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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

114 122 107 177 162 116 221 8644 0

N.S.

1 1.07 0.94 1.55 1.42 1.02 1.94 75.82 0.00

time (sec)

N/A 0.263 0.107 0.330 0.206 0.283 8.733 1.120 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 81 63 153 3862 0

N.S.

1 1.09 0.81 0.89 0.91 0.71 1.72 43.39 0.00

time (sec)

N/A 0.257 0.073 0.239 0.203 0.283 2.034 0.321 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 97 141 131 107 175 4828 0

N.S.

1 1.04 1.09 1.58 1.47 1.20 1.97 54.25 0.00

time (sec)

N/A 0.248 0.058 0.260 0.202 0.287 3.422 0.791 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 60 53 107 1926 0

N.S.

1 1.06 0.97 1.09 0.94 0.83 1.67 30.09 0.00

time (sec)

N/A 0.224 0.086 0.298 0.203 0.269 1.275 0.315 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 98 94 107 2101 0

N.S.

1 1.00 1.33 1.47 1.53 1.47 1.67 32.83 0.00

time (sec)

N/A 0.224 0.055 0.242 0.204 0.286 1.796 0.590 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 37 40 58 634 40

N.S.

1 1.00 1.28 1.56 0.95 1.03 1.49 16.26 1.03

time (sec)

N/A 0.189 0.025 0.247 0.215 0.269 0.810 0.287 0.779

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

32 32 59 38 53 63 32 63 34

N.S.

1 1.00 1.84 1.19 1.66 1.97 1.00 1.97 1.06

time (sec)

N/A 0.173 0.041 0.112 0.228 0.280 1.205 0.277 0.987

Problem 8

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

64 87 59 84 0 0 0 0 0

N.S.

1 1.36 0.92 1.31 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.425 0.020 0.618 0.000 0.000 0.000 0.000 0.000

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

31 31 40 58 33 27 36 43 36

N.S.

1 1.00 1.29 1.87 1.06 0.87 1.16 1.39 1.16

time (sec)

N/A 0.202 0.028 0.193 0.217 0.263 0.361 0.298 0.756

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 95 83 39 119 58 50

N.S.

1 1.25 1.29 1.86 1.63 0.76 2.33 1.14 0.98

time (sec)

N/A 0.228 0.036 0.243 0.314 0.254 1.854 0.280 0.825

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 40 110 65 0

N.S.

1 1.08 0.98 1.18 0.97 0.67 1.83 1.08 0.00

time (sec)

N/A 0.245 0.044 0.250 0.187 0.253 1.509 0.283 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 52 192 83 0

N.S.

1 1.26 1.03 1.82 1.64 0.68 2.53 1.09 0.00

time (sec)

N/A 0.249 0.056 0.240 0.279 0.258 3.407 0.284 0.000

Problem 13

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 86 69 79 76 51 156 87 0

N.S.

1 1.05 0.84 0.96 0.93 0.62 1.90 1.06 0.00

time (sec)

N/A 0.258 0.057 0.244 0.191 0.269 3.601 0.289 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

101 128 88 174 165 62 241 104 0

N.S.

1 1.27 0.87 1.72 1.63 0.61 2.39 1.03 0.00

time (sec)

N/A 0.277 0.068 0.313 0.272 0.254 8.615 0.287 0.000

Problem 15

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

107 114 124 170 163 146 0 6625 0

N.S.

1 1.07 1.16 1.59 1.52 1.36 0.00 61.92 0.00

time (sec)

N/A 0.531 0.151 0.710 0.466 0.298 0.000 0.608 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

147 140 226 285 0 0 0 0 0

N.S.

1 0.95 1.54 1.94 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.539 0.943 1.174 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

56 64 90 123 87 111 0 2181 0

N.S.

1 1.14 1.61 2.20 1.55 1.98 0.00 38.95 0.00

time (sec)

N/A 0.400 0.195 0.674 0.200 0.283 0.000 0.447 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

92 87 163 194 0 0 0 0 0

N.S.

1 0.95 1.77 2.11 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.396 0.179 0.500 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 F F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 107 129 206 0 0 0 0 0

N.S.

1 1.15 1.39 2.22 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.524 0.103 0.773 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 56 75 114 78 57 0 105 89

N.S.

