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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 C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 52 67 45 61 51 49 245 41

N.S.

1 1.02 1.31 0.88 1.20 1.00 0.96 4.80 0.80

time (sec)

N/A 0.216 0.009 0.160 0.212 0.244 0.333 0.268 4.487

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 52 50 47 46 55 54 255 43

N.S.

1 1.04 1.00 0.94 0.92 1.10 1.08 5.10 0.86

time (sec)

N/A 0.234 0.008 0.099 0.185 0.252 0.301 0.277 4.323

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 42 57 37 52 43 41 195 33

N.S.

1 1.02 1.39 0.90 1.27 1.05 1.00 4.76 0.80

time (sec)

N/A 0.223 0.011 0.077 0.188 0.260 0.266 0.268 4.532

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 42 40 38 35 44 46 206 35

N.S.

1 1.05 1.00 0.95 0.88 1.10 1.15 5.15 0.88

time (sec)

N/A 0.217 0.008 0.060 0.209 0.248 0.231 0.276 4.403

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 32 47 27 41 34 32 144 26

N.S.

1 1.03 1.52 0.87 1.32 1.10 1.03 4.65 0.84

time (sec)

N/A 0.190 0.008 0.059 0.180 0.246 0.196 0.265 4.125

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 23 25 33 27 153 22

N.S.

1 1.00 1.00 0.92 1.00 1.32 1.08 6.12 0.88

time (sec)

N/A 0.173 0.002 0.070 0.208 0.241 0.113 0.254 4.099

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 26 28 86 0 0 0 0

N.S.

1 1.00 0.93 1.00 3.07 0.00 0.00 0.00 0.00

time (sec)

N/A 0.183 0.008 0.073 0.195 0.000 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 33 30 35 30 39 26 143 27

N.S.

1 1.10 1.00 1.17 1.00 1.30 0.87 4.77 0.90

time (sec)

N/A 0.192 0.008 0.064 0.229 0.254 0.128 0.285 4.169

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 29 47 26 36 35 24 140 40

N.S.

1 0.94 1.52 0.84 1.16 1.13 0.77 4.52 1.29

time (sec)

N/A 0.190 0.008 0.071 0.180 0.259 0.194 0.267 4.194

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 47 48 40 50 46 209 39

N.S.

1 1.00 1.00 1.02 0.85 1.06 0.98 4.45 0.83

time (sec)

N/A 0.222 0.010 0.085 0.188 0.256 0.227 0.266 4.610

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 57 36 51 43 32 205 60

N.S.

1 1.00 1.39 0.88 1.24 1.05 0.78 5.00 1.46

time (sec)

N/A 0.209 0.008 0.095 0.188 0.248 0.257 0.278 4.635

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 177 80 92 135 98 114 534 85

N.S.

1 1.69 0.76 0.88 1.29 0.93 1.09 5.09 0.81

time (sec)

N/A 1.250 0.018 0.300 0.188 0.257 0.400 0.280 4.627

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 172 87 164 155 0 0 0 0

N.S.

1 1.35 0.69 1.29 1.22 0.00 0.00 0.00 0.00

time (sec)

N/A 1.131 0.331 0.473 0.191 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 115 62 72 118 81 90 335 65

N.S.

1 1.42 0.77 0.89 1.46 1.00 1.11 4.14 0.80

time (sec)

N/A 0.813 0.014 0.201 0.204 0.260 0.324 0.273 4.240

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 120 66 144 134 0 0 0 0

N.S.

1 1.17 0.64 1.40 1.30 0.00 0.00 0.00 0.00

time (sec)

N/A 0.732 0.179 0.486 0.193 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 61 43 49 97 62 60 154 44

N.S.

1 1.13 0.80 0.91 1.80 1.15 1.11 2.85 0.81

time (sec)

N/A 0.457 0.010 0.166 0.196 0.253 0.234 0.276 4.359

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 71 46 116 135 0 0 0 0

N.S.

1 1.22 0.79 2.00 2.33 0.00 0.00 0.00 0.00

time (sec)

N/A 0.435 0.063 0.500 0.212 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

97 128 114 459 0 0 0 0 0

N.S.

1 1.32 1.18 4.73 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.707 0.051 3.368 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 60 49 145 146 0 0 0 0

N.S.

1 1.09 0.89 2.64 2.65 0.00 0.00 0.00 0.00

time (sec)

N/A 0.424 0.081 0.082 0.209 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 60 57 72 96 79 56 137 145

N.S.

