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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 76 539 481 169 311 170 219

N.S.

1 1.00 0.84 5.92 5.29 1.86 3.42 1.87 2.41

time (sec)

N/A 0.063 0.174 0.145 0.340 0.379 0.356 0.455 0.418

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 61 302 278 109 202 110 147

N.S.

1 1.00 0.87 4.31 3.97 1.56 2.89 1.57 2.10

time (sec)

N/A 0.044 0.117 0.090 0.333 0.368 0.220 0.429 0.294

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 44 143 136 62 112 64 84

N.S.

1 1.00 0.90 2.92 2.78 1.27 2.29 1.31 1.71

time (sec)

N/A 0.028 0.096 0.072 0.331 0.375 0.146 0.520 0.120

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 26 51 50 28 46 30 34

N.S.

1 1.00 0.96 1.89 1.85 1.04 1.70 1.11 1.26

time (sec)

N/A 0.011 0.044 0.047 0.306 0.369 0.086 0.468 0.180

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 50 77 142 78 0 577 -1

N.S.

1 1.00 0.96 1.48 2.73 1.50 0.00 11.10 -0.02

time (sec)

N/A 0.065 0.057 0.079 0.354 0.394 0.000 0.459 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 65 114 164 123 0 523 -1

N.S.

1 1.00 0.89 1.56 2.25 1.68 0.00 7.16 -0.01

time (sec)

N/A 0.077 0.236 0.102 0.375 0.381 0.000 0.464 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C B F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 89 148 199 209 0 5518 -1

N.S.

1 1.00 0.86 1.42 1.91 2.01 0.00 53.06 -0.01

time (sec)

N/A 0.093 0.434 0.151 0.423 0.374 0.000 0.570 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C B F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 144 184 249 295 0 8378 -1

N.S.

1 1.00 1.13 1.45 1.96 2.32 0.00 65.97 -0.01

time (sec)

N/A 0.109 0.385 0.190 0.486 0.376 0.000 0.704 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 132 1027 717 287 660 222 349

N.S.

1 1.00 0.82 6.38 4.45 1.78 4.10 1.38 2.17

time (sec)

N/A 0.068 0.361 0.175 0.333 0.375 0.562 0.487 0.614

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 106 587 428 190 456 153 229

N.S.

1 1.00 0.79 4.38 3.19 1.42 3.40 1.14 1.71

time (sec)

N/A 0.049 0.280 0.109 0.335 0.369 0.369 0.437 0.458

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 77 289 222 113 264 94 179

N.S.

1 1.00 0.81 3.04 2.34 1.19 2.78 0.99 1.88

time (sec)

N/A 0.036 0.202 0.086 0.307 0.364 0.240 0.415 0.207

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 50 112 90 53 126 48 57

N.S.

1 1.00 0.91 2.04 1.64 0.96 2.29 0.87 1.04

time (sec)

N/A 0.017 0.123 0.059 0.288 0.387 0.123 0.550 0.096

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 65 114 163 88 0 610 -1

N.S.

1 1.00 0.83 1.46 2.09 1.13 0.00 7.82 -0.01

time (sec)

N/A 0.114 0.079 0.084 0.383 0.381 0.000 0.437 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 75 156 171 127 0 534 -1

N.S.

1 1.00 0.90 1.88 2.06 1.53 0.00 6.43 -0.01

time (sec)

N/A 0.095 0.413 0.123 0.381 0.379 0.000 0.503 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 102 193 204 218 0 5136 -1

N.S.

1 1.00 0.91 1.72 1.82 1.95 0.00 45.86 -0.01

time (sec)

N/A 0.128 0.637 0.202 0.423 0.373 0.000 0.647 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

225 225 385 1023 925 350 772 351 532

N.S.

1 1.00 1.71 4.55 4.11 1.56 3.43 1.56 2.36

time (sec)

N/A 0.164 0.589 0.182 0.336 0.394 0.782 0.500 1.143

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

175 175 121 560 535 227 495 231 364

N.S.

1 1.00 0.69 3.20 3.06 1.30 2.83 1.32 2.08

time (sec)

N/A 0.110 0.614 0.176 0.318 0.384 0.528 0.484 0.724

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 93 265 267 128 284 137 173

N.S.

