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2.2.1 Integrals 1 to 46

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 F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

227 227 218 756 936 1085 0 0 0

N.S.

1 1.00 0.96 3.33 4.12 4.78 0.00 0.00 0.00

time (sec)

N/A 0.428 0.125 1.459 0.432 0.345 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 157 151 440 516 675 0 0 0

N.S.

1 1.00 0.96 2.80 3.29 4.30 0.00 0.00 0.00

time (sec)

N/A 0.360 0.152 1.340 0.400 0.344 0.000 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 93 87 142 0 343 0 0 0

N.S.

1 1.00 0.94 1.53 0.00 3.69 0.00 0.00 0.00

time (sec)

N/A 0.263 0.062 0.389 0.000 0.330 0.000 0.000 0.000

Problem 4

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 18 116 20 22 20 22

N.S.

1 1.00 1.11 1.00 6.44 1.11 1.22 1.11 1.22

time (sec)

N/A 0.197 6.839 0.436 0.540 0.302 0.655 0.395 12.767

Problem 5

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 18 172 31 46 20 22

N.S.

1 1.00 1.11 1.00 9.56 1.72 2.56 1.11 1.22

time (sec)

N/A 0.200 5.629 0.501 0.593 0.269 2.549 2.127 13.044

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

371 371 329 1517 3403 1887 0 0 0

N.S.

1 1.00 0.89 4.09 9.17 5.09 0.00 0.00 0.00

time (sec)

N/A 0.721 2.046 1.705 0.709 0.376 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

262 262 232 679 1704 1096 0 0 0

N.S.

1 1.00 0.89 2.59 6.50 4.18 0.00 0.00 0.00

time (sec)

N/A 0.555 2.730 1.731 0.465 0.344 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 134 123 191 0 525 0 0 0

N.S.

1 1.00 0.92 1.43 0.00 3.92 0.00 0.00 0.00

time (sec)

N/A 0.342 1.108 0.418 0.000 0.311 0.000 0.000 0.000

Problem 9

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

20 20 22 20 507 37 41 22 24

N.S.

1 1.00 1.10 1.00 25.35 1.85 2.05 1.10 1.20

time (sec)

N/A 0.228 30.852 0.759 1.029 0.289 1.069 1.342 13.128

Problem 10

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

20 20 22 20 624 48 76 22 24

N.S.

1 1.00 1.10 1.00 31.20 2.40 3.80 1.10 1.20

time (sec)

N/A 0.223 24.751 0.956 1.378 0.282 2.133 29.705 13.161

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 152 216 417 1285 516 0 0 0

N.S.

1 1.00 1.42 2.74 8.45 3.39 0.00 0.00 0.00

time (sec)

N/A 0.544 2.107 0.551 0.456 0.296 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

119 119 528 236 377 292 0 0 0

N.S.

1 1.00 4.44 1.98 3.17 2.45 0.00 0.00 0.00

time (sec)

N/A 0.456 6.693 0.529 0.426 0.269 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 104 53 273 99 0 248 79

N.S.

1 1.00 1.55 0.79 4.07 1.48 0.00 3.70 1.18

time (sec)

N/A 0.306 1.000 0.463 0.314 0.291 0.000 0.319 13.613

Problem 14

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

20 20 22 20 391 27 27 22 24

N.S.

1 1.00 1.10 1.00 19.55 1.35 1.35 1.10 1.20

time (sec)

N/A 0.230 7.803 0.480 0.522 0.245 1.052 0.302 13.254

Problem 15

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

20 20 22 20 522 51 58 22 24

N.S.

1 1.00 1.10 1.00 26.10 2.55 2.90 1.10 1.20

time (sec)

N/A 0.236 6.312 0.414 0.901 0.266 2.118 0.566 13.149

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

288 288 1447 810 4283 933 0 0 0

N.S.

1 1.00 5.02 2.81 14.87 3.24 0.00 0.00 0.00

time (sec)

N/A 0.916 7.953 0.656 1.332 0.304 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 F F F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

229 229 925 453 1035 493 0 0 0

N.S.

1 1.00 4.04 1.98 4.52 2.15 0.00 0.00 0.00

time (sec)

N/A 0.705 7.169 0.584 0.781 0.296 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 140 172 86 1058 183 0 798 247

N.S.

1 1.00 1.23 0.61 7.56 1.31 0.00 5.70 1.76

time (sec)

N/A 0.400 1.977 0.615 0.356 0.290 0.000 0.565 19.320

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

20 20 22 20 3956 57 54 22 24

N.S.

1 1.00 1.10 1.00 197.80 2.85 2.70 1.10 1.20

time (sec)

N/A 0.232 13.653 0.444 10.617 0.292 1.967 0.315 14.134

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

20 20 22 20 4471 99 105 22 24

N.S.

1 1.00 1.10 1.00 223.55 4.95 5.25 1.10 1.20

time (sec)

N/A 0.228 15.908 0.440 38.235 0.271 7.338 1.185 14.172

Problem 21

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

20 20 22 20 22 22 0 22 24

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.00 1.10 1.20

time (sec)

N/A 0.218 1.225 0.323 0.647 0.282 0.000 0.400 13.490

Problem 22

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 18 124 20 24 20 22

N.S.

1 1.00 1.11 1.00 6.89 1.11 1.33 1.11 1.22

time (sec)

N/A 0.205 11.379 0.321 0.363 0.280 5.083 0.287 13.550

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

20 20 22 20 22 22 17 22 24

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.85 1.10 1.20

time (sec)

N/A 0.231 1.219 0.184 0.573 0.268 1.820 0.303 13.379

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

227 227 365 756 936 1085 0 0 0

N.S.

