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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 A A F F F F(-2) F F(-1)

verified

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

size

144 146 180 176 0 0 0 0 108 0

N.S.

1 1.01 1.25 1.22 0.00 0.00 0.00 0.00 0.75 0.00

time (sec)

N/A 0.628 0.055 0.469 0.000 0.000 0.000 0.000 0.182 0.000

Problem 2

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

115 106 138 180 0 0 0 0 82 0

N.S.

1 0.92 1.20 1.57 0.00 0.00 0.00 0.00 0.71 0.00

time (sec)

N/A 0.507 0.046 0.347 0.000 0.000 0.000 0.000 0.182 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

82 79 115 142 0 0 0 0 58 0

N.S.

1 0.96 1.40 1.73 0.00 0.00 0.00 0.00 0.71 0.00

time (sec)

N/A 0.411 0.022 0.289 0.000 0.000 0.000 0.000 0.177 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

76 66 107 140 0 0 0 0 54 0

N.S.

1 0.87 1.41 1.84 0.00 0.00 0.00 0.00 0.71 0.00

time (sec)

N/A 0.338 0.017 0.478 0.000 0.000 0.000 0.000 0.184 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

71 67 143 196 0 0 0 0 58 0

N.S.

1 0.94 2.01 2.76 0.00 0.00 0.00 0.00 0.82 0.00

time (sec)

N/A 0.436 0.033 0.331 0.000 0.000 0.000 0.000 0.183 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

107 102 158 146 0 0 0 0 65 0

N.S.

1 0.95 1.48 1.36 0.00 0.00 0.00 0.00 0.61 0.00

time (sec)

N/A 0.576 0.037 0.348 0.000 0.000 0.000 0.000 0.190 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

124 115 220 248 0 0 0 0 87 0

N.S.

1 0.93 1.77 2.00 0.00 0.00 0.00 0.00 0.70 0.00

time (sec)

N/A 0.639 0.056 0.345 0.000 0.000 0.000 0.000 0.190 0.000

Problem 8

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

180 191 294 250 0 0 0 0 167 0

N.S.

1 1.06 1.63 1.39 0.00 0.00 0.00 0.00 0.93 0.00

time (sec)

N/A 0.885 0.090 0.408 0.000 0.000 0.000 0.000 0.197 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

155 152 203 207 0 0 0 0 160 0

N.S.

1 0.98 1.31 1.34 0.00 0.00 0.00 0.00 1.03 0.00

time (sec)

N/A 0.673 0.234 0.307 0.000 0.000 0.000 0.000 0.186 0.000

Problem 10

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

136 125 251 189 0 0 0 0 156 0

N.S.

1 0.92 1.85 1.39 0.00 0.00 0.00 0.00 1.15 0.00

time (sec)

N/A 0.549 0.098 0.306 0.000 0.000 0.000 0.000 0.189 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

57 57 49 98 136 54 0 100 89 0

N.S.

1 1.00 0.86 1.72 2.39 0.95 0.00 1.75 1.56 0.00

time (sec)

N/A 0.225 0.024 0.203 0.163 0.106 0.000 0.153 0.182 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

132 122 220 189 0 0 0 0 148 0

N.S.

1 0.92 1.67 1.43 0.00 0.00 0.00 0.00 1.12 0.00

time (sec)

N/A 0.500 0.109 0.296 0.000 0.000 0.000 0.000 0.183 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

122 119 233 255 0 0 0 0 164 0

N.S.

1 0.98 1.91 2.09 0.00 0.00 0.00 0.00 1.34 0.00

time (sec)

N/A 0.597 0.206 0.352 0.000 0.000 0.000 0.000 0.188 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

177 193 251 332 0 0 0 0 165 0

N.S.

1 1.09 1.42 1.88 0.00 0.00 0.00 0.00 0.93 0.00

time (sec)

N/A 0.809 0.208 0.505 0.000 0.000 0.000 0.000 0.186 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

159 198 309 281 0 0 0 0 195 0

N.S.

1 1.25 1.94 1.77 0.00 0.00 0.00 0.00 1.23 0.00

time (sec)

N/A 0.891 0.303 0.351 0.000 0.000 0.000 0.000 0.198 0.000

Problem 16

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 Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

149 145 153 170 165 125 211 165 172 0

N.S.

1 0.97 1.03 1.14 1.11 0.84 1.42 1.11 1.15 0.00

time (sec)

N/A 0.319 0.077 0.227 0.129 0.100 0.553 0.148 0.190 0.000

Problem 17

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 Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

120 122 125 154 144 108 177 141 150 0

N.S.

1 1.02 1.04 1.28 1.20 0.90 1.48 1.18 1.25 0.00

time (sec)

N/A 0.334 0.062 0.217 0.121 0.115 0.383 0.147 0.188 0.000

Problem 18

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 Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

120 136 131 161 124 103 158 121 130 0

N.S.

1 1.13 1.09 1.34 1.03 0.86 1.32 1.01 1.08 0.00

time (sec)

N/A 0.306 0.062 0.197 0.135 0.121 0.354 0.142 0.192 0.000

Problem 19

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 Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

81 84 91 100 94 83 114 91 104 0

N.S.

1 1.04 1.12 1.23 1.16 1.02 1.41 1.12 1.28 0.00

time (sec)

N/A 0.271 0.042 0.099 0.131 0.121 0.271 0.126 0.178 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

132 142 121 128 0 0 0 0 80 0

N.S.

1 1.08 0.92 0.97 0.00 0.00 0.00 0.00 0.61 0.00

time (sec)

N/A 0.536 0.096 0.404 0.000 0.000 0.000 0.000 0.183 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

66 71 80 79 81 155 78 859 72 71

N.S.

1 1.08 1.21 1.20 1.23 2.35 1.18 13.02 1.09 1.08

time (sec)

N/A 0.276 0.035 0.107 0.127 0.147 2.415 0.611 0.186 0.568

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

119 127 108 137 0 0 0 0 60 0

N.S.

1 1.07 0.91 1.15 0.00 0.00 0.00 0.00 0.50 0.00

time (sec)

N/A 0.534 0.057 0.646 0.000 0.000 0.000 0.000 0.188 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

85 84 130 113 119 168 170 3082 86 0

N.S.

1 0.99 1.53 1.33 1.40 1.98 2.00 36.26 1.01 0.00

time (sec)

N/A 0.289 0.031 0.126 0.127 0.148 2.875 122.787 0.188 0.000

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