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2.2.1 Integrals 1 to 93

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 A A F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 121 102 191 94 120 0 0 0

N.S.

1 1.10 0.93 1.74 0.85 1.09 0.00 0.00 0.00

time (sec)

N/A 0.616 0.053 0.038 0.199 0.255 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 92 83 162 72 100 0 0 0

N.S.

1 1.10 0.99 1.93 0.86 1.19 0.00 0.00 0.00

time (sec)

N/A 0.498 0.036 0.014 0.185 0.254 0.000 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 63 53 84 48 72 0 0 0

N.S.

1 1.09 0.91 1.45 0.83 1.24 0.00 0.00 0.00

time (sec)

N/A 0.346 0.024 0.011 0.190 0.253 0.000 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 34 42 25 32 24 17 31 24

N.S.

1 1.31 1.62 0.96 1.23 0.92 0.65 1.19 0.92

time (sec)

N/A 0.171 0.022 0.016 0.183 0.269 0.064 0.346 0.098

Problem 5

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

17 17 19 16 18 17 15 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.00 0.88 1.06 1.06

time (sec)

N/A 0.183 0.132 0.063 0.215 0.249 1.172 0.321 0.086

Problem 6

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

17 17 19 16 18 21 17 18 18

N.S.

1 1.00 1.12 0.94 1.06 1.24 1.00 1.06 1.06

time (sec)

N/A 0.183 0.208 0.046 0.221 0.251 0.897 0.394 0.089

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 37 21 24 34 23 17 33 23

N.S.

1 1.42 0.81 0.92 1.31 0.88 0.65 1.27 0.88

time (sec)

N/A 0.173 0.020 0.014 0.185 0.263 0.063 0.400 0.065

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 41 19 26 34 25 19 33 25

N.S.

1 1.46 0.68 0.93 1.21 0.89 0.68 1.18 0.89

time (sec)

N/A 0.177 0.023 0.014 0.191 0.259 0.068 0.397 0.049

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

217 257 158 382 195 330 0 0 0

N.S.

1 1.18 0.73 1.76 0.90 1.52 0.00 0.00 0.00

time (sec)

N/A 1.656 0.176 0.092 0.202 0.257 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 199 113 324 149 263 0 0 0

N.S.

1 1.21 0.68 1.96 0.90 1.59 0.00 0.00 0.00

time (sec)

N/A 1.236 0.229 0.059 0.197 0.260 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 134 85 154 95 176 0 0 0

N.S.

1 1.25 0.79 1.44 0.89 1.64 0.00 0.00 0.00

time (sec)

N/A 0.698 0.118 0.030 0.201 0.262 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 51 45 49 51 60 39 51 66

N.S.

1 1.11 0.98 1.07 1.11 1.30 0.85 1.11 1.43

time (sec)

N/A 0.198 0.044 0.020 0.188 0.251 0.074 0.397 0.169

Problem 13

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

17 17 19 16 53 35 70 18 18

N.S.

1 1.00 1.12 0.94 3.12 2.06 4.12 1.06 1.06

time (sec)

N/A 0.188 1.789 0.129 0.224 0.258 1.415 0.350 0.112

Problem 14

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

17 17 19 16 57 41 73 18 18

N.S.

1 1.00 1.12 0.94 3.35 2.41 4.29 1.06 1.06

time (sec)

N/A 0.189 0.920 0.125 0.218 0.250 1.331 0.349 0.119

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 55 45 53 55 65 39 54 68

N.S.

1 1.15 0.94 1.10 1.15 1.35 0.81 1.12 1.42

time (sec)

N/A 0.203 0.074 0.020 0.184 0.244 0.075 0.398 0.151

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 61 66 59 57 73 42 58 76

N.S.

1 1.17 1.27 1.13 1.10 1.40 0.81 1.12 1.46

time (sec)

N/A 0.208 0.184 0.019 0.182 0.244 0.089 0.429 0.167

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

333 504 241 548 303 702 0 0 0

N.S.

1 1.51 0.72 1.65 0.91 2.11 0.00 0.00 0.00

time (sec)

N/A 3.947 0.189 0.129 0.197 0.270 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

243 378 203 385 234 521 0 0 0

N.S.

1 1.56 0.84 1.58 0.96 2.14 0.00 0.00 0.00

time (sec)

N/A 2.585 0.147 0.095 0.196 0.262 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 227 120 216 149 338 0 0 0

N.S.