1 0.98 0.93 1.18 1.57 1.30 0.92 2.25 2.38

time (sec)

N/A 0.466 0.014 0.090 0.190 0.245 0.210 0.266 4.376

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 97 87 184 176 0 0 0 0

N.S.

1 0.94 0.84 1.79 1.71 0.00 0.00 0.00 0.00

time (sec)

N/A 0.692 0.166 0.117 0.200 0.000 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 114 82 101 154 97 90 319 196

N.S.

1 1.27 0.91 1.12 1.71 1.08 1.00 3.54 2.18

time (sec)

N/A 0.796 0.018 0.109 0.243 0.286 0.261 0.275 5.550

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

186 421 117 2133 289 0 0 0 0

N.S.

1 2.26 0.63 11.47 1.55 0.00 0.00 0.00 0.00

time (sec)

N/A 2.904 0.392 5.819 0.244 0.000 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

196 304 178 737 0 0 0 0 0

N.S.

1 1.55 0.91 3.76 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.571 0.506 5.114 0.000 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

139 239 88 871 262 0 0 0 0

N.S.

1 1.72 0.63 6.27 1.88 0.00 0.00 0.00 0.00

time (sec)

N/A 1.748 0.234 4.399 0.203 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

149 177 143 681 0 0 0 0 0

N.S.

1 1.19 0.96 4.57 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.489 0.308 3.880 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

95 109 68 2910 215 0 0 0 0

N.S.

1 1.15 0.72 30.63 2.26 0.00 0.00 0.00 0.00

time (sec)

N/A 0.801 0.110 3.285 0.197 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 101 79 168 0 0 0 0 0

N.S.

1 1.19 0.93 1.98 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.636 0.087 0.399 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

150 182 156 536 0 0 0 0 0

N.S.

1 1.21 1.04 3.57 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.984 0.061 3.673 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

79 93 72 718 0 0 0 0 0

N.S.

1 1.18 0.91 9.09 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.662 0.101 4.614 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

95 90 79 3498 252 0 0 0 0

N.S.

1 0.95 0.83 36.82 2.65 0.00 0.00 0.00 0.00

time (sec)

N/A 0.792 0.125 3.316 0.223 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

154 158 142 840 0 0 0 0 0

N.S.

1 1.03 0.92 5.45 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.514 0.163 6.865 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

141 191 118 657 342 0 0 0 0

N.S.

1 1.35 0.84 4.66 2.43 0.00 0.00 0.00 0.00

time (sec)

N/A 1.442 0.169 4.726 0.217 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

164 164 864 869 0 0 0 0 0

N.S.

1 1.00 5.27 5.30 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.296 5.734 8.678 0.000 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 247 213 245 276 247 427 1473 296

N.S.

1 1.01 0.87 1.00 1.13 1.01 1.74 6.01 1.21

time (sec)

N/A 0.676 0.067 0.606 0.205 0.247 0.640 0.310 4.789

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 171 150 167 198 177 282 932 190

N.S.

1 1.01 0.89 0.99 1.17 1.05 1.67 5.51 1.12

time (sec)

N/A 0.567 0.043 0.482 0.196 0.249 0.468 0.306 4.570

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 112 98 105 131 118 182 529 115

N.S.

1 1.02 0.89 0.95 1.19 1.07 1.65 4.81 1.05

time (sec)

N/A 0.389 0.033 0.485 0.205 0.254 0.357 0.283 4.398

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 59 69 55 65 64 87 268 60

N.S.

1 1.04 1.21 0.96 1.14 1.12 1.53 4.70 1.05

time (sec)

N/A 0.269 0.019 0.085 0.201 0.262 0.259 0.277 4.248

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

390 617 671 358 406 0 0 0 0

N.S.

1 1.58 1.72 0.92 1.04 0.00 0.00 0.00 0.00

time (sec)

N/A 1.043 1.286 1.046 0.378 0.000 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

590 618 755 1926 550 0 0 0 0

N.S.

1 1.05 1.28 3.26 0.93 0.00 0.00 0.00 0.00

time (sec)

N/A 1.333 5.781 1.213 0.414 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

657 682 1559 3791 1087 0 0 0 0

N.S.

1 1.04 2.37 5.77 1.65 0.00 0.00 0.00 0.00

time (sec)

N/A 1.343 9.814 1.477 0.418 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

16 16 18 14 16 16 15 16 16

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.00

time (sec)

N/A 0.200 4.335 0.387 0.587 0.252 0.567 0.299 4.242

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

16 16 18 14 16 16 15 16 16

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.00

time (sec)

N/A 0.208 3.127 0.293 0.641 0.260 0.412 0.293 4.834

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

62 62 119 0 153 354 0 79 0

N.S.

