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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 B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

212 189 261 574 1022 504 1158 3637 1195

N.S.

1 0.89 1.23 2.71 4.82 2.38 5.46 17.16 5.64

time (sec)

N/A 0.395 0.155 0.957 0.241 0.370 4.095 0.506 2.014

Problem 2

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

180 165 217 396 671 370 850 2418 638

N.S.

1 0.92 1.21 2.20 3.73 2.06 4.72 13.43 3.54

time (sec)

N/A 0.375 0.111 0.800 0.216 0.382 2.478 0.457 1.589

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 137 181 206 361 226 498 1254 282

N.S.

1 0.98 1.29 1.47 2.58 1.61 3.56 8.96 2.01

time (sec)

N/A 0.332 0.164 0.634 0.206 0.327 1.444 0.497 1.312

Problem 4

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 77 70 108 144 127 253 627 126

N.S.

1 0.95 0.86 1.33 1.78 1.57 3.12 7.74 1.56

time (sec)

N/A 0.236 0.025 0.559 0.207 0.325 0.943 0.407 1.068

Problem 5

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

133 126 164 417 241 0 0 0 0

N.S.

1 0.95 1.23 3.14 1.81 0.00 0.00 0.00 0.00

time (sec)

N/A 0.608 0.078 1.491 0.262 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 F F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 134 175 370 0 0 0 0 0

N.S.

1 0.94 1.23 2.61 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.484 0.096 1.378 0.000 0.000 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 72 208 153 570 177 384 134 197

N.S.

1 0.85 2.45 1.80 6.71 2.08 4.52 1.58 2.32

time (sec)

N/A 0.242 0.101 0.810 0.219 0.330 2.273 0.427 2.139

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

173 136 187 279 933 363 629 270 361

N.S.

1 0.79 1.08 1.61 5.39 2.10 3.64 1.56 2.09

time (sec)

N/A 0.311 0.237 0.953 0.240 0.371 4.169 0.531 2.523

Problem 9

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

269 201 210 390 1386 602 928 426 590

N.S.

1 0.75 0.78 1.45 5.15 2.24 3.45 1.58 2.19

time (sec)

N/A 0.369 0.277 1.506 0.261 0.365 6.868 0.532 3.114

Problem 10

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

423 375 429 925 1789 724 1727 4746 2473

N.S.

1 0.89 1.01 2.19 4.23 1.71 4.08 11.22 5.85

time (sec)

N/A 0.600 0.229 1.185 0.244 0.507 7.850 0.597 2.519

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

337 301 362 636 1200 534 1266 3144 1287

N.S.

1 0.89 1.07 1.89 3.56 1.58 3.76 9.33 3.82

time (sec)

N/A 0.493 0.164 1.003 0.228 0.417 3.866 0.517 1.925

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 227 216 396 671 367 850 1975 636

N.S.

1 0.95 0.90 1.66 2.81 1.54 3.56 8.26 2.66

time (sec)

N/A 0.385 0.133 0.812 0.216 0.400 2.347 0.483 1.588

Problem 13

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

118 105 97 206 280 223 491 1056 290

N.S.

1 0.89 0.82 1.75 2.37 1.89 4.16 8.95 2.46

time (sec)

N/A 0.257 0.029 0.672 0.204 0.341 1.434 0.436 1.272

Problem 14

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

276 307 252 698 518 0 0 0 0

N.S.

1 1.11 0.91 2.53 1.88 0.00 0.00 0.00 0.00

time (sec)

N/A 0.827 0.132 1.570 0.261 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 B F F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

247 223 221 568 992 0 0 0 0

N.S.

1 0.90 0.89 2.30 4.02 0.00 0.00 0.00 0.00

time (sec)

N/A 0.462 0.140 1.556 0.266 0.000 0.000 0.000 0.000

Problem 16

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

230 203 244 522 0 0 0 0 0

N.S.

1 0.88 1.06 2.27 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.688 0.187 1.489 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 B B B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 74 315 185 1515 271 614 140 423

N.S.

