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2.2.1 Integrals 1 to 100

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 C A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 114 76 144 326 171 311 324 215

N.S.

1 1.25 0.84 1.58 3.58 1.88 3.42 3.56 2.36

time (sec)

N/A 0.586 0.187 5.561 0.196 0.256 0.356 0.259 0.224

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 83 61 111 222 111 202 204 143

N.S.

1 1.19 0.87 1.59 3.17 1.59 2.89 2.91 2.04

time (sec)

N/A 0.456 0.117 0.205 0.190 0.248 0.286 0.261 1.779

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 59 44 77 135 64 112 112 82

N.S.

1 1.20 0.90 1.57 2.76 1.31 2.29 2.29 1.67

time (sec)

N/A 0.344 0.099 0.181 0.187 0.248 0.214 0.254 1.767

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 27 37 68 30 46 46 35

N.S.

1 1.00 0.96 1.32 2.43 1.07 1.64 1.64 1.25

time (sec)

N/A 0.240 0.074 0.060 0.190 0.256 0.161 0.259 0.090

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 49 82 57 94 0 56 0

N.S.

1 1.00 0.96 1.61 1.12 1.84 0.00 1.10 0.00

time (sec)

N/A 0.401 0.057 0.273 0.223 0.239 0.000 0.265 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 84 65 133 81 150 0 615 0

N.S.

1 1.18 0.92 1.87 1.14 2.11 0.00 8.66 0.00

time (sec)

N/A 0.490 0.164 0.222 0.228 0.246 0.000 0.285 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 111 88 277 95 254 0 298 0

N.S.

1 1.07 0.85 2.66 0.91 2.44 0.00 2.87 0.00

time (sec)

N/A 0.622 0.343 0.267 0.221 0.247 0.000 0.258 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 167 132 145 382 312 660 372 332

N.S.

1 1.03 0.81 0.90 2.36 1.93 4.07 2.30 2.05

time (sec)

N/A 0.493 0.367 0.345 0.206 0.259 0.527 0.262 2.396

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 129 104 121 263 209 456 243 229

N.S.

1 0.96 0.78 0.90 1.96 1.56 3.40 1.81 1.71

time (sec)

N/A 0.361 0.271 0.281 0.195 0.259 0.391 0.273 0.440

Problem 10

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

95 97 75 79 165 123 264 136 127

N.S.

1 1.02 0.79 0.83 1.74 1.29 2.78 1.43 1.34

time (sec)

N/A 0.329 0.184 0.223 0.197 0.246 0.302 0.264 1.788

Problem 11

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

55 55 51 52 88 66 126 63 58

N.S.

1 1.00 0.93 0.95 1.60 1.20 2.29 1.15 1.05

time (sec)

N/A 0.214 0.167 0.094 0.191 0.255 0.208 0.264 0.118

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 78 64 97 72 104 0 68 0

N.S.

1 1.00 0.82 1.24 0.92 1.33 0.00 0.87 0.00

time (sec)

N/A 0.362 0.159 0.436 0.247 0.262 0.000 0.263 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 94 75 152 88 164 0 574 0

N.S.

1 1.16 0.93 1.88 1.09 2.02 0.00 7.09 0.00

time (sec)

N/A 0.547 0.286 0.360 0.228 0.261 0.000 0.297 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 148 102 299 99 278 0 330 0

N.S.

1 1.32 0.91 2.67 0.88 2.48 0.00 2.95 0.00

time (sec)

N/A 0.500 0.615 0.458 0.223 0.256 0.000 0.280 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 171 121 555 110 409 0 537 0

N.S.

1 1.06 0.75 3.43 0.68 2.52 0.00 3.31 0.00

time (sec)

N/A 0.762 0.568 0.559 0.226 0.255 0.000 0.265 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

225 330 158 173 644 528 772 654 532

N.S.

1 1.47 0.70 0.77 2.86 2.35 3.43 2.91 2.36

time (sec)

N/A 1.818 0.762 0.510 0.208 0.254 0.671 0.279 2.305

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 224 122 284 439 343 495 414 364

N.S.

1 1.28 0.70 1.62 2.51 1.96 2.83 2.37 2.08

time (sec)

N/A 1.157 0.655 0.316 0.201 0.251 0.497 0.276 2.040

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 150 93 191 272 199 284 230 183

N.S.

1 1.22 0.76 1.55 2.21 1.62 2.31 1.87 1.49

time (sec)

N/A 0.630 0.372 0.244 0.196 0.249 0.378 0.265 2.147

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 52 62 143 95 126 98 77

N.S.