1 1.00 0.76 2.15 2.17 1.04 2.31 1.11 1.41

time (sec)

N/A 0.064 0.392 0.136 0.309 0.379 0.337 0.463 0.592

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 52 95 103 60 126 69 77

N.S.

1 1.00 0.69 1.27 1.37 0.80 1.68 0.92 1.03

time (sec)

N/A 0.028 0.127 0.087 0.305 0.378 0.204 0.511 0.260

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 103 171 278 153 0 6075 -1

N.S.

1 1.00 0.85 1.41 2.30 1.26 0.00 50.21 -0.01

time (sec)

N/A 0.169 0.149 0.105 0.398 0.358 0.000 0.613 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 200 247 304 227 0 1000 -1

N.S.

1 1.00 1.38 1.70 2.10 1.57 0.00 6.90 -0.01

time (sec)

N/A 0.160 0.464 0.164 0.436 0.462 0.000 0.565 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C B F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 221 316 339 375 0 115446 -1

N.S.

1 1.00 1.20 1.72 1.84 2.04 0.00 627.42 -0.01

time (sec)

N/A 0.220 0.530 0.287 0.527 0.433 0.000 2.712 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 100 432 303 115 253 108 138

N.S.

1 1.00 0.58 2.51 1.76 0.67 1.47 0.63 0.80

time (sec)

N/A 0.103 0.282 0.122 0.305 0.389 0.640 0.463 0.796

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 92 237 188 88 209 84 104

N.S.

1 1.00 0.69 1.77 1.40 0.66 1.56 0.63 0.78

time (sec)

N/A 0.072 0.124 0.119 0.312 0.427 0.445 0.439 0.543

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 53 106 98 63 138 64 63

N.S.

1 1.00 0.66 1.32 1.22 0.79 1.72 0.80 0.79

time (sec)

N/A 0.029 0.086 0.093 0.301 0.398 0.266 0.414 0.339

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A A C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 52 52 91 61 60 428 -1

N.S.

1 1.00 0.88 0.88 1.54 1.03 1.02 7.25 -0.02

time (sec)

N/A 0.104 0.055 0.095 0.362 0.418 1.298 0.508 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 79 90 717 87 0 3220 -1

N.S.

1 1.00 1.20 1.36 10.86 1.32 0.00 48.79 -0.02

time (sec)

N/A 0.102 0.146 0.122 0.385 0.358 0.000 0.475 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 119 124 790 130 0 3920 -1

N.S.

1 1.00 1.32 1.38 8.78 1.44 0.00 43.56 -0.01

time (sec)

N/A 0.172 0.186 0.111 0.384 0.368 0.000 0.501 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

205 205 196 685 722 970 0 0 -1

N.S.

1 1.00 0.96 3.34 3.52 4.73 0.00 0.00 -0.00

time (sec)

N/A 0.095 0.122 0.191 0.630 0.446 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 130 392 402 598 0 0 -1

N.S.

1 1.00 0.95 2.86 2.93 4.36 0.00 0.00 -0.01

time (sec)

N/A 0.063 0.068 0.100 0.585 0.439 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 87 128 0 306 0 0 -1

N.S.

1 1.00 1.16 1.71 0.00 4.08 0.00 0.00 -0.01

time (sec)

N/A 0.027 0.007 0.040 0.000 0.406 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

17 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.015 3.042 0.046 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 109 316 1059 790 0 0 -1

N.S.

1 1.00 0.96 2.77 9.29 6.93 0.00 0.00 -0.01

time (sec)

N/A 0.133 0.345 0.127 0.611 0.432 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 75 170 324 450 0 0 -1

N.S.

1 1.00 0.91 2.07 3.95 5.49 0.00 0.00 -0.01

time (sec)

N/A 0.089 0.171 0.074 0.582 0.427 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 36 52 159 45 0 1459 55

N.S.