1 0.83 3.54 2.08 17.02 3.04 6.90 1.57 4.75

time (sec)

N/A 0.268 0.204 1.013 0.252 0.335 10.028 0.503 2.731

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

181 138 454 319 2218 510 928 282 647

N.S.

1 0.76 2.51 1.76 12.25 2.82 5.13 1.56 3.57

time (sec)

N/A 0.337 0.240 1.591 0.304 0.366 23.848 0.549 3.578

Problem 19

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

281 205 344 430 3029 807 1300 444 941

N.S.

1 0.73 1.22 1.53 10.78 2.87 4.63 1.58 3.35

time (sec)

N/A 0.388 0.499 1.701 0.355 0.374 76.593 0.548 4.614

Problem 20

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

457 401 586 1194 2637 912 2161 5520 4347

N.S.

1 0.88 1.28 2.61 5.77 2.00 4.73 12.08 9.51

time (sec)

N/A 0.613 0.408 1.438 0.257 0.587 16.359 0.669 3.180

Problem 21

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

371 327 429 925 1789 722 1727 4110 2465

N.S.

1 0.88 1.16 2.49 4.82 1.95 4.65 11.08 6.64

time (sec)

N/A 0.510 0.216 1.157 0.250 0.470 7.138 0.551 2.573

Problem 22

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

271 253 261 568 1022 502 1158 2589 1192

N.S.

1 0.93 0.96 2.10 3.77 1.85 4.27 9.55 4.40

time (sec)

N/A 0.402 0.135 0.886 0.311 0.425 3.835 0.477 2.063

Problem 23

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

149 129 120 314 439 322 706 1506 566

N.S.

1 0.87 0.81 2.11 2.95 2.16 4.74 10.11 3.80

time (sec)

N/A 0.279 0.040 0.738 0.265 0.348 2.024 0.473 1.429

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

356 462 352 1086 850 0 0 0 0

N.S.

1 1.30 0.99 3.05 2.39 0.00 0.00 0.00 0.00

time (sec)

N/A 1.217 0.194 1.806 0.315 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

373 326 374 863 1501 0 0 0 0

N.S.

1 0.87 1.00 2.31 4.02 0.00 0.00 0.00 0.00

time (sec)

N/A 0.576 0.244 1.658 0.349 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

345 293 314 732 2302 0 0 0 0

N.S.

1 0.85 0.91 2.12 6.67 0.00 0.00 0.00 0.00

time (sec)

N/A 0.550 0.231 1.608 0.359 0.000 0.000 0.000 0.000

Problem 27

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

310 270 308 685 0 0 0 0 0

N.S.

1 0.87 0.99 2.21 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.949 0.261 1.609 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 74 427 185 3107 355 0 140 780

N.S.

1 0.83 4.80 2.08 34.91 3.99 0.00 1.57 8.76

time (sec)

N/A 0.280 0.278 1.575 0.353 0.354 0.000 0.547 3.723

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

181 138 608 357 4218 644 0 282 1053

N.S.

1 0.76 3.36 1.97 23.30 3.56 0.00 1.56 5.82

time (sec)

N/A 0.355 0.354 1.602 0.447 0.347 0.000 0.546 4.818

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

281 205 642 481 5524 991 0 444 1396

N.S.

1 0.73 2.28 1.71 19.66 3.53 0.00 1.58 4.97

time (sec)

N/A 0.419 0.581 2.259 0.564 0.394 0.000 0.612 6.099

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

252 298 354 1105 790 0 0 3552 0

N.S.

1 1.18 1.40 4.38 3.13 0.00 0.00 14.10 0.00

time (sec)

N/A 0.712 0.184 1.646 0.260 0.000 0.000 66.529 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 225 254 657 477 0 0 2364 0

N.S.

1 1.14 1.28 3.32 2.41 0.00 0.00 11.94 0.00

time (sec)

N/A 0.579 0.123 1.773 0.263 0.000 0.000 55.791 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 145 162 332 221 0 0 1230 0

N.S.

