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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 A A A A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 147 103 97 116 95 146 83 0

N.S.

1 1.11 0.78 0.73 0.88 0.72 1.11 0.63 0.00

time (sec)

N/A 0.247 0.285 0.460 0.280 0.391 0.461 0.297 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 246 147 141 189 138 202 130 0

N.S.

1 1.22 0.73 0.70 0.94 0.69 1.00 0.65 0.00

time (sec)

N/A 0.356 0.434 0.369 0.277 0.335 0.565 0.313 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 211 136 130 164 127 189 118 0

N.S.

1 1.23 0.79 0.76 0.95 0.74 1.10 0.69 0.00

time (sec)

N/A 0.312 0.395 0.352 0.283 0.329 0.529 0.303 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 176 125 119 139 116 173 107 0

N.S.

1 1.11 0.79 0.75 0.87 0.73 1.09 0.67 0.00

time (sec)

N/A 0.275 0.361 0.359 0.287 0.336 0.531 0.292 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 140 114 108 114 105 158 94 0

N.S.

1 1.21 0.98 0.93 0.98 0.91 1.36 0.81 0.00

time (sec)

N/A 0.233 0.335 0.342 0.280 0.323 0.533 0.294 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 140 114 108 114 105 158 94 0

N.S.

1 1.21 0.98 0.93 0.98 0.91 1.36 0.81 0.00

time (sec)

N/A 0.233 0.003 0.297 0.290 0.354 0.551 0.307 0.000

Problem 7

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

113 118 142 157 137 107 400 113 107

N.S.

1 1.04 1.26 1.39 1.21 0.95 3.54 1.00 0.95

time (sec)

N/A 0.270 0.384 0.336 0.287 0.319 5.955 0.308 11.738

Problem 8

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

117 116 143 165 143 124 389 178 114

N.S.

1 0.99 1.22 1.41 1.22 1.06 3.32 1.52 0.97

time (sec)

N/A 0.273 0.329 0.364 0.289 0.397 2.579 0.293 12.364

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 108 148 150 172 133 444 244 120

N.S.

1 0.89 1.22 1.24 1.42 1.10 3.67 2.02 0.99

time (sec)

N/A 0.281 0.369 0.362 0.284 0.336 3.222 0.287 12.526

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 118 149 137 196 129 457 285 0

N.S.

1 0.98 1.24 1.14 1.63 1.08 3.81 2.38 0.00

time (sec)

N/A 0.281 0.304 0.368 0.293 0.352 3.460 0.282 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 124 151 125 222 119 541 327 0

N.S.

1 1.05 1.28 1.06 1.88 1.01 4.58 2.77 0.00

time (sec)

N/A 0.285 0.281 0.383 0.283 0.306 4.588 0.297 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 113 122 107 155 98 774 388 93

N.S.

1 1.05 1.13 0.99 1.44 0.91 7.17 3.59 0.86

time (sec)

N/A 0.228 0.278 0.394 0.290 0.385 4.208 0.287 13.170

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 148 142 121 180 109 918 463 118

N.S.

1 1.03 0.99 0.85 1.26 0.76 6.42 3.24 0.83

time (sec)

N/A 0.256 0.293 0.402 0.279 0.313 8.065 0.295 13.786

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 183 153 132 205 120 1037 518 192

N.S.

1 1.06 0.89 0.77 1.19 0.70 6.03 3.01 1.12

time (sec)

N/A 0.298 0.355 0.419 0.275 0.274 8.683 0.290 14.487

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 218 164 143 230 131 1159 463 212

N.S.

1 1.08 0.82 0.71 1.14 0.65 5.77 2.30 1.05

time (sec)

N/A 0.335 0.325 0.395 0.284 0.299 25.087 0.294 14.951

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 116 83 75 93 72 129 64 112

N.S.

1 1.13 0.81 0.73 0.90 0.70 1.25 0.62 1.09

time (sec)

N/A 0.232 0.188 0.358 0.281 0.272 0.431 0.301 11.929

Problem 17

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

73 79 75 99 90 87 134 82 87

N.S.

