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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 A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 96 56 96 154 120 0 142 101

N.S.

1 1.32 0.77 1.32 2.11 1.64 0.00 1.95 1.38

time (sec)

N/A 0.286 0.685 1.469 0.196 0.267 0.000 0.316 0.248

Problem 2

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

47 42 73 75 136 91 0 105 99

N.S.

1 0.89 1.55 1.60 2.89 1.94 0.00 2.23 2.11

time (sec)

N/A 0.258 0.300 0.634 0.213 0.258 0.000 0.320 1.845

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 60 41 66 101 71 0 107 64

N.S.

1 1.36 0.93 1.50 2.30 1.61 0.00 2.43 1.45

time (sec)

N/A 0.246 0.433 0.319 0.218 0.246 0.000 0.295 1.786

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 26 45 44 67 42 0 63 27

N.S.

1 1.04 1.80 1.76 2.68 1.68 0.00 2.52 1.08

time (sec)

N/A 0.230 0.219 0.212 0.214 0.246 0.000 0.287 1.735

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 24 52 27 40 167 0 68 64

N.S.

1 0.92 2.00 1.04 1.54 6.42 0.00 2.62 2.46

time (sec)

N/A 0.221 0.039 0.201 0.206 0.251 0.000 0.284 0.137

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 22 24 25 39 88 0 45 43

N.S.

1 0.92 1.00 1.04 1.62 3.67 0.00 1.88 1.79

time (sec)

N/A 0.229 0.019 0.425 0.218 0.242 0.000 0.289 0.102

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 59 123 50 152 924 0 142 156

N.S.

1 1.16 2.41 0.98 2.98 18.12 0.00 2.78 3.06

time (sec)

N/A 0.251 0.278 1.258 0.205 0.271 0.000 0.295 1.856

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 39 61 55 113 244 0 80 173

N.S.

1 0.89 1.39 1.25 2.57 5.55 0.00 1.82 3.93

time (sec)

N/A 0.241 0.346 2.637 0.206 0.257 0.000 0.296 1.809

Problem 9

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

118 137 94 166 295 394 0 293 293

N.S.

1 1.16 0.80 1.41 2.50 3.34 0.00 2.48 2.48

time (sec)

N/A 0.381 2.232 3.167 0.200 0.267 0.000 0.403 1.982

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 69 71 148 265 259 0 205 215

N.S.

1 0.90 0.92 1.92 3.44 3.36 0.00 2.66 2.79

time (sec)

N/A 0.290 1.827 1.966 0.211 0.247 0.000 0.373 0.305

Problem 11

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

79 82 70 118 217 291 0 213 248

N.S.

1 1.04 0.89 1.49 2.75 3.68 0.00 2.70 3.14

time (sec)

N/A 0.297 1.546 0.876 0.218 0.258 0.000 0.342 1.872

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 46 46 98 171 167 0 139 154

N.S.

1 0.94 0.94 2.00 3.49 3.41 0.00 2.84 3.14

time (sec)

N/A 0.252 1.109 0.527 0.197 0.271 0.000 0.332 1.828

Problem 13

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

51 46 64 63 196 890 0 123 160

N.S.

1 0.90 1.25 1.24 3.84 17.45 0.00 2.41 3.14

time (sec)

N/A 0.265 0.979 0.451 0.200 0.258 0.000 0.327 0.169

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 41 43 68 136 264 0 86 209

N.S.

1 0.89 0.93 1.48 2.96 5.74 0.00 1.87 4.54

time (sec)

N/A 0.258 1.199 1.838 0.200 0.252 0.000 0.348 1.866

Problem 15

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

82 79 127 67 181 2462 0 153 261

N.S.

1 0.96 1.55 0.82 2.21 30.02 0.00 1.87 3.18

time (sec)

N/A 0.292 5.638 3.711 0.202 0.287 0.000 0.360 0.177

Problem 16

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

72 64 59 81 210 393 0 143 143

N.S.

1 0.89 0.82 1.12 2.92 5.46 0.00 1.99 1.99

time (sec)

N/A 0.282 2.067 8.706 0.202 0.260 0.000 0.336 1.930

Problem 17

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

182 198 125 246 480 879 0 505 730

N.S.

