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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 103 87 79 0 205 214 81 0

N.S.

1 1.01 0.85 0.77 0.00 2.01 2.10 0.79 0.00

time (sec)

N/A 0.270 0.700 1.101 0.000 0.287 0.384 0.313 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 204 491 0 1079 0 851 0

N.S.

1 1.00 2.49 5.99 0.00 13.16 0.00 10.38 0.00

time (sec)

N/A 0.239 0.407 1.000 0.000 0.481 0.000 0.963 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 189 307 0 813 0 0 0

N.S.

1 1.00 2.86 4.65 0.00 12.32 0.00 0.00 0.00

time (sec)

N/A 0.216 0.394 0.931 0.000 0.367 0.000 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 129 1333 827 0 1544 0 1170 0

N.S.

1 1.00 10.33 6.41 0.00 11.97 0.00 9.07 0.00

time (sec)

N/A 0.295 3.017 1.006 0.000 0.604 0.000 0.880 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

224 243 940 1868 0 3818 0 0 0

N.S.

1 1.08 4.20 8.34 0.00 17.04 0.00 0.00 0.00

time (sec)

N/A 0.578 14.808 1.322 0.000 2.887 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

328 374 3382 3649 0 8134 0 30280 0

N.S.

1 1.14 10.31 11.12 0.00 24.80 0.00 92.32 0.00

time (sec)

N/A 1.089 16.443 1.949 0.000 11.832 0.000 4.506 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 162 1420 1352 0 2005 0 1305 0

N.S.

1 1.00 8.77 8.35 0.00 12.38 0.00 8.06 0.00

time (sec)

N/A 0.364 2.116 1.184 0.000 0.989 0.000 1.063 0.000

Problem 8

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

28 28 39 27 0 38 0 52 0

N.S.

1 1.00 1.39 0.96 0.00 1.36 0.00 1.86 0.00

time (sec)

N/A 0.161 0.166 1.121 0.000 0.267 0.000 0.275 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

136 136 142 0 0 0 0 0 0

N.S.

1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.251 0.146 0.000 0.000 0.000 0.000 0.000 0.000

Problem 10

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

200 200 172 0 0 0 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.313 0.402 0.000 0.000 0.000 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

48 30 41 16 0 22 0 49 0

N.S.

1 0.62 0.85 0.33 0.00 0.46 0.00 1.02 0.00

time (sec)

N/A 0.157 0.072 0.485 0.000 0.294 0.000 0.290 0.000

Problem 12

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

70 75 62 63 0 82 0 143 0

N.S.

1 1.07 0.89 0.90 0.00 1.17 0.00 2.04 0.00

time (sec)

N/A 0.227 0.173 0.617 0.000 0.328 0.000 0.299 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

1077 1077 600 721 0 0 0 0 0

N.S.

1 1.00 0.56 0.67 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.219 4.027 5.287 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

98 99 75 322 0 161 0 171 0

N.S.

1 1.01 0.77 3.29 0.00 1.64 0.00 1.74 0.00

time (sec)

N/A 0.470 0.162 1.145 0.000 0.296 0.000 0.303 0.000

Problem 15

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

68 68 68 55 54 54 65 54 54

N.S.

1 1.00 1.00 0.81 0.79 0.79 0.96 0.79 0.79

time (sec)

N/A 0.241 0.003 0.541 0.193 0.401 0.031 0.283 0.086

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

56 56 56 45 44 44 53 44 44

N.S.

1 1.00 1.00 0.80 0.79 0.79 0.95 0.79 0.79

time (sec)

N/A 0.231 0.002 0.515 0.196 0.369 0.028 0.294 0.034

Problem 17

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

44 44 44 35 34 34 41 34 34

N.S.

1 1.00 1.00 0.80 0.77 0.77 0.93 0.77 0.77

time (sec)

N/A 0.211 0.002 0.525 0.210 0.340 0.025 0.279 0.026

Problem 18

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

30 30 30 25 24 24 26 24 24

N.S.

1 1.00 1.00 0.83 0.80 0.80 0.87 0.80 0.80

time (sec)

N/A 0.186 0.002 0.052 0.198 0.342 0.021 0.276 0.022

Problem 19

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

42 42 42 34 33 33 49 33 35

N.S.