1 1.08 1.03 1.36 1.23 1.19 1.84 1.12 1.19

time (sec)

N/A 0.198 0.205 0.362 0.281 0.268 3.265 0.287 11.780

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 63 59 55 88 104 231 0 55

N.S.

1 1.09 1.02 0.95 1.52 1.79 3.98 0.00 0.95

time (sec)

N/A 0.181 0.217 0.353 0.200 0.265 3.441 0.000 11.493

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 204 140 251 324 278 2004 0 0

N.S.

1 1.27 0.87 1.56 2.01 1.73 12.45 0.00 0.00

time (sec)

N/A 0.597 0.493 0.437 0.283 0.298 13.692 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 168 127 220 290 263 1821 0 0

N.S.

1 1.14 0.86 1.50 1.97 1.79 12.39 0.00 0.00

time (sec)

N/A 0.450 0.436 0.415 0.290 0.286 10.507 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 141 115 189 262 247 1739 0 0

N.S.

1 1.16 0.94 1.55 2.15 2.02 14.25 0.00 0.00

time (sec)

N/A 0.398 0.409 0.378 0.288 0.302 10.203 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 102 82 77 159 171 418 0 78

N.S.

1 1.21 0.98 0.92 1.89 2.04 4.98 0.00 0.93

time (sec)

N/A 0.296 0.277 0.369 0.199 0.338 7.364 0.000 11.854

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 97 82 77 134 172 337 0 78

N.S.

1 1.08 0.91 0.86 1.49 1.91 3.74 0.00 0.87

time (sec)

N/A 0.262 0.268 0.360 0.197 0.260 6.831 0.000 11.597

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 95 82 77 112 173 513 0 78

N.S.

1 1.01 0.87 0.82 1.19 1.84 5.46 0.00 0.83

time (sec)

N/A 0.196 0.276 0.352 0.190 0.267 7.106 0.000 11.441

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 85 82 77 87 172 432 0 78

N.S.

1 1.02 0.99 0.93 1.05 2.07 5.20 0.00 0.94

time (sec)

N/A 0.195 0.271 0.346 0.199 0.279 6.599 0.000 11.531

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 88 82 77 80 171 604 0 78

N.S.

1 1.10 1.02 0.96 1.00 2.14 7.55 0.00 0.98

time (sec)

N/A 0.188 0.009 0.339 0.189 0.269 7.511 0.000 11.456

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 130 129 182 157 244 2378 0 127

N.S.

1 1.11 1.10 1.56 1.34 2.09 20.32 0.00 1.09

time (sec)

N/A 0.281 0.353 0.348 0.188 0.278 14.974 0.000 11.973

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 161 134 213 189 270 2404 0 141

N.S.

1 1.05 0.88 1.39 1.24 1.76 15.71 0.00 0.92

time (sec)

N/A 0.497 0.407 0.412 0.206 0.287 12.159 0.000 12.182

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

184 202 147 244 221 291 2691 0 181

N.S.

1 1.10 0.80 1.33 1.20 1.58 14.62 0.00 0.98

time (sec)

N/A 0.667 0.468 0.388 0.197 0.329 14.955 0.000 12.280

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 127 104 99 135 239 903 0 164

N.S.

1 1.05 0.86 0.82 1.12 1.98 7.46 0.00 1.36

time (sec)

N/A 0.217 0.360 0.365 0.194 0.407 8.458 0.000 11.539

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 159 126 121 158 305 1401 0 202

N.S.

1 1.07 0.85 0.82 1.07 2.06 9.47 0.00 1.36

time (sec)

N/A 0.257 0.467 0.356 0.222 0.500 16.452 0.000 11.617

Problem 32

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

54 58 59 90 63 66 119 70 84

N.S.

1 1.07 1.09 1.67 1.17 1.22 2.20 1.30 1.56

time (sec)

N/A 0.180 0.184 0.374 0.274 0.277 3.399 0.293 0.090

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

173 215 114 108 165 105 182 96 0

N.S.

1 1.24 0.66 0.62 0.95 0.61 1.05 0.55 0.00

time (sec)

N/A 0.368 0.325 0.392 0.293 0.289 0.473 0.291 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 175 103 97 140 94 168 84 0

N.S.

