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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 A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 86 88 86 85 139 937 84

N.S.

1 1.00 0.99 1.01 0.99 0.98 1.60 10.77 0.97

time (sec)

N/A 0.158 0.647 0.279 0.337 0.245 0.114 0.908 8.205

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 67 69 66 66 105 556 63

N.S.

1 1.00 1.02 1.05 1.00 1.00 1.59 8.42 0.95

time (sec)

N/A 0.056 0.329 0.046 0.308 0.244 0.103 0.652 7.970

Problem 3

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

42 42 59 46 50 50 82 50 58

N.S.

1 1.00 1.40 1.10 1.19 1.19 1.95 1.19 1.38

time (sec)

N/A 0.075 0.075 1.460 0.329 0.247 0.294 0.726 7.988

Problem 4

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

37 37 49 43 52 59 85 53 69

N.S.

1 1.00 1.32 1.16 1.41 1.59 2.30 1.43 1.86

time (sec)

N/A 0.148 0.064 0.286 0.330 0.257 0.412 0.902 8.309

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 88 53 68 73 116 119 87

N.S.

1 1.00 2.05 1.23 1.58 1.70 2.70 2.77 2.02

time (sec)

N/A 0.168 0.033 0.286 0.330 0.260 0.719 1.067 8.489

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 77 77 86 95 143 179 108

N.S.

1 1.00 1.17 1.17 1.30 1.44 2.17 2.71 1.64

time (sec)

N/A 0.207 0.507 0.339 0.322 0.242 1.072 1.308 7.977

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 101 95 104 121 173 237 127

N.S.

1 1.00 1.16 1.09 1.20 1.39 1.99 2.72 1.46

time (sec)

N/A 0.253 1.081 0.355 0.334 0.247 1.875 1.609 7.863

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 108 100 108 122 138 204 299 145

N.S.

1 1.00 0.93 1.00 1.13 1.28 1.89 2.77 1.34

time (sec)

N/A 0.295 1.255 0.348 0.315 0.254 2.321 1.337 8.637

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 148 221 148 147 146 250 2078 151

N.S.

1 1.00 1.49 1.00 0.99 0.99 1.69 14.04 1.02

time (sec)

N/A 0.361 6.256 0.096 0.321 0.273 0.155 1.794 8.465

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 112 172 120 120 119 194 1389 121

N.S.

1 1.00 1.54 1.07 1.07 1.06 1.73 12.40 1.08

time (sec)

N/A 0.136 1.961 0.063 0.312 0.255 0.130 1.192 8.432

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 96 87 91 91 151 95 91

N.S.

1 1.00 1.10 1.00 1.05 1.05 1.74 1.09 1.05

time (sec)

N/A 0.156 0.522 0.253 0.308 0.252 0.459 1.006 8.301

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 91 80 85 92 136 86 90

N.S.

1 1.00 1.30 1.14 1.21 1.31 1.94 1.23 1.29

time (sec)

N/A 0.215 0.311 0.224 0.441 0.282 0.750 1.336 8.589

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 100 84 93 112 158 118 100

N.S.

1 1.00 1.39 1.17 1.29 1.56 2.19 1.64 1.39

time (sec)

N/A 0.242 0.299 0.350 0.377 0.254 1.010 1.674 8.563

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 123 107 120 122 206 237 127

N.S.

1 1.00 1.40 1.22 1.36 1.39 2.34 2.69 1.44

time (sec)

N/A 0.311 0.384 0.385 0.380 0.255 1.760 0.868 8.697

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 118 152 136 149 157 252 334 156

N.S.

1 1.00 1.29 1.15 1.26 1.33 2.14 2.83 1.32

time (sec)

N/A 0.363 1.266 0.404 0.382 0.260 2.315 0.908 8.740

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 151 180 162 175 191 304 435 182

N.S.

1 1.00 1.19 1.07 1.16 1.26 2.01 2.88 1.21

time (sec)

N/A 0.431 3.147 0.464 0.630 0.252 4.123 0.978 8.709

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 165 209 180 179 178 313 2670 181

N.S.

