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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 82 359 306 85 151 86 122

N.S.

1 1.00 0.65 2.85 2.43 0.67 1.20 0.68 0.97

time (sec)

N/A 0.226 0.113 0.052 0.298 0.346 0.354 3.710 0.279

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 65 225 201 67 117 68 92

N.S.

1 1.00 0.68 2.34 2.09 0.70 1.22 0.71 0.96

time (sec)

N/A 0.149 0.101 0.037 0.314 0.367 0.193 3.336 4.619

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 45 121 117 48 82 49 62

N.S.

1 1.00 0.69 1.86 1.80 0.74 1.26 0.75 0.95

time (sec)

N/A 0.073 0.074 0.035 0.308 0.343 0.136 3.652 4.499

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 27 52 53 30 46 31 35

N.S.

1 1.00 0.96 1.86 1.89 1.07 1.64 1.11 1.25

time (sec)

N/A 0.012 0.056 0.033 0.294 0.359 0.080 4.509 4.485

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A A C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 40 31 522 44 37 339 -1

N.S.

1 1.00 1.38 1.07 18.00 1.52 1.28 11.69 -0.03

time (sec)

N/A 0.105 0.025 0.068 0.353 0.338 3.116 5.447 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 60 56 108 75 0 569 -1

N.S.

1 1.00 1.25 1.17 2.25 1.56 0.00 11.85 -0.02

time (sec)

N/A 0.156 0.102 0.088 0.483 0.352 0.000 5.791 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 76 88 112 111 0 796 -1

N.S.

1 1.00 0.85 0.99 1.26 1.25 0.00 8.94 -0.01

time (sec)

N/A 0.191 0.183 0.090 0.563 0.342 0.000 4.467 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 110 117 111 137 0 961 -1

N.S.

1 1.00 0.83 0.89 0.84 1.04 0.00 7.28 -0.01

time (sec)

N/A 0.224 0.229 0.122 0.651 0.334 0.000 3.245 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 138 145 110 154 0 1108 -1

N.S.

1 1.00 0.83 0.87 0.66 0.93 0.00 6.67 -0.01

time (sec)

N/A 0.249 0.186 0.116 0.575 0.346 0.000 2.893 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

186 186 101 468 406 126 228 128 172

N.S.

1 1.00 0.54 2.52 2.18 0.68 1.23 0.69 0.92

time (sec)

N/A 0.214 0.167 0.069 0.358 0.355 0.322 2.742 0.295

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 87 281 259 95 172 95 128

N.S.

1 1.00 0.64 2.08 1.92 0.70 1.27 0.70 0.95

time (sec)

N/A 0.127 0.122 0.067 0.293 0.337 0.203 4.630 4.763

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 57 148 141 63 112 65 84

N.S.

1 1.00 1.14 2.96 2.82 1.26 2.24 1.30 1.68

time (sec)

N/A 0.028 0.105 0.062 0.327 0.354 0.135 5.151 4.700

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A A C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 51 79 80 78 92 551 -1

N.S.

1 1.00 0.82 1.27 1.29 1.26 1.48 8.89 -0.02

time (sec)

N/A 0.129 0.188 0.102 0.540 0.349 2.245 5.818 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 64 74 122 111 0 743 -1

N.S.

1 1.00 0.89 1.03 1.69 1.54 0.00 10.32 -0.01

time (sec)

N/A 0.168 0.156 0.089 0.896 0.350 0.000 5.908 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 95 114 189 147 0 1182 -1

N.S.

1 1.00 0.79 0.94 1.56 1.21 0.00 9.77 -0.01

time (sec)

N/A 0.240 0.259 0.104 1.397 0.375 0.000 4.325 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

175 175 154 158 187 186 0 1400 -1

N.S.

1 1.00 0.88 0.90 1.07 1.06 0.00 8.00 -0.01

time (sec)

N/A 0.274 0.322 0.122 1.417 0.362 0.000 6.543 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

248 248 204 201 186 222 0 1712 -1

N.S.

