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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 C F A A A B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

77 88 143 43 0 76 60 55 51

N.S.

1 1.14 1.86 0.56 0.00 0.99 0.78 0.71 0.66

time (sec)

N/A 0.250 0.035 0.113 0.000 0.246 0.152 0.300 0.118

Problem 2

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

30 25 25 26 25 43 0 73 52

N.S.

1 0.83 0.83 0.87 0.83 1.43 0.00 2.43 1.73

time (sec)

N/A 0.162 0.013 0.051 0.192 0.234 0.000 0.282 9.335

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 98 216 97 107 97 97

N.S.

1 1.00 1.00 7.00 15.43 6.93 7.64 6.93 6.93

time (sec)

N/A 0.146 0.001 0.034 0.197 0.258 0.033 0.290 9.169

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 65 99 64 66 64 64

N.S.

1 1.00 1.00 4.64 7.07 4.57 4.71 4.57 4.57

time (sec)

N/A 0.147 0.002 0.032 0.198 0.247 0.027 0.338 0.017

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 14 35 13 31 31 32 31 31

N.S.

1 0.40 1.00 0.37 0.89 0.89 0.91 0.89 0.89

time (sec)

N/A 0.144 0.000 0.026 0.191 0.230 0.018 0.286 0.022

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 13 24 24 26 12 26

N.S.

1 1.00 1.00 0.93 1.71 1.71 1.86 0.86 1.86

time (sec)

N/A 0.149 0.003 0.035 0.200 0.237 0.078 0.298 0.021

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 13 57 57 61 12 59

N.S.

1 1.00 1.00 0.93 4.07 4.07 4.36 0.86 4.21

time (sec)

N/A 0.150 0.005 0.075 0.202 0.255 0.171 0.296 9.285

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 13 90 90 97 12 92

N.S.

1 1.00 1.00 0.93 6.43 6.43 6.93 0.86 6.57

time (sec)

N/A 0.149 0.002 0.107 0.201 0.240 0.251 0.277 9.019

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 93 159 159 204 156 175 166 149

N.S.

1 1.11 1.89 1.89 2.43 1.86 2.08 1.98 1.77

time (sec)

N/A 0.297 0.016 0.035 0.211 0.250 0.044 0.276 9.303

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 64 82 82 93 80 87 83 79

N.S.

1 1.14 1.46 1.46 1.66 1.43 1.55 1.48 1.41

time (sec)

N/A 0.245 0.007 0.029 0.209 0.254 0.030 0.297 0.026

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 32 29 28 28 31 28 28

N.S.

1 1.00 1.00 0.91 0.88 0.88 0.97 0.88 0.88

time (sec)

N/A 0.158 0.000 0.021 0.195 0.252 0.020 0.283 0.022

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 194 63 57 0 387 53 212 174

N.S.

1 1.03 0.34 0.30 0.00 2.06 0.28 1.13 0.93

time (sec)

N/A 0.459 0.014 0.048 0.000 0.288 0.204 0.278 0.321

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 268 112 134 0 704 192 289 247

N.S.

1 1.09 0.46 0.55 0.00 2.87 0.78 1.18 1.01

time (sec)

N/A 0.486 0.044 0.085 0.000 0.275 0.664 0.321 10.171

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

305 342 149 277 0 1268 474 366 483

N.S.

1 1.12 0.49 0.91 0.00 4.16 1.55 1.20 1.58

time (sec)

N/A 0.548 0.058 0.146 0.000 0.283 1.390 0.278 10.188

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

361 361 653 842 461 727 1018 987 787

N.S.

1 1.00 1.81 2.33 1.28 2.01 2.82 2.73 2.18

time (sec)

N/A 0.985 0.160 0.053 0.212 0.251 0.087 0.286 9.629

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 193 241 188 180 269 345 346 270

N.S.

1 1.00 1.25 0.97 0.93 1.39 1.79 1.79 1.40

time (sec)

N/A 0.501 0.056 0.037 0.206 0.231 0.043 0.351 0.048

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 76 53 50 52 63 50 54

N.S.