1 1.12 1.50 2.28 1.56 1.14 0.00 2.10 1.78

time (sec)

N/A 0.371 0.097 0.555 0.203 0.274 0.000 0.293 0.917

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 97 102 177 0 82 0 147 0

N.S.

1 1.03 1.09 1.88 0.00 0.87 0.00 1.56 0.00

time (sec)

N/A 0.334 0.083 0.494 0.000 0.257 0.000 0.308 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 110 108 153 164 93 0 168 0

N.S.

1 1.08 1.06 1.50 1.61 0.91 0.00 1.65 0.00

time (sec)

N/A 0.486 0.126 0.903 0.455 0.276 0.000 0.299 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 139 148 265 0 120 0 215 0

N.S.

1 1.04 1.10 1.98 0.00 0.90 0.00 1.60 0.00

time (sec)

N/A 0.441 0.119 0.819 0.000 0.283 0.000 0.297 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

207 213 288 365 0 0 0 0 0

N.S.

1 1.03 1.39 1.76 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.853 0.595 1.158 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 A B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

236 227 403 574 0 0 0 0 0

N.S.

1 0.96 1.71 2.43 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.841 1.178 1.438 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 A F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 132 184 252 0 0 0 0 0

N.S.

1 1.05 1.46 2.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.593 0.478 1.096 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 F F F F F F(-1)

verified

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

size

158 149 289 0 0 0 0 0 0

N.S.

1 0.94 1.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.572 0.247 0.000 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

128 145 204 364 0 0 0 0 0

N.S.

1 1.13 1.59 2.84 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.645 0.141 0.859 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 86 141 196 146 98 0 196 156

N.S.

1 1.08 1.76 2.45 1.82 1.22 0.00 2.45 1.95

time (sec)

N/A 0.468 0.133 0.685 0.200 0.286 0.000 0.311 0.964

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

137 149 185 293 0 150 0 278 0

N.S.

1 1.09 1.35 2.14 0.00 1.09 0.00 2.03 0.00

time (sec)

N/A 0.430 0.144 0.806 0.000 0.271 0.000 0.304 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 189 204 299 575 172 0 336 0

N.S.

1 1.11 1.20 1.76 3.38 1.01 0.00 1.98 0.00

time (sec)

N/A 0.737 0.206 1.156 0.703 0.275 0.000 0.324 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

208 268 283 470 0 225 0 427 0

N.S.

1 1.29 1.36 2.26 0.00 1.08 0.00 2.05 0.00

time (sec)

N/A 0.772 0.229 1.095 0.000 0.283 0.000 0.314 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 0.182 2.467 0.708 0.304 0.264 0.374 33.763 0.743

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 0.173 0.024 0.413 0.305 0.259 0.386 11.353 0.720

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 0.192 0.240 0.342 0.327 0.251 0.901 1.689 0.788

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

46 46 43 47 0 0 0 55 0

N.S.

1 1.00 0.93 1.02 0.00 0.00 0.00 1.20 0.00

time (sec)

N/A 0.449 0.067 0.451 0.000 0.000 0.000 0.286 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 0.505 0.059 0.372 0.000 0.000 0.000 0.275 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

117 109 91 102 0 0 0 199 0

N.S.

1 0.93 0.78 0.87 0.00 0.00 0.00 1.70 0.00

time (sec)

N/A 0.464 0.148 0.368 0.000 0.000 0.000 0.288 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

12 12 14 12 583 28 12 14 18

N.S.

1 1.00 1.17 1.00 48.58 2.33 1.00 1.17 1.50

time (sec)

N/A 0.187 11.915 0.561 0.954 0.265 0.927 105.842 0.781

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

10 10 12 10 577 26 12 12 16

N.S.

1 1.00 1.20 1.00 57.70 2.60 1.20 1.20 1.60

time (sec)

N/A 0.171 23.964 0.504 0.951 0.254 0.999 23.495 0.743

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

14 14 16 14 560 30 14 16 20

N.S.

1 1.00 1.14 1.00 40.00 2.14 1.00 1.14 1.43

time (sec)

N/A 0.190 3.274 0.400 0.826 0.277 1.839 4.042 0.822

Problem 42

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

75 79 69 78 0 0 0 226 0

N.S.

