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Integrals 1 to 98

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 Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

63 63 44 43 72 54 121 55 52 156

N.S.

1 1.00 0.70 0.68 1.14 0.86 1.92 0.87 0.83 2.48

time (sec)

N/A 0.238 3.851 7.242 0.034 0.076 0.124 0.125 0.173 28.280

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

45 45 34 32 47 41 78 38 36 123

N.S.

1 1.00 0.76 0.71 1.04 0.91 1.73 0.84 0.80 2.73

time (sec)

N/A 0.182 0.502 0.422 0.034 0.102 0.095 0.125 0.161 26.097

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

16 16 27 17 16 18 19 16 17 25

N.S.

1 1.00 1.69 1.06 1.00 1.12 1.19 1.00 1.06 1.56

time (sec)

N/A 0.139 0.037 0.082 0.029 0.083 0.056 0.126 0.262 25.714

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A A A A B B

verified

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

size

23 23 48 22 27 42 27 21 30 21

N.S.

1 1.00 2.09 0.96 1.17 1.83 1.17 0.91 1.30 0.91

time (sec)

N/A 0.173 0.265 0.079 0.036 0.080 0.407 0.130 0.218 25.750

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C B A B A B B

verified

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

size

55 54 54 38 117 95 221 47 60 76

N.S.

1 0.98 0.98 0.69 2.13 1.73 4.02 0.85 1.09 1.38

time (sec)

N/A 0.248 0.463 0.158 0.045 0.071 0.710 0.112 0.160 25.737

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C B A B A B B

verified

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

size

83 87 76 48 203 147 558 73 112 133

N.S.

1 1.05 0.92 0.58 2.45 1.77 6.72 0.88 1.35 1.60

time (sec)

N/A 0.330 0.424 0.211 0.038 0.084 1.368 0.121 0.162 25.902

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

63 63 46 45 72 54 121 55 52 156

N.S.

1 1.00 0.73 0.71 1.14 0.86 1.92 0.87 0.83 2.48

time (sec)

N/A 0.241 5.378 7.089 0.029 0.083 0.124 0.125 0.169 28.209

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

45 45 36 34 47 41 78 38 36 123

N.S.

1 1.00 0.80 0.76 1.04 0.91 1.73 0.84 0.80 2.73

time (sec)

N/A 0.185 0.641 0.404 0.030 0.087 0.091 0.119 0.170 25.933

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

15 15 27 16 15 17 19 15 15 25

N.S.

1 1.00 1.80 1.07 1.00 1.13 1.27 1.00 1.00 1.67

time (sec)

N/A 0.142 0.039 0.071 0.027 0.092 0.060 0.114 0.150 25.641

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A A A A B B

verified

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

size

23 23 51 22 28 40 27 21 30 21

N.S.

1 1.00 2.22 0.96 1.22 1.74 1.17 0.91 1.30 0.91

time (sec)

N/A 0.175 0.261 0.077 0.027 0.076 0.384 0.119 0.157 25.771

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C B A B A B B

verified

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

size

57 56 56 38 118 95 219 47 62 78

N.S.

1 0.98 0.98 0.67 2.07 1.67 3.84 0.82 1.09 1.37

time (sec)

N/A 0.251 0.390 0.149 0.037 0.073 0.693 0.121 0.161 25.951

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C B A B A B B

verified

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

size

86 90 74 48 204 147 556 73 112 135

N.S.

1 1.05 0.86 0.56 2.37 1.71 6.47 0.85 1.30 1.57

time (sec)

N/A 0.335 0.458 0.209 0.039 0.066 1.318 0.127 0.160 25.908

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

119 127 154 75 0 140 0 132 80 0

N.S.

1 1.07 1.29 0.63 0.00 1.18 0.00 1.11 0.67 0.00

time (sec)

N/A 0.433 3.145 0.273 0.000 0.088 0.000 0.143 0.175 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

89 93 117 65 0 115 0 102 58 0

N.S.

