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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 F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 170 168 272 0 0 0 0 0

N.S.

1 1.00 0.99 1.60 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.618 0.010 0.706 0.000 0.000 0.000 0.000 0.000

Problem 2

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

260 256 240 0 0 0 0 0 0

N.S.

1 0.98 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.935 0.102 0.000 0.000 0.000 0.000 0.000 0.000

Problem 3

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

348 346 322 0 0 0 0 0 0

N.S.

1 0.99 0.93 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.216 0.039 0.000 0.000 0.000 0.000 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

176 202 166 242 230 214 316 0 0

N.S.

1 1.15 0.94 1.38 1.31 1.22 1.80 0.00 0.00

time (sec)

N/A 0.392 0.111 0.312 0.183 0.282 0.304 0.000 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 147 121 174 150 147 190 0 0

N.S.

1 1.19 0.98 1.40 1.21 1.19 1.53 0.00 0.00

time (sec)

N/A 0.301 0.079 0.323 0.180 0.252 0.229 0.000 0.000

Problem 6

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

97 106 91 84 82 87 99 122 78

N.S.

1 1.09 0.94 0.87 0.85 0.90 1.02 1.26 0.80

time (sec)

N/A 0.256 0.032 0.016 0.182 0.255 0.173 0.345 2.758

Problem 7

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 31 30 43 26 41 28

N.S.

1 1.00 1.00 1.03 1.00 1.43 0.87 1.37 0.93

time (sec)

N/A 0.157 0.007 0.013 0.189 0.250 0.070 0.275 0.032

Problem 8

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

187 187 175 279 0 0 0 0 0

N.S.

1 1.00 0.94 1.49 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.641 0.043 0.538 0.000 0.000 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 79 174 103 253 0 232 0

N.S.

1 1.00 0.96 2.12 1.26 3.09 0.00 2.83 0.00

time (sec)

N/A 0.246 0.071 0.961 0.196 0.270 0.000 0.470 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 129 166 273 158 566 0 0 0

N.S.

1 1.01 1.30 2.13 1.23 4.42 0.00 0.00 0.00

time (sec)

N/A 0.287 0.247 0.573 0.192 0.319 0.000 0.000 0.000

Problem 11

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

183 199 205 510 0 977 0 0 0

N.S.

1 1.09 1.12 2.79 0.00 5.34 0.00 0.00 0.00

time (sec)

N/A 0.353 0.300 0.406 0.000 0.619 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

368 387 354 526 590 475 743 0 0

N.S.

1 1.05 0.96 1.43 1.60 1.29 2.02 0.00 0.00

time (sec)

N/A 1.050 0.357 0.444 0.213 0.269 0.450 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 262 248 364 378 319 454 0 0

N.S.

1 1.10 1.04 1.52 1.58 1.33 1.90 0.00 0.00

time (sec)

N/A 0.782 0.225 0.455 0.194 0.264 0.326 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 162 142 183 219 183 233 0 0

N.S.

1 1.16 1.01 1.31 1.56 1.31 1.66 0.00 0.00

time (sec)

N/A 0.577 1.148 0.306 0.193 0.262 0.234 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 50 74 72 72 96 82 111 0

N.S.

1 1.09 1.61 1.57 1.57 2.09 1.78 2.41 0.00

time (sec)

N/A 0.285 0.033 0.000 0.203 0.256 0.099 0.363 0.000

Problem 16

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

291 285 273 0 0 0 0 0 0

N.S.

1 0.98 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.044 0.178 0.000 0.000 0.000 0.000 0.000 0.000

Problem 17

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

263 239 191 525 0 0 0 0 0

N.S.

1 0.91 0.73 2.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.996 0.145 0.543 0.000 0.000 0.000 0.000 0.000

Problem 18

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

349 331 270 815 0 0 0 0 0

N.S.

1 0.95 0.77 2.34 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.350 0.443 0.653 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 A F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

394 378 305 394 0 0 0 0 0

N.S.

1 0.96 0.77 1.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.423 0.535 1.838 0.000 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 F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 233 188 254 0 0 0 0 0

N.S.

1 0.95 0.77 1.04 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.929 0.345 1.003 0.000 0.000 0.000 0.000 0.000

Problem 21

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

116 110 98 120 0 0 0 0 0

N.S.

1 0.95 0.84 1.03 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.566 0.148 0.589 0.000 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 F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 49 45 56 0 0 0 0 0

N.S.

1 0.91 0.83 1.04 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.406 0.043 0.000 0.000 0.000 0.000 0.000 0.000

Problem 23

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 0.212 0.162 0.366 0.257 0.256 0.893 0.287 2.669

Problem 24

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 0.209 0.317 0.277 0.265 0.241 1.707 0.861 2.630

Problem 25

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

359 359 288 616 0 0 0 0 0

N.S.

