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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 38 15 14 38 17 27 27

N.S.

1 1.00 3.17 1.25 1.17 3.17 1.42 2.25 2.25

time (sec)

N/A 0.171 0.021 0.092 0.187 0.265 0.239 0.273 0.090

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 18 43 0 18 18

N.S.

1 1.00 1.00 1.09 1.64 3.91 0.00 1.64 1.64

time (sec)

N/A 0.179 0.017 0.763 0.184 0.244 0.000 0.278 0.074

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 42 75 27 84 387 0 84 86

N.S.

1 1.24 2.21 0.79 2.47 11.38 0.00 2.47 2.53

time (sec)

N/A 0.243 0.019 0.763 0.190 0.260 0.000 0.280 2.091

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 32 35 23 90 164 0 31 31

N.S.

1 1.23 1.35 0.88 3.46 6.31 0.00 1.19 1.19

time (sec)

N/A 0.193 0.013 0.804 0.189 0.246 0.000 0.281 2.092

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 70 113 41 133 1114 0 110 193

N.S.

1 1.27 2.05 0.75 2.42 20.25 0.00 2.00 3.51

time (sec)

N/A 0.336 0.024 0.788 0.199 0.253 0.000 0.268 2.042

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 46 56 33 205 344 0 42 42

N.S.

1 1.10 1.33 0.79 4.88 8.19 0.00 1.00 1.00

time (sec)

N/A 0.197 0.021 0.755 0.191 0.240 0.000 0.289 0.075

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 61 101 0 194 0 0 0

N.S.

1 1.00 0.76 1.26 0.00 2.42 0.00 0.00 0.00

time (sec)

N/A 0.339 0.101 0.362 0.000 0.078 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 57 154 0 96 0 0 0

N.S.

1 1.00 0.75 2.03 0.00 1.26 0.00 0.00 0.00

time (sec)

N/A 0.348 0.173 0.368 0.000 0.078 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 48 87 0 24 0 0 0

N.S.

1 1.00 0.89 1.61 0.00 0.44 0.00 0.00 0.00

time (sec)

N/A 0.246 0.158 0.308 0.000 0.077 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 50 108 0 150 0 0 0

N.S.

1 1.00 0.93 2.00 0.00 2.78 0.00 0.00 0.00

time (sec)

N/A 0.244 0.031 0.474 0.000 0.088 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 63 100 0 223 0 0 0

N.S.

1 1.00 0.79 1.25 0.00 2.79 0.00 0.00 0.00

time (sec)

N/A 0.327 0.053 0.393 0.000 0.100 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 67 164 0 370 0 0 0

N.S.

1 1.00 0.84 2.05 0.00 4.62 0.00 0.00 0.00

time (sec)

N/A 0.327 0.094 0.398 0.000 0.086 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

116 118 79 0 0 484 0 0 0

N.S.

1 1.02 0.68 0.00 0.00 4.17 0.00 0.00 0.00

time (sec)

N/A 0.481 0.149 0.000 0.000 0.083 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

88 88 66 0 0 217 0 0 0

N.S.

1 1.00 0.75 0.00 0.00 2.47 0.00 0.00 0.00

time (sec)

N/A 0.356 0.087 0.000 0.000 0.079 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

84 84 60 0 0 107 0 0 0

N.S.

1 1.00 0.71 0.00 0.00 1.27 0.00 0.00 0.00

time (sec)

N/A 0.341 0.053 0.000 0.000 0.075 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 56 54 0 0 27 0 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.48 0.00 0.00 0.00

time (sec)

N/A 0.247 0.037 0.000 0.000 0.072 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 52 227 0 154 0 0 0

N.S.

1 1.00 0.93 4.05 0.00 2.75 0.00 0.00 0.00

time (sec)

N/A 0.249 0.047 0.504 0.000 0.082 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

90 90 73 0 0 232 0 0 0

N.S.

1 1.00 0.81 0.00 0.00 2.58 0.00 0.00 0.00

time (sec)

N/A 0.350 0.076 0.000 0.000 0.086 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

90 90 68 0 0 378 0 0 0

N.S.