1 1.16 1.30 2.66 1.77 0.00 0.00 9.84 0.00

time (sec)

N/A 0.397 0.065 1.343 0.247 0.000 0.000 42.824 0.000

Problem 34

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

76 81 95 146 0 0 0 617 0

N.S.

1 1.07 1.25 1.92 0.00 0.00 0.00 8.12 0.00

time (sec)

N/A 0.533 0.024 1.370 0.000 0.000 0.000 36.747 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 207 72 172 60 170 104 69

N.S.

1 1.00 4.70 1.64 3.91 1.36 3.86 2.36 1.57

time (sec)

N/A 0.292 0.078 0.622 0.210 0.319 0.310 0.324 2.516

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

173 127 292 230 424 144 386 0 241

N.S.

1 0.73 1.69 1.33 2.45 0.83 2.23 0.00 1.39

time (sec)

N/A 0.399 0.176 0.977 0.217 0.358 0.618 0.000 2.446

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

255 194 418 365 885 349 889 139 545

N.S.

1 0.76 1.64 1.43 3.47 1.37 3.49 0.55 2.14

time (sec)

N/A 0.426 0.223 1.257 0.243 0.341 2.588 42.817 3.504

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

373 262 492 500 1469 611 1392 270 970

N.S.

1 0.70 1.32 1.34 3.94 1.64 3.73 0.72 2.60

time (sec)

N/A 0.505 0.386 1.634 0.310 0.372 9.881 55.044 5.995

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

341 304 359 846 1341 0 0 2814 0

N.S.

1 0.89 1.05 2.48 3.93 0.00 0.00 8.25 0.00

time (sec)

N/A 0.605 0.257 1.674 0.275 0.000 0.000 72.934 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

260 227 239 532 886 0 0 1774 0

N.S.

1 0.87 0.92 2.05 3.41 0.00 0.00 6.82 0.00

time (sec)

N/A 0.479 0.145 1.488 0.273 0.000 0.000 63.252 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 146 175 295 0 0 0 895 0

N.S.

1 0.91 1.09 1.84 0.00 0.00 0.00 5.59 0.00

time (sec)

N/A 0.338 0.102 1.475 0.000 0.000 0.000 48.777 0.000

Problem 42

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

98 73 104 82 134 88 231 115 106

N.S.

1 0.74 1.06 0.84 1.37 0.90 2.36 1.17 1.08

time (sec)

N/A 0.203 0.031 0.595 0.200 0.346 0.613 0.398 1.440

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 109 292 231 421 151 386 233 247

N.S.

1 0.70 1.87 1.48 2.70 0.97 2.47 1.49 1.58

time (sec)

N/A 0.364 0.164 0.901 0.223 0.339 0.601 0.434 2.503

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

261 182 324 366 859 334 828 133 415

N.S.

1 0.70 1.24 1.40 3.29 1.28 3.17 0.51 1.59

time (sec)

N/A 0.378 0.245 1.136 0.238 0.306 1.900 44.472 2.927

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

364 254 453 506 1721 664 0 276 984

N.S.

1 0.70 1.24 1.39 4.73 1.82 0.00 0.76 2.70

time (sec)

N/A 0.483 0.373 2.875 0.330 0.292 0.000 54.532 5.636

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

457 313 520 640 2560 1019 0 436 1679

N.S.

1 0.68 1.14 1.40 5.60 2.23 0.00 0.95 3.67

time (sec)

N/A 0.489 0.705 2.645 0.428 0.325 0.000 64.990 9.157

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

361 300 317 681 2037 0 0 0 0

N.S.

1 0.83 0.88 1.89 5.64 0.00 0.00 0.00 0.00

time (sec)

N/A 0.561 0.254 1.598 0.316 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 F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

251 217 245 463 0 0 0 0 0

N.S.

1 0.86 0.98 1.84 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.442 0.196 1.561 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 B B B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 72 207 174 567 185 382 132 198

N.S.