1 1.00 1.00 0.81 0.79 0.79 1.17 0.79 0.83

time (sec)

N/A 0.211 0.013 0.688 0.286 0.348 0.059 0.279 12.427

Problem 20

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 43 34 36 45 42 36 35

N.S.

1 1.00 1.00 0.79 0.84 1.05 0.98 0.84 0.81

time (sec)

N/A 0.198 0.013 0.633 0.274 0.279 0.067 0.283 12.489

Problem 21

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

64 69 53 47 56 75 63 46 55

N.S.

1 1.08 0.83 0.73 0.88 1.17 0.98 0.72 0.86

time (sec)

N/A 0.212 0.038 0.633 0.276 0.359 0.079 0.282 0.053

Problem 22

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

80 80 80 65 64 64 76 64 64

N.S.

1 1.00 1.00 0.81 0.80 0.80 0.95 0.80 0.80

time (sec)

N/A 0.257 0.003 0.578 0.228 0.362 0.034 0.263 0.110

Problem 23

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

66 66 66 55 54 54 63 54 54

N.S.

1 1.00 1.00 0.83 0.82 0.82 0.95 0.82 0.82

time (sec)

N/A 0.249 0.005 0.612 0.200 0.386 0.029 0.271 0.079

Problem 24

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 54 45 44 44 51 44 44

N.S.

1 1.00 1.00 0.83 0.81 0.81 0.94 0.81 0.81

time (sec)

N/A 0.228 0.002 0.632 0.216 0.352 0.024 0.263 0.035

Problem 25

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

46 46 46 35 34 34 41 34 34

N.S.

1 1.00 1.00 0.76 0.74 0.74 0.89 0.74 0.74

time (sec)

N/A 0.204 0.001 0.552 0.205 0.319 0.022 0.273 0.025

Problem 26

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

56 56 53 44 43 43 63 43 45

N.S.

1 1.00 0.95 0.79 0.77 0.77 1.12 0.77 0.80

time (sec)

N/A 0.208 0.015 0.710 0.283 0.312 0.065 0.279 12.295

Problem 27

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 66 59 50 52 78 65 52 51

N.S.

1 1.05 0.94 0.79 0.83 1.24 1.03 0.83 0.81

time (sec)

N/A 0.250 0.022 0.707 0.264 0.316 0.084 0.281 0.052

Problem 28

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

64 69 53 47 56 75 63 46 55

N.S.

1 1.08 0.83 0.73 0.88 1.17 0.98 0.72 0.86

time (sec)

N/A 0.251 0.017 0.631 0.276 0.422 0.080 0.269 12.438

Problem 29

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

85 95 63 57 76 105 83 56 75

N.S.

1 1.12 0.74 0.67 0.89 1.24 0.98 0.66 0.88

time (sec)

N/A 0.277 0.035 0.717 0.273 0.413 0.094 0.275 12.441

Problem 30

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

96 96 96 75 74 74 92 74 74

N.S.

1 1.00 1.00 0.78 0.77 0.77 0.96 0.77 0.77

time (sec)

N/A 0.297 0.004 0.615 0.186 0.371 0.038 0.280 0.145

Problem 31

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

82 82 82 65 64 64 78 64 64

N.S.

1 1.00 1.00 0.79 0.78 0.78 0.95 0.78 0.78

time (sec)

N/A 0.252 0.005 0.635 0.185 0.362 0.028 0.278 0.105

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

68 68 68 55 54 54 65 54 54

N.S.

1 1.00 1.00 0.81 0.79 0.79 0.96 0.79 0.79

time (sec)

N/A 0.247 0.005 0.613 0.201 0.361 0.026 0.279 0.079

Problem 33

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

56 56 56 45 44 44 53 44 44

N.S.

1 1.00 1.00 0.80 0.79 0.79 0.95 0.79 0.79

time (sec)

N/A 0.227 0.001 0.557 0.205 0.353 0.026 0.275 0.035

Problem 34

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

70 70 63 54 53 53 76 53 55

N.S.

1 1.00 0.90 0.77 0.76 0.76 1.09 0.76 0.79

time (sec)

N/A 0.226 0.016 0.702 0.267 0.339 0.072 0.284 0.045

Problem 35

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

77 78 77 60 62 88 78 62 61

N.S.