1 1.00 0.80 1.72 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.847 1.661 0.973 0.000 0.000 0.000 0.000 0.000

Problem 26

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

180 180 150 272 0 0 0 0 0

N.S.

1 1.00 0.83 1.51 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.534 0.890 0.556 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 89 71 118 0 0 0 0 0

N.S.

1 1.05 0.84 1.39 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.598 0.161 0.001 0.000 0.000 0.000 0.000 0.000

Problem 28

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 18 746 51 17 20 20

N.S.

1 1.00 1.11 1.00 41.44 2.83 0.94 1.11 1.11

time (sec)

N/A 0.202 5.834 0.308 0.829 0.262 1.609 0.318 2.911

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 1050 92 19 20 20

N.S.

1 1.00 1.11 1.00 58.33 5.11 1.06 1.11 1.11

time (sec)

N/A 0.211 4.551 0.353 1.221 0.265 5.726 1.299 2.675

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 18 271 32 17 20 20

N.S.

1 1.00 1.11 1.00 15.06 1.78 0.94 1.11 1.11

time (sec)

N/A 0.545 5.324 1.562 0.852 0.281 5.170 0.383 2.810

Problem 31

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

179 179 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.329 0.000 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 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 0.197 0.302 0.948 0.239 0.251 0.901 0.281 2.899

Problem 33

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 18 607 34 17 20 20

N.S.

1 1.00 1.11 1.00 33.72 1.89 0.94 1.11 1.11

time (sec)

N/A 0.205 0.669 0.928 0.961 0.277 14.414 0.297 2.650

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

640 363 410 1309 0 0 0 0 0

N.S.

1 0.57 0.64 2.05 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.038 0.843 0.856 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 B F(-2) F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

431 257 301 913 0 0 0 0 0

N.S.

1 0.60 0.70 2.12 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.835 0.769 0.715 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 B F(-2) F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

227 136 208 582 0 0 0 0 0

N.S.

1 0.60 0.92 2.56 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.528 0.959 0.781 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 C A F F F F(-2) F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

664 461 1358 747 0 0 0 0 0

N.S.

1 0.69 2.05 1.12 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.163 4.933 0.771 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 C B F F F F(-2) F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

781 572 1384 1701 0 0 0 0 0

N.S.

1 0.73 1.77 2.18 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.737 7.674 0.817 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 B F(-2) F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

918 488 536 2079 0 0 0 0 0

N.S.

1 0.53 0.58 2.26 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.267 1.604 0.875 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 B F(-2) F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

651 359 416 1568 0 0 0 0 0

N.S.

1 0.55 0.64 2.41 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.005 1.163 0.818 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 B F(-2) F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

353 188 289 1065 0 0 0 0 0

N.S.

1 0.53 0.82 3.02 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.597 0.633 0.828 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 C A F(-2) F F F(-2) F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

984 641 2869 1557 0 0 0 0 0

N.S.

1 0.65 2.92 1.58 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.241 12.244 0.858 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 B F(-2) F F(-1) F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1228 617 810 2884 0 0 0 0 0

N.S.

1 0.50 0.66 2.35 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.421 2.221 1.054 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 B F(-2) F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

901 470 555 2309 0 0 0 0 0

N.S.

1 0.52 0.62 2.56 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.194 1.726 1.026 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 B F(-2) F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

494 249 390 1679 0 0 0 0 0

N.S.

1 0.50 0.79 3.40 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.691 0.887 0.997 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 C B F(-2) F F F(-2) F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

1536 945 7168 3499 0 0 0 0 0

N.S.

1 0.62 4.67 2.28 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.731 23.148 0.937 0.000 0.000 0.000 0.000 0.000

Problem 47

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

430 256 304 785 0 0 0 0 0

N.S.

1 0.60 0.71 1.83 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.860 1.015 0.930 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 B F(-2) F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

258 158 233 484 0 0 0 0 0

N.S.

1 0.61 0.90 1.88 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.686 0.710 0.758 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 B A F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 84 158 227 87 0 0 0 0

N.S.

1 0.70 1.32 1.89 0.72 0.00 0.00 0.00 0.00

time (sec)

N/A 0.471 0.348 0.830 0.211 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 F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 76 77 28 0 0 0 0

N.S.

1 1.00 1.62 1.64 0.60 0.00 0.00 0.00 0.00

time (sec)

N/A 0.217 0.034 0.375 0.194 0.000 0.000 0.000 0.000

Problem 51

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

325 238 240 529 0 0 0 0 0

N.S.

1 0.73 0.74 1.63 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.009 0.352 0.691 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 B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

444 327 251 1770 0 0 0 0 0

N.S.

