 2.34 0.00 0.00 0.24 0.00

time (sec)

N/A 0.435 3.676 2.144 0.154 0.119 0.000 0.000 0.206 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A F(-2) N/A F(-1) 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 19 0 36 0 21 24 22

N.S.

1 1.00 1.10 0.90 0.00 1.71 0.00 1.00 1.14 1.05

time (sec)

N/A 0.267 0.256 0.396 0.000 0.101 0.000 0.778 0.186 1.108

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

155 199 141 1449 312 321 0 0 26 0

N.S.

1 1.28 0.91 9.35 2.01 2.07 0.00 0.00 0.17 0.00

time (sec)

N/A 0.846 0.172 3.470 0.077 0.110 0.000 0.000 0.241 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

124 156 111 1414 220 270 0 0 24 0

N.S.

1 1.26 0.90 11.40 1.77 2.18 0.00 0.00 0.19 0.00

time (sec)

N/A 0.625 0.068 2.782 0.054 0.122 0.000 0.000 0.216 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

86 108 847 595 450 201 0 0 22 0

N.S.

1 1.26 9.85 6.92 5.23 2.34 0.00 0.00 0.26 0.00

time (sec)

N/A 0.434 2.004 2.436 0.137 0.101 0.000 0.000 0.201 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 24 20 0 36 0 22 26 22

N.S.

1 1.00 1.09 0.91 0.00 1.64 0.00 1.00 1.18 1.00

time (sec)

N/A 0.339 0.621 0.546 0.000 0.104 0.000 0.830 0.198 1.196

Problem 22

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

16 16 18 17 10 10 19 10 14 16

N.S.

1 1.00 1.12 1.06 0.62 0.62 1.19 0.62 0.88 1.00

time (sec)

N/A 0.161 0.006 0.417 0.028 0.051 0.063 0.118 0.230 0.104

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

399 515 360 7868 0 1589 0 0 17 0

N.S.

1 1.29 0.90 19.72 0.00 3.98 0.00 0.00 0.04 0.00

time (sec)

N/A 1.520 2.144 46.439 0.000 0.277 0.000 0.000 0.206 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

303 394 275 7482 0 1289 0 0 15 0

N.S.

1 1.30 0.91 24.69 0.00 4.25 0.00 0.00 0.05 0.00

time (sec)

N/A 1.099 1.732 5.579 0.000 0.255 0.000 0.000 0.203 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

198 277 701 1146 532 965 0 0 13 0

N.S.

1 1.40 3.54 5.79 2.69 4.87 0.00 0.00 0.07 0.00

time (sec)

N/A 0.678 4.185 5.121 0.205 0.283 0.000 0.000 0.197 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A F(-1) N/A F(-1) 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 0 17 0 17 17 17

N.S.

1 1.00 1.13 1.00 0.00 1.13 0.00 1.13 1.13 1.13

time (sec)

N/A 0.285 0.287 0.363 0.000 0.091 0.000 2.493 0.237 0.938

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

154 198 140 1448 0 174 0 0 37 0

N.S.

1 1.29 0.91 9.40 0.00 1.13 0.00 0.00 0.24 0.00

time (sec)

N/A 0.782 0.148 4.378 0.000 0.096 0.000 0.000 0.247 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

123 155 110 1413 0 152 0 0 35 0

N.S.

1 1.26 0.89 11.49 0.00 1.24 0.00 0.00 0.28 0.00

time (sec)

N/A 0.627 0.078 3.231 0.000 0.098 0.000 0.000 0.251 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

85 107 929 587 0 116 0 0 30 0

N.S.

1 1.26 10.93 6.91 0.00 1.36 0.00 0.00 0.35 0.00

time (sec)

N/A 0.459 3.834 1.181 0.000 0.111 0.000 0.000 0.228 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A F(-2) N/A F(-1) 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 26 0 42 0 28 35 25

N.S.

1 1.00 1.10 1.24 0.00 2.00 0.00 1.33 1.67 1.19

time (sec)

N/A 0.274 0.301 0.201 0.000 0.099 0.000 1.832 0.214 1.515

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

155 199 136 1449 0 174 0 0 35 0

N.S.

1 1.28 0.88 9.35 0.00 1.12 0.00 0.00 0.23 0.00

time (sec)

N/A 0.823 0.165 4.198 0.000 0.102 0.000 0.000 0.243 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

124 156 110 1414 0 152 0 0 33 0

N.S.

1 1.26 0.89 11.40 0.00 1.23 0.00 0.00 0.27 0.00

time (sec)

N/A 0.637 0.084 2.876 0.000 0.107 0.000 0.000 0.251 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

86 108 872 630 0 116 0 0 28 0

N.S.

