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Integrals 1 to 34

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 A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

436 436 495 440 621 668 1027 854 713

N.S.

1 1.00 1.14 1.01 1.42 1.53 2.36 1.96 1.64

time (sec)

N/A 0.269 0.452 2.304 0.198 0.257 1.795 0.313 4.908

Problem 2

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

324 324 323 285 387 410 639 558 514

N.S.

1 1.00 1.00 0.88 1.19 1.27 1.97 1.72 1.59

time (sec)

N/A 0.182 0.255 1.703 0.204 0.271 1.505 0.346 4.087

Problem 3

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

212 212 184 162 198 204 320 309 351

N.S.

1 1.00 0.87 0.76 0.93 0.96 1.51 1.46 1.66

time (sec)

N/A 0.115 0.135 1.646 0.205 0.257 1.248 0.287 3.706

Problem 4

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

115 115 82 72 128 90 163 128 128

N.S.

1 1.00 0.71 0.63 1.11 0.78 1.42 1.11 1.11

time (sec)

N/A 0.052 0.058 1.633 0.191 0.249 0.618 0.300 3.244

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 188 161 157 0 565 275 248 0

N.S.

1 1.00 0.86 0.84 0.00 3.01 1.46 1.32 0.00

time (sec)

N/A 0.142 0.250 1.720 0.000 0.267 3.942 0.322 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 201 231 226 0 1004 0 271 0

N.S.

1 1.00 1.15 1.12 0.00 5.00 0.00 1.35 0.00

time (sec)

N/A 0.367 0.585 1.768 0.000 0.277 0.000 0.349 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

279 279 298 289 0 1661 0 529 0

N.S.

1 1.00 1.07 1.04 0.00 5.95 0.00 1.90 0.00

time (sec)

N/A 0.491 0.862 1.842 0.000 0.316 0.000 0.304 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

375 375 409 382 0 2446 0 976 0

N.S.

1 1.00 1.09 1.02 0.00 6.52 0.00 2.60 0.00

time (sec)

N/A 0.562 1.229 1.828 0.000 0.371 0.000 0.306 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

495 495 602 540 0 3624 0 1512 0

N.S.

1 1.00 1.22 1.09 0.00 7.32 0.00 3.05 0.00

time (sec)

N/A 0.682 3.203 1.916 0.000 0.488 0.000 0.325 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

434 434 500 440 629 677 853 1067 0

N.S.

1 1.00 1.15 1.01 1.45 1.56 1.97 2.46 0.00

time (sec)

N/A 0.253 0.472 1.771 0.203 0.279 70.974 0.313 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

322 322 326 289 395 419 534 651 0

N.S.

1 1.00 1.01 0.90 1.23 1.30 1.66 2.02 0.00

time (sec)

N/A 0.190 0.321 1.738 0.199 0.308 27.760 0.297 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

210 210 188 173 206 213 280 323 0

N.S.

1 1.00 0.90 0.82 0.98 1.01 1.33 1.54 0.00

time (sec)

N/A 0.119 0.164 1.685 0.208 0.268 7.845 0.289 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 113 82 74 102 100 144 127 0

N.S.

1 1.00 0.73 0.65 0.90 0.88 1.27 1.12 0.00

time (sec)

N/A 0.058 0.059 1.611 0.188 0.265 1.995 0.301 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 193 191 161 0 866 262 200 0

N.S.

1 1.00 0.99 0.83 0.00 4.49 1.36 1.04 0.00

time (sec)

N/A 0.171 0.352 1.722 0.000 0.333 8.481 0.285 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

253 253 259 228 0 1583 0 388 0

N.S.

1 1.00 1.02 0.90 0.00 6.26 0.00 1.53 0.00

time (sec)

N/A 0.387 0.649 1.826 0.000 0.329 0.000 0.291 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

350 350 387 379 0 2594 0 617 0

N.S.

1 1.00 1.11 1.08 0.00 7.41 0.00 1.76 0.00

time (sec)

N/A 0.537 1.381 1.956 0.000 0.387 0.000 0.295 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

463 463 561 511 0 3834 0 1085 0

N.S.

1 1.00 1.21 1.10 0.00 8.28 0.00 2.34 0.00

time (sec)

N/A 0.778 2.307 1.946 0.000 0.564 0.000 0.318 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

434 434 485 439 627 689 729 1030 0

N.S.

1 1.00 1.12 1.01 1.44 1.59 1.68 2.37 0.00

time (sec)

N/A 0.242 0.526 1.766 0.205 0.297 73.782 0.322 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

322 322 317 288 393 431 476 622 0

N.S.

1 1.00 0.98 0.89 1.22 1.34 1.48 1.93 0.00

time (sec)

N/A 0.165 0.355 1.727 0.206 0.293 29.349 0.301 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

210 210 177 168 204 225 282 302 0

N.S.

1 1.00 0.84 0.80 0.97 1.07 1.34 1.44 0.00

time (sec)

N/A 0.120 0.171 1.675 0.204 0.264 8.266 0.316 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 113 75 72 98 110 425 115 0

N.S.

1 1.00 0.66 0.64 0.87 0.97 3.76 1.02 0.00

time (sec)

N/A 0.044 0.068 1.637 0.190 0.280 0.363 0.294 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

210 210 230 202 0 1287 306 281 0

N.S.

1 1.00 1.10 0.96 0.00 6.13 1.46 1.34 0.00

time (sec)

N/A 0.207 0.470 1.817 0.000 0.299 10.433 0.300 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

336 336 354 275 0 2444 0 439 0

N.S.

1 1.00 1.05 0.82 0.00 7.27 0.00 1.31 0.00

time (sec)

N/A 0.528 0.902 2.005 0.000 0.371 0.000 0.302 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

438 438 554 459 0 3889 0 767 0

N.S.

1 1.00 1.26 1.05 0.00 8.88 0.00 1.75 0.00

time (sec)

N/A 0.823 1.537 1.955 0.000 0.513 0.000 0.326 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

455 455 418 3932 1802 4115 65321 9032 0

N.S.

1 1.00 0.92 8.64 3.96 9.04 143.56 19.85 0.00

time (sec)

N/A 0.265 2.034 1.769 0.267 0.357 11.925 0.350 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

338 338 308 2175 1118 2258 32849 4972 0

N.S.

1 1.00 0.91 6.43 3.31 6.68 97.19 14.71 0.00

time (sec)

N/A 0.186 0.771 1.694 0.238 0.323 6.732 0.335 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

226 226 199 964 596 988 13522 2224 0

N.S.

1 1.00 0.88 4.27 2.64 4.37 59.83 9.84 0.00

time (sec)

N/A 0.112 0.441 1.656 0.218 0.273 2.682 0.312 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 126 108 308 234 394 3798 728 0

N.S.

1 1.00 0.86 2.44 1.86 3.13 30.14 5.78 0.00

time (sec)

N/A 0.054 0.139 1.613 0.217 0.272 1.146 0.279 0.000

Problem 29

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

203 203 181 0 0 0 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.130 0.361 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(-2) F F(-1)

verified

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

size

220 220 180 0 0 0 0 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.357 0.691 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

329 329 188 0 0 0 0 0 0

N.S.

1 1.00 0.57 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.397 1.310 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 F(-2) F F(-1)

verified

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

size

141 141 117 0 0 0 0 0 0

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.063 0.105 0.000 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

268 266 187 0 0 0 0 0 0

N.S.

1 0.99 0.70 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.205 0.187 0.000 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

610 605 254 0 0 0 0 0 0

N.S.

1 0.99 0.42 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.709 0.241 0.000 0.000 0.000 0.000 0.000 0.000

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