1 1.09 0.69 1.35 2.64 4.83 0.00 2.77 4.01

time (sec)

N/A 0.419 5.624 10.637 0.204 0.266 0.000 0.554 2.120

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 94 91 239 439 540 0 330 361

N.S.

1 0.90 0.87 2.28 4.18 5.14 0.00 3.14 3.44

time (sec)

N/A 0.326 11.183 5.004 0.212 0.255 0.000 0.502 2.033

Problem 19

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

122 155 95 180 377 725 0 393 668

N.S.

1 1.27 0.78 1.48 3.09 5.94 0.00 3.22 5.48

time (sec)

N/A 0.386 3.990 2.975 0.211 0.274 0.000 0.476 0.328

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 63 62 170 321 383 0 236 308

N.S.

1 0.90 0.89 2.43 4.59 5.47 0.00 3.37 4.40

time (sec)

N/A 0.263 0.546 1.809 0.202 0.280 0.000 0.413 1.870

Problem 21

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

84 76 93 118 560 2277 0 196 317

N.S.

1 0.90 1.11 1.40 6.67 27.11 0.00 2.33 3.77

time (sec)

N/A 0.291 11.331 1.218 0.205 0.276 0.000 0.420 0.266

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 56 70 141 348 572 0 202 590

N.S.

1 0.88 1.09 2.20 5.44 8.94 0.00 3.16 9.22

time (sec)

N/A 0.272 2.803 5.620 0.203 0.257 0.000 0.422 1.885

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 161 159 103 403 5037 0 206 412

N.S.

1 1.06 1.05 0.68 2.65 33.14 0.00 1.36 2.71

time (sec)

N/A 0.394 17.146 11.550 0.214 0.305 0.000 0.439 0.299

Problem 24

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

98 87 87 136 493 925 0 257 622

N.S.

1 0.89 0.89 1.39 5.03 9.44 0.00 2.62 6.35

time (sec)

N/A 0.305 3.337 27.663 0.195 0.253 0.000 0.464 1.932

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 151 93 215 514 2024 0 0 250

N.S.

1 1.28 0.79 1.82 4.36 17.15 0.00 0.00 2.12

time (sec)

N/A 0.360 0.885 11.143 0.339 0.298 0.000 0.000 2.316

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 76 135 202 0 1367 0 0 955

N.S.

1 1.01 1.80 2.69 0.00 18.23 0.00 0.00 12.73

time (sec)

N/A 0.292 1.228 3.896 0.000 0.285 0.000 0.000 3.336

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 97 67 151 316 916 0 0 198

N.S.

1 1.24 0.86 1.94 4.05 11.74 0.00 0.00 2.54

time (sec)

N/A 0.301 0.668 1.190 0.303 0.291 0.000 0.000 2.207

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 52 107 104 0 666 0 0 520

N.S.

1 0.98 2.02 1.96 0.00 12.57 0.00 0.00 9.81

time (sec)

N/A 0.245 0.658 0.475 0.000 0.308 0.000 0.000 2.694

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 53 135 67 0 587 0 0 284

N.S.

1 0.96 2.45 1.22 0.00 10.67 0.00 0.00 5.16

time (sec)

N/A 0.271 0.686 0.357 0.000 0.290 0.000 0.000 2.598

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 46 48 112 62 618 0 0 136

N.S.

1 0.96 1.00 2.33 1.29 12.88 0.00 0.00 2.83

time (sec)

N/A 0.256 0.586 0.488 0.293 0.279 0.000 0.000 1.976

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 94 198 111 0 1790 0 0 787

N.S.

1 1.11 2.33 1.31 0.00 21.06 0.00 0.00 9.26

time (sec)

N/A 0.306 1.414 0.737 0.000 0.305 0.000 0.000 2.599

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 71 246 134 1628 0 0 254

N.S.

1 1.00 1.01 3.51 1.91 23.26 0.00 0.00 3.63

time (sec)

N/A 0.266 0.690 1.570 0.305 0.276 0.000 0.000 2.281

Problem 33

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

192 223 132 512 1690 7366 0 0 0

N.S.

1 1.16 0.69 2.67 8.80 38.36 0.00 0.00 0.00

time (sec)

N/A 0.435 1.679 69.258 0.479 0.376 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 126 160 267 0 5025 0 0 0

N.S.

