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2.2.1 Integrals 1 to 31

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 F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

184 185 255 246 252 264 345 0 273

N.S.

1 1.01 1.39 1.34 1.37 1.43 1.88 0.00 1.48

time (sec)

N/A 0.347 0.516 2.574 0.299 0.255 0.451 0.000 0.922

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 139 218 191 186 196 262 0 197

N.S.

1 0.97 1.51 1.33 1.29 1.36 1.82 0.00 1.37

time (sec)

N/A 0.309 0.475 1.485 0.289 0.257 0.371 0.000 0.868

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 110 163 119 126 133 160 0 127

N.S.

1 1.07 1.58 1.16 1.22 1.29 1.55 0.00 1.23

time (sec)

N/A 0.283 0.395 1.224 0.289 0.247 0.323 0.000 0.378

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 77 77 69 71 71 87 0 67

N.S.

1 1.01 1.01 0.91 0.93 0.93 1.14 0.00 0.88

time (sec)

N/A 0.249 0.009 0.418 0.266 0.250 0.249 0.000 0.438

Problem 5

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

138 138 138 156 0 0 0 0 0

N.S.

1 1.00 1.00 1.13 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.433 0.076 3.097 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 A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 94 111 110 107 116 658 0 112

N.S.

1 0.96 1.13 1.12 1.09 1.18 6.71 0.00 1.14

time (sec)

N/A 0.249 0.232 1.576 0.281 0.268 1.503 0.000 3.760

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

146 157 192 153 214 313 2866 0 591

N.S.

1 1.08 1.32 1.05 1.47 2.14 19.63 0.00 4.05

time (sec)

N/A 0.332 0.356 1.623 0.285 0.346 3.271 0.000 4.808

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

206 210 254 204 374 642 9202 0 0

N.S.

1 1.02 1.23 0.99 1.82 3.12 44.67 0.00 0.00

time (sec)

N/A 0.402 0.678 1.947 0.278 0.639 7.693 0.000 0.000

Problem 9

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

376 375 472 667 0 0 0 0 0

N.S.

1 1.00 1.26 1.77 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.751 0.951 3.124 0.000 0.000 0.000 0.000 0.000

Problem 10

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

270 284 312 503 0 0 0 0 0

N.S.

1 1.05 1.16 1.86 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.592 0.605 2.078 0.000 0.000 0.000 0.000 0.000

Problem 11

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

171 184 172 292 0 0 0 0 0

N.S.

1 1.08 1.01 1.71 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.473 0.482 1.333 0.000 0.000 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes N/A No TBD TBD TBD TBD TBD

size

223 223 0 1199 0 0 0 0 0

N.S.

1 1.00 0.00 5.38 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.294 0.000 68.260 0.000 0.000 0.000 0.000 0.000

Problem 13

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

341 350 300 513 0 0 0 0 0

N.S.

1 1.03 0.88 1.50 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.630 3.199 21.774 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 A F(-1) F F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

496 496 479 729 0 0 0 0 0

N.S.

1 1.00 0.97 1.47 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.815 6.540 28.132 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 C F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

652 645 855 3122 0 0 0 0 0

N.S.

1 0.99 1.31 4.79 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.369 2.007 93.443 0.000 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

411 430 621 2633 0 0 0 0 0

N.S.

1 1.05 1.51 6.41 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.951 1.163 32.974 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 A C F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

264 278 342 3886 0 0 0 0 0

N.S.

1 1.05 1.30 14.72 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.718 0.978 7.927 0.000 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes N/A No TBD TBD TBD TBD TBD

size

320 320 0 2398 0 0 0 0 0

N.S.

1 1.00 0.00 7.49 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.347 0.000 18.202 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes N/A No TBD TBD TBD TBD TBD

size

499 502 0 2398 0 0 0 0 0

N.S.

1 1.01 0.00 4.81 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.783 0.000 22.853 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes N/A No TBD TBD TBD TBD TBD

size

936 921 0 40258 0 0 0 0 0

N.S.

1 0.98 0.00 43.01 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.365 0.000 93.310 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 A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

250 256 252 303 323 1013 403 304 419

N.S.

1 1.02 1.01 1.21 1.29 4.05 1.61 1.22 1.68

time (sec)

N/A 0.497 3.220 2.214 0.298 0.278 10.176 1.052 3.590

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

192 200 153 146 168 274 1266 184 203

N.S.

1 1.04 0.80 0.76 0.88 1.43 6.59 0.96 1.06

time (sec)

N/A 0.404 0.112 0.569 0.300 0.256 6.616 0.461 2.689

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

501 469 326 138 0 0 0 0 0

N.S.

1 0.94 0.65 0.28 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.081 21.058 1.266 0.000 0.000 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

328 338 321 297 287 2478078 0 0 883

N.S.

1 1.03 0.98 0.91 0.88 7555.12 0.00 0.00 2.69

time (sec)

N/A 0.708 0.756 1.395 0.278 74.552 0.000 0.000 0.702

Problem 25

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 No N/A TBD TBD TBD TBD TBD

size

1325 1325 4824 0 0 0 0 0 0

N.S.

1 1.00 3.64 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.309 36.630 0.000 0.000 0.000 0.000 0.000 0.000

Problem 26

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 47 36 0 22 22

N.S.

1 1.00 1.10 1.00 2.35 1.80 0.00 1.10 1.10

time (sec)

N/A 0.183 51.612 0.450 0.618 0.230 0.000 0.280 0.385

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A F(-2) 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 0 47 0 22 22

N.S.

1 1.00 1.10 1.00 0.00 2.35 0.00 1.10 1.10

time (sec)

N/A 0.183 108.058 1.016 0.000 0.247 0.000 2.098 0.491

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

315 325 297 503 280 0 151 312 988

N.S.

1 1.03 0.94 1.60 0.89 0.00 0.48 0.99 3.14

time (sec)

N/A 0.784 106.475 33.358 0.296 0.000 22.953 9.729 0.588

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

285 297 310 305 232 0 104 236 485

N.S.

1 1.04 1.09 1.07 0.81 0.00 0.36 0.83 1.70

time (sec)

N/A 0.715 0.076 0.698 0.305 0.000 10.826 0.825 0.478

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

739 687 522 172 0 0 0 0 0

N.S.

1 0.93 0.71 0.23 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.382 11.976 1.235 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 A A F(-1) F(-1) F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

906 913 536 862 464 0 0 0 2105

N.S.

1 1.01 0.59 0.95 0.51 0.00 0.00 0.00 2.32

time (sec)

N/A 1.450 10.475 1.727 0.314 0.000 0.000 0.000 0.836

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