1 1.00 0.82 0.81 0.75 0.90 0.00 6.90 -0.00

time (sec)

N/A 0.320 0.252 0.138 1.577 0.357 0.000 4.043 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

218 218 158 784 0 213 0 3337 -1

N.S.

1 1.00 0.72 3.60 0.00 0.98 0.00 15.31 -0.00

time (sec)

N/A 0.320 0.416 0.230 0.000 0.361 0.000 3.536 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 117 516 0 167 0 2709 -1

N.S.

1 1.00 0.77 3.39 0.00 1.10 0.00 17.82 -0.01

time (sec)

N/A 0.218 0.347 0.066 0.000 0.345 0.000 3.554 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 87 318 0 133 0 2205 -1

N.S.

1 1.00 0.88 3.21 0.00 1.34 0.00 22.27 -0.01

time (sec)

N/A 0.180 0.191 0.059 0.000 0.354 0.000 3.296 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 63 180 776 99 0 1647 -1

N.S.

1 1.00 0.91 2.61 11.25 1.43 0.00 23.87 -0.01

time (sec)

N/A 0.115 0.101 0.060 0.424 0.346 0.000 4.389 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 49 73 141 78 0 597 -1

N.S.

1 1.00 0.96 1.43 2.76 1.53 0.00 11.71 -0.02

time (sec)

N/A 0.050 0.054 0.053 0.388 0.347 0.000 3.467 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 63 99 0 99 0 838 -1

N.S.

1 1.00 0.86 1.36 0.00 1.36 0.00 11.48 -0.01

time (sec)

N/A 0.175 0.087 0.069 0.000 0.386 0.000 3.453 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 101 144 0 157 0 2897 -1

N.S.

1 1.00 0.89 1.26 0.00 1.38 0.00 25.41 -0.01

time (sec)

N/A 0.239 0.252 0.099 0.000 0.353 0.000 3.826 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 176 202 0 245 0 4565 -1

N.S.

1 1.00 0.93 1.07 0.00 1.30 0.00 24.15 -0.01

time (sec)

N/A 0.335 0.382 0.135 0.000 0.386 0.000 3.894 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

233 233 177 1216 0 357 0 1973 -1

N.S.

1 1.00 0.76 5.22 0.00 1.53 0.00 8.47 -0.00

time (sec)

N/A 0.358 0.648 0.236 0.000 0.362 0.000 3.523 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

181 181 153 851 0 316 0 1474 -1

N.S.

1 1.00 0.85 4.70 0.00 1.75 0.00 8.14 -0.01

time (sec)

N/A 0.275 0.578 0.092 0.000 0.351 0.000 3.787 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 117 553 0 264 0 1120 -1

N.S.

1 1.00 0.79 3.71 0.00 1.77 0.00 7.52 -0.01

time (sec)

N/A 0.253 0.546 0.072 0.000 0.350 0.000 4.119 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 96 315 0 208 0 951 -1

N.S.

1 1.00 0.77 2.54 0.00 1.68 0.00 7.67 -0.01

time (sec)

N/A 0.197 0.308 0.063 0.000 0.359 0.000 5.016 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 66 107 164 123 0 518 -1

N.S.

1 1.00 0.92 1.49 2.28 1.71 0.00 7.19 -0.01

time (sec)

N/A 0.067 0.161 0.054 0.368 0.338 0.000 5.987 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 138 210 0 260 0 1281 -1

N.S.

1 1.00 0.93 1.41 0.00 1.74 0.00 8.60 -0.01

time (sec)

N/A 0.276 0.701 0.110 0.000 0.356 0.000 4.154 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

188 188 184 256 0 355 0 3180 -1

N.S.

1 1.00 0.98 1.36 0.00 1.89 0.00 16.91 -0.01

time (sec)

N/A 0.353 1.223 0.122 0.000 0.381 0.000 3.935 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

265 265 235 1208 0 515 0 16724 -1

N.S.

1 1.00 0.89 4.56 0.00 1.94 0.00 63.11 -0.00

time (sec)

N/A 0.419 0.644 0.240 0.000 0.381 0.000 3.247 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

241 241 154 779 0 438 0 15410 -1

N.S.

