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2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA and IntegrateAlgebraic to I.A.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A F(-1) B B B

verified

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

size

436 436 391 841 621 668 0 854 713 1261

N.S.

1 1.00 0.90 1.93 1.42 1.53 0.00 1.96 1.64 2.89

time (sec)

N/A 0.408 1.309 0.009 0.475 1.103 0.000 1.305 3.903 0.420

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B A

verified

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

size

324 324 287 505 387 410 1510 558 514 599

N.S.

1 1.00 0.89 1.56 1.19 1.27 4.66 1.72 1.59 1.85

time (sec)

N/A 0.272 0.690 0.007 0.473 0.614 157.827 1.281 3.488 0.243

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B A

verified

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

size

212 212 184 241 198 204 848 309 351 286

N.S.

1 1.00 0.87 1.14 0.93 0.96 4.00 1.46 1.66 1.35

time (sec)

N/A 0.173 0.314 0.006 0.441 0.578 87.368 1.247 3.301 0.137

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A B A

verified

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

size

115 115 82 91 128 90 354 128 128 107

N.S.

1 1.00 0.71 0.79 1.11 0.78 3.08 1.11 1.11 0.93

time (sec)

N/A 0.072 0.097 0.006 0.437 0.979 18.094 1.209 2.846 0.053

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B F(-2) A A A F A

verified

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

size

188 188 185 338 0 565 192 248 -1 201

N.S.

1 1.00 0.98 1.80 0.00 3.01 1.02 1.32 -0.01 1.07

time (sec)

N/A 0.206 0.270 0.015 0.000 0.800 66.262 1.261 0.000 0.294

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

201 201 244 566 0 1004 0 271 -1 346

N.S.

1 1.00 1.21 2.82 0.00 5.00 0.00 1.35 -0.00 1.72

time (sec)

N/A 0.518 0.442 0.022 0.000 0.739 0.000 1.321 0.000 0.586

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

279 279 359 1207 0 1661 0 529 -1 538

N.S.

1 1.00 1.29 4.33 0.00 5.95 0.00 1.90 -0.00 1.93

time (sec)

N/A 0.741 0.866 0.030 0.000 0.859 0.000 1.239 0.000 0.999

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

375 375 493 1186 0 2446 0 976 -1 776

N.S.

1 1.00 1.31 3.16 0.00 6.52 0.00 2.60 -0.00 2.07

time (sec)

N/A 0.821 1.394 0.029 0.000 0.934 0.000 1.564 0.000 1.669

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

495 495 621 3252 0 3624 0 1512 -1 1575

N.S.

1 1.00 1.25 6.57 0.00 7.32 0.00 3.05 -0.00 3.18

time (sec)

N/A 1.009 2.419 0.030 0.000 0.977 0.000 1.654 0.000 3.922

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A F(-1) B F B

verified

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

size

434 434 391 841 629 677 0 1067 -1 1000

N.S.

1 1.00 0.90 1.94 1.45 1.56 0.00 2.46 -0.00 2.30

time (sec)

N/A 0.359 1.161 0.010 0.472 0.626 0.000 1.489 0.000 0.436

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A B F A

verified

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

size

322 322 287 505 395 419 435 651 -1 599

N.S.

1 1.00 0.89 1.57 1.23 1.30 1.35 2.02 -0.00 1.86

time (sec)

N/A 0.259 0.667 0.009 0.465 0.657 148.595 1.373 0.000 0.297

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A F A

verified

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

size

210 210 188 241 206 213 230 323 -1 286

N.S.

1 1.00 0.90 1.15 0.98 1.01 1.10 1.54 -0.00 1.36

time (sec)

N/A 0.166 0.328 0.007 0.458 0.754 60.709 1.269 0.000 0.156

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A F A

verified

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

size

113 113 82 91 102 100 114 127 -1 107

N.S.

1 1.00 0.73 0.81 0.90 0.88 1.01 1.12 -0.01 0.95

time (sec)

N/A 0.081 0.093 0.005 0.434 0.849 20.138 1.288 0.000 0.057

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B F(-2) B A A F A

verified

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

size

193 193 174 366 0 866 172 200 -1 243

N.S.

1 1.00 0.90 1.90 0.00 4.49 0.89 1.04 -0.01 1.26

time (sec)

N/A 0.240 0.527 0.017 0.000 1.039 85.725 1.332 0.000 0.285

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

253 253 283 604 0 1583 0 388 -1 410

N.S.