1 1.00 1.92 0.00 2.47 5.71 0.00 1.27 0.00

time (sec)

N/A 0.291 0.087 0.000 0.223 0.279 0.000 0.293 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

128 130 226 0 223 728 0 143 0

N.S.

1 1.02 1.77 0.00 1.74 5.69 0.00 1.12 0.00

time (sec)

N/A 0.347 0.197 0.000 0.293 0.300 0.000 0.295 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

200 194 329 0 401 1278 0 226 0

N.S.

1 0.97 1.64 0.00 2.00 6.39 0.00 1.13 0.00

time (sec)

N/A 1.095 0.386 0.000 0.296 0.341 0.000 0.309 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

283 281 431 0 639 2004 0 357 0

N.S.

1 0.99 1.52 0.00 2.26 7.08 0.00 1.26 0.00

time (sec)

N/A 1.298 0.596 0.000 0.349 0.436 0.000 0.312 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

186 139 125 199 0 0 0 0 0

N.S.

1 0.75 0.67 1.07 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.416 0.789 0.484 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 99 77 190 0 0 0 0 0

N.S.

1 0.69 0.53 1.32 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.300 0.143 0.422 0.000 0.000 0.000 0.000 0.000

Problem 50

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

37 37 30 45 63 41 0 58 0

N.S.

1 1.00 0.81 1.22 1.70 1.11 0.00 1.57 0.00

time (sec)

N/A 0.210 0.054 0.359 0.290 0.258 0.000 0.293 0.000

Problem 51

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

83 86 45 81 67 61 0 90 0

N.S.

1 1.04 0.54 0.98 0.81 0.73 0.00 1.08 0.00

time (sec)

N/A 0.329 0.060 0.598 0.214 0.279 0.000 0.303 0.000

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

124 135 55 100 99 81 0 122 0

N.S.

1 1.09 0.44 0.81 0.80 0.65 0.00 0.98 0.00

time (sec)

N/A 0.446 0.059 0.584 0.215 0.251 0.000 0.299 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

3 3 3 4 3 11 3 12 3

N.S.

1 1.00 1.00 1.33 1.00 3.67 1.00 4.00 1.00

time (sec)

N/A 0.183 0.069 0.343 0.194 0.240 0.106 0.273 0.338

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 12 13 12 62 15 22 22

N.S.

1 1.00 1.00 1.08 1.00 5.17 1.25 1.83 1.83

time (sec)

N/A 0.201 0.009 0.432 0.196 0.254 0.806 0.294 4.341

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 67 61 159 171 63 0 53 201

N.S.

1 1.08 0.98 2.56 2.76 1.02 0.00 0.85 3.24

time (sec)

N/A 0.304 0.052 1.026 0.207 0.246 0.000 0.327 5.813

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 39 35 59 76 0 0 0 0

N.S.

1 1.05 0.95 1.59 2.05 0.00 0.00 0.00 0.00

time (sec)

N/A 0.338 0.060 0.361 0.201 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 8 13 6 14 5 14 21

N.S.

1 1.00 1.00 1.62 0.75 1.75 0.62 1.75 2.62

time (sec)

N/A 0.177 0.005 0.360 0.190 0.259 0.282 0.273 4.092

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 41 44 22 34 29 31 101 21

N.S.

1 1.14 1.22 0.61 0.94 0.81 0.86 2.81 0.58

time (sec)

N/A 0.217 0.029 0.335 0.211 0.246 0.207 0.275 0.108

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 28 80 76 42 0 80 81

N.S.

1 1.00 0.74 2.11 2.00 1.11 0.00 2.11 2.13

time (sec)

N/A 0.199 0.031 0.355 0.232 0.264 0.000 0.317 4.141

Problem 60

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

50 60 50 37 47 47 88 154 34

N.S.

1 1.20 1.00 0.74 0.94 0.94 1.76 3.08 0.68

time (sec)

N/A 0.228 0.051 0.355 0.202 0.250 0.292 0.263 4.502

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 72 43 128 118 66 0 0 112

N.S.

1 1.07 0.64 1.91 1.76 0.99 0.00 0.00 1.67

time (sec)

N/A 0.282 0.041 0.365 0.205 0.254 0.000 0.000 4.297

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 99 81 106 106 112 153 512 134

N.S.