1 1.01 1.00 0.78 0.81 1.14 1.01 0.81 0.79

time (sec)

N/A 0.274 0.019 0.704 0.267 0.592 0.082 0.267 0.044

Problem 36

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

84 92 78 63 72 118 85 62 71

N.S.

1 1.10 0.93 0.75 0.86 1.40 1.01 0.74 0.85

time (sec)

N/A 0.318 0.025 0.713 0.275 0.257 0.092 0.277 0.052

Problem 37

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

84 84 72 64 63 63 87 63 65

N.S.

1 1.00 0.86 0.76 0.75 0.75 1.04 0.75 0.77

time (sec)

N/A 0.236 0.023 1.056 0.266 0.264 0.072 0.277 12.425

Problem 38

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

70 70 63 54 53 53 73 53 55

N.S.

1 1.00 0.90 0.77 0.76 0.76 1.04 0.76 0.79

time (sec)

N/A 0.218 0.017 0.711 0.270 0.255 0.067 0.269 12.373

Problem 39

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

56 56 52 44 43 43 60 43 45

N.S.

1 1.00 0.93 0.79 0.77 0.77 1.07 0.77 0.80

time (sec)

N/A 0.218 0.015 0.648 0.265 0.262 0.071 0.267 12.381

Problem 40

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

42 42 42 34 33 33 46 33 35

N.S.

1 1.00 1.00 0.81 0.79 0.79 1.10 0.79 0.83

time (sec)

N/A 0.199 0.009 0.648 0.288 0.265 0.067 0.274 0.041

Problem 41

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

73 79 73 60 59 59 83 59 79

N.S.

1 1.08 1.00 0.82 0.81 0.81 1.14 0.81 1.08

time (sec)

N/A 0.249 0.026 0.831 0.265 0.264 0.122 0.279 0.191

Problem 42

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

94 105 94 76 78 117 102 78 95

N.S.

1 1.12 1.00 0.81 0.83 1.24 1.09 0.83 1.01

time (sec)

N/A 0.335 0.055 0.835 0.264 0.285 0.166 0.268 12.608

Problem 43

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

115 131 104 89 98 177 119 88 115

N.S.

1 1.14 0.90 0.77 0.85 1.54 1.03 0.77 1.00

time (sec)

N/A 0.427 0.099 0.836 0.273 0.293 0.167 0.278 0.186

Problem 44

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

91 86 91 70 72 98 90 72 72

N.S.

1 0.95 1.00 0.77 0.79 1.08 0.99 0.79 0.79

time (sec)

N/A 0.290 0.037 0.680 0.260 0.264 0.099 0.272 12.308

Problem 45

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

77 76 77 60 62 88 75 62 61

N.S.

1 0.99 1.00 0.78 0.81 1.14 0.97 0.81 0.79

time (sec)

N/A 0.287 0.022 0.629 0.259 0.263 0.090 0.281 0.043

Problem 46

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 64 63 50 52 78 61 52 52

N.S.

1 1.02 1.00 0.79 0.83 1.24 0.97 0.83 0.83

time (sec)

N/A 0.248 0.023 0.694 0.261 0.301 0.082 0.273 12.444

Problem 47

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 43 34 36 45 42 36 36

N.S.

1 1.00 1.00 0.79 0.84 1.05 0.98 0.84 0.84

time (sec)

N/A 0.184 0.011 0.650 0.259 0.271 0.071 0.280 0.041

Problem 48

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

94 105 94 76 78 117 102 78 96

N.S.

1 1.12 1.00 0.81 0.83 1.24 1.09 0.83 1.02

time (sec)

N/A 0.344 0.040 0.887 0.261 0.260 0.135 0.274 12.494

Problem 49

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

127 143 106 94 96 167 122 96 115

N.S.

1 1.13 0.83 0.74 0.76 1.31 0.96 0.76 0.91

time (sec)

N/A 0.425 0.038 0.794 0.269 0.289 0.147 0.266 0.187

Problem 50

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

148 169 136 106 118 237 143 110 135

N.S.