1 1.00 1.12 2.39 0.00 6.26 0.00 1.53 -0.00 1.62

time (sec)

N/A 0.601 0.720 0.028 0.000 1.041 0.000 1.328 0.000 0.735

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

350 350 482 1225 0 2594 0 617 -1 729

N.S.

1 1.00 1.38 3.50 0.00 7.41 0.00 1.76 -0.00 2.08

time (sec)

N/A 0.832 1.418 0.033 0.000 1.100 0.000 1.413 0.000 1.411

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

463 463 697 2108 0 3834 0 1085 -1 1146

N.S.

1 1.00 1.51 4.55 0.00 8.28 0.00 2.34 -0.00 2.48

time (sec)

N/A 1.150 2.344 0.041 0.000 1.277 0.000 1.558 0.000 3.187

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A F(-1) B F B

verified

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

size

434 434 391 841 627 689 0 1030 -1 1000

N.S.

1 1.00 0.90 1.94 1.44 1.59 0.00 2.37 -0.00 2.30

time (sec)

N/A 0.353 0.727 0.010 0.476 0.958 0.000 1.451 0.000 0.438

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A F(-1) B F A

verified

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

size

322 322 287 505 393 431 0 622 -1 599

N.S.

1 1.00 0.89 1.57 1.22 1.34 0.00 1.93 -0.00 1.86

time (sec)

N/A 0.243 0.703 0.009 0.474 0.688 0.000 1.393 0.000 0.307

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A F A

verified

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

size

210 210 177 241 204 225 230 302 -1 286

N.S.

1 1.00 0.84 1.15 0.97 1.07 1.10 1.44 -0.00 1.36

time (sec)

N/A 0.172 0.309 0.007 0.456 0.821 82.476 1.217 0.000 0.157

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A A A F A

verified

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

size

113 113 75 90 98 110 425 115 -1 104

N.S.

1 1.00 0.66 0.80 0.87 0.97 3.76 1.02 -0.01 0.92

time (sec)

N/A 0.072 0.094 0.005 0.439 0.880 1.418 1.229 0.000 0.062

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B F(-2) B A A F A

verified

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

size

210 210 210 464 0 1287 214 281 -1 317

N.S.

1 1.00 1.00 2.21 0.00 6.13 1.02 1.34 -0.00 1.51

time (sec)

N/A 0.313 0.661 0.019 0.000 0.831 153.497 1.313 0.000 0.377

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

336 336 334 730 0 2444 0 439 -1 607

N.S.

1 1.00 0.99 2.17 0.00 7.27 0.00 1.31 -0.00 1.81

time (sec)

N/A 0.791 1.045 0.028 0.000 0.873 0.000 1.417 0.000 0.929

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

438 438 536 1376 0 3889 0 767 -1 1068

N.S.

1 1.00 1.22 3.14 0.00 8.88 0.00 1.75 -0.00 2.44

time (sec)

N/A 1.214 2.097 0.037 0.000 1.248 0.000 1.450 0.000 1.550

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B B B F(-1) B F F

verified

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

size

455 455 418 5003 1802 4115 0 9032 -1 0

N.S.

1 1.00 0.92 11.00 3.96 9.04 0.00 19.85 -0.00 0.00

time (sec)

N/A 0.338 0.680 0.035 0.764 1.071 0.000 1.865 0.000 1.171

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B B B F(-1) B F F

verified

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

size

338 338 308 2588 1118 2258 0 4972 -1 0

N.S.

1 1.00 0.91 7.66 3.31 6.68 0.00 14.71 -0.00 0.00

time (sec)

N/A 0.247 0.486 0.021 0.640 0.920 0.000 1.477 0.000 0.524

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B B B A B F F

verified

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

size

226 226 199 1039 596 988 13522 2224 -1 0

N.S.

1 1.00 0.88 4.60 2.64 4.37 59.83 9.84 -0.00 0.00

time (sec)

N/A 0.161 0.270 0.012 0.559 1.047 12.514 1.390 0.000 0.250

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A B A B F F

verified

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

size

126 126 108 308 234 394 3798 728 -1 0

N.S.

1 1.00 0.86 2.44 1.86 3.13 30.14 5.78 -0.01 0.00

time (sec)

N/A 0.072 0.113 0.008 0.485 0.873 4.322 1.316 0.000 0.076

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