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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 B B B F(-1) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 158 146 1004 676 569 0 4462 1046

N.S.

1 0.84 0.78 5.34 3.60 3.03 0.00 23.73 5.56

time (sec)

N/A 0.310 0.079 17.529 0.207 0.337 0.000 1.060 1.378

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 134 124 755 479 426 0 3034 588

N.S.

1 0.86 0.79 4.84 3.07 2.73 0.00 19.45 3.77

time (sec)

N/A 0.294 0.072 7.215 0.215 0.317 0.000 0.813 1.142

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 110 103 528 309 296 0 1866 303

N.S.

1 0.89 0.83 4.26 2.49 2.39 0.00 15.05 2.44

time (sec)

N/A 0.272 0.041 2.894 0.197 0.281 0.000 0.810 0.962

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 82 73 276 156 160 352 880 134

N.S.

1 0.95 0.85 3.21 1.81 1.86 4.09 10.23 1.56

time (sec)

N/A 0.247 0.029 1.066 0.191 0.274 57.622 0.485 0.897

Problem 5

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

84 84 101 0 0 0 0 0 0

N.S.

1 1.00 1.20 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.504 0.037 0.000 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 A B A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 115 131 137 103 0 88 112

N.S.

1 1.00 1.72 1.96 2.04 1.54 0.00 1.31 1.67

time (sec)

N/A 0.228 0.043 3.125 0.189 0.280 0.000 0.758 2.516

Problem 7

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

151 142 114 271 259 265 2139 224 222

N.S.

1 0.94 0.75 1.79 1.72 1.75 14.17 1.48 1.47

time (sec)

N/A 0.322 0.101 7.393 0.205 0.268 100.059 0.782 1.292

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 167 145 440 432 482 0 381 349

N.S.

1 0.91 0.79 2.40 2.36 2.63 0.00 2.08 1.91

time (sec)

N/A 0.343 0.112 15.869 0.200 0.276 0.000 0.663 1.622

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 190 162 1043 651 733 0 541 603

N.S.

1 0.88 0.75 4.85 3.03 3.41 0.00 2.52 2.80

time (sec)

N/A 0.379 0.136 42.201 0.208 0.308 0.000 0.882 1.812

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

396 461 535 0 2945 0 0 0 0

N.S.

1 1.16 1.35 0.00 7.44 0.00 0.00 0.00 0.00

time (sec)

N/A 0.982 0.326 0.000 0.729 0.000 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

335 386 411 0 2175 0 0 0 0

N.S.

1 1.15 1.23 0.00 6.49 0.00 0.00 0.00 0.00

time (sec)

N/A 0.814 0.226 0.000 0.718 0.000 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

274 309 303 0 1501 0 0 0 0

N.S.

1 1.13 1.11 0.00 5.48 0.00 0.00 0.00 0.00

time (sec)

N/A 0.666 0.164 0.000 0.690 0.000 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

196 225 215 0 828 0 0 0 0

N.S.

1 1.15 1.10 0.00 4.22 0.00 0.00 0.00 0.00

time (sec)

N/A 0.478 0.136 0.000 0.697 0.000 0.000 0.000 0.000

Problem 14

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 Yes N/A TBD TBD TBD TBD TBD

size

138 127 537 0 0 0 0 0 0

N.S.

1 0.92 3.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.459 0.814 0.000 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 C B B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 110 330 296 430 258 0 174 238

N.S.

1 0.81 2.43 2.18 3.16 1.90 0.00 1.28 1.75

time (sec)

N/A 0.299 0.331 3.136 0.216 0.272 0.000 0.989 2.608

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

288 224 463 672 861 651 0 478 506

N.S.

1 0.78 1.61 2.33 2.99 2.26 0.00 1.66 1.76

time (sec)

N/A 0.404 0.288 7.388 0.246 0.287 0.000 1.039 3.078

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

448 345 612 1146 1432 1164 0 840 1038

N.S.