1 1.26 10.14 7.33 0.00 1.35 0.00 0.00 0.33 0.00

time (sec)

N/A 0.447 2.040 1.127 0.000 0.097 0.000 0.000 0.272 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 24 25 0 42 0 27 33 25

N.S.

1 1.00 1.09 1.14 0.00 1.91 0.00 1.23 1.50 1.14

time (sec)

N/A 0.297 0.292 0.192 0.000 0.086 0.000 2.201 0.232 1.507

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

299 327 600 3570 0 1460 0 0 67 0

N.S.

1 1.09 2.01 11.94 0.00 4.88 0.00 0.00 0.22 0.00

time (sec)

N/A 1.140 0.209 23.627 0.000 0.245 0.000 0.000 0.207 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

229 251 375 2668 0 1002 0 0 46 0

N.S.

1 1.10 1.64 11.65 0.00 4.38 0.00 0.00 0.20 0.00

time (sec)

N/A 0.844 0.120 15.365 0.000 0.181 0.000 0.000 0.199 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

159 175 237 1776 0 600 0 0 25 0

N.S.

1 1.10 1.49 11.17 0.00 3.77 0.00 0.00 0.16 0.00

time (sec)

N/A 0.665 0.085 2.405 0.000 0.150 0.000 0.000 0.226 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

73 79 91 106 0 334 0 0 9 0

N.S.

1 1.08 1.25 1.45 0.00 4.58 0.00 0.00 0.12 0.00

time (sec)

N/A 0.346 0.019 1.320 0.000 0.139 0.000 0.000 0.186 0.000

Problem 39

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 3 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.93 0.20 1.13 1.13

time (sec)

N/A 0.231 0.953 0.374 1.556 0.143 3.399 73.833 0.196 0.803

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

355 441 438 6916 0 1289 0 0 17 0

N.S.

1 1.24 1.23 19.48 0.00 3.63 0.00 0.00 0.05 0.00

time (sec)

N/A 1.423 0.319 40.817 0.000 0.214 0.000 0.000 0.193 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

267 343 330 6566 0 1067 0 0 15 0

N.S.

1 1.28 1.24 24.59 0.00 4.00 0.00 0.00 0.06 0.00

time (sec)

N/A 1.050 0.693 5.811 0.000 0.197 0.000 0.000 0.208 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

174 237 288 352 0 825 0 0 13 0

N.S.

1 1.36 1.66 2.02 0.00 4.74 0.00 0.00 0.07 0.00

time (sec)

N/A 0.646 0.268 2.272 0.000 0.243 0.000 0.000 0.223 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A F(-1) 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 0 17 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.00 1.13 1.13 1.13

time (sec)

N/A 0.287 3.480 0.203 1.373 0.099 0.000 0.405 0.199 0.888

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

142 167 134 1405 129 292 0 0 25 0

N.S.

1 1.18 0.94 9.89 0.91 2.06 0.00 0.00 0.18 0.00

time (sec)

N/A 0.822 0.137 1.925 1.446 0.112 0.000 0.000 0.206 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

113 132 103 1369 107 246 0 0 23 0

N.S.

1 1.17 0.91 12.12 0.95 2.18 0.00 0.00 0.20 0.00

time (sec)

N/A 0.635 0.054 1.128 1.430 0.119 0.000 0.000 0.224 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

79 93 71 544 80 186 0 0 21 0

N.S.

1 1.18 0.90 6.89 1.01 2.35 0.00 0.00 0.27 0.00

time (sec)

N/A 0.437 0.088 1.174 1.443 0.135 0.000 0.000 0.189 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A F(-1) 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 17 81 36 0 19 25 20

N.S.

1 1.00 1.11 0.89 4.26 1.89 0.00 1.00 1.32 1.05

time (sec)

N/A 0.293 2.802 0.298 0.775 0.094 0.000 0.187 0.207 0.994

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

145 170 134 1409 129 292 0 0 26 0

N.S.

1 1.17 0.92 9.72 0.89 2.01 0.00 0.00 0.18 0.00

time (sec)

N/A 0.778 0.140 2.158 1.591 0.151 0.000 0.000 0.197 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

116 136 103 1373 106 246 0 0 24 0

N.S.

1 1.17 0.89 11.84 0.91 2.12 0.00 0.00 0.21 0.00

time (sec)

N/A 0.617 0.074 1.377 1.401 0.142 0.000 0.000 0.236 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

82 95 71 517 80 186 0 0 22 0

N.S.

1 1.16 0.87 6.30 0.98 2.27 0.00 0.00 0.27 0.00

time (sec)

N/A 0.428 0.080 1.430 1.398 0.115 0.000 0.000 0.206 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 24 20 73 36 0 19 26 20

N.S.

