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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 B F F F F F F(-1)

verified

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

size

49 53 117 0 0 0 0 0 0

N.S.

1 1.08 2.39 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.193 0.370 0.000 0.000 0.000 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 123 68 319 0 377 0 0 144

N.S.

1 1.06 0.59 2.75 0.00 3.25 0.00 0.00 1.24

time (sec)

N/A 0.612 0.215 0.161 0.000 0.286 0.000 0.000 13.778

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 101 67 303 0 334 0 0 98

N.S.

1 1.07 0.71 3.22 0.00 3.55 0.00 0.00 1.04

time (sec)

N/A 0.453 0.130 0.045 0.000 0.278 0.000 0.000 13.505

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 74 154 287 0 236 0 0 128

N.S.

1 1.04 2.17 4.04 0.00 3.32 0.00 0.00 1.80

time (sec)

N/A 0.327 0.327 0.053 0.000 0.269 0.000 0.000 13.278

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 53 165 273 0 172 0 0 65

N.S.

1 1.08 3.37 5.57 0.00 3.51 0.00 0.00 1.33

time (sec)

N/A 0.236 0.233 0.112 0.000 0.277 0.000 0.000 13.062

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 78 191 294 0 321 0 0 84

N.S.

1 1.04 2.55 3.92 0.00 4.28 0.00 0.00 1.12

time (sec)

N/A 0.337 0.272 0.046 0.000 0.274 0.000 0.000 13.330

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 108 203 309 0 358 0 0 103

N.S.

1 1.09 2.05 3.12 0.00 3.62 0.00 0.00 1.04

time (sec)

N/A 0.507 0.444 0.049 0.000 0.280 0.000 0.000 13.898

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

269 261 187 187 0 507 0 0 125

N.S.

1 0.97 0.70 0.70 0.00 1.88 0.00 0.00 0.46

time (sec)

N/A 0.756 1.318 0.152 0.000 0.289 0.000 0.000 13.912

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

246 231 112 172 0 423 0 0 104

N.S.

1 0.94 0.46 0.70 0.00 1.72 0.00 0.00 0.42

time (sec)

N/A 0.627 1.041 0.041 0.000 0.279 0.000 0.000 13.366

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

244 235 175 170 0 372 0 0 104

N.S.

1 0.96 0.72 0.70 0.00 1.52 0.00 0.00 0.43

time (sec)

N/A 0.639 0.514 0.049 0.000 0.303 0.000 0.000 13.070

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

222 200 253 155 0 323 0 0 86

N.S.

1 0.90 1.14 0.70 0.00 1.45 0.00 0.00 0.39

time (sec)

N/A 0.532 6.107 0.054 0.000 0.299 0.000 0.000 12.740

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

222 206 184 159 0 413 0 0 86

N.S.

1 0.93 0.83 0.72 0.00 1.86 0.00 0.00 0.39

time (sec)

N/A 0.515 0.422 0.043 0.000 0.282 0.000 0.000 12.877

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No No Yes TBD TBD TBD TBD TBD

size

247 231 400 174 0 446 0 0 99

N.S.

1 0.94 1.62 0.70 0.00 1.81 0.00 0.00 0.40

time (sec)

N/A 0.613 3.060 0.053 0.000 0.287 0.000 0.000 13.090

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

249 239 173 174 0 542 0 0 99

N.S.

1 0.96 0.69 0.70 0.00 2.18 0.00 0.00 0.40

time (sec)

N/A 0.618 1.547 0.068 0.000 0.285 0.000 0.000 13.749

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

186 203 847 354 0 535 0 0 177

N.S.

1 1.09 4.55 1.90 0.00 2.88 0.00 0.00 0.95

time (sec)

N/A 1.096 6.159 0.363 0.000 0.282 0.000 0.000 14.778

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

160 179 380 339 0 487 0 0 143

N.S.

1 1.12 2.38 2.12 0.00 3.04 0.00 0.00 0.89

time (sec)

N/A 0.851 5.179 0.043 0.000 0.282 0.000 0.000 14.193

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

138 153 360 323 0 366 0 0 136

N.S.

