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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 F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 64 52 57 54 63 0 52

N.S.

1 1.00 1.08 0.88 0.97 0.92 1.07 0.00 0.88

time (sec)

N/A 0.021 0.006 0.559 0.267 0.244 0.354 0.000 0.497

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 61 54 56 59 60 0 54

N.S.

1 1.00 1.09 0.96 1.00 1.05 1.07 0.00 0.96

time (sec)

N/A 0.029 0.019 0.388 0.197 0.256 0.303 0.000 0.474

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 53 44 48 47 53 0 44

N.S.

1 1.00 1.10 0.92 1.00 0.98 1.10 0.00 0.92

time (sec)

N/A 0.019 0.006 0.557 0.276 0.248 0.274 0.000 0.236

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 50 46 46 49 49 0 42

N.S.

1 1.00 1.11 1.02 1.02 1.09 1.09 0.00 0.93

time (sec)

N/A 0.024 0.012 0.383 0.199 0.240 0.251 0.000 0.404

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 42 36 37 34 42 0 34

N.S.

1 1.00 1.14 0.97 1.00 0.92 1.14 0.00 0.92

time (sec)

N/A 0.011 0.005 0.526 0.264 0.236 0.229 0.000 0.137

Problem 6

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

29 29 29 28 31 33 26 31 27

N.S.

1 1.00 1.00 0.97 1.07 1.14 0.90 1.07 0.93

time (sec)

N/A 0.008 0.004 0.313 0.193 0.255 0.108 0.259 0.107

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 35 34 0 0 0 0 28

N.S.

1 1.00 1.00 0.97 0.00 0.00 0.00 0.00 0.80

time (sec)

N/A 0.022 0.005 0.480 0.000 0.000 0.000 0.000 0.314

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 38 39 39 37 37 0 36

N.S.

1 1.00 1.09 1.11 1.11 1.06 1.06 0.00 1.03

time (sec)

N/A 0.018 0.005 0.303 0.179 0.251 0.270 0.000 0.349

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 46 39 31 26 37 0 42

N.S.

1 1.00 1.24 1.05 0.84 0.70 1.00 0.00 1.14

time (sec)

N/A 0.015 0.006 0.481 0.264 0.242 0.229 0.000 0.370

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 54 52 51 50 61 0 46

N.S.

1 1.00 1.02 0.98 0.96 0.94 1.15 0.00 0.87

time (sec)

N/A 0.024 0.019 0.324 0.187 0.253 0.359 0.000 0.130

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 46 44 46 41 46 0 42

N.S.

1 1.00 0.96 0.92 0.96 0.85 0.96 0.00 0.88

time (sec)

N/A 0.018 0.005 0.500 0.280 0.239 0.289 0.000 0.396

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 69 60 62 59 71 0 56

N.S.

1 1.00 1.08 0.94 0.97 0.92 1.11 0.00 0.88

time (sec)

N/A 0.026 0.013 0.340 0.182 0.256 0.470 0.000 0.412

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 144 138 146 163 152 199 0 171

N.S.

1 1.00 0.96 1.01 1.13 1.06 1.38 0.00 1.19

time (sec)

N/A 0.214 0.137 1.002 0.277 0.261 0.478 0.000 0.728

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 170 169 266 0 0 0 0 0

N.S.

1 1.00 0.99 1.56 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.198 0.602 1.991 0.000 0.000 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 112 111 118 136 121 155 0 134

N.S.

1 1.00 0.99 1.05 1.21 1.08 1.38 0.00 1.20

time (sec)

N/A 0.154 0.100 1.024 0.298 0.254 0.383 0.000 0.343

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 138 131 238 0 0 0 0 0

N.S.

1 1.00 0.95 1.72 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.142 0.339 1.833 0.000 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 75 88 104 83 107 0 88

N.S.

1 1.00 0.99 1.16 1.37 1.09 1.41 0.00 1.16

time (sec)

N/A 0.078 0.161 0.973 0.296 0.241 0.274 0.000 0.444

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 83 90 123 0 0 0 0 0

N.S.

1 1.00 1.08 1.48 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.075 0.144 2.193 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

132 132 179 1002 0 0 0 0 0

N.S.