1 0.85 2.44 2.05 6.67 2.18 4.49 1.55 2.33

time (sec)

N/A 0.252 0.102 0.806 0.217 0.279 2.324 0.405 2.197

Problem 50

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

144 138 111 221 255 221 422 236 208

N.S.

1 0.96 0.77 1.53 1.77 1.53 2.93 1.64 1.44

time (sec)

N/A 0.312 0.072 0.771 0.209 0.285 1.084 0.394 1.982

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

243 182 418 367 885 355 889 442 545

N.S.

1 0.75 1.72 1.51 3.64 1.46 3.66 1.82 2.24

time (sec)

N/A 0.409 0.267 1.217 0.255 0.316 2.505 0.406 3.614

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

365 253 452 506 1721 672 0 0 983

N.S.

1 0.69 1.24 1.39 4.72 1.84 0.00 0.00 2.69

time (sec)

N/A 0.429 0.378 2.830 0.327 0.310 0.000 0.000 5.707

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

463 319 533 649 2380 1011 2106 0 1443

N.S.

1 0.69 1.15 1.40 5.14 2.18 4.55 0.00 3.12

time (sec)

N/A 0.478 0.631 2.085 0.352 0.326 138.117 0.000 9.101

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

563 388 637 787 3816 1509 0 0 2291

N.S.

1 0.69 1.13 1.40 6.78 2.68 0.00 0.00 4.07

time (sec)

N/A 0.586 0.887 7.993 0.570 0.352 0.000 0.000 13.330

Problem 55

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

539 617 905 0 3186 0 0 0 0

N.S.

1 1.14 1.68 0.00 5.91 0.00 0.00 0.00 0.00

time (sec)

N/A 1.352 0.449 0.000 0.331 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 B F F(-1) F F(-1)

verified

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

size

450 516 680 0 2243 0 0 0 0

N.S.

1 1.15 1.51 0.00 4.98 0.00 0.00 0.00 0.00

time (sec)

N/A 1.148 0.342 0.000 0.307 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

343 405 869 0 1252 0 0 0 0

N.S.

1 1.18 2.53 0.00 3.65 0.00 0.00 0.00 0.00

time (sec)

N/A 0.821 0.405 0.000 0.295 0.000 0.000 0.000 0.000

Problem 58

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

203 227 205 0 633 0 0 0 0

N.S.

1 1.12 1.01 0.00 3.12 0.00 0.00 0.00 0.00

time (sec)

N/A 0.568 0.119 0.000 0.284 0.000 0.000 0.000 0.000

Problem 59

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

286 272 1214 0 0 0 0 0 0

N.S.

1 0.95 4.24 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.992 0.818 0.000 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 B F F F F(-1) F F(-1)

verified

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

size

241 218 1407 0 0 0 0 0 0

N.S.

1 0.90 5.84 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.865 1.207 0.000 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 C B B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 114 765 330 1987 289 714 206 469

N.S.

1 0.81 5.43 2.34 14.09 2.05 5.06 1.46 3.33

time (sec)

N/A 0.319 0.527 0.797 0.304 0.315 5.020 0.452 2.812

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

287 218 1032 643 3282 601 1387 455 955

N.S.

1 0.76 3.60 2.24 11.44 2.09 4.83 1.59 3.33

time (sec)

N/A 0.416 0.596 0.988 0.424 0.310 10.342 0.511 4.173

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

445 334 1255 926 4808 985 0 744 1870

N.S.

1 0.75 2.82 2.08 10.80 2.21 0.00 1.67 4.20

time (sec)

N/A 0.500 0.687 1.609 0.568 0.306 0.000 0.557 7.441

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

711 963 1559 0 5178 0 0 0 0

N.S.

1 1.35 2.19 0.00 7.28 0.00 0.00 0.00 0.00

time (sec)

N/A 2.051 0.794 0.000 0.374 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 B F F(-1) F F(-1)

verified

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

size

761 852 1194 0 3656 0 0 0 0

N.S.