1 1.00 0.64 3.23 0.00 1.82 0.00 63.94 -0.00

time (sec)

N/A 0.366 0.796 0.093 0.000 0.378 0.000 5.157 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

179 179 157 419 0 346 0 10535 -1

N.S.

1 1.00 0.88 2.34 0.00 1.93 0.00 58.85 -0.01

time (sec)

N/A 0.243 0.364 0.073 0.000 0.352 0.000 4.500 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C B F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 87 145 199 210 0 5727 -1

N.S.

1 1.00 0.84 1.39 1.91 2.02 0.00 55.07 -0.01

time (sec)

N/A 0.090 0.525 0.054 0.387 0.364 0.000 3.039 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

261 261 449 359 0 532 0 17806 -1

N.S.

1 1.00 1.72 1.38 0.00 2.04 0.00 68.22 -0.00

time (sec)

N/A 0.374 0.620 0.138 0.000 0.404 0.000 3.619 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

299 299 540 405 0 689 0 20808 -1

N.S.

1 1.00 1.81 1.35 0.00 2.30 0.00 69.59 -0.00

time (sec)

N/A 0.455 1.312 0.174 0.000 0.398 0.000 5.155 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

377 377 630 466 0 816 0 24116 -1

N.S.

1 1.00 1.67 1.24 0.00 2.16 0.00 63.97 -0.00

time (sec)

N/A 0.543 1.184 0.207 0.000 0.410 0.000 4.112 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 92 449 372 95 168 97 121

N.S.

1 1.00 0.65 3.18 2.64 0.67 1.19 0.69 0.86

time (sec)

N/A 0.142 0.132 0.051 0.291 0.359 0.436 3.486 0.344

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 75 302 258 77 134 79 97

N.S.

1 1.00 0.68 2.72 2.32 0.69 1.21 0.71 0.87

time (sec)

N/A 0.109 0.104 0.049 0.300 0.417 0.321 2.885 4.733

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 57 181 165 60 99 60 73

N.S.

1 1.00 0.71 2.26 2.06 0.75 1.24 0.75 0.91

time (sec)

N/A 0.070 0.090 0.038 0.282 0.358 0.206 3.401 0.144

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 41 99 91 41 65 42 49

N.S.

1 1.00 0.77 1.87 1.72 0.77 1.23 0.79 0.92

time (sec)

N/A 0.040 0.063 0.036 0.286 0.354 0.143 5.311 4.692

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A A C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 54 60 66 61 65 432 -1

N.S.

1 1.00 1.32 1.46 1.61 1.49 1.59 10.54 -0.02

time (sec)

N/A 0.061 0.097 0.047 0.501 0.398 2.598 5.304 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 44 48 937 68 0 411 -1

N.S.

1 1.00 1.00 1.09 21.30 1.55 0.00 9.34 -0.02

time (sec)

N/A 0.069 0.071 0.068 0.461 0.393 0.000 4.033 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 82 73 123 85 0 766 -1

N.S.

1 1.00 1.11 0.99 1.66 1.15 0.00 10.35 -0.01

time (sec)

N/A 0.109 0.135 0.079 0.768 0.362 0.000 3.725 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 95 102 121 105 0 834 -1

N.S.

1 1.00 0.90 0.96 1.14 0.99 0.00 7.87 -0.01

time (sec)

N/A 0.146 0.133 0.111 0.953 0.380 0.000 5.391 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 125 131 121 127 0 1086 -1

N.S.

1 1.00 0.84 0.88 0.81 0.85 0.00 7.29 -0.01

time (sec)

N/A 0.186 0.163 0.111 0.888 0.358 0.000 5.900 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

236 236 139 746 612 154 286 162 186

N.S.

1 1.00 0.59 3.16 2.59 0.65 1.21 0.69 0.79

time (sec)

N/A 0.221 0.240 0.072 0.328 0.377 0.675 6.184 0.581

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

185 185 113 514 438 126 226 129 151

N.S.