1 1.00 1.27 1.09 1.08 1.08 1.90 16.18 1.10

time (sec)

N/A 0.216 1.765 0.109 0.422 0.265 0.166 2.372 8.544

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 140 130 139 143 142 248 158 142

N.S.

1 1.00 0.93 0.99 1.02 1.01 1.77 1.13 1.01

time (sec)

N/A 0.245 1.128 0.283 0.329 0.253 0.767 1.527 8.716

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 113 121 124 133 211 129 118

N.S.

1 1.00 0.97 1.03 1.06 1.14 1.80 1.10 1.01

time (sec)

N/A 0.387 0.504 0.265 0.333 0.274 0.976 1.621 9.325

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 119 113 118 125 145 214 152 114

N.S.

1 1.00 0.95 0.99 1.05 1.22 1.80 1.28 0.96

time (sec)

N/A 0.393 0.518 0.256 0.346 0.266 1.701 1.220 8.777

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 127 126 136 142 162 253 193 135

N.S.

1 1.00 0.99 1.07 1.12 1.28 1.99 1.52 1.06

time (sec)

N/A 0.421 0.487 0.243 0.335 0.276 2.326 1.285 8.766

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 154 164 172 180 181 323 390 169

N.S.

1 1.00 1.06 1.12 1.17 1.18 2.10 2.53 1.10

time (sec)

N/A 0.514 1.337 0.311 0.336 0.254 4.109 1.431 8.509

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

191 191 199 209 215 225 391 528 204

N.S.

1 1.00 1.04 1.09 1.13 1.18 2.05 2.76 1.07

time (sec)

N/A 0.626 0.807 0.314 0.320 0.259 5.461 1.477 8.472

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

233 233 237 243 250 266 462 670 238

N.S.

1 1.00 1.02 1.04 1.07 1.14 1.98 2.88 1.02

time (sec)

N/A 0.701 1.245 0.357 0.376 0.258 12.364 1.573 8.427

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 127 138 127 130 190 1306 135 144

N.S.

1 1.00 1.09 1.00 1.02 1.50 10.28 1.06 1.13

time (sec)

N/A 0.565 1.577 0.122 0.297 0.271 0.928 0.655 8.201

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 101 118 101 109 149 1020 110 117

N.S.

1 1.00 1.17 1.00 1.08 1.48 10.10 1.09 1.16

time (sec)

N/A 0.311 0.664 0.132 0.293 0.281 0.666 0.487 8.249

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 85 98 87 94 110 711 95 100

N.S.

1 1.00 1.15 1.02 1.11 1.29 8.36 1.12 1.18

time (sec)

N/A 0.212 0.205 0.078 0.309 0.264 0.563 0.499 8.910

Problem 28

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

58 58 67 66 88 76 541 94 93

N.S.

1 1.00 1.16 1.14 1.52 1.31 9.33 1.62 1.60

time (sec)

N/A 0.161 0.157 0.255 0.438 0.258 1.203 0.668 9.091

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 113 95 107 118 966 113 115

N.S.

1 1.00 1.41 1.19 1.34 1.48 12.08 1.41 1.44

time (sec)

N/A 0.245 0.369 0.282 0.381 0.271 2.169 0.802 9.197

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 138 122 131 177 2067 157 140

N.S.

1 1.00 1.34 1.18 1.27 1.72 20.07 1.52 1.36

time (sec)

N/A 0.409 0.981 0.316 0.424 0.267 3.717 1.075 9.882

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 137 163 152 158 234 2596 214 175

N.S.

1 1.00 1.19 1.11 1.15 1.71 18.95 1.56 1.28

time (sec)

N/A 0.716 1.517 0.350 0.314 0.280 10.291 1.355 10.245

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

208 208 193 172 220 434 4541 290 210

N.S.

1 1.00 0.93 0.83 1.06 2.09 21.83 1.39 1.01

time (sec)

N/A 0.636 6.086 0.191 0.319 0.310 1.408 0.688 9.236

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 157 146 155 197 311 3497 244 165

N.S.

1 1.00 0.93 0.99 1.25 1.98 22.27 1.55 1.05

time (sec)

N/A 0.358 2.900 0.128 0.325 0.289 1.084 0.561 8.649

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 115 140 145 185 221 2995 241 163

N.S.

