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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 A A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 206 165 248 231 201 316 317 0

N.S.

1 1.15 0.92 1.39 1.29 1.12 1.77 1.77 0.00

time (sec)

N/A 0.369 0.108 0.220 0.266 0.258 0.310 0.295 0.000

Problem 2

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

124 151 121 178 150 135 190 194 0

N.S.

1 1.22 0.98 1.44 1.21 1.09 1.53 1.56 0.00

time (sec)

N/A 0.289 0.077 0.230 0.267 0.259 0.237 0.283 0.000

Problem 3

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

98 106 92 86 81 76 99 98 77

N.S.

1 1.08 0.94 0.88 0.83 0.78 1.01 1.00 0.79

time (sec)

N/A 0.234 0.028 0.016 0.268 0.251 0.172 0.279 0.419

Problem 4

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 30 29 31 26 29 28

N.S.

1 1.00 1.00 1.00 0.97 1.03 0.87 0.97 0.93

time (sec)

N/A 0.148 0.008 0.043 0.266 0.243 0.069 0.269 0.295

Problem 5

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

229 229 214 758 0 0 0 0 0

N.S.

1 1.00 0.93 3.31 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.654 0.133 1.005 0.000 0.000 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 85 83 187 0 371 0 200 0

N.S.

1 1.00 0.98 2.20 0.00 4.36 0.00 2.35 0.00

time (sec)

N/A 0.227 0.101 1.010 0.000 0.280 0.000 0.313 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 134 207 295 0 673 0 0 0

N.S.

1 0.99 1.53 2.19 0.00 4.99 0.00 0.00 0.00

time (sec)

N/A 0.269 0.288 0.326 0.000 0.354 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

191 208 241 554 0 1125 0 0 0

N.S.

1 1.09 1.26 2.90 0.00 5.89 0.00 0.00 0.00

time (sec)

N/A 0.339 0.361 0.211 0.000 0.860 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

374 393 355 541 0 446 743 816 0

N.S.

1 1.05 0.95 1.45 0.00 1.19 1.99 2.18 0.00

time (sec)

N/A 0.966 0.351 0.568 0.000 0.275 0.478 0.308 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

242 266 249 374 0 290 454 487 0

N.S.

1 1.10 1.03 1.55 0.00 1.20 1.88 2.01 0.00

time (sec)

N/A 0.719 0.239 0.316 0.000 0.273 0.320 0.308 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 164 154 189 0 156 233 244 0

N.S.

1 1.15 1.08 1.33 0.00 1.10 1.64 1.72 0.00

time (sec)

N/A 0.531 0.695 0.197 0.000 0.243 0.246 0.284 0.000

Problem 12

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

47 51 47 72 72 65 82 75 142

N.S.

1 1.09 1.00 1.53 1.53 1.38 1.74 1.60 3.02

time (sec)

N/A 0.249 0.030 0.000 0.275 0.254 0.102 0.273 0.387

Problem 13

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

347 343 332 0 0 0 0 0 0

N.S.

1 0.99 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.053 0.263 0.000 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

309 287 231 642 0 0 0 0 0

N.S.

1 0.93 0.75 2.08 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.972 0.273 0.780 0.000 0.000 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

401 386 315 966 0 0 0 0 0

N.S.

1 0.96 0.79 2.41 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.283 0.826 1.338 0.000 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 F F F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

393 377 304 327 0 0 0 609 0

N.S.

1 0.96 0.77 0.83 0.00 0.00 0.00 1.55 0.00

time (sec)

N/A 1.249 0.606 0.214 0.000 0.000 0.000 0.316 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

244 232 187 206 0 0 0 337 0

N.S.

1 0.95 0.77 0.84 0.00 0.00 0.00 1.38 0.00

time (sec)

N/A 0.866 0.402 0.204 0.000 0.000 0.000 0.313 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 109 98 103 0 0 0 139 0

N.S.

1 0.95 0.85 0.90 0.00 0.00 0.00 1.21 0.00

time (sec)

N/A 0.510 0.169 0.080 0.000 0.000 0.000 0.303 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 48 44 48 0 0 0 49 0

N.S.

1 0.91 0.83 0.91 0.00 0.00 0.00 0.92 0.00

time (sec)

N/A 0.356 0.013 0.011 0.000 0.000 0.000 0.297 0.000

Problem 20

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

18 18 20 18 20 25 15 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.39 0.83 1.11 1.11

time (sec)

N/A 0.184 0.196 3.372 0.348 0.251 0.904 0.337 0.232

Problem 21

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

18 18 20 18 20 49 17 20 20

N.S.