1 1.00 1.36 7.59 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.207 0.189 0.743 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 102 270 0 0 0 0 0

N.S.

1 1.00 1.24 3.29 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.104 0.197 2.348 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 79 90 98 98 94 119 0 140

N.S.

1 1.00 1.14 1.24 1.24 1.19 1.51 0.00 1.77

time (sec)

N/A 0.086 0.081 0.725 0.272 0.248 0.326 0.000 2.580

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 140 153 310 0 0 0 0 0

N.S.

1 1.00 1.09 2.21 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.158 0.473 2.908 0.000 0.000 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 116 128 132 152 135 170 0 171

N.S.

1 1.00 1.10 1.14 1.31 1.16 1.47 0.00 1.47

time (sec)

N/A 0.150 0.114 0.974 0.272 0.258 0.437 0.000 2.553

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

255 255 291 402 0 0 0 0 0

N.S.

1 1.00 1.14 1.58 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.639 0.953 2.524 0.000 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

271 271 396 1185 0 0 0 0 0

N.S.

1 1.00 1.46 4.37 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.521 1.124 6.276 0.000 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 194 225 340 0 0 0 0 0

N.S.

1 1.00 1.16 1.75 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.375 0.626 2.563 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

206 206 269 1088 0 0 0 0 0

N.S.

1 1.00 1.31 5.28 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.300 0.680 4.188 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 131 152 276 0 0 0 0 0

N.S.

1 1.00 1.16 2.11 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.177 0.427 2.888 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 119 192 240 0 0 0 0 0

N.S.

1 1.00 1.61 2.02 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.146 0.157 5.707 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

206 206 368 2026 0 0 0 0 0

N.S.

1 1.00 1.79 9.83 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.302 0.321 0.575 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

116 116 214 1862 0 0 0 0 0

N.S.

1 1.00 1.84 16.05 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.188 1.296 1.912 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 133 176 354 0 0 0 0 0

N.S.

1 1.00 1.32 2.66 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.202 0.376 4.621 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

213 213 305 2097 0 0 0 0 0

N.S.

1 1.00 1.43 9.85 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.348 1.383 6.803 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 198 265 423 0 0 0 0 0

N.S.

1 1.00 1.34 2.14 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.415 0.864 4.497 0.000 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

8 8 10 8 10 10 7 3 10

N.S.

1 1.00 1.25 1.00 1.25 1.25 0.88 0.38 1.25

time (sec)

N/A 0.006 0.742 10.581 0.255 0.231 0.269 23.919 0.293

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

6 6 8 6 8 8 7 3 8

N.S.

1 1.00 1.33 1.00 1.33 1.33 1.17 0.50 1.33

time (sec)

N/A 0.003 0.020 4.118 0.231 0.250 0.257 21.736 0.291

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

10 10 12 10 12 12 8 3 12

N.S.

1 1.00 1.20 1.00 1.20 1.20 0.80 0.30 1.20

time (sec)

N/A 0.010 0.514 4.589 0.238 0.233 0.368 24.442 0.274

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

8 8 10 8 45 10 8 3 10

N.S.

1 1.00 1.25 1.00 5.62 1.25 1.00 0.38 1.25

time (sec)

N/A 0.006 0.715 10.509 0.258 0.234 0.310 49.107 0.294

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

6 6 8 6 39 8 8 3 8

N.S.

1 1.00 1.33 1.00 6.50 1.33 1.33 0.50 1.33

time (sec)

N/A 0.003 1.095 5.540 0.234 0.251 0.298 47.802 0.300

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

10 10 12 10 51 12 10 3 12

N.S.

1 1.00 1.20 1.00 5.10 1.20 1.00 0.30 1.20

time (sec)

N/A 0.009 1.238 4.234 0.265 0.245 0.375 49.411 0.299

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 8 0 0 10 3 10

N.S.

1 1.00 1.20 0.80 0.00 0.00 1.00 0.30 1.00

time (sec)

N/A 0.005 1.483 2.086 0.000 0.000 0.400 53.543 0.307

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

8 8 10 6 0 0 8 3 8

N.S.