1 1.00 1.36 0.95 0.89 0.93 1.12 0.89 0.96

time (sec)

N/A 0.187 0.000 0.027 0.201 0.238 0.019 0.262 0.026

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 86 80 87 112 112 0 131 106

N.S.

1 1.00 0.93 1.01 1.30 1.30 0.00 1.52 1.23

time (sec)

N/A 0.284 0.048 0.126 0.217 2.906 0.000 0.285 9.712

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

234 234 232 235 2096 0 0 1435 1940

N.S.

1 1.00 0.99 1.00 8.96 0.00 0.00 6.13 8.29

time (sec)

N/A 0.633 0.368 0.716 0.316 0.000 0.000 0.282 13.890

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

495 495 490 514 11005 0 0 7111 82532

N.S.

1 1.00 0.99 1.04 22.23 0.00 0.00 14.37 166.73

time (sec)

N/A 1.598 0.718 2.373 0.740 0.000 0.000 0.404 23.447

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 20 19 19 19 20 25

N.S.

1 1.00 1.00 0.80 0.76 0.76 0.76 0.80 1.00

time (sec)

N/A 0.179 0.006 0.056 0.286 0.313 0.057 0.278 0.030

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 31 26 25 25 24 26 25

N.S.

1 1.00 1.00 0.84 0.81 0.81 0.77 0.84 0.81

time (sec)

N/A 0.197 0.006 0.063 0.288 0.332 0.065 0.321 0.034

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 9 8 8 8 8 8

N.S.

1 1.00 1.00 0.90 0.80 0.80 0.80 0.80 0.80

time (sec)

N/A 0.155 0.001 0.016 0.200 0.329 0.019 0.284 0.019

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 28 26 28 26 19 30 25

N.S.

1 1.00 1.00 0.93 1.00 0.93 0.68 1.07 0.89

time (sec)

N/A 0.190 0.005 0.691 0.198 0.310 0.082 0.296 0.038

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 26 22 21 20 18 15 24 18

N.S.

1 1.18 1.00 0.95 0.91 0.82 0.68 1.09 0.82

time (sec)

N/A 0.168 0.005 0.683 0.193 0.311 0.098 0.276 9.264

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 63 61 61 0 211 564 62 213

N.S.

1 1.02 0.98 0.98 0.00 3.40 9.10 1.00 3.44

time (sec)

N/A 0.252 0.052 0.089 0.000 0.323 4.405 0.333 0.283

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 111 89 27 98 299 20 112 99

N.S.

1 0.97 0.77 0.23 0.85 2.60 0.17 0.97 0.86

time (sec)

N/A 0.280 0.021 0.680 0.282 0.320 0.071 0.277 0.143

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 17 17 16 29 16 16

N.S.

1 1.00 1.00 1.06 1.06 1.00 1.81 1.00 1.00

time (sec)

N/A 0.144 0.002 0.027 0.202 0.298 0.277 0.266 9.845

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F B

verified

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

size

55 55 53 0 0 0 0 0 56

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 1.02

time (sec)

N/A 0.192 0.027 0.000 0.000 0.000 0.000 0.000 9.640

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F B

verified

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

size

53 59 61 0 0 0 0 0 56

N.S.

1 1.11 1.15 0.00 0.00 0.00 0.00 0.00 1.06

time (sec)

N/A 0.197 0.030 0.000 0.000 0.000 0.000 0.000 10.146

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

132 132 129 0 0 0 0 0 0

N.S.

1 1.00 0.98 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.339 0.138 0.000 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F C F B

verified

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

size

35 44 203 0 0 0 34 0 41

N.S.

1 1.26 5.80 0.00 0.00 0.00 0.97 0.00 1.17

time (sec)

N/A 0.171 0.136 0.000 0.000 0.000 5.126 0.000 10.478

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

270 276 285 267 372 271 299 277 261

N.S.

1 1.02 1.06 0.99 1.38 1.00 1.11 1.03 0.97

time (sec)

N/A 0.591 0.032 0.050 0.196 0.271 0.048 0.279 10.568

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 189 171 163 205 163 180 166 160

N.S.

