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Integrals 1 to 35

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 C A A A B A B B

verified

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

size

22 22 77 18 20 25 61 18 17 16

N.S.

1 1.00 3.50 0.82 0.91 1.14 2.77 0.82 0.77 0.73

time (sec)

N/A 0.160 0.050 0.189 0.104 0.084 3.797 0.126 0.147 0.147

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

32 30 49 50 0 44 0 147 59 49

N.S.

1 0.94 1.53 1.56 0.00 1.38 0.00 4.59 1.84 1.53

time (sec)

N/A 0.190 0.116 0.025 0.000 0.070 0.000 0.143 0.154 0.529

Problem 3

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

25 25 16 16 23 20 14 15 14 14

N.S.

1 1.00 0.64 0.64 0.92 0.80 0.56 0.60 0.56 0.56

time (sec)

N/A 0.190 0.008 0.056 0.029 0.068 0.147 0.122 0.149 0.106

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

58 58 68 42 112 46 53 43 11 0

N.S.

1 1.00 1.17 0.72 1.93 0.79 0.91 0.74 0.19 0.00

time (sec)

N/A 0.349 0.013 0.138 0.112 0.081 0.823 0.120 0.153 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

50 55 26 30 56 67 838 32 67 88

N.S.

1 1.10 0.52 0.60 1.12 1.34 16.76 0.64 1.34 1.76

time (sec)

N/A 0.269 0.026 0.369 0.032 0.071 2.347 0.122 0.150 0.156

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

334 362 30 34 0 149 26 248 216 313

N.S.

1 1.08 0.09 0.10 0.00 0.45 0.08 0.74 0.65 0.94

time (sec)

N/A 0.615 0.004 0.230 0.000 0.080 1.144 0.127 0.152 0.149

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

291 0 310 172 366 0 0 0 335 0

N.S.

1 0.00 1.07 0.59 1.26 0.00 0.00 0.00 1.15 0.00

time (sec)

N/A 0.000 0.186 0.222 0.115 0.000 0.000 0.000 0.187 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

308 0 326 199 378 0 0 0 17 0

N.S.

1 0.00 1.06 0.65 1.23 0.00 0.00 0.00 0.06 0.00

time (sec)

N/A 0.000 0.095 0.028 0.126 0.000 0.000 0.000 0.150 0.000

Problem 9

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 No Yes N/A TBD TBD TBD TBD TBD TBD

size

84 73 105 0 0 66 0 0 155 0

N.S.

1 0.87 1.25 0.00 0.00 0.79 0.00 0.00 1.85 0.00

time (sec)

N/A 0.252 0.129 0.000 0.000 0.073 0.000 0.000 29.220 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

41 71 41 34 51 101 65 51 46 0

N.S.

1 1.73 1.00 0.83 1.24 2.46 1.59 1.24 1.12 0.00

time (sec)

N/A 0.432 0.058 0.066 0.109 0.073 4.681 0.129 0.153 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

73 75 69 46 63 112 76 67 73 0

N.S.

1 1.03 0.95 0.63 0.86 1.53 1.04 0.92 1.00 0.00

time (sec)

N/A 0.356 0.082 0.146 0.111 0.077 2.396 0.380 0.148 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

73 103 52 60 77 110 88 79 55 0

N.S.

1 1.41 0.71 0.82 1.05 1.51 1.21 1.08 0.75 0.00

time (sec)

N/A 0.514 0.051 0.049 0.113 0.084 3.937 0.333 0.157 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

365 367 217 109 0 5235 0 0 25 0

N.S.

1 1.01 0.59 0.30 0.00 14.34 0.00 0.00 0.07 0.00

time (sec)

N/A 0.989 0.157 0.116 0.000 5.681 0.000 0.000 0.158 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

337 339 212 105 0 4535 0 0 17 0

N.S.

1 1.01 0.63 0.31 0.00 13.46 0.00 0.00 0.05 0.00

time (sec)

N/A 0.835 0.144 0.119 0.000 3.086 0.000 0.000 0.169 0.000

Problem 15

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

77 77 74 0 0 56 0 0 17 0

N.S.

1 1.00 0.96 0.00 0.00 0.73 0.00 0.00 0.22 0.00

time (sec)

N/A 0.245 10.027 0.000 0.000 0.358 0.000 0.000 0.172 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

118 118 112 0 0 73 0 0 20 0

N.S.

1 1.00 0.95 0.00 0.00 0.62 0.00 0.00 0.17 0.00

time (sec)

N/A 0.391 10.055 0.000 0.000 0.724 0.000 0.000 0.173 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

83 92 77 298 0 81 0 188 86 0

N.S.

1 1.11 0.93 3.59 0.00 0.98 0.00 2.27 1.04 0.00

time (sec)

N/A 0.307 0.144 0.042 0.000 1.654 0.000 0.363 0.174 0.000

Problem 18

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

96 106 89 0 0 122 0 0 15 0

N.S.