1 1.02 1.29 2.15 0.00 40.52 0.00 0.00 0.00

time (sec)

N/A 0.427 2.283 14.742 0.000 0.343 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 152 105 381 840 3918 0 0 0

N.S.

1 1.15 0.80 2.89 6.36 29.68 0.00 0.00 0.00

time (sec)

N/A 0.350 1.496 4.502 0.396 0.336 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 93 133 167 0 2252 0 0 0

N.S.

1 1.01 1.45 1.82 0.00 24.48 0.00 0.00 0.00

time (sec)

N/A 0.269 1.474 1.719 0.000 0.308 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 112 188 161 0 2614 0 0 0

N.S.

1 1.09 1.83 1.56 0.00 25.38 0.00 0.00 0.00

time (sec)

N/A 0.318 1.501 0.951 0.000 0.348 0.000 0.000 0.000

Problem 38

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

82 81 86 252 212 2562 0 0 0

N.S.

1 0.99 1.05 3.07 2.59 31.24 0.00 0.00 0.00

time (sec)

N/A 0.269 1.134 1.546 0.338 0.311 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 150 221 187 0 6335 0 0 0

N.S.

1 1.06 1.57 1.33 0.00 44.93 0.00 0.00 0.00

time (sec)

N/A 0.355 5.852 2.454 0.000 0.348 0.000 0.000 0.000

Problem 40

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

113 115 114 338 282 5062 0 0 0

N.S.

1 1.02 1.01 2.99 2.50 44.80 0.00 0.00 0.00

time (sec)

N/A 0.372 1.625 3.720 0.384 0.330 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

240 273 184 610 3392 18818 0 0 0

N.S.

1 1.14 0.77 2.54 14.13 78.41 0.00 0.00 0.00

time (sec)

N/A 0.507 1.643 193.922 0.733 0.533 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

166 168 227 341 0 13095 0 0 0

N.S.

1 1.01 1.37 2.05 0.00 78.89 0.00 0.00 0.00

time (sec)

N/A 0.499 3.094 77.406 0.000 0.449 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 220 158 488 1806 12965 0 0 0

N.S.

1 1.19 0.85 2.64 9.76 70.08 0.00 0.00 0.00

time (sec)

N/A 0.429 2.286 15.259 0.585 0.453 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 134 157 252 0 7119 0 0 0

N.S.

1 1.06 1.25 2.00 0.00 56.50 0.00 0.00 0.00

time (sec)

N/A 0.296 2.294 5.912 0.000 0.370 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 177 249 304 0 10716 0 0 0

N.S.

1 1.13 1.60 1.95 0.00 68.69 0.00 0.00 0.00

time (sec)

N/A 0.410 2.234 2.878 0.000 0.473 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

112 116 109 306 478 8312 0 0 0

N.S.

1 1.04 0.97 2.73 4.27 74.21 0.00 0.00 0.00

time (sec)

N/A 0.288 1.838 5.215 0.427 0.379 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 222 401 304 0 21301 0 0 0

N.S.

1 1.13 2.05 1.55 0.00 108.68 0.00 0.00 0.00

time (sec)

N/A 0.442 7.605 7.892 0.000 0.563 0.000 0.000 0.000

Problem 48

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

151 154 149 397 615 14334 0 0 0

N.S.

1 1.02 0.99 2.63 4.07 94.93 0.00 0.00 0.00

time (sec)

N/A 0.444 2.026 11.279 0.505 0.435 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 133 92 100 194 1530 0 203 156

N.S.

1 1.01 0.70 0.76 1.47 11.59 0.00 1.54 1.18

time (sec)

N/A 0.430 0.206 1.491 0.277 0.282 0.000 0.321 0.288

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 114 112 104 174 1070 0 132 171

N.S.

1 1.16 1.14 1.06 1.78 10.92 0.00 1.35 1.74

time (sec)

N/A 0.342 0.040 0.975 0.282 0.276 0.000 0.309 0.247

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 90 69 68 141 924 0 140 115

N.S.

1 0.90 0.69 0.68 1.41 9.24 0.00 1.40 1.15

time (sec)

N/A 0.382 0.107 0.426 0.280 0.323 0.000 0.317 2.008

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 76 77 73 105 528 0 86 128

N.S.

