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Integrals 1 to 33

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 B B F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

225 225 149 252 755 429 0 163 0

N.S.

1 1.00 0.66 1.12 3.36 1.91 0.00 0.72 0.00

time (sec)

N/A 0.128 0.207 0.079 0.452 0.265 0.000 0.262 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 111 130 124 611 344 0 121 0

N.S.

1 1.00 1.17 1.12 5.50 3.10 0.00 1.09 0.00

time (sec)

N/A 0.034 0.103 0.048 0.399 0.290 0.000 0.268 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 105 83 464 112 0 79 0

N.S.

1 1.00 1.15 0.91 5.10 1.23 0.00 0.87 0.00

time (sec)

N/A 0.024 0.051 0.033 0.366 0.264 0.000 0.271 0.000

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 0.009 0.259 0.023 0.752 0.264 0.643 0.263 1.555

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

107 107 132 0 0 330 0 0 0

N.S.

1 1.00 1.23 0.00 0.00 3.08 0.00 0.00 0.00

time (sec)

N/A 0.064 4.537 0.000 0.000 0.247 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

227 227 152 244 834 466 0 167 0

N.S.

1 1.00 0.67 1.07 3.67 2.05 0.00 0.74 0.00

time (sec)

N/A 0.120 0.202 0.083 0.454 0.260 0.000 0.270 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 112 134 120 674 384 0 123 0

N.S.

1 1.00 1.20 1.07 6.02 3.43 0.00 1.10 0.00

time (sec)

N/A 0.046 0.103 0.050 0.390 0.261 0.000 0.266 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 109 79 511 116 0 81 0

N.S.

1 1.00 1.20 0.87 5.62 1.27 0.00 0.89 0.00

time (sec)

N/A 0.024 0.051 0.035 0.368 0.250 0.000 0.263 0.000

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 0.009 0.446 0.023 0.727 0.250 0.657 0.271 1.557

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

108 108 136 0 0 370 0 0 0

N.S.

1 1.00 1.26 0.00 0.00 3.43 0.00 0.00 0.00

time (sec)

N/A 0.067 5.784 0.000 0.000 0.266 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 72 75 183 129 0 53 0

N.S.

1 1.00 1.09 1.14 2.77 1.95 0.00 0.80 0.00

time (sec)

N/A 0.050 0.109 0.077 0.278 0.270 0.000 0.264 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 52 76 49 123 106 0 43 0

N.S.

1 1.00 1.46 0.94 2.37 2.04 0.00 0.83 0.00

time (sec)

N/A 0.020 0.054 0.047 0.265 0.253 0.000 0.267 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 22 25 94 14 0 21 0

N.S.

1 1.00 0.56 0.64 2.41 0.36 0.00 0.54 0.00

time (sec)

N/A 0.012 0.018 0.028 0.264 0.244 0.000 0.262 0.000

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 0.011 4.956 0.034 0.641 0.249 0.652 0.251 1.551

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 0.032 6.318 0.024 0.477 0.243 0.439 0.268 1.567

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

268 268 176 281 294 766 0 182 0

N.S.

1 1.00 0.66 1.05 1.10 2.86 0.00 0.68 0.00

time (sec)

N/A 0.189 0.516 0.177 0.301 0.261 0.000 0.263 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 136 155 141 200 647 0 142 0

N.S.

1 1.00 1.14 1.04 1.47 4.76 0.00 1.04 0.00

time (sec)

N/A 0.075 0.274 0.136 0.274 0.259 0.000 0.265 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 110 140 94 96 128 0 94 0

N.S.

1 1.00 1.27 0.85 0.87 1.16 0.00 0.85 0.00

time (sec)

N/A 0.050 0.097 0.092 0.272 0.248 0.000 0.262 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 51 19 15 19 19

N.S.

1 1.00 1.12 1.00 3.00 1.12 0.88 1.12 1.12

time (sec)

N/A 0.023 4.715 0.052 0.349 0.275 0.841 0.283 1.570

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

268 268 181 273 322 843 0 186 0

N.S.

1 1.00 0.68 1.02 1.20 3.15 0.00 0.69 0.00

time (sec)

N/A 0.168 0.509 0.159 0.294 0.271 0.000 0.274 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 136 161 137 216 729 0 144 0

N.S.

1 1.00 1.18 1.01 1.59 5.36 0.00 1.06 0.00

time (sec)

N/A 0.071 0.273 0.127 0.289 0.283 0.000 0.283 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 110 144 90 96 132 0 96 0

N.S.

1 1.00 1.31 0.82 0.87 1.20 0.00 0.87 0.00

time (sec)

N/A 0.051 0.103 0.097 0.262 0.251 0.000 0.266 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 51 22 15 20 20

N.S.

1 1.00 1.11 1.00 2.83 1.22 0.83 1.11 1.11

time (sec)

N/A 0.026 5.765 0.055 0.343 0.247 0.867 0.286 1.559

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 99 77 113 268 0 61 0

N.S.

1 1.00 1.46 1.13 1.66 3.94 0.00 0.90 0.00

time (sec)

N/A 0.084 0.155 0.200 0.304 0.250 0.000 0.260 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 88 75 121 306 0 70 0

N.S.

1 1.00 1.17 1.00 1.61 4.08 0.00 0.93 0.00

time (sec)

N/A 0.044 0.152 0.168 0.317 0.268 0.000 0.282 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 48 49 45 41 0 42 0

N.S.

1 1.00 0.86 0.88 0.80 0.73 0.00 0.75 0.00

time (sec)

N/A 0.026 0.050 0.109 0.264 0.249 0.000 0.265 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 43 15 14 15 15

N.S.

1 1.00 1.13 0.87 2.87 1.00 0.93 1.00 1.00

time (sec)

N/A 0.022 6.504 0.069 0.322 0.248 0.766 0.263 1.558

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

261 261 194 460 536 633 0 227 0

N.S.

1 1.00 0.74 1.76 2.05 2.43 0.00 0.87 0.00

time (sec)

N/A 0.141 0.360 0.219 0.365 0.269 0.000 0.266 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 128 146 200 254 412 0 139 0

N.S.

1 1.00 1.14 1.56 1.98 3.22 0.00 1.09 0.00

time (sec)

N/A 0.054 0.162 0.061 0.282 0.260 0.000 0.268 0.000

Problem 30

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 0.012 0.892 0.023 0.676 0.249 0.538 0.269 1.573

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

311 311 240 528 603 1142 0 263 0

N.S.

1 1.00 0.77 1.70 1.94 3.67 0.00 0.85 0.00

time (sec)

N/A 0.289 0.920 0.293 0.466 0.266 0.000 0.281 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 160 177 231 301 777 0 165 0

N.S.

1 1.00 1.11 1.44 1.88 4.86 0.00 1.03 0.00

time (sec)

N/A 0.112 0.440 0.162 0.373 0.273 0.000 0.281 0.000

Problem 33

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 72 23 19 23 23

N.S.

1 1.00 1.10 1.00 3.43 1.10 0.90 1.10 1.10

time (sec)

N/A 0.032 2.490 0.049 0.364 0.246 41.993 0.298 1.613

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