1 1.11 1.00 0.95 1.20 0.95 1.05 0.97 0.94

time (sec)

N/A 0.422 0.015 0.047 0.218 0.263 0.037 0.281 10.577

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 117 92 83 94 82 95 83 82

N.S.

1 1.27 1.00 0.90 1.02 0.89 1.03 0.90 0.89

time (sec)

N/A 0.312 0.010 0.038 0.190 0.284 0.028 0.269 0.023

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 32 29 28 28 31 28 28

N.S.

1 1.00 1.00 0.91 0.88 0.88 0.97 0.88 0.88

time (sec)

N/A 0.167 0.000 0.029 0.195 0.279 0.020 0.266 0.021

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

529 555 71 64 0 905 88 603 1551

N.S.

1 1.05 0.13 0.12 0.00 1.71 0.17 1.14 2.93

time (sec)

N/A 1.027 0.020 0.137 0.000 0.293 0.595 0.290 12.187

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

746 797 182 230 0 3222 0 1057 5844

N.S.

1 1.07 0.24 0.31 0.00 4.32 0.00 1.42 7.83

time (sec)

N/A 1.260 0.071 0.122 0.000 0.373 0.000 0.389 12.090

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

295 304 345 332 383 332 366 353 331

N.S.

1 1.03 1.17 1.13 1.30 1.13 1.24 1.20 1.12

time (sec)

N/A 0.594 0.045 0.059 0.195 0.286 0.051 0.295 10.542

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

203 215 207 200 214 198 218 205 201

N.S.

1 1.06 1.02 0.99 1.05 0.98 1.07 1.01 0.99

time (sec)

N/A 0.427 0.019 0.048 0.202 0.274 0.038 0.295 0.100

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 135 109 99 101 98 112 99 98

N.S.

1 1.26 1.02 0.93 0.94 0.92 1.05 0.93 0.92

time (sec)

N/A 0.314 0.011 0.038 0.198 0.272 0.026 0.293 10.174

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 37 34 33 33 36 33 33

N.S.

1 1.00 1.00 0.92 0.89 0.89 0.97 0.89 0.89

time (sec)

N/A 0.169 0.000 0.030 0.191 0.258 0.020 0.275 0.023

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 165 71 67 0 1115 122 577 1264

N.S.

1 1.08 0.46 0.44 0.00 7.29 0.80 3.77 8.26

time (sec)

N/A 0.361 0.018 0.261 0.000 0.310 0.991 0.284 11.302

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

342 377 234 288 0 4285 0 1115 10351

N.S.

1 1.10 0.68 0.84 0.00 12.53 0.00 3.26 30.27

time (sec)

N/A 0.582 0.096 0.133 0.000 0.482 0.000 0.317 13.831

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 96 96 85 84 84 94 84 84

N.S.

1 1.00 1.00 0.89 0.88 0.88 0.98 0.88 0.88

time (sec)

N/A 0.239 0.003 0.030 0.193 0.281 0.028 0.294 0.197

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 74 65 64 64 71 64 64

N.S.

1 1.00 1.00 0.88 0.86 0.86 0.96 0.86 0.86

time (sec)

N/A 0.221 0.001 0.028 0.187 0.289 0.027 0.279 0.066

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 54 45 44 44 49 44 44

N.S.

1 1.00 1.00 0.83 0.81 0.81 0.91 0.81 0.81

time (sec)

N/A 0.199 0.002 0.022 0.187 0.308 0.022 0.336 0.020

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 23 20 19 19 19 19 19

N.S.

1 1.00 1.00 0.87 0.83 0.83 0.83 0.83 0.83

time (sec)

N/A 0.150 0.000 0.022 0.194 0.281 0.026 0.291 0.017

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

268 321 45 41 0 1015 41 0 123

N.S.

1 1.20 0.17 0.15 0.00 3.79 0.15 0.00 0.46

time (sec)

N/A 0.656 0.008 0.047 0.000 1.086 0.540 0.000 10.581

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

357 432 113 83 0 1201 3834 0 176

N.S.

1 1.21 0.32 0.23 0.00 3.36 10.74 0.00 0.49

time (sec)

N/A 0.862 0.014 0.055 0.000 1.049 1.777 0.000 0.136

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 97 97 78 77 77 94 77 77

N.S.