1 1.12 1.57 0.00 4.80 0.00 0.00 0.00 0.00

time (sec)

N/A 1.943 0.541 0.000 0.344 0.000 0.000 0.000 0.000

Problem 66

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

589 670 677 0 2259 0 0 0 0

N.S.

1 1.14 1.15 0.00 3.84 0.00 0.00 0.00 0.00

time (sec)

N/A 1.444 0.356 0.000 0.318 0.000 0.000 0.000 0.000

Problem 67

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

334 360 287 0 1202 0 0 0 0

N.S.

1 1.08 0.86 0.00 3.60 0.00 0.00 0.00 0.00

time (sec)

N/A 0.934 0.129 0.000 0.285 0.000 0.000 0.000 0.000

Problem 68

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

535 501 2615 0 0 0 0 0 0

N.S.

1 0.94 4.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.967 2.442 0.000 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 B F F F F(-1) F F(-1)

verified

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

size

442 366 2649 0 0 0 0 0 0

N.S.

1 0.83 5.99 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.713 2.542 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 B F F F F F F(-1)

verified

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

size

387 329 3426 0 0 0 0 0 0

N.S.

1 0.85 8.85 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.370 4.105 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 C B B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 119 1352 367 5532 444 1182 219 1153

N.S.

1 0.81 9.20 2.50 37.63 3.02 8.04 1.49 7.84

time (sec)

N/A 0.384 1.080 1.049 0.578 0.310 28.408 0.520 3.993

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

299 220 1703 685 8031 837 2055 479 1940

N.S.

1 0.74 5.70 2.29 26.86 2.80 6.87 1.60 6.49

time (sec)

N/A 0.490 1.456 1.638 0.788 0.303 69.337 0.577 6.382

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

463 336 2010 968 10880 1323 0 780 3434

N.S.

1 0.73 4.34 2.09 23.50 2.86 0.00 1.68 7.42

time (sec)

N/A 0.576 1.999 1.812 1.134 0.340 0.000 0.566 9.112

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1089 1398 2330 0 6921 0 0 0 0

N.S.

1 1.28 2.14 0.00 6.36 0.00 0.00 0.00 0.00

time (sec)

N/A 3.478 1.735 0.000 0.397 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 B F F(-1) F F(-1)

verified

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

size

908 1213 1555 0 5196 0 0 0 0

N.S.

1 1.34 1.71 0.00 5.72 0.00 0.00 0.00 0.00

time (sec)

N/A 2.998 0.798 0.000 0.364 0.000 0.000 0.000 0.000

Problem 76

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

730 959 901 0 3218 0 0 0 0

N.S.

1 1.31 1.23 0.00 4.41 0.00 0.00 0.00 0.00

time (sec)

N/A 2.074 0.444 0.000 0.322 0.000 0.000 0.000 0.000

Problem 77

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

420 515 389 0 1789 0 0 0 0

N.S.

1 1.23 0.93 0.00 4.26 0.00 0.00 0.00 0.00

time (sec)

N/A 1.314 0.191 0.000 0.287 0.000 0.000 0.000 0.000

Problem 78

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

712 857 5044 0 0 0 0 0 0

N.S.

1 1.20 7.08 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.032 4.053 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 B F F F F(-1) F F(-1)

verified

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

size

692 577 4506 0 0 0 0 0 0

N.S.

1 0.83 6.51 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.917 5.813 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 B F F F F F F(-1)

verified

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

size

604 486 5989 0 0 0 0 0 0

N.S.

1 0.80 9.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.786 6.894 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 C B B B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 119 2401 367 11688 559 0 218 1565

N.S.

1 0.81 16.33 2.50 79.51 3.80 0.00 1.48 10.65

time (sec)

N/A 0.371 0.715 1.646 1.032 0.315 0.000 0.644 6.018

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

299 220 2456 722 15765 1045 0 479 3720

N.S.

1 0.74 8.21 2.41 52.73 3.49 0.00 1.60 12.44

time (sec)

N/A 0.486 2.529 1.857 1.496 0.344 0.000 0.641 8.871

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

463 336 2606 1019 20330 1610 0 780 6275

N.S.