1 0.77 1.37 2.56 3.20 2.60 0.00 1.88 2.32

time (sec)

N/A 0.505 0.415 16.000 0.287 0.317 0.000 1.321 4.562

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

615 473 700 2326 2136 1762 0 1206 1769

N.S.

1 0.77 1.14 3.78 3.47 2.87 0.00 1.96 2.88

time (sec)

N/A 0.580 0.556 42.228 0.336 0.332 0.000 1.694 6.460

Problem 19

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 35 37 53 95 37 37

N.S.

1 1.00 1.06 1.00 1.06 1.51 2.71 1.06 1.06

time (sec)

N/A 0.194 0.408 0.053 0.431 0.253 34.232 27.573 0.758

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

33 33 35 33 35 35 56 35 35

N.S.

1 1.00 1.06 1.00 1.06 1.06 1.70 1.06 1.06

time (sec)

N/A 0.185 0.128 0.099 0.441 0.265 16.309 16.773 0.672

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

35 35 37 35 37 43 61 37 37

N.S.

1 1.00 1.06 1.00 1.06 1.23 1.74 1.06 1.06

time (sec)

N/A 0.199 0.151 0.210 0.342 0.249 16.193 9.085 0.617

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

94 94 94 0 0 62 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.66 0.00 0.00 0.00

time (sec)

N/A 0.314 0.144 0.000 0.000 0.262 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

197 185 172 0 0 149 0 0 0

N.S.

1 0.94 0.87 0.00 0.00 0.76 0.00 0.00 0.00

time (sec)

N/A 0.456 0.282 0.000 0.000 0.280 0.000 0.000 0.000

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

35 35 37 35 329 81 187 37 37

N.S.

1 1.00 1.06 1.00 9.40 2.31 5.34 1.06 1.06

time (sec)

N/A 0.200 0.429 0.053 0.478 0.273 44.805 1.456 1.310

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

33 33 35 33 251 63 117 35 35

N.S.

1 1.00 1.06 1.00 7.61 1.91 3.55 1.06 1.06

time (sec)

N/A 0.188 0.463 0.018 0.488 0.264 58.784 0.789 0.835

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

35 35 37 35 186 85 128 37 37

N.S.

1 1.00 1.06 1.00 5.31 2.43 3.66 1.06 1.06

time (sec)

N/A 0.200 0.278 0.076 0.357 0.282 130.893 0.681 0.701

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

153 141 146 0 0 274 0 0 0

N.S.

1 0.92 0.95 0.00 0.00 1.79 0.00 0.00 0.00

time (sec)

N/A 0.380 0.161 0.000 0.000 0.273 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

314 276 254 0 0 755 0 0 0

N.S.

1 0.88 0.81 0.00 0.00 2.40 0.00 0.00 0.00

time (sec)

N/A 0.528 0.400 0.000 0.000 0.291 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 157 146 864 676 572 0 1876 1045

N.S.

1 0.84 0.78 4.60 3.60 3.04 0.00 9.98 5.56

time (sec)

N/A 0.321 0.072 17.540 0.207 0.327 0.000 1.090 1.314

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 133 124 652 479 429 0 1402 588

N.S.

1 0.85 0.79 4.18 3.07 2.75 0.00 8.99 3.77

time (sec)

N/A 0.291 0.060 7.138 0.199 0.297 0.000 0.836 1.141

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 109 101 463 309 297 0 990 303

N.S.

1 0.88 0.81 3.73 2.49 2.40 0.00 7.98 2.44

time (sec)

N/A 0.273 0.040 2.921 0.191 0.287 0.000 0.629 1.023

Problem 32

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

86 81 74 250 156 162 382 580 134

N.S.

1 0.94 0.86 2.91 1.81 1.88 4.44 6.74 1.56

time (sec)

N/A 0.250 0.026 1.069 0.195 0.276 55.240 0.441 0.871

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

80 85 101 0 0 0 0 566 0

N.S.

1 1.06 1.26 0.00 0.00 0.00 0.00 7.08 0.00

time (sec)

N/A 0.518 0.031 0.000 0.000 0.000 0.000 57.494 0.000

Problem 34

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

102 77 114 81 136 105 0 91 113

N.S.