1 1.04 1.31 0.73 0.00 1.29 0.00 1.15 0.65 0.00

time (sec)

N/A 0.336 1.943 0.162 0.000 0.096 0.000 0.138 0.180 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

59 59 89 53 0 76 0 67 34 0

N.S.

1 1.00 1.51 0.90 0.00 1.29 0.00 1.14 0.58 0.00

time (sec)

N/A 0.247 0.757 0.115 0.000 0.091 0.000 0.136 0.152 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A F B F A F B

verified

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

size

26 26 65 43 0 50 0 36 14 33

N.S.

1 1.00 2.50 1.65 0.00 1.92 0.00 1.38 0.54 1.27

time (sec)

N/A 0.173 0.083 0.115 0.000 0.076 0.000 0.125 0.159 0.222

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A F A F A F B

verified

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

size

47 47 73 75 0 193 0 61 28 49

N.S.

1 1.00 1.55 1.60 0.00 4.11 0.00 1.30 0.60 1.04

time (sec)

N/A 0.190 0.224 0.328 0.000 0.098 0.000 0.140 0.158 0.405

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

77 77 108 125 0 252 0 133 38 0

N.S.

1 1.00 1.40 1.62 0.00 3.27 0.00 1.73 0.49 0.00

time (sec)

N/A 0.261 0.344 0.117 0.000 0.114 0.000 0.135 0.154 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

107 112 196 199 0 320 0 153 48 0

N.S.

1 1.05 1.83 1.86 0.00 2.99 0.00 1.43 0.45 0.00

time (sec)

N/A 0.356 0.345 0.122 0.000 0.106 0.000 0.145 0.169 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

123 131 157 76 0 143 0 132 90 0

N.S.

1 1.07 1.28 0.62 0.00 1.16 0.00 1.07 0.73 0.00

time (sec)

N/A 0.448 3.503 0.220 0.000 0.078 0.000 0.202 0.176 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

92 96 133 66 0 116 0 102 64 0

N.S.

1 1.04 1.45 0.72 0.00 1.26 0.00 1.11 0.70 0.00

time (sec)

N/A 0.354 2.251 0.149 0.000 0.105 0.000 0.180 0.166 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

61 61 103 54 0 79 0 68 40 0

N.S.

1 1.00 1.69 0.89 0.00 1.30 0.00 1.11 0.66 0.00

time (sec)

N/A 0.258 0.926 0.102 0.000 0.095 0.000 0.158 0.169 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A F A F A F B

verified

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

size

27 27 66 44 0 50 0 36 16 34

N.S.

1 1.00 2.44 1.63 0.00 1.85 0.00 1.33 0.59 1.26

time (sec)

N/A 0.177 0.049 0.113 0.000 0.074 0.000 0.133 0.179 25.976

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

47 47 76 74 0 190 0 42 31 0

N.S.

1 1.00 1.62 1.57 0.00 4.04 0.00 0.89 0.66 0.00

time (sec)

N/A 0.194 0.311 0.311 0.000 0.089 0.000 0.141 0.166 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

79 79 122 123 0 246 0 206 40 0

N.S.

1 1.00 1.54 1.56 0.00 3.11 0.00 2.61 0.51 0.00

time (sec)

N/A 0.277 0.421 0.100 0.000 0.109 0.000 0.185 0.180 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

110 115 160 194 0 321 0 303 51 0

N.S.

1 1.05 1.45 1.76 0.00 2.92 0.00 2.75 0.46 0.00

time (sec)

N/A 0.372 0.586 0.097 0.000 0.100 0.000 0.198 0.165 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

127 135 156 77 0 144 0 134 82 0

N.S.

1 1.06 1.23 0.61 0.00 1.13 0.00 1.06 0.65 0.00

time (sec)

N/A 0.456 2.858 0.167 0.000 0.084 0.000 0.200 0.179 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

95 99 119 67 0 117 0 104 58 0

N.S.