1 1.10 0.93 0.00 0.00 1.27 0.00 0.00 0.16 0.00

time (sec)

N/A 0.292 0.350 0.000 0.000 1.675 0.000 0.000 180.019 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

25 25 65 49 36 34 0 55 27 0

N.S.

1 1.00 2.60 1.96 1.44 1.36 0.00 2.20 1.08 0.00

time (sec)

N/A 0.241 0.111 0.071 0.110 0.072 0.000 0.147 0.161 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

25 25 57 33 35 55 0 54 20 0

N.S.

1 1.00 2.28 1.32 1.40 2.20 0.00 2.16 0.80 0.00

time (sec)

N/A 0.234 0.050 0.217 0.104 0.074 0.000 0.137 0.147 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

108 184 213 95 12209 219 0 104 59 307

N.S.

1 1.70 1.97 0.88 113.05 2.03 0.00 0.96 0.55 2.84

time (sec)

N/A 0.330 3.885 134.336 0.688 0.113 0.000 0.122 0.160 0.699

Problem 22

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

29 29 56 27 40 46 66 30 46 26

N.S.

1 1.00 1.93 0.93 1.38 1.59 2.28 1.03 1.59 0.90

time (sec)

N/A 0.221 0.025 0.185 0.027 0.081 0.298 0.112 0.157 0.158

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

26 26 26 20 43 129 0 21 9 19

N.S.

1 1.00 1.00 0.77 1.65 4.96 0.00 0.81 0.35 0.73

time (sec)

N/A 0.180 0.014 0.141 0.107 0.074 0.000 0.131 0.155 0.090

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

110 126 121 366 0 501 0 470 24 0

N.S.

1 1.15 1.10 3.33 0.00 4.55 0.00 4.27 0.22 0.00

time (sec)

N/A 0.546 0.089 0.414 0.000 0.093 0.000 0.241 0.155 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

40 40 86 75 0 23 0 0 15 0

N.S.

1 1.00 2.15 1.88 0.00 0.58 0.00 0.00 0.38 0.00

time (sec)

N/A 0.437 10.899 0.316 0.000 0.070 0.000 0.000 0.167 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

185 349 920 469 0 270 0 301 179 608

N.S.

1 1.89 4.97 2.54 0.00 1.46 0.00 1.63 0.97 3.29

time (sec)

N/A 1.107 0.359 0.179 0.000 0.114 0.000 0.190 0.177 1.194

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

102 102 102 83 0 0 0 0 18 0

N.S.

1 1.00 1.00 0.81 0.00 0.00 0.00 0.00 0.18 0.00

time (sec)

N/A 0.316 0.015 0.058 0.000 0.000 0.000 0.000 0.159 0.000

Problem 28

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

159 161 122 0 0 0 0 0 342 0

N.S.

1 1.01 0.77 0.00 0.00 0.00 0.00 0.00 2.15 0.00

time (sec)

N/A 0.401 0.071 0.000 0.000 0.000 0.000 0.000 0.167 0.000

Problem 29

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

395 410 389 0 0 0 0 0 15 0

N.S.

1 1.04 0.98 0.00 0.00 0.00 0.00 0.00 0.04 0.00

time (sec)

N/A 0.730 0.158 0.000 0.000 0.000 0.000 0.000 0.154 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

981 983 0 722 0 0 0 0 17 0

N.S.

1 1.00 0.00 0.74 0.00 0.00 0.00 0.00 0.02 0.00

time (sec)

N/A 1.398 0.000 0.109 0.000 0.000 0.000 0.000 0.161 0.000

Problem 31

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

555 580 1280 0 0 0 0 0 22 0

N.S.

1 1.05 2.31 0.00 0.00 0.00 0.00 0.00 0.04 0.00

time (sec)

N/A 0.928 6.916 0.000 0.000 0.000 0.000 0.000 0.156 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

313 337 303 252 0 0 0 0 13 0

N.S.

1 1.08 0.97 0.81 0.00 0.00 0.00 0.00 0.04 0.00

time (sec)

N/A 0.569 0.071 0.135 0.000 0.000 0.000 0.000 0.160 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

80 83 262 113 84 220 0 0 7 0

N.S.

1 1.04 3.28 1.41 1.05 2.75 0.00 0.00 0.09 0.00

time (sec)

N/A 0.323 0.178 0.533 0.109 0.099 0.000 0.000 0.153 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

57 51 44 71 31 0 0 0 10 0

N.S.

1 0.89 0.77 1.25 0.54 0.00 0.00 0.00 0.18 0.00

time (sec)

N/A 0.304 0.043 0.642 0.147 0.000 0.000 0.000 0.162 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

121 134 131 178 0 0 0 0 13 0

N.S.

1 1.11 1.08 1.47 0.00 0.00 0.00 0.00 0.11 0.00

time (sec)

N/A 0.533 0.142 0.468 0.000 0.000 0.000 0.000 0.152 0.000

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