1 1.00 0.76 0.00 0.00 4.20 0.00 0.00 0.00

time (sec)

N/A 0.344 0.110 0.000 0.000 0.089 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

118 126 80 0 0 483 0 0 0

N.S.

1 1.07 0.68 0.00 0.00 4.09 0.00 0.00 0.00

time (sec)

N/A 0.463 0.136 0.000 0.000 0.091 0.000 0.000 0.000

Problem 21

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

74 74 90 0 0 0 0 0 0

N.S.

1 1.00 1.22 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.293 0.126 0.000 0.000 0.000 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 49 51 114 74 117 0 72 0

N.S.

1 1.22 1.28 2.85 1.85 2.92 0.00 1.80 0.00

time (sec)

N/A 0.204 0.154 0.274 0.270 0.263 0.000 0.275 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 26 51 99 49 67 0 57 0

N.S.

1 1.08 2.12 4.12 2.04 2.79 0.00 2.38 0.00

time (sec)

N/A 0.196 0.040 0.156 0.264 0.256 0.000 0.290 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

3 3 30 67 19 15 0 27 0

N.S.

1 1.00 10.00 22.33 6.33 5.00 0.00 9.00 0.00

time (sec)

N/A 0.178 0.009 0.173 0.265 0.258 0.000 0.274 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B C C F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 15 13 58 11 14 0 25 31

N.S.

1 1.15 1.00 4.46 0.85 1.08 0.00 1.92 2.38

time (sec)

N/A 0.188 0.004 0.146 0.266 0.259 0.000 0.274 2.285

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 37 27 118 23 26 0 38 0

N.S.

1 1.12 0.82 3.58 0.70 0.79 0.00 1.15 0.00

time (sec)

N/A 0.197 0.038 0.149 0.266 0.257 0.000 0.282 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 60 33 178 35 38 0 50 0

N.S.

1 1.22 0.67 3.63 0.71 0.78 0.00 1.02 0.00

time (sec)

N/A 0.206 0.044 0.154 0.264 0.260 0.000 0.289 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 83 39 238 47 50 0 62 0

N.S.

1 1.28 0.60 3.66 0.72 0.77 0.00 0.95 0.00

time (sec)

N/A 0.215 0.051 0.175 0.266 0.252 0.000 0.280 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 82 51 123 92 1128 0 75 0

N.S.

1 1.26 0.78 1.89 1.42 17.35 0.00 1.15 0.00

time (sec)

N/A 0.229 0.120 0.328 0.264 0.267 0.000 0.266 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 56 39 103 60 340 0 58 0

N.S.

1 1.22 0.85 2.24 1.30 7.39 0.00 1.26 0.00

time (sec)

N/A 0.209 0.082 0.155 0.265 0.276 0.000 0.275 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 30 30 67 24 97 0 29 0

N.S.

1 1.15 1.15 2.58 0.92 3.73 0.00 1.12 0.00

time (sec)

N/A 0.200 0.033 0.169 0.264 0.264 0.000 0.271 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 17 13 58 17 83 0 24 33

N.S.

1 1.31 1.00 4.46 1.31 6.38 0.00 1.85 2.54

time (sec)

N/A 0.194 0.027 0.161 0.268 0.274 0.000 0.275 2.314

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 50 27 130 35 285 0 41 0

N.S.

1 1.39 0.75 3.61 0.97 7.92 0.00 1.14 0.00

time (sec)

N/A 0.208 0.042 0.165 0.266 0.273 0.000 0.276 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 81 36 196 53 590 0 53 0

N.S.

1 1.47 0.65 3.56 0.96 10.73 0.00 0.96 0.00

time (sec)

N/A 0.219 0.053 0.158 0.263 0.274 0.000 0.279 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 112 42 262 71 984 0 65 0

N.S.