1 1.00 1.29 1.86 5.68 1.61 0.00 52.11 1.96

time (sec)

N/A 0.019 0.012 0.051 0.524 0.376 0.000 0.659 0.832

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.026 3.749 0.060 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F F F(-1)

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

337 337 311 1127 3831 1315 0 0 -1

N.S.

1 1.00 0.92 3.34 11.37 3.90 0.00 0.00 -0.00

time (sec)

N/A 0.160 1.818 0.273 1.982 0.488 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F F F(-1)

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

193 193 184 584 1891 795 0 0 -1

N.S.

1 1.00 0.95 3.03 9.80 4.12 0.00 0.00 -0.01

time (sec)

N/A 0.097 0.620 0.160 0.865 0.443 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F B F F F(-1)

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 389 267 0 435 0 0 -1

N.S.

1 1.00 3.32 2.28 0.00 3.72 0.00 0.00 -0.01

time (sec)

N/A 0.047 2.424 0.092 0.000 0.410 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.026 0.994 0.000 0.000 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

194 194 124 232 263 190 0 1239 -1

N.S.

1 1.00 0.64 1.20 1.36 0.98 0.00 6.39 -0.01

time (sec)

N/A 0.289 0.038 0.061 0.336 0.394 0.000 0.609 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 122 189 242 156 0 773 -1

N.S.

1 1.00 0.72 1.12 1.43 0.92 0.00 4.57 -0.01

time (sec)

N/A 0.170 0.061 0.041 0.324 0.369 0.000 0.495 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 124 144 196 126 0 422 -1

N.S.

1 1.00 0.87 1.01 1.38 0.89 0.00 2.97 -0.01

time (sec)

N/A 0.116 0.061 0.040 0.321 0.382 0.000 0.443 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 124 100 159 108 0 166 -1

N.S.

1 1.00 1.05 0.85 1.35 0.92 0.00 1.41 -0.01

time (sec)

N/A 0.092 0.037 0.043 0.325 0.376 0.000 0.451 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 147 140 129 144 0 0 -1

N.S.

1 1.00 1.06 1.01 0.93 1.04 0.00 0.00 -0.01

time (sec)

N/A 0.139 0.218 0.040 0.622 0.389 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

168 168 190 180 129 208 0 0 -1

N.S.

1 1.00 1.13 1.07 0.77 1.24 0.00 0.00 -0.01

time (sec)

N/A 0.167 0.211 0.041 0.627 0.404 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

193 193 228 220 129 296 0 0 -1

N.S.

1 1.00 1.18 1.14 0.67 1.53 0.00 0.00 -0.01

time (sec)

N/A 0.199 0.239 0.040 0.606 0.422 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

231 231 194 242 295 258 0 1325 -1

N.S.

1 1.00 0.84 1.05 1.28 1.12 0.00 5.74 -0.00

time (sec)

N/A 0.299 1.366 0.067 0.541 0.389 0.000 0.643 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

203 203 175 197 274 195 0 817 -1

N.S.

1 1.00 0.86 0.97 1.35 0.96 0.00 4.02 -0.00

time (sec)

N/A 0.237 1.061 0.060 0.539 0.432 0.000 0.615 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

158 158 146 150 229 148 0 434 -1

N.S.

1 1.00 0.92 0.95 1.45 0.94 0.00 2.75 -0.01

time (sec)

N/A 0.184 0.349 0.059 0.530 0.442 0.000 0.521 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 145 108 187 114 0 165 -1

N.S.

1 1.00 1.12 0.83 1.44 0.88 0.00 1.27 -0.01

time (sec)

N/A 0.151 0.153 0.061 0.524 0.389 0.000 0.438 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 133 146 135 136 0 0 -1

N.S.

1 1.00 0.99 1.08 1.00 1.01 0.00 0.00 -0.01

time (sec)

N/A 0.167 0.409 0.087 0.629 0.384 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

170 170 181 189 136 206 0 0 -1

N.S.

1 1.00 1.06 1.11 0.80 1.21 0.00 0.00 -0.01

time (sec)

N/A 0.214 0.927 0.088 0.636 0.411 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

216 216 244 230 136 323 0 0 -1

N.S.