1 1.00 1.09 0.91 3.32 1.64 0.00 0.86 1.18 0.91

time (sec)

N/A 0.296 2.800 0.450 0.547 0.113 0.000 0.183 0.192 1.027

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

299 327 600 3570 0 1460 0 0 67 0

N.S.

1 1.09 2.01 11.94 0.00 4.88 0.00 0.00 0.22 0.00

time (sec)

N/A 1.156 0.202 13.898 0.000 0.206 0.000 0.000 0.209 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

229 251 375 2668 0 1002 0 0 46 0

N.S.

1 1.10 1.64 11.65 0.00 4.38 0.00 0.00 0.20 0.00

time (sec)

N/A 0.844 0.128 8.696 0.000 0.188 0.000 0.000 0.226 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

159 175 237 1776 0 600 0 0 25 0

N.S.

1 1.10 1.49 11.17 0.00 3.77 0.00 0.00 0.16 0.00

time (sec)

N/A 0.599 0.087 1.414 0.000 0.157 0.000 0.000 0.211 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

74 80 91 105 0 334 0 0 9 0

N.S.

1 1.08 1.23 1.42 0.00 4.51 0.00 0.00 0.12 0.00

time (sec)

N/A 0.344 0.022 0.752 0.000 0.161 0.000 0.000 0.185 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A F(-1) 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 0 3 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.00 0.20 1.13 1.13

time (sec)

N/A 0.212 0.611 0.223 1.684 0.099 0.000 88.496 0.194 0.830

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

351 437 442 6844 0 1269 0 0 17 0

N.S.

1 1.25 1.26 19.50 0.00 3.62 0.00 0.00 0.05 0.00

time (sec)

N/A 1.419 0.318 23.303 0.000 0.205 0.000 0.000 0.216 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

265 339 334 6494 0 1051 0 0 15 0

N.S.

1 1.28 1.26 24.51 0.00 3.97 0.00 0.00 0.06 0.00

time (sec)

N/A 1.053 0.835 3.809 0.000 0.204 0.000 0.000 0.206 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

174 237 287 352 0 813 0 0 13 0

N.S.

1 1.36 1.65 2.02 0.00 4.67 0.00 0.00 0.07 0.00

time (sec)

N/A 0.666 0.274 2.541 0.000 0.243 0.000 0.000 0.189 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A F(-1) 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 0 17 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.00 1.13 1.13 1.13

time (sec)

N/A 0.285 3.379 0.213 1.070 0.100 0.000 0.375 0.193 0.859

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

142 167 134 1404 129 292 0 0 25 0

N.S.

1 1.18 0.94 9.89 0.91 2.06 0.00 0.00 0.18 0.00

time (sec)

N/A 0.805 0.143 2.028 1.462 0.111 0.000 0.000 0.228 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

113 133 103 1368 107 246 0 0 23 0

N.S.

1 1.18 0.91 12.11 0.95 2.18 0.00 0.00 0.20 0.00

time (sec)

N/A 0.620 0.068 1.202 1.440 0.102 0.000 0.000 0.204 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

79 93 71 544 80 186 0 0 21 0

N.S.

1 1.18 0.90 6.89 1.01 2.35 0.00 0.00 0.27 0.00

time (sec)

N/A 0.424 0.096 1.445 1.448 0.103 0.000 0.000 0.193 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A F(-1) 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 17 73 36 0 19 25 20

N.S.

1 1.00 1.11 0.89 3.84 1.89 0.00 1.00 1.32 1.05

time (sec)

N/A 0.278 2.734 0.358 0.549 0.087 0.000 0.175 0.187 1.023

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

145 170 134 1410 129 292 0 0 26 0

N.S.

1 1.17 0.92 9.72 0.89 2.01 0.00 0.00 0.18 0.00

time (sec)

N/A 0.794 0.139 2.308 1.405 0.098 0.000 0.000 0.223 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

116 135 103 1374 106 246 0 0 24 0

N.S.

1 1.16 0.89 11.84 0.91 2.12 0.00 0.00 0.21 0.00

time (sec)

N/A 0.624 0.075 1.500 1.516 0.101 0.000 0.000 0.199 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

82 95 71 517 80 186 0 0 22 0

N.S.

1 1.16 0.87 6.30 0.98 2.27 0.00 0.00 0.27 0.00

time (sec)

N/A 0.427 0.089 1.472 1.453 0.094 0.000 0.000 0.192 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 24 20 81 36 0 19 26 20

N.S.

1 1.00 1.09 0.91 3.68 1.64 0.00 0.86 1.18 0.91

time (sec)

N/A 0.288 2.685 0.440 0.540 0.087 0.000 0.166 0.194 0.988

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

187 187 132 566 0 250 0 0 64 0

N.S.