1 1.00 1.61 3.33 4.12 4.78 0.00 0.00 0.00

time (sec)

N/A 0.442 0.478 1.012 0.423 0.336 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 157 203 440 516 675 0 0 0

N.S.

1 1.00 1.29 2.80 3.29 4.30 0.00 0.00 0.00

time (sec)

N/A 0.366 0.252 0.984 0.382 0.324 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 93 104 142 0 343 0 0 0

N.S.

1 1.00 1.12 1.53 0.00 3.69 0.00 0.00 0.00

time (sec)

N/A 0.270 0.013 0.296 0.000 0.274 0.000 0.000 0.000

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 18 116 20 15 20 22

N.S.

1 1.00 1.11 1.00 6.44 1.11 0.83 1.11 1.22

time (sec)

N/A 0.205 0.995 0.326 0.489 0.258 0.680 0.414 13.145

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 18 172 31 17 20 22

N.S.

1 1.00 1.11 1.00 9.56 1.72 0.94 1.11 1.22

time (sec)

N/A 0.202 1.529 0.526 0.519 0.260 2.616 2.205 13.624

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

364 364 646 1489 3267 1823 0 0 0

N.S.

1 1.00 1.77 4.09 8.98 5.01 0.00 0.00 0.00

time (sec)

N/A 0.730 2.593 1.649 0.720 0.375 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

257 257 356 662 1641 1056 0 0 0

N.S.

1 1.00 1.39 2.58 6.39 4.11 0.00 0.00 0.00

time (sec)

N/A 0.549 1.541 1.375 0.473 0.366 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 131 151 190 0 505 0 0 0

N.S.

1 1.00 1.15 1.45 0.00 3.85 0.00 0.00 0.00

time (sec)

N/A 0.338 0.547 0.493 0.000 0.325 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

20 20 22 20 501 36 17 22 24

N.S.

1 1.00 1.10 1.00 25.05 1.80 0.85 1.10 1.20

time (sec)

N/A 0.225 46.000 0.936 1.050 0.270 1.017 2.190 13.948

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

20 20 22 20 618 47 19 22 24

N.S.

1 1.00 1.10 1.00 30.90 2.35 0.95 1.10 1.20

time (sec)

N/A 0.221 28.327 0.649 1.459 0.272 2.037 53.580 13.595

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

526 526 449 0 0 2309 0 0 0

N.S.

1 1.00 0.85 0.00 0.00 4.39 0.00 0.00 0.00

time (sec)

N/A 1.300 1.442 0.000 0.000 0.516 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

394 394 338 0 0 1625 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 4.12 0.00 0.00 0.00

time (sec)

N/A 1.118 1.122 0.000 0.000 0.459 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) B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

257 257 214 516 0 1041 0 0 0

N.S.

1 1.00 0.83 2.01 0.00 4.05 0.00 0.00 0.00

time (sec)

N/A 0.744 0.725 0.560 0.000 0.451 0.000 0.000 0.000

Problem 37

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

20 20 22 20 298 27 17 22 24

N.S.

1 1.00 1.10 1.00 14.90 1.35 0.85 1.10 1.20

time (sec)

N/A 0.235 1.743 0.456 0.843 0.265 1.013 0.353 13.376

Problem 38

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

20 20 22 20 439 51 19 22 24

N.S.

1 1.00 1.10 1.00 21.95 2.55 0.95 1.10 1.20

time (sec)

N/A 0.229 12.303 0.413 1.331 0.278 2.025 0.793 13.353

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1523 1523 20116 0 0 7008 0 0 0

N.S.

1 1.00 13.21 0.00 0.00 4.60 0.00 0.00 0.00

time (sec)

N/A 3.244 22.307 0.000 0.000 0.714 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1117 1117 11147 0 0 4274 0 0 0

N.S.

1 1.00 9.98 0.00 0.00 3.83 0.00 0.00 0.00

time (sec)

N/A 2.520 20.077 0.000 0.000 0.638 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) B F F F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

582 582 1037 1289 0 2080 0 0 0

N.S.

1 1.00 1.78 2.21 0.00 3.57 0.00 0.00 0.00

time (sec)

N/A 1.422 11.645 0.639 0.000 0.491 0.000 0.000 0.000

Problem 42

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

20 20 22 20 2279 55 19 22 24

N.S.

1 1.00 1.10 1.00 113.95 2.75 0.95 1.10 1.20

time (sec)

N/A 0.233 22.663 0.493 13.539 0.291 1.916 0.512 16.839

Problem 43

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

20 20 22 20 2918 96 20 22 24

N.S.

1 1.00 1.10 1.00 145.90 4.80 1.00 1.10 1.20

time (sec)

N/A 0.228 41.364 0.394 39.391 0.301 7.220 3.119 17.963

Problem 44

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

20 20 22 20 22 22 0 22 24

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.00 1.10 1.20

time (sec)

N/A 0.223 2.654 0.434 0.731 0.295 0.000 0.438 14.158

Problem 45

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 18 124 20 17 20 22

N.S.

1 1.00 1.11 1.00 6.89 1.11 0.94 1.11 1.22

time (sec)

N/A 0.203 0.662 0.174 0.388 0.285 4.680 0.298 12.978

Problem 46

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

20 20 22 20 22 22 17 22 24

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.85 1.10 1.20

time (sec)

N/A 0.226 0.883 0.175 0.530 0.256 1.518 0.362 13.157

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