1 0.98 0.80 1.05 1.05 1.11 1.51 5.07 1.33

time (sec)

N/A 0.339 0.031 0.118 0.204 0.255 0.444 0.297 4.523

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 82 92 85 79 84 117 360 98

N.S.

1 1.05 1.18 1.09 1.01 1.08 1.50 4.62 1.26

time (sec)

N/A 0.318 0.020 0.102 0.210 0.266 0.376 0.291 4.654

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 71 56 63 61 66 76 259 62

N.S.

1 1.09 0.86 0.97 0.94 1.02 1.17 3.98 0.95

time (sec)

N/A 0.303 0.019 0.094 0.199 0.248 0.321 0.281 4.964

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 33 43 30 31 48 41 197 42

N.S.

1 0.94 1.23 0.86 0.89 1.37 1.17 5.63 1.20

time (sec)

N/A 0.224 0.013 0.069 0.202 0.249 0.179 0.274 4.635

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 92 259 68 128 0 0 0 0

N.S.

1 1.00 2.82 0.74 1.39 0.00 0.00 0.00 0.00

time (sec)

N/A 0.479 0.123 0.343 0.201 0.000 0.000 0.000 0.000

Problem 67

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

64 67 55 61 54 68 144 259 62

N.S.

1 1.05 0.86 0.95 0.84 1.06 2.25 4.05 0.97

time (sec)

N/A 0.280 0.044 0.098 0.205 0.262 0.520 0.286 4.721

Problem 68

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

90 93 76 78 85 111 410 360 247

N.S.

1 1.03 0.84 0.87 0.94 1.23 4.56 4.00 2.74

time (sec)

N/A 0.307 0.084 0.128 0.221 0.279 0.782 0.285 5.595

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

263 244 210 448 320 0 0 0 0

N.S.

1 0.93 0.80 1.70 1.22 0.00 0.00 0.00 0.00

time (sec)

N/A 0.569 1.486 0.241 0.195 0.000 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

204 193 644 350 259 0 0 0 0

N.S.

1 0.95 3.16 1.72 1.27 0.00 0.00 0.00 0.00

time (sec)

N/A 0.500 3.586 0.188 0.217 0.000 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 127 106 244 202 0 0 0 0

N.S.

1 0.93 0.78 1.79 1.49 0.00 0.00 0.00 0.00

time (sec)

N/A 0.435 0.242 0.171 0.213 0.000 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 76 55 133 139 0 0 0 0

N.S.

1 0.94 0.68 1.64 1.72 0.00 0.00 0.00 0.00

time (sec)

N/A 0.447 0.069 0.246 0.211 0.000 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

148 148 777 866 0 0 0 0 0

N.S.

1 1.00 5.25 5.85 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.326 2.449 5.624 0.000 0.000 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

251 257 206 299 244 0 0 0 0

N.S.

1 1.02 0.82 1.19 0.97 0.00 0.00 0.00 0.00

time (sec)

N/A 1.018 0.824 0.144 0.217 0.000 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

370 347 291 386 360 0 0 0 0

N.S.

1 0.94 0.79 1.04 0.97 0.00 0.00 0.00 0.00

time (sec)

N/A 1.126 1.604 0.187 0.221 0.000 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

673 709 529 426 591 0 0 0 0

N.S.

1 1.05 0.79 0.63 0.88 0.00 0.00 0.00 0.00

time (sec)

N/A 1.468 0.410 0.889 0.418 0.000 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 138 185 164 192 0 0 0 0

N.S.

1 1.15 1.54 1.37 1.60 0.00 0.00 0.00 0.00

time (sec)

N/A 0.535 0.048 1.302 0.231 0.000 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

292 436 507 259 192 0 0 0 0

N.S.

1 1.49 1.74 0.89 0.66 0.00 0.00 0.00 0.00

time (sec)

N/A 1.033 3.764 1.165 0.213 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

738 1165 843 554 651 0 0 0 0

N.S.

1 1.58 1.14 0.75 0.88 0.00 0.00 0.00 0.00

time (sec)

N/A 2.176 0.616 1.472 0.401 0.000 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

619 619 575 646 0 0 0 0 0

N.S.

1 1.00 0.93 1.04 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.375 0.448 0.407 0.000 0.000 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

738 738 719 752 0 0 0 0 0

N.S.

1 1.00 0.97 1.02 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.665 0.487 0.391 0.000 0.000 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

335 356 596 750 0 0 0 0 0

N.S.

1 1.06 1.78 2.24 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.059 0.581 1.383 0.000 0.000 0.000 0.000 0.000

Problem 83

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

51 52 59 42 41 38 0 164 31

N.S.