1 0.74 0.57 3.99 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.350 0.407 0.846 0.000 0.000 0.000 0.000 0.000

Problem 53

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

34 34 36 32 34 34 0 34 34

N.S.

1 1.00 1.06 0.94 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.351 0.103 2.496 0.923 0.263 0.000 73.328 2.651

Problem 54

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

438 426 397 0 0 0 0 0 0

N.S.

1 0.97 0.91 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.712 0.141 0.000 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 A F F F F F F(-1)

verified

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

size

332 328 304 0 0 0 0 0 0

N.S.

1 0.99 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.281 0.154 0.000 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 A F F F F F F(-1)

verified

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

size

197 196 206 0 0 0 0 0 0

N.S.

1 0.99 1.05 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.700 0.016 0.000 0.000 0.000 0.000 0.000 0.000

Problem 57

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

34 34 36 32 34 51 31 34 34

N.S.

1 1.00 1.06 0.94 1.00 1.50 0.91 1.00 1.00

time (sec)

N/A 0.377 0.294 1.941 0.806 0.266 7.693 0.910 2.547

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 158 95 200 318 110 255 162 0

N.S.

1 1.21 0.73 1.53 2.43 0.84 1.95 1.24 0.00

time (sec)

N/A 0.383 0.063 0.053 0.183 0.257 0.323 0.574 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 117 74 130 210 91 170 131 0

N.S.

1 1.30 0.82 1.44 2.33 1.01 1.89 1.46 0.00

time (sec)

N/A 0.325 0.043 0.015 0.184 0.248 0.248 0.430 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 82 60 74 149 75 104 111 0

N.S.

1 1.08 0.79 0.97 1.96 0.99 1.37 1.46 0.00

time (sec)

N/A 0.292 0.031 0.012 0.191 0.251 0.181 0.286 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 32 78 31 30 57 46 92 76

N.S.

1 0.94 2.29 0.91 0.88 1.68 1.35 2.71 2.24

time (sec)

N/A 0.213 0.158 0.013 0.179 0.246 0.078 0.303 2.933

Problem 62

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

131 131 153 388 0 0 0 0 0

N.S.

1 1.00 1.17 2.96 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.596 0.011 0.658 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 A B B F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 61 57 68 111 167 0 110 0

N.S.

1 1.07 1.00 1.19 1.95 2.93 0.00 1.93 0.00

time (sec)

N/A 0.291 0.030 0.242 0.179 0.273 0.000 0.355 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 99 110 103 146 236 0 199 0

N.S.

1 1.08 1.20 1.12 1.59 2.57 0.00 2.16 0.00

time (sec)

N/A 0.316 0.163 0.017 0.185 0.275 0.000 0.360 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 148 149 203 284 285 0 381 0

N.S.

1 1.15 1.16 1.57 2.20 2.21 0.00 2.95 0.00

time (sec)

N/A 0.356 0.189 0.015 0.185 0.289 0.000 0.376 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 200 179 345 357 343 0 709 0

N.S.

1 1.20 1.07 2.07 2.14 2.05 0.00 4.25 0.00

time (sec)

N/A 0.408 0.181 0.016 0.192 0.300 0.000 0.357 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

331 305 145 293 0 182 366 0 0

N.S.

1 0.92 0.44 0.89 0.00 0.55 1.11 0.00 0.00

time (sec)

N/A 0.728 0.501 0.204 0.000 0.265 0.441 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 204 107 190 0 146 243 0 0

N.S.

1 0.97 0.51 0.90 0.00 0.69 1.15 0.00 0.00

time (sec)

N/A 0.604 0.411 0.167 0.000 0.252 0.300 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 120 79 113 0 114 138 0 0

N.S.

1 0.95 0.63 0.90 0.00 0.90 1.10 0.00 0.00

time (sec)

N/A 0.497 0.226 0.127 0.000 0.246 0.226 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 49 47 46 0 88 63 0 0

N.S.

1 1.09 1.04 1.02 0.00 1.96 1.40 0.00 0.00

time (sec)

N/A 0.300 0.019 0.081 0.000 0.270 0.100 0.000 0.000

Problem 71

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

205 207 251 0 0 0 0 0 0

N.S.

1 1.01 1.22 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.826 0.026 0.000 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 A F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

178 174 178 206 0 0 0 0 0

N.S.

1 0.98 1.00 1.16 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.814 0.089 0.250 0.000 0.000 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

235 237 279 374 0 0 0 0 0

N.S.

1 1.01 1.19 1.59 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.067 0.089 0.461 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 F F F F F(-1)

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

478 696 1830 764 0 0 0 0 0

N.S.

1 1.46 3.83 1.60 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.633 10.001 0.408 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 A F A A F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

355 317 175 297 0 225 432 0 0

N.S.

