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2.2.1 Integrals 1 to 31

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.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 255 241 248 257 345 0 273

N.S.

1 1.00 1.39 1.31 1.35 1.40 1.88 0.00 1.48

time (sec)

N/A 0.100 0.323 0.251 0.467 1.383 0.441 0.000 1.049

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 218 179 184 190 262 0 197

N.S.

1 1.00 1.51 1.24 1.28 1.32 1.82 0.00 1.37

time (sec)

N/A 0.085 0.300 0.116 0.486 1.494 0.348 0.000 0.802

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 163 123 126 132 160 0 127

N.S.

1 1.00 1.58 1.19 1.22 1.28 1.55 0.00 1.23

time (sec)

N/A 0.063 0.225 0.112 0.474 1.540 0.269 0.000 0.353

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 77 78 73 73 87 0 67

N.S.

1 1.00 1.01 1.03 0.96 0.96 1.14 0.00 0.88

time (sec)

N/A 0.044 0.007 0.045 0.478 1.187 0.162 0.000 0.410

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 245 178 0 0 0 0 -1

N.S.

1 1.00 1.78 1.29 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.070 0.143 0.056 0.000 0.000 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 111 130 106 114 682 0 112

N.S.

1 1.00 1.13 1.33 1.08 1.16 6.96 0.00 1.14

time (sec)

N/A 0.037 0.133 0.102 0.471 1.136 1.485 0.000 3.460

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

146 146 192 188 206 299 2866 0 591

N.S.

1 1.00 1.32 1.29 1.41 2.05 19.63 0.00 4.05

time (sec)

N/A 0.086 0.220 0.143 0.480 1.358 3.419 0.000 4.428

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

206 206 254 286 354 620 9202 0 -1

N.S.

1 1.00 1.23 1.39 1.72 3.01 44.67 0.00 -0.00

time (sec)

N/A 0.130 0.427 0.196 0.491 1.991 7.258 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

376 376 472 880 0 0 0 0 -1

N.S.

1 1.00 1.26 2.34 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.394 0.524 0.356 0.000 0.000 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

270 270 312 700 0 0 0 0 -1

N.S.

1 1.00 1.16 2.59 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.264 0.352 0.232 0.000 0.000 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 172 340 0 0 0 0 -1

N.S.

1 1.00 1.01 1.99 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.204 0.137 0.124 0.000 0.000 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F C F F F F F

verified

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

size

223 223 0 1324 0 0 0 0 -1

N.S.

1 1.00 0.00 5.94 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.033 78.300 2.899 0.000 0.000 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

341 341 300 740 0 0 0 0 -1

N.S.

1 1.00 0.88 2.17 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.258 1.956 2.340 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

496 496 479 965 0 0 0 0 -1

N.S.

1 1.00 0.97 1.95 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.393 4.051 5.139 0.000 0.000 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

652 652 855 3456 0 0 0 0 -1

N.S.

1 1.00 1.31 5.30 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.822 1.211 22.015 0.000 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

411 411 621 2921 0 0 0 0 -1

N.S.

1 1.00 1.51 7.11 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.524 0.718 7.533 0.000 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

264 264 342 7195 0 0 0 0 -1

N.S.

1 1.00 1.30 27.25 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.384 0.321 1.451 0.000 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F C F F F F F

verified

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

size

320 320 0 2664 0 0 0 0 -1

N.S.

1 1.00 0.00 8.32 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.039 137.065 2.777 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F C F F F F(-1) F

verified

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

size

499 499 0 3050 0 0 0 0 -1

N.S.

1 1.00 0.00 6.11 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.364 85.555 2.879 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F C F(-1) F F(-1) F(-1) F

verified

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

size

936 936 0 41275 0 0 0 0 -1

N.S.

1 1.00 0.00 44.10 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.770 45.789 14.874 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

250 250 252 363 323 4652 403 308 419

N.S.

1 1.00 1.01 1.45 1.29 18.61 1.61 1.23 1.68

time (sec)

N/A 0.197 2.008 0.437 0.479 1.435 11.146 1.149 3.366

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 153 168 170 538 1266 184 203

N.S.

1 1.00 0.80 0.88 0.89 2.80 6.59 0.96 1.06

time (sec)

N/A 0.129 0.070 0.092 0.464 1.051 7.522 0.594 2.534

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

501 501 326 138 0 0 0 0 -1

N.S.

1 1.00 0.65 0.28 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.649 22.379 0.119 0.000 0.000 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

328 328 321 433 286 0 0 0 883

N.S.

1 1.00 0.98 1.32 0.87 0.00 0.00 0.00 2.69

time (sec)

N/A 0.349 0.473 0.182 0.483 0.000 0.000 0.000 0.661

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

1325 1325 5420 0 0 0 0 0 -1

N.S.

1 1.00 4.09 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.624 30.640 0.095 0.000 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.019 47.024 0.027 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 A F(-2) A F(-1) A A

verified

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

size

23 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.019 44.473 0.221 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

315 315 297 518 280 0 151 318 988

N.S.

1 1.00 0.94 1.64 0.89 0.00 0.48 1.01 3.14

time (sec)

N/A 0.496 102.002 9.230 0.567 0.000 28.537 9.908 0.517

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

285 285 310 315 234 0 104 250 485

N.S.

1 1.00 1.09 1.11 0.82 0.00 0.36 0.88 1.70

time (sec)

N/A 0.404 0.064 0.246 0.474 0.000 12.693 0.952 0.436

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F(-1) C F F F(-1) F F

verified

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

size

739 739 0 172 0 0 0 0 -1

N.S.

1 1.00 0.00 0.23 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.930 180.003 0.108 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

906 906 536 1220 449 0 0 0 2105

N.S.

1 1.00 0.59 1.35 0.50 0.00 0.00 0.00 2.32

time (sec)

N/A 0.936 10.004 0.398 0.490 0.000 0.000 0.000 0.776

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