1 1.00 1.13 1.06 0.63 1.50 0.00 0.00 -0.00

time (sec)

N/A 0.217 0.829 0.089 0.645 0.443 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

247 247 237 273 136 417 0 0 -1

N.S.

1 1.00 0.96 1.11 0.55 1.69 0.00 0.00 -0.00

time (sec)

N/A 0.269 0.544 0.091 0.660 0.453 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F(-1) C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

410 410 542 474 547 368 0 2469 -1

N.S.

1 1.00 1.32 1.16 1.33 0.90 0.00 6.02 -0.00

time (sec)

N/A 0.755 1.989 0.066 0.557 0.422 0.000 0.868 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

354 354 390 386 497 299 0 1541 -1

N.S.

1 1.00 1.10 1.09 1.40 0.84 0.00 4.35 -0.00

time (sec)

N/A 0.639 1.030 0.060 0.582 0.409 0.000 0.723 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

304 304 254 294 424 245 0 844 -1

N.S.

1 1.00 0.84 0.97 1.39 0.81 0.00 2.78 -0.00

time (sec)

N/A 0.313 0.282 0.059 0.561 0.425 0.000 0.567 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

257 257 236 212 377 213 0 330 -1

N.S.

1 1.00 0.92 0.82 1.47 0.83 0.00 1.28 -0.00

time (sec)

N/A 0.260 0.234 0.061 0.524 0.391 0.000 0.465 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

271 271 299 286 253 265 0 0 -1

N.S.

1 1.00 1.10 1.06 0.93 0.98 0.00 0.00 -0.00

time (sec)

N/A 0.341 1.008 0.061 0.705 0.385 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

292 292 268 368 253 367 0 0 -1

N.S.

1 1.00 0.92 1.26 0.87 1.26 0.00 0.00 -0.00

time (sec)

N/A 0.487 1.313 0.060 0.703 0.449 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A C A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

356 356 465 450 254 528 0 0 -1

N.S.

1 1.00 1.31 1.26 0.71 1.48 0.00 0.00 -0.00

time (sec)

N/A 0.518 4.470 0.058 0.712 0.443 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A A C F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 55 34 74 35 83 69 -1

N.S.

1 1.00 1.12 0.69 1.51 0.71 1.69 1.41 -0.02

time (sec)

N/A 0.037 0.009 0.042 0.523 0.378 3.167 0.443 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A A C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 48 27 67 26 61 53 26

N.S.

1 1.00 1.33 0.75 1.86 0.72 1.69 1.47 0.72

time (sec)

N/A 0.023 0.005 0.031 0.516 0.395 0.511 0.564 0.028

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A A C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 51 19 60 18 37 35 18

N.S.

1 1.00 2.12 0.79 2.50 0.75 1.54 1.46 0.75

time (sec)

N/A 0.014 0.007 0.030 0.521 0.385 0.463 0.409 0.033

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A C A A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

35 35 63 28 21 31 61 0 -1

N.S.

1 1.00 1.80 0.80 0.60 0.89 1.74 0.00 -0.03

time (sec)

N/A 0.023 0.029 0.035 0.563 0.407 1.005 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

183 183 122 0 235 132 0 0 -1

N.S.

1 1.00 0.67 0.00 1.28 0.72 0.00 0.00 -0.01

time (sec)

N/A 0.160 0.073 0.038 0.361 0.126 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 124 0 186 102 0 0 -1

N.S.

1 1.00 0.82 0.00 1.22 0.67 0.00 0.00 -0.01

time (sec)

N/A 0.098 0.074 0.037 0.358 0.102 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 124 0 186 102 0 0 -1

N.S.

1 1.00 0.82 0.00 1.22 0.67 0.00 0.00 -0.01

time (sec)

N/A 0.097 0.065 0.036 0.351 0.109 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 124 0 137 86 0 0 -1

N.S.

1 1.00 0.92 0.00 1.01 0.64 0.00 0.00 -0.01

time (sec)

N/A 0.072 0.039 0.036 0.357 0.118 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 124 0 138 86 0 0 -1

N.S.

1 1.00 0.92 0.00 1.02 0.64 0.00 0.00 -0.01

time (sec)

N/A 0.078 0.040 0.036 0.340 0.095 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 121 0 138 117 0 0 -1

N.S.

