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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 B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 122 107 177 161 115 221 646 0

N.S.

1 1.07 0.94 1.55 1.41 1.01 1.94 5.67 0.00

time (sec)

N/A 0.265 0.102 0.368 0.188 0.313 8.747 0.747 0.000

Problem 2

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

89 97 72 79 80 62 153 518 0

N.S.

1 1.09 0.81 0.89 0.90 0.70 1.72 5.82 0.00

time (sec)

N/A 0.251 0.092 0.362 0.186 0.287 1.981 0.315 0.000

Problem 3

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

89 93 97 141 132 106 175 480 0

N.S.

1 1.04 1.09 1.58 1.48 1.19 1.97 5.39 0.00

time (sec)

N/A 0.243 0.056 0.342 0.188 0.288 3.376 0.626 0.000

Problem 4

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

64 68 62 70 59 52 107 352 0

N.S.

1 1.06 0.97 1.09 0.92 0.81 1.67 5.50 0.00

time (sec)

N/A 0.222 0.078 0.345 0.182 0.273 1.352 0.304 0.000

Problem 5

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

64 64 85 94 97 94 107 310 0

N.S.

1 1.00 1.33 1.47 1.52 1.47 1.67 4.84 0.00

time (sec)

N/A 0.216 0.045 0.329 0.205 0.291 1.809 0.452 0.000

Problem 6

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

39 39 50 61 36 39 58 182 40

N.S.

1 1.00 1.28 1.56 0.92 1.00 1.49 4.67 1.03

time (sec)

N/A 0.193 0.028 0.341 0.190 0.328 0.820 0.288 0.872

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 58 37 53 64 32 62 33

N.S.

1 1.00 1.87 1.19 1.71 2.06 1.03 2.00 1.06

time (sec)

N/A 0.171 0.038 0.131 0.200 0.278 1.224 0.270 1.127

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 87 53 136 0 0 0 0 65

N.S.

1 1.36 0.83 2.12 0.00 0.00 0.00 0.00 1.02

time (sec)

N/A 0.432 0.043 0.890 0.000 0.000 0.000 0.000 0.939

Problem 9

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

32 32 41 59 33 26 37 42 37

N.S.

1 1.00 1.28 1.84 1.03 0.81 1.16 1.31 1.16

time (sec)

N/A 0.203 0.029 0.352 0.181 0.281 0.375 0.297 0.785

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 64 66 96 83 40 121 66 50

N.S.

1 1.25 1.29 1.88 1.63 0.78 2.37 1.29 0.98

time (sec)

N/A 0.231 0.035 0.372 0.274 0.278 1.787 0.286 0.901

Problem 11

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

60 65 59 71 58 39 112 87 0

N.S.

1 1.08 0.98 1.18 0.97 0.65 1.87 1.45 0.00

time (sec)

N/A 0.242 0.056 0.352 0.184 0.268 1.510 0.276 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 96 78 138 125 53 194 117 0

N.S.

1 1.26 1.03 1.82 1.64 0.70 2.55 1.54 0.00

time (sec)

N/A 0.251 0.050 0.359 0.271 0.270 3.458 0.277 0.000

Problem 13

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

82 86 69 79 76 50 158 149 0

N.S.

1 1.05 0.84 0.96 0.93 0.61 1.93 1.82 0.00

time (sec)

N/A 0.255 0.066 0.329 0.182 0.279 3.601 0.303 0.000

Problem 14

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

101 128 88 174 165 63 243 174 0

N.S.

1 1.27 0.87 1.72 1.63 0.62 2.41 1.72 0.00

time (sec)

N/A 0.274 0.079 0.361 0.274 0.284 8.632 0.283 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 116 124 170 197 146 0 811 0

N.S.

1 1.08 1.16 1.59 1.84 1.36 0.00 7.58 0.00

time (sec)

N/A 0.518 0.137 1.028 0.426 0.296 0.000 0.429 0.000

Problem 16

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

139 133 213 268 0 0 0 0 0

N.S.

1 0.96 1.53 1.93 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.545 0.997 1.439 0.000 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 65 89 122 84 111 0 427 0

N.S.

1 1.18 1.62 2.22 1.53 2.02 0.00 7.76 0.00

time (sec)

N/A 0.394 0.166 1.007 0.190 0.287 0.000 0.350 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

84 81 147 176 0 0 0 0 0

N.S.

1 0.96 1.75 2.10 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.400 0.197 0.752 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 B F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 105 137 338 0 0 0 0 0

N.S.