1 1.22 0.72 0.67 0.97 0.65 1.17 0.58 0.00

time (sec)

N/A 0.327 0.275 0.378 0.300 0.265 0.459 0.292 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 145 92 86 115 83 155 73 0

N.S.

1 1.26 0.80 0.75 1.00 0.72 1.35 0.63 0.00

time (sec)

N/A 0.284 0.246 0.380 0.280 0.295 0.421 0.298 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 105 80 73 89 71 134 58 0

N.S.

1 1.27 0.96 0.88 1.07 0.86 1.61 0.70 0.00

time (sec)

N/A 0.232 0.220 0.391 0.283 0.250 0.454 0.281 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 81 69 60 62 60 112 45 0

N.S.

1 0.98 0.83 0.72 0.75 0.72 1.35 0.54 0.00

time (sec)

N/A 0.186 0.017 0.360 0.279 0.279 0.471 0.285 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 67 100 91 75 73 144 78 0

N.S.

1 1.02 1.52 1.38 1.14 1.11 2.18 1.18 0.00

time (sec)

N/A 0.251 0.173 0.349 0.286 0.291 2.289 0.291 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 112 93 78 79 168 126 0

N.S.

1 1.00 1.65 1.37 1.15 1.16 2.47 1.85 0.00

time (sec)

N/A 0.239 0.181 0.385 0.278 0.270 1.564 0.287 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 81 116 72 83 63 214 188 0

N.S.

1 1.01 1.45 0.90 1.04 0.79 2.68 2.35 0.00

time (sec)

N/A 0.232 0.237 0.371 0.277 0.279 2.416 0.284 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 111 99 86 108 74 303 255 0

N.S.

1 1.04 0.93 0.80 1.01 0.69 2.83 2.38 0.00

time (sec)

N/A 0.275 0.234 0.355 0.279 0.426 2.165 0.285 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 151 104 99 133 87 449 329 0

N.S.

1 1.08 0.74 0.71 0.95 0.62 3.21 2.35 0.00

time (sec)

N/A 0.314 0.280 0.395 0.280 0.358 4.328 0.314 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 181 131 110 158 98 510 385 0

N.S.

1 1.07 0.78 0.65 0.93 0.58 3.02 2.28 0.00

time (sec)

N/A 0.354 0.250 0.405 0.275 0.339 3.964 0.292 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 169 126 238 288 188 0 0 0

N.S.

1 1.18 0.88 1.66 2.01 1.31 0.00 0.00 0.00

time (sec)

N/A 0.504 0.427 0.418 0.284 0.356 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 141 104 324 310 172 0 0 0

N.S.

1 1.17 0.86 2.68 2.56 1.42 0.00 0.00 0.00

time (sec)

N/A 0.419 0.396 0.409 0.426 0.343 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 100 70 65 155 116 0 0 66

N.S.

1 1.03 0.72 0.67 1.60 1.20 0.00 0.00 0.68

time (sec)

N/A 0.322 0.303 0.382 0.273 0.404 0.000 0.000 11.604

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 92 70 66 131 117 0 0 67

N.S.

1 1.06 0.80 0.76 1.51 1.34 0.00 0.00 0.77

time (sec)

N/A 0.210 0.334 0.378 0.265 0.337 0.000 0.000 11.400

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 94 69 64 109 117 0 0 65

N.S.

1 1.06 0.78 0.72 1.22 1.31 0.00 0.00 0.73

time (sec)

N/A 0.202 0.329 0.386 0.269 0.570 0.000 0.000 11.333

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 82 70 65 78 116 0 0 66

N.S.

1 1.06 0.91 0.84 1.01 1.51 0.00 0.00 0.86

time (sec)

N/A 0.188 0.012 0.345 0.241 0.267 0.000 0.000 11.494

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 130 107 202 154 169 0 0 0

N.S.

1 1.11 0.91 1.73 1.32 1.44 0.00 0.00 0.00

time (sec)

N/A 0.288 0.481 0.361 0.238 0.264 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 164 135 250 187 195 0 0 0

N.S.

