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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 A A A A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 79 51 72 71 49 70 113 0

N.S.

1 1.05 0.68 0.96 0.95 0.65 0.93 1.51 0.00

time (sec)

N/A 0.213 0.043 0.560 0.275 0.245 0.298 0.267 0.000

Problem 2

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

69 83 50 60 61 47 61 84 0

N.S.

1 1.20 0.72 0.87 0.88 0.68 0.88 1.22 0.00

time (sec)

N/A 0.195 0.029 0.010 0.284 0.251 0.241 0.272 0.000

Problem 3

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

54 58 41 52 50 40 48 64 0

N.S.

1 1.07 0.76 0.96 0.93 0.74 0.89 1.19 0.00

time (sec)

N/A 0.198 0.035 0.008 0.303 0.246 0.166 0.278 0.000

Problem 4

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

45 51 40 40 40 36 37 46 38

N.S.

1 1.13 0.89 0.89 0.89 0.80 0.82 1.02 0.84

time (sec)

N/A 0.169 0.018 0.007 0.292 0.245 0.141 0.269 0.055

Problem 5

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

25 25 25 24 24 24 20 24 23

N.S.

1 1.00 1.00 0.96 0.96 0.96 0.80 0.96 0.92

time (sec)

N/A 0.153 0.008 0.006 0.309 0.248 0.063 0.261 0.071

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 59 46 111 0 0 0 0 41

N.S.

1 1.16 0.90 2.18 0.00 0.00 0.00 0.00 0.80

time (sec)

N/A 0.308 0.054 0.118 0.000 0.000 0.000 0.000 0.052

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 28 27 39 49 32 48 26

N.S.

1 1.00 1.00 0.96 1.39 1.75 1.14 1.71 0.93

time (sec)

N/A 0.184 0.009 0.007 0.275 0.280 0.823 0.269 0.014

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 29 29 28 25 51 68 0

N.S.

1 1.00 0.85 0.85 0.82 0.74 1.50 2.00 0.00

time (sec)

N/A 0.167 0.010 0.009 0.281 0.261 0.625 0.277 0.000

Problem 9

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

56 57 53 50 60 73 107 77 0

N.S.

1 1.02 0.95 0.89 1.07 1.30 1.91 1.38 0.00

time (sec)

N/A 0.190 0.018 0.007 0.296 0.272 1.413 0.269 0.000

Problem 10

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

58 63 41 52 50 37 100 130 0

N.S.

1 1.09 0.71 0.90 0.86 0.64 1.72 2.24 0.00

time (sec)

N/A 0.192 0.024 0.010 0.280 0.269 0.858 0.279 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 86 51 73 82 85 182 101 0

N.S.

1 1.08 0.64 0.91 1.02 1.06 2.28 1.26 0.00

time (sec)

N/A 0.208 0.022 0.011 0.286 0.259 2.792 0.278 0.000

Problem 12

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

120 140 82 76 102 76 114 169 0

N.S.

1 1.17 0.68 0.63 0.85 0.63 0.95 1.41 0.00

time (sec)

N/A 0.511 0.041 0.108 0.295 0.251 0.405 0.274 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 115 74 91 0 70 90 133 0

N.S.

1 1.17 0.76 0.93 0.00 0.71 0.92 1.36 0.00

time (sec)

N/A 0.475 0.056 0.066 0.000 0.275 0.296 0.281 0.000

Problem 14

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

82 94 64 59 72 59 76 97 0

N.S.

1 1.15 0.78 0.72 0.88 0.72 0.93 1.18 0.00

time (sec)

N/A 0.361 0.039 0.073 0.307 0.242 0.225 0.279 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 67 55 65 0 51 51 73 0

N.S.

1 1.12 0.92 1.08 0.00 0.85 0.85 1.22 0.00

time (sec)

N/A 0.329 0.031 0.025 0.000 0.250 0.186 0.269 0.000

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

35 41 35 37 33 36 32 33 32

N.S.

1 1.17 1.00 1.06 0.94 1.03 0.91 0.94 0.91

time (sec)

N/A 0.232 0.017 0.030 0.273 0.241 0.081 0.272 0.088

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 88 71 169 0 0 0 0 0

N.S.

1 1.24 1.00 2.38 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.414 0.087 0.043 0.000 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 67 87 120 0 0 0 0 0

N.S.

1 1.02 1.32 1.82 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.379 0.231 0.037 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 44 48 40 44 0 82 0

N.S.

1 1.00 1.00 1.09 0.91 1.00 0.00 1.86 0.00

time (sec)

N/A 0.258 0.025 0.034 0.274 0.274 0.000 0.286 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 112 139 149 0 0 0 0 0

N.S.