1 1.05 0.92 1.04 0.00 0.00 0.00 3.01 0.00

time (sec)

N/A 0.537 0.263 0.408 0.000 0.000 0.000 0.281 0.000

Problem 43

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

84 86 80 77 0 0 0 357 0

N.S.

1 1.02 0.95 0.92 0.00 0.00 0.00 4.25 0.00

time (sec)

N/A 0.617 0.326 0.371 0.000 0.000 0.000 0.272 0.000

Problem 44

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

178 164 223 153 0 0 0 694 0

N.S.

1 0.92 1.25 0.86 0.00 0.00 0.00 3.90 0.00

time (sec)

N/A 0.541 0.599 0.373 0.000 0.000 0.000 0.304 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 14 12 1790 42 12 0 18

N.S.

1 1.00 1.17 1.00 149.17 3.50 1.00 0.00 1.50

time (sec)

N/A 0.171 2.736 0.603 29.312 0.253 1.942 0.000 0.788

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

10 10 12 10 1744 40 12 12 16

N.S.

1 1.00 1.20 1.00 174.40 4.00 1.20 1.20 1.60

time (sec)

N/A 0.166 9.570 0.575 28.499 0.251 2.032 52.479 0.754

Problem 47

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 1568 45 14 16 20

N.S.

1 1.00 1.14 1.00 112.00 3.21 1.00 1.14 1.43

time (sec)

N/A 0.185 1.368 0.507 21.865 0.256 3.576 7.963 0.833

Problem 48

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

103 112 88 154 0 0 0 580 0

N.S.

1 1.09 0.85 1.50 0.00 0.00 0.00 5.63 0.00

time (sec)

N/A 0.658 0.299 0.468 0.000 0.000 0.000 0.311 0.000

Problem 49

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

112 116 114 157 0 0 0 929 0

N.S.

1 1.04 1.02 1.40 0.00 0.00 0.00 8.29 0.00

time (sec)

N/A 0.748 0.315 0.398 0.000 0.000 0.000 0.298 0.000

Problem 50

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

228 211 169 307 0 0 0 1640 0

N.S.

1 0.93 0.74 1.35 0.00 0.00 0.00 7.19 0.00

time (sec)

N/A 0.566 0.371 0.393 0.000 0.000 0.000 0.306 0.000

Problem 51

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 16 991 44 15 18 22

N.S.

1 1.00 1.12 1.00 61.94 2.75 0.94 1.12 1.38

time (sec)

N/A 0.180 4.374 0.760 14.782 0.287 22.090 0.803 1.069

Problem 52

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 16 512 30 15 18 22

N.S.

1 1.00 1.12 1.00 32.00 1.88 0.94 1.12 1.38

time (sec)

N/A 0.182 2.770 0.612 6.847 0.274 10.072 0.577 1.075

Problem 53

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

67 67 82 0 0 0 0 0 0

N.S.

1 1.00 1.22 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.242 0.200 0.000 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 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 0.194 0.725 1.937 0.359 0.249 1.121 0.940 0.723

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

16 16 18 16 643 32 15 18 22

N.S.

1 1.00 1.12 1.00 40.19 2.00 0.94 1.12 1.38

time (sec)

N/A 0.195 1.430 1.370 1.900 0.258 5.312 1.654 0.716

Problem 56

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

167 168 166 402 272 291 362 9430 0

N.S.

1 1.01 0.99 2.41 1.63 1.74 2.17 56.47 0.00

time (sec)

N/A 0.757 0.181 0.391 0.239 0.376 3.941 3.068 0.000

Problem 57

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

124 130 124 306 200 209 228 6416 0

N.S.

1 1.05 1.00 2.47 1.61 1.69 1.84 51.74 0.00

time (sec)

N/A 0.531 0.113 0.385 0.242 0.316 3.528 2.894 0.000

Problem 58

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

84 87 114 110 93 130 104 1547 77

N.S.

1 1.04 1.36 1.31 1.11 1.55 1.24 18.42 0.92

time (sec)

N/A 0.368 0.146 0.316 0.219 0.315 2.286 0.528 0.984

Problem 59

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

32 32 59 38 53 63 32 63 34

N.S.

1 1.00 1.84 1.19 1.66 1.97 1.00 1.97 1.06

time (sec)

N/A 0.177 0.029 0.090 0.224 0.275 1.188 0.285 0.982

Problem 60

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

247 247 333 453 0 0 0 0 0

N.S.