1 1.13 0.93 1.72 1.29 1.34 0.00 0.00 0.00

time (sec)

N/A 0.507 0.424 0.382 0.209 0.368 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 194 136 257 218 216 0 0 0

N.S.

1 1.07 0.75 1.41 1.20 1.19 0.00 0.00 0.00

time (sec)

N/A 0.648 0.473 0.398 0.199 0.267 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 236 161 270 243 227 0 0 0

N.S.

1 1.13 0.77 1.29 1.16 1.09 0.00 0.00 0.00

time (sec)

N/A 0.867 0.457 0.424 0.196 0.328 0.000 0.000 0.000

Problem 54

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

81 101 58 42 70 50 73 34 36

N.S.

1 1.25 0.72 0.52 0.86 0.62 0.90 0.42 0.44

time (sec)

N/A 0.237 0.140 0.367 0.307 0.273 0.210 0.278 11.175

Problem 55

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

63 85 53 37 56 45 60 30 31

N.S.

1 1.35 0.84 0.59 0.89 0.71 0.95 0.48 0.49

time (sec)

N/A 0.207 0.122 0.392 0.277 0.269 0.156 0.286 0.031

Problem 56

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

41 55 46 28 40 38 37 21 22

N.S.

1 1.34 1.12 0.68 0.98 0.93 0.90 0.51 0.54

time (sec)

N/A 0.189 0.096 0.355 0.269 0.274 0.111 0.282 0.029

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 39 41 25 28 33 27 19 21

N.S.

1 0.98 1.02 0.62 0.70 0.82 0.68 0.48 0.52

time (sec)

N/A 0.158 0.097 0.342 0.277 0.280 0.082 0.289 0.031

Problem 58

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

32 32 52 29 41 46 31 34 32

N.S.

1 1.00 1.62 0.91 1.28 1.44 0.97 1.06 1.00

time (sec)

N/A 0.181 0.086 0.378 0.271 0.284 2.515 0.277 11.438

Problem 59

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

33 33 57 30 42 53 51 55 35

N.S.

1 1.00 1.73 0.91 1.27 1.61 1.55 1.67 1.06

time (sec)

N/A 0.184 0.086 0.352 0.278 0.262 1.871 0.280 0.082

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 54 48 39 54 43 116 91 47

N.S.

1 1.06 0.94 0.76 1.06 0.84 2.27 1.78 0.92

time (sec)

N/A 0.191 0.090 0.371 0.277 0.295 3.098 0.294 11.488

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 70 47 44 68 48 128 125 67

N.S.

1 1.04 0.70 0.66 1.01 0.72 1.91 1.87 1.00

time (sec)

N/A 0.212 0.087 0.370 0.269 0.269 3.378 0.306 0.034

Problem 62

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

89 100 58 49 82 53 223 163 77

N.S.

1 1.12 0.65 0.55 0.92 0.60 2.51 1.83 0.87

time (sec)

N/A 0.239 0.095 0.398 0.276 0.265 5.407 0.288 0.033

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 116 63 54 96 58 201 199 90

N.S.

1 1.08 0.59 0.50 0.90 0.54 1.88 1.86 0.84

time (sec)

N/A 0.269 0.102 0.373 0.289 0.255 5.687 0.284 0.034

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 150 127 116 171 111 544 325 0

N.S.

1 1.12 0.95 0.87 1.28 0.83 4.06 2.43 0.00

time (sec)

N/A 0.434 0.431 0.404 0.288 0.279 4.416 0.298 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

310 380 202 196 282 194 303 188 0

N.S.

1 1.23 0.65 0.63 0.91 0.63 0.98 0.61 0.00

time (sec)

N/A 0.650 0.784 0.486 0.281 0.280 0.794 0.309 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

281 345 191 185 257 183 286 177 0

N.S.

1 1.23 0.68 0.66 0.91 0.65 1.02 0.63 0.00

time (sec)

N/A 0.600 0.678 0.434 0.284 0.272 0.685 0.301 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

252 310 180 174 232 172 274 165 0

N.S.

1 1.23 0.71 0.69 0.92 0.68 1.09 0.65 0.00

time (sec)

N/A 0.547 0.656 0.437 0.287 0.312 0.677 0.290 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

223 275 169 163 207 161 262 154 0

N.S.