1 1.04 1.25 0.71 0.00 1.23 0.00 1.09 0.61 0.00

time (sec)

N/A 0.349 1.828 0.165 0.000 0.097 0.000 0.180 0.169 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

63 63 93 55 0 80 0 70 36 0

N.S.

1 1.00 1.48 0.87 0.00 1.27 0.00 1.11 0.57 0.00

time (sec)

N/A 0.252 0.691 0.116 0.000 0.105 0.000 0.156 0.174 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A F A F A F B

verified

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

size

28 28 65 45 0 51 0 38 14 33

N.S.

1 1.00 2.32 1.61 0.00 1.82 0.00 1.36 0.50 1.18

time (sec)

N/A 0.178 0.059 0.116 0.000 0.103 0.000 0.126 0.183 0.250

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

48 48 75 76 0 192 0 40 28 0

N.S.

1 1.00 1.56 1.58 0.00 4.00 0.00 0.83 0.58 0.00

time (sec)

N/A 0.193 0.171 0.253 0.000 0.104 0.000 0.146 0.166 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

81 81 108 134 0 252 0 215 38 0

N.S.

1 1.00 1.33 1.65 0.00 3.11 0.00 2.65 0.47 0.00

time (sec)

N/A 0.269 0.283 0.118 0.000 0.109 0.000 0.174 0.168 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

113 118 146 211 0 327 0 313 48 0

N.S.

1 1.04 1.29 1.87 0.00 2.89 0.00 2.77 0.42 0.00

time (sec)

N/A 0.371 0.427 0.119 0.000 0.106 0.000 0.204 0.170 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

67 67 223 0 0 0 0 0 36 0

N.S.

1 1.00 3.33 0.00 0.00 0.00 0.00 0.00 0.54 0.00

time (sec)

N/A 0.253 1.843 0.000 0.000 0.000 0.000 0.000 0.174 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

66 66 124 0 0 0 0 0 16 0

N.S.

1 1.00 1.88 0.00 0.00 0.00 0.00 0.00 0.24 0.00

time (sec)

N/A 0.259 0.470 0.000 0.000 0.000 0.000 0.000 0.176 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

66 66 169 0 0 0 0 0 16 0

N.S.

1 1.00 2.56 0.00 0.00 0.00 0.00 0.00 0.24 0.00

time (sec)

N/A 0.258 0.695 0.000 0.000 0.000 0.000 0.000 0.164 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

66 66 70 0 0 0 0 0 16 0

N.S.

1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 0.24 0.00

time (sec)

N/A 0.260 0.332 0.000 0.000 0.000 0.000 0.000 0.177 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

66 66 215 0 0 0 0 0 16 0

N.S.

1 1.00 3.26 0.00 0.00 0.00 0.00 0.00 0.24 0.00

time (sec)

N/A 0.256 1.130 0.000 0.000 0.000 0.000 0.000 0.235 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

69 69 130 0 0 0 0 0 36 0

N.S.

1 1.00 1.88 0.00 0.00 0.00 0.00 0.00 0.52 0.00

time (sec)

N/A 0.259 0.535 0.000 0.000 0.000 0.000 0.000 0.225 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

74 74 70 0 0 0 0 0 14 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.19 0.00

time (sec)

N/A 0.253 0.185 0.000 0.000 0.000 0.000 0.000 0.166 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

74 74 80 0 0 0 0 0 15 0

N.S.

1 1.00 1.08 0.00 0.00 0.00 0.00 0.00 0.20 0.00

time (sec)

N/A 0.267 0.294 0.000 0.000 0.000 0.000 0.000 0.162 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

60 60 46 0 0 0 0 0 14 0

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 0.23 0.00

time (sec)

N/A 0.195 0.217 0.000 0.000 0.000 0.000 0.000 0.159 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

59 59 49 0 0 0 0 0 14 0

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 0.24 0.00

time (sec)

N/A 0.197 0.223 0.000 0.000 0.000 0.000 0.000 0.157 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

31 31 56 20 26 26 46 49 19 40

N.S.