1 1.43 0.75 1.36 0.94 2.13 0.00 0.00 0.00

time (sec)

N/A 1.094 0.114 0.050 0.219 0.261 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 71 64 66 84 127 76 65 121

N.S.

1 1.03 0.93 0.96 1.22 1.84 1.10 0.94 1.75

time (sec)

N/A 0.212 0.071 0.030 0.185 0.252 0.105 0.336 0.322

Problem 21

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

17 17 19 16 128 53 165 18 18

N.S.

1 1.00 1.12 0.94 7.53 3.12 9.71 1.06 1.06

time (sec)

N/A 0.187 2.208 0.162 0.235 0.264 2.221 0.325 0.162

Problem 22

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

17 17 19 16 128 61 165 18 18

N.S.

1 1.00 1.12 0.94 7.53 3.59 9.71 1.06 1.06

time (sec)

N/A 0.187 1.167 0.159 0.233 0.247 2.081 0.373 0.155

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 76 67 71 88 132 78 71 124

N.S.

1 1.06 0.93 0.99 1.22 1.83 1.08 0.99 1.72

time (sec)

N/A 0.215 0.121 0.030 0.185 0.277 0.093 0.319 0.304

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 84 54 77 92 140 85 75 132

N.S.

1 1.08 0.69 0.99 1.18 1.79 1.09 0.96 1.69

time (sec)

N/A 0.218 0.812 0.028 0.183 0.267 0.098 0.347 0.267

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 153 130 392 282 267 496 5716 225

N.S.

1 1.00 0.85 2.56 1.84 1.75 3.24 37.36 1.47

time (sec)

N/A 0.423 0.325 0.563 0.199 0.277 1.772 0.409 0.364

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 115 91 163 171 166 294 2716 135

N.S.

1 1.00 0.79 1.42 1.49 1.44 2.56 23.62 1.17

time (sec)

N/A 0.341 0.250 0.249 0.191 0.252 0.736 0.409 0.263

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 73 84 85 87 144 1101 72

N.S.

1 1.00 0.95 1.09 1.10 1.13 1.87 14.30 0.94

time (sec)

N/A 0.257 0.237 0.059 0.201 0.246 0.425 0.364 0.203

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 30 31 29 37 41 31 31

N.S.

1 1.00 1.00 1.03 0.97 1.23 1.37 1.03 1.03

time (sec)

N/A 0.161 0.029 0.080 0.179 0.274 0.216 0.294 0.249

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

68 68 56 0 0 50 0 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.74 0.00 0.00 0.00

time (sec)

N/A 0.306 0.278 0.000 0.000 0.261 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

100 100 78 0 0 87 0 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.87 0.00 0.00 0.00

time (sec)

N/A 0.342 0.338 0.000 0.000 0.268 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

147 147 111 0 0 160 0 0 0

N.S.

1 1.00 0.76 0.00 0.00 1.09 0.00 0.00 0.00

time (sec)

N/A 0.427 0.371 0.000 0.000 0.280 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

322 322 239 739 568 482 913 12013 438

N.S.

1 1.00 0.74 2.30 1.76 1.50 2.84 37.31 1.36

time (sec)

N/A 0.687 0.554 1.087 0.225 0.271 4.993 0.548 0.594

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 239 171 424 347 287 527 5675 267

N.S.

1 1.00 0.72 1.77 1.45 1.20 2.21 23.74 1.12

time (sec)

N/A 0.526 0.439 0.519 0.208 0.273 1.923 0.431 0.411

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 156 117 174 178 139 258 2284 146

N.S.

1 1.00 0.75 1.12 1.14 0.89 1.65 14.64 0.94

time (sec)

N/A 0.363 0.357 0.142 0.194 0.262 0.717 0.380 0.295

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

67 63 65 60 62 61 88 74 75

N.S.

1 0.94 0.97 0.90 0.93 0.91 1.31 1.10 1.12

time (sec)

N/A 0.215 0.138 0.058 0.182 0.262 0.333 0.318 0.326

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

134 134 108 0 0 95 0 0 0

N.S.

1 1.00 0.81 0.00 0.00 0.71 0.00 0.00 0.00

time (sec)

N/A 0.457 0.465 0.000 0.000 0.265 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

202 202 136 0 0 171 0 0 0

N.S.

1 1.00 0.67 0.00 0.00 0.85 0.00 0.00 0.00

time (sec)

N/A 0.565 0.671 0.000 0.000 0.275 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

286 286 217 0 0 314 0 0 0

N.S.