1 1.15 1.51 3.71 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.527 0.107 1.091 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 57 71 115 79 57 0 104 88

N.S.

1 1.14 1.42 2.30 1.58 1.14 0.00 2.08 1.76

time (sec)

N/A 0.368 0.102 0.761 0.191 0.260 0.000 0.296 1.012

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 90 102 184 0 82 0 163 0

N.S.

1 1.02 1.16 2.09 0.00 0.93 0.00 1.85 0.00

time (sec)

N/A 0.338 0.078 0.589 0.000 0.259 0.000 0.301 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 112 108 153 197 93 0 224 0

N.S.

1 1.10 1.06 1.50 1.93 0.91 0.00 2.20 0.00

time (sec)

N/A 0.479 0.156 1.345 0.455 0.265 0.000 0.287 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 140 148 265 0 120 0 304 0

N.S.

1 1.04 1.10 1.98 0.00 0.90 0.00 2.27 0.00

time (sec)

N/A 0.434 0.119 1.270 0.000 0.259 0.000 0.301 0.000

Problem 24

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

207 215 285 417 0 0 0 0 0

N.S.

1 1.04 1.38 2.01 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.843 0.704 1.561 0.000 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

220 214 580 535 0 0 0 0 0

N.S.

1 0.97 2.64 2.43 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.819 7.394 1.897 0.000 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 134 182 303 0 0 0 0 0

N.S.

1 1.06 1.44 2.40 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.601 0.469 1.589 0.000 0.000 0.000 0.000 0.000

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

144 137 265 378 0 0 0 0 0

N.S.

1 0.95 1.84 2.62 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.563 0.281 1.155 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 B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 141 242 608 0 0 0 0 0

N.S.

1 1.14 1.95 4.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.670 0.154 1.204 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 B A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 86 135 197 147 98 0 195 155

N.S.

1 1.08 1.69 2.46 1.84 1.22 0.00 2.44 1.94

time (sec)

N/A 0.471 0.135 0.890 0.198 0.259 0.000 0.318 1.023

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 142 186 318 0 150 0 302 0

N.S.

1 1.14 1.49 2.54 0.00 1.20 0.00 2.42 0.00

time (sec)

N/A 0.418 0.156 1.072 0.000 0.270 0.000 0.316 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 189 204 299 0 173 0 428 0

N.S.

1 1.11 1.20 1.76 0.00 1.02 0.00 2.52 0.00

time (sec)

N/A 0.718 0.196 1.513 0.000 0.280 0.000 0.314 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

208 269 283 479 0 225 0 576 0

N.S.

1 1.29 1.36 2.30 0.00 1.08 0.00 2.77 0.00

time (sec)

N/A 0.753 0.229 1.655 0.000 0.267 0.000 0.315 0.000

Problem 33

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 14 10 14 18

N.S.

1 1.00 1.17 1.00 1.17 1.17 0.83 1.17 1.50

time (sec)

N/A 0.178 2.624 0.842 0.268 0.255 0.358 33.774 0.787

Problem 34

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 16

N.S.

1 1.00 1.20 1.00 1.20 1.20 1.00 1.20 1.60

time (sec)

N/A 0.179 2.557 0.590 0.294 0.245 0.400 11.266 0.790

Problem 35

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

14 14 16 14 16 15 12 16 20

N.S.

1 1.00 1.14 1.00 1.14 1.07 0.86 1.14 1.43

time (sec)

N/A 0.183 0.236 0.505 0.290 0.275 0.873 1.776 0.841

Problem 36

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

47 46 43 48 0 0 0 54 0

N.S.

1 0.98 0.91 1.02 0.00 0.00 0.00 1.15 0.00

time (sec)

N/A 0.440 0.061 0.593 0.000 0.000 0.000 0.282 0.000

Problem 37

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

63 59 56 58 0 0 0 95 0

N.S.

1 0.94 0.89 0.92 0.00 0.00 0.00 1.51 0.00

time (sec)

N/A 0.519 0.059 0.503 0.000 0.000 0.000 0.289 0.000

Problem 38

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

117 110 91 102 0 0 0 200 0

N.S.

1 0.94 0.78 0.87 0.00 0.00 0.00 1.71 0.00

time (sec)

N/A 0.499 0.139 0.508 0.000 0.000 0.000 0.287 0.000

Problem 39

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

16 16 18 16 1279 44 15 18 22

N.S.