1 1.00 1.00 0.80 0.79 0.79 0.97 0.79 0.79

time (sec)

N/A 0.244 0.002 0.029 0.199 0.256 0.029 0.303 0.118

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 69 69 58 57 57 66 57 57

N.S.

1 1.00 1.00 0.84 0.83 0.83 0.96 0.83 0.83

time (sec)

N/A 0.220 0.002 0.026 0.196 0.270 0.026 0.277 0.063

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 45 38 37 37 42 37 37

N.S.

1 1.00 1.00 0.84 0.82 0.82 0.93 0.82 0.82

time (sec)

N/A 0.197 0.002 0.024 0.199 0.292 0.025 0.306 0.018

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 18 17 17 19 17 17

N.S.

1 1.00 1.00 0.86 0.81 0.81 0.90 0.81 0.81

time (sec)

N/A 0.152 0.000 0.021 0.190 0.242 0.018 0.304 0.016

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

234 270 47 41 0 499 3432 265 87

N.S.

1 1.15 0.20 0.18 0.00 2.13 14.67 1.13 0.37

time (sec)

N/A 0.586 0.018 0.059 0.000 0.989 1.343 0.309 10.965

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B C B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

317 350 108 79 0 704 3834 315 174

N.S.

1 1.10 0.34 0.25 0.00 2.22 12.09 0.99 0.55

time (sec)

N/A 0.755 0.019 0.079 0.000 0.975 1.936 0.380 10.660

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 104 104 85 84 84 100 84 84

N.S.

1 1.00 1.00 0.82 0.81 0.81 0.96 0.81 0.81

time (sec)

N/A 0.248 0.002 0.034 0.208 0.257 0.031 0.300 10.543

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 76 65 64 64 73 64 64

N.S.

1 1.00 1.00 0.86 0.84 0.84 0.96 0.84 0.84

time (sec)

N/A 0.223 0.002 0.029 0.196 0.259 0.027 0.293 0.065

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 52 52 45 44 44 49 44 44

N.S.

1 1.00 1.00 0.87 0.85 0.85 0.94 0.85 0.85

time (sec)

N/A 0.197 0.002 0.025 0.194 0.242 0.024 0.285 0.020

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 30 25 24 24 27 24 24

N.S.

1 1.00 1.00 0.83 0.80 0.80 0.90 0.80 0.80

time (sec)

N/A 0.151 0.000 0.021 0.200 0.267 0.018 0.290 0.012

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

263 313 55 49 0 1297 41 0 123

N.S.

1 1.19 0.21 0.19 0.00 4.93 0.16 0.00 0.47

time (sec)

N/A 0.708 0.009 0.045 0.000 0.977 1.271 0.000 0.267

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

366 428 128 96 0 1540 3839 0 181

N.S.

1 1.17 0.35 0.26 0.00 4.21 10.49 0.00 0.49

time (sec)

N/A 0.888 0.014 0.055 0.000 1.099 2.232 0.000 0.150

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 164 592 163 185 163 163

N.S.

1 1.00 1.00 11.71 42.29 11.64 13.21 11.64 11.64

time (sec)

N/A 0.165 0.002 0.052 0.206 0.276 0.040 0.271 0.127

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 109 228 108 114 108 108

N.S.

1 1.00 1.00 7.79 16.29 7.71 8.14 7.71 7.71

time (sec)

N/A 0.167 0.002 0.040 0.207 0.300 0.031 0.279 0.055

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 61 13 53 53 60 53 53

N.S.

1 1.00 4.36 0.93 3.79 3.79 4.29 3.79 3.79

time (sec)

N/A 0.159 0.000 0.032 0.203 0.275 0.021 0.295 0.016

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 13 46 46 49 12 48

N.S.

1 1.00 1.00 0.93 3.29 3.29 3.50 0.86 3.43

time (sec)

N/A 0.162 0.004 0.058 0.196 0.290 0.134 0.294 0.033

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 13 101 101 109 12 103

N.S.

1 1.00 1.00 0.93 7.21 7.21 7.79 0.86 7.36

time (sec)

N/A 0.165 0.003 0.130 0.203 0.266 0.282 0.280 10.735

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 13 156 156 168 12 158

N.S.