1 1.00 1.81 0.65 0.84 0.84 1.48 1.58 0.61 1.29

time (sec)

N/A 0.184 0.060 0.142 0.104 0.092 0.367 0.122 0.166 26.027

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

56 61 91 63 93 59 388 95 64 83

N.S.

1 1.09 1.62 1.12 1.66 1.05 6.93 1.70 1.14 1.48

time (sec)

N/A 0.265 0.212 0.230 0.110 0.132 0.911 0.122 0.173 25.950

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A C A B B

verified

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

size

81 91 113 91 173 94 918 121 131 111

N.S.

1 1.12 1.40 1.12 2.14 1.16 11.33 1.49 1.62 1.37

time (sec)

N/A 0.368 0.427 0.352 0.127 0.081 1.966 0.122 0.155 26.004

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A C A B B

verified

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

size

106 121 133 117 253 130 1693 147 191 187

N.S.

1 1.14 1.25 1.10 2.39 1.23 15.97 1.39 1.80 1.76

time (sec)

N/A 0.503 0.563 0.535 0.121 0.116 4.553 0.125 0.170 26.516

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

33 33 56 20 26 26 46 50 19 40

N.S.

1 1.00 1.70 0.61 0.79 0.79 1.39 1.52 0.58 1.21

time (sec)

N/A 0.183 0.054 0.138 0.108 0.110 0.387 0.120 0.156 25.853

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

58 63 91 63 93 59 384 96 64 83

N.S.

1 1.09 1.57 1.09 1.60 1.02 6.62 1.66 1.10 1.43

time (sec)

N/A 0.267 0.298 0.237 0.112 0.121 0.916 0.123 0.155 26.006

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A C A B B

verified

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

size

83 93 113 91 173 94 915 122 131 111

N.S.

1 1.12 1.36 1.10 2.08 1.13 11.02 1.47 1.58 1.34

time (sec)

N/A 0.387 0.746 0.353 0.117 0.118 2.043 0.122 0.168 25.976

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A C A B B

verified

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

size

108 123 133 117 253 130 1690 148 191 187

N.S.

1 1.14 1.23 1.08 2.34 1.20 15.65 1.37 1.77 1.73

time (sec)

N/A 0.506 0.674 0.535 0.112 0.103 4.661 0.124 0.163 26.423

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

33 33 56 20 26 26 48 50 19 40

N.S.

1 1.00 1.70 0.61 0.79 0.79 1.45 1.52 0.58 1.21

time (sec)

N/A 0.183 0.044 0.070 0.109 0.088 0.361 0.126 0.160 25.859

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

58 63 91 63 93 59 384 96 64 83

N.S.

1 1.09 1.57 1.09 1.60 1.02 6.62 1.66 1.10 1.43

time (sec)

N/A 0.261 0.092 0.099 0.112 0.101 0.913 0.119 0.167 0.002

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A C A B B

verified

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

size

83 93 113 91 173 94 915 122 131 112

N.S.

1 1.12 1.36 1.10 2.08 1.13 11.02 1.47 1.58 1.35

time (sec)

N/A 0.365 0.411 0.243 0.111 0.090 1.951 0.123 0.172 25.999

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A C A B B

verified

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

size

108 123 133 117 253 130 1690 148 191 187

N.S.

1 1.14 1.23 1.08 2.34 1.20 15.65 1.37 1.77 1.73

time (sec)

N/A 0.486 0.123 0.212 0.111 0.107 4.479 0.123 0.170 0.002

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

31 31 56 20 26 26 49 49 19 40

N.S.

1 1.00 1.81 0.65 0.84 0.84 1.58 1.58 0.61 1.29

time (sec)

N/A 0.183 0.046 0.086 0.115 0.121 0.381 0.128 0.178 25.855

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A C A B B

verified

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

size

56 61 91 63 93 59 389 95 64 83

N.S.