1 1.00 1.11 1.00 1.11 2.72 0.94 1.11 1.11

time (sec)

N/A 0.184 0.338 1.359 0.358 0.253 1.782 0.823 0.249

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

362 362 290 526 0 0 0 1276 0

N.S.

1 1.00 0.80 1.45 0.00 0.00 0.00 3.52 0.00

time (sec)

N/A 0.784 1.634 0.355 0.000 0.000 0.000 0.381 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

181 181 149 257 0 0 0 554 0

N.S.

1 1.00 0.82 1.42 0.00 0.00 0.00 3.06 0.00

time (sec)

N/A 0.487 0.893 0.154 0.000 0.000 0.000 0.359 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 83 72 76 0 0 0 192 0

N.S.

1 0.97 0.84 0.88 0.00 0.00 0.00 2.23 0.00

time (sec)

N/A 0.546 0.179 0.014 0.000 0.000 0.000 0.311 0.000

Problem 25

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

18 18 20 18 297 51 17 20 20

N.S.

1 1.00 1.11 1.00 16.50 2.83 0.94 1.11 1.11

time (sec)

N/A 0.182 10.233 5.662 1.603 0.245 1.668 0.398 0.237

Problem 26

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

18 18 20 18 426 92 19 20 20

N.S.

1 1.00 1.11 1.00 23.67 5.11 1.06 1.11 1.11

time (sec)

N/A 0.184 12.804 1.961 2.601 0.249 6.159 0.965 0.224

Problem 27

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

18 18 20 18 227 32 17 20 20

N.S.

1 1.00 1.11 1.00 12.61 1.78 0.94 1.11 1.11

time (sec)

N/A 0.416 11.395 0.236 1.682 0.264 14.916 0.420 0.386

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

154 125 0 0 0 0 0 0 0

N.S.

1 0.81 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.279 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 29

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

18 18 20 18 20 20 15 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.83 1.11 1.11

time (sec)

N/A 0.190 0.353 2.317 0.368 0.242 0.952 0.363 0.229

Problem 30

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

18 18 20 18 237 34 17 20 20

N.S.

1 1.00 1.11 1.00 13.17 1.89 0.94 1.11 1.11

time (sec)

N/A 0.187 0.732 1.448 1.793 0.260 15.553 0.455 0.249

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

669 371 356 1396 0 0 0 0 0

N.S.

1 0.55 0.53 2.09 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.960 0.331 0.625 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 A C F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

450 263 237 973 0 0 0 0 0

N.S.

1 0.58 0.53 2.16 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.743 0.409 0.499 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 F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

238 140 132 628 0 0 0 0 0

N.S.

1 0.59 0.55 2.64 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.481 0.178 0.499 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

736 517 368 823 0 0 0 0 0

N.S.

1 0.70 0.50 1.12 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.214 0.746 0.647 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 F(-2) F F F(-2) F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

860 632 600 1352 0 0 0 0 0

N.S.

1 0.73 0.70 1.57 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.693 2.373 0.661 0.000 0.000 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

959 498 463 2074 0 0 0 0 0

N.S.

1 0.52 0.48 2.16 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.180 0.831 0.721 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

680 367 332 1535 0 0 0 0 0

N.S.

1 0.54 0.49 2.26 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.948 0.356 0.565 0.000 0.000 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

370 193 216 1014 0 0 0 0 0

N.S.

1 0.52 0.58 2.74 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.547 0.219 0.557 0.000 0.000 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1073 709 507 1546 0 0 0 0 0

N.S.

1 0.66 0.47 1.44 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.337 1.192 0.643 0.000 0.000 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1281 630 587 2903 0 0 0 0 0

N.S.

1 0.49 0.46 2.27 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.342 0.745 0.766 0.000 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

940 481 390 2090 0 0 0 0 0

N.S.

1 0.51 0.41 2.22 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.092 0.523 0.657 0.000 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

517 256 251 1423 0 0 0 0 0

N.S.

1 0.50 0.49 2.75 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.633 0.292 0.627 0.000 0.000 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1648 1019 787 2580 0 0 0 0 0

N.S.

1 0.62 0.48 1.57 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.854 2.131 0.734 0.000 0.000 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

450 262 343 856 0 0 0 0 0

N.S.

1 0.58 0.76 1.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.791 1.139 0.546 0.000 0.000 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

270 162 266 505 0 0 0 0 0

N.S.

1 0.60 0.99 1.87 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.624 0.661 0.497 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 87 172 247 90 0 0 0 0

N.S.