1 0.97 1.20 1.28 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.531 0.687 0.112 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 88 69 82 74 62 0 185 0

N.S.

1 1.01 0.79 0.94 0.85 0.71 0.00 2.13 0.00

time (sec)

N/A 0.378 0.033 0.033 0.282 0.261 0.000 0.329 0.000

Problem 22

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

201 302 122 159 171 105 196 249 0

N.S.

1 1.50 0.61 0.79 0.85 0.52 0.98 1.24 0.00

time (sec)

N/A 1.216 0.067 0.048 0.285 0.262 0.544 0.275 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 244 112 154 0 96 160 185 0

N.S.

1 1.46 0.67 0.92 0.00 0.57 0.96 1.11 0.00

time (sec)

N/A 0.949 0.039 0.093 0.000 0.266 0.420 0.282 0.000

Problem 24

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

136 176 95 106 120 79 128 142 0

N.S.

1 1.29 0.70 0.78 0.88 0.58 0.94 1.04 0.00

time (sec)

N/A 0.685 0.038 0.043 0.286 0.259 0.307 0.281 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 116 82 96 0 69 92 101 0

N.S.

1 1.17 0.83 0.97 0.00 0.70 0.93 1.02 0.00

time (sec)

N/A 0.488 0.025 0.049 0.000 0.267 0.232 0.289 0.000

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

60 68 60 57 57 44 54 56 40

N.S.

1 1.13 1.00 0.95 0.95 0.73 0.90 0.93 0.67

time (sec)

N/A 0.302 0.012 0.026 0.272 0.248 0.111 0.267 0.093

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 119 97 229 0 0 0 0 0

N.S.

1 1.23 1.00 2.36 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.509 0.058 0.042 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 113 133 178 0 0 0 0 0

N.S.

1 1.05 1.23 1.65 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.531 0.115 0.052 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 107 92 161 0 0 0 0 0

N.S.

1 1.05 0.90 1.58 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.553 0.284 0.060 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 179 284 234 0 0 0 0 0

N.S.

1 1.00 1.59 1.31 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.960 2.302 0.107 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 181 116 231 0 0 0 0 0

N.S.

1 1.07 0.69 1.37 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.932 0.680 0.101 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

282 501 167 345 0 153 269 362 0

N.S.

1 1.78 0.59 1.22 0.00 0.54 0.95 1.28 0.00

time (sec)

N/A 2.388 0.097 0.114 0.000 0.255 1.035 0.275 0.000

Problem 33

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

250 412 150 197 207 134 241 305 0

N.S.

1 1.65 0.60 0.79 0.83 0.54 0.96 1.22 0.00

time (sec)

N/A 2.136 0.055 0.047 0.300 0.270 0.761 0.276 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 293 135 215 0 121 190 234 0

N.S.

1 1.48 0.68 1.09 0.00 0.61 0.96 1.18 0.00

time (sec)

N/A 1.466 0.051 0.069 0.000 0.266 0.567 0.286 0.000

Problem 35

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

166 227 114 130 147 99 158 176 0

N.S.

1 1.37 0.69 0.78 0.89 0.60 0.95 1.06 0.00

time (sec)

N/A 1.176 0.048 0.042 0.299 0.262 0.414 0.280 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 133 96 117 0 82 104 127 0

N.S.

1 1.20 0.86 1.05 0.00 0.74 0.94 1.14 0.00

time (sec)

N/A 0.717 0.034 0.055 0.000 0.250 0.303 0.274 0.000

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

69 84 69 67 75 55 65 65 48

N.S.

1 1.22 1.00 0.97 1.09 0.80 0.94 0.94 0.70

time (sec)

N/A 0.402 0.024 0.030 0.272 0.243 0.152 0.277 0.088

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 148 113 287 0 0 0 0 0

N.S.

1 1.31 1.00 2.54 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.604 0.055 0.046 0.000 0.000 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 165 198 238 0 0 0 0 0

N.S.

1 1.06 1.27 1.53 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.670 0.233 0.051 0.000 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 F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 134 124 219 0 0 0 0 0

N.S.

1 1.13 1.04 1.84 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.676 0.298 0.061 0.000 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

276 276 399 377 0 0 0 0 0

N.S.

1 1.00 1.45 1.37 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.319 3.425 0.095 0.000 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 47 40 40 0 0 0 47 0

N.S.