1 1.51 0.57 3.54 0.96 13.30 0.00 0.88 0.00

time (sec)

N/A 0.251 0.069 0.148 0.269 0.284 0.000 0.267 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

135 150 68 0 0 1389 0 0 0

N.S.

1 1.11 0.50 0.00 0.00 10.29 0.00 0.00 0.00

time (sec)

N/A 0.688 0.139 0.000 0.000 0.106 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

81 108 56 0 0 395 0 0 0

N.S.

1 1.33 0.69 0.00 0.00 4.88 0.00 0.00 0.00

time (sec)

N/A 0.461 0.106 0.000 0.000 0.087 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 77 42 0 0 60 0 0 0

N.S.

1 1.38 0.75 0.00 0.00 1.07 0.00 0.00 0.00

time (sec)

N/A 0.386 0.036 0.000 0.000 0.081 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

62 81 43 0 0 127 0 0 0

N.S.

1 1.31 0.69 0.00 0.00 2.05 0.00 0.00 0.00

time (sec)

N/A 0.390 0.070 0.000 0.000 0.083 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

89 110 57 0 0 407 0 0 0

N.S.

1 1.24 0.64 0.00 0.00 4.57 0.00 0.00 0.00

time (sec)

N/A 0.470 0.074 0.000 0.000 0.088 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

135 154 71 0 0 718 0 0 0

N.S.

1 1.14 0.53 0.00 0.00 5.32 0.00 0.00 0.00

time (sec)

N/A 0.665 0.107 0.000 0.000 0.108 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 84 59 72 620 2825 0 51 498

N.S.

1 0.51 0.36 0.44 3.78 17.23 0.00 0.31 3.04

time (sec)

N/A 0.282 0.058 0.832 0.278 0.398 0.000 0.278 2.241

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 68 47 60 322 1493 0 39 356

N.S.

1 0.58 0.40 0.51 2.73 12.65 0.00 0.33 3.02

time (sec)

N/A 0.271 0.044 0.758 0.274 0.289 0.000 0.271 2.158

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 46 33 46 120 529 0 27 46

N.S.

1 0.74 0.53 0.74 1.94 8.53 0.00 0.44 0.74

time (sec)

N/A 0.264 0.037 0.159 0.272 0.271 0.000 0.275 2.155

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 29 13 81 0 13 71

N.S.

1 1.00 1.00 1.81 0.81 5.06 0.00 0.81 4.44

time (sec)

N/A 0.234 0.027 0.194 0.268 0.263 0.000 0.259 2.142

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 30 24 89 22 253 0 26 0

N.S.

1 0.83 0.67 2.47 0.61 7.03 0.00 0.72 0.00

time (sec)

N/A 0.228 0.043 0.181 0.261 0.262 0.000 0.266 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 63 38 230 46 1141 0 50 0

N.S.

1 0.73 0.44 2.67 0.53 13.27 0.00 0.58 0.00

time (sec)

N/A 0.350 0.058 0.162 0.268 0.274 0.000 0.282 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 93 55 362 72 2600 0 76 0

N.S.

1 0.70 0.42 2.74 0.55 19.70 0.00 0.58 0.00

time (sec)

N/A 0.488 0.103 0.168 0.284 0.322 0.000 0.268 0.000

Problem 49

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

32 32 54 27 35 32 0 29 26

N.S.

1 1.00 1.69 0.84 1.09 1.00 0.00 0.91 0.81

time (sec)

N/A 0.193 0.320 0.406 0.183 0.261 0.000 0.292 2.250

Problem 50

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

32 32 54 27 35 32 0 29 26

N.S.

1 1.00 1.69 0.84 1.09 1.00 0.00 0.91 0.81

time (sec)

N/A 0.196 0.255 0.395 0.177 0.261 0.000 0.267 2.286

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

107 111 136 0 0 566 0 0 0

N.S.

1 1.04 1.27 0.00 0.00 5.29 0.00 0.00 0.00

time (sec)

N/A 0.567 1.438 0.000 0.000 0.293 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

72 72 100 0 0 461 0 0 0

N.S.