1 1.00 0.71 3.03 0.00 1.34 0.00 0.00 0.34 0.00

time (sec)

N/A 0.842 0.221 196.373 0.000 0.123 0.000 0.000 0.223 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

35 35 59 53 34 40 0 0 6 0

N.S.

1 1.00 1.69 1.51 0.97 1.14 0.00 0.00 0.17 0.00

time (sec)

N/A 0.230 0.014 0.268 0.151 0.103 0.000 0.000 0.190 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

71 63 58 50 0 65 0 0 8 0

N.S.

1 0.89 0.82 0.70 0.00 0.92 0.00 0.00 0.11 0.00

time (sec)

N/A 0.347 0.009 0.371 0.000 0.103 0.000 0.000 0.191 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 105 92 76 0 87 0 0 10 0

N.S.

1 1.02 0.89 0.74 0.00 0.84 0.00 0.00 0.10 0.00

time (sec)

N/A 0.474 0.012 0.512 0.000 0.104 0.000 0.000 0.210 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

51 49 83 95 63 103 0 0 10 0

N.S.

1 0.96 1.63 1.86 1.24 2.02 0.00 0.00 0.20 0.00

time (sec)

N/A 0.239 0.035 0.232 0.172 0.106 0.000 0.000 0.265 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 97 83 355 0 151 0 0 12 0

N.S.

1 0.94 0.81 3.45 0.00 1.47 0.00 0.00 0.12 0.00

time (sec)

N/A 0.401 0.012 0.341 0.000 0.115 0.000 0.000 0.256 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

151 159 133 413 0 187 0 0 14 0

N.S.

1 1.05 0.88 2.74 0.00 1.24 0.00 0.00 0.09 0.00

time (sec)

N/A 0.582 0.016 0.407 0.000 0.108 0.000 0.000 0.278 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

196 177 167 162 189 212 0 0 14 0

N.S.

1 0.90 0.85 0.83 0.96 1.08 0.00 0.00 0.07 0.00

time (sec)

N/A 0.527 0.111 0.821 0.250 0.113 0.000 0.000 0.270 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

250 484 250 678 0 304 0 0 16 0

N.S.

1 1.94 1.00 2.71 0.00 1.22 0.00 0.00 0.06 0.00

time (sec)

N/A 4.222 0.267 0.817 0.000 0.128 0.000 0.000 0.269 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

313 621 313 764 0 378 0 0 18 0

N.S.

1 1.98 1.00 2.44 0.00 1.21 0.00 0.00 0.06 0.00

time (sec)

N/A 3.955 0.192 1.238 0.000 0.138 0.000 0.000 0.272 0.000

Problem 79

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

27 33 27 25 19 28 19 21 32 22

N.S.

1 1.22 1.00 0.93 0.70 1.04 0.70 0.78 1.19 0.81

time (sec)

N/A 0.219 0.014 0.095 0.037 0.102 1.052 0.130 0.263 0.115

Problem 80

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

17 17 17 14 17 15 12 18 15 15

N.S.

1 1.00 1.00 0.82 1.00 0.88 0.71 1.06 0.88 0.88

time (sec)

N/A 0.209 0.097 0.148 0.037 0.103 0.223 0.125 0.263 0.147

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

47 44 61 1281 47 131 0 65 63 65

N.S.

1 0.94 1.30 27.26 1.00 2.79 0.00 1.38 1.34 1.38

time (sec)

N/A 0.326 0.056 1.241 0.132 0.109 0.000 0.133 0.283 0.914

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 104 146 1354 131 276 0 155 173 133

N.S.

1 1.01 1.42 13.15 1.27 2.68 0.00 1.50 1.68 1.29

time (sec)

N/A 0.490 0.077 6.309 0.137 0.108 0.000 0.135 0.412 0.375

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

135 175 89 1323 167 210 0 239 169 164

N.S.

1 1.30 0.66 9.80 1.24 1.56 0.00 1.77 1.25 1.21

time (sec)

N/A 0.511 0.057 1.629 0.122 0.113 0.000 0.136 0.283 2.964

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

134 175 89 1323 167 210 0 236 169 164

N.S.

1 1.31 0.66 9.87 1.25 1.57 0.00 1.76 1.26 1.22

time (sec)

N/A 0.493 0.059 1.468 0.131 0.122 0.000 0.141 0.266 2.733

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 104 145 855 169 221 0 155 178 135

N.S.

1 1.01 1.41 8.30 1.64 2.15 0.00 1.50 1.73 1.31

time (sec)

N/A 0.477 0.075 6.106 0.162 0.115 0.000 0.120 0.377 1.113

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

48 46 59 903 48 75 0 66 65 68

N.S.

1 0.96 1.23 18.81 1.00 1.56 0.00 1.38 1.35 1.42

time (sec)

N/A 0.324 0.050 1.244 0.139 0.114 0.000 0.134 0.318 0.877

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