1 1.00 0.76 0.00 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.700 0.578 0.000 0.000 0.268 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

496 496 341 1097 854 708 1324 18707 652

N.S.

1 1.00 0.69 2.21 1.72 1.43 2.67 37.72 1.31

time (sec)

N/A 0.967 0.744 2.323 0.233 0.263 11.921 0.595 0.859

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

366 366 248 620 523 414 775 8820 399

N.S.

1 1.00 0.68 1.69 1.43 1.13 2.12 24.10 1.09

time (sec)

N/A 0.700 0.560 1.263 0.214 0.256 5.039 0.544 0.561

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

236 236 161 263 269 192 369 3528 219

N.S.

1 1.00 0.68 1.11 1.14 0.81 1.56 14.95 0.93

time (sec)

N/A 0.442 0.451 0.352 0.226 0.251 1.787 0.514 0.370

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

103 83 87 82 94 84 121 98 124

N.S.

1 0.81 0.84 0.80 0.91 0.82 1.17 0.95 1.20

time (sec)

N/A 0.222 0.108 0.135 0.197 0.258 0.614 0.425 0.377

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

200 200 160 0 0 140 0 0 0

N.S.

1 1.00 0.80 0.00 0.00 0.70 0.00 0.00 0.00

time (sec)

N/A 0.588 0.680 0.000 0.000 0.273 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

305 305 250 0 0 259 0 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.85 0.00 0.00 0.00

time (sec)

N/A 0.742 1.081 0.000 0.000 0.268 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

447 447 325 0 0 475 0 0 0

N.S.

1 1.00 0.73 0.00 0.00 1.06 0.00 0.00 0.00

time (sec)

N/A 0.970 0.800 0.000 0.000 0.268 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

192 219 166 3075 480 413 0 0 0

N.S.

1 1.14 0.86 16.02 2.50 2.15 0.00 0.00 0.00

time (sec)

N/A 0.904 0.681 0.414 0.278 0.260 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 161 121 1124 303 271 0 0 0

N.S.

1 1.11 0.83 7.75 2.09 1.87 0.00 0.00 0.00

time (sec)

N/A 0.681 0.501 0.296 0.254 0.258 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 103 74 456 0 147 0 0 0

N.S.

1 1.05 0.76 4.65 0.00 1.50 0.00 0.00 0.00

time (sec)

N/A 0.418 0.240 0.062 0.000 0.261 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 52 55 44 59 44 51 72 44

N.S.

1 1.30 1.38 1.10 1.48 1.10 1.28 1.80 1.10

time (sec)

N/A 0.207 0.095 0.036 0.195 0.268 1.887 0.332 0.113

Problem 50

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

25 25 27 25 26 33 22 27 27

N.S.

1 1.00 1.08 1.00 1.04 1.32 0.88 1.08 1.08

time (sec)

N/A 0.285 1.703 0.037 0.239 0.252 1.826 0.345 0.134

Problem 51

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

25 25 27 25 26 57 24 27 27

N.S.

1 1.00 1.08 1.00 1.04 2.28 0.96 1.08 1.08

time (sec)

N/A 0.275 0.360 0.046 0.254 0.251 3.924 0.457 0.125

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

388 453 0 3319 699 1390 0 0 0

N.S.

1 1.17 0.00 8.55 1.80 3.58 0.00 0.00 0.00

time (sec)

N/A 2.481 0.000 0.455 0.296 0.308 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

294 337 0 1650 468 834 0 0 0

N.S.

1 1.15 0.00 5.61 1.59 2.84 0.00 0.00 0.00

time (sec)

N/A 1.838 0.000 0.310 0.294 0.263 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

191 211 0 591 0 400 0 0 0

N.S.

1 1.10 0.00 3.09 0.00 2.09 0.00 0.00 0.00

time (sec)

N/A 0.966 0.000 0.128 0.000 0.265 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 73 107 74 94 100 0 108 80

N.S.

1 0.99 1.45 1.00 1.27 1.35 0.00 1.46 1.08

time (sec)

N/A 0.229 0.152 0.079 0.201 0.254 0.000 0.371 0.098

Problem 56

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

25 25 27 25 192 67 24 27 27

N.S.

1 1.00 1.08 1.00 7.68 2.68 0.96 1.08 1.08

time (sec)

N/A 0.280 0.789 0.090 0.274 0.256 3.954 0.389 0.167

Problem 57

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

25 25 27 25 280 108 26 27 27

N.S.

