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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 Reduce Mupad

grade

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

verified

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

size

249 257 160 204 1570 173 0 225 17 0

N.S.

1 1.03 0.64 0.82 6.31 0.69 0.00 0.90 0.07 0.00

time (sec)

N/A 0.751 0.793 2.021 0.761 0.086 0.000 0.328 0.167 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

123 125 112 99 580 119 0 181 33 0

N.S.

1 1.02 0.91 0.80 4.72 0.97 0.00 1.47 0.27 0.00

time (sec)

N/A 0.332 0.335 1.137 0.420 0.083 0.000 0.333 0.187 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

98 98 85 81 112 103 88 135 13 99

N.S.

1 1.00 0.87 0.83 1.14 1.05 0.90 1.38 0.13 1.01

time (sec)

N/A 0.270 0.193 0.677 0.044 0.082 0.197 0.343 0.166 41.469

Problem 4

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 N/A N/A N/A

verified

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

size

15 15 17 15 17 17 14 17 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.93 1.13 1.13 1.13

time (sec)

N/A 0.167 2.496 0.216 0.207 0.070 0.355 0.342 0.175 41.381

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

111 111 110 0 0 115 0 0 52 0

N.S.

1 1.00 0.99 0.00 0.00 1.04 0.00 0.00 0.47 0.00

time (sec)

N/A 0.304 2.962 0.000 0.000 0.090 0.000 0.000 0.163 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

251 261 164 224 1570 178 0 227 18 0

N.S.

1 1.04 0.65 0.89 6.25 0.71 0.00 0.90 0.07 0.00

time (sec)

N/A 0.723 0.756 1.731 0.906 0.082 0.000 0.366 0.180 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

124 127 116 110 580 125 0 183 36 0

N.S.

1 1.02 0.94 0.89 4.68 1.01 0.00 1.48 0.29 0.00

time (sec)

N/A 0.339 0.377 1.155 0.393 0.079 0.000 0.349 0.190 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

99 99 88 88 112 106 94 137 14 105

N.S.

1 1.00 0.89 0.89 1.13 1.07 0.95 1.38 0.14 1.06

time (sec)

N/A 0.277 0.192 0.698 0.044 0.077 0.208 0.339 0.194 0.051

Problem 9

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 N/A N/A N/A

verified

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

size

16 16 18 16 20 20 14 18 18 18

N.S.

1 1.00 1.12 1.00 1.25 1.25 0.88 1.12 1.12 1.12

time (sec)

N/A 0.169 2.064 0.217 0.159 0.069 0.390 0.374 0.249 41.214

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

111 111 114 0 0 123 0 0 54 0

N.S.

1 1.00 1.03 0.00 0.00 1.11 0.00 0.00 0.49 0.00

time (sec)

N/A 0.303 4.281 0.000 0.000 0.079 0.000 0.000 0.257 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

82 87 67 59 160 59 0 75 31 64

N.S.

1 1.06 0.82 0.72 1.95 0.72 0.00 0.91 0.38 0.78

time (sec)

N/A 0.367 0.159 1.640 0.223 0.075 0.000 0.345 0.264 41.310

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

41 41 39 30 126 32 155 65 21 32

N.S.

1 1.00 0.95 0.73 3.07 0.78 3.78 1.59 0.51 0.78

time (sec)

N/A 0.220 0.056 1.342 0.183 0.073 0.570 0.328 0.173 0.259

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 24 20 70 22 29 39 9 19

N.S.

1 1.00 1.00 0.83 2.92 0.92 1.21 1.62 0.38 0.79

time (sec)

N/A 0.181 0.031 0.834 0.134 0.074 0.190 0.300 0.197 41.348

Problem 14

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 N/A N/A N/A

verified

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

size

13 13 15 11 13 13 12 13 13 13

N.S.

1 1.00 1.15 0.85 1.00 1.00 0.92 1.00 1.00 1.00

time (sec)

N/A 0.164 13.433 0.185 0.149 0.066 0.316 0.320 0.182 41.306

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 N/A N/A N/A

verified

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

size

13 13 15 11 13 13 14 13 28 13

N.S.

1 1.00 1.15 0.85 1.00 1.00 1.08 1.00 2.15 1.00

time (sec)

N/A 0.297 11.246 0.171 0.196 0.080 0.296 0.357 0.192 41.396

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

248 248 170 191 1617 178 0 212 318 0

N.S.

1 1.00 0.69 0.77 6.52 0.72 0.00 0.85 1.28 0.00

time (sec)

N/A 0.452 0.743 1.706 0.800 0.084 0.000 0.333 0.198 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

126 126 116 95 610 124 0 170 17 0

N.S.

1 1.00 0.92 0.75 4.84 0.98 0.00 1.35 0.13 0.00

time (sec)

N/A 0.267 0.284 1.515 0.419 0.091 0.000 0.385 0.210 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

100 100 97 72 124 93 83 122 15 0

N.S.