1 0.85 0.73 0.73 0.00 0.00 0.00 0.85 0.00

time (sec)

N/A 0.284 0.028 0.046 0.000 0.000 0.000 0.287 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 38 33 33 0 0 0 37 0

N.S.

1 0.88 0.77 0.77 0.00 0.00 0.00 0.86 0.00

time (sec)

N/A 0.269 0.156 0.046 0.000 0.000 0.000 0.289 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 36 31 31 0 0 0 35 0

N.S.

1 0.88 0.76 0.76 0.00 0.00 0.00 0.85 0.00

time (sec)

N/A 0.266 0.014 0.030 0.000 0.000 0.000 0.279 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 27 24 24 0 0 0 25 0

N.S.

1 0.93 0.83 0.83 0.00 0.00 0.00 0.86 0.00

time (sec)

N/A 0.256 0.106 0.026 0.000 0.000 0.000 0.279 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 25 22 22 0 0 0 23 0

N.S.

1 0.93 0.81 0.81 0.00 0.00 0.00 0.85 0.00

time (sec)

N/A 0.254 0.009 0.024 0.000 0.000 0.000 0.277 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 13 0 0 0 12 0

N.S.

1 1.00 1.00 0.93 0.00 0.00 0.00 0.86 0.00

time (sec)

N/A 0.247 0.051 0.035 0.000 0.000 0.000 0.283 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 10 0 0 0 9 0

N.S.

1 1.00 1.00 1.11 0.00 0.00 0.00 1.00 0.00

time (sec)

N/A 0.197 0.024 0.025 0.000 0.000 0.000 0.274 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 10 12 12 8 12 12

N.S.

1 1.00 1.20 1.00 1.20 1.20 0.80 1.20 1.20

time (sec)

N/A 0.158 0.208 0.030 0.372 0.229 0.263 0.304 0.035

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 10 12 12 10 12 12

N.S.

1 1.00 1.20 1.00 1.20 1.20 1.00 1.20 1.20

time (sec)

N/A 0.160 1.594 0.095 0.374 0.241 0.282 0.313 0.035

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 76 86 105 0 0 0 161 0

N.S.

1 0.92 1.04 1.27 0.00 0.00 0.00 1.94 0.00

time (sec)

N/A 0.250 0.357 0.046 0.000 0.000 0.000 0.286 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 67 78 78 0 0 0 120 0

N.S.

1 0.94 1.10 1.10 0.00 0.00 0.00 1.69 0.00

time (sec)

N/A 0.236 0.040 0.044 0.000 0.000 0.000 0.289 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 65 61 81 0 0 0 115 0

N.S.

1 0.94 0.88 1.17 0.00 0.00 0.00 1.67 0.00

time (sec)

N/A 0.233 0.353 0.030 0.000 0.000 0.000 0.280 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 56 56 54 0 0 0 72 0

N.S.

1 0.98 0.98 0.95 0.00 0.00 0.00 1.26 0.00

time (sec)

N/A 0.223 0.023 0.032 0.000 0.000 0.000 0.293 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 54 50 57 0 0 0 68 0

N.S.

1 0.98 0.91 1.04 0.00 0.00 0.00 1.24 0.00

time (sec)

N/A 0.217 0.282 0.029 0.000 0.000 0.000 0.289 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 29 28 0 0 0 36 0

N.S.

1 1.00 0.76 0.74 0.00 0.00 0.00 0.95 0.00

time (sec)

N/A 0.232 0.015 0.033 0.000 0.000 0.000 0.285 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 32 33 0 0 0 34 0

N.S.

1 1.00 0.89 0.92 0.00 0.00 0.00 0.94 0.00

time (sec)

N/A 0.315 0.130 0.023 0.000 0.000 0.000 0.277 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 10 126 12 10 12 12

N.S.

1 1.00 1.20 1.00 12.60 1.20 1.00 1.20 1.20

time (sec)

N/A 0.157 1.328 0.030 0.571 0.263 0.320 0.310 0.034

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 10 137 12 12 12 12

N.S.

1 1.00 1.20 1.00 13.70 1.20 1.20 1.20 1.20

time (sec)

N/A 0.157 10.918 0.060 0.678 0.250 0.366 0.371 0.040

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 134 103 121 0 0 0 170 0

N.S.

1 1.37 1.05 1.23 0.00 0.00 0.00 1.73 0.00

time (sec)

N/A 0.667 0.163 0.045 0.000 0.000 0.000 0.297 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 110 73 82 0 0 0 125 0

N.S.

1 1.33 0.88 0.99 0.00 0.00 0.00 1.51 0.00

time (sec)

N/A 0.719 0.183 0.039 0.000 0.000 0.000 0.293 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 103 68 82 0 0 0 102 0

N.S.