1 1.00 1.08 1.00 11.20 4.32 1.04 1.08 1.08

time (sec)

N/A 0.272 0.724 0.004 0.304 0.267 23.593 0.528 0.179

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

594 867 0 4005 1005 2704 0 0 0

N.S.

1 1.46 0.00 6.74 1.69 4.55 0.00 0.00 0.00

time (sec)

N/A 6.078 0.000 0.443 0.311 0.321 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

439 622 0 1887 694 1518 0 0 0

N.S.

1 1.42 0.00 4.30 1.58 3.46 0.00 0.00 0.00

time (sec)

N/A 4.032 0.000 0.427 0.294 0.299 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

276 345 0 668 0 696 0 0 0

N.S.

1 1.25 0.00 2.42 0.00 2.52 0.00 0.00 0.00

time (sec)

N/A 1.580 0.000 0.285 0.000 0.259 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 97 128 96 138 190 0 132 142

N.S.

1 0.87 1.15 0.86 1.24 1.71 0.00 1.19 1.28

time (sec)

N/A 0.242 0.196 0.231 0.217 0.265 0.000 0.350 0.117

Problem 62

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

25 25 27 25 651 101 24 27 27

N.S.

1 1.00 1.08 1.00 26.04 4.04 0.96 1.08 1.08

time (sec)

N/A 0.287 1.212 0.006 0.314 0.265 12.850 0.417 0.225

Problem 63

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

25 25 27 25 807 159 26 27 27

N.S.

1 1.00 1.08 1.00 32.28 6.36 1.04 1.08 1.08

time (sec)

N/A 0.278 0.965 0.006 0.371 0.241 138.507 0.605 0.252

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 71 77 82 70 0 132 0

N.S.

1 1.00 1.00 1.08 1.15 0.99 0.00 1.86 0.00

time (sec)

N/A 0.259 0.258 0.167 0.200 0.261 0.000 0.360 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 145 134 144 160 133 0 250 0

N.S.

1 1.00 0.92 0.99 1.10 0.92 0.00 1.72 0.00

time (sec)

N/A 0.392 0.560 0.228 0.273 0.263 0.000 0.318 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

224 224 196 211 238 196 0 368 0

N.S.

1 1.00 0.88 0.94 1.06 0.88 0.00 1.64 0.00

time (sec)

N/A 0.482 1.375 0.182 0.288 0.259 0.000 0.358 0.000

Problem 67

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

19 19 21 16 18 18 15 18 18

N.S.

1 1.00 1.11 0.84 0.95 0.95 0.79 0.95 0.95

time (sec)

N/A 0.184 0.549 0.016 0.242 0.239 0.895 0.329 0.104

Problem 68

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

19 19 21 16 18 30 17 18 18

N.S.

1 1.00 1.11 0.84 0.95 1.58 0.89 0.95 0.95

time (sec)

N/A 0.188 1.650 0.004 0.291 0.237 5.027 0.377 0.243

Problem 69

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

19 19 21 16 18 42 17 18 18

N.S.

1 1.00 1.11 0.84 0.95 2.21 0.89 0.95 0.95

time (sec)

N/A 0.186 6.234 0.004 0.304 0.262 6.410 0.420 0.338

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

340 340 0 0 0 270 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.79 0.00 0.00 0.00

time (sec)

N/A 0.698 0.000 0.000 0.000 0.086 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

228 228 0 0 0 191 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.84 0.00 0.00 0.00

time (sec)

N/A 0.498 0.000 0.000 0.000 0.082 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

116 116 112 0 0 111 0 0 0

N.S.

1 1.00 0.97 0.00 0.00 0.96 0.00 0.00 0.00

time (sec)

N/A 0.316 1.202 0.000 0.000 0.082 0.000 0.000 0.000

Problem 73

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

25 25 27 25 26 28 22 27 27

N.S.

1 1.00 1.08 1.00 1.04 1.12 0.88 1.08 1.08

time (sec)

N/A 0.199 0.454 0.017 0.254 0.242 3.406 0.393 0.134

Problem 74

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

25 25 27 25 26 50 24 27 27

N.S.

1 1.00 1.08 1.00 1.04 2.00 0.96 1.08 1.08

time (sec)

N/A 0.199 0.718 0.007 0.247 0.248 56.073 0.389 0.198

Problem 75

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

25 25 27 25 26 28 1 27 27

N.S.