1 1.00 0.61 2.78 2.37 0.68 1.22 0.70 0.82

time (sec)

N/A 0.165 0.153 0.072 0.301 0.373 0.487 4.866 4.928

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 86 336 292 97 172 99 118

N.S.

1 1.00 0.62 2.43 2.12 0.70 1.25 0.72 0.86

time (sec)

N/A 0.112 0.117 0.062 0.299 0.367 0.338 4.079 4.834

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B C A A C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 82 236 116 114 160 725 -1

N.S.

1 1.00 0.74 2.13 1.05 1.03 1.44 6.53 -0.01

time (sec)

N/A 0.118 0.254 0.136 1.727 0.370 4.353 3.527 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 97 156 97 113 0 1638 -1

N.S.

1 1.00 1.00 1.61 1.00 1.16 0.00 16.89 -0.01

time (sec)

N/A 0.112 0.168 0.149 1.438 0.350 0.000 3.560 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 99 124 150 136 0 1058 -1

N.S.

1 1.00 0.87 1.09 1.32 1.19 0.00 9.28 -0.01

time (sec)

N/A 0.142 0.265 0.151 2.378 0.374 0.000 4.144 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 114 120 140 145 0 1032 -1

N.S.

1 1.00 0.85 0.90 1.04 1.08 0.00 7.70 -0.01

time (sec)

N/A 0.159 0.269 0.161 1.816 0.357 0.000 3.817 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 122 157 222 162 0 1497 -1

N.S.

1 1.00 0.69 0.89 1.25 0.92 0.00 8.46 -0.01

time (sec)

N/A 0.224 0.259 0.227 9.934 0.371 0.000 4.494 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

273 273 275 1630 0 240 0 0 -1

N.S.

1 1.00 1.01 5.97 0.00 0.88 0.00 0.00 -0.00

time (sec)

N/A 0.541 0.314 0.303 0.000 0.385 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 202 1164 0 185 0 0 -1

N.S.

1 1.00 0.97 5.57 0.00 0.89 0.00 0.00 -0.00

time (sec)

N/A 0.249 0.264 0.099 0.000 0.400 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

227 227 216 782 0 195 0 0 -1

N.S.

1 1.00 0.95 3.44 0.00 0.86 0.00 0.00 -0.00

time (sec)

N/A 0.301 0.233 0.071 0.000 0.374 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 163 486 0 146 0 0 -1

N.S.

1 1.00 0.92 2.75 0.00 0.82 0.00 0.00 -0.01

time (sec)

N/A 0.175 0.129 0.059 0.000 0.361 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

213 213 172 225 0 187 0 0 -1

N.S.

1 1.00 0.81 1.06 0.00 0.88 0.00 0.00 -0.00

time (sec)

N/A 0.209 0.131 0.045 0.000 0.382 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 179 200 0 168 0 0 -1

N.S.

1 1.00 0.91 1.02 0.00 0.85 0.00 0.00 -0.01

time (sec)

N/A 0.266 0.226 0.093 0.000 0.375 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

250 250 238 266 0 240 0 0 -1

N.S.

1 1.00 0.95 1.06 0.00 0.96 0.00 0.00 -0.00

time (sec)

N/A 0.400 0.345 0.118 0.000 0.377 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

270 270 247 259 0 231 0 0 -1

N.S.

1 1.00 0.91 0.96 0.00 0.86 0.00 0.00 -0.00

time (sec)

N/A 0.348 0.434 0.146 0.000 0.390 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

450 450 632 3411 0 351 0 0 -1

N.S.

1 1.00 1.40 7.58 0.00 0.78 0.00 0.00 -0.00

time (sec)

N/A 0.607 0.698 0.570 0.000 0.373 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

431 431 583 2531 0 291 0 0 -1

N.S.

1 1.00 1.35 5.87 0.00 0.68 0.00 0.00 -0.00

time (sec)

N/A 0.521 0.505 0.164 0.000 0.383 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

416 416 583 1780 0 333 0 0 -1

N.S.