1 1.00 1.00 0.93 11.14 11.14 12.00 0.86 11.29

time (sec)

N/A 0.161 0.003 0.244 0.219 0.282 0.426 0.281 11.831

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 38 31 30 30 29 31 36

N.S.

1 1.00 1.00 0.82 0.79 0.79 0.76 0.82 0.95

time (sec)

N/A 0.196 0.006 0.081 0.281 0.261 0.073 0.268 0.030

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 84 84 65 64 64 80 64 64

N.S.

1 1.00 1.00 0.77 0.76 0.76 0.95 0.76 0.76

time (sec)

N/A 0.852 0.003 0.039 0.197 0.257 0.033 0.272 0.077

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 63 63 50 49 49 60 49 49

N.S.

1 1.00 1.00 0.79 0.78 0.78 0.95 0.78 0.78

time (sec)

N/A 0.890 0.003 0.033 0.193 0.245 0.028 0.281 0.053

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 44 35 34 34 41 34 34

N.S.

1 1.00 1.00 0.80 0.77 0.77 0.93 0.77 0.77

time (sec)

N/A 0.608 0.001 0.028 0.190 0.272 0.026 0.276 0.015

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 20 19 19 22 19 19

N.S.

1 1.00 1.00 0.80 0.76 0.76 0.88 0.76 0.76

time (sec)

N/A 0.157 0.000 0.046 0.189 0.254 0.019 0.287 0.020

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 62 42 54 56 63 62 27

N.S.

1 1.00 2.00 1.35 1.74 1.81 2.03 2.00 0.87

time (sec)

N/A 0.187 0.012 0.069 0.288 0.288 0.072 0.290 10.332

Problem 75

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

89 89 103 84 89 177 104 97 64

N.S.

1 1.00 1.16 0.94 1.00 1.99 1.17 1.09 0.72

time (sec)

N/A 0.245 0.039 0.117 0.273 0.264 0.817 0.296 0.047

Problem 76

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

161 161 137 108 119 282 134 112 93

N.S.

1 1.00 0.85 0.67 0.74 1.75 0.83 0.70 0.58

time (sec)

N/A 0.335 0.061 0.140 0.278 0.298 0.877 0.301 0.049

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 245 132 116 114 223 296 134 126

N.S.

1 2.69 1.45 1.27 1.25 2.45 3.25 1.47 1.38

time (sec)

N/A 0.443 0.065 0.131 0.286 0.277 0.806 0.298 10.083

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 74 73 111 81 198 209 77 87

N.S.

1 0.95 0.94 1.42 1.04 2.54 2.68 0.99 1.12

time (sec)

N/A 0.224 0.035 0.906 0.284 0.283 0.395 0.273 9.963

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 47 54 70 61 157 153 54 206

N.S.

1 0.94 1.08 1.40 1.22 3.14 3.06 1.08 4.12

time (sec)

N/A 0.199 0.021 0.882 0.278 0.285 0.257 0.285 0.057

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 39 38 54 50 136 124 43 46

N.S.

1 0.95 0.93 1.32 1.22 3.32 3.02 1.05 1.12

time (sec)

N/A 0.172 0.012 0.845 0.284 0.282 0.116 0.281 9.987

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 28 24 83 54 17 17

N.S.

1 1.00 1.00 1.33 1.14 3.95 2.57 0.81 0.81

time (sec)

N/A 0.144 0.007 0.826 0.277 0.272 0.085 0.291 0.026

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 57 48 74 68 154 738 62 173

N.S.

1 0.97 0.81 1.25 1.15 2.61 12.51 1.05 2.93

time (sec)

N/A 0.195 0.028 0.843 0.292 0.284 1.845 0.295 10.576

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 93 81 96 123 229 1620 117 425

N.S.

1 1.18 1.03 1.22 1.56 2.90 20.51 1.48 5.38

time (sec)

N/A 0.256 0.031 0.865 0.288 0.295 6.884 0.295 10.100

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 134 106 151 197 371 3284 195 573

N.S.

