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2.2.4 Integrals 301 to 321

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 301

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 17 11 12 54 17 15 16 11

N.S.

1 1.55 1.00 1.09 4.91 1.55 1.36 1.45 1.00

time (sec)

N/A 0.269 0.016 0.175 0.281 0.255 92.250 0.271 16.288

Problem 302

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

13 13 13 0 41 0 83 41 9

N.S.

1 1.00 1.00 0.00 3.15 0.00 6.38 3.15 0.69

time (sec)

N/A 0.170 0.019 0.000 0.286 0.000 0.243 0.272 16.432

Problem 303

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 12 13 94 22 83 12 35

N.S.

1 1.00 1.00 1.08 7.83 1.83 6.92 1.00 2.92

time (sec)

N/A 0.201 0.020 0.451 0.289 0.248 1.468 0.272 16.939

Problem 304

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 86 19 85 82 85 85

N.S.

1 1.00 1.00 4.53 1.00 4.47 4.32 4.47 4.47

time (sec)

N/A 0.233 0.051 0.264 0.195 0.233 0.466 0.289 17.036

Problem 305

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 190 86 67 0 71 100 66 66

N.S.

1 2.21 1.00 0.78 0.00 0.83 1.16 0.77 0.77

time (sec)

N/A 1.243 0.028 0.306 0.000 0.362 69.501 0.272 0.197

Problem 306

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

26 26 26 23 22 22 19 22 22

N.S.

1 1.00 1.00 0.88 0.85 0.85 0.73 0.85 0.85

time (sec)

N/A 0.172 0.027 0.215 0.276 0.242 0.030 0.276 0.051

Problem 307

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 0 25 0 0 12 0 12 0

N.S.

1 0.00 1.09 0.00 0.00 0.52 0.00 0.52 0.00

time (sec)

N/A 0.000 0.063 0.000 0.000 0.247 0.000 0.273 0.000

Problem 308

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

12 12 12 11 10 10 8 10 10

N.S.

1 1.00 1.00 0.92 0.83 0.83 0.67 0.83 0.83

time (sec)

N/A 0.132 0.056 0.219 0.199 0.232 0.232 0.264 0.104

Problem 309

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 22 34 46 15 27 42 0

N.S.

1 1.00 0.96 1.48 2.00 0.65 1.17 1.83 0.00

time (sec)

N/A 0.175 0.041 0.178 0.301 0.246 1.344 0.295 0.000

Problem 310

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 24 8 12 17 7 8 7

N.S.

1 1.00 2.67 0.89 1.33 1.89 0.78 0.89 0.78

time (sec)

N/A 0.174 0.027 0.167 0.206 0.258 0.099 0.267 0.097

Problem 311

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

22 22 22 23 34 24 20 22 18

N.S.

1 1.00 1.00 1.05 1.55 1.09 0.91 1.00 0.82

time (sec)

N/A 0.241 0.012 0.061 0.194 0.237 0.051 0.276 0.044

Problem 312

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 39 34 40 17 31 38

N.S.

1 1.00 1.00 1.77 1.55 1.82 0.77 1.41 1.73

time (sec)

N/A 0.150 0.042 0.112 0.185 0.244 0.764 0.283 0.102

Problem 313

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A C F B F B B

verified

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

size

21 0 21 52 0 84 0 136 15

N.S.

1 0.00 1.00 2.48 0.00 4.00 0.00 6.48 0.71

time (sec)

N/A 0.000 0.089 2.167 0.000 0.261 0.000 0.277 17.185

Problem 314

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

17 17 17 18 17 17 15 21 17

N.S.

1 1.00 1.00 1.06 1.00 1.00 0.88 1.24 1.00

time (sec)

N/A 0.290 0.065 0.315 0.248 0.244 0.061 0.272 17.009

Problem 315

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

45 37 107 0 0 37 4362 0 0

N.S.

1 0.82 2.38 0.00 0.00 0.82 96.93 0.00 0.00

time (sec)

N/A 0.282 0.535 0.000 0.000 0.302 3.878 0.000 0.000

Problem 316

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

54 54 54 45 44 44 49 44 44

N.S.

1 1.00 1.00 0.83 0.81 0.81 0.91 0.81 0.81

time (sec)

N/A 0.221 0.005 0.198 0.214 0.230 0.023 0.272 0.111

Problem 317

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A C A A F A B

verified

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

size

18 0 18 34 23 23 0 23 18

N.S.

1 0.00 1.00 1.89 1.28 1.28 0.00 1.28 1.00

time (sec)

N/A 0.000 0.014 0.336 0.292 0.234 0.000 0.277 16.642

Problem 318

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

61 65 77 0 56 108 0 57 0

N.S.

1 1.07 1.26 0.00 0.92 1.77 0.00 0.93 0.00

time (sec)

N/A 0.269 0.284 0.000 0.277 0.249 0.000 0.290 0.000

Problem 319

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 136 64 228 52 55 0 61 66

N.S.

1 2.12 1.00 3.56 0.81 0.86 0.00 0.95 1.03

time (sec)

N/A 2.076 0.478 0.737 0.206 0.284 0.000 37.520 19.383

Problem 320

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

105 0 105 0 0 148 0 0 0

N.S.

1 0.00 1.00 0.00 0.00 1.41 0.00 0.00 0.00

time (sec)

N/A 0.000 0.549 0.000 0.000 0.648 0.000 0.000 0.000

Problem 321

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

25 29 25 18 17 17 15 19 23

N.S.

1 1.16 1.00 0.72 0.68 0.68 0.60 0.76 0.92

time (sec)

N/A 0.182 0.006 0.055 0.202 0.236 0.080 0.335 0.105

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