1 1.00 1.40 4.28 0.00 0.80 0.00 0.00 -0.00

time (sec)

N/A 0.425 0.468 0.129 0.000 0.364 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

239 239 309 1093 0 244 0 0 -1

N.S.

1 1.00 1.29 4.57 0.00 1.02 0.00 0.00 -0.00

time (sec)

N/A 0.254 0.286 0.084 0.000 0.358 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

476 476 585 491 0 333 0 0 -1

N.S.

1 1.00 1.23 1.03 0.00 0.70 0.00 0.00 -0.00

time (sec)

N/A 0.590 0.454 0.060 0.000 0.379 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

435 435 650 478 0 332 0 0 -1

N.S.

1 1.00 1.49 1.10 0.00 0.76 0.00 0.00 -0.00

time (sec)

N/A 0.632 0.535 0.157 0.000 0.399 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

501 501 768 761 0 406 0 0 -1

N.S.

1 1.00 1.53 1.52 0.00 0.81 0.00 0.00 -0.00

time (sec)

N/A 0.999 0.617 0.191 0.000 0.387 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

476 476 647 3353 0 492 0 0 -1

N.S.

1 1.00 1.36 7.04 0.00 1.03 0.00 0.00 -0.00

time (sec)

N/A 0.804 1.348 0.815 0.000 0.384 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

746 746 927 2284 0 604 0 0 -1

N.S.

1 1.00 1.24 3.06 0.00 0.81 0.00 0.00 -0.00

time (sec)

N/A 0.893 1.859 0.188 0.000 0.404 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

512 512 634 1360 0 483 0 0 -1

N.S.

1 1.00 1.24 2.66 0.00 0.94 0.00 0.00 -0.00

time (sec)

N/A 0.599 1.238 0.127 0.000 0.377 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

856 856 932 598 0 611 0 0 -1

N.S.

1 1.00 1.09 0.70 0.00 0.71 0.00 0.00 -0.00

time (sec)

N/A 0.889 1.708 0.090 0.000 0.399 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

730 730 924 580 0 647 0 0 -1

N.S.

1 1.00 1.27 0.79 0.00 0.89 0.00 0.00 -0.00

time (sec)

N/A 1.256 1.680 0.313 0.000 0.505 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

875 875 1177 1363 0 720 0 0 -1

N.S.

1 1.00 1.35 1.56 0.00 0.82 0.00 0.00 -0.00

time (sec)

N/A 2.031 1.811 0.371 0.000 0.483 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

791 791 995 697 0 768 0 0 -1

N.S.

1 1.00 1.26 0.88 0.00 0.97 0.00 0.00 -0.00

time (sec)

N/A 1.385 1.718 1.836 0.000 0.470 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 101 556 449 104 185 106 151

N.S.

1 1.00 0.65 3.56 2.88 0.67 1.19 0.68 0.97

time (sec)

N/A 0.162 0.135 0.056 0.325 0.357 0.677 5.043 0.586

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 84 392 326 87 151 88 121

N.S.

1 1.00 0.67 3.11 2.59 0.69 1.20 0.70 0.96

time (sec)

N/A 0.128 0.112 0.047 0.329 0.376 0.443 4.726 4.954

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 66 258 224 68 116 69 92

N.S.

1 1.00 0.69 2.72 2.36 0.72 1.22 0.73 0.97

time (sec)

N/A 0.088 0.090 0.042 0.313 0.398 0.292 5.101 4.795

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 50 159 141 52 82 54 65

N.S.

1 1.00 0.74 2.34 2.07 0.76 1.21 0.79 0.96

time (sec)

N/A 0.056 0.067 0.036 0.296 0.362 0.181 5.117 0.111

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A A C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 50 112 76 72 83 510 -1

N.S.

1 1.00 0.88 1.96 1.33 1.26 1.46 8.95 -0.02

time (sec)

N/A 0.078 0.139 0.056 0.753 0.425 2.900 4.641 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 56 79 69 79 0 489 -1

N.S.