1 1.11 2.61 2.34 0.00 2.65 0.00 0.00 0.99

time (sec)

N/A 0.665 3.428 0.054 0.000 0.274 0.000 0.000 13.523

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 127 342 309 0 349 0 0 100

N.S.

1 1.09 2.92 2.64 0.00 2.98 0.00 0.00 0.85

time (sec)

N/A 0.525 1.629 0.057 0.000 0.277 0.000 0.000 13.031

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

114 128 357 305 0 372 0 0 119

N.S.

1 1.12 3.13 2.68 0.00 3.26 0.00 0.00 1.04

time (sec)

N/A 0.550 3.125 0.043 0.000 0.277 0.000 0.000 12.453

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 132 599 303 0 378 0 0 101

N.S.

1 1.13 5.12 2.59 0.00 3.23 0.00 0.00 0.86

time (sec)

N/A 0.593 6.212 0.043 0.000 0.323 0.000 0.000 12.308

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

141 162 415 323 0 485 0 0 126

N.S.

1 1.15 2.94 2.29 0.00 3.44 0.00 0.00 0.89

time (sec)

N/A 0.787 5.755 0.047 0.000 0.285 0.000 0.000 13.545

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 194 625 338 0 514 0 0 129

N.S.

1 1.18 3.79 2.05 0.00 3.12 0.00 0.00 0.78

time (sec)

N/A 0.933 6.309 0.090 0.000 0.293 0.000 0.000 14.208

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

111 115 296 312 0 400 0 0 123

N.S.

1 1.04 2.67 2.81 0.00 3.60 0.00 0.00 1.11

time (sec)

N/A 0.898 0.923 0.101 0.000 0.293 0.000 0.000 12.929

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

87 87 280 298 0 333 0 0 79

N.S.

1 1.00 3.22 3.43 0.00 3.83 0.00 0.00 0.91

time (sec)

N/A 0.655 0.549 0.046 0.000 0.275 0.000 0.000 12.784

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

87 85 283 304 0 331 0 0 102

N.S.

1 0.98 3.25 3.49 0.00 3.80 0.00 0.00 1.17

time (sec)

N/A 0.635 0.431 0.046 0.000 0.290 0.000 0.000 12.728

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

83 81 283 304 0 321 0 0 79

N.S.

1 0.98 3.41 3.66 0.00 3.87 0.00 0.00 0.95

time (sec)

N/A 0.625 0.516 0.042 0.000 0.282 0.000 0.000 12.775

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

111 118 229 319 0 472 0 0 123

N.S.

1 1.06 2.06 2.87 0.00 4.25 0.00 0.00 1.11

time (sec)

N/A 0.918 0.819 0.041 0.000 0.282 0.000 0.000 12.671

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

135 146 86 333 0 500 0 0 132

N.S.

1 1.08 0.64 2.47 0.00 3.70 0.00 0.00 0.98

time (sec)

N/A 1.224 0.622 0.042 0.000 0.279 0.000 0.000 13.312

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

281 254 288 191 0 1173 0 0 375

N.S.

1 0.90 1.02 0.68 0.00 4.17 0.00 0.00 1.33

time (sec)

N/A 1.198 2.376 0.324 0.000 0.297 0.000 0.000 13.298

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

279 244 155 197 0 1172 0 0 376

N.S.

1 0.87 0.56 0.71 0.00 4.20 0.00 0.00 1.35

time (sec)

N/A 1.216 1.220 0.040 0.000 0.296 0.000 0.000 13.435

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

278 249 221 200 0 1114 0 0 366

N.S.

1 0.90 0.79 0.72 0.00 4.01 0.00 0.00 1.32

time (sec)

N/A 1.127 2.197 0.041 0.000 0.330 0.000 0.000 13.129

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

281 249 131 197 0 1181 0 0 366

N.S.

1 0.89 0.47 0.70 0.00 4.20 0.00 0.00 1.30

time (sec)

N/A 1.212 1.598 0.045 0.000 0.301 0.000 0.000 13.137

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

306 288 227 212 0 1257 0 0 414

N.S.

1 0.94 0.74 0.69 0.00 4.11 0.00 0.00 1.35

time (sec)

N/A 1.572 1.174 0.042 0.000 0.315 0.000 0.000 13.241

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

331 316 84 227 0 1751 0 0 425

N.S.