1 1.14 0.92 0.72 0.80 1.60 0.97 0.74 0.91

time (sec)

N/A 0.535 0.043 0.834 0.259 0.306 0.172 0.277 12.589

Problem 51

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

98 106 98 73 82 128 95 72 81

N.S.

1 1.08 1.00 0.74 0.84 1.31 0.97 0.73 0.83

time (sec)

N/A 0.365 0.027 0.724 0.261 0.284 0.104 0.282 0.048

Problem 52

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

84 94 84 63 72 118 82 62 72

N.S.

1 1.12 1.00 0.75 0.86 1.40 0.98 0.74 0.86

time (sec)

N/A 0.328 0.028 0.690 0.267 0.269 0.095 0.275 12.437

Problem 53

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

64 69 51 47 56 75 63 46 56

N.S.

1 1.08 0.80 0.73 0.88 1.17 0.98 0.72 0.88

time (sec)

N/A 0.252 0.022 0.702 0.269 0.293 0.076 0.279 12.428

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

64 69 51 47 56 75 61 46 55

N.S.

1 1.08 0.80 0.73 0.88 1.17 0.95 0.72 0.86

time (sec)

N/A 0.218 0.020 0.645 0.270 0.282 0.078 0.271 0.047

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

115 131 99 89 98 177 122 88 116

N.S.

1 1.14 0.86 0.77 0.85 1.54 1.06 0.77 1.01

time (sec)

N/A 0.426 0.105 0.836 0.266 0.285 0.150 0.275 12.537

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

160 181 136 106 116 227 143 110 136

N.S.

1 1.13 0.85 0.66 0.72 1.42 0.89 0.69 0.85

time (sec)

N/A 0.550 0.072 0.838 0.263 0.283 0.178 0.270 12.493

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

181 207 151 118 138 297 163 116 155

N.S.

1 1.14 0.83 0.65 0.76 1.64 0.90 0.64 0.86

time (sec)

N/A 0.656 0.057 0.862 0.265 0.289 0.192 0.276 0.196

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

208 248 95 75 177 98 97 93 221

N.S.

1 1.19 0.46 0.36 0.85 0.47 0.47 0.45 1.06

time (sec)

N/A 0.759 0.809 0.766 0.271 0.289 0.444 0.293 14.079

Problem 59

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

166 196 85 65 143 88 83 83 187

N.S.

1 1.18 0.51 0.39 0.86 0.53 0.50 0.50 1.13

time (sec)

N/A 0.532 0.589 0.737 0.271 0.279 0.399 0.280 13.656

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

124 144 75 55 109 78 70 73 153

N.S.

1 1.16 0.60 0.44 0.88 0.63 0.56 0.59 1.23

time (sec)

N/A 0.365 0.371 0.711 0.272 0.297 0.379 0.286 13.202

Problem 61

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

82 92 65 45 75 68 56 63 119

N.S.

1 1.12 0.79 0.55 0.91 0.83 0.68 0.77 1.45

time (sec)

N/A 0.230 0.232 0.641 0.262 0.278 0.327 0.279 13.035

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

174 180 206 484 0 285 0 0 0

N.S.

1 1.03 1.18 2.78 0.00 1.64 0.00 0.00 0.00

time (sec)

N/A 0.502 0.220 1.405 0.000 0.311 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

188 194 419 473 0 336 0 0 0

N.S.

1 1.03 2.23 2.52 0.00 1.79 0.00 0.00 0.00

time (sec)

N/A 0.500 0.491 1.918 0.000 0.331 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

223 234 392 483 0 396 0 0 0

N.S.

1 1.05 1.76 2.17 0.00 1.78 0.00 0.00 0.00

time (sec)

N/A 0.637 0.650 2.309 0.000 0.303 0.000 0.000 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

231 276 105 85 206 108 110 103 0

N.S.

1 1.19 0.45 0.37 0.89 0.47 0.48 0.45 0.00

time (sec)

N/A 0.817 1.039 0.741 0.278 0.292 0.585 0.282 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

189 224 95 75 172 98 95 93 0

N.S.

1 1.19 0.50 0.40 0.91 0.52 0.50 0.49 0.00

time (sec)

N/A 0.573 0.788 0.764 0.283 0.293 0.490 0.285 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

147 172 85 65 138 88 83 83 0

N.S.