1 1.26 0.83 1.00 0.00 0.00 0.00 1.24 0.00

time (sec)

N/A 0.737 0.111 0.025 0.000 0.000 0.000 0.300 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 71 61 45 0 0 0 67 0

N.S.

1 1.11 0.95 0.70 0.00 0.00 0.00 1.05 0.00

time (sec)

N/A 0.633 0.049 0.038 0.000 0.000 0.000 0.288 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 55 48 43 0 0 0 43 0

N.S.

1 1.08 0.94 0.84 0.00 0.00 0.00 0.84 0.00

time (sec)

N/A 0.374 0.025 0.027 0.000 0.000 0.000 0.263 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 10 125 12 10 12 12

N.S.

1 1.00 1.20 1.00 12.50 1.20 1.00 1.20 1.20

time (sec)

N/A 0.158 0.544 0.029 1.395 0.260 0.398 0.321 0.035

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 10 142 12 12 12 12

N.S.

1 1.00 1.20 1.00 14.20 1.20 1.20 1.20 1.20

time (sec)

N/A 0.160 6.637 0.049 1.549 0.244 0.478 0.376 0.036

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 210 159 171 0 0 0 250 0

N.S.

1 1.33 1.01 1.08 0.00 0.00 0.00 1.58 0.00

time (sec)

N/A 0.612 0.364 0.045 0.000 0.000 0.000 0.290 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 177 107 114 0 0 0 174 0

N.S.

1 1.23 0.74 0.79 0.00 0.00 0.00 1.21 0.00

time (sec)

N/A 0.699 0.351 0.037 0.000 0.000 0.000 0.282 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 177 112 117 0 0 0 148 0

N.S.

1 1.26 0.79 0.83 0.00 0.00 0.00 1.05 0.00

time (sec)

N/A 0.940 0.290 0.032 0.000 0.000 0.000 0.277 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 106 86 60 0 0 0 92 0

N.S.

1 1.09 0.89 0.62 0.00 0.00 0.00 0.95 0.00

time (sec)

N/A 0.616 0.151 0.031 0.000 0.000 0.000 0.269 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 91 70 63 0 0 0 66 0

N.S.

1 1.17 0.90 0.81 0.00 0.00 0.00 0.85 0.00

time (sec)

N/A 0.518 0.088 0.030 0.000 0.000 0.000 0.262 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 10 201 12 10 12 12

N.S.

1 1.00 1.20 1.00 20.10 1.20 1.00 1.20 1.20

time (sec)

N/A 0.159 3.264 0.028 3.976 0.249 0.514 0.316 0.037

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 10 230 12 12 12 12

N.S.

1 1.00 1.20 1.00 23.00 1.20 1.20 1.20 1.20

time (sec)

N/A 0.158 13.773 0.049 4.899 0.240 0.662 0.402 0.039

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 120 192 143 0 0 0 247 0

N.S.

1 0.99 1.59 1.18 0.00 0.00 0.00 2.04 0.00

time (sec)

N/A 0.461 0.048 0.098 0.000 0.000 0.000 0.330 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 94 131 90 0 0 0 153 0

N.S.

1 0.99 1.38 0.95 0.00 0.00 0.00 1.61 0.00

time (sec)

N/A 0.425 0.028 0.059 0.000 0.000 0.000 0.328 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 88 126 96 0 0 0 165 0

N.S.

1 1.02 1.47 1.12 0.00 0.00 0.00 1.92 0.00

time (sec)

N/A 0.414 0.034 0.044 0.000 0.000 0.000 0.326 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 57 74 43 0 0 0 71 0

N.S.

1 0.97 1.25 0.73 0.00 0.00 0.00 1.20 0.00

time (sec)

N/A 0.379 0.014 0.038 0.000 0.000 0.000 0.308 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 66 49 0 0 0 83 0

N.S.

1 1.00 1.50 1.11 0.00 0.00 0.00 1.89 0.00

time (sec)

N/A 0.332 0.026 0.036 0.000 0.000 0.000 0.295 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 14 10 0 0 10 12 12

N.S.

1 1.00 1.17 0.83 0.00 0.00 0.83 1.00 1.00

time (sec)

N/A 0.155 0.195 0.052 0.000 0.000 0.329 0.443 0.036

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

214 337 202 193 0 0 0 355 0

N.S.

1 1.57 0.94 0.90 0.00 0.00 0.00 1.66 0.00

time (sec)

N/A 1.847 0.057 0.074 0.000 0.000 0.000 0.331 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 201 130 121 0 0 0 225 0

N.S.