1 0.95 0.25 0.69 0.00 5.29 0.00 0.00 1.28

time (sec)

N/A 1.949 1.025 0.043 0.000 0.326 0.000 0.000 13.570

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

164 179 390 349 0 567 0 0 154

N.S.

1 1.09 2.38 2.13 0.00 3.46 0.00 0.00 0.94

time (sec)

N/A 1.251 3.684 1.233 0.000 0.294 0.000 0.000 13.529

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

164 178 365 349 0 533 0 0 178

N.S.

1 1.09 2.23 2.13 0.00 3.25 0.00 0.00 1.09

time (sec)

N/A 1.332 4.128 0.042 0.000 0.295 0.000 0.000 13.267

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

161 175 443 349 0 518 0 0 151

N.S.

1 1.09 2.75 2.17 0.00 3.22 0.00 0.00 0.94

time (sec)

N/A 1.276 6.925 0.048 0.000 0.283 0.000 0.000 13.339

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

165 180 339 349 0 504 0 0 173

N.S.

1 1.09 2.05 2.12 0.00 3.05 0.00 0.00 1.05

time (sec)

N/A 1.338 3.388 0.056 0.000 0.286 0.000 0.000 13.412

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

189 209 325 364 0 697 0 0 175

N.S.

1 1.11 1.72 1.93 0.00 3.69 0.00 0.00 0.93

time (sec)

N/A 1.698 1.285 0.046 0.000 0.287 0.000 0.000 13.337

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

215 244 124 379 0 718 0 0 193

N.S.

1 1.13 0.58 1.76 0.00 3.34 0.00 0.00 0.90

time (sec)

N/A 2.102 1.109 0.050 0.000 0.303 0.000 0.000 13.533

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

223 233 69 356 0 180 0 0 119

N.S.

1 1.04 0.31 1.60 0.00 0.81 0.00 0.00 0.53

time (sec)

N/A 0.544 0.522 0.152 0.000 0.269 0.000 0.000 12.981

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 153 61 174 0 142 0 0 210

N.S.

1 1.13 0.45 1.29 0.00 1.05 0.00 0.00 1.56

time (sec)

N/A 0.531 0.319 0.043 0.000 0.265 0.000 0.000 12.260

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 168 75 197 0 202 0 0 254

N.S.

1 1.21 0.54 1.42 0.00 1.45 0.00 0.00 1.83

time (sec)

N/A 0.613 0.569 0.042 0.000 0.268 0.000 0.000 12.865

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

221 255 67 452 0 190 0 0 254

N.S.

1 1.15 0.30 2.05 0.00 0.86 0.00 0.00 1.15

time (sec)

N/A 0.596 0.440 0.035 0.000 0.262 0.000 0.000 12.595

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

214 243 67 442 0 178 0 0 238

N.S.

1 1.14 0.31 2.07 0.00 0.83 0.00 0.00 1.11

time (sec)

N/A 0.493 0.466 0.043 0.000 0.288 0.000 0.000 12.460

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 143 51 181 0 157 0 0 230

N.S.

1 1.18 0.42 1.50 0.00 1.30 0.00 0.00 1.90

time (sec)

N/A 0.399 0.258 0.092 0.000 0.253 0.000 0.000 12.872

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 156 62 173 0 198 0 0 208

N.S.

1 1.12 0.45 1.24 0.00 1.42 0.00 0.00 1.50

time (sec)

N/A 0.513 0.450 0.043 0.000 0.259 0.000 0.000 13.077

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

226 230 71 356 0 202 0 0 121

N.S.

1 1.02 0.31 1.58 0.00 0.89 0.00 0.00 0.54

time (sec)

N/A 0.503 0.581 0.039 0.000 0.259 0.000 0.000 12.836

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 170 62 195 0 238 0 0 242

N.S.

1 1.19 0.43 1.36 0.00 1.66 0.00 0.00 1.69

time (sec)

N/A 0.581 0.537 0.043 0.000 0.265 0.000 0.000 13.178

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

216 242 69 444 0 230 0 0 238

N.S.

1 1.12 0.32 2.06 0.00 1.06 0.00 0.00 1.10

time (sec)

N/A 0.496 0.452 0.032 0.000 0.275 0.000 0.000 13.103

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

247 240 68 303 0 843 0 0 153

N.S.