1 1.00 1.25 0.75 0.00 0.00 1.00 0.38 1.00

time (sec)

N/A 0.003 1.812 1.641 0.000 0.000 0.315 53.952 0.326

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 14 10 0 0 10 3 12

N.S.

1 1.00 1.17 0.83 0.00 0.00 0.83 0.25 1.00

time (sec)

N/A 0.009 1.102 1.947 0.000 0.000 0.361 148.199 0.293

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 8 0 0 10 3 10

N.S.

1 1.00 1.20 0.80 0.00 0.00 1.00 0.30 1.00

time (sec)

N/A 0.005 0.839 1.792 0.000 0.000 1.406 81.002 0.301

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

8 8 10 6 0 0 8 3 8

N.S.

1 1.00 1.25 0.75 0.00 0.00 1.00 0.38 1.00

time (sec)

N/A 0.002 1.711 1.527 0.000 0.000 0.852 81.253 0.323

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 14 10 0 0 10 3 12

N.S.

1 1.00 1.17 0.83 0.00 0.00 0.83 0.25 1.00

time (sec)

N/A 0.009 0.957 2.726 0.000 0.000 0.858 142.203 0.316

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 8 0 0 10 3 10

N.S.

1 1.00 1.20 0.80 0.00 0.00 1.00 0.30 1.00

time (sec)

N/A 0.005 0.935 1.751 0.000 0.000 0.364 70.975 0.292

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

8 8 10 6 0 0 10 3 8

N.S.

1 1.00 1.25 0.75 0.00 0.00 1.25 0.38 1.00

time (sec)

N/A 0.002 0.006 1.588 0.000 0.000 0.324 64.900 0.313

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 14 10 0 0 12 3 12

N.S.

1 1.00 1.17 0.83 0.00 0.00 1.00 0.25 1.00

time (sec)

N/A 0.009 1.304 2.352 0.000 0.000 0.476 68.146 0.296

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 8 0 0 10 3 10

N.S.

1 1.00 1.20 0.80 0.00 0.00 1.00 0.30 1.00

time (sec)

N/A 0.005 1.035 1.943 0.000 0.000 0.670 249.366 0.329

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

8 8 10 6 0 0 10 3 8

N.S.

1 1.00 1.25 0.75 0.00 0.00 1.25 0.38 1.00

time (sec)

N/A 0.002 1.735 1.520 0.000 0.000 0.638 239.105 0.351

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 14 10 0 0 12 3 12

N.S.

1 1.00 1.17 0.83 0.00 0.00 1.00 0.25 1.00

time (sec)

N/A 0.009 2.338 2.635 0.000 0.000 0.909 184.339 0.354

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 117 108 69 86 80 110 86 49

N.S.

1 1.00 0.92 0.59 0.74 0.68 0.94 0.74 0.42

time (sec)

N/A 0.049 0.035 0.253 0.269 0.256 1.953 0.271 0.357

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 387 44 15 3 18

N.S.

1 1.00 1.12 1.00 24.19 2.75 0.94 0.19 1.12

time (sec)

N/A 0.016 4.832 2.559 3.735 0.261 7.445 72.748 0.650

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 295 30 15 3 18

N.S.

1 1.00 1.12 1.00 18.44 1.88 0.94 0.19 1.12

time (sec)

N/A 0.016 3.147 3.820 2.202 0.248 4.351 72.162 0.622

Problem 56

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

73 73 60 0 0 0 0 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.024 0.041 0.000 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 18 18 14 3 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.88 0.19 1.12

time (sec)

N/A 0.018 0.346 3.526 0.268 0.245 1.260 87.381 0.273

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

10 10 12 10 12 12 10 3 12

N.S.

1 1.00 1.20 1.00 1.20 1.20 1.00 0.30 1.20

time (sec)

N/A 0.005 0.499 1.693 0.371 0.239 1.814 80.207 0.406

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 18 18 15 3 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 0.19 1.12

time (sec)

N/A 0.016 0.418 4.359 0.538 0.250 155.449 79.272 0.406

Problem 60

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 54 59 50 54 51 58 60 49

N.S.

