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Integrals 1 to 23

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 B A B A F A B B

verified

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

size

55 64 111 84 194 58 0 80 181 83

N.S.

1 1.16 2.02 1.53 3.53 1.05 0.00 1.45 3.29 1.51

time (sec)

N/A 0.456 0.196 0.207 0.113 0.076 0.000 0.132 0.164 15.272

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

68 57 50 44 58 71 0 52 181 134

N.S.

1 0.84 0.74 0.65 0.85 1.04 0.00 0.76 2.66 1.97

time (sec)

N/A 0.260 0.109 0.167 0.033 0.087 0.000 0.140 0.169 15.423

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

39 43 62 50 94 38 0 49 61 51

N.S.

1 1.10 1.59 1.28 2.41 0.97 0.00 1.26 1.56 1.31

time (sec)

N/A 0.353 0.150 0.125 0.104 0.075 0.000 0.165 0.165 15.243

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

40 35 30 28 31 35 0 34 77 62

N.S.

1 0.88 0.75 0.70 0.78 0.88 0.00 0.85 1.92 1.55

time (sec)

N/A 0.235 0.042 0.113 0.030 0.088 0.000 0.135 0.172 15.222

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

9 9 9 17 9 9 0 9 25 25

N.S.

1 1.00 1.00 1.89 1.00 1.00 0.00 1.00 2.78 2.78

time (sec)

N/A 0.182 0.008 0.107 0.024 0.072 0.000 0.132 0.160 15.011

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

15 15 30 18 30 25 0 17 13 45

N.S.

1 1.00 2.00 1.20 2.00 1.67 0.00 1.13 0.87 3.00

time (sec)

N/A 0.209 0.110 0.138 0.107 0.081 0.000 0.159 0.164 14.951

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

16 14 11 13 18 19 0 14 31 36

N.S.

1 0.88 0.69 0.81 1.12 1.19 0.00 0.88 1.94 2.25

time (sec)

N/A 0.220 0.018 0.210 0.023 0.082 0.000 0.112 0.160 14.922

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

31 36 90 51 86 64 0 65 38 85

N.S.

1 1.16 2.90 1.65 2.77 2.06 0.00 2.10 1.23 2.74

time (sec)

N/A 0.285 0.103 0.315 0.107 0.091 0.000 0.137 0.162 15.047

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

36 26 26 25 29 45 0 29 53 80

N.S.

1 0.72 0.72 0.69 0.81 1.25 0.00 0.81 1.47 2.22

time (sec)

N/A 0.229 0.022 0.456 0.025 0.078 0.000 0.139 0.167 15.186

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

49 58 163 83 134 104 0 109 54 123

N.S.

1 1.18 3.33 1.69 2.73 2.12 0.00 2.22 1.10 2.51

time (sec)

N/A 0.380 0.112 0.632 0.118 0.088 0.000 0.138 0.173 15.241

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

58 44 39 37 42 70 0 41 65 113

N.S.

1 0.76 0.67 0.64 0.72 1.21 0.00 0.71 1.12 1.95

time (sec)

N/A 0.254 0.038 1.018 0.037 0.087 0.000 0.165 0.170 15.575

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

178 210 172 160 251 260 0 252 1150 445

N.S.

1 1.18 0.97 0.90 1.41 1.46 0.00 1.42 6.46 2.50

time (sec)

N/A 0.514 0.582 0.412 0.036 0.219 0.000 0.178 0.186 17.288

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

113 139 115 101 120 144 0 139 497 172

N.S.

1 1.23 1.02 0.89 1.06 1.27 0.00 1.23 4.40 1.52

time (sec)

N/A 0.389 0.363 0.215 0.033 0.130 0.000 0.167 0.201 16.002

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

66 80 56 60 50 58 0 53 110 80

N.S.

1 1.21 0.85 0.91 0.76 0.88 0.00 0.80 1.67 1.21

time (sec)

N/A 0.302 0.042 0.133 0.031 0.093 0.000 0.112 0.185 15.140

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

19 22 11 21 11 11 0 12 34 55

N.S.

1 1.16 0.58 1.11 0.58 0.58 0.00 0.63 1.79 2.89

time (sec)

N/A 0.195 0.009 0.108 0.024 0.096 0.000 0.148 0.196 15.590

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

38 42 39 43 42 47 0 44 92 75

N.S.

1 1.11 1.03 1.13 1.11 1.24 0.00 1.16 2.42 1.97

time (sec)

N/A 0.247 0.039 0.271 0.035 0.092 0.000 0.151 0.200 15.504

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

72 77 85 86 84 151 0 90 194 157

N.S.

1 1.07 1.18 1.19 1.17 2.10 0.00 1.25 2.69 2.18

time (sec)

N/A 0.282 0.099 0.673 0.027 0.104 0.000 0.179 0.209 15.928

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

122 125 132 149 149 327 0 155 311 284

N.S.

1 1.02 1.08 1.22 1.22 2.68 0.00 1.27 2.55 2.33

time (sec)

N/A 0.329 0.210 1.413 0.028 0.127 0.000 0.151 0.184 15.496

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

159 177 194 190 0 483 0 216 632 4468

N.S.

1 1.11 1.22 1.19 0.00 3.04 0.00 1.36 3.97 28.10

time (sec)

N/A 1.170 0.899 0.289 0.000 0.113 0.000 0.148 0.183 21.907

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

84 107 87 106 0 296 0 103 162 2341

N.S.

1 1.27 1.04 1.26 0.00 3.52 0.00 1.23 1.93 27.87

time (sec)

N/A 0.625 0.272 0.143 0.000 0.109 0.000 0.170 0.181 16.932

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

61 73 71 75 0 206 0 80 53 697

N.S.

1 1.20 1.16 1.23 0.00 3.38 0.00 1.31 0.87 11.43

time (sec)

N/A 0.601 0.071 0.223 0.000 0.112 0.000 0.162 0.182 15.177

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

91 107 158 141 0 453 0 163 152 2163

N.S.

1 1.18 1.74 1.55 0.00 4.98 0.00 1.79 1.67 23.77

time (sec)

N/A 0.671 0.394 0.512 0.000 0.193 0.000 0.194 0.200 16.014

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

186 186 312 251 0 852 0 299 267 4075

N.S.

1 1.00 1.68 1.35 0.00 4.58 0.00 1.61 1.44 21.91

time (sec)

N/A 0.536 0.748 1.023 0.000 0.379 0.000 0.193 0.189 16.890

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