1 0.75 1.12 0.79 1.33 1.03 0.00 0.89 1.11

time (sec)

N/A 0.211 0.040 3.108 0.194 0.271 0.000 0.598 1.064

Problem 35

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

151 142 115 272 259 266 2103 207 221

N.S.

1 0.94 0.76 1.80 1.72 1.76 13.93 1.37 1.46

time (sec)

N/A 0.317 0.089 7.432 0.194 0.276 127.349 0.927 1.265

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 166 146 440 433 483 0 405 349

N.S.

1 0.91 0.80 2.40 2.37 2.64 0.00 2.21 1.91

time (sec)

N/A 0.351 0.100 16.009 0.205 0.280 0.000 0.676 1.623

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 190 162 1043 652 735 0 684 603

N.S.

1 0.88 0.75 4.85 3.03 3.42 0.00 3.18 2.80

time (sec)

N/A 0.375 0.129 42.246 0.209 0.306 0.000 0.848 1.902

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

544 720 533 0 2880 0 0 0 0

N.S.

1 1.32 0.98 0.00 5.29 0.00 0.00 0.00 0.00

time (sec)

N/A 1.849 0.311 0.000 0.715 0.000 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

454 535 409 0 2129 0 0 0 0

N.S.

1 1.18 0.90 0.00 4.69 0.00 0.00 0.00 0.00

time (sec)

N/A 1.313 0.226 0.000 0.715 0.000 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

361 376 303 0 1473 0 0 0 0

N.S.

1 1.04 0.84 0.00 4.08 0.00 0.00 0.00 0.00

time (sec)

N/A 0.933 0.154 0.000 0.706 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

220 239 216 0 825 0 0 0 0

N.S.

1 1.09 0.98 0.00 3.75 0.00 0.00 0.00 0.00

time (sec)

N/A 0.595 0.124 0.000 0.677 0.000 0.000 0.000 0.000

Problem 42

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

137 128 268 0 0 0 0 0 0

N.S.

1 0.93 1.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.415 0.527 0.000 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 C A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 119 331 294 428 263 0 175 237

N.S.

1 0.73 2.03 1.80 2.63 1.61 0.00 1.07 1.45

time (sec)

N/A 0.265 0.257 3.121 0.200 0.277 0.000 0.987 2.422

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

317 240 464 672 861 654 0 407 505

N.S.

1 0.76 1.46 2.12 2.72 2.06 0.00 1.28 1.59

time (sec)

N/A 0.341 0.258 7.409 0.240 0.285 0.000 0.967 2.183

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

429 331 612 1146 1435 1167 0 776 1040

N.S.

1 0.77 1.43 2.67 3.34 2.72 0.00 1.81 2.42

time (sec)

N/A 0.464 0.382 16.052 0.277 0.294 0.000 1.308 3.823

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

536 399 700 2326 2138 1768 0 1265 1765

N.S.

1 0.74 1.31 4.34 3.99 3.30 0.00 2.36 3.29

time (sec)

N/A 0.499 0.510 42.183 0.332 0.317 0.000 1.685 6.344

Problem 47

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 35 37 53 95 37 37

N.S.

1 1.00 1.06 1.00 1.06 1.51 2.71 1.06 1.06

time (sec)

N/A 0.196 0.165 0.053 0.437 0.257 24.070 27.328 0.703

Problem 48

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

33 33 35 33 35 35 56 35 35

N.S.

1 1.00 1.06 1.00 1.06 1.06 1.70 1.06 1.06

time (sec)

N/A 0.184 0.117 0.097 0.428 0.265 14.064 15.913 0.670

Problem 49

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 35 37 43 61 37 37

N.S.

1 1.00 1.06 1.00 1.06 1.23 1.74 1.06 1.06

time (sec)

N/A 0.201 0.217 0.205 0.329 0.270 18.380 9.260 0.648

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

96 96 96 0 0 62 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.65 0.00 0.00 0.00

time (sec)

N/A 0.304 0.125 0.000 0.000 0.269 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

199 187 174 0 0 147 0 0 0

N.S.