1 0.97 0.28 1.23 0.00 3.41 0.00 0.00 0.62

time (sec)

N/A 0.628 0.181 0.042 0.000 0.276 0.000 0.000 13.860

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

226 217 155 287 0 730 0 0 128

N.S.

1 0.96 0.69 1.27 0.00 3.23 0.00 0.00 0.57

time (sec)

N/A 0.502 0.315 0.030 0.000 0.274 0.000 0.000 13.492

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

208 197 166 273 0 721 0 0 118

N.S.

1 0.95 0.80 1.31 0.00 3.47 0.00 0.00 0.57

time (sec)

N/A 0.380 0.242 0.061 0.000 0.273 0.000 0.000 13.200

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

229 222 194 295 0 890 0 0 137

N.S.

1 0.97 0.85 1.29 0.00 3.89 0.00 0.00 0.60

time (sec)

N/A 0.518 0.382 0.032 0.000 0.289 0.000 0.000 13.314

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

252 244 196 311 0 905 0 0 158

N.S.

1 0.97 0.78 1.23 0.00 3.59 0.00 0.00 0.63

time (sec)

N/A 0.690 0.754 0.034 0.000 0.274 0.000 0.000 13.333

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

317 292 224 360 0 1313 0 0 1274

N.S.

1 0.92 0.71 1.14 0.00 4.14 0.00 0.00 4.02

time (sec)

N/A 0.854 2.168 0.033 0.000 0.298 0.000 0.000 15.244

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

288 261 220 321 0 1230 0 0 1157

N.S.

1 0.91 0.76 1.11 0.00 4.27 0.00 0.00 4.02

time (sec)

N/A 0.690 0.606 0.035 0.000 0.293 0.000 0.000 13.899

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

267 239 192 306 0 1183 0 0 1234

N.S.

1 0.90 0.72 1.15 0.00 4.43 0.00 0.00 4.62

time (sec)

N/A 0.549 0.943 0.048 0.000 0.286 0.000 0.000 13.425

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

267 242 188 301 0 1298 0 0 1196

N.S.

1 0.91 0.70 1.13 0.00 4.86 0.00 0.00 4.48

time (sec)

N/A 0.593 0.825 0.042 0.000 0.309 0.000 0.000 12.918

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

291 265 82 326 0 1318 0 0 1214

N.S.

1 0.91 0.28 1.12 0.00 4.53 0.00 0.00 4.17

time (sec)

N/A 0.746 0.316 0.042 0.000 0.315 0.000 0.000 14.232

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

322 301 85 347 0 1436 0 0 1227

N.S.

1 0.93 0.26 1.08 0.00 4.46 0.00 0.00 3.81

time (sec)

N/A 0.977 0.408 0.037 0.000 0.318 0.000 0.000 15.093

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

372 351 251 410 0 1795 0 0 2317

N.S.

1 0.94 0.67 1.10 0.00 4.83 0.00 0.00 6.23

time (sec)

N/A 1.268 2.984 0.041 0.000 0.344 0.000 0.000 18.064

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

342 317 247 371 0 1643 0 0 2071

N.S.

1 0.93 0.72 1.08 0.00 4.80 0.00 0.00 6.06

time (sec)

N/A 1.019 2.643 0.037 0.000 0.343 0.000 0.000 15.059

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

313 285 215 337 0 1633 0 0 1896

N.S.

1 0.91 0.69 1.08 0.00 5.22 0.00 0.00 6.06

time (sec)

N/A 0.822 1.068 0.039 0.000 0.414 0.000 0.000 13.685

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

313 287 193 332 0 1679 0 0 1951

N.S.

1 0.92 0.62 1.06 0.00 5.36 0.00 0.00 6.23

time (sec)

N/A 0.845 3.552 0.036 0.000 0.376 0.000 0.000 13.428

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

313 286 104 331 0 1692 0 0 1946

N.S.

1 0.91 0.33 1.06 0.00 5.41 0.00 0.00 6.22

time (sec)

N/A 0.859 0.425 0.034 0.000 0.370 0.000 0.000 14.342

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

343 324 108 359 0 1804 0 0 1969

N.S.