1 1.00 0.97 0.72 1.24 0.93 0.83 1.22 0.15 0.00

time (sec)

N/A 0.236 0.117 1.419 0.124 0.083 0.436 0.333 0.179 0.000

Problem 19

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 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 17 28 19 15 19 19 19

N.S.

1 1.00 1.12 1.00 1.65 1.12 0.88 1.12 1.12 1.12

time (sec)

N/A 0.203 2.625 0.405 0.242 0.084 0.785 0.387 0.180 40.576

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

248 248 175 199 1617 187 0 214 324 0

N.S.

1 1.00 0.71 0.80 6.52 0.75 0.00 0.86 1.31 0.00

time (sec)

N/A 0.435 0.655 1.694 0.826 0.094 0.000 0.377 0.191 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

126 126 122 99 611 133 0 172 18 0

N.S.

1 1.00 0.97 0.79 4.85 1.06 0.00 1.37 0.14 0.00

time (sec)

N/A 0.284 0.284 1.556 0.421 0.082 0.000 0.345 0.170 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

100 100 100 76 124 96 88 124 16 0

N.S.

1 1.00 1.00 0.76 1.24 0.96 0.88 1.24 0.16 0.00

time (sec)

N/A 0.246 0.121 1.355 0.121 0.079 0.418 0.358 0.178 0.000

Problem 23

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 N/A N/A N/A

verified

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

size

18 18 20 18 28 22 15 20 20 20

N.S.

1 1.00 1.11 1.00 1.56 1.22 0.83 1.11 1.11 1.11

time (sec)

N/A 0.202 3.347 0.397 0.192 0.079 0.779 0.374 0.178 41.389

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

85 85 77 64 171 57 0 64 232 0

N.S.

1 1.00 0.91 0.75 2.01 0.67 0.00 0.75 2.73 0.00

time (sec)

N/A 0.246 0.169 2.157 0.220 0.077 0.000 0.354 0.186 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 46 41 35 136 37 121 54 13 0

N.S.

1 1.00 0.89 0.76 2.96 0.80 2.63 1.17 0.28 0.00

time (sec)

N/A 0.203 0.070 1.799 0.229 0.078 0.779 0.368 0.169 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

27 27 26 20 34 19 22 26 11 0

N.S.

1 1.00 0.96 0.74 1.26 0.70 0.81 0.96 0.41 0.00

time (sec)

N/A 0.185 0.018 1.660 0.112 0.073 0.342 0.386 0.171 0.000

Problem 27

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 N/A N/A N/A

verified

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

size

15 15 17 13 24 15 14 15 15 15

N.S.

1 1.00 1.13 0.87 1.60 1.00 0.93 1.00 1.00 1.00

time (sec)

N/A 0.197 7.554 0.372 0.220 0.074 0.608 0.365 0.191 42.253

Problem 28

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 N/A N/A N/A

verified

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

size

15 15 17 13 26 15 15 15 15 15

N.S.

1 1.00 1.13 0.87 1.73 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.232 8.606 0.375 0.151 0.078 0.511 0.391 0.177 42.600

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

285 282 187 396 2271 230 0 291 133 0

N.S.

1 0.99 0.66 1.39 7.97 0.81 0.00 1.02 0.47 0.00

time (sec)

N/A 0.791 1.381 1.977 1.059 0.110 0.000 0.377 0.175 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

140 134 129 182 695 136 0 201 82 0

N.S.

1 0.96 0.92 1.30 4.96 0.97 0.00 1.44 0.59 0.00

time (sec)

N/A 0.360 0.733 1.237 0.415 0.159 0.000 0.375 0.186 0.000

Problem 31

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 N/A N/A N/A

verified

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

size

19 19 21 19 21 21 17 21 21 21

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.89 1.11 1.11 1.11

time (sec)

N/A 0.174 3.701 0.460 0.196 0.070 0.331 0.369 0.171 42.521

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

291 291 215 378 2360 257 0 294 532 0

N.S.

1 1.00 0.74 1.30 8.11 0.88 0.00 1.01 1.83 0.00

time (sec)

N/A 0.559 1.113 2.251 1.059 0.090 0.000 0.400 0.202 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

150 150 139 170 737 149 0 195 37 0

N.S.

1 1.00 0.93 1.13 4.91 0.99 0.00 1.30 0.25 0.00

time (sec)

N/A 0.296 0.549 1.805 0.435 0.085 0.000 0.383 0.181 0.000

Problem 34

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 N/A N/A N/A

verified

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

size

21 21 23 21 120 23 19 23 23 23

N.S.

1 1.00 1.10 1.00 5.71 1.10 0.90 1.10 1.10 1.10

time (sec)

N/A 0.225 3.920 0.575 0.239 0.078 4.849 0.383 0.193 42.268

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