1 1.00 1.12 1.00 79.94 2.75 0.94 1.12 1.38

time (sec)

N/A 0.198 4.271 0.862 15.475 0.286 21.443 0.883 1.086

Problem 40

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

16 16 18 16 551 30 15 18 22

N.S.

1 1.00 1.12 1.00 34.44 1.88 0.94 1.12 1.38

time (sec)

N/A 0.201 2.799 0.828 6.868 0.273 9.777 0.614 1.119

Problem 41

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

66 66 83 0 0 0 0 0 0

N.S.

1 1.00 1.26 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.264 0.139 0.000 0.000 0.000 0.000 0.000 0.000

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

16 16 18 16 18 18 14 18 22

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.88 1.12 1.38

time (sec)

N/A 0.206 0.662 3.506 0.313 0.261 1.137 0.963 0.788

Problem 43

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

16 16 18 16 684 32 15 18 22

N.S.

1 1.00 1.12 1.00 42.75 2.00 0.94 1.12 1.38

time (sec)

N/A 0.203 1.392 1.998 1.740 0.273 5.312 1.732 0.819

Problem 44

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

167 168 165 401 269 290 362 1130 0

N.S.

1 1.01 0.99 2.40 1.61 1.74 2.17 6.77 0.00

time (sec)

N/A 0.796 0.170 0.630 0.198 0.388 3.977 2.480 0.000

Problem 45

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

123 130 122 304 198 209 228 602 0

N.S.

1 1.06 0.99 2.47 1.61 1.70 1.85 4.89 0.00

time (sec)

N/A 0.547 0.110 0.570 0.199 0.329 3.402 2.191 0.000

Problem 46

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

83 87 113 110 92 129 104 341 0

N.S.

1 1.05 1.36 1.33 1.11 1.55 1.25 4.11 0.00

time (sec)

N/A 0.366 0.138 0.483 0.213 0.289 2.280 0.444 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 58 37 53 64 32 62 33

N.S.

1 1.00 1.87 1.19 1.71 2.06 1.03 2.00 1.06

time (sec)

N/A 0.182 0.030 0.163 0.217 0.276 1.168 0.283 0.002

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

257 257 411 868 0 0 0 0 0

N.S.

1 1.00 1.60 3.38 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.741 0.494 3.599 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 110 141 192 0 475 0 0 0

N.S.

1 1.08 1.38 1.88 0.00 4.66 0.00 0.00 0.00

time (sec)

N/A 0.377 0.150 3.020 0.000 0.330 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 199 250 573 0 1111 0 0 0

N.S.

1 1.16 1.45 3.33 0.00 6.46 0.00 0.00 0.00

time (sec)

N/A 0.489 0.312 3.244 0.000 0.558 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

496 547 870 1204 0 0 0 0 0

N.S.

1 1.10 1.75 2.43 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.515 44.493 12.327 0.000 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

404 473 368 826 0 0 0 0 0

N.S.

1 1.17 0.91 2.04 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.183 12.419 9.987 0.000 0.000 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

315 350 657 386 0 0 0 0 0

N.S.

1 1.11 2.09 1.23 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.872 32.090 8.517 0.000 0.000 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 23 19 73 21 0 21 25

N.S.

1 1.00 1.10 0.90 3.48 1.00 0.00 1.00 1.19

time (sec)

N/A 0.247 38.504 0.716 0.689 0.255 0.000 1.133 0.909

Problem 55

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

21 21 23 19 88 21 20 21 25

N.S.

1 1.00 1.10 0.90 4.19 1.00 0.95 1.00 1.19

time (sec)

N/A 0.251 5.295 0.582 0.676 0.271 22.263 1.148 0.871

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

372 396 333 798 0 0 0 0 0

N.S.

1 1.06 0.90 2.15 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.022 12.335 9.266 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

714 489 873 1233 0 0 0 0 0

N.S.

1 0.68 1.22 1.73 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.348 33.902 10.845 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

530 414 784 850 0 0 0 0 0

N.S.

1 0.78 1.48 1.60 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.865 34.012 9.159 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

344 276 383 410 0 0 0 0 0

N.S.

1 0.80 1.11 1.19 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.643 0.911 8.052 0.000 0.000 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

212 237 243 252 0 0 0 0 0

N.S.

1 1.12 1.15 1.19 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.575 5.235 3.325 0.000 0.000 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 23 19 67 29 0 21 25

N.S.