1 1.00 1.35 1.83 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.718 0.453 2.082 0.000 0.000 0.000 0.000 0.000

Problem 61

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

104 111 142 193 0 477 0 0 0

N.S.

1 1.07 1.37 1.86 0.00 4.59 0.00 0.00 0.00

time (sec)

N/A 0.370 0.139 2.190 0.000 0.308 0.000 0.000 0.000

Problem 62

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

172 199 247 574 0 1117 0 0 0

N.S.

1 1.16 1.44 3.34 0.00 6.49 0.00 0.00 0.00

time (sec)

N/A 0.504 0.316 2.069 0.000 0.546 0.000 0.000 0.000

Problem 63

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 1.028 12.350 9.077 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 F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

315 350 277 386 0 0 0 0 0

N.S.

1 1.11 0.88 1.23 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.849 33.340 7.735 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

212 237 212 252 0 0 0 0 0

N.S.

1 1.12 1.00 1.19 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.593 16.108 5.207 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 0.436 0.212 3.125 0.000 0.000 0.000 0.000 0.000

Problem 67

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

298 320 326 875 0 0 0 0 0

N.S.

1 1.07 1.09 2.94 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.721 30.378 7.329 0.000 0.000 0.000 0.000 0.000

Problem 68

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

540 516 407 1618 0 0 0 0 0

N.S.

1 0.96 0.75 3.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.074 33.621 8.780 0.000 0.000 0.000 0.000 0.000

Problem 69

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

206 167 141 328 296 192 408 17474 0

N.S.

1 0.81 0.68 1.59 1.44 0.93 1.98 84.83 0.00

time (sec)

N/A 0.341 0.176 0.658 0.230 0.379 10.861 2.764 0.000

Problem 70

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

161 136 123 254 232 170 294 9792 0

N.S.

1 0.84 0.76 1.58 1.44 1.06 1.83 60.82 0.00

time (sec)

N/A 0.316 0.131 0.603 0.205 0.335 4.376 1.928 0.000

Problem 71

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

109 101 150 132 154 141 153 4051 0

N.S.

1 0.93 1.38 1.21 1.41 1.29 1.40 37.17 0.00

time (sec)

N/A 0.264 0.180 0.313 0.194 0.309 3.220 1.280 0.000

Problem 72

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 83 104 116 89 123 73 1088 72

N.S.

1 0.95 1.20 1.33 1.02 1.41 0.84 12.51 0.83

time (sec)

N/A 0.278 0.100 0.326 0.221 0.298 2.723 0.631 0.951

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 101 69 108 94 67 150 113 0

N.S.

1 0.96 0.66 1.03 0.90 0.64 1.43 1.08 0.00

time (sec)

N/A 0.281 0.086 0.308 0.200 0.273 2.108 0.286 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 131 94 127 137 89 279 158 0

N.S.

1 0.86 0.62 0.84 0.90 0.59 1.84 1.04 0.00

time (sec)

N/A 0.304 0.101 0.310 0.198 0.281 4.696 0.288 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 159 110 145 172 110 371 202 0

N.S.

1 0.81 0.56 0.74 0.87 0.56 1.88 1.03 0.00

time (sec)

N/A 0.324 0.128 0.329 0.212 0.271 29.280 0.292 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

196 161 118 139 185 128 364 13018 0

N.S.

1 0.82 0.60 0.71 0.94 0.65 1.86 66.42 0.00

time (sec)

N/A 0.368 0.190 0.622 0.210 0.317 4.036 0.470 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

153 131 98 121 144 107 272 7820 0

N.S.

1 0.86 0.64 0.79 0.94 0.70 1.78 51.11 0.00

time (sec)

N/A 0.340 0.212 0.639 0.194 0.276 2.459 0.367 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

138 116 79 217 100 86 177 3346 0

N.S.

1 0.84 0.57 1.57 0.72 0.62 1.28 24.25 0.00

time (sec)

N/A 0.307 0.089 0.722 0.196 0.283 1.595 0.334 0.000

Problem 79

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

124 152 115 137 0 0 0 0 0

N.S.