1 1.02 1.16 0.82 0.80 0.75 0.00 3.22 0.61

time (sec)

N/A 0.204 0.015 0.039 0.203 0.251 0.000 0.264 4.301

Problem 84

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

42 43 52 37 36 31 0 114 26

N.S.

1 1.02 1.24 0.88 0.86 0.74 0.00 2.71 0.62

time (sec)

N/A 0.199 0.012 0.040 0.198 0.255 0.000 0.279 4.246

Problem 85

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

22 29 22 27 26 24 0 65 16

N.S.

1 1.32 1.00 1.23 1.18 1.09 0.00 2.95 0.73

time (sec)

N/A 0.182 0.017 0.038 0.209 0.264 0.000 0.274 4.236

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 27 19 33 66 0 0 0 0

N.S.

1 1.42 1.00 1.74 3.47 0.00 0.00 0.00 0.00

time (sec)

N/A 0.223 0.009 0.162 0.209 0.000 0.000 0.000 0.000

Problem 87

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

25 32 45 32 31 30 92 65 18

N.S.

1 1.28 1.80 1.28 1.24 1.20 3.68 2.60 0.72

time (sec)

N/A 0.192 0.015 0.048 0.201 0.252 0.552 0.278 4.683

Problem 88

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

42 43 58 37 36 38 160 114 45

N.S.

1 1.02 1.38 0.88 0.86 0.90 3.81 2.71 1.07

time (sec)

N/A 0.192 0.017 0.043 0.195 0.276 1.281 0.268 4.700

Problem 89

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

38 35 31 35 24 35 121 168 24

N.S.

1 0.92 0.82 0.92 0.63 0.92 3.18 4.42 0.63

time (sec)

N/A 0.199 0.012 0.043 0.189 0.275 0.994 0.270 4.562

Problem 90

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

31 28 25 30 19 30 0 119 0

N.S.

1 0.90 0.81 0.97 0.61 0.97 0.00 3.84 0.00

time (sec)

N/A 0.196 0.011 0.038 0.195 0.257 0.000 0.276 0.000

Problem 91

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

20 20 20 15 16 24 87 70 14

N.S.

1 1.00 1.00 0.75 0.80 1.20 4.35 3.50 0.70

time (sec)

N/A 0.173 0.007 0.037 0.206 0.255 0.201 0.262 3.981

Problem 92

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

24 24 24 29 18 36 126 70 22

N.S.

1 1.00 1.00 1.21 0.75 1.50 5.25 2.92 0.92

time (sec)

N/A 0.179 0.015 0.042 0.207 0.262 0.400 0.260 3.944

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 32 26 95 104 0 0 0 0

N.S.

1 1.14 0.93 3.39 3.71 0.00 0.00 0.00 0.00

time (sec)

N/A 0.228 0.015 0.181 0.216 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 18 15 23 15 104 26

N.S.

1 1.00 1.00 0.95 0.79 1.21 0.79 5.47 1.37

time (sec)

N/A 0.176 0.001 0.147 0.201 0.257 0.084 0.281 4.150

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 36 52 45 147 128 0 0 0

N.S.

1 0.95 1.37 1.18 3.87 3.37 0.00 0.00 0.00

time (sec)

N/A 0.233 0.039 0.285 0.275 0.257 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 66 46 62 44 56 188 50

N.S.

1 1.00 1.69 1.18 1.59 1.13 1.44 4.82 1.28

time (sec)

N/A 0.234 0.032 0.103 0.194 0.253 0.220 0.280 4.782

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

54 41 42 48 81 86 97 255 114

N.S.

1 0.76 0.78 0.89 1.50 1.59 1.80 4.72 2.11

time (sec)

N/A 0.268 0.033 0.446 0.188 0.258 0.310 0.281 4.381

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 33 144 43 112 0 0 0 0

N.S.

1 0.94 4.11 1.23 3.20 0.00 0.00 0.00 0.00

time (sec)

N/A 0.235 0.030 0.453 0.198 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

48 45 43 45 53 67 136 198 93

N.S.

1 0.94 0.90 0.94 1.10 1.40 2.83 4.12 1.94

time (sec)

N/A 0.259 0.033 0.484 0.204 0.250 0.524 0.274 4.143

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 29 117 22 58 0 0 0 0

N.S.

1 1.16 4.68 0.88 2.32 0.00 0.00 0.00 0.00

time (sec)

N/A 0.230 0.014 0.361 0.188 0.000 0.000 0.000 0.000

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