1 1.00 1.22 1.26 1.61 1.92 26.04 2.10 1.42

time (sec)

N/A 0.167 2.304 0.091 0.316 0.256 0.869 0.535 8.715

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 111 190 141 177 222 2895 234 153

N.S.

1 1.00 1.71 1.27 1.59 2.00 26.08 2.11 1.38

time (sec)

N/A 0.235 2.448 0.292 0.372 0.281 2.073 0.869 8.615

Problem 36

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

137 137 159 163 208 323 4502 279 180

N.S.

1 1.00 1.16 1.19 1.52 2.36 32.86 2.04 1.31

time (sec)

N/A 0.458 2.607 0.405 0.350 0.314 3.788 1.175 10.179

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

192 192 193 196 262 465 8143 362 230

N.S.

1 1.00 1.01 1.02 1.36 2.42 42.41 1.89 1.20

time (sec)

N/A 0.722 3.807 0.536 0.348 0.317 6.028 1.233 11.128

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

331 331 275 263 389 890 0 505 335

N.S.

1 1.00 0.83 0.79 1.18 2.69 0.00 1.53 1.01

time (sec)

N/A 0.969 5.214 0.216 0.336 0.344 0.000 1.018 9.470

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

250 250 235 242 366 666 0 458 307

N.S.

1 1.00 0.94 0.97 1.46 2.66 0.00 1.83 1.23

time (sec)

N/A 0.636 6.388 0.152 0.373 0.308 0.000 0.834 8.518

Problem 40

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

189 189 288 223 333 478 0 410 280

N.S.

1 1.00 1.52 1.18 1.76 2.53 0.00 2.17 1.48

time (sec)

N/A 0.468 6.238 0.112 0.372 0.268 0.000 0.682 8.768

Problem 41

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

179 179 188 213 330 488 0 410 282

N.S.

1 1.00 1.05 1.19 1.84 2.73 0.00 2.29 1.58

time (sec)

N/A 0.302 4.350 0.140 0.394 0.285 0.000 0.689 8.648

Problem 42

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

175 175 243 208 321 482 0 409 279

N.S.

1 1.00 1.39 1.19 1.83 2.75 0.00 2.34 1.59

time (sec)

N/A 0.383 4.743 0.496 0.320 0.282 0.000 1.250 8.562

Problem 43

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

215 215 223 243 372 683 0 479 315

N.S.

1 1.00 1.04 1.13 1.73 3.18 0.00 2.23 1.47

time (sec)

N/A 0.801 3.311 0.665 0.341 0.329 0.000 1.241 10.872

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

287 287 288 289 454 917 0 560 380

N.S.

1 1.00 1.00 1.01 1.58 3.20 0.00 1.95 1.32

time (sec)

N/A 1.089 6.448 1.033 0.344 0.368 0.000 1.578 13.886

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

132 132 110 0 0 0 0 0 0

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.210 0.628 0.000 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

154 154 115 0 0 0 0 0 0

N.S.

1 1.00 0.75 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.175 0.423 0.000 0.000 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

170 170 133 0 0 0 0 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.185 0.547 0.000 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

170 170 133 0 0 0 0 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.174 0.532 0.000 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

328 328 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.928 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

353 353 300 347 416 415 1001 10353 477

N.S.

1 1.00 0.85 0.98 1.18 1.18 2.84 29.33 1.35

time (sec)

N/A 0.921 6.420 0.302 0.397 0.270 0.294 9.657 8.875

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 248 243 246 274 273 617 5631 300

N.S.

1 1.00 0.98 0.99 1.10 1.10 2.49 22.71 1.21

time (sec)

N/A 0.497 3.673 0.151 0.381 0.253 0.209 4.129 8.987

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 161 161 147 151 150 326 2475 153

N.S.

1 1.00 1.00 0.91 0.94 0.93 2.02 15.37 0.95

time (sec)

N/A 0.276 1.691 0.085 0.403 0.260 0.145 1.789 8.420

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 76 75 74 74 131 761 75

N.S.