1 0.94 0.87 0.00 0.00 0.74 0.00 0.00 0.00

time (sec)

N/A 0.398 0.260 0.000 0.000 0.261 0.000 0.000 0.000

Problem 52

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 35 329 81 187 37 37

N.S.

1 1.00 1.06 1.00 9.40 2.31 5.34 1.06 1.06

time (sec)

N/A 0.201 0.429 0.054 0.474 0.263 45.489 0.997 1.316

Problem 53

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

33 33 35 33 251 63 117 35 35

N.S.

1 1.00 1.06 1.00 7.61 1.91 3.55 1.06 1.06

time (sec)

N/A 0.184 0.470 0.019 0.484 0.261 58.587 0.691 0.894

Problem 54

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 35 186 85 128 37 37

N.S.

1 1.00 1.06 1.00 5.31 2.43 3.66 1.06 1.06

time (sec)

N/A 0.203 0.256 0.074 0.366 0.260 139.335 0.628 0.757

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

154 142 180 0 0 291 0 146 0

N.S.

1 0.92 1.17 0.00 0.00 1.89 0.00 0.95 0.00

time (sec)

N/A 0.354 0.145 0.000 0.000 0.278 0.000 0.362 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

256 342 288 0 0 770 0 325 0

N.S.

1 1.34 1.12 0.00 0.00 3.01 0.00 1.27 0.00

time (sec)

N/A 0.613 0.347 0.000 0.000 0.281 0.000 0.420 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

364 347 285 1160 631 736 0 11996 1433

N.S.

1 0.95 0.78 3.19 1.73 2.02 0.00 32.96 3.94

time (sec)

N/A 0.671 0.390 5.459 0.201 0.663 0.000 1.674 1.659

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

235 227 219 976 443 521 0 6772 766

N.S.

1 0.97 0.93 4.15 1.89 2.22 0.00 28.82 3.26

time (sec)

N/A 0.478 0.184 2.960 0.196 0.414 0.000 1.050 1.405

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 159 146 617 282 334 0 3408 371

N.S.

1 1.01 0.93 3.93 1.80 2.13 0.00 21.71 2.36

time (sec)

N/A 0.355 0.094 1.631 0.198 0.329 0.000 0.721 1.117

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 127 120 366 150 179 493 1215 153

N.S.

1 1.10 1.04 3.18 1.30 1.56 4.29 10.57 1.33

time (sec)

N/A 0.303 0.081 0.814 0.184 0.272 59.226 0.566 0.933

Problem 61

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

56 56 56 82 52 63 150 243 52

N.S.

1 1.00 1.00 1.46 0.93 1.12 2.68 4.34 0.93

time (sec)

N/A 0.188 0.008 0.218 0.182 0.292 1.388 0.332 0.694

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

147 154 122 0 0 0 0 0 0

N.S.

1 1.05 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.471 0.046 0.000 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 B A B F(-1) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 141 109 364 142 294 0 461 140

N.S.

1 1.55 1.20 4.00 1.56 3.23 0.00 5.07 1.54

time (sec)

N/A 0.288 0.089 3.514 0.191 3.144 0.000 0.546 1.365

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

190 190 173 1376 355 1175 0 2994 430

N.S.

1 1.00 0.91 7.24 1.87 6.18 0.00 15.76 2.26

time (sec)

N/A 0.421 0.296 14.207 0.202 45.636 0.000 0.865 3.156

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

283 274 264 3257 852 0 0 9692 1182

N.S.

1 0.97 0.93 11.51 3.01 0.00 0.00 34.25 4.18

time (sec)

N/A 0.575 0.424 41.680 0.237 0.000 0.000 0.852 5.886

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

388 371 359 5206 1761 0 0 21743 2569

N.S.

1 0.96 0.93 13.42 4.54 0.00 0.00 56.04 6.62

time (sec)

N/A 0.763 0.613 256.759 0.313 0.000 0.000 1.213 10.342

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

923 1100 757 0 2651 0 0 0 0

N.S.