1 1.17 0.58 0.44 0.94 0.60 0.56 0.56 0.00

time (sec)

N/A 0.395 0.575 0.730 0.273 0.297 0.442 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

105 120 75 55 104 78 70 73 0

N.S.

1 1.14 0.71 0.52 0.99 0.74 0.67 0.70 0.00

time (sec)

N/A 0.267 0.359 0.686 0.266 0.280 0.373 0.275 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

197 208 228 590 0 316 0 0 0

N.S.

1 1.06 1.16 2.99 0.00 1.60 0.00 0.00 0.00

time (sec)

N/A 0.635 0.338 2.500 0.000 0.320 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

232 248 416 511 0 384 0 0 0

N.S.

1 1.07 1.79 2.20 0.00 1.66 0.00 0.00 0.00

time (sec)

N/A 0.775 0.508 2.395 0.000 0.301 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

223 234 572 483 0 396 0 0 0

N.S.

1 1.05 2.57 2.17 0.00 1.78 0.00 0.00 0.00

time (sec)

N/A 0.570 0.828 2.810 0.000 0.296 0.000 0.000 0.000

Problem 72

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

254 304 115 95 235 118 124 113 0

N.S.

1 1.20 0.45 0.37 0.93 0.46 0.49 0.44 0.00

time (sec)

N/A 0.862 1.313 0.839 0.287 0.300 0.896 0.287 0.000

Problem 73

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

212 252 105 85 201 108 110 103 0

N.S.

1 1.19 0.50 0.40 0.95 0.51 0.52 0.49 0.00

time (sec)

N/A 0.609 1.007 0.767 0.271 0.281 0.698 0.287 0.000

Problem 74

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

170 200 95 75 167 98 95 93 0

N.S.

1 1.18 0.56 0.44 0.98 0.58 0.56 0.55 0.00

time (sec)

N/A 0.428 0.770 0.754 0.268 0.273 0.587 0.287 0.000

Problem 75

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

128 148 85 65 133 88 83 83 0

N.S.

1 1.16 0.66 0.51 1.04 0.69 0.65 0.65 0.00

time (sec)

N/A 0.289 0.547 0.701 0.275 0.270 0.481 0.288 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

222 240 238 599 0 322 0 0 0

N.S.

1 1.08 1.07 2.70 0.00 1.45 0.00 0.00 0.00

time (sec)

N/A 0.732 0.544 3.638 0.000 0.341 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

255 276 433 522 0 404 0 0 0

N.S.

1 1.08 1.70 2.05 0.00 1.58 0.00 0.00 0.00

time (sec)

N/A 0.858 0.689 3.102 0.000 0.310 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

281 288 616 613 0 454 0 0 0

N.S.

1 1.02 2.19 2.18 0.00 1.62 0.00 0.00 0.00

time (sec)

N/A 0.894 0.886 5.005 0.000 0.375 0.000 0.000 0.000

Problem 79

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

185 220 85 65 148 88 83 83 0

N.S.

1 1.19 0.46 0.35 0.80 0.48 0.45 0.45 0.00

time (sec)

N/A 0.753 0.657 0.732 0.271 0.275 0.430 0.411 0.000

Problem 80

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

143 168 75 55 114 78 70 73 0

N.S.

1 1.17 0.52 0.38 0.80 0.55 0.49 0.51 0.00

time (sec)

N/A 0.500 0.446 0.727 0.272 0.405 0.380 0.361 0.000

Problem 81

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

101 116 65 45 80 68 56 63 0

N.S.

1 1.15 0.64 0.45 0.79 0.67 0.55 0.62 0.00

time (sec)

N/A 0.333 0.287 0.743 0.273 0.317 0.384 0.371 0.000

Problem 82

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

59 64 55 35 46 58 42 53 0

N.S.

1 1.08 0.93 0.59 0.78 0.98 0.71 0.90 0.00

time (sec)

N/A 0.210 0.148 0.727 0.267 0.295 0.332 0.362 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

148 154 135 441 0 265 0 0 0

N.S.

1 1.04 0.91 2.98 0.00 1.79 0.00 0.00 0.00

time (sec)

N/A 0.416 0.195 2.137 0.000 0.295 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

188 194 230 473 0 336 0 0 0

N.S.