1 1.23 0.93 1.10 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.654 0.074 1.855 0.000 0.000 0.000 0.000 0.000

Problem 80

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

137 175 132 143 0 0 0 0 0

N.S.

1 1.28 0.96 1.04 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.644 0.090 1.528 0.000 0.000 0.000 0.000 0.000

Problem 81

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

252 215 186 459 405 273 542 4760 0

N.S.

1 0.85 0.74 1.82 1.61 1.08 2.15 18.89 0.00

time (sec)

N/A 0.449 0.226 0.773 0.244 0.473 11.903 6.385 0.000

Problem 82

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

191 179 153 340 296 237 355 14166 0

N.S.

1 0.94 0.80 1.78 1.55 1.24 1.86 74.17 0.00

time (sec)

N/A 0.361 0.145 0.421 0.230 0.389 5.834 4.602 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

162 146 136 249 198 230 207 6018 0

N.S.

1 0.90 0.84 1.54 1.22 1.42 1.28 37.15 0.00

time (sec)

N/A 0.378 0.129 0.447 0.196 0.351 4.358 2.472 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

158 147 127 231 159 221 211 4968 0

N.S.

1 0.93 0.80 1.46 1.01 1.40 1.34 31.44 0.00

time (sec)

N/A 0.379 0.144 0.421 0.207 0.321 4.017 99.042 0.000

Problem 85

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

183 171 127 175 181 127 333 222 0

N.S.

1 0.93 0.69 0.96 0.99 0.69 1.82 1.21 0.00

time (sec)

N/A 0.396 0.157 0.456 0.203 0.295 5.191 0.306 0.000

Problem 86

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

241 201 153 207 241 159 508 293 0

N.S.

1 0.83 0.63 0.86 1.00 0.66 2.11 1.22 0.00

time (sec)

N/A 0.411 0.174 0.488 0.202 0.278 30.110 0.301 0.000

Problem 87

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

242 207 162 198 256 187 493 17666 0

N.S.

1 0.86 0.67 0.82 1.06 0.77 2.04 73.00 0.00

time (sec)

N/A 0.473 0.188 0.824 0.199 0.319 4.378 0.502 0.000

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

195 160 125 352 192 153 352 11858 0

N.S.

1 0.82 0.64 1.81 0.98 0.78 1.81 60.81 0.00

time (sec)

N/A 0.363 0.192 0.819 0.198 0.325 2.689 0.446 0.000

Problem 89

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

186 217 160 231 0 0 0 0 0

N.S.

1 1.17 0.86 1.24 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.790 0.254 2.524 0.000 0.000 0.000 0.000 0.000

Problem 90

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

189 228 194 216 0 0 0 0 0

N.S.

1 1.21 1.03 1.14 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.804 0.649 2.418 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

546 598 1023 374 0 0 0 0 0

N.S.

1 1.10 1.87 0.68 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.597 1.883 34.293 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

487 547 891 446 0 0 0 0 0

N.S.

1 1.12 1.83 0.92 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.509 0.508 2.713 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

509 557 871 272 0 0 0 0 0

N.S.

1 1.09 1.71 0.53 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.324 0.498 16.106 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

459 511 876 1970 0 0 0 0 0

N.S.

1 1.11 1.91 4.29 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.328 0.147 2.329 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

551 603 997 331 0 0 0 0 0

N.S.

1 1.09 1.81 0.60 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.523 1.792 27.443 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

608 676 1255 701 0 0 0 0 0

N.S.

1 1.11 2.06 1.15 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.768 3.185 9.589 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 B C F F F(-1) F(-1) F(-1)

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

570 634 1213 577 0 0 0 0 0

N.S.

1 1.11 2.13 1.01 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.663 1.169 2.806 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 C B F A F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 118 286 265 0 384 0 0 0

N.S.

1 0.90 2.18 2.02 0.00 2.93 0.00 0.00 0.00

time (sec)

N/A 0.309 0.520 6.497 0.000 0.300 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(-1) F(-2) F(-1)

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

546 602 1190 2108 0 0 0 0 0

N.S.

1 1.10 2.18 3.86 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.567 0.985 9.061 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 A C F(-2) F F F(-1) F(-1)

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

784 844 1331 941 0 0 0 0 0

N.S.

1 1.08 1.70 1.20 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.938 1.804 88.106 0.000 0.000 0.000 0.000 0.000

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