1 1.00 1.04 1.03 1.01 1.01 1.79 10.42 1.03

time (sec)

N/A 0.063 0.521 0.053 0.387 0.239 0.116 0.778 8.703

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 155 148 173 183 226 2387 182 186

N.S.

1 0.99 0.95 1.11 1.17 1.45 15.30 1.17 1.19

time (sec)

N/A 0.388 1.195 0.148 0.420 0.366 0.964 0.550 9.559

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

265 265 216 321 338 556 9721 518 1875

N.S.

1 1.00 0.82 1.21 1.28 2.10 36.68 1.95 7.08

time (sec)

N/A 0.519 2.788 0.140 0.374 0.394 1.410 0.655 21.300

Problem 56

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

320 320 379 494 574 987 0 1006 502

N.S.

1 1.00 1.18 1.54 1.79 3.08 0.00 3.14 1.57

time (sec)

N/A 0.773 6.337 0.195 0.419 0.299 0.000 0.807 15.528

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

661 661 573 546 691 690 1819 21368 891

N.S.

1 1.00 0.87 0.83 1.05 1.04 2.75 32.33 1.35

time (sec)

N/A 2.261 6.735 0.447 0.351 0.276 0.393 23.581 8.861

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

443 443 383 392 463 462 1134 11957 561

N.S.

1 1.00 0.86 0.88 1.05 1.04 2.56 26.99 1.27

time (sec)

N/A 1.352 6.552 0.256 0.388 0.263 0.296 10.518 8.359

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

266 264 241 246 260 259 617 5631 300

N.S.

1 0.99 0.91 0.92 0.98 0.97 2.32 21.17 1.13

time (sec)

N/A 0.512 3.015 0.146 0.318 0.261 0.201 4.094 8.421

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 131 176 141 135 134 241 1825 141

N.S.

1 1.00 1.34 1.08 1.03 1.02 1.84 13.93 1.08

time (sec)

N/A 0.186 1.133 0.077 0.292 0.268 0.132 1.363 8.379

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

254 252 190 317 290 397 4444 331 325

N.S.

1 0.99 0.75 1.25 1.14 1.56 17.50 1.30 1.28

time (sec)

N/A 0.900 3.211 0.184 0.308 0.493 2.172 0.697 10.714

Problem 62

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

415 415 277 552 496 964 16225 893 3958

N.S.

1 1.00 0.67 1.33 1.20 2.32 39.10 2.15 9.54

time (sec)

N/A 1.166 6.407 0.309 0.309 0.589 2.972 0.837 32.728

Problem 63

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

597 597 1041 865 839 1699 0 1668 807

N.S.

1 1.00 1.74 1.45 1.41 2.85 0.00 2.79 1.35

time (sec)

N/A 1.447 7.045 0.439 0.331 0.742 0.000 1.015 27.621

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

603 603 419 546 680 679 1819 21368 891

N.S.

1 1.00 0.69 0.91 1.13 1.13 3.02 35.44 1.48

time (sec)

N/A 1.663 6.655 0.435 0.315 0.285 0.391 23.088 8.632

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

389 387 297 347 387 386 1001 10353 478

N.S.

1 0.99 0.76 0.89 0.99 0.99 2.57 26.61 1.23

time (sec)

N/A 0.792 6.368 0.237 0.323 0.279 0.275 9.706 8.378

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

191 191 212 210 202 201 410 3720 221

N.S.

1 1.00 1.11 1.10 1.06 1.05 2.15 19.48 1.16

time (sec)

N/A 0.283 2.612 0.106 0.320 0.259 0.170 3.192 8.170

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

363 363 255 501 436 623 7096 559 508

N.S.

1 1.00 0.70 1.38 1.20 1.72 19.55 1.54 1.40

time (sec)

N/A 1.658 4.894 0.253 0.345 0.794 20.196 0.968 12.193

Problem 68

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

574 574 1024 829 685 1512 24300 1329 701

N.S.

1 1.00 1.78 1.44 1.19 2.63 42.33 2.32 1.22

time (sec)

N/A 2.390 7.593 0.364 0.324 1.156 26.693 1.133 15.062

Problem 69

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

798 798 1409 1271 1119 2549 0 2441 1172

N.S.