1 1.00 1.39 0.00 0.00 6.40 0.00 0.00 0.00

time (sec)

N/A 0.303 1.186 0.000 0.000 0.272 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

40 40 80 0 0 383 0 0 0

N.S.

1 1.00 2.00 0.00 0.00 9.58 0.00 0.00 0.00

time (sec)

N/A 0.198 0.989 0.000 0.000 0.278 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

91 91 118 0 0 551 0 0 0

N.S.

1 1.00 1.30 0.00 0.00 6.05 0.00 0.00 0.00

time (sec)

N/A 0.404 1.777 0.000 0.000 0.292 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

123 129 327 0 0 873 0 0 0

N.S.

1 1.05 2.66 0.00 0.00 7.10 0.00 0.00 0.00

time (sec)

N/A 0.580 3.422 0.000 0.000 0.297 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

40 40 80 0 0 383 0 0 0

N.S.

1 1.00 2.00 0.00 0.00 9.58 0.00 0.00 0.00

time (sec)

N/A 0.193 1.007 0.000 0.000 0.290 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

91 91 117 0 0 551 0 0 0

N.S.

1 1.00 1.29 0.00 0.00 6.05 0.00 0.00 0.00

time (sec)

N/A 0.409 1.761 0.000 0.000 0.283 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 46 0 0 212 0 0 0

N.S.

1 1.00 2.00 0.00 0.00 9.22 0.00 0.00 0.00

time (sec)

N/A 0.188 0.655 0.000 0.000 0.266 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 46 0 0 212 0 0 0

N.S.

1 1.00 2.00 0.00 0.00 9.22 0.00 0.00 0.00

time (sec)

N/A 0.197 0.630 0.000 0.000 0.269 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 46 0 0 218 0 0 0

N.S.

1 1.00 2.00 0.00 0.00 9.48 0.00 0.00 0.00

time (sec)

N/A 0.197 0.630 0.000 0.000 0.277 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 46 0 0 218 0 0 0

N.S.

1 1.00 2.00 0.00 0.00 9.48 0.00 0.00 0.00

time (sec)

N/A 0.191 0.602 0.000 0.000 0.297 0.000 0.000 0.000

Problem 62

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

58 63 63 65 71 79 0 62 64

N.S.

1 1.09 1.09 1.12 1.22 1.36 0.00 1.07 1.10

time (sec)

N/A 0.447 0.154 1.660 0.184 0.259 0.000 0.278 2.420

Problem 63

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

46 52 56 53 59 67 0 50 52

N.S.

1 1.13 1.22 1.15 1.28 1.46 0.00 1.09 1.13

time (sec)

N/A 0.391 0.153 1.068 0.176 0.266 0.000 0.256 0.168

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 42 46 39 47 55 0 38 38

N.S.

1 1.17 1.28 1.08 1.31 1.53 0.00 1.06 1.06

time (sec)

N/A 0.364 0.160 0.905 0.185 0.258 0.000 0.282 2.306

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 24 35 25 31 39 0 24 24

N.S.

1 1.20 1.75 1.25 1.55 1.95 0.00 1.20 1.20

time (sec)

N/A 0.308 0.089 0.643 0.184 0.255 0.000 0.268 2.322

Problem 66

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

14 13 27 11 12 8 0 8 10

N.S.

1 0.93 1.93 0.79 0.86 0.57 0.00 0.57 0.71

time (sec)

N/A 0.187 0.094 0.282 0.175 0.244 0.000 0.274 0.068

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 26 46 19 27 31 0 22 26

N.S.

1 1.53 2.71 1.12 1.59 1.82 0.00 1.29 1.53

time (sec)

N/A 0.320 0.130 0.450 0.185 0.247 0.000 0.286 0.204

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 70 35 53 77 0 46 60

N.S.

1 1.00 2.69 1.35 2.04 2.96 0.00 1.77 2.31

time (sec)

N/A 0.385 0.196 0.768 0.172 0.267 0.000 0.276 2.482

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 47 90 53 77 120 0 50 63

N.S.