1 0.94 0.31 1.05 0.00 5.26 0.00 0.00 5.74

time (sec)

N/A 1.080 0.683 0.037 0.000 0.363 0.000 0.000 15.672

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

377 365 116 388 0 1839 0 0 1992

N.S.

1 0.97 0.31 1.03 0.00 4.88 0.00 0.00 5.28

time (sec)

N/A 1.365 0.802 0.043 0.000 0.341 0.000 0.000 18.021

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

325 292 286 347 0 3267 0 0 5579

N.S.

1 0.90 0.88 1.07 0.00 10.05 0.00 0.00 17.17

time (sec)

N/A 1.249 0.818 0.110 0.000 0.373 0.000 0.000 14.684

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

302 262 249 326 0 3137 0 0 5129

N.S.

1 0.87 0.82 1.08 0.00 10.39 0.00 0.00 16.98

time (sec)

N/A 0.984 0.512 0.043 0.000 0.384 0.000 0.000 14.514

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

302 260 226 332 0 3088 0 0 4808

N.S.

1 0.86 0.75 1.10 0.00 10.23 0.00 0.00 15.92

time (sec)

N/A 0.950 0.266 0.042 0.000 0.360 0.000 0.000 13.900

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

302 259 245 332 0 3160 0 0 4871

N.S.

1 0.86 0.81 1.10 0.00 10.46 0.00 0.00 16.13

time (sec)

N/A 0.958 0.312 0.048 0.000 0.381 0.000 0.000 13.881

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

325 295 198 354 0 3637 0 0 4899

N.S.

1 0.91 0.61 1.09 0.00 11.19 0.00 0.00 15.07

time (sec)

N/A 1.297 0.460 0.044 0.000 0.413 0.000 0.000 13.929

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

351 329 109 371 0 3742 0 0 6042

N.S.

1 0.94 0.31 1.06 0.00 10.66 0.00 0.00 17.21

time (sec)

N/A 1.687 0.291 0.042 0.000 0.475 0.000 0.000 14.960

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

437 397 461 409 0 6403 0 0 13244

N.S.

1 0.91 1.05 0.94 0.00 14.65 0.00 0.00 30.31

time (sec)

N/A 2.034 6.191 0.331 0.000 0.712 0.000 0.000 16.405

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

393 353 390 387 0 6258 0 0 12617

N.S.

1 0.90 0.99 0.98 0.00 15.92 0.00 0.00 32.10

time (sec)

N/A 1.476 3.046 0.302 0.000 0.586 0.000 0.000 15.910

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

387 343 321 391 0 6150 0 0 11953

N.S.

1 0.89 0.83 1.01 0.00 15.89 0.00 0.00 30.89

time (sec)

N/A 1.449 3.304 0.040 0.000 0.473 0.000 0.000 16.253

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

386 341 399 391 0 6104 0 0 11731

N.S.

1 0.88 1.03 1.01 0.00 15.81 0.00 0.00 30.39

time (sec)

N/A 1.398 6.112 0.044 0.000 0.452 0.000 0.000 15.694

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

394 355 295 396 0 6248 0 0 9400

N.S.

1 0.90 0.75 1.01 0.00 15.86 0.00 0.00 23.86

time (sec)

N/A 1.492 2.786 0.045 0.000 0.607 0.000 0.000 20.823

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

437 401 244 414 0 6519 0 0 15251

N.S.

1 0.92 0.56 0.95 0.00 14.92 0.00 0.00 34.90

time (sec)

N/A 2.089 0.615 0.048 0.000 0.723 0.000 0.000 16.753

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

529 494 626 471 0 9101 0 0 20651

N.S.

1 0.93 1.18 0.89 0.00 17.20 0.00 0.00 39.04

time (sec)

N/A 2.855 6.319 1.205 0.000 2.082 0.000 0.000 23.643

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

476 446 574 460 0 9029 0 0 20089

N.S.

1 0.94 1.21 0.97 0.00 18.97 0.00 0.00 42.20

time (sec)

N/A 2.131 6.245 1.161 0.000 63.174 0.000 0.000 20.486

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

470 440 520 457 0 8955 0 0 19256

N.S.