1 1.00 1.08 1.00 1.04 1.12 0.04 1.08 1.08

time (sec)

N/A 0.196 0.420 0.032 0.282 0.261 0.000 0.687 0.167

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 128 115 225 106 134 0 0 0

N.S.

1 1.11 1.00 1.96 0.92 1.17 0.00 0.00 0.00

time (sec)

N/A 0.557 0.160 0.059 0.207 0.245 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 91 85 194 78 108 0 0 0

N.S.

1 1.07 1.00 2.28 0.92 1.27 0.00 0.00 0.00

time (sec)

N/A 0.427 0.207 0.046 0.231 0.252 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 54 154 48 75 0 0 0

N.S.

1 1.00 1.00 2.85 0.89 1.39 0.00 0.00 0.00

time (sec)

N/A 0.272 0.159 0.036 0.220 0.246 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 23 24 23 23 17 24 23

N.S.

1 1.00 1.00 1.04 1.00 1.00 0.74 1.04 1.00

time (sec)

N/A 0.183 0.045 0.016 0.196 0.249 0.061 0.352 0.122

Problem 80

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

24 24 26 24 32 26 19 26 26

N.S.

1 1.00 1.08 1.00 1.33 1.08 0.79 1.08 1.08

time (sec)

N/A 0.212 0.270 0.006 0.268 0.258 0.776 0.352 0.117

Problem 81

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

24 24 26 24 38 30 20 26 26

N.S.

1 1.00 1.08 1.00 1.58 1.25 0.83 1.08 1.08

time (sec)

N/A 0.204 0.242 0.006 0.255 0.306 0.693 0.323 0.130

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 149 137 274 129 246 0 0 0

N.S.

1 1.06 0.98 1.96 0.92 1.76 0.00 0.00 0.00

time (sec)

N/A 0.646 0.160 0.046 0.207 0.242 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 112 103 231 99 186 0 0 0

N.S.

1 1.05 0.96 2.16 0.93 1.74 0.00 0.00 0.00

time (sec)

N/A 0.464 0.112 0.037 0.209 0.284 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 68 54 67 72 74 58 0 63

N.S.

1 0.99 0.78 0.97 1.04 1.07 0.84 0.00 0.91

time (sec)

N/A 0.259 0.095 0.024 0.196 0.278 0.078 0.000 0.257

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 26 25 25 26 26 31

N.S.

1 1.00 1.00 1.04 1.00 1.00 1.04 1.04 1.24

time (sec)

N/A 0.178 0.028 0.022 0.182 0.286 0.053 0.360 0.136

Problem 86

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

24 24 26 24 63 45 65 26 26

N.S.

1 1.00 1.08 1.00 2.62 1.88 2.71 1.08 1.08

time (sec)

N/A 0.293 0.173 0.006 0.265 0.272 0.784 0.457 0.143

Problem 87

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

24 24 26 24 67 51 70 26 26

N.S.

1 1.00 1.08 1.00 2.79 2.12 2.92 1.08 1.08

time (sec)

N/A 0.290 0.310 0.007 0.249 0.273 0.813 0.421 0.147

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

261 276 220 501 266 577 0 0 0

N.S.

1 1.06 0.84 1.92 1.02 2.21 0.00 0.00 0.00

time (sec)

N/A 1.517 0.264 0.076 0.208 0.277 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 192 177 304 202 379 0 0 0

N.S.

1 1.05 0.97 1.67 1.11 2.08 0.00 0.00 0.00

time (sec)

N/A 0.874 0.163 0.075 0.207 0.261 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 90 98 111 150 148 122 0 155

N.S.

1 0.85 0.92 1.05 1.42 1.40 1.15 0.00 1.46

time (sec)

N/A 0.309 0.114 0.045 0.203 0.263 0.098 0.000 0.362

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 27 26 25 46 53 26 25

N.S.

1 1.00 1.00 0.96 0.93 1.70 1.96 0.96 0.93

time (sec)

N/A 0.184 0.027 0.033 0.197 0.267 0.061 0.335 0.254

Problem 92

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

24 24 26 24 145 64 170 26 26

N.S.

1 1.00 1.08 1.00 6.04 2.67 7.08 1.08 1.08

time (sec)

N/A 0.310 0.783 0.007 0.264 0.253 2.759 0.431 0.161

Problem 93

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

24 24 26 24 147 72 172 26 26

N.S.

1 1.00 1.08 1.00 6.12 3.00 7.17 1.08 1.08

time (sec)

N/A 0.299 0.898 0.013 0.252 0.276 2.843 0.416 0.165

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