1 0.73 5.63 2.20 43.91 3.48 0.00 1.68 13.55

time (sec)

N/A 0.566 2.686 2.524 2.080 0.368 0.000 0.665 10.601

Problem 84

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

718 629 1020 0 0 0 0 0 0

N.S.

1 0.88 1.42 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.093 1.093 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 A F F F F F F(-1)

verified

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

size

536 470 727 0 0 0 0 0 0

N.S.

1 0.88 1.36 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.792 0.869 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 B F F F F F F(-1)

verified

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

size

283 260 1227 0 0 0 0 0 0

N.S.

1 0.92 4.34 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.513 0.662 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 A A B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 120 252 338 0 0 0 0 0

N.S.

1 0.94 1.98 2.66 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.405 0.580 1.407 0.000 0.000 0.000 0.000 0.000

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 No Yes Yes TBD TBD TBD TBD TBD

size

44 37 79 106 397 87 206 132 96

N.S.

1 0.84 1.80 2.41 9.02 1.98 4.68 3.00 2.18

time (sec)

N/A 0.332 0.242 0.664 0.222 0.310 0.376 0.467 2.579

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 136 186 400 1008 231 541 0 419

N.S.

1 0.74 1.02 2.19 5.51 1.26 2.96 0.00 2.29

time (sec)

N/A 0.442 0.430 0.984 0.262 0.310 0.743 0.000 2.971

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

343 248 318 767 2115 540 1488 211 981

N.S.

1 0.72 0.93 2.24 6.17 1.57 4.34 0.62 2.86

time (sec)

N/A 0.544 0.650 1.307 0.350 0.313 4.236 58.157 4.841

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

507 364 442 1076 3434 940 2388 451 1882

N.S.

1 0.72 0.87 2.12 6.77 1.85 4.71 0.89 3.71

time (sec)

N/A 0.618 0.800 1.839 0.480 0.313 29.821 71.588 8.266

Problem 92

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

722 592 4443 0 0 0 0 0 0

N.S.

1 0.82 6.15 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.835 6.293 0.000 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 B F F F F(-1) F F(-1)

verified

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

size

469 380 2622 0 0 0 0 0 0

N.S.

1 0.81 5.59 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.610 3.223 0.000 0.000 0.000 0.000 0.000 0.000

Problem 94

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

261 239 1412 0 0 0 0 0 0

N.S.

1 0.92 5.41 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.450 1.022 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 C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 111 315 182 416 155 432 173 222

N.S.

1 0.73 2.07 1.20 2.74 1.02 2.84 1.14 1.46

time (sec)

N/A 0.258 0.240 0.677 0.216 0.321 1.140 0.400 2.256

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

214 140 187 398 1004 236 539 339 423

N.S.

1 0.65 0.87 1.86 4.69 1.10 2.52 1.58 1.98

time (sec)

N/A 0.511 0.352 0.982 0.261 0.332 0.725 0.430 2.923

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

365 254 307 766 1995 515 1404 203 731

N.S.

1 0.70 0.84 2.10 5.47 1.41 3.85 0.56 2.00

time (sec)

N/A 0.544 0.518 1.220 0.315 0.328 3.080 57.239 3.762

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

523 364 466 1080 4187 1005 0 460 1497

N.S.

1 0.70 0.89 2.07 8.01 1.92 0.00 0.88 2.86

time (sec)

N/A 0.603 0.703 2.713 0.511 0.312 0.000 74.128 7.222

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

682 475 613 1386 6160 1534 0 754 2701

N.S.

1 0.70 0.90 2.03 9.03 2.25 0.00 1.11 3.96

time (sec)

N/A 0.675 0.997 2.935 0.703 0.362 0.000 88.805 10.025

Problem 100

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

635 504 5929 0 0 0 0 0 0

N.S.

1 0.79 9.34 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.697 7.357 0.000 0.000 0.000 0.000 0.000 0.000

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