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2.2.1 Integrals 1 to 68

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 B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 33 31 41 80 29 36 75 28

N.S.

1 0.97 0.91 1.21 2.35 0.85 1.06 2.21 0.82

time (sec)

N/A 0.288 0.029 0.067 0.196 0.251 0.217 0.254 0.088

Problem 2

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

69 77 67 74 110 189 0 75 0

N.S.

1 1.12 0.97 1.07 1.59 2.74 0.00 1.09 0.00

time (sec)

N/A 0.304 0.052 0.049 0.183 0.253 0.000 0.258 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 31 14 13 13 19 27 13

N.S.

1 1.00 2.07 0.93 0.87 0.87 1.27 1.80 0.87

time (sec)

N/A 0.209 0.011 0.034 0.180 0.245 0.087 0.276 1.543

Problem 4

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

53 53 45 40 87 49 0 41 0

N.S.

1 1.00 0.85 0.75 1.64 0.92 0.00 0.77 0.00

time (sec)

N/A 0.224 0.025 0.028 0.204 0.235 0.000 0.262 0.000

Problem 5

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

25 25 23 33 24 39 0 24 0

N.S.

1 1.00 0.92 1.32 0.96 1.56 0.00 0.96 0.00

time (sec)

N/A 0.290 0.012 0.047 0.254 0.240 0.000 0.253 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 70 70 70 55 183 0 0 0

N.S.

1 1.06 1.06 1.06 0.83 2.77 0.00 0.00 0.00

time (sec)

N/A 0.295 0.053 0.050 0.178 0.252 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 48 38 58 40 71 0 108 0

N.S.

1 1.14 0.90 1.38 0.95 1.69 0.00 2.57 0.00

time (sec)

N/A 0.439 0.032 0.058 0.239 0.252 0.000 0.272 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 55 40 46 59 60 78 142 42

N.S.

1 1.08 0.78 0.90 1.16 1.18 1.53 2.78 0.82

time (sec)

N/A 0.258 0.076 0.148 0.197 0.248 0.287 0.265 0.111

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 99 101 90 95 427 0 97 0

N.S.

1 1.00 1.02 0.91 0.96 4.31 0.00 0.98 0.00

time (sec)

N/A 0.282 0.157 0.104 0.259 0.256 0.000 0.276 0.000

Problem 10

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

31 35 27 24 38 28 60 54 22

N.S.

1 1.13 0.87 0.77 1.23 0.90 1.94 1.74 0.71

time (sec)

N/A 0.228 0.020 0.071 0.190 0.245 0.114 0.254 0.061

Problem 11

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

78 78 86 51 56 73 0 58 0

N.S.

1 1.00 1.10 0.65 0.72 0.94 0.00 0.74 0.00

time (sec)

N/A 0.225 0.053 0.065 0.267 0.246 0.000 0.276 0.000

Problem 12

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

37 37 33 34 31 49 0 35 0

N.S.

1 1.00 0.89 0.92 0.84 1.32 0.00 0.95 0.00

time (sec)

N/A 0.237 0.016 0.104 0.233 0.240 0.000 0.279 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 92 94 86 61 394 0 0 0

N.S.

1 1.05 1.07 0.98 0.69 4.48 0.00 0.00 0.00

time (sec)

N/A 0.424 0.181 0.101 0.258 0.257 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 46 66 36 90 0 126 0

N.S.

1 1.00 0.81 1.16 0.63 1.58 0.00 2.21 0.00

time (sec)

N/A 0.313 0.069 0.110 0.243 0.245 0.000 0.257 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 83 55 93 100 96 92 192 70

N.S.

1 1.05 0.70 1.18 1.27 1.22 1.16 2.43 0.89

time (sec)

N/A 0.405 0.126 0.223 0.196 0.252 0.418 0.265 1.621

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 160 184 157 162 903 0 166 0

N.S.