1 1.21 1.22 1.16 1.67 8.38 0.00 1.37 2.03

time (sec)

N/A 0.276 0.031 0.410 0.283 0.334 0.000 0.300 0.150

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 59 75 56 83 522 0 74 233

N.S.

1 1.20 1.53 1.14 1.69 10.65 0.00 1.51 4.76

time (sec)

N/A 0.274 0.018 0.440 0.279 0.278 0.000 0.293 3.242

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 27 29 28 44 141 0 45 79

N.S.

1 0.93 1.00 0.97 1.52 4.86 0.00 1.55 2.72

time (sec)

N/A 0.249 0.024 0.672 0.202 0.251 0.000 0.313 0.171

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 83 114 54 156 1188 0 143 173

N.S.

1 1.17 1.61 0.76 2.20 16.73 0.00 2.01 2.44

time (sec)

N/A 0.291 0.027 1.961 0.278 0.269 0.000 0.310 3.304

Problem 56

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

56 48 74 46 184 1739 0 149 162

N.S.

1 0.86 1.32 0.82 3.29 31.05 0.00 2.66 2.89

time (sec)

N/A 0.289 0.214 4.062 0.294 0.268 0.000 0.308 1.991

Problem 57

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

170 197 156 180 379 5034 0 374 359

N.S.

1 1.16 0.92 1.06 2.23 29.61 0.00 2.20 2.11

time (sec)

N/A 0.638 7.056 7.300 0.281 0.313 0.000 0.472 0.480

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 208 121 195 348 3341 0 289 397

N.S.

1 1.14 0.66 1.07 1.91 18.36 0.00 1.59 2.18

time (sec)

N/A 0.468 2.228 3.698 0.290 0.293 0.000 0.456 0.411

Problem 59

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

129 148 137 130 301 3649 0 296 306

N.S.

1 1.15 1.06 1.01 2.33 28.29 0.00 2.29 2.37

time (sec)

N/A 0.487 2.204 2.022 0.284 0.280 0.000 0.416 2.054

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 145 90 145 253 2230 0 203 338

N.S.

1 1.18 0.73 1.18 2.06 18.13 0.00 1.65 2.75

time (sec)

N/A 0.361 1.564 1.427 0.279 0.278 0.000 0.378 0.311

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 115 125 111 447 2498 0 178 522

N.S.

1 1.17 1.28 1.13 4.56 25.49 0.00 1.82 5.33

time (sec)

N/A 0.355 0.955 1.036 0.288 0.286 0.000 0.377 4.052

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 42 94 98 256 518 0 122 483

N.S.

1 0.89 2.00 2.09 5.45 11.02 0.00 2.60 10.28

time (sec)

N/A 0.261 0.975 4.037 0.206 0.252 0.000 0.400 2.003

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 125 159 91 378 4642 0 192 561

N.S.

1 1.17 1.49 0.85 3.53 43.38 0.00 1.79 5.24

time (sec)

N/A 0.380 1.741 8.677 0.292 0.318 0.000 0.391 3.771

Problem 64

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

97 83 147 101 468 4125 0 249 344

N.S.

1 0.86 1.52 1.04 4.82 42.53 0.00 2.57 3.55

time (sec)

N/A 0.344 1.207 20.507 0.297 0.282 0.000 0.380 0.276

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

275 283 294 274 647 12323 0 694 682

N.S.

1 1.03 1.07 1.00 2.35 44.81 0.00 2.52 2.48

time (sec)

N/A 0.876 7.365 41.602 0.298 0.403 0.000 0.887 2.550

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

351 392 291 366 604 8462 0 580 757

N.S.

1 1.12 0.83 1.04 1.72 24.11 0.00 1.65 2.16

time (sec)

N/A 0.643 8.227 23.771 0.317 0.358 0.000 0.739 2.458

Problem 67

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

220 223 244 206 544 9862 0 577 617

N.S.

1 1.01 1.11 0.94 2.47 44.83 0.00 2.62 2.80

time (sec)

N/A 0.611 7.376 8.875 0.316 0.369 0.000 0.710 0.582

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

269 302 233 297 484 6410 0 463 707

N.S.