1 1.00 1.77 1.59 1.40 3.19 0.00 3.06 1.47

time (sec)

N/A 2.959 7.565 0.496 0.390 1.444 0.000 1.358 17.390

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

337 337 258 500 445 627 7096 559 508

N.S.

1 1.00 0.77 1.48 1.32 1.86 21.06 1.66 1.51

time (sec)

N/A 1.618 4.863 0.245 0.473 0.773 20.489 0.964 12.131

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

236 236 190 317 294 390 4444 331 325

N.S.

1 1.00 0.81 1.34 1.25 1.65 18.83 1.40 1.38

time (sec)

N/A 0.880 3.228 0.208 0.438 0.468 2.234 0.672 10.243

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 156 148 173 178 212 2387 182 186

N.S.

1 1.00 0.95 1.11 1.14 1.36 15.30 1.17 1.19

time (sec)

N/A 0.378 1.176 0.147 0.394 0.325 0.924 0.528 9.169

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 99 117 100 106 118 966 106 109

N.S.

1 1.00 1.18 1.01 1.07 1.19 9.76 1.07 1.10

time (sec)

N/A 0.114 0.238 0.099 0.399 0.272 0.582 0.475 8.809

Problem 74

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

165 164 313 197 243 301 24052 268 196

N.S.

1 0.99 1.90 1.19 1.47 1.82 145.77 1.62 1.19

time (sec)

N/A 0.305 1.617 0.275 0.562 0.455 34.895 0.602 20.811

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

281 281 572 364 520 1345 0 832 393

N.S.

1 1.00 2.04 1.30 1.85 4.79 0.00 2.96 1.40

time (sec)

N/A 0.866 7.287 0.521 0.329 1.075 0.000 0.769 60.064

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

477 477 898 647 1096 3643 0 2080 65819

N.S.

1 1.00 1.88 1.36 2.30 7.64 0.00 4.36 137.99

time (sec)

N/A 1.937 8.915 1.580 0.381 3.390 0.000 1.095 22.517

Problem 77

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

579 579 1022 829 684 1477 24300 1327 701

N.S.

1 1.00 1.77 1.43 1.18 2.55 41.97 2.29 1.21

time (sec)

N/A 2.523 7.599 0.336 0.337 1.103 27.015 1.138 15.618

Problem 78

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

417 417 277 552 493 939 16225 893 3958

N.S.

1 1.00 0.66 1.32 1.18 2.25 38.91 2.14 9.49

time (sec)

N/A 1.203 5.568 0.270 0.340 0.561 3.011 0.781 33.596

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

292 288 221 321 319 505 9721 515 1875

N.S.

1 0.99 0.76 1.10 1.09 1.73 33.29 1.76 6.42

time (sec)

N/A 0.548 2.479 0.245 0.320 0.338 1.619 0.622 21.226

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 140 207 173 205 256 4396 291 184

N.S.

1 1.00 1.48 1.24 1.46 1.83 31.40 2.08 1.31

time (sec)

N/A 0.254 2.714 0.085 0.339 0.265 0.918 0.545 10.549

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

293 293 592 365 513 1275 0 832 430

N.S.

1 1.00 2.02 1.25 1.75 4.35 0.00 2.84 1.47

time (sec)

N/A 0.898 7.593 0.398 0.354 1.110 0.000 0.767 65.171

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

509 508 984 577 1185 4174 0 2823 73684

N.S.

1 1.00 1.93 1.13 2.33 8.20 0.00 5.55 144.76

time (sec)

N/A 2.292 9.124 1.811 0.414 3.540 0.000 1.074 25.217

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

841 841 1758 951 2519 9594 0 3115 128667

N.S.

1 1.00 2.09 1.13 3.00 11.41 0.00 3.70 152.99

time (sec)

N/A 4.426 8.883 6.321 0.483 10.632 0.000 1.102 44.526

Problem 84

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

804 804 454 1271 1110 2490 0 2441 1172

N.S.

