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Integrals 1 to 20

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 136 239 160 0 491 0 153 197

N.S.

1 1.00 1.76 1.18 0.00 3.61 0.00 1.12 1.45

time (sec)

N/A 0.263 0.470 2.360 0.000 0.356 0.000 0.303 2.743

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 131 82 0 258 0 76 226

N.S.

1 1.00 1.72 1.08 0.00 3.39 0.00 1.00 2.97

time (sec)

N/A 0.152 0.233 0.982 0.000 0.308 0.000 0.303 0.219

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 39 36 0 126 99 35 47

N.S.

1 1.00 1.11 1.03 0.00 3.60 2.83 1.00 1.34

time (sec)

N/A 0.049 0.046 0.279 0.000 0.274 1.279 0.298 3.183

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 129 126 121 0 470 0 130 1003

N.S.

1 1.00 0.98 0.94 0.00 3.64 0.00 1.01 7.78

time (sec)

N/A 0.201 0.153 0.869 0.000 0.681 0.000 0.280 5.482

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 205 392 241 0 1991 0 378 2742

N.S.

1 1.00 1.91 1.18 0.00 9.71 0.00 1.84 13.38

time (sec)

N/A 0.574 1.757 3.206 0.000 5.428 0.000 0.299 21.564

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

388 386 374 406 0 5045 0 11375 46613

N.S.

1 0.99 0.96 1.05 0.00 13.00 0.00 29.32 120.14

time (sec)

N/A 11.373 0.649 5.471 0.000 2.397 0.000 2.799 15.415

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

260 260 238 185 0 971 0 6566 16390

N.S.

1 1.00 0.92 0.71 0.00 3.73 0.00 25.25 63.04

time (sec)

N/A 1.448 0.462 0.709 0.000 0.343 0.000 2.512 14.827

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

326 326 335 393 0 16741 0 21750 39229

N.S.

1 1.00 1.03 1.21 0.00 51.35 0.00 66.72 120.33

time (sec)

N/A 3.457 0.699 11.984 0.000 3.380 0.000 2.628 15.471

Problem 9

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

21 21 19 16 15 17 15 17 9

N.S.

1 1.00 0.90 0.76 0.71 0.81 0.71 0.81 0.43

time (sec)

N/A 0.028 0.022 0.195 0.216 0.246 0.093 0.299 0.200

Problem 10

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

23 23 29 16 15 19 15 19 9

N.S.

1 1.00 1.26 0.70 0.65 0.83 0.65 0.83 0.39

time (sec)

N/A 0.028 0.014 0.205 0.303 0.244 0.102 0.291 0.143

Problem 11

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

19 19 18 18 15 19 26 15 15

N.S.

1 1.00 0.95 0.95 0.79 1.00 1.37 0.79 0.79

time (sec)

N/A 0.038 0.050 0.165 0.378 0.244 0.153 0.292 0.068

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 34 31 28 38 116 28 30

N.S.

1 1.00 0.94 0.86 0.78 1.06 3.22 0.78 0.83

time (sec)

N/A 0.036 0.087 0.765 0.688 0.254 0.470 0.320 0.075

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

326 326 356 431 0 8167 0 12587 45364

N.S.

1 1.00 1.09 1.32 0.00 25.05 0.00 38.61 139.15

time (sec)

N/A 4.624 0.602 4.716 0.000 5.516 0.000 2.775 16.240

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

299 299 309 331 0 6529 0 4810 29362

N.S.

1 1.00 1.03 1.11 0.00 21.84 0.00 16.09 98.20

time (sec)

N/A 7.401 0.469 3.276 0.000 2.349 0.000 3.237 14.653

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

255 255 264 261 0 4983 0 9030 20133

N.S.

1 1.00 1.04 1.02 0.00 19.54 0.00 35.41 78.95

time (sec)

N/A 1.296 1.359 2.203 0.000 1.063 0.000 2.162 16.964

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

230 230 227 208 0 3513 0 2973 5488

N.S.

1 1.00 0.99 0.90 0.00 15.27 0.00 12.93 23.86

time (sec)

N/A 0.594 0.840 1.173 0.000 0.568 0.000 2.341 13.304

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

223 223 198 204 0 3493 0 2994 5514

N.S.

1 1.00 0.89 0.91 0.00 15.66 0.00 13.43 24.73

time (sec)

N/A 0.359 0.662 1.121 0.000 0.517 0.000 1.456 13.765

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 245 281 274 0 5292 0 8954 20126

N.S.

1 1.00 1.15 1.12 0.00 21.60 0.00 36.55 82.15

time (sec)

N/A 0.805 1.035 2.746 0.000 74.287 0.000 2.382 15.389

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

275 275 348 354 0 6851 0 4784 29417

N.S.

1 1.00 1.27 1.29 0.00 24.91 0.00 17.40 106.97

time (sec)

N/A 1.298 1.905 4.664 0.000 257.772 0.000 2.905 14.792

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

334 334 446 481 0 0 0 12615 45255

N.S.

1 1.00 1.34 1.44 0.00 0.00 0.00 37.77 135.49

time (sec)

N/A 4.994 3.612 7.691 0.000 0.000 0.000 2.840 16.991

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