1 1.00 0.80 0.00 0.91 0.77 0.00 0.00 -0.01

time (sec)

N/A 0.093 0.034 0.036 0.369 0.111 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

153 153 121 0 138 117 0 0 -1

N.S.

1 1.00 0.79 0.00 0.90 0.76 0.00 0.00 -0.01

time (sec)

N/A 0.097 0.036 0.036 0.366 0.131 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

182 182 125 0 137 185 0 0 -1

N.S.

1 1.00 0.69 0.00 0.75 1.02 0.00 0.00 -0.01

time (sec)

N/A 0.129 0.035 0.036 0.368 0.104 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07

time (sec)

N/A 0.012 107.445 0.021 0.000 0.000 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 133 0 57 0 0 15

N.S.

1 1.00 1.00 8.31 0.00 3.56 0.00 0.00 0.94

time (sec)

N/A 0.006 0.013 0.046 0.000 0.100 0.000 0.000 0.183

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

17 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.018 0.380 0.019 0.000 0.000 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

61 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.024 1.197 0.022 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 36 179 0 68 0 0 35

N.S.

1 1.00 0.86 4.26 0.00 1.62 0.00 0.00 0.83

time (sec)

N/A 0.013 0.023 0.000 0.000 0.119 0.000 0.000 0.188

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

17 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.019 9.493 0.020 0.000 0.000 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 40 0 0 0 0 0 -1

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.039 0.193 0.161 0.000 0.000 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

63 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.055 3.119 0.018 0.000 0.000 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07

time (sec)

N/A 0.012 0.203 0.002 0.000 0.000 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 18 0 51 0 0 15

N.S.

1 1.00 1.00 1.12 0.00 3.19 0.00 0.00 0.94

time (sec)

N/A 0.007 0.013 0.000 0.000 0.087 0.000 0.000 0.200

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

17 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.020 0.138 0.019 0.000 0.000 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

55 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.025 1.610 0.019 0.000 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 38 182 0 93 0 0 42

N.S.

1 1.00 1.00 4.79 0.00 2.45 0.00 0.00 1.11

time (sec)

N/A 0.013 0.036 0.000 0.000 0.121 0.000 0.000 0.437

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

17 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06

time (sec)

N/A 0.020 8.428 0.021 0.000 0.000 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 33 0 0 0 0 0 51

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 1.34

time (sec)

N/A 0.040 0.215 0.143 0.000 0.000 0.000 0.000 0.657

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 17 0 0 0 0 0 15

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 0.75

time (sec)

N/A 0.030 0.063 0.204 0.000 0.000 0.000 0.000 0.332

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 17 0 0 15 0 0 16

N.S.

1 1.00 0.71 0.00 0.00 0.62 0.00 0.00 0.67

time (sec)

N/A 0.032 0.043 0.211 0.000 0.352 0.000 0.000 0.139

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F(-2) F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 33 0 0 0 0 0 31

N.S.

1 1.00 0.70 0.00 0.00 0.00 0.00 0.00 0.66

time (sec)

N/A 0.044 0.086 0.308 0.000 0.000 0.000 0.000 0.527

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 29 0 0 0 0 0 -1

N.S.

1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.060 0.091 0.205 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 17 0 0 0 0 0 -1

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.059 0.053 0.110 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 17 0 0 0 0 0 -1

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.056 0.085 0.114 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 45 0 0 0 0 0 -1

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.068 0.078 0.135 0.000 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 51 0 0 0 0 0 -1

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.110 0.058 0.110 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

21 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.028 0.501 0.032 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

275 275 253 0 0 188 0 0 -1

N.S.

1 1.00 0.92 0.00 0.00 0.68 0.00 0.00 -0.00

time (sec)

N/A 0.214 0.118 0.132 0.000 0.113 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 150 0 0 136 0 0 -1

N.S.

1 1.00 0.93 0.00 0.00 0.84 0.00 0.00 -0.01

time (sec)

N/A 0.149 0.132 0.092 0.000 0.117 0.000 0.000 0.000

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