1 0.89 0.49 0.84 0.00 0.63 1.22 0.00 0.00

time (sec)

N/A 0.681 0.510 0.199 0.000 0.256 0.420 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

203 191 129 169 0 180 248 0 0

N.S.

1 0.94 0.64 0.83 0.00 0.89 1.22 0.00 0.00

time (sec)

N/A 0.581 0.281 0.120 0.000 0.261 0.292 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 74 70 67 0 139 109 0 0

N.S.

1 0.95 0.90 0.86 0.00 1.78 1.40 0.00 0.00

time (sec)

N/A 0.372 0.022 0.093 0.000 0.295 0.142 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 F(-1)

verified

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

size

275 285 346 0 0 0 0 0 0

N.S.

1 1.04 1.26 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.057 0.031 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 F F F F F F(-1)

verified

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

size

268 246 259 0 0 0 0 0 0

N.S.

1 0.92 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.129 0.097 0.000 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 F F F F F F(-1)

verified

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

size

514 446 524 0 0 0 0 0 0

N.S.

1 0.87 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.127 0.160 0.000 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 F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 52 44 49 0 0 0 0 0

N.S.

1 0.87 0.73 0.82 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.581 0.233 0.244 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 A F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 28 30 27 0 0 0 0 0

N.S.

1 0.93 1.00 0.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.410 0.127 0.096 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 F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 0 0 0 0 0

N.S.

1 1.00 1.00 1.09 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.269 0.011 0.080 0.000 0.000 0.000 0.000 0.000

Problem 84

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

12 12 14 12 14 14 10 14 14

N.S.

1 1.00 1.17 1.00 1.17 1.17 0.83 1.17 1.17

time (sec)

N/A 0.255 0.233 0.983 0.246 0.242 0.316 0.345 2.726

Problem 85

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

154 137 83 146 0 0 0 0 0

N.S.

1 0.89 0.54 0.95 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.421 0.770 0.279 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 A F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 77 62 73 0 0 0 0 0

N.S.

1 0.92 0.74 0.87 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.349 0.186 0.171 0.000 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 F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 35 35 34 0 0 0 0 0

N.S.

1 0.92 0.92 0.89 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.367 0.069 0.083 0.000 0.000 0.000 0.000 0.000

Problem 88

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

12 12 14 12 527 14 12 14 14

N.S.

1 1.00 1.17 1.00 43.92 1.17 1.00 1.17 1.17

time (sec)

N/A 0.258 2.129 0.846 0.948 0.244 0.390 0.340 2.707

Problem 89

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

257 225 110 215 0 0 0 0 0

N.S.

1 0.88 0.43 0.84 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.680 0.330 0.146 0.000 0.000 0.000 0.000 0.000

Problem 90

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

147 131 117 107 0 0 0 0 0

N.S.

1 0.89 0.80 0.73 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.464 0.135 0.131 0.000 0.000 0.000 0.000 0.000

Problem 91

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

63 57 53 51 0 0 0 0 0

N.S.

1 0.90 0.84 0.81 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.435 0.033 0.091 0.000 0.000 0.000 0.000 0.000

Problem 92

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

12 12 14 12 3273 14 12 14 14

N.S.

1 1.00 1.17 1.00 272.75 1.17 1.00 1.17 1.17

time (sec)

N/A 0.255 1.587 0.835 15.191 0.246 0.472 0.330 2.835

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

16 16 18 16 18 18 15 0 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 0.00 1.12

time (sec)

N/A 0.283 0.344 0.322 0.575 0.272 12.848 0.000 2.820

Problem 94

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

545 525 345 0 0 0 0 0 0

N.S.

1 0.96 0.63 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.140 0.664 0.000 0.000 0.000 0.000 0.000 0.000

Problem 95

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

267 262 228 0 0 0 0 0 0

N.S.

1 0.98 0.85 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.695 0.135 0.000 0.000 0.000 0.000 0.000 0.000

Problem 96

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

128 131 109 0 0 0 0 0 0

N.S.

1 1.02 0.85 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.411 0.087 0.000 0.000 0.000 0.000 0.000 0.000

Problem 97

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 16 18 18 14 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.88 1.12 1.12

time (sec)

N/A 0.281 0.212 0.310 0.595 0.257 0.573 1.398 2.662

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

496 525 656 0 0 0 0 0 0

N.S.

1 1.06 1.32 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.860 2.525 0.000 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

259 284 250 0 0 0 0 0 0

N.S.

1 1.10 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.048 2.267 0.000 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

115 121 111 0 0 0 0 0 0

N.S.

1 1.05 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.623 0.133 0.000 0.000 0.000 0.000 0.000 0.000

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