1 1.00 1.10 0.90 3.19 1.38 0.00 1.00 1.19

time (sec)

N/A 0.255 3.686 0.681 0.904 0.265 0.000 0.679 0.865

Problem 62

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

21 21 23 19 89 31 20 21 25

N.S.

1 1.00 1.10 0.90 4.24 1.48 0.95 1.00 1.19

time (sec)

N/A 0.253 6.466 0.630 0.638 0.269 19.500 0.701 0.865

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

551 393 814 880 0 0 0 0 0

N.S.

1 0.71 1.48 1.60 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.041 34.378 10.080 0.000 0.000 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

369 318 750 439 0 0 0 0 0

N.S.

1 0.86 2.03 1.19 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.754 34.083 9.296 0.000 0.000 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

238 225 226 280 0 0 0 0 0

N.S.

1 0.95 0.95 1.18 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.532 12.570 6.606 0.000 0.000 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 137 124 215 0 0 0 0 0

N.S.

1 1.15 1.04 1.81 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.439 0.198 3.235 0.000 0.000 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 23 19 97 40 0 21 25

N.S.

1 1.00 1.10 0.90 4.62 1.90 0.00 1.00 1.19

time (sec)

N/A 0.258 11.987 0.783 0.697 0.290 0.000 0.684 0.890

Problem 68

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

21 21 23 19 145 42 20 21 25

N.S.

1 1.00 1.10 0.90 6.90 2.00 0.95 1.00 1.19

time (sec)

N/A 0.269 15.768 0.834 0.703 0.274 84.989 0.696 0.913

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

602 559 887 1067 0 0 0 0 0

N.S.

1 0.93 1.47 1.77 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.543 34.213 9.564 0.000 0.000 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

440 517 856 1026 0 0 0 0 0

N.S.

1 1.18 1.95 2.33 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.204 34.074 9.030 0.000 0.000 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

314 413 345 900 0 0 0 0 0

N.S.

1 1.32 1.10 2.87 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.002 12.464 9.512 0.000 0.000 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

298 320 608 875 0 0 0 0 0

N.S.

1 1.07 2.04 2.94 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.740 21.287 7.162 0.000 0.000 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 23 19 177 51 0 21 25

N.S.

1 1.00 1.10 0.90 8.43 2.43 0.00 1.00 1.19

time (sec)

N/A 0.266 30.013 0.907 0.780 0.265 0.000 0.695 0.900

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 23 19 179 53 0 21 25

N.S.

1 1.00 1.10 0.90 8.52 2.52 0.00 1.00 1.19

time (sec)

N/A 0.284 27.563 0.869 0.760 0.260 0.000 0.696 0.912

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

540 516 1002 1618 0 0 0 0 0

N.S.

1 0.96 1.86 3.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.112 34.051 9.336 0.000 0.000 0.000 0.000 0.000

Problem 76

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

206 167 140 328 296 191 408 1166 0

N.S.

1 0.81 0.68 1.59 1.44 0.93 1.98 5.66 0.00

time (sec)

N/A 0.355 0.164 0.629 0.197 0.374 10.788 1.665 0.000

Problem 77

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

161 136 121 254 232 170 294 822 0

N.S.

1 0.84 0.75 1.58 1.44 1.06 1.83 5.11 0.00

time (sec)

N/A 0.323 0.130 0.630 0.198 0.341 4.328 1.162 0.000

Problem 78

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

109 101 149 132 153 141 153 473 0

N.S.

1 0.93 1.37 1.21 1.40 1.29 1.40 4.34 0.00

time (sec)

N/A 0.266 0.169 0.314 0.196 0.325 3.234 0.943 0.000

Problem 79

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

87 84 104 116 89 125 73 1052 75

N.S.

1 0.97 1.20 1.33 1.02 1.44 0.84 12.09 0.86

time (sec)

N/A 0.279 0.096 0.329 0.197 0.297 2.705 0.565 1.089

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

105 101 69 108 94 66 151 136 0

N.S.

1 0.96 0.66 1.03 0.90 0.63 1.44 1.30 0.00

time (sec)

N/A 0.286 0.088 0.322 0.215 0.283 2.118 0.303 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

152 131 94 127 137 88 280 245 0

N.S.

1 0.86 0.62 0.84 0.90 0.58 1.84 1.61 0.00

time (sec)

N/A 0.304 0.138 0.327 0.192 0.280 4.492 0.292 0.000

Problem 82

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

197 159 110 145 172 109 372 367 0

N.S.