1 1.12 0.87 1.10 1.80 23.83 0.00 1.72 2.63

time (sec)

N/A 0.538 7.689 5.718 0.297 0.317 0.000 0.586 2.211

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

219 245 168 245 654 7127 0 414 671

N.S.

1 1.12 0.77 1.12 2.99 32.54 0.00 1.89 3.06

time (sec)

N/A 0.510 8.517 3.445 0.294 0.345 0.000 0.547 7.234

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 63 113 171 679 1192 0 311 1515

N.S.

1 0.89 1.59 2.41 9.56 16.79 0.00 4.38 21.34

time (sec)

N/A 0.272 2.387 20.423 0.208 0.273 0.000 0.553 2.085

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

232 258 264 208 586 10985 0 426 731

N.S.

1 1.11 1.14 0.90 2.53 47.35 0.00 1.84 3.15

time (sec)

N/A 0.567 13.337 38.158 0.294 0.382 0.000 0.557 8.786

Problem 72

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

138 118 213 156 997 9459 0 437 646

N.S.

1 0.86 1.54 1.13 7.22 68.54 0.00 3.17 4.68

time (sec)

N/A 0.350 1.737 62.879 0.291 0.353 0.000 0.584 0.538

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

491 465 645 452 0 17123 0 0 3313

N.S.

1 0.95 1.31 0.92 0.00 34.87 0.00 0.00 6.75

time (sec)

N/A 1.085 2.145 18.727 0.000 1.241 0.000 0.000 5.254

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 826 289 533 62017 0 3 0

N.S.

1 1.00 35.91 12.57 23.17 2696.39 0.00 0.13 0.00

time (sec)

N/A 0.235 1.064 7.246 0.844 4.169 0.000 3.880 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

384 364 423 301 0 10695 0 0 2100

N.S.

1 0.95 1.10 0.78 0.00 27.85 0.00 0.00 5.47

time (sec)

N/A 0.892 1.315 2.074 0.000 1.052 0.000 0.000 3.332

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 409 159 250 40923 0 3 4474

N.S.

1 1.00 19.48 7.57 11.90 1948.71 0.00 0.14 213.05

time (sec)

N/A 0.211 0.719 1.616 0.506 1.738 0.000 3.415 83.407

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 331 96 160 20085 19 3 3679

N.S.

1 1.00 15.76 4.57 7.62 956.43 0.90 0.14 175.19

time (sec)

N/A 0.223 0.628 0.632 0.397 1.726 0.436 2.970 15.272

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 158 190 116 0 640 0 21 669

N.S.

1 1.01 1.21 0.74 0.00 4.08 0.00 0.13 4.26

time (sec)

N/A 0.398 0.663 0.668 0.000 0.281 0.000 0.349 8.731

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 214 136 188 6846 20 0 3643

N.S.

1 1.00 9.30 5.91 8.17 297.65 0.87 0.00 158.39

time (sec)

N/A 0.242 0.919 1.233 0.448 2.937 0.351 0.000 27.782

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 198 322 173 0 3726 0 180 4563

N.S.

1 0.92 1.50 0.80 0.00 17.33 0.00 0.84 21.22

time (sec)

N/A 0.478 1.122 1.599 0.000 1.247 0.000 0.365 3.728

Problem 81

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

63 79 44 82 104 63 0 104 74

N.S.

1 1.25 0.70 1.30 1.65 1.00 0.00 1.65 1.17

time (sec)

N/A 0.243 0.132 4.873 0.203 0.248 0.000 0.321 0.188

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 28 44 37 83 45 0 84 74

N.S.

1 0.93 1.47 1.23 2.77 1.50 0.00 2.80 2.47

time (sec)

N/A 0.233 0.013 1.898 0.198 0.259 0.000 0.303 0.196

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 48 32 54 69 30 0 78 27

N.S.

1 1.45 0.97 1.64 2.09 0.91 0.00 2.36 0.82

time (sec)

N/A 0.244 0.050 0.623 0.194 0.262 0.000 0.293 1.852

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 25 47 32 55 102 0 47 66

N.S.

