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2.2.1 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 F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 146 180 176 0 0 0 0 0

N.S.

1 1.01 1.25 1.22 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.600 0.425 1.671 0.000 0.000 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 106 138 180 0 0 0 0 0

N.S.

1 0.92 1.20 1.57 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.502 0.312 1.855 0.000 0.000 0.000 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 79 115 142 0 0 0 0 0

N.S.

1 0.96 1.40 1.73 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.393 0.209 1.217 0.000 0.000 0.000 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 66 107 140 0 0 0 0 0

N.S.

1 0.87 1.41 1.84 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.316 0.180 1.700 0.000 0.000 0.000 0.000 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 67 143 196 0 0 0 0 0

N.S.

1 0.94 2.01 2.76 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.394 0.320 1.899 0.000 0.000 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 102 158 146 0 0 0 0 0

N.S.

1 0.95 1.48 1.36 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.517 0.479 3.487 0.000 0.000 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 115 220 248 0 0 0 0 0

N.S.

1 0.93 1.77 2.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.573 0.440 2.247 0.000 0.000 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

180 191 294 250 0 0 0 0 0

N.S.

1 1.06 1.63 1.39 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.791 0.476 2.413 0.000 0.000 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 152 203 207 0 0 0 0 0

N.S.

1 0.98 1.31 1.34 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.631 0.589 1.500 0.000 0.000 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 125 251 189 0 0 0 0 0

N.S.

1 0.92 1.85 1.39 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.514 0.386 1.982 0.000 0.000 0.000 0.000 0.000

Problem 11

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

57 57 49 98 136 54 0 100 0

N.S.

1 1.00 0.86 1.72 2.39 0.95 0.00 1.75 0.00

time (sec)

N/A 0.214 0.186 0.704 0.302 0.256 0.000 0.274 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 122 220 189 0 0 0 0 0

N.S.

1 0.92 1.67 1.43 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.460 0.341 1.859 0.000 0.000 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 119 233 255 0 0 0 0 0

N.S.

1 0.98 1.91 2.09 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.571 0.706 2.221 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

177 193 251 332 0 0 0 0 0

N.S.

1 1.09 1.42 1.88 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.766 0.578 4.348 0.000 0.000 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 198 309 281 0 0 0 0 0

N.S.

1 1.25 1.94 1.77 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.846 0.736 2.403 0.000 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 145 153 170 165 125 211 165 0

N.S.

1 0.97 1.03 1.14 1.11 0.84 1.42 1.11 0.00

time (sec)

N/A 0.294 0.163 0.990 0.275 0.247 0.577 0.285 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 122 125 154 144 108 177 141 0

N.S.

1 1.02 1.04 1.28 1.20 0.90 1.48 1.18 0.00

time (sec)

N/A 0.311 0.136 0.760 0.270 0.260 0.427 0.294 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 136 131 161 124 103 158 121 0

N.S.

1 1.11 1.07 1.32 1.02 0.84 1.30 0.99 0.00

time (sec)

N/A 0.285 0.143 0.886 0.274 0.254 0.343 0.279 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 84 91 100 94 83 114 91 0

N.S.

1 1.04 1.12 1.23 1.16 1.02 1.41 1.12 0.00

time (sec)

N/A 0.265 0.094 0.220 0.269 0.258 0.267 0.284 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 142 121 128 0 0 0 0 0

N.S.

1 1.08 0.92 0.97 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.507 0.191 4.928 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 71 80 79 81 155 78 859 71

N.S.

1 1.08 1.21 1.20 1.23 2.35 1.18 13.02 1.08

time (sec)

N/A 0.258 0.075 0.221 0.278 0.289 2.036 0.570 0.425

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 127 108 137 0 0 0 0 0

N.S.

1 1.07 0.91 1.15 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.497 0.126 3.993 0.000 0.000 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 84 130 113 119 168 170 3082 0

N.S.

1 0.99 1.53 1.33 1.40 1.98 2.00 36.26 0.00

time (sec)

N/A 0.267 0.093 0.194 0.260 0.298 3.116 124.141 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 139 99 169 160 110 197 160 0

N.S.

1 1.03 0.73 1.25 1.19 0.81 1.46 1.19 0.00

time (sec)

N/A 0.351 0.124 0.342 0.281 0.251 0.418 0.293 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 209 149 270 267 168 326 270 0

N.S.

1 1.02 0.73 1.32 1.30 0.82 1.59 1.32 0.00

time (sec)

N/A 0.518 0.158 0.364 0.276 0.273 0.677 0.303 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

292 296 212 393 400 239 502 408 0

N.S.

1 1.01 0.73 1.35 1.37 0.82 1.72 1.40 0.00

time (sec)

N/A 0.638 0.177 0.368 0.269 0.251 1.329 0.294 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

521 521 811 216 0 0 0 0 0

N.S.

1 1.00 1.56 0.41 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.144 1.806 4.617 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

727 727 1065 796 0 0 0 0 0

N.S.

1 1.00 1.46 1.09 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.410 2.830 5.748 0.000 0.000 0.000 0.000 0.000

Problem 29

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 14 16 16 15 16 16

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.00

time (sec)

N/A 0.166 4.121 2.648 1.108 0.246 8.865 0.401 0.264

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

16 16 18 14 16 16 15 16 16

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.00

time (sec)

N/A 0.171 2.305 2.703 1.090 0.246 5.034 0.375 0.282

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

66 66 68 0 0 276 0 75 0

N.S.

1 1.00 1.03 0.00 0.00 4.18 0.00 1.14 0.00

time (sec)

N/A 0.231 0.084 0.000 0.000 0.296 0.000 0.307 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

136 138 120 0 0 580 0 152 0

N.S.

1 1.01 0.88 0.00 0.00 4.26 0.00 1.12 0.00

time (sec)

N/A 0.306 0.200 0.000 0.000 0.306 0.000 0.366 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

211 229 162 0 0 1066 0 283 0

N.S.

1 1.09 0.77 0.00 0.00 5.05 0.00 1.34 0.00

time (sec)

N/A 0.940 0.314 0.000 0.000 0.350 0.000 0.385 0.000

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