1 1.09 1.62 1.12 1.66 1.05 6.95 1.70 1.14 1.48

time (sec)

N/A 0.254 0.114 0.141 0.110 0.097 0.906 0.124 0.168 0.002

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A C A B B

verified

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

size

81 91 114 91 173 94 921 121 131 112

N.S.

1 1.12 1.41 1.12 2.14 1.16 11.37 1.49 1.62 1.38

time (sec)

N/A 0.359 0.660 0.331 0.109 0.107 1.960 0.129 0.177 26.054

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A C A B B

verified

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

size

106 121 133 117 253 130 1695 147 191 187

N.S.

1 1.14 1.25 1.10 2.39 1.23 15.99 1.39 1.80 1.76

time (sec)

N/A 0.485 0.424 0.361 0.128 0.110 4.497 0.122 0.171 0.002

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

63 42 63 36 49 46 42 36 34 19

N.S.

1 0.67 1.00 0.57 0.78 0.73 0.67 0.57 0.54 0.30

time (sec)

N/A 0.216 0.053 0.115 0.026 0.082 0.321 0.121 0.166 26.021

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

88 70 126 68 115 88 466 81 98 64

N.S.

1 0.80 1.43 0.77 1.31 1.00 5.30 0.92 1.11 0.73

time (sec)

N/A 0.296 0.288 0.263 0.028 0.112 0.719 0.128 0.180 25.972

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

113 100 180 100 195 133 1227 107 187 115

N.S.

1 0.88 1.59 0.88 1.73 1.18 10.86 0.95 1.65 1.02

time (sec)

N/A 0.417 0.576 0.302 0.034 0.084 1.444 0.137 0.166 27.202

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A B A B B

verified

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

size

138 130 235 132 275 181 2356 133 269 168

N.S.

1 0.94 1.70 0.96 1.99 1.31 17.07 0.96 1.95 1.22

time (sec)

N/A 0.556 1.016 0.441 0.036 0.094 3.219 0.132 0.168 28.666

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

65 44 65 36 49 46 42 36 34 19

N.S.

1 0.68 1.00 0.55 0.75 0.71 0.65 0.55 0.52 0.29

time (sec)

N/A 0.222 0.053 0.123 0.029 0.142 0.325 0.132 0.172 26.030

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

90 72 130 68 115 88 462 81 98 64

N.S.

1 0.80 1.44 0.76 1.28 0.98 5.13 0.90 1.09 0.71

time (sec)

N/A 0.293 0.349 0.269 0.030 0.080 0.761 0.126 0.192 25.983

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

115 102 184 100 195 133 1224 107 187 116

N.S.

1 0.89 1.60 0.87 1.70 1.16 10.64 0.93 1.63 1.01

time (sec)

N/A 0.424 0.826 0.312 0.034 0.087 1.414 0.126 0.178 27.197

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A B A B B

verified

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

size

140 132 241 132 275 181 2353 133 269 168

N.S.

1 0.94 1.72 0.94 1.96 1.29 16.81 0.95 1.92 1.20

time (sec)

N/A 0.549 1.110 0.451 0.036 0.092 3.248 0.126 0.169 28.212

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

65 44 65 36 49 46 42 36 34 19

N.S.

1 0.68 1.00 0.55 0.75 0.71 0.65 0.55 0.52 0.29

time (sec)

N/A 0.217 0.044 0.066 0.032 0.085 0.323 0.127 0.171 25.426

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

90 72 130 68 115 88 462 81 98 64

N.S.

1 0.80 1.44 0.76 1.28 0.98 5.13 0.90 1.09 0.71

time (sec)

N/A 0.296 0.132 0.069 0.030 0.082 0.755 0.135 0.168 0.003

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

115 102 183 100 195 133 1224 107 187 115

N.S.