1 0.69 1.37 1.96 0.71 0.00 0.00 0.00 0.00

time (sec)

N/A 0.426 0.264 0.472 0.310 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

380 288 232 508 0 0 0 0 0

N.S.

1 0.76 0.61 1.34 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.015 0.159 0.494 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

507 384 295 932 0 0 0 0 0

N.S.

1 0.76 0.58 1.84 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.352 0.372 0.654 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 C F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

315 213 194 724 0 0 0 0 0

N.S.

1 0.68 0.62 2.30 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.730 0.814 0.860 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 C F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

213 143 156 488 0 0 0 0 0

N.S.

1 0.67 0.73 2.29 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.610 0.555 0.781 0.000 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 100 135 305 0 0 0 0 0

N.S.

1 0.69 0.94 2.12 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.388 0.419 0.867 0.000 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

654 431 359 1094 0 0 0 0 0

N.S.

1 0.66 0.55 1.67 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.402 1.564 1.388 0.000 0.000 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

528 452 868 6743 0 0 0 0 0

N.S.

1 0.86 1.64 12.77 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.896 2.548 1.023 0.000 0.000 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

410 277 366 5114 0 0 0 0 0

N.S.

1 0.68 0.89 12.47 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.661 0.946 1.009 0.000 0.000 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

271 192 285 3783 0 0 0 0 0

N.S.

1 0.71 1.05 13.96 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.537 0.754 0.877 0.000 0.000 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

228 159 208 2237 0 0 0 0 0

N.S.

1 0.70 0.91 9.81 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.442 0.571 0.959 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

1300 821 2078 7971 0 0 0 0 0

N.S.

1 0.63 1.60 6.13 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.080 12.894 1.497 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1154 750 708 2728 0 0 0 0 0

N.S.

1 0.65 0.61 2.36 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.740 0.744 0.865 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

737 477 441 1852 0 0 0 0 0

N.S.

1 0.65 0.60 2.51 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.141 0.595 0.728 0.000 0.000 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

396 256 225 1236 0 0 0 0 0

N.S.

1 0.65 0.57 3.12 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.695 0.176 0.646 0.000 0.000 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1442 1018 516 0 0 0 0 0 0

N.S.

1 0.71 0.36 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.193 0.967 0.000 0.000 0.000 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1685 1066 872 4176 0 0 0 0 0

N.S.

1 0.63 0.52 2.48 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.413 1.495 1.046 0.000 0.000 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1108 699 616 3032 0 0 0 0 0

N.S.

1 0.63 0.56 2.74 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.585 0.667 0.928 0.000 0.000 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

621 384 395 2021 0 0 0 0 0

N.S.

1 0.62 0.64 3.25 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.875 0.418 0.799 0.000 0.000 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1992 1369 740 0 0 0 0 0 0

N.S.

1 0.69 0.37 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.772 1.730 0.000 0.000 0.000 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2290 1379 1114 5977 0 0 0 0 0

N.S.

1 0.60 0.49 2.61 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.236 1.282 1.215 0.000 0.000 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1533 922 742 4170 0 0 0 0 0

N.S.

1 0.60 0.48 2.72 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.150 0.940 1.055 0.000 0.000 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

878 513 470 2852 0 0 0 0 0

N.S.

1 0.58 0.54 3.25 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.121 0.594 0.941 0.000 0.000 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

2989 1986 1275 0 0 0 0 0 0

N.S.

1 0.66 0.43 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.963 3.674 0.000 0.000 0.000 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

692 417 582 1636 0 0 0 0 0

N.S.

1 0.60 0.84 2.36 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.865 1.565 0.810 0.000 0.000 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

410 240 400 928 0 0 0 0 0

N.S.

1 0.59 0.98 2.26 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.740 1.348 0.700 0.000 0.000 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 128 118 460 184 0 0 0 0

N.S.

1 0.75 0.69 2.69 1.08 0.00 0.00 0.00 0.00

time (sec)

N/A 0.557 0.677 0.639 0.313 0.000 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

589 402 357 0 0 0 0 0 0

N.S.

1 0.68 0.61 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.596 0.294 0.000 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 A F F F F F(-2) F(-1)

verified

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

size

1113 721 651 0 0 0 0 0 0

N.S.

1 0.65 0.58 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.998 0.573 0.000 0.000 0.000 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

738 447 325 1528 0 0 0 0 0

N.S.

1 0.61 0.44 2.07 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.274 2.523 1.193 0.000 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 F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

513 314 259 975 0 0 0 0 0

N.S.

1 0.61 0.50 1.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.107 1.583 1.075 0.000 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 F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

410 243 237 612 0 0 0 0 0

N.S.