1 1.28 0.83 0.77 0.00 0.00 0.00 1.43 0.00

time (sec)

N/A 1.449 0.028 0.059 0.000 0.000 0.000 0.332 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 193 136 131 0 0 0 237 0

N.S.

1 1.31 0.93 0.89 0.00 0.00 0.00 1.61 0.00

time (sec)

N/A 1.018 0.058 0.051 0.000 0.000 0.000 0.334 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 95 71 64 0 0 0 107 0

N.S.

1 1.07 0.80 0.72 0.00 0.00 0.00 1.20 0.00

time (sec)

N/A 0.743 0.016 0.045 0.000 0.000 0.000 0.314 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 76 76 72 0 0 0 119 0

N.S.

1 1.01 1.01 0.96 0.00 0.00 0.00 1.59 0.00

time (sec)

N/A 0.411 0.041 0.042 0.000 0.000 0.000 0.347 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 14 10 0 0 10 12 12

N.S.

1 1.00 1.17 0.83 0.00 0.00 0.83 1.00 1.00

time (sec)

N/A 0.157 0.151 0.052 0.000 0.000 1.340 0.530 0.036

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

263 402 192 233 0 0 0 463 0

N.S.

1 1.53 0.73 0.89 0.00 0.00 0.00 1.76 0.00

time (sec)

N/A 2.254 0.057 0.076 0.000 0.000 0.000 0.343 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 272 131 154 0 0 0 297 0

N.S.

1 1.33 0.64 0.75 0.00 0.00 0.00 1.45 0.00

time (sec)

N/A 1.588 0.040 0.062 0.000 0.000 0.000 0.336 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

178 235 125 156 0 0 0 309 0

N.S.

1 1.32 0.70 0.88 0.00 0.00 0.00 1.74 0.00

time (sec)

N/A 1.351 0.040 0.051 0.000 0.000 0.000 0.335 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 131 74 79 0 0 0 143 0

N.S.

1 1.10 0.62 0.66 0.00 0.00 0.00 1.20 0.00

time (sec)

N/A 0.809 0.015 0.042 0.000 0.000 0.000 0.327 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 95 68 88 0 0 0 155 0

N.S.

1 1.08 0.77 1.00 0.00 0.00 0.00 1.76 0.00

time (sec)

N/A 0.525 0.032 0.039 0.000 0.000 0.000 0.343 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 14 10 0 0 10 12 12

N.S.

1 1.00 1.17 0.83 0.00 0.00 0.83 1.00 1.00

time (sec)

N/A 0.155 0.172 0.060 0.000 0.000 17.626 0.548 0.036

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 101 193 72 0 0 0 139 0

N.S.

1 0.95 1.82 0.68 0.00 0.00 0.00 1.31 0.00

time (sec)

N/A 0.295 0.043 0.069 0.000 0.000 0.000 0.324 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 63 128 44 0 0 0 81 0

N.S.

1 0.97 1.97 0.68 0.00 0.00 0.00 1.25 0.00

time (sec)

N/A 0.267 0.026 0.056 0.000 0.000 0.000 0.327 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 69 128 51 0 0 0 93 0

N.S.

1 0.97 1.80 0.72 0.00 0.00 0.00 1.31 0.00

time (sec)

N/A 0.269 0.038 0.046 0.000 0.000 0.000 0.309 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 71 21 0 0 0 35 0

N.S.

1 1.00 2.54 0.75 0.00 0.00 0.00 1.25 0.00

time (sec)

N/A 0.272 0.015 0.034 0.000 0.000 0.000 0.297 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 69 25 0 0 0 47 0

N.S.

1 1.00 2.30 0.83 0.00 0.00 0.00 1.57 0.00

time (sec)

N/A 0.231 0.024 0.028 0.000 0.000 0.000 0.309 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 14 10 0 0 12 12 12

N.S.

1 1.00 1.17 0.83 0.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.152 0.178 0.055 0.000 0.000 0.361 0.382 0.039

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 14 10 0 0 14 12 12

N.S.

1 1.00 1.17 0.83 0.00 0.00 1.17 1.00 1.00

time (sec)

N/A 0.154 2.289 0.069 0.000 0.000 0.495 0.395 0.038

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 165 427 184 0 0 0 0 0

N.S.

1 0.96 2.50 1.08 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.318 0.202 0.086 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 126 231 121 0 0 0 0 0

N.S.

1 0.99 1.82 0.95 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.291 0.125 0.082 0.000 0.000 0.000 0.000 0.000

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