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2.2.1 Integrals 1 to 51

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 A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 189 151 1229 338 911 5992 1708 469

N.S.

1 1.00 0.80 6.50 1.79 4.82 31.70 9.04 2.48

time (sec)

N/A 0.386 0.447 4.369 0.230 0.281 0.948 0.323 5.945

Problem 2

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

144 144 113 711 242 532 3271 1009 305

N.S.

1 1.00 0.78 4.94 1.68 3.69 22.72 7.01 2.12

time (sec)

N/A 0.320 0.132 3.375 0.227 0.284 0.661 0.302 5.626

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 97 73 96 146 235 1460 478 185

N.S.

1 1.00 0.75 0.99 1.51 2.42 15.05 4.93 1.91

time (sec)

N/A 0.240 0.072 0.090 0.222 0.341 0.460 0.311 5.570

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

60 60 43 59 70 94 439 167 97

N.S.

1 1.00 0.72 0.98 1.17 1.57 7.32 2.78 1.62

time (sec)

N/A 0.198 0.049 0.055 0.227 0.282 0.322 0.304 5.465

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

118 118 93 0 0 0 418 0 0

N.S.

1 1.00 0.79 0.00 0.00 0.00 3.54 0.00 0.00

time (sec)

N/A 0.265 0.133 0.000 0.000 0.000 3.518 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

171 174 108 0 0 0 2069 0 0

N.S.

1 1.02 0.63 0.00 0.00 0.00 12.10 0.00 0.00

time (sec)

N/A 0.360 0.211 0.000 0.000 0.000 29.417 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

209 220 133 0 0 0 6411 0 0

N.S.

1 1.05 0.64 0.00 0.00 0.00 30.67 0.00 0.00

time (sec)

N/A 0.394 0.418 0.000 0.000 0.000 96.012 0.000 0.000

Problem 8

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

292 292 247 2443 550 1711 11914 3283 694

N.S.

1 1.00 0.85 8.37 1.88 5.86 40.80 11.24 2.38

time (sec)

N/A 0.522 0.702 3.741 0.285 0.296 1.357 0.354 6.223

Problem 9

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

216 216 178 1471 396 1043 6836 2010 499

N.S.

1 1.00 0.82 6.81 1.83 4.83 31.65 9.31 2.31

time (sec)

N/A 0.417 0.279 3.484 0.251 0.291 0.965 0.359 5.876

Problem 10

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

144 144 113 711 242 495 3271 1009 305

N.S.

1 1.00 0.78 4.94 1.68 3.44 22.72 7.01 2.12

time (sec)

N/A 0.309 0.143 3.392 0.230 0.274 0.671 0.330 5.602

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 67 90 116 217 1096 380 179

N.S.

1 1.00 0.74 0.99 1.27 2.38 12.04 4.18 1.97

time (sec)

N/A 0.232 0.065 3.347 0.219 0.285 0.444 0.329 5.478

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

178 178 146 0 0 0 649 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 3.65 0.00 0.00

time (sec)

N/A 0.364 0.238 0.000 0.000 0.000 5.861 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

247 245 156 0 0 0 0 0 0

N.S.

1 0.99 0.63 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.520 0.581 0.000 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

292 305 165 0 0 0 0 0 0

N.S.

1 1.04 0.57 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.511 0.740 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 A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

379 379 327 3953 762 2657 20086 5234 933

N.S.

1 1.00 0.86 10.43 2.01 7.01 53.00 13.81 2.46

time (sec)

N/A 0.652 0.963 3.965 0.294 0.324 1.927 0.414 6.608

Problem 16

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

284 284 239 2443 550 1690 11914 3283 694

N.S.

1 1.00 0.84 8.60 1.94 5.95 41.95 11.56 2.44

time (sec)

N/A 0.522 0.612 3.627 0.265 0.285 1.329 0.370 6.263

Problem 17

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

189 189 151 1229 338 837 5992 1708 469

N.S.

1 1.00 0.80 6.50 1.79 4.43 31.70 9.04 2.48

time (sec)

N/A 0.378 0.435 3.472 0.239 0.280 0.941 0.345 5.906

Problem 18

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

121 121 90 475 162 381 2152 673 280

N.S.

1 1.00 0.74 3.93 1.34 3.15 17.79 5.56 2.31

time (sec)

N/A 0.273 0.102 3.406 0.222 0.273 0.632 0.324 5.600

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

258 258 217 0 0 0 887 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 3.44 0.00 0.00

time (sec)

N/A 0.506 0.587 0.000 0.000 0.000 9.384 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

347 340 209 0 0 0 0 0 0

N.S.

1 0.98 0.60 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.708 0.783 0.000 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 F F F F F F(-1)

verified

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

size

480 489 218 0 0 0 0 0 0

N.S.