1 1.00 1.09 0.93 1.00 0.94 1.07 1.11 0.91

time (sec)

N/A 0.026 0.012 0.583 0.280 0.245 29.725 0.274 0.403

Problem 61

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

47 47 52 45 48 51 80 47 44

N.S.

1 1.00 1.11 0.96 1.02 1.09 1.70 1.00 0.94

time (sec)

N/A 0.024 0.017 0.661 0.213 0.255 22.305 0.274 0.374

Problem 62

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

43 43 48 41 43 38 48 43 40

N.S.

1 1.00 1.12 0.95 1.00 0.88 1.12 1.00 0.93

time (sec)

N/A 0.020 0.008 0.734 0.288 0.229 9.849 0.267 0.353

Problem 63

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

36 36 41 36 38 39 66 40 35

N.S.

1 1.00 1.14 1.00 1.06 1.08 1.83 1.11 0.97

time (sec)

N/A 0.011 0.024 0.536 0.191 0.238 5.410 0.279 0.357

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F F F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 39 63 0 0 0 0 32

N.S.

1 1.00 1.00 1.62 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.041 0.008 0.747 0.000 0.000 0.000 0.000 0.389

Problem 65

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

39 39 44 39 41 43 75 60 38

N.S.

1 1.00 1.13 1.00 1.05 1.10 1.92 1.54 0.97

time (sec)

N/A 0.018 0.010 0.266 0.190 0.252 12.925 0.273 0.395

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 48 39 35 30 42 72 41

N.S.

1 1.00 1.17 0.95 0.85 0.73 1.02 1.76 1.00

time (sec)

N/A 0.019 0.009 0.375 0.272 0.238 12.686 0.286 0.406

Problem 67

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

55 55 60 53 53 54 92 69 50

N.S.

1 1.00 1.09 0.96 0.96 0.98 1.67 1.25 0.91

time (sec)

N/A 0.028 0.016 0.303 0.189 0.247 38.959 0.262 0.408

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 161 179 121 147 171 153 169 64

N.S.

1 1.00 1.11 0.75 0.91 1.06 0.95 1.05 0.40

time (sec)

N/A 0.081 0.068 0.869 0.289 0.257 15.270 0.329 0.400

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 159 177 118 145 152 143 165 62

N.S.

1 1.00 1.11 0.74 0.91 0.96 0.90 1.04 0.39

time (sec)

N/A 0.079 0.056 0.535 0.277 0.261 7.490 0.337 0.452

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 140 107 103 127 140 617 149 49

N.S.

1 1.00 0.76 0.74 0.91 1.00 4.41 1.06 0.35

time (sec)

N/A 0.076 0.061 0.358 0.285 0.244 4.336 0.280 0.453

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 143 158 107 132 139 121 138 55

N.S.

1 1.00 1.10 0.75 0.92 0.97 0.85 0.97 0.38

time (sec)

N/A 0.064 0.074 0.349 0.276 0.251 8.534 0.289 0.240

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 159 177 115 142 170 529 159 63

N.S.

1 1.00 1.11 0.72 0.89 1.07 3.33 1.00 0.40

time (sec)

N/A 0.074 0.085 0.417 0.278 0.252 20.038 0.334 0.500

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 159 177 118 138 163 155 150 63

N.S.

1 1.00 1.11 0.74 0.87 1.03 0.97 0.94 0.40

time (sec)

N/A 0.073 0.086 0.468 0.288 0.250 29.701 0.339 0.528

Problem 74

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

124 124 121 151 169 137 199 145 150

N.S.

1 1.00 0.98 1.22 1.36 1.10 1.60 1.17 1.21

time (sec)

N/A 0.179 0.120 0.855 0.377 0.252 44.486 0.279 1.170

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

154 154 141 333 0 0 0 0 0

N.S.

1 1.00 0.92 2.16 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.171 0.364 3.561 0.000 0.000 0.000 0.000 0.000

Problem 76

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

90 90 85 110 126 100 155 100 112

N.S.

1 1.00 0.94 1.22 1.40 1.11 1.72 1.11 1.24

time (sec)

N/A 0.108 0.083 1.290 0.331 0.257 16.832 0.269 0.805

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 101 107 140 0 0 0 0 0

N.S.