1 1.00 1.15 0.98 1.01 5.64 0.00 1.04 0.00

time (sec)

N/A 0.357 0.241 0.186 0.274 0.264 0.000 0.289 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A A A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

33 29 33 28 62 38 44 56 26

N.S.

1 0.88 1.00 0.85 1.88 1.15 1.33 1.70 0.79

time (sec)

N/A 0.249 0.009 0.088 0.175 0.255 0.233 0.257 0.063

Problem 18

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

125 125 136 86 91 113 0 95 0

N.S.

1 1.00 1.09 0.69 0.73 0.90 0.00 0.76 0.00

time (sec)

N/A 0.278 0.097 0.104 0.276 0.264 0.000 0.254 0.000

Problem 19

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

55 55 49 69 50 83 0 50 0

N.S.

1 1.00 0.89 1.25 0.91 1.51 0.00 0.91 0.00

time (sec)

N/A 0.281 0.025 0.170 0.263 0.247 0.000 0.258 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 144 204 149 102 891 0 0 0

N.S.

1 1.06 1.50 1.10 0.75 6.55 0.00 0.00 0.00

time (sec)

N/A 0.355 0.251 0.178 0.263 0.258 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 92 121 58 168 0 224 0

N.S.

1 1.00 1.01 1.33 0.64 1.85 0.00 2.46 0.00

time (sec)

N/A 0.413 0.063 0.181 0.267 0.247 0.000 0.259 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B A A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

67 41 67 52 126 128 94 108 52

N.S.

1 0.61 1.00 0.78 1.88 1.91 1.40 1.61 0.78

time (sec)

N/A 0.257 0.022 0.793 0.180 0.243 0.750 0.266 1.661

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 8 7 6 6 5 15 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.62 1.88 0.75

time (sec)

N/A 0.205 0.003 0.053 0.179 0.238 0.108 0.261 1.509

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 8 7 6 6 8 15 15

N.S.

1 1.00 1.00 0.88 0.75 0.75 1.00 1.88 1.88

time (sec)

N/A 0.201 0.005 0.086 0.197 0.236 2.502 0.252 1.557

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 41 33 56 37 58 0 173 0

N.S.

1 1.24 1.00 1.70 1.12 1.76 0.00 5.24 0.00

time (sec)

N/A 0.436 0.021 0.110 0.223 0.243 0.000 0.278 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 27 24 39 17 43 0

N.S.

1 1.00 1.00 1.29 1.14 1.86 0.81 2.05 0.00

time (sec)

N/A 0.287 0.008 0.075 0.218 0.240 0.462 0.254 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 14 13 15 15 29 13

N.S.

1 1.00 1.00 1.08 1.00 1.15 1.15 2.23 1.00

time (sec)

N/A 0.219 0.005 0.052 0.179 0.236 0.259 0.296 1.548

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 29 43 47 33 29 93 29

N.S.

1 1.00 1.00 1.48 1.62 1.14 1.00 3.21 1.00

time (sec)

N/A 0.280 0.020 0.088 0.252 0.244 0.394 0.274 1.556

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A C A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 58 39 65 48 43 46 216 66

N.S.

1 1.26 0.85 1.41 1.04 0.93 1.00 4.70 1.43

time (sec)

N/A 0.366 0.035 0.117 0.226 0.242 0.503 0.313 1.598

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 71 71 70 72 225 0 0 0

N.S.

1 1.06 1.06 1.04 1.07 3.36 0.00 0.00 0.00

time (sec)

N/A 0.351 0.060 0.079 0.215 0.261 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 33 24 39 0 0 0

N.S.

1 1.00 1.00 1.32 0.96 1.56 0.00 0.00 0.00

time (sec)

N/A 0.286 0.014 0.073 0.229 0.246 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 F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 49 44 63 53 0 0 0

N.S.

1 1.00 0.86 0.77 1.11 0.93 0.00 0.00 0.00

time (sec)

N/A 0.296 0.026 0.078 0.240 0.245 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 14 13 17 22 33 13

N.S.

