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Integrals 1 to 34

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 C A F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

249 249 160 204 1570 173 0 227 0

N.S.

1 1.00 0.64 0.82 6.31 0.69 0.00 0.91 0.00

time (sec)

N/A 0.345 0.471 1.853 1.070 0.320 0.000 0.338 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 123 112 99 580 119 0 183 0

N.S.

1 1.00 0.91 0.80 4.72 0.97 0.00 1.49 0.00

time (sec)

N/A 0.074 0.197 0.844 0.630 0.272 0.000 0.333 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 98 85 81 112 103 88 135 99

N.S.

1 1.00 0.87 0.83 1.14 1.05 0.90 1.38 1.01

time (sec)

N/A 0.031 0.115 0.357 0.239 0.302 0.218 0.333 0.080

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

15 15 17 15 17 17 14 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.93 1.13 1.13

time (sec)

N/A 0.013 2.150 0.227 0.361 0.262 0.383 0.340 13.744

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

111 111 110 0 0 115 0 0 0

N.S.

1 1.00 0.99 0.00 0.00 1.04 0.00 0.00 0.00

time (sec)

N/A 0.144 1.719 0.000 0.000 0.287 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

251 251 164 224 1570 178 0 229 0

N.S.

1 1.00 0.65 0.89 6.25 0.71 0.00 0.91 0.00

time (sec)

N/A 0.326 0.458 1.755 1.104 0.286 0.000 0.325 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 124 116 110 580 125 0 185 0

N.S.

1 1.00 0.94 0.89 4.68 1.01 0.00 1.49 0.00

time (sec)

N/A 0.060 0.206 0.855 0.618 0.293 0.000 0.373 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 99 88 88 112 106 94 137 105

N.S.

1 1.00 0.89 0.89 1.13 1.07 0.95 1.38 1.06

time (sec)

N/A 0.032 0.118 0.332 0.246 0.275 0.226 0.363 0.054

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 20 20 14 18 18

N.S.

1 1.00 1.12 1.00 1.25 1.25 0.88 1.12 1.12

time (sec)

N/A 0.017 2.046 0.251 0.366 0.266 0.398 0.338 14.376

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

111 111 114 0 0 123 0 0 0

N.S.

1 1.00 1.03 0.00 0.00 1.11 0.00 0.00 0.00

time (sec)

N/A 0.156 2.419 0.000 0.000 0.274 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 67 59 160 59 0 75 64

N.S.

1 1.00 0.82 0.72 1.95 0.72 0.00 0.91 0.78

time (sec)

N/A 0.055 0.095 1.862 0.440 0.260 0.000 0.433 0.116

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 39 30 126 32 155 65 32

N.S.

1 1.00 0.95 0.73 3.07 0.78 3.78 1.59 0.78

time (sec)

N/A 0.022 0.033 1.584 0.401 0.266 0.661 0.473 14.528

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 20 70 22 29 39 19

N.S.

1 1.00 1.00 0.83 2.92 0.92 1.21 1.62 0.79

time (sec)

N/A 0.007 0.019 0.662 0.320 0.274 0.200 0.398 0.043

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

13 13 15 11 13 13 12 13 13

N.S.

1 1.00 1.15 0.85 1.00 1.00 0.92 1.00 1.00

time (sec)

N/A 0.010 9.941 0.183 0.349 0.268 0.354 0.406 13.770

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

13 13 15 11 13 13 14 13 13

N.S.

1 1.00 1.15 0.85 1.00 1.00 1.08 1.00 1.00

time (sec)

N/A 0.043 10.619 0.208 0.360 0.281 0.326 0.407 14.017

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 248 170 191 1617 178 0 214 0

N.S.

1 1.00 0.69 0.77 6.52 0.72 0.00 0.86 0.00

time (sec)

N/A 0.333 0.454 0.684 1.061 0.345 0.000 0.462 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 126 116 95 610 124 0 172 0

N.S.

1 1.00 0.92 0.75 4.84 0.98 0.00 1.37 0.00

time (sec)

N/A 0.075 0.173 0.722 0.635 0.290 0.000 0.438 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 100 97 72 124 93 83 122 0

N.S.