1 0.81 0.56 0.74 0.87 0.55 1.89 1.86 0.00

time (sec)

N/A 0.339 0.133 0.352 0.183 0.285 29.200 0.292 0.000

Problem 83

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

196 161 115 139 183 127 364 1244 0

N.S.

1 0.82 0.59 0.71 0.93 0.65 1.86 6.35 0.00

time (sec)

N/A 0.374 0.173 0.637 0.185 0.309 3.857 0.426 0.000

Problem 84

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

153 131 97 121 142 106 272 900 0

N.S.

1 0.86 0.63 0.79 0.93 0.69 1.78 5.88 0.00

time (sec)

N/A 0.346 0.161 0.722 0.211 0.305 2.408 0.339 0.000

Problem 85

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

138 116 78 217 98 85 177 556 0

N.S.

1 0.84 0.57 1.57 0.71 0.62 1.28 4.03 0.00

time (sec)

N/A 0.317 0.101 0.738 0.212 0.294 1.579 0.328 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 152 108 190 0 0 0 0 111

N.S.

1 1.23 0.87 1.53 0.00 0.00 0.00 0.00 0.90

time (sec)

N/A 0.652 0.082 2.043 0.000 0.000 0.000 0.000 1.235

Problem 87

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

137 175 125 191 0 0 0 0 124

N.S.

1 1.28 0.91 1.39 0.00 0.00 0.00 0.00 0.91

time (sec)

N/A 0.683 0.088 2.759 0.000 0.000 0.000 0.000 1.161

Problem 88

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

252 215 184 459 404 273 542 1579 0

N.S.

1 0.85 0.73 1.82 1.60 1.08 2.15 6.27 0.00

time (sec)

N/A 0.452 0.231 0.974 0.228 0.458 11.857 5.134 0.000

Problem 89

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

191 179 151 339 296 237 355 1033 0

N.S.

1 0.94 0.79 1.77 1.55 1.24 1.86 5.41 0.00

time (sec)

N/A 0.375 0.144 0.511 0.221 0.396 5.950 3.505 0.000

Problem 90

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

163 146 134 250 197 232 207 2502 0

N.S.

1 0.90 0.82 1.53 1.21 1.42 1.27 15.35 0.00

time (sec)

N/A 0.374 0.124 0.521 0.212 0.338 4.362 2.318 0.000

Problem 91

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

157 147 125 230 158 222 211 4288 0

N.S.

1 0.94 0.80 1.46 1.01 1.41 1.34 27.31 0.00

time (sec)

N/A 0.387 0.175 0.469 0.224 0.321 4.024 98.895 0.000

Problem 92

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

183 171 127 175 181 126 335 314 0

N.S.

1 0.93 0.69 0.96 0.99 0.69 1.83 1.72 0.00

time (sec)

N/A 0.398 0.176 0.502 0.215 0.276 5.190 0.297 0.000

Problem 93

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

241 201 153 207 241 158 510 491 0

N.S.

1 0.83 0.63 0.86 1.00 0.66 2.12 2.04 0.00

time (sec)

N/A 0.437 0.165 0.534 0.218 0.283 30.569 0.303 0.000

Problem 94

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

242 207 159 198 253 186 493 1706 0

N.S.

1 0.86 0.66 0.82 1.05 0.77 2.04 7.05 0.00

time (sec)

N/A 0.485 0.202 1.046 0.214 0.336 4.391 0.450 0.000

Problem 95

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

195 160 124 352 189 152 352 1160 0

N.S.

1 0.82 0.64 1.81 0.97 0.78 1.81 5.95 0.00

time (sec)

N/A 0.379 0.172 0.972 0.210 0.308 2.782 0.392 0.000

Problem 96

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

186 217 157 288 0 0 0 0 0

N.S.

1 1.17 0.84 1.55 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.820 0.283 3.061 0.000 0.000 0.000 0.000 0.000

Problem 97

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

189 228 194 274 0 0 0 0 0

N.S.

1 1.21 1.03 1.45 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.817 0.504 4.461 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

565 617 1260 415 0 0 0 0 0

N.S.

1 1.09 2.23 0.73 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.646 1.823 44.193 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

507 567 1123 394 0 0 0 0 0

N.S.

1 1.12 2.21 0.78 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.523 0.451 4.277 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 B C F(-2) F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

529 577 1068 272 0 0 0 0 0

N.S.

1 1.09 2.02 0.51 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.358 0.450 24.994 0.000 0.000 0.000 0.000 0.000

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