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Integrals 1 to 29

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 Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

31 31 31 34 30 109 61 24 32 27

N.S.

1 1.00 1.00 1.10 0.97 3.52 1.97 0.77 1.03 0.87

time (sec)

N/A 0.240 0.014 0.624 0.117 0.075 0.093 0.120 0.219 0.078

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

63 61 60 86 75 253 117 65 175 76

N.S.

1 0.97 0.95 1.37 1.19 4.02 1.86 1.03 2.78 1.21

time (sec)

N/A 0.256 0.033 0.549 0.111 0.089 0.256 0.132 0.223 0.104

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B B B A B B

verified

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

size

91 94 75 139 184 595 257 103 469 181

N.S.

1 1.03 0.82 1.53 2.02 6.54 2.82 1.13 5.15 1.99

time (sec)

N/A 0.284 0.070 0.540 0.117 0.085 0.577 0.125 0.217 8.967

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

10 10 10 11 18 10 24 10 10 10

N.S.

1 1.00 1.00 1.10 1.80 1.00 2.40 1.00 1.00 1.00

time (sec)

N/A 0.218 0.009 0.704 0.108 0.072 0.078 0.118 0.221 0.044

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

37 35 31 43 51 55 56 41 88 42

N.S.

1 0.95 0.84 1.16 1.38 1.49 1.51 1.11 2.38 1.14

time (sec)

N/A 0.240 0.018 0.681 0.108 0.073 0.204 0.119 0.228 0.072

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B B C A B B

verified

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

size

60 60 52 71 115 153 146 73 239 111

N.S.

1 1.00 0.87 1.18 1.92 2.55 2.43 1.22 3.98 1.85

time (sec)

N/A 0.276 0.023 0.697 0.117 0.083 0.448 0.127 0.282 9.054

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B B B B B B B B

verified

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

size

10 10 32 23 25 22 22 27 22 10

N.S.

1 1.00 3.20 2.30 2.50 2.20 2.20 2.70 2.20 1.00

time (sec)

N/A 0.225 0.007 0.524 0.026 0.078 0.074 0.121 0.221 0.065

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B A A B B

verified

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

size

39 37 45 52 56 85 54 56 142 43

N.S.

1 0.95 1.15 1.33 1.44 2.18 1.38 1.44 3.64 1.10

time (sec)

N/A 0.244 0.025 0.513 0.032 0.075 0.222 0.134 0.213 8.729

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B B B A B B

verified

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

size

64 64 65 78 122 220 141 88 378 114

N.S.

1 1.00 1.02 1.22 1.91 3.44 2.20 1.38 5.91 1.78

time (sec)

N/A 0.268 0.037 0.513 0.033 0.082 0.474 0.125 0.212 0.129

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B B B B B B B B

verified

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

size

4 4 15 12 11 11 10 13 11 4

N.S.

1 1.00 3.75 3.00 2.75 2.75 2.50 3.25 2.75 1.00

time (sec)

N/A 0.212 0.006 0.246 0.027 0.069 0.039 0.122 0.243 0.170

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

27 27 26 24 25 39 24 27 42 23

N.S.

1 1.00 0.96 0.89 0.93 1.44 0.89 1.00 1.56 0.85

time (sec)

N/A 0.238 0.024 0.264 0.030 0.067 0.048 0.129 0.206 0.074

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B A A B B

verified

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

size

45 50 37 36 44 71 44 39 78 36

N.S.

1 1.11 0.82 0.80 0.98 1.58 0.98 0.87 1.73 0.80

time (sec)

N/A 0.250 0.023 0.269 0.031 0.070 0.060 0.136 0.209 8.676

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A B A B A F B

verified

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

size

35 35 198 42 66 279 92 30 263 31

N.S.

1 1.00 5.66 1.20 1.89 7.97 2.63 0.86 7.51 0.89

time (sec)

N/A 0.260 0.137 0.690 0.105 0.115 0.098 0.127 0.221 0.116

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A B B B

verified

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

size

20 20 34 17 0 29 27 37 28 19

N.S.