1 1.00 0.97 0.72 1.24 0.93 0.83 1.22 0.00

time (sec)

N/A 0.060 0.070 0.590 0.325 0.270 0.466 0.444 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

17 17 19 17 28 19 15 19 19

N.S.

1 1.00 1.12 1.00 1.65 1.12 0.88 1.12 1.12

time (sec)

N/A 0.034 3.959 0.428 0.399 0.270 0.798 0.485 13.750

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 248 175 199 1617 187 0 216 0

N.S.

1 1.00 0.71 0.80 6.52 0.75 0.00 0.87 0.00

time (sec)

N/A 0.258 0.399 0.663 1.055 0.269 0.000 0.418 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 126 122 99 611 133 0 174 0

N.S.

1 1.00 0.97 0.79 4.85 1.06 0.00 1.38 0.00

time (sec)

N/A 0.081 0.173 0.666 0.699 0.287 0.000 0.431 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 100 100 76 124 96 88 124 0

N.S.

1 1.00 1.00 0.76 1.24 0.96 0.88 1.24 0.00

time (sec)

N/A 0.057 0.072 0.682 0.330 0.285 0.452 0.438 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 28 22 15 20 20

N.S.

1 1.00 1.11 1.00 1.56 1.22 0.83 1.11 1.11

time (sec)

N/A 0.032 4.132 0.393 0.382 0.270 0.838 0.500 13.403

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 85 77 64 171 57 0 64 0

N.S.

1 1.00 0.91 0.75 2.01 0.67 0.00 0.75 0.00

time (sec)

N/A 0.070 0.104 1.428 0.430 0.275 0.000 0.503 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 41 35 136 37 121 54 0

N.S.

1 1.00 0.89 0.76 2.96 0.80 2.63 1.17 0.00

time (sec)

N/A 0.035 0.043 1.313 0.382 0.273 0.919 0.460 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 26 20 34 19 22 26 0

N.S.

1 1.00 0.96 0.74 1.26 0.70 0.81 0.96 0.00

time (sec)

N/A 0.017 0.011 1.264 0.304 0.266 0.374 0.593 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

15 15 17 13 24 15 14 15 15

N.S.

1 1.00 1.13 0.87 1.60 1.00 0.93 1.00 1.00

time (sec)

N/A 0.029 7.145 0.363 0.358 0.265 0.662 0.533 13.385

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

15 15 17 13 26 15 15 15 15

N.S.

1 1.00 1.13 0.87 1.73 1.00 1.00 1.00 1.00

time (sec)

N/A 0.058 7.053 0.401 0.339 0.273 0.594 0.405 13.308

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

285 285 187 396 2271 230 0 289 0

N.S.

1 1.00 0.66 1.39 7.97 0.81 0.00 1.01 0.00

time (sec)

N/A 0.310 0.788 2.376 1.336 0.269 0.000 0.347 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 140 129 182 695 136 0 199 0

N.S.

1 1.00 0.92 1.30 4.96 0.97 0.00 1.42 0.00

time (sec)

N/A 0.055 0.440 0.752 0.593 0.287 0.000 0.333 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

19 19 21 19 21 21 17 21 21

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.89 1.11 1.11

time (sec)

N/A 0.014 3.237 0.429 0.385 0.269 0.345 0.351 13.456

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

291 291 215 378 2360 257 0 292 0

N.S.

1 1.00 0.74 1.30 8.11 0.88 0.00 1.00 0.00

time (sec)

N/A 0.370 0.699 1.391 1.382 0.303 0.000 0.371 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 150 139 170 737 149 0 195 0

N.S.

1 1.00 0.93 1.13 4.91 0.99 0.00 1.30 0.00

time (sec)

N/A 0.112 0.326 0.776 0.649 0.280 0.000 0.353 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

21 21 23 21 120 23 19 23 23

N.S.

1 1.00 1.10 1.00 5.71 1.10 0.90 1.10 1.10

time (sec)

N/A 0.045 4.466 0.544 0.382 0.279 41.990 0.396 14.124

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