1 1.00 0.69 0.83 1.91 1.27 1.68 1.31 1.03

time (sec)

N/A 0.359 0.189 0.113 0.182 0.247 0.246 0.269 0.257

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 121 102 166 117 186 0 112 0

N.S.

1 1.00 0.84 1.37 0.97 1.54 0.00 0.93 0.00

time (sec)

N/A 0.468 0.279 0.365 0.244 0.256 0.000 0.273 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 158 196 271 145 305 0 1075 0

N.S.

1 1.09 1.35 1.87 1.00 2.10 0.00 7.41 0.00

time (sec)

N/A 0.480 0.468 0.421 0.244 0.248 0.000 0.316 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

184 242 218 562 145 527 0 602 0

N.S.

1 1.32 1.18 3.05 0.79 2.86 0.00 3.27 0.00

time (sec)

N/A 0.968 0.612 0.513 0.247 0.259 0.000 0.282 0.000

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

172 237 100 102 176 195 253 150 129

N.S.

1 1.38 0.58 0.59 1.02 1.13 1.47 0.87 0.75

time (sec)

N/A 0.738 0.279 0.366 0.194 0.255 0.559 0.272 0.428

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

134 181 90 81 132 147 209 118 94

N.S.

1 1.35 0.67 0.60 0.99 1.10 1.56 0.88 0.70

time (sec)

N/A 0.647 0.113 0.161 0.197 0.260 0.407 0.261 0.275

Problem 25

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

80 85 53 64 96 114 138 86 68

N.S.

1 1.06 0.66 0.80 1.20 1.42 1.72 1.08 0.85

time (sec)

N/A 0.286 0.124 0.131 0.184 0.273 0.317 0.287 0.160

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

179 185 343 0 0 497 0 0 0

N.S.

1 1.03 1.92 0.00 0.00 2.78 0.00 0.00 0.00

time (sec)

N/A 0.684 0.360 0.000 0.000 0.267 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

119 121 199 0 0 305 0 0 0

N.S.

1 1.02 1.67 0.00 0.00 2.56 0.00 0.00 0.00

time (sec)

N/A 0.468 0.207 0.000 0.000 0.270 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 84 101 0 157 0 0 0

N.S.

1 1.00 1.38 1.66 0.00 2.57 0.00 0.00 0.00

time (sec)

N/A 0.292 0.059 0.103 0.000 0.268 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

14 14 16 14 16 16 12 16 18

N.S.

1 1.00 1.14 1.00 1.14 1.14 0.86 1.14 1.29

time (sec)

N/A 0.201 2.819 0.032 0.434 0.244 0.458 0.361 1.728

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

14 14 16 14 16 27 14 16 18

N.S.

1 1.00 1.14 1.00 1.14 1.93 1.00 1.14 1.29

time (sec)

N/A 0.209 5.736 0.037 0.404 0.252 0.662 1.911 1.799

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 127 145 298 238 1332 0 0 0

N.S.

1 1.23 1.41 2.89 2.31 12.93 0.00 0.00 0.00

time (sec)

N/A 0.667 0.617 0.313 0.305 0.277 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 93 91 159 0 715 0 0 0

N.S.

1 1.27 1.25 2.18 0.00 9.79 0.00 0.00 0.00

time (sec)

N/A 0.481 0.498 0.244 0.000 0.258 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 51 57 72 161 0 78 50

N.S.

1 1.00 1.76 1.97 2.48 5.55 0.00 2.69 1.72

time (sec)

N/A 0.263 0.088 0.123 0.179 0.253 0.000 0.261 0.096

Problem 34

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 16 102 18 14 18 18

N.S.

1 1.00 1.12 1.00 6.38 1.12 0.88 1.12 1.12

time (sec)

N/A 0.213 25.540 0.027 0.269 0.254 0.491 0.270 1.756

Problem 35

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 16 156 29 15 18 18

N.S.

1 1.00 1.12 1.00 9.75 1.81 0.94 1.12 1.12

time (sec)

N/A 0.223 25.787 0.028 0.307 0.253 0.668 0.325 1.803

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

296 306 455 0 0 4785 0 0 0

N.S.

1 1.03 1.54 0.00 0.00 16.17 0.00 0.00 0.00

time (sec)

N/A 1.224 4.662 0.000 0.000 0.353 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

175 183 270 0 0 2651 0 0 0

N.S.

1 1.05 1.54 0.00 0.00 15.15 0.00 0.00 0.00

time (sec)

N/A 0.725 1.740 0.000 0.000 0.319 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 104 156 216 0 1267 0 0 0

N.S.