1 1.00 1.70 0.85 0.00 1.45 1.35 1.85 1.40 0.95

time (sec)

N/A 0.343 0.084 0.092 0.000 0.081 0.687 0.127 0.212 8.695

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

17 17 19 15 17 32 14 0 37 17

N.S.

1 1.00 1.12 0.88 1.00 1.88 0.82 0.00 2.18 1.00

time (sec)

N/A 0.717 3.826 0.023 0.127 56.101 55.730 0.000 0.292 9.392

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

166 257 195 0 0 0 0 0 25 0

N.S.

1 1.55 1.17 0.00 0.00 0.00 0.00 0.00 0.15 0.00

time (sec)

N/A 0.761 2.669 0.000 0.000 0.000 0.000 0.000 0.259 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

180 268 0 0 0 0 0 0 29 0

N.S.

1 1.49 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 0.917 0.000 0.000 0.000 0.000 0.000 0.000 0.246 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

17 17 19 15 17 0 0 17 52 17

N.S.

1 1.00 1.12 0.88 1.00 0.00 0.00 1.00 3.06 1.00

time (sec)

N/A 0.853 3.310 0.010 0.277 0.000 0.000 0.349 0.290 9.211

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

41 39 40 36 35 33 49 38 31 33

N.S.

1 0.95 0.98 0.88 0.85 0.80 1.20 0.93 0.76 0.80

time (sec)

N/A 0.307 0.049 0.036 0.028 0.090 0.256 0.122 0.211 8.523

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

135 135 92 1013 0 1164 0 0 305 116

N.S.

1 1.00 0.68 7.50 0.00 8.62 0.00 0.00 2.26 0.86

time (sec)

N/A 0.657 0.301 0.062 0.000 0.166 0.000 0.000 0.246 9.574

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

292 292 452 910 0 0 0 0 258 0

N.S.

1 1.00 1.55 3.12 0.00 0.00 0.00 0.00 0.88 0.00

time (sec)

N/A 0.953 11.159 0.316 0.000 0.000 0.000 0.000 0.482 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

948 948 484 528 0 0 0 0 228 0

N.S.

1 1.00 0.51 0.56 0.00 0.00 0.00 0.00 0.24 0.00

time (sec)

N/A 3.548 11.016 0.569 0.000 0.000 0.000 0.000 0.477 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

559 559 773 0 0 0 0 0 61 0

N.S.

1 1.00 1.38 0.00 0.00 0.00 0.00 0.00 0.11 0.00

time (sec)

N/A 2.166 11.481 0.000 0.000 0.000 0.000 0.000 0.224 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

129 129 304 0 0 0 0 0 61 0

N.S.

1 1.00 2.36 0.00 0.00 0.00 0.00 0.00 0.47 0.00

time (sec)

N/A 0.633 0.702 0.000 0.000 0.000 0.000 0.000 0.405 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B B B B B B

verified

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

size

120 120 97 116 373 368 1535 478 330 115

N.S.

1 1.00 0.81 0.97 3.11 3.07 12.79 3.98 2.75 0.96

time (sec)

N/A 0.570 0.168 0.780 0.039 0.107 2.539 0.136 0.228 8.773

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B B B B

verified

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

size

58 58 57 56 70 112 478 168 102 55

N.S.

1 1.00 0.98 0.97 1.21 1.93 8.24 2.90 1.76 0.95

time (sec)

N/A 0.326 0.095 0.329 0.026 0.099 0.287 0.128 0.213 8.730

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

191 137 114 0 0 0 0 0 168 0

N.S.

1 0.72 0.60 0.00 0.00 0.00 0.00 0.00 0.88 0.00

time (sec)

N/A 0.587 0.389 0.000 0.000 0.000 0.000 0.000 0.213 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

312 437 324 0 0 0 0 0 0 0

N.S.

1 1.40 1.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.567 2.477 0.000 0.000 0.000 0.000 0.000 0.281 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

200 0 0 0 0 0 0 0 453 0

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.26 0.00

time (sec)

N/A 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.236 0.000

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