1 1.03 1.22 2.52 0.00 1.79 0.00 0.00 0.00

time (sec)

N/A 0.524 0.365 2.824 0.000 0.320 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

223 234 396 483 0 396 0 0 0

N.S.

1 1.05 1.78 2.17 0.00 1.78 0.00 0.00 0.00

time (sec)

N/A 0.620 0.636 3.123 0.000 0.307 0.000 0.000 0.000

Problem 86

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

166 192 85 65 148 112 0 82 0

N.S.

1 1.16 0.51 0.39 0.89 0.67 0.00 0.49 0.00

time (sec)

N/A 0.619 0.890 0.762 0.272 0.279 0.000 0.274 0.000

Problem 87

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

124 137 75 55 114 102 0 72 0

N.S.

1 1.10 0.60 0.44 0.92 0.82 0.00 0.58 0.00

time (sec)

N/A 0.421 0.614 0.815 0.261 0.290 0.000 0.279 0.000

Problem 88

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

82 90 65 45 80 92 0 62 0

N.S.

1 1.10 0.79 0.55 0.98 1.12 0.00 0.76 0.00

time (sec)

N/A 0.285 0.467 0.793 0.269 0.303 0.000 0.274 0.000

Problem 89

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

45 45 55 35 46 82 0 53 87

N.S.

1 1.00 1.22 0.78 1.02 1.82 0.00 1.18 1.93

time (sec)

N/A 0.195 0.255 0.679 0.276 0.270 0.000 0.278 0.242

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

176 182 199 460 0 338 0 0 0

N.S.

1 1.03 1.13 2.61 0.00 1.92 0.00 0.00 0.00

time (sec)

N/A 0.504 0.342 2.714 0.000 0.291 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 222 414 491 0 388 0 0 0

N.S.

1 1.05 1.96 2.33 0.00 1.84 0.00 0.00 0.00

time (sec)

N/A 0.627 0.679 3.168 0.000 0.332 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

246 262 607 493 0 458 0 0 0

N.S.

1 1.07 2.47 2.00 0.00 1.86 0.00 0.00 0.00

time (sec)

N/A 0.760 1.064 3.559 0.000 0.316 0.000 0.000 0.000

Problem 93

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

147 163 85 65 253 132 0 81 0

N.S.

1 1.11 0.58 0.44 1.72 0.90 0.00 0.55 0.00

time (sec)

N/A 0.517 1.043 0.690 0.273 0.281 0.000 0.276 0.000

Problem 94

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

105 116 75 55 219 122 0 72 0

N.S.

1 1.10 0.71 0.52 2.09 1.16 0.00 0.69 0.00

time (sec)

N/A 0.364 0.774 0.797 0.270 0.292 0.000 0.288 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 71 65 45 185 112 0 61 0

N.S.

1 1.04 0.96 0.66 2.72 1.65 0.00 0.90 0.00

time (sec)

N/A 0.259 0.562 0.733 0.282 0.291 0.000 0.288 0.000

Problem 96

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

47 47 33 30 59 51 0 29 29

N.S.

1 1.00 0.70 0.64 1.26 1.09 0.00 0.62 0.62

time (sec)

N/A 0.187 0.338 0.670 0.188 0.275 0.000 0.282 0.098

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

199 212 209 472 0 398 0 0 0

N.S.

1 1.07 1.05 2.37 0.00 2.00 0.00 0.00 0.00

time (sec)

N/A 0.604 0.637 2.639 0.000 0.315 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

234 250 416 493 0 448 0 0 0

N.S.

1 1.07 1.78 2.11 0.00 1.91 0.00 0.00 0.00

time (sec)

N/A 0.742 1.067 2.961 0.000 0.301 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

269 290 605 511 0 518 0 0 0

N.S.

1 1.08 2.25 1.90 0.00 1.93 0.00 0.00 0.00

time (sec)

N/A 0.865 1.169 3.634 0.000 0.317 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

436 383 459 645 0 1269 1544 627 1299

N.S.

1 0.88 1.05 1.48 0.00 2.91 3.54 1.44 2.98

time (sec)

N/A 0.935 5.401 1.089 0.000 0.480 0.738 0.306 15.152

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