1 1.00 1.00 1.41 1.23 1.41 0.00 8.73 -0.02

time (sec)

N/A 0.080 0.098 0.083 0.695 0.373 0.000 4.685 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 66 65 1146 84 0 564 -1

N.S.

1 1.00 0.94 0.93 16.37 1.20 0.00 8.06 -0.01

time (sec)

N/A 0.084 0.111 0.091 0.543 0.371 0.000 5.133 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 104 87 132 114 0 796 -1

N.S.

1 1.00 1.14 0.96 1.45 1.25 0.00 8.75 -0.01

time (sec)

N/A 0.130 0.151 0.085 1.085 0.375 0.000 5.283 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

235 235 139 822 662 161 284 161 225

N.S.

1 1.00 0.59 3.50 2.82 0.69 1.21 0.69 0.96

time (sec)

N/A 0.221 0.240 0.094 0.338 0.353 0.944 5.483 5.086

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

188 188 112 599 489 129 226 131 184

N.S.

1 1.00 0.60 3.19 2.60 0.69 1.20 0.70 0.98

time (sec)

N/A 0.166 0.196 0.075 0.340 0.349 0.644 4.838 0.619

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B C A A C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 108 487 147 145 207 921 -1

N.S.

1 1.00 0.67 3.02 0.91 0.90 1.29 5.72 -0.01

time (sec)

N/A 0.167 0.326 0.177 6.407 0.367 4.155 5.587 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 145 365 129 145 0 2038 -1

N.S.

1 1.00 1.00 2.52 0.89 1.00 0.00 14.06 -0.01

time (sec)

N/A 0.151 0.227 0.215 7.430 0.346 0.000 4.969 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 138 251 110 142 0 2171 -1

N.S.

1 1.00 0.97 1.77 0.77 1.00 0.00 15.29 -0.01

time (sec)

N/A 0.139 0.234 0.247 2.459 0.359 0.000 3.861 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 135 196 173 176 0 1181 -1

N.S.

1 1.00 0.89 1.30 1.15 1.17 0.00 7.82 -0.01

time (sec)

N/A 0.169 0.354 0.244 8.164 0.364 0.000 4.545 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

167 167 148 167 164 186 0 1255 -1

N.S.

1 1.00 0.89 1.00 0.98 1.11 0.00 7.51 -0.01

time (sec)

N/A 0.196 0.349 0.345 6.919 0.368 0.000 4.380 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

371 371 231 558 0 397 0 0 -1

N.S.

1 1.00 0.62 1.50 0.00 1.07 0.00 0.00 -0.00

time (sec)

N/A 0.609 0.329 0.175 0.000 0.415 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

357 357 216 392 0 393 0 0 -1

N.S.

1 1.00 0.61 1.10 0.00 1.10 0.00 0.00 -0.00

time (sec)

N/A 0.420 0.209 0.062 0.000 0.390 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

281 281 186 266 0 292 0 0 -1

N.S.

1 1.00 0.66 0.95 0.00 1.04 0.00 0.00 -0.00

time (sec)

N/A 0.291 0.174 0.052 0.000 0.425 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

343 343 196 176 0 379 0 0 -1

N.S.

1 1.00 0.57 0.51 0.00 1.10 0.00 0.00 -0.00

time (sec)

N/A 0.256 0.157 0.057 0.000 0.401 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

343 343 196 85 0 385 0 0 -1

N.S.

1 1.00 0.57 0.25 0.00 1.12 0.00 0.00 -0.00

time (sec)

N/A 0.256 0.101 0.050 0.000 0.411 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

301 301 206 88 0 314 0 0 -1

N.S.

1 1.00 0.68 0.29 0.00 1.04 0.00 0.00 -0.00

time (sec)

N/A 0.344 0.221 0.094 0.000 0.399 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

380 380 233 116 0 454 0 0 -1

N.S.

1 1.00 0.61 0.31 0.00 1.19 0.00 0.00 -0.00

time (sec)

N/A 0.392 0.260 0.125 0.000 0.430 0.000 0.000 0.000

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