1 1.02 1.53 2.12 0.00 12.42 0.00 0.00 0.00

time (sec)

N/A 0.403 0.477 0.153 0.000 0.288 0.000 0.000 0.000

Problem 39

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 16 321 18 14 18 18

N.S.

1 1.00 1.12 1.00 20.06 1.12 0.88 1.12 1.12

time (sec)

N/A 0.218 124.558 0.033 0.443 0.263 0.523 2.517 1.738

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A F(-1) 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 0 16 405 29 15 18 18

N.S.

1 1.00 0.00 1.00 25.31 1.81 0.94 1.12 1.12

time (sec)

N/A 0.217 0.000 0.034 0.516 0.267 0.748 27.399 1.823

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

171 201 107 0 308 523 0 232 0

N.S.

1 1.18 0.63 0.00 1.80 3.06 0.00 1.36 0.00

time (sec)

N/A 0.821 0.043 0.000 0.190 0.268 0.000 0.312 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

146 167 107 0 268 387 0 202 0

N.S.

1 1.14 0.73 0.00 1.84 2.65 0.00 1.38 0.00

time (sec)

N/A 0.630 0.072 0.000 0.189 0.273 0.000 0.297 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

123 138 105 0 230 302 0 169 0

N.S.

1 1.12 0.85 0.00 1.87 2.46 0.00 1.37 0.00

time (sec)

N/A 0.492 0.054 0.000 0.188 0.274 0.000 0.279 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

104 104 105 0 180 123 0 89 0

N.S.

1 1.00 1.01 0.00 1.73 1.18 0.00 0.86 0.00

time (sec)

N/A 0.381 0.027 0.000 0.197 0.266 0.000 0.266 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

119 137 118 0 104 338 0 0 0

N.S.

1 1.15 0.99 0.00 0.87 2.84 0.00 0.00 0.00

time (sec)

N/A 0.501 0.247 0.000 0.185 0.270 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

149 168 150 0 115 534 0 0 0

N.S.

1 1.13 1.01 0.00 0.77 3.58 0.00 0.00 0.00

time (sec)

N/A 0.627 0.454 0.000 0.272 0.277 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

174 205 191 0 115 853 0 0 0

N.S.

1 1.18 1.10 0.00 0.66 4.90 0.00 0.00 0.00

time (sec)

N/A 0.772 0.289 0.000 0.263 0.280 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

239 246 137 0 281 1001 0 0 0

N.S.

1 1.03 0.57 0.00 1.18 4.19 0.00 0.00 0.00

time (sec)

N/A 0.698 0.333 0.000 0.276 0.287 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

211 218 137 0 239 755 0 0 0

N.S.

1 1.03 0.65 0.00 1.13 3.58 0.00 0.00 0.00

time (sec)

N/A 0.608 0.168 0.000 0.276 0.276 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

166 166 129 0 189 590 0 0 0

N.S.

1 1.00 0.78 0.00 1.14 3.55 0.00 0.00 0.00

time (sec)

N/A 0.490 0.304 0.000 0.267 0.259 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

138 138 141 0 107 155 0 115 0

N.S.

1 1.00 1.02 0.00 0.78 1.12 0.00 0.83 0.00

time (sec)

N/A 0.419 0.099 0.000 0.266 0.255 0.000 0.285 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

142 160 152 0 116 569 0 0 0

N.S.

1 1.13 1.07 0.00 0.82 4.01 0.00 0.00 0.00

time (sec)

N/A 0.559 0.265 0.000 0.255 0.276 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

174 221 156 0 118 861 0 0 0

N.S.

1 1.27 0.90 0.00 0.68 4.95 0.00 0.00 0.00

time (sec)

N/A 0.595 0.924 0.000 0.255 0.282 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

220 243 204 0 116 1350 0 0 0

N.S.

1 1.10 0.93 0.00 0.53 6.14 0.00 0.00 0.00

time (sec)

N/A 0.801 0.299 0.000 0.258 0.307 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

251 304 222 0 116 1825 0 0 0

N.S.

1 1.21 0.88 0.00 0.46 7.27 0.00 0.00 0.00

time (sec)

N/A 0.807 0.535 0.000 0.259 0.306 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

381 546 195 0 513 2092 0 0 0

N.S.

1 1.43 0.51 0.00 1.35 5.49 0.00 0.00 0.00

time (sec)

N/A 2.042 0.370 0.000 0.288 0.287 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

326 465 209 0 429 1545 0 0 0

N.S.