1 1.02 0.45 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.086 0.795 0.000 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 F F F C F F(-1)

verified

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

size

363 363 315 0 0 0 1102 0 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 3.04 0.00 0.00

time (sec)

N/A 0.646 0.693 0.000 0.000 0.000 13.386 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

260 260 219 0 0 0 887 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 3.41 0.00 0.00

time (sec)

N/A 0.490 0.560 0.000 0.000 0.000 9.122 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

180 180 147 0 0 0 649 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 3.61 0.00 0.00

time (sec)

N/A 0.375 0.253 0.000 0.000 0.000 5.841 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

120 120 93 0 0 0 418 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 3.48 0.00 0.00

time (sec)

N/A 0.274 0.123 0.000 0.000 0.000 3.501 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

77 77 56 0 0 0 201 0 0

N.S.

1 1.00 0.73 0.00 0.00 0.00 2.61 0.00 0.00

time (sec)

N/A 0.197 0.064 0.000 0.000 0.000 1.794 0.000 0.000

Problem 27

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

125 125 100 0 0 0 0 0 0

N.S.

1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.288 0.162 0.000 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 A F F F F(-1) F F(-1)

verified

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

size

206 223 149 0 0 0 0 0 0

N.S.

1 1.08 0.72 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.477 0.355 0.000 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

342 0 195 0 0 0 0 0 0

N.S.

1 0.00 0.57 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 0.891 0.000 0.000 0.000 0.000 0.000 0.000

Problem 30

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

340 333 212 0 0 0 0 0 0

N.S.

1 0.98 0.62 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.733 0.800 0.000 0.000 0.000 0.000 0.000 0.000

Problem 31

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

246 245 158 0 0 0 0 0 0

N.S.

1 1.00 0.64 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.523 0.653 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 A A F F F C F F(-1)

verified

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

size

171 174 108 0 0 0 2069 0 0

N.S.

1 1.02 0.63 0.00 0.00 0.00 12.10 0.00 0.00

time (sec)

N/A 0.356 0.209 0.000 0.000 0.000 29.820 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

103 103 81 0 0 0 954 0 0

N.S.

1 1.00 0.79 0.00 0.00 0.00 9.26 0.00 0.00

time (sec)

N/A 0.212 0.078 0.000 0.000 0.000 15.021 0.000 0.000

Problem 34

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

205 222 147 0 0 0 0 0 0

N.S.

1 1.08 0.72 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.485 0.344 0.000 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 F F F F(-1) F F(-1)

verified

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

size

304 329 207 0 0 0 0 0 0

N.S.

1 1.08 0.68 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.742 0.936 0.000 0.000 0.000 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

491 0 265 0 0 0 0 0 0

N.S.

1 0.00 0.54 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 1.200 0.000 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

433 443 222 0 0 0 0 0 0

N.S.

1 1.02 0.51 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.049 0.827 0.000 0.000 0.000 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

292 304 169 0 0 0 0 0 0

N.S.

1 1.04 0.58 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.515 0.755 0.000 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 F F F C F F(-1)

verified

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

size

208 219 133 0 0 0 6411 0 0

N.S.

1 1.05 0.64 0.00 0.00 0.00 30.82 0.00 0.00

time (sec)

N/A 0.400 0.427 0.000 0.000 0.000 94.112 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

103 103 81 0 0 0 3199 0 0

N.S.

1 1.00 0.79 0.00 0.00 0.00 31.06 0.00 0.00

time (sec)

N/A 0.221 0.089 0.000 0.000 0.000 52.496 0.000 0.000

Problem 41

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

333 370 197 0 0 0 0 0 0

N.S.

1 1.11 0.59 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.784 0.868 0.000 0.000 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

452 500 266 0 0 0 0 0 0

N.S.

1 1.11 0.59 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.191 1.236 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 F A F F F F(-1) F F(-1)

verified

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

size

665 0 329 0 0 0 0 0 0

N.S.

1 0.00 0.49 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 1.509 0.000 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 F F F F(-1) F F(-1)

verified

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

size

1059 1020 248 0 0 0 0 0 0

N.S.

1 0.96 0.23 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.729 0.332 0.000 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 F F F F(-1) F F(-1)

verified

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

size

495 455 198 0 0 0 0 0 0

N.S.

1 0.92 0.40 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.858 0.209 0.000 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

253 241 147 0 0 0 0 0 0

N.S.

1 0.95 0.58 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.426 0.118 0.000 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 F F F F(-1) F F(-1)

verified

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

size

162 162 118 0 0 0 0 0 0

N.S.

1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.329 0.353 0.000 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 F F F F(-1) F F(-1)

verified

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

size

295 286 128 0 0 0 0 0 0

N.S.

1 0.97 0.43 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.523 0.380 0.000 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 F F F F(-1) F F(-1)

verified

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

size

483 491 128 0 0 0 0 0 0

N.S.

1 1.02 0.27 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.952 0.553 0.000 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 89 91 95 100 231 151 113 101

N.S.

1 1.06 1.08 1.13 1.19 2.75 1.80 1.35 1.20

time (sec)

N/A 0.209 0.115 3.401 0.199 0.284 9.664 0.284 5.994

Problem 51

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

84 89 91 95 100 217 151 113 101

N.S.

1 1.06 1.08 1.13 1.19 2.58 1.80 1.35 1.20

time (sec)

N/A 0.218 0.123 3.409 0.221 0.264 9.668 0.290 5.937

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