1 0.89 1.59 0.87 1.70 1.16 10.64 0.93 1.63 1.00

time (sec)

N/A 0.407 0.618 0.269 0.036 0.144 1.481 0.132 0.162 26.711

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A B A B B

verified

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

size

140 132 241 132 275 181 2353 133 269 168

N.S.

1 0.94 1.72 0.94 1.96 1.29 16.81 0.95 1.92 1.20

time (sec)

N/A 0.536 0.014 0.124 0.039 0.103 3.240 0.125 0.171 0.002

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

63 42 63 36 49 46 44 36 34 19

N.S.

1 0.67 1.00 0.57 0.78 0.73 0.70 0.57 0.54 0.30

time (sec)

N/A 0.214 0.045 0.083 0.028 0.102 0.324 0.127 0.234 25.469

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

88 70 126 68 115 88 468 81 98 64

N.S.

1 0.80 1.43 0.77 1.31 1.00 5.32 0.92 1.11 0.73

time (sec)

N/A 0.291 0.189 0.125 0.034 0.092 0.731 0.129 0.276 0.002

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A B A B B

verified

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

size

113 100 179 100 195 133 1229 107 187 116

N.S.

1 0.88 1.58 0.88 1.73 1.18 10.88 0.95 1.65 1.03

time (sec)

N/A 0.413 0.769 0.296 0.037 0.094 1.434 0.130 0.170 26.870

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A B A B B

verified

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

size

138 130 235 132 275 181 2358 133 269 168

N.S.

1 0.94 1.70 0.96 1.99 1.31 17.09 0.96 1.95 1.22

time (sec)

N/A 0.524 0.898 0.146 0.037 0.116 3.236 0.129 0.169 0.002

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

256 267 220 1040 0 479 0 0 98 0

N.S.

1 1.04 0.86 4.06 0.00 1.87 0.00 0.00 0.38 0.00

time (sec)

N/A 1.409 1.240 1.506 0.000 0.115 0.000 0.000 0.204 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

207 213 185 890 0 435 0 0 68 0

N.S.

1 1.03 0.89 4.30 0.00 2.10 0.00 0.00 0.33 0.00

time (sec)

N/A 0.993 1.155 0.587 0.000 0.121 0.000 0.000 0.168 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

167 168 142 656 0 394 0 0 38 0

N.S.

1 1.01 0.85 3.93 0.00 2.36 0.00 0.00 0.23 0.00

time (sec)

N/A 0.734 0.953 0.418 0.000 0.104 0.000 0.000 0.182 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B F C F F F B

verified

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

size

62 62 61 239 0 351 0 0 13 55

N.S.

1 1.00 0.98 3.85 0.00 5.66 0.00 0.00 0.21 0.89

time (sec)

N/A 0.280 2.580 0.804 0.000 0.095 0.000 0.000 0.169 25.708

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B F C F F F B

verified

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

size

62 62 61 126 0 143 0 0 26 55

N.S.

1 1.00 0.98 2.03 0.00 2.31 0.00 0.00 0.42 0.89

time (sec)

N/A 0.286 0.133 0.122 0.000 0.095 0.000 0.000 0.163 25.849

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

111 111 87 443 0 460 0 0 42 0

N.S.

1 1.00 0.78 3.99 0.00 4.14 0.00 0.00 0.38 0.00

time (sec)

N/A 0.422 0.379 0.181 0.000 0.139 0.000 0.000 0.188 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

231 241 166 495 0 687 0 0 58 0

N.S.

1 1.04 0.72 2.14 0.00 2.97 0.00 0.00 0.25 0.00

time (sec)

N/A 1.071 1.149 0.237 0.000 0.163 0.000 0.000 0.172 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

292 318 198 582 0 985 0 0 74 0

N.S.

1 1.09 0.68 1.99 0.00 3.37 0.00 0.00 0.25 0.00

time (sec)

N/A 1.471 1.555 0.313 0.000 0.123 0.000 0.000 0.172 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

106 109 244 0 0 0 0 0 40 0

N.S.