1 1.27 2.43 1.43 2.08 3.24 0.00 1.35 1.70

time (sec)

N/A 0.452 0.241 0.948 0.174 0.255 0.000 0.302 2.496

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 116 567 92 234 1440 0 169 239

N.S.

1 1.06 5.20 0.84 2.15 13.21 0.00 1.55 2.19

time (sec)

N/A 0.441 11.817 1.480 0.180 0.272 0.000 0.283 0.200

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 77 151 66 136 769 0 122 170

N.S.

1 1.03 2.01 0.88 1.81 10.25 0.00 1.63 2.27

time (sec)

N/A 0.267 5.874 1.114 0.186 0.271 0.000 0.306 0.147

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 75 37 44 222 0 59 74

N.S.

1 1.00 2.21 1.09 1.29 6.53 0.00 1.74 2.18

time (sec)

N/A 0.303 0.549 0.860 0.177 0.276 0.000 0.301 2.301

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 43 20 19 44 22 32 42

N.S.

1 1.00 2.53 1.18 1.12 2.59 1.29 1.88 2.47

time (sec)

N/A 0.146 0.005 0.133 0.177 0.270 0.238 0.285 0.064

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

54 53 64 82 85 186 0 84 121

N.S.

1 0.98 1.19 1.52 1.57 3.44 0.00 1.56 2.24

time (sec)

N/A 0.302 0.200 0.322 0.275 0.274 0.000 0.288 0.304

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

101 121 142 176 187 645 0 161 269

N.S.

1 1.20 1.41 1.74 1.85 6.39 0.00 1.59 2.66

time (sec)

N/A 0.665 0.403 0.344 0.270 0.277 0.000 0.329 2.717

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

163 202 213 328 373 2094 0 293 0

N.S.

1 1.24 1.31 2.01 2.29 12.85 0.00 1.80 0.00

time (sec)

N/A 1.063 1.286 0.513 0.305 0.317 0.000 0.317 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 146 104 198 157 807 0 155 199

N.S.

1 1.36 0.97 1.85 1.47 7.54 0.00 1.45 1.86

time (sec)

N/A 1.050 1.521 0.422 0.272 0.292 0.000 0.282 2.532

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 105 82 152 116 456 0 115 157

N.S.

1 1.31 1.02 1.90 1.45 5.70 0.00 1.44 1.96

time (sec)

N/A 0.726 0.825 0.318 0.265 0.269 0.000 0.281 2.404

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 77 61 92 84 238 0 86 129

N.S.

1 1.35 1.07 1.61 1.47 4.18 0.00 1.51 2.26

time (sec)

N/A 0.384 0.287 0.277 0.272 0.261 0.000 0.285 2.364

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 45 45 35 54 111 0 56 49

N.S.

1 1.22 1.22 0.95 1.46 3.00 0.00 1.51 1.32

time (sec)

N/A 0.285 0.023 0.103 0.266 0.258 0.000 0.296 0.166

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 58 67 49 83 156 0 82 287

N.S.

1 1.16 1.34 0.98 1.66 3.12 0.00 1.64 5.74

time (sec)

N/A 0.428 0.214 0.169 0.258 0.279 0.000 0.277 2.421

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 79 92 73 100 345 0 98 292

N.S.

1 1.34 1.56 1.24 1.69 5.85 0.00 1.66 4.95

time (sec)

N/A 0.553 0.480 0.234 0.265 0.275 0.000 0.278 2.501

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 111 148 108 158 947 0 141 617

N.S.

1 1.34 1.78 1.30 1.90 11.41 0.00 1.70 7.43

time (sec)

N/A 0.792 0.627 0.302 0.264 0.322 0.000 0.285 2.838

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 43 32 116 42 43 0 38 41

N.S.

1 1.13 0.84 3.05 1.11 1.13 0.00 1.00 1.08

time (sec)

N/A 0.455 0.054 0.152 0.173 0.252 0.000 0.285 2.292

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 23 19 15 39 36 0 35 39

N.S.