1 1.19 0.82 0.00 2.87 0.00 0.00 0.00 0.00

time (sec)

N/A 1.615 0.662 0.000 0.712 0.000 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

565 706 506 0 1659 0 0 0 0

N.S.

1 1.25 0.90 0.00 2.94 0.00 0.00 0.00 0.00

time (sec)

N/A 1.159 0.361 0.000 0.689 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 B F F(-1) F F(-1)

verified

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

size

290 410 362 0 899 0 0 0 0

N.S.

1 1.41 1.25 0.00 3.10 0.00 0.00 0.00 0.00

time (sec)

N/A 0.782 0.203 0.000 0.682 0.000 0.000 0.000 0.000

Problem 70

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

135 128 226 0 0 0 0 0 0

N.S.

1 0.95 1.67 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.604 0.113 0.000 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 B F F F F(-1) F F(-1)

verified

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

size

297 367 1441 0 0 0 0 0 0

N.S.

1 1.24 4.85 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.716 0.304 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 B F F F F(-1) F F(-1)

verified

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

size

206 220 418 0 0 0 0 0 0

N.S.

1 1.07 2.03 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.454 0.280 0.000 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 F F F F(-1) F F(-1)

verified

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

size

389 517 615 0 0 0 0 0 0

N.S.

1 1.33 1.58 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.991 0.809 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(-1) F F(-1)

verified

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

size

747 909 918 0 0 0 0 0 0

N.S.

1 1.22 1.23 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.497 1.627 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 F F F F(-1) F F(-1)

verified

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

size

1208 1429 1329 0 0 0 0 0 0

N.S.

1 1.18 1.10 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.178 3.893 0.000 0.000 0.000 0.000 0.000 0.000

Problem 76

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

32 32 34 32 34 43 31 34 34

N.S.

1 1.00 1.06 1.00 1.06 1.34 0.97 1.06 1.06

time (sec)

N/A 0.188 0.170 0.055 0.434 0.279 28.897 26.492 0.723

Problem 77

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

30 30 32 30 32 32 29 32 32

N.S.

1 1.00 1.07 1.00 1.07 1.07 0.97 1.07 1.07

time (sec)

N/A 0.182 0.126 0.095 0.430 0.254 16.379 16.024 0.667

Problem 78

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

24 24 26 24 26 26 20 26 26

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.83 1.08 1.08

time (sec)

N/A 0.164 0.014 0.065 0.328 0.260 4.036 11.363 0.589

Problem 79

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

32 32 34 32 34 39 0 34 34

N.S.

1 1.00 1.06 1.00 1.06 1.22 0.00 1.06 1.06

time (sec)

N/A 0.198 0.557 0.213 0.336 0.262 0.000 17.042 0.656

Problem 80

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

32 32 34 32 34 63 0 34 34

N.S.

1 1.00 1.06 1.00 1.06 1.97 0.00 1.06 1.06

time (sec)

N/A 0.193 0.529 0.073 0.336 0.251 0.000 26.964 0.690

Problem 81

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

32 32 34 32 34 87 0 34 34

N.S.

1 1.00 1.06 1.00 1.06 2.72 0.00 1.06 1.06

time (sec)

N/A 0.195 5.458 0.075 0.356 0.263 0.000 35.221 0.687

Problem 82

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

32 32 34 32 342 71 32 34 34

N.S.

1 1.00 1.06 1.00 10.69 2.22 1.00 1.06 1.06

time (sec)

N/A 0.192 0.437 0.056 0.496 0.264 51.515 1.117 1.346

Problem 83

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

30 30 32 30 249 60 31 32 32

N.S.

1 1.00 1.07 1.00 8.30 2.00 1.03 1.07 1.07

time (sec)

N/A 0.181 0.325 0.017 0.514 0.263 60.304 0.777 0.823

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

24 24 26 24 195 54 22 26 26

N.S.

1 1.00 1.08 1.00 8.12 2.25 0.92 1.08 1.08

time (sec)

N/A 0.164 0.276 0.089 0.362 0.264 22.704 1.022 0.618

Problem 85

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

32 32 34 32 500 79 32 34 34

N.S.