1 0.59 0.58 1.49 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.783 0.999 1.204 0.000 0.000 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1137 722 597 0 0 0 0 0 0

N.S.

1 0.64 0.53 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.259 3.807 0.000 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1589 918 715 13140 0 0 0 0 0

N.S.

1 0.58 0.45 8.27 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.341 6.256 1.402 0.000 0.000 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1025 614 711 9720 0 0 0 0 0

N.S.

1 0.60 0.69 9.48 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.435 6.275 1.239 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 B F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

641 398 683 5894 0 0 0 0 0

N.S.

1 0.62 1.07 9.20 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.941 6.232 1.248 0.000 0.000 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

35 35 37 33 35 47 0 35 35

N.S.

1 1.00 1.06 0.94 1.00 1.34 0.00 1.00 1.00

time (sec)

N/A 0.317 0.167 7.071 1.933 0.260 0.000 0.425 0.254

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

634 628 0 0 0 0 0 0 0

N.S.

1 0.99 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.081 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

514 506 0 0 0 0 0 0 0

N.S.

1 0.98 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.655 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

390 386 2724 0 0 0 0 0 0

N.S.

1 0.99 6.98 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.260 10.459 0.000 0.000 0.000 0.000 0.000 0.000

Problem 86

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

237 238 246 0 0 0 0 0 0

N.S.

1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.704 0.034 0.000 0.000 0.000 0.000 0.000 0.000

Problem 87

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

35 35 37 33 35 57 34 35 35

N.S.

1 1.00 1.06 0.94 1.00 1.63 0.97 1.00 1.00

time (sec)

N/A 0.335 0.420 12.391 1.011 0.241 9.436 0.419 0.241

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

351 379 305 445 528 441 770 784 0

N.S.

1 1.08 0.87 1.27 1.50 1.26 2.19 2.23 0.00

time (sec)

N/A 1.280 0.421 0.197 0.282 0.269 0.505 0.308 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 275 211 304 353 295 502 491 0

N.S.

1 1.11 0.85 1.23 1.42 1.19 2.02 1.98 0.00

time (sec)

N/A 0.807 0.323 0.198 0.281 0.269 0.357 0.309 0.000

Problem 90

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

148 168 138 178 199 161 267 259 0

N.S.

1 1.14 0.93 1.20 1.34 1.09 1.80 1.75 0.00

time (sec)

N/A 0.438 0.203 0.080 0.279 0.255 0.246 0.308 0.000

Problem 91

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

344 345 322 1566 0 0 0 0 0

N.S.

1 1.00 0.94 4.55 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.916 0.593 1.905 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

358 354 334 954 0 0 0 0 0

N.S.

1 0.99 0.93 2.66 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.523 0.587 2.267 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

202 238 263 535 0 1184 0 0 0

N.S.

1 1.18 1.30 2.65 0.00 5.86 0.00 0.00 0.00

time (sec)

N/A 0.463 0.739 2.562 0.000 3.243 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

257 271 321 908 0 1920 0 0 0

N.S.

1 1.05 1.25 3.53 0.00 7.47 0.00 0.00 0.00

time (sec)

N/A 0.531 0.757 3.434 0.000 16.148 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

360 382 418 1550 0 2839 0 0 0

N.S.

1 1.06 1.16 4.31 0.00 7.89 0.00 0.00 0.00

time (sec)

N/A 0.686 1.069 3.389 0.000 64.657 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

457 497 494 2406 0 3904 0 0 0

N.S.

1 1.09 1.08 5.26 0.00 8.54 0.00 0.00 0.00

time (sec)

N/A 0.906 1.314 3.401 0.000 175.625 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

512 556 463 633 859 676 1263 1337 0

N.S.

1 1.09 0.90 1.24 1.68 1.32 2.47 2.61 0.00

time (sec)

N/A 2.235 0.527 0.366 0.287 0.288 0.670 0.335 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

361 389 307 449 581 449 821 847 0

N.S.

1 1.08 0.85 1.24 1.61 1.24 2.27 2.35 0.00

time (sec)

N/A 1.362 0.519 0.375 0.291 0.275 0.506 0.331 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

223 249 186 273 334 245 449 448 0

N.S.

1 1.12 0.83 1.22 1.50 1.10 2.01 2.01 0.00

time (sec)

N/A 0.735 0.298 0.315 0.292 0.262 0.341 0.295 0.000

Problem 100

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

459 476 457 2438 0 0 0 0 0

N.S.

1 1.04 1.00 5.31 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.169 0.929 2.265 0.000 0.000 0.000 0.000 0.000

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