1 1.23 0.76 0.73 0.93 0.72 1.17 0.69 0.00

time (sec)

N/A 0.504 0.622 0.444 0.280 0.291 0.641 0.297 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

230 240 158 152 182 150 241 142 0

N.S.

1 1.04 0.69 0.66 0.79 0.65 1.05 0.62 0.00

time (sec)

N/A 0.427 0.582 0.434 0.287 0.372 0.615 0.305 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 206 155 138 145 139 206 127 0

N.S.

1 1.10 0.82 0.73 0.77 0.74 1.10 0.68 0.00

time (sec)

N/A 0.295 0.399 0.404 0.275 0.259 0.621 0.293 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

190 216 186 353 217 151 954 161 0

N.S.

1 1.14 0.98 1.86 1.14 0.79 5.02 0.85 0.00

time (sec)

N/A 0.498 0.597 0.375 0.282 0.276 8.890 0.306 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 212 193 265 231 167 887 224 0

N.S.

1 1.10 1.00 1.37 1.20 0.87 4.60 1.16 0.00

time (sec)

N/A 0.499 0.590 0.430 0.280 0.276 3.247 0.297 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

207 219 203 175 241 179 887 293 0

N.S.

1 1.06 0.98 0.85 1.16 0.86 4.29 1.42 0.00

time (sec)

N/A 0.498 0.609 0.397 0.279 0.278 3.957 0.295 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

210 222 189 238 238 179 843 346 0

N.S.

1 1.06 0.90 1.13 1.13 0.85 4.01 1.65 0.00

time (sec)

N/A 0.501 0.577 0.401 0.277 0.272 4.179 0.295 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 208 198 223 262 180 959 409 0

N.S.

1 1.00 0.95 1.07 1.25 0.86 4.59 1.96 0.00

time (sec)

N/A 0.513 0.616 0.426 0.283 0.284 5.954 0.302 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

216 219 195 210 290 180 1182 460 0

N.S.

1 1.01 0.90 0.97 1.34 0.83 5.47 2.13 0.00

time (sec)

N/A 0.518 0.542 0.463 0.298 0.291 6.314 0.297 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

214 224 196 196 315 179 1380 526 0

N.S.

1 1.05 0.92 0.92 1.47 0.84 6.45 2.46 0.00

time (sec)

N/A 0.510 0.543 0.454 0.290 0.286 10.646 0.310 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

206 224 193 173 338 173 1513 542 0

N.S.

1 1.09 0.94 0.84 1.64 0.84 7.34 2.63 0.00

time (sec)

N/A 0.511 0.504 0.519 0.283 0.269 11.745 0.305 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

204 230 198 170 364 163 1719 584 0

N.S.

1 1.13 0.97 0.83 1.78 0.80 8.43 2.86 0.00

time (sec)

N/A 0.515 0.523 0.490 0.284 0.313 29.730 0.311 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 214 169 151 247 142 1889 648 0

N.S.

1 1.14 0.90 0.81 1.32 0.76 10.10 3.47 0.00

time (sec)

N/A 0.419 0.489 0.584 0.281 0.315 31.652 0.317 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

225 249 186 165 272 153 2159 731 0

N.S.

1 1.11 0.83 0.73 1.21 0.68 9.60 3.25 0.00

time (sec)

N/A 0.466 0.524 0.546 0.276 0.331 136.085 0.311 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

254 284 189 176 297 164 2397 778 0

N.S.

1 1.12 0.74 0.69 1.17 0.65 9.44 3.06 0.00

time (sec)

N/A 0.508 0.556 0.745 0.278 0.352 146.794 0.317 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 203 111 207 317 192 0 233 0

N.S.

1 1.17 0.64 1.19 1.82 1.10 0.00 1.34 0.00

time (sec)

N/A 0.685 0.548 0.464 0.279 0.281 0.000 0.303 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 164 98 195 336 177 0 211 0

N.S.

1 1.15 0.69 1.37 2.37 1.25 0.00 1.49 0.00

time (sec)

N/A 0.554 0.387 0.496 0.295 0.267 0.000 0.301 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 135 86 377 308 161 0 186 0

N.S.