1 0.94 1.11 0.97 0.00 19.05 0.00 0.00 40.97

time (sec)

N/A 2.125 6.227 1.153 0.000 39.249 0.000 0.000 19.079

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

461 429 535 456 0 8913 0 0 19000

N.S.

1 0.93 1.16 0.99 0.00 19.33 0.00 0.00 41.21

time (sec)

N/A 2.122 6.195 0.051 0.000 0.776 0.000 0.000 19.029

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

463 431 481 460 0 8853 0 0 19534

N.S.

1 0.93 1.04 0.99 0.00 19.12 0.00 0.00 42.19

time (sec)

N/A 2.034 6.215 0.051 0.000 0.931 0.000 0.000 18.849

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

476 450 402 465 0 8991 0 0 20155

N.S.

1 0.95 0.84 0.98 0.00 18.89 0.00 0.00 42.34

time (sec)

N/A 2.111 6.166 0.051 0.000 1.580 0.000 0.000 19.447

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

529 499 303 480 0 10308 0 0 21158

N.S.

1 0.94 0.57 0.91 0.00 19.49 0.00 0.00 40.00

time (sec)

N/A 2.814 1.747 0.048 0.000 2.307 0.000 0.000 22.776

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

167 165 118 0 0 0 0 0 0

N.S.

1 0.99 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.368 0.360 0.000 0.000 0.000 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

193 214 0 0 0 0 0 0 0

N.S.

1 1.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.496 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

45 35 45 734 0 159 0 0 1410

N.S.

1 0.78 1.00 16.31 0.00 3.53 0.00 0.00 31.33

time (sec)

N/A 0.249 0.099 0.419 0.000 0.299 0.000 0.000 15.159

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

45 35 45 739 0 159 0 0 1410

N.S.

1 0.78 1.00 16.42 0.00 3.53 0.00 0.00 31.33

time (sec)

N/A 0.254 0.481 0.080 0.000 0.285 0.000 0.000 14.073

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 67 66 89 79 524 95 155

N.S.

1 1.00 1.14 1.12 1.51 1.34 8.88 1.61 2.63

time (sec)

N/A 0.350 0.177 0.081 0.430 0.273 0.527 0.310 0.797

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 122 144 147 185 340 3964 241 268

N.S.

1 1.10 1.30 1.32 1.67 3.06 35.71 2.17 2.41

time (sec)

N/A 0.545 2.132 0.125 0.437 0.296 1.615 0.353 14.088

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 197 202 216 337 549 0 412 481

N.S.

1 1.13 1.15 1.23 1.93 3.14 0.00 2.35 2.75

time (sec)

N/A 0.828 5.318 0.254 0.397 0.340 0.000 0.431 15.121

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B F B F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

188 171 379 2392 0 5073 0 0 3864

N.S.

1 0.91 2.02 12.72 0.00 26.98 0.00 0.00 20.55

time (sec)

N/A 1.046 1.908 0.170 0.000 1.217 0.000 0.000 45.238

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

150 133 294 1657 0 3252 0 0 2823

N.S.

1 0.89 1.96 11.05 0.00 21.68 0.00 0.00 18.82

time (sec)

N/A 0.776 1.016 0.116 0.000 0.628 0.000 0.000 26.830

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

122 105 212 814 0 1329 0 0 843

N.S.

1 0.86 1.74 6.67 0.00 10.89 0.00 0.00 6.91

time (sec)

N/A 0.582 0.662 0.146 0.000 0.326 0.000 0.000 15.521

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

151 123 222 1375 0 1684 0 0 3442

N.S.

1 0.81 1.47 9.11 0.00 11.15 0.00 0.00 22.79

time (sec)

N/A 0.680 1.208 0.079 0.000 0.312 0.000 0.000 40.088

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

408 432 178 986 0 1148 0 0 2529

N.S.

1 1.06 0.44 2.42 0.00 2.81 0.00 0.00 6.20

time (sec)

N/A 0.714 6.621 0.069 0.000 0.290 0.000 0.000 25.166

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

422 453 153 816 0 849 0 0 583

N.S.

1 1.07 0.36 1.93 0.00 2.01 0.00 0.00 1.38

time (sec)

N/A 0.747 0.753 0.062 0.000 0.305 0.000 0.000 14.202

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