1 1.03 2.30 0.00 0.00 0.00 0.00 0.00 0.38 0.00

time (sec)

N/A 0.260 1.881 0.000 0.000 0.000 0.000 0.000 0.180 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

106 106 118 0 0 0 0 0 14 0

N.S.

1 1.00 1.11 0.00 0.00 0.00 0.00 0.00 0.13 0.00

time (sec)

N/A 0.254 0.324 0.000 0.000 0.000 0.000 0.000 0.166 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

106 106 118 0 0 0 0 0 14 0

N.S.

1 1.00 1.11 0.00 0.00 0.00 0.00 0.00 0.13 0.00

time (sec)

N/A 0.261 0.312 0.000 0.000 0.000 0.000 0.000 0.178 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

106 106 118 0 0 0 0 0 14 0

N.S.

1 1.00 1.11 0.00 0.00 0.00 0.00 0.00 0.13 0.00

time (sec)

N/A 0.256 0.296 0.000 0.000 0.000 0.000 0.000 0.163 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

106 106 116 0 0 0 0 0 14 0

N.S.

1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 0.13 0.00

time (sec)

N/A 0.255 0.264 0.000 0.000 0.000 0.000 0.000 0.167 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

106 111 262 0 0 0 0 0 39 0

N.S.

1 1.05 2.47 0.00 0.00 0.00 0.00 0.00 0.37 0.00

time (sec)

N/A 0.255 2.097 0.000 0.000 0.000 0.000 0.000 0.166 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

104 104 120 0 0 0 0 0 14 0

N.S.

1 1.00 1.15 0.00 0.00 0.00 0.00 0.00 0.13 0.00

time (sec)

N/A 0.253 0.360 0.000 0.000 0.000 0.000 0.000 0.170 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

72 72 83 0 0 0 0 0 14 0

N.S.

1 1.00 1.15 0.00 0.00 0.00 0.00 0.00 0.19 0.00

time (sec)

N/A 0.233 0.195 0.000 0.000 0.000 0.000 0.000 0.175 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

69 69 84 0 0 0 0 0 14 0

N.S.

1 1.00 1.22 0.00 0.00 0.00 0.00 0.00 0.20 0.00

time (sec)

N/A 0.229 0.192 0.000 0.000 0.000 0.000 0.000 0.221 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

72 64 99 0 0 0 0 0 14 0

N.S.

1 0.89 1.38 0.00 0.00 0.00 0.00 0.00 0.19 0.00

time (sec)

N/A 0.224 0.157 0.000 0.000 0.000 0.000 0.000 0.258 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

67 69 96 0 0 0 0 0 14 0

N.S.

1 1.03 1.43 0.00 0.00 0.00 0.00 0.00 0.21 0.00

time (sec)

N/A 0.226 0.179 0.000 0.000 0.000 0.000 0.000 0.164 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

67 67 83 0 0 0 0 0 14 0

N.S.

1 1.00 1.24 0.00 0.00 0.00 0.00 0.00 0.21 0.00

time (sec)

N/A 0.229 0.185 0.000 0.000 0.000 0.000 0.000 0.173 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

64 64 84 0 0 0 0 0 14 0

N.S.

1 1.00 1.31 0.00 0.00 0.00 0.00 0.00 0.22 0.00

time (sec)

N/A 0.227 0.200 0.000 0.000 0.000 0.000 0.000 0.189 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

93 95 95 0 0 0 0 0 14 0

N.S.

1 1.02 1.02 0.00 0.00 0.00 0.00 0.00 0.15 0.00

time (sec)

N/A 0.249 0.170 0.000 0.000 0.000 0.000 0.000 0.165 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

98 110 100 0 0 0 0 0 14 0

N.S.

1 1.12 1.02 0.00 0.00 0.00 0.00 0.00 0.14 0.00

time (sec)

N/A 0.260 0.181 0.000 0.000 0.000 0.000 0.000 0.174 0.000

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