1 0.93 1.74 1.19 2.04 3.78 0.00 1.74 2.44

time (sec)

N/A 0.217 0.018 0.328 0.281 0.268 0.000 0.283 0.126

Problem 85

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

40 44 48 56 80 323 0 84 125

N.S.

1 1.10 1.20 1.40 2.00 8.08 0.00 2.10 3.12

time (sec)

N/A 0.223 0.014 0.615 0.275 0.255 0.000 0.293 0.121

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 26 28 25 34 159 0 59 59

N.S.

1 0.93 1.00 0.89 1.21 5.68 0.00 2.11 2.11

time (sec)

N/A 0.227 0.013 1.415 0.193 0.257 0.000 0.296 1.872

Problem 87

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

66 71 93 85 181 1046 0 153 280

N.S.

1 1.08 1.41 1.29 2.74 15.85 0.00 2.32 4.24

time (sec)

N/A 0.238 0.010 4.028 0.281 0.265 0.000 0.300 1.896

Problem 88

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

48 43 86 42 371 345 0 95 304

N.S.

1 0.90 1.79 0.88 7.73 7.19 0.00 1.98 6.33

time (sec)

N/A 0.245 0.021 8.915 0.205 0.257 0.000 0.309 0.154

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 108 63 124 171 95 0 186 102

N.S.

1 1.27 0.74 1.46 2.01 1.12 0.00 2.19 1.20

time (sec)

N/A 0.296 1.683 13.067 0.204 0.264 0.000 0.359 0.252

Problem 90

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

54 49 72 72 161 519 0 152 130

N.S.

1 0.91 1.33 1.33 2.98 9.61 0.00 2.81 2.41

time (sec)

N/A 0.270 0.622 5.132 0.282 0.264 0.000 0.351 1.982

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 63 54 96 140 105 0 167 77

N.S.

1 1.24 1.06 1.88 2.75 2.06 0.00 3.27 1.51

time (sec)

N/A 0.282 1.080 1.943 0.193 0.255 0.000 0.353 1.930

Problem 92

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

60 61 54 97 152 774 0 160 182

N.S.

1 1.02 0.90 1.62 2.53 12.90 0.00 2.67 3.03

time (sec)

N/A 0.278 0.212 0.961 0.279 0.279 0.000 0.325 0.210

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

91 101 427 134 199 1373 0 170 303

N.S.

1 1.11 4.69 1.47 2.19 15.09 0.00 1.87 3.33

time (sec)

N/A 0.279 7.314 2.113 0.289 0.262 0.000 0.319 0.157

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 44 49 126 53 391 0 169 482

N.S.

1 0.90 1.00 2.57 1.08 7.98 0.00 3.45 9.84

time (sec)

N/A 0.246 0.216 6.236 0.201 0.272 0.000 0.333 1.957

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

125 128 792 174 345 2824 0 267 572

N.S.

1 1.02 6.34 1.39 2.76 22.59 0.00 2.14 4.58

time (sec)

N/A 0.309 9.279 14.466 0.278 0.277 0.000 0.358 0.169

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 68 83 158 928 677 0 238 732

N.S.

1 0.89 1.09 2.08 12.21 8.91 0.00 3.13 9.63

time (sec)

N/A 0.279 1.855 29.886 0.205 0.254 0.000 0.364 1.869

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 106 81 184 267 227 0 282 133

N.S.

1 1.16 0.89 2.02 2.93 2.49 0.00 3.10 1.46

time (sec)

N/A 0.335 6.865 55.729 0.205 0.259 0.000 0.539 2.039

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

87 85 494 155 284 1840 0 264 232

N.S.

1 0.98 5.68 1.78 3.26 21.15 0.00 3.03 2.67

time (sec)

N/A 0.307 7.062 22.770 0.280 0.282 0.000 0.473 0.333

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 87 69 148 256 369 0 265 243

N.S.

1 1.12 0.88 1.90 3.28 4.73 0.00 3.40 3.12

time (sec)

N/A 0.300 2.558 6.308 0.206 0.257 0.000 0.466 2.014

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 101 89 193 295 2411 0 272 355

N.S.

1 1.02 0.90 1.95 2.98 24.35 0.00 2.75 3.59

time (sec)

N/A 0.317 0.437 2.813 0.289 0.277 0.000 0.410 0.287

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