1 1.11 0.88 1.25 1.63 3.07 27.14 1.61 4.74

time (sec)

N/A 0.315 0.097 0.882 0.298 0.288 42.252 0.291 10.425

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 31 34 30 109 61 24 27

N.S.

1 1.00 1.00 1.10 0.97 3.52 1.97 0.77 0.87

time (sec)

N/A 0.156 0.009 1.112 0.281 0.270 0.089 0.301 0.037

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 61 60 86 75 253 117 65 76

N.S.

1 0.97 0.95 1.37 1.19 4.02 1.86 1.03 1.21

time (sec)

N/A 0.168 0.021 0.990 0.288 0.282 0.294 0.289 9.907

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 94 75 139 184 595 257 103 181

N.S.

1 1.03 0.82 1.53 2.02 6.54 2.82 1.13 1.99

time (sec)

N/A 0.183 0.044 0.963 0.298 0.282 0.619 0.305 10.264

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 198 42 66 279 92 30 31

N.S.

1 1.00 5.66 1.20 1.89 7.97 2.63 0.86 0.89

time (sec)

N/A 0.167 0.089 1.077 0.277 0.273 0.098 0.280 0.073

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 11 18 10 24 10 10

N.S.

1 1.00 1.00 1.10 1.80 1.00 2.40 1.00 1.00

time (sec)

N/A 0.138 0.005 0.981 0.273 0.250 0.078 0.294 0.025

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 35 31 43 51 55 56 41 42

N.S.

1 0.95 0.84 1.16 1.38 1.49 1.51 1.11 1.14

time (sec)

N/A 0.147 0.011 0.924 0.301 0.272 0.225 0.304 10.887

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 52 71 115 153 146 73 111

N.S.

1 1.00 0.87 1.18 1.92 2.55 2.43 1.22 1.85

time (sec)

N/A 0.159 0.014 0.935 0.282 0.253 0.480 0.282 0.077

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 32 23 25 22 22 27 10

N.S.

1 1.00 3.20 2.30 2.50 2.20 2.20 2.70 1.00

time (sec)

N/A 0.136 0.005 0.875 0.189 0.285 0.080 0.299 10.474

Problem 93

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

39 37 45 52 56 85 54 56 43

N.S.

1 0.95 1.15 1.33 1.44 2.18 1.38 1.44 1.10

time (sec)

N/A 0.148 0.019 0.822 0.198 0.288 0.225 0.278 10.358

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 65 78 122 220 141 88 114

N.S.

1 1.00 1.02 1.22 1.91 3.44 2.20 1.38 1.78

time (sec)

N/A 0.165 0.023 0.844 0.196 0.258 0.513 0.288 10.060

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

4 4 15 12 11 11 10 13 4

N.S.

1 1.00 3.75 3.00 2.75 2.75 2.50 3.25 1.00

time (sec)

N/A 0.128 0.003 0.708 0.202 0.264 0.044 0.297 0.110

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 26 24 25 39 24 27 23

N.S.

1 1.00 0.96 0.89 0.93 1.44 0.89 1.00 0.85

time (sec)

N/A 0.145 0.013 0.760 0.192 0.268 0.052 0.302 0.046

Problem 97

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

45 50 37 36 44 71 44 39 36

N.S.

1 1.11 0.82 0.80 0.98 1.58 0.98 0.87 0.80

time (sec)

N/A 0.157 0.014 0.731 0.188 0.254 0.067 0.284 10.257

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 65 64 61 54 54 58 62 55

N.S.

1 1.10 1.08 1.03 0.92 0.92 0.98 1.05 0.93

time (sec)

N/A 0.208 0.018 0.899 0.186 0.259 0.076 0.284 0.033

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 11 11 12 11 11 10 11 11

N.S.

1 1.10 1.10 1.20 1.10 1.10 1.00 1.10 1.10

time (sec)

N/A 0.163 0.007 0.892 0.187 0.266 0.038 0.285 10.372

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 41 55 25 36 35 26 23 0

N.S.

1 0.93 1.25 0.57 0.82 0.80 0.59 0.52 0.00

time (sec)

N/A 0.175 0.050 0.987 0.268 0.294 0.441 0.286 0.000

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