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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 C B B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

210 210 172 4939 464 3073 64068 27992 1089

N.S.

1 1.00 0.82 23.52 2.21 14.63 305.09 133.30 5.19

time (sec)

N/A 0.176 0.923 7.531 0.253 0.372 13.378 0.488 9.903

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

160 160 129 2377 332 1524 25315 11834 588

N.S.

1 1.00 0.81 14.86 2.08 9.52 158.22 73.96 3.68

time (sec)

N/A 0.109 0.392 2.404 0.237 0.325 7.330 0.375 9.505

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

108 108 84 858 200 562 7796 3764 271

N.S.

1 1.00 0.78 7.94 1.85 5.20 72.19 34.85 2.51

time (sec)

N/A 0.057 0.251 0.346 0.211 0.272 3.819 0.303 9.134

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

66 66 49 229 91 185 1498 763 91

N.S.

1 1.00 0.74 3.47 1.38 2.80 22.70 11.56 1.38

time (sec)

N/A 0.026 0.101 0.167 0.202 0.272 1.658 0.284 9.056

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

120 120 95 0 0 0 872 0 0

N.S.

1 1.00 0.79 0.00 0.00 0.00 7.27 0.00 0.00

time (sec)

N/A 0.077 0.250 0.000 0.000 0.000 4.665 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

177 177 110 0 0 0 5176 0 0

N.S.

1 1.00 0.62 0.00 0.00 0.00 29.24 0.00 0.00

time (sec)

N/A 0.165 0.253 0.000 0.000 0.000 26.100 0.000 0.000

Problem 7

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

228 227 136 0 0 0 0 0 0

N.S.

1 1.00 0.60 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.171 0.421 0.000 0.000 0.000 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

318 318 273 11356 748 6638 168099 70422 1882

N.S.

1 1.00 0.86 35.71 2.35 20.87 528.61 221.45 5.92

time (sec)

N/A 0.266 1.575 7.880 0.278 0.460 23.345 0.851 10.779

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

237 237 199 5875 540 3515 72500 32523 1119

N.S.

1 1.00 0.84 24.79 2.28 14.83 305.91 137.23 4.72

time (sec)

N/A 0.194 0.885 3.334 0.280 0.367 14.262 0.508 9.870

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

160 160 129 2377 332 1426 25315 11834 588

N.S.

1 1.00 0.81 14.86 2.08 8.91 158.22 73.96 3.68

time (sec)

N/A 0.111 0.420 2.407 0.235 0.335 7.304 0.393 9.472

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

102 102 78 699 155 527 5882 2951 265

N.S.

1 1.00 0.76 6.85 1.52 5.17 57.67 28.93 2.60

time (sec)

N/A 0.051 0.181 4.920 0.197 0.285 3.126 0.295 9.124

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

185 185 153 0 0 0 1402 0 0

N.S.

1 1.00 0.83 0.00 0.00 0.00 7.58 0.00 0.00

time (sec)

N/A 0.144 0.403 0.000 0.000 0.000 9.548 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

268 268 159 0 0 0 0 0 0

N.S.

1 1.00 0.59 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.407 0.449 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(-1) F F(-1)

verified

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

size

322 322 168 0 0 0 0 0 0

N.S.

1 1.00 0.52 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.333 0.646 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 C B B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

410 410 358 20904 1032 11628 365145 143220 2949

N.S.

1 1.00 0.87 50.99 2.52 28.36 890.60 349.32 7.19

time (sec)

N/A 0.397 1.517 10.708 0.297 1.223 40.538 1.810 11.973

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

310 310 265 11356 748 6557 168099 70422 1882

N.S.

1 1.00 0.85 36.63 2.41 21.15 542.25 227.17 6.07

time (sec)

N/A 0.260 1.643 5.100 0.286 0.476 23.291 0.850 10.842

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

210 210 172 4939 464 2833 64068 27992 1089

N.S.

1 1.00 0.82 23.52 2.21 13.49 305.09 133.30 5.19

time (sec)

N/A 0.169 0.834 3.266 0.244 0.371 13.331 0.479 9.825

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B B B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

137 137 106 1576 219 1104 16781 7893 563

N.S.

1 1.00 0.77 11.50 1.60 8.06 122.49 57.61 4.11

time (sec)

N/A 0.076 0.225 2.430 0.207 0.307 5.488 0.325 9.287

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

270 270 229 0 0 0 1933 0 0

N.S.