1 1.43 0.64 0.00 1.32 4.74 0.00 0.00 0.00

time (sec)

N/A 1.637 0.334 0.000 0.285 0.286 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

275 275 210 0 334 1217 0 0 0

N.S.

1 1.00 0.76 0.00 1.21 4.43 0.00 0.00 0.00

time (sec)

N/A 0.696 0.214 0.000 0.283 0.283 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

228 228 192 0 177 253 0 0 0

N.S.

1 1.00 0.84 0.00 0.78 1.11 0.00 0.00 0.00

time (sec)

N/A 0.589 0.152 0.000 0.273 0.265 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

246 267 246 0 196 1344 0 0 0

N.S.

1 1.09 1.00 0.00 0.80 5.46 0.00 0.00 0.00

time (sec)

N/A 0.633 0.585 0.000 0.296 0.266 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

277 402 253 0 194 2058 0 0 0

N.S.

1 1.45 0.91 0.00 0.70 7.43 0.00 0.00 0.00

time (sec)

N/A 1.216 1.886 0.000 0.303 0.285 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

331 480 376 0 196 3280 0 0 0

N.S.

1 1.45 1.14 0.00 0.59 9.91 0.00 0.00 0.00

time (sec)

N/A 1.486 0.665 0.000 0.315 0.319 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 132 51 133 174 191 131 145 0

N.S.

1 1.19 0.46 1.20 1.57 1.72 1.18 1.31 0.00

time (sec)

N/A 0.534 0.011 0.059 0.194 0.270 11.163 0.274 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 107 48 121 148 138 100 108 0

N.S.

1 1.16 0.52 1.32 1.61 1.50 1.09 1.17 0.00

time (sec)

N/A 0.425 0.011 0.038 0.186 0.279 0.828 0.269 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 48 72 117 59 66 60 0

N.S.

1 1.00 0.62 0.94 1.52 0.77 0.86 0.78 0.00

time (sec)

N/A 0.326 0.009 0.029 0.192 0.259 0.543 0.255 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 106 67 115 76 136 99 0 0

N.S.

1 1.20 0.76 1.31 0.86 1.55 1.12 0.00 0.00

time (sec)

N/A 0.424 0.030 0.034 0.181 0.266 1.425 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 133 78 126 58 179 124 0 0

N.S.

1 1.17 0.68 1.11 0.51 1.57 1.09 0.00 0.00

time (sec)

N/A 0.519 0.067 0.034 0.230 0.266 11.478 0.000 0.000

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

16 16 18 14 16 16 15 16 18

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.12

time (sec)

N/A 0.206 3.426 0.045 0.784 0.266 1.275 0.300 1.745

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

16 16 18 14 16 16 15 16 18

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.12

time (sec)

N/A 0.215 5.275 0.043 0.940 0.252 0.928 0.276 1.759

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 8 10 0 10 10 10

N.S.

1 1.00 1.20 0.80 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.315 2.618 0.019 0.326 0.000 101.615 0.272 1.716

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

20 20 46 0 0 0 0 0 39

N.S.

1 1.00 2.30 0.00 0.00 0.00 0.00 0.00 1.95

time (sec)

N/A 0.191 0.311 0.000 0.000 0.000 0.000 0.000 1.791

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F B F F B

verified

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

size

24 24 16 0 0 109 0 0 42

N.S.

1 1.00 0.67 0.00 0.00 4.54 0.00 0.00 1.75

time (sec)

N/A 0.199 0.076 0.000 0.000 0.245 0.000 0.000 1.802

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

47 47 64 0 0 0 0 0 110

N.S.

1 1.00 1.36 0.00 0.00 0.00 0.00 0.00 2.34

time (sec)

N/A 0.208 0.489 0.000 0.000 0.000 0.000 0.000 1.963

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

36 36 76 0 0 0 0 0 0

N.S.

1 1.00 2.11 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.224 0.776 0.000 0.000 0.000 0.000 0.000 0.000

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

18 18 20 18 20 20 17 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.94 1.11 1.11

time (sec)

N/A 0.215 2.379 0.045 0.337 0.269 8.059 0.328 1.819

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

237 237 205 0 161 340 0 0 0

N.S.

1 1.00 0.86 0.00 0.68 1.43 0.00 0.00 0.00

time (sec)

N/A 0.514 0.133 0.000 0.092 0.091 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

144 144 132 0 102 241 0 0 0

N.S.

1 1.00 0.92 0.00 0.71 1.67 0.00 0.00 0.00

time (sec)

N/A 0.413 0.167 0.000 0.070 0.086 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

110 110 102 0 79 168 0 0 0

N.S.