1 1.21 1.00 0.79 2.05 1.89 0.00 1.84 2.05

time (sec)

N/A 0.363 0.008 222.886 0.174 0.248 0.000 0.279 2.235

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 24 20 30 30 31 0 26 29

N.S.

1 1.20 1.00 1.50 1.50 1.55 0.00 1.30 1.45

time (sec)

N/A 0.343 0.042 9.222 0.174 0.252 0.000 0.285 2.213

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 25 21 28 0 21 12

N.S.

1 1.00 1.00 1.56 1.31 1.75 0.00 1.31 0.75

time (sec)

N/A 0.278 0.011 2.259 0.173 0.252 0.000 0.281 0.084

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 30 20 30 41 52 0 51 46

N.S.

1 1.07 0.71 1.07 1.46 1.86 0.00 1.82 1.64

time (sec)

N/A 0.414 0.027 1.185 0.173 0.256 0.000 0.287 0.218

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 23 64 31 81 32 0 27 31

N.S.

1 1.21 3.37 1.63 4.26 1.68 0.00 1.42 1.63

time (sec)

N/A 0.399 0.062 0.606 0.183 0.252 0.000 0.283 2.307

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 45 32 61 0 142 0 94 122

N.S.

1 1.12 0.80 1.52 0.00 3.55 0.00 2.35 3.05

time (sec)

N/A 0.526 0.043 13.089 0.000 0.254 0.000 0.280 2.655

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 40 96 93 0 68 0 55 207

N.S.

1 1.38 3.31 3.21 0.00 2.34 0.00 1.90 7.14

time (sec)

N/A 0.423 0.100 0.229 0.000 0.254 0.000 0.270 2.663

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 101 97 378 242 1398 0 194 228

N.S.

1 0.99 0.95 3.71 2.37 13.71 0.00 1.90 2.24

time (sec)

N/A 0.419 0.198 0.129 0.181 0.264 0.000 0.293 2.968

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 152 180 215 217 924 0 221 247

N.S.

1 1.22 1.44 1.72 1.74 7.39 0.00 1.77 1.98

time (sec)

N/A 0.824 0.827 60.041 0.266 0.264 0.000 0.281 2.613

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 56 56 136 127 476 0 97 121

N.S.

1 0.98 0.98 2.39 2.23 8.35 0.00 1.70 2.12

time (sec)

N/A 0.371 0.028 14.752 0.180 0.255 0.000 0.266 2.415

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 96 80 122 122 304 0 121 159

N.S.

1 1.25 1.04 1.58 1.58 3.95 0.00 1.57 2.06

time (sec)

N/A 0.542 0.127 3.476 0.268 0.261 0.000 0.284 2.335

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 19 19 31 48 80 0 39 20

N.S.

1 0.95 0.95 1.55 2.40 4.00 0.00 1.95 1.00

time (sec)

N/A 0.294 0.008 0.656 0.171 0.260 0.000 0.271 0.075

Problem 97

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

64 54 56 72 66 57 0 89 93

N.S.

1 0.84 0.88 1.12 1.03 0.89 0.00 1.39 1.45

time (sec)

N/A 0.328 0.048 0.266 0.255 0.259 0.000 0.284 2.991

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 73 67 81 91 256 0 85 133

N.S.

1 1.22 1.12 1.35 1.52 4.27 0.00 1.42 2.22

time (sec)

N/A 0.423 0.176 0.490 0.271 0.243 0.000 0.302 2.371

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 123 127 143 161 675 0 218 256

N.S.

1 1.29 1.34 1.51 1.69 7.11 0.00 2.29 2.69

time (sec)

N/A 0.445 0.250 2.237 0.272 0.271 0.000 0.294 3.589

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 128 114 170 226 1155 0 174 269

N.S.

1 1.23 1.10 1.63 2.17 11.11 0.00 1.67 2.59

time (sec)

N/A 0.634 0.507 7.646 0.287 0.260 0.000 0.285 2.522

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