1 1.00 0.56 1.58 1.38 3.10 0.00 3.04 1.46

time (sec)

N/A 2.971 7.366 0.581 0.369 1.326 0.000 1.388 18.168

Problem 85

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

597 597 1044 865 827 1618 0 1663 807

N.S.

1 1.00 1.75 1.45 1.39 2.71 0.00 2.79 1.35

time (sec)

N/A 1.451 6.980 0.400 0.341 0.649 0.000 1.047 27.059

Problem 86

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

352 349 378 493 543 897 0 1006 502

N.S.

1 0.99 1.07 1.40 1.54 2.55 0.00 2.86 1.43

time (sec)

N/A 0.743 6.404 0.171 0.338 0.291 0.000 0.809 15.424

Problem 87

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

209 209 261 262 367 566 0 531 327

N.S.

1 1.00 1.25 1.25 1.76 2.71 0.00 2.54 1.56

time (sec)

N/A 0.445 5.515 0.142 0.330 0.297 0.000 0.689 10.858

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

487 487 912 649 1078 3496 0 2078 65817

N.S.

1 1.00 1.87 1.33 2.21 7.18 0.00 4.27 135.15

time (sec)

N/A 2.063 9.018 1.771 0.381 4.009 0.000 1.036 23.069

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

861 860 1732 949 2537 9567 0 3115 128666

N.S.

1 1.00 2.01 1.10 2.95 11.11 0.00 3.62 149.44

time (sec)

N/A 4.762 8.626 5.789 0.550 12.033 0.000 1.100 43.729

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

464 464 1232 4473 0 35153 0 0 0

N.S.

1 1.00 2.66 9.64 0.00 75.76 0.00 0.00 0.00

time (sec)

N/A 2.701 6.545 0.531 0.000 10.873 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

325 325 314 3353 0 23984 0 0 0

N.S.

1 1.00 0.97 10.32 0.00 73.80 0.00 0.00 0.00

time (sec)

N/A 1.458 5.243 0.158 0.000 4.685 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

224 224 220 2218 0 12410 0 0 22955

N.S.

1 1.00 0.98 9.90 0.00 55.40 0.00 0.00 102.48

time (sec)

N/A 0.703 2.159 0.182 0.000 1.664 0.000 0.000 57.645

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 155 150 1312 0 2588 0 0 1199

N.S.

1 1.00 0.97 8.46 0.00 16.70 0.00 0.00 7.74

time (sec)

N/A 0.331 0.592 0.129 0.000 0.353 0.000 0.000 16.041

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

234 234 233 3576 0 0 0 0 62245

N.S.

1 1.00 1.00 15.28 0.00 0.00 0.00 0.00 266.00

time (sec)

N/A 1.192 0.761 0.153 0.000 0.000 0.000 0.000 33.934

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

317 317 764 5778 0 0 0 0 138318

N.S.

1 1.00 2.41 18.23 0.00 0.00 0.00 0.00 436.33

time (sec)

N/A 1.535 6.461 0.133 0.000 0.000 0.000 0.000 42.933

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

543 543 2819 9797 0 0 0 0 0

N.S.

1 1.00 5.19 18.04 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.683 6.721 0.150 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 B B F(-1) B F F(-1) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

550 550 1290 10952 0 84950 0 0 0

N.S.

1 1.00 2.35 19.91 0.00 154.45 0.00 0.00 0.00

time (sec)

N/A 2.854 6.574 0.335 0.000 194.267 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

396 396 510 7939 0 58971 0 0 0

N.S.

1 1.00 1.29 20.05 0.00 148.92 0.00 0.00 0.00

time (sec)

N/A 1.835 6.434 0.212 0.000 69.930 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

273 273 260 5107 0 31081 0 0 0

N.S.

1 1.00 0.95 18.71 0.00 113.85 0.00 0.00 0.00

time (sec)

N/A 0.998 4.837 0.194 0.000 16.158 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 187 202 2500 0 6846 0 0 4260

N.S.

1 1.00 1.08 13.37 0.00 36.61 0.00 0.00 22.78

time (sec)

N/A 0.492 1.319 0.138 0.000 0.950 0.000 0.000 42.332

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