1 1.00 0.93 0.00 0.72 1.53 0.00 0.00 0.00

time (sec)

N/A 0.318 0.046 0.000 0.069 0.087 0.000 0.000 0.000

Problem 79

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

14 14 16 14 16 16 14 16 18

N.S.

1 1.00 1.14 1.00 1.14 1.14 1.00 1.14 1.29

time (sec)

N/A 0.199 4.789 0.021 0.290 0.249 1.935 0.268 1.719

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

16 16 18 16 18 18 15 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.12

time (sec)

N/A 0.220 3.007 0.024 0.286 0.251 4.181 0.275 1.798

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 54 73 55 86 0 0 0

N.S.

1 1.00 0.92 1.24 0.93 1.46 0.00 0.00 0.00

time (sec)

N/A 0.274 0.031 0.087 0.083 0.076 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 54 73 55 86 0 0 0

N.S.

1 1.00 0.92 1.24 0.93 1.46 0.00 0.00 0.00

time (sec)

N/A 0.280 0.016 0.092 0.081 0.080 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 54 73 55 86 0 0 0

N.S.

1 1.00 0.92 1.24 0.93 1.46 0.00 0.00 0.00

time (sec)

N/A 0.277 0.025 0.078 0.082 0.075 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 54 73 55 78 0 0 0

N.S.

1 1.00 0.92 1.24 0.93 1.32 0.00 0.00 0.00

time (sec)

N/A 0.261 0.015 0.077 0.081 0.081 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 49 67 43 78 0 0 0

N.S.

1 1.00 1.00 1.37 0.88 1.59 0.00 0.00 0.00

time (sec)

N/A 0.266 0.016 0.076 0.093 0.079 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 55 52 67 55 86 0 0 0

N.S.

1 1.00 0.95 1.22 1.00 1.56 0.00 0.00 0.00

time (sec)

N/A 0.267 0.017 0.084 0.096 0.078 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 55 71 55 86 0 0 0

N.S.

1 1.00 0.93 1.20 0.93 1.46 0.00 0.00 0.00

time (sec)

N/A 0.269 0.018 0.073 0.096 0.077 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

86 86 79 0 71 136 0 0 0

N.S.

1 1.00 0.92 0.00 0.83 1.58 0.00 0.00 0.00

time (sec)

N/A 0.345 0.078 0.000 0.083 0.080 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

85 85 78 0 71 136 0 0 0

N.S.

1 1.00 0.92 0.00 0.84 1.60 0.00 0.00 0.00

time (sec)

N/A 0.337 0.075 0.000 0.082 0.082 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

86 86 79 0 71 136 0 0 0

N.S.

1 1.00 0.92 0.00 0.83 1.58 0.00 0.00 0.00

time (sec)

N/A 0.341 0.075 0.000 0.085 0.079 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

85 85 76 0 71 122 0 0 0

N.S.

1 1.00 0.89 0.00 0.84 1.44 0.00 0.00 0.00

time (sec)

N/A 0.332 0.060 0.000 0.086 0.079 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

72 72 64 0 55 117 0 0 0

N.S.

1 1.00 0.89 0.00 0.76 1.62 0.00 0.00 0.00

time (sec)

N/A 0.322 0.045 0.000 0.098 0.084 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

83 83 73 0 0 136 0 0 0

N.S.

1 1.00 0.88 0.00 0.00 1.64 0.00 0.00 0.00

time (sec)

N/A 0.334 0.073 0.000 0.000 0.083 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

84 84 84 0 0 136 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 1.62 0.00 0.00 0.00

time (sec)

N/A 0.343 0.079 0.000 0.000 0.079 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 24 17 0 0 0 0 0 0

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.222 0.058 0.000 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 24 17 0 0 0 0 0 0

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.220 0.199 0.000 0.000 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

47 47 45 0 0 0 0 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.243 0.093 0.000 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

66 66 49 0 0 0 0 0 0

N.S.

1 1.00 0.74 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.318 0.097 0.000 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 122 104 237 168 264 258 187

N.S.

1 1.00 1.37 1.17 2.66 1.89 2.97 2.90 2.10

time (sec)

N/A 0.356 0.342 0.230 0.196 0.249 0.302 0.275 1.844

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 80 77 141 102 151 146 112

N.S.

1 1.00 1.19 1.15 2.10 1.52 2.25 2.18 1.67

time (sec)

N/A 0.313 0.232 0.202 0.189 0.254 0.217 0.274 0.145

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