1 1.00 1.06 1.00 15.62 2.47 1.00 1.06 1.06

time (sec)

N/A 0.194 0.587 0.074 0.378 0.258 146.187 1.176 0.783

Problem 86

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

32 32 34 32 752 120 0 34 34

N.S.

1 1.00 1.06 1.00 23.50 3.75 0.00 1.06 1.06

time (sec)

N/A 0.190 1.114 0.077 0.385 0.264 0.000 1.344 1.018

Problem 87

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

32 32 34 32 1001 161 0 34 34

N.S.

1 1.00 1.06 1.00 31.28 5.03 0.00 1.06 1.06

time (sec)

N/A 0.189 18.026 0.078 0.393 0.267 0.000 2.181 2.173

Problem 88

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

180 154 142 444 623 431 969 4036 1009

N.S.

1 0.86 0.79 2.47 3.46 2.39 5.38 22.42 5.61

time (sec)

N/A 0.312 0.072 1.115 0.206 0.305 3.516 0.531 1.470

Problem 89

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

149 130 120 315 439 318 706 2776 566

N.S.

1 0.87 0.81 2.11 2.95 2.13 4.74 18.63 3.80

time (sec)

N/A 0.288 0.064 0.883 0.204 0.283 2.043 0.447 1.254

Problem 90

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

118 106 99 207 280 222 491 1742 290

N.S.

1 0.90 0.84 1.75 2.37 1.88 4.16 14.76 2.46

time (sec)

N/A 0.267 0.040 0.700 0.213 0.263 1.314 0.422 1.127

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

81 78 69 109 144 125 253 869 126

N.S.

1 0.96 0.85 1.35 1.78 1.54 3.12 10.73 1.56

time (sec)

N/A 0.236 0.026 0.553 0.195 0.277 0.869 0.375 0.991

Problem 92

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

80 80 95 229 0 0 0 0 0

N.S.

1 1.00 1.19 2.86 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.489 0.035 1.149 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 A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 63 105 87 132 83 233 125 104

N.S.

1 1.00 1.67 1.38 2.10 1.32 3.70 1.98 1.65

time (sec)

N/A 0.226 0.038 0.696 0.199 0.263 0.626 0.360 1.833

Problem 94

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

144 138 110 229 255 217 422 262 209

N.S.

1 0.96 0.76 1.59 1.77 1.51 2.93 1.82 1.45

time (sec)

N/A 0.318 0.079 0.986 0.209 0.255 1.057 0.404 1.734

Problem 95

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

175 163 141 361 428 406 656 416 339

N.S.

1 0.93 0.81 2.06 2.45 2.32 3.75 2.38 1.94

time (sec)

N/A 0.336 0.101 1.203 0.212 0.282 1.625 0.461 2.440

Problem 96

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

206 186 158 474 647 629 944 573 577

N.S.

1 0.90 0.77 2.30 3.14 3.05 4.58 2.78 2.80

time (sec)

N/A 0.362 0.121 2.155 0.223 0.264 2.408 0.494 2.974

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

365 436 511 0 2389 0 0 0 0

N.S.

1 1.19 1.40 0.00 6.55 0.00 0.00 0.00 0.00

time (sec)

N/A 0.915 0.306 0.000 0.325 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

309 365 391 0 1732 0 0 0 0

N.S.

1 1.18 1.27 0.00 5.61 0.00 0.00 0.00 0.00

time (sec)

N/A 0.766 0.214 0.000 0.316 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 B F F(-1) F F(-1)

verified

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

size

253 292 287 0 1165 0 0 0 0

N.S.

1 1.15 1.13 0.00 4.60 0.00 0.00 0.00 0.00

time (sec)

N/A 0.635 0.142 0.000 0.289 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

180 212 203 0 611 0 0 0 0

N.S.

1 1.18 1.13 0.00 3.39 0.00 0.00 0.00 0.00

time (sec)

N/A 0.467 0.112 0.000 0.287 0.000 0.000 0.000 0.000

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