1 1.00 1.06 1.39 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.097 0.152 4.438 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 F F F F F F(-1)

verified

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

size

151 151 201 0 0 0 0 0 0

N.S.

1 1.00 1.33 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.227 0.172 0.000 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

97 97 127 339 0 0 0 0 0

N.S.

1 1.00 1.31 3.49 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.129 0.194 3.328 0.000 0.000 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 98 118 110 115 167 0 152

N.S.

1 1.00 1.13 1.36 1.26 1.32 1.92 0.00 1.75

time (sec)

N/A 0.116 0.107 0.651 0.357 0.256 22.225 0.000 0.688

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1393 1393 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 1.878 0.000 0.000 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 B F F F F F F(-1)

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

1191 1191 4697 0 0 0 0 0 0

N.S.

1 1.00 3.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.256 38.101 0.000 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 B F F F F F F(-1)

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

1164 1164 4697 0 0 0 0 0 0

N.S.

1 1.00 4.04 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.201 35.915 0.000 0.000 0.000 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1360 1360 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 1.518 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1444 1444 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 1.684 0.000 0.000 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 C F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

149 149 170 399 0 0 0 0 0

N.S.

1 1.00 1.14 2.68 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.213 0.512 4.665 0.000 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 144 224 275 0 0 0 0 0

N.S.

1 1.00 1.56 1.91 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.182 0.134 9.388 0.000 0.000 0.000 0.000 0.000

Problem 88

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

229 229 417 0 0 0 0 0 0

N.S.

1 1.00 1.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.355 0.301 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 A F F F F F F(-1)

verified

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

size

138 138 239 0 0 0 0 0 0

N.S.

1 1.00 1.73 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.218 0.469 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 C F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

149 149 196 465 0 0 0 0 0

N.S.

1 1.00 1.32 3.12 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.230 0.369 4.421 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

18 18 20 18 406 50 0 20 20

N.S.

1 1.00 1.11 1.00 22.56 2.78 0.00 1.11 1.11

time (sec)

N/A 0.017 2.263 0.171 3.974 0.244 0.000 0.423 0.336

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 303 34 17 20 20

N.S.

1 1.00 1.11 1.00 16.83 1.89 0.94 1.11 1.11

time (sec)

N/A 0.017 1.467 0.176 2.349 0.247 111.972 0.521 0.320

Problem 93

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

75 75 65 0 0 0 0 0 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.027 0.087 0.000 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

18 18 20 18 20 20 0 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.00 1.11 1.11

time (sec)

N/A 0.018 0.457 0.188 0.240 0.247 0.000 0.278 0.283

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

18 18 20 18 124 36 0 20 20

N.S.

1 1.00 1.11 1.00 6.89 2.00 0.00 1.11 1.11

time (sec)

N/A 0.019 0.478 0.164 0.394 0.238 0.000 0.300 0.351

Problem 96

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 54 59 50 54 51 58 60 49

N.S.

1 1.00 1.09 0.93 1.00 0.94 1.07 1.11 0.91

time (sec)

N/A 0.025 0.012 0.750 0.274 0.238 129.726 0.266 0.439

Problem 97

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

47 47 52 45 48 51 117 47 44

N.S.

1 1.00 1.11 0.96 1.02 1.09 2.49 1.00 0.94

time (sec)

N/A 0.023 0.019 0.688 0.203 0.240 73.035 0.285 0.384

Problem 98

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

43 43 48 41 43 38 48 43 40

N.S.

1 1.00 1.12 0.95 1.00 0.88 1.12 1.00 0.93

time (sec)

N/A 0.020 0.010 0.816 0.267 0.251 36.158 0.265 0.384

Problem 99

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

36 36 41 36 38 39 102 40 35

N.S.

1 1.00 1.14 1.00 1.06 1.08 2.83 1.11 0.97

time (sec)

N/A 0.014 0.023 0.589 0.180 0.241 20.583 0.268 0.111

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F F F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 39 63 0 0 0 0 32

N.S.

1 1.00 1.00 1.62 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.037 0.009 0.517 0.000 0.000 0.000 0.000 0.375

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