1 1.00 0.85 0.00 0.00 0.00 7.16 0.00 0.00

time (sec)

N/A 0.249 0.809 0.000 0.000 0.000 16.884 0.000 0.000

Problem 20

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

394 389 217 0 0 0 0 0 0

N.S.

1 0.99 0.55 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.597 1.060 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 C F F(-1)

verified

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

size

380 380 332 0 0 0 2463 0 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 6.48 0.00 0.00

time (sec)

N/A 0.406 1.307 0.000 0.000 0.000 28.346 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

272 272 231 0 0 0 1933 0 0

N.S.

1 1.00 0.85 0.00 0.00 0.00 7.11 0.00 0.00

time (sec)

N/A 0.252 0.853 0.000 0.000 0.000 16.644 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

187 187 154 0 0 0 1402 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 7.50 0.00 0.00

time (sec)

N/A 0.157 0.449 0.000 0.000 0.000 9.442 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

122 122 95 0 0 0 872 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 7.15 0.00 0.00

time (sec)

N/A 0.081 0.243 0.000 0.000 0.000 4.568 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

78 78 57 0 0 0 377 0 0

N.S.

1 1.00 0.73 0.00 0.00 0.00 4.83 0.00 0.00

time (sec)

N/A 0.025 0.128 0.000 0.000 0.000 1.786 0.000 0.000

Problem 26

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

127 127 102 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 0.091 0.258 0.000 0.000 0.000 0.000 0.000 0.000

Problem 27

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

212 212 152 0 0 0 0 0 0

N.S.

1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.331 0.363 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(-2) F F(-1)

verified

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

size

407 407 199 0 0 0 0 0 0

N.S.

1 1.00 0.49 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.774 0.519 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 A A F F F F(-1) F F(-1)

verified

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

size

386 381 220 0 0 0 0 0 0

N.S.

1 0.99 0.57 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.672 1.132 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

267 267 161 0 0 0 0 0 0

N.S.

1 1.00 0.60 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.409 0.523 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 C F F(-1)

verified

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

size

178 178 110 0 0 0 5176 0 0

N.S.

1 1.00 0.62 0.00 0.00 0.00 29.08 0.00 0.00

time (sec)

N/A 0.162 0.271 0.000 0.000 0.000 25.678 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

107 107 83 0 0 0 2382 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 22.26 0.00 0.00

time (sec)

N/A 0.036 0.142 0.000 0.000 0.000 8.803 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

211 211 150 0 0 0 0 0 0

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.322 0.383 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

315 315 209 0 0 0 0 0 0

N.S.

1 1.00 0.66 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.659 0.567 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

567 567 270 0 0 0 0 0 0

N.S.

1 1.00 0.48 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.456 0.971 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 A A F F F F(-1) F F(-1)

verified

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

size

322 322 172 0 0 0 0 0 0

N.S.

1 1.00 0.53 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.350 0.698 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(-1) F F(-1)

verified

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

size

228 227 136 0 0 0 0 0 0

N.S.

1 1.00 0.60 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.180 0.425 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(-1) F F(-1)

verified

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

size

112 112 83 0 0 0 0 0 0

N.S.

1 1.00 0.74 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.037 0.145 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 F(-2) F F(-1)

verified

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

size

366 366 201 0 0 0 0 0 0

N.S.

1 1.00 0.55 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.767 0.496 0.000 0.000 0.000 0.000 0.000 0.000

Problem 40

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

482 482 271 0 0 0 0 0 0

N.S.

1 1.00 0.56 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.275 0.968 0.000 0.000 0.000 0.000 0.000 0.000

Problem 41

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

211 211 162 0 0 0 0 0 0

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.163 0.818 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(-2) F(-1)

verified

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

size

271 255 164 0 0 0 0 0 0

N.S.

1 0.94 0.61 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.206 0.278 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 A A F F F F(-2) F F(-1)

verified

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

size

164 164 138 0 0 0 0 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.119 0.642 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(-2) F F(-1)

verified

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

size

304 304 138 0 0 0 0 0 0

N.S.

1 1.00 0.45 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.331 0.774 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

139 139 124 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 0.074 0.410 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

139 167 124 0 0 0 0 0 0

N.S.

1 1.20 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.076 0.014 0.000 0.000 0.000 0.000 0.000 0.000

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