1 1.00 1.00 0.93 0.87 1.13 1.47 2.20 0.87

time (sec)

N/A 0.222 0.005 0.060 0.182 0.237 0.534 0.262 1.534

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 83 74 82 63 250 0 0 0

N.S.

1 1.11 0.99 1.09 0.84 3.33 0.00 0.00 0.00

time (sec)

N/A 0.355 0.051 0.112 0.242 0.249 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 62 74 61 0 0 0 0

N.S.

1 1.00 0.93 1.10 0.91 0.00 0.00 0.00 0.00

time (sec)

N/A 0.222 0.040 0.111 0.095 0.000 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 23 33 30 54 0 0 0

N.S.

1 1.00 0.92 1.32 1.20 2.16 0.00 0.00 0.00

time (sec)

N/A 0.277 0.020 0.130 0.247 0.255 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

89 89 81 0 68 0 0 0 0

N.S.

1 1.00 0.91 0.00 0.76 0.00 0.00 0.00 0.00

time (sec)

N/A 0.267 0.075 0.000 0.100 0.000 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 36 40 37 69 0 0 0

N.S.

1 1.00 0.84 0.93 0.86 1.60 0.00 0.00 0.00

time (sec)

N/A 0.243 0.022 0.495 0.254 0.256 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

150 150 138 0 125 0 0 0 0

N.S.

1 1.00 0.92 0.00 0.83 0.00 0.00 0.00 0.00

time (sec)

N/A 0.301 0.067 0.000 0.149 0.000 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 F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 52 67 62 114 0 0 0

N.S.

1 1.00 0.78 1.00 0.93 1.70 0.00 0.00 0.00

time (sec)

N/A 0.277 0.039 0.891 0.273 0.260 0.000 0.000 0.000

Problem 41

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 20 20 17 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.94 1.11 1.11

time (sec)

N/A 0.185 4.106 0.042 0.401 0.255 8.296 1.354 1.573

Problem 42

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

20 20 22 20 22 22 19 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.10

time (sec)

N/A 0.191 6.143 0.035 0.413 0.268 25.338 7.712 1.591

Problem 43

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

95 95 90 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.370 0.100 0.000 0.000 0.000 0.000 0.000 0.000

Problem 44

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

22 22 24 22 24 24 20 24 24

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.91 1.09 1.09

time (sec)

N/A 0.287 4.414 0.053 0.420 0.256 7.942 1.322 1.547

Problem 45

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

131 131 148 0 0 0 0 0 0

N.S.

1 1.00 1.13 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.443 0.374 0.000 0.000 0.000 0.000 0.000 0.000

Problem 46

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

24 24 26 24 26 26 22 26 26

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.92 1.08 1.08

time (sec)

N/A 0.291 6.373 0.051 0.421 0.277 24.084 7.296 1.547

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 84 110 85 0 0 0 0

N.S.

1 1.00 0.94 1.24 0.96 0.00 0.00 0.00 0.00

time (sec)

N/A 0.283 0.104 0.295 0.115 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

128 128 116 0 101 0 0 0 0

N.S.

1 1.00 0.91 0.00 0.79 0.00 0.00 0.00 0.00

time (sec)

N/A 0.360 0.190 0.000 0.112 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

200 200 182 0 173 0 0 0 0

N.S.

1 1.00 0.91 0.00 0.86 0.00 0.00 0.00 0.00

time (sec)

N/A 0.427 0.144 0.000 0.164 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 50 46 63 34 140 0 0 0

N.S.

1 1.11 1.02 1.40 0.76 3.11 0.00 0.00 0.00

time (sec)

N/A 0.459 0.044 0.281 0.245 0.261 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 54 75 47 182 0 0 0

N.S.

1 1.00 0.81 1.12 0.70 2.72 0.00 0.00 0.00

time (sec)

N/A 0.329 0.094 1.352 0.240 0.257 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 113 97 126 70 320 0 0 0

N.S.

1 1.00 0.86 1.12 0.62 2.83 0.00 0.00 0.00

time (sec)

N/A 0.438 0.107 7.612 0.286 0.257 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 70 57 54 69 98 0 52 0

N.S.