1 1.14 0.73 3.19 2.61 1.36 0.00 1.58 0.00

time (sec)

N/A 0.393 0.366 0.400 0.296 0.281 0.000 0.300 0.000

Problem 86

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

93 101 53 50 154 106 0 106 49

N.S.

1 1.09 0.57 0.54 1.66 1.14 0.00 1.14 0.53

time (sec)

N/A 0.231 0.308 0.415 0.195 0.260 0.000 0.311 11.568

Problem 87

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

86 91 50 47 128 104 0 137 46

N.S.

1 1.06 0.58 0.55 1.49 1.21 0.00 1.59 0.53

time (sec)

N/A 0.203 0.293 0.395 0.197 0.328 0.000 0.308 11.725

Problem 88

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

103 111 53 50 101 106 0 165 49

N.S.

1 1.08 0.51 0.49 0.98 1.03 0.00 1.60 0.48

time (sec)

N/A 0.221 0.011 0.381 0.186 0.278 0.000 0.317 11.685

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 124 100 305 152 158 0 212 0

N.S.

1 1.09 0.88 2.68 1.33 1.39 0.00 1.86 0.00

time (sec)

N/A 0.290 0.415 0.380 0.198 0.279 0.000 0.307 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 155 117 208 184 184 0 304 0

N.S.

1 1.07 0.81 1.43 1.27 1.27 0.00 2.10 0.00

time (sec)

N/A 0.510 0.410 0.431 0.202 0.286 0.000 0.299 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 201 132 214 216 205 0 381 0

N.S.

1 1.10 0.73 1.18 1.19 1.13 0.00 2.09 0.00

time (sec)

N/A 0.698 0.444 0.408 0.195 0.287 0.000 0.314 0.000

Problem 92

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

147 186 103 97 125 95 0 88 0

N.S.

1 1.27 0.70 0.66 0.85 0.65 0.00 0.60 0.00

time (sec)

N/A 0.351 0.246 0.406 0.292 0.270 0.000 0.281 0.000

Problem 93

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

118 151 92 86 101 83 0 76 0

N.S.

1 1.28 0.78 0.73 0.86 0.70 0.00 0.64 0.00

time (sec)

N/A 0.306 0.216 0.388 0.275 0.276 0.000 0.282 0.000

Problem 94

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

86 116 83 75 77 73 0 64 0

N.S.

1 1.35 0.97 0.87 0.90 0.85 0.00 0.74 0.00

time (sec)

N/A 0.256 0.167 0.382 0.274 0.265 0.000 0.285 0.000

Problem 95

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

62 81 70 64 56 60 0 52 0

N.S.

1 1.31 1.13 1.03 0.90 0.97 0.00 0.84 0.00

time (sec)

N/A 0.191 0.161 0.402 0.275 0.291 0.000 0.289 0.000

Problem 96

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

46 46 63 49 31 52 0 36 0

N.S.

1 1.00 1.37 1.07 0.67 1.13 0.00 0.78 0.00

time (sec)

N/A 0.173 0.113 0.368 0.284 0.271 0.000 0.276 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 78 141 56 54 0 60 0

N.S.

1 1.00 1.70 3.07 1.22 1.17 0.00 1.30 0.00

time (sec)

N/A 0.213 0.130 0.376 0.282 0.279 0.000 0.297 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 73 63 0 50 0 115 0

N.S.

1 1.00 1.43 1.24 0.00 0.98 0.00 2.25 0.00

time (sec)

N/A 0.207 0.125 0.392 0.000 0.268 0.000 0.282 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 86 93 75 0 63 0 193 0

N.S.

1 1.05 1.13 0.91 0.00 0.77 0.00 2.35 0.00

time (sec)

N/A 0.245 0.148 0.395 0.000 0.273 0.000 0.284 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 122 109 88 0 75 0 255 0

N.S.

1 1.07 0.96 0.77 0.00 0.66 0.00 2.24 0.00

time (sec)

N/A 0.282 0.164 0.430 0.000 0.273 0.000 0.285 0.000

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