1 0.99 0.80 0.76 0.97 1.38 0.00 0.73 0.00

time (sec)

N/A 0.297 0.033 0.244 0.258 0.245 0.000 0.270 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 99 62 136 818 321 0 137 0

N.S.

1 0.88 0.55 1.20 7.24 2.84 0.00 1.21 0.00

time (sec)

N/A 0.325 0.091 0.081 0.443 0.261 0.000 0.264 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 49 39 66 650 261 0 99 0

N.S.

1 0.91 0.72 1.22 12.04 4.83 0.00 1.83 0.00

time (sec)

N/A 0.288 0.025 0.050 0.405 0.259 0.000 0.268 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 35 25 36 478 59 0 39 0

N.S.

1 0.95 0.68 0.97 12.92 1.59 0.00 1.05 0.00

time (sec)

N/A 0.250 0.006 0.029 0.387 0.262 0.000 0.277 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

12 12 14 12 14 23 20 14 14

N.S.

1 1.00 1.17 1.00 1.17 1.92 1.67 1.17 1.17

time (sec)

N/A 0.254 1.091 0.020 0.846 0.246 3.020 0.273 1.651

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

12 12 14 12 14 23 22 14 14

N.S.

1 1.00 1.17 1.00 1.17 1.92 1.83 1.17 1.17

time (sec)

N/A 0.256 3.360 0.020 0.610 0.251 3.036 0.271 1.572

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

346 313 209 831 486 104 269 915 0

N.S.

1 0.90 0.60 2.40 1.40 0.30 0.78 2.64 0.00

time (sec)

N/A 0.652 0.323 0.183 0.211 0.259 0.331 0.289 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 153 72 301 291 68 151 300 0

N.S.

1 0.92 0.43 1.80 1.74 0.41 0.90 1.80 0.00

time (sec)

N/A 0.458 0.153 0.125 0.203 0.278 0.254 0.263 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 52 50 63 110 44 65 65 43

N.S.

1 0.96 0.93 1.17 2.04 0.81 1.20 1.20 0.80

time (sec)

N/A 0.347 0.046 0.011 0.188 0.265 0.239 0.259 1.606

Problem 62

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

124 143 127 0 0 217 0 0 0

N.S.

1 1.15 1.02 0.00 0.00 1.75 0.00 0.00 0.00

time (sec)

N/A 0.581 0.288 0.000 0.000 0.267 0.000 0.000 0.000

Problem 63

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

182 194 204 0 0 317 0 0 0

N.S.

1 1.07 1.12 0.00 0.00 1.74 0.00 0.00 0.00

time (sec)

N/A 0.662 1.027 0.000 0.000 0.261 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

537 486 353 1815 642 181 0 2163 0

N.S.

1 0.91 0.66 3.38 1.20 0.34 0.00 4.03 0.00

time (sec)

N/A 0.880 0.489 0.207 0.208 0.259 0.000 0.364 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

261 238 118 659 369 109 0 707 0

N.S.

1 0.91 0.45 2.52 1.41 0.42 0.00 2.71 0.00

time (sec)

N/A 0.538 0.254 0.186 0.193 0.264 0.000 0.279 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 92 65 133 136 58 94 128 75

N.S.

1 1.08 0.76 1.56 1.60 0.68 1.11 1.51 0.88

time (sec)

N/A 0.445 0.062 0.009 0.201 0.270 0.296 0.263 1.637

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

232 253 231 0 0 503 0 0 0

N.S.

1 1.09 1.00 0.00 0.00 2.17 0.00 0.00 0.00

time (sec)

N/A 0.801 0.053 0.000 0.000 0.269 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

329 334 211 0 0 706 0 0 0

N.S.

1 1.02 0.64 0.00 0.00 2.15 0.00 0.00 0.00

time (sec)

N/A 0.973 0.364 0.000 0.000 0.292 0.000 0.000 0.000

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