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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 C C A A F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 145 88 29 126 84 184 0 0

N.S.

1 1.17 0.71 0.23 1.02 0.68 1.48 0.00 0.00

time (sec)

N/A 0.508 0.053 0.438 0.296 0.282 1.161 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 125 83 29 74 78 156 0 0

N.S.

1 1.15 0.76 0.27 0.68 0.72 1.43 0.00 0.00

time (sec)

N/A 0.597 0.043 0.399 0.211 0.256 1.028 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 113 79 29 110 85 53 0 0

N.S.

1 1.14 0.80 0.29 1.11 0.86 0.54 0.00 0.00

time (sec)

N/A 0.410 0.056 0.437 0.320 0.264 0.511 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 93 71 29 62 65 121 0 0

N.S.

1 1.11 0.85 0.35 0.74 0.77 1.44 0.00 0.00

time (sec)

N/A 0.468 0.032 0.455 0.205 0.260 1.073 0.000 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 82 74 62 94 58 112 0 0

N.S.

1 1.11 1.00 0.84 1.27 0.78 1.51 0.00 0.00

time (sec)

N/A 0.334 0.013 0.383 0.292 0.267 0.566 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 61 59 54 49 53 80 0 0

N.S.

1 1.03 1.00 0.92 0.83 0.90 1.36 0.00 0.00

time (sec)

N/A 0.351 0.010 0.408 0.262 0.258 0.528 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 50 49 29 70 51 53 0 0

N.S.

1 1.02 1.00 0.59 1.43 1.04 1.08 0.00 0.00

time (sec)

N/A 0.260 0.009 0.434 0.311 0.265 0.316 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 25 26 26 48 0 0

N.S.

1 1.00 1.00 0.96 1.00 1.00 1.85 0.00 0.00

time (sec)

N/A 0.177 0.005 0.525 0.184 0.259 0.572 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

73 73 0 29 0 0 46 0 0

N.S.

1 1.00 0.00 0.40 0.00 0.00 0.63 0.00 0.00

time (sec)

N/A 0.334 0.000 0.549 0.000 0.000 0.368 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 27 24 38 25 42 0 0

N.S.

1 1.00 1.00 0.89 1.41 0.93 1.56 0.00 0.00

time (sec)

N/A 0.219 0.010 0.444 0.278 0.265 0.360 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 42 44 27 61 45 51 0 0

N.S.

1 0.95 1.00 0.61 1.39 1.02 1.16 0.00 0.00

time (sec)

N/A 0.257 0.010 0.392 0.370 0.265 0.421 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 55 52 46 42 44 56 0 0

N.S.

1 1.06 1.00 0.88 0.81 0.85 1.08 0.00 0.00

time (sec)

N/A 0.360 0.012 0.611 0.283 0.266 0.775 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 71 69 65 61 54 110 0 0

N.S.

1 1.03 1.00 0.94 0.88 0.78 1.59 0.00 0.00

time (sec)

N/A 0.318 0.012 0.396 0.355 0.266 0.670 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 83 77 29 48 65 46 0 0

N.S.

1 1.08 1.00 0.38 0.62 0.84 0.60 0.00 0.00

time (sec)

N/A 0.451 0.016 0.467 0.274 0.265 0.682 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 98 76 29 61 80 56 0 0

N.S.

1 1.04 0.81 0.31 0.65 0.85 0.60 0.00 0.00

time (sec)

N/A 0.379 0.046 0.388 0.361 0.270 0.748 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 111 85 79 46 78 68 0 0

N.S.

1 1.09 0.83 0.77 0.45 0.76 0.67 0.00 0.00

time (sec)

N/A 0.568 0.048 0.498 0.268 0.268 2.950 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 127 84 29 61 80 185 0 0

N.S.

1 1.07 0.71 0.24 0.51 0.67 1.55 0.00 0.00

time (sec)

N/A 0.454 0.045 0.506 0.337 0.258 1.720 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 139 96 29 48 91 48 0 0

N.S.

1 1.09 0.76 0.23 0.38 0.72 0.38 0.00 0.00

time (sec)

N/A 0.692 0.129 0.454 0.276 0.275 1.584 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

296 271 424 276 0 376 0 0 0

N.S.

1 0.92 1.43 0.93 0.00 1.27 0.00 0.00 0.00

time (sec)

N/A 0.561 0.589 1.055 0.000 0.278 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 183 236 189 0 248 0 0 0

N.S.

1 0.95 1.22 0.98 0.00 1.28 0.00 0.00 0.00

time (sec)

N/A 0.445 0.344 0.911 0.000 0.271 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 115 61 109 0 132 0 0 0

N.S.

1 0.95 0.50 0.90 0.00 1.09 0.00 0.00 0.00

time (sec)

N/A 0.343 0.176 0.537 0.000 0.264 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 89 33 43 45 0 0 0

N.S.

1 1.00 2.47 0.92 1.19 1.25 0.00 0.00 0.00

time (sec)

N/A 0.185 0.026 0.493 0.189 0.241 0.000 0.000 0.000

Problem 23

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 16 12 16 16

N.S.

1 1.00 1.14 1.00 1.14 1.14 0.86 1.14 1.14

time (sec)

N/A 0.189 0.021 0.344 0.796 0.253 0.466 0.263 4.941

Problem 24

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 27 14 16 16

N.S.

1 1.00 1.14 1.00 1.14 1.93 1.00 1.14 1.14

time (sec)

N/A 0.190 2.304 0.310 0.458 0.271 0.582 0.276 4.817

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

229 197 166 189 503 175 0 0 0

N.S.

1 0.86 0.72 0.83 2.20 0.76 0.00 0.00 0.00

time (sec)

N/A 0.396 0.238 0.571 1.129 0.262 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 133 115 121 424 147 0 0 0

N.S.

1 0.90 0.78 0.82 2.88 1.00 0.00 0.00 0.00

time (sec)

N/A 0.351 0.174 0.593 0.805 0.259 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 84 51 80 307 104 0 0 0

N.S.

1 0.88 0.53 0.83 3.20 1.08 0.00 0.00 0.00

time (sec)

N/A 0.292 0.130 0.510 0.737 0.255 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 89 33 43 45 0 0 0

N.S.

1 1.00 2.47 0.92 1.19 1.25 0.00 0.00 0.00

time (sec)

N/A 0.186 0.019 0.423 0.192 0.259 0.000 0.000 0.000

Problem 29

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 0.180 0.015 0.171 0.780 0.253 0.378 0.256 4.650

Problem 30

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 0.182 1.498 0.157 0.445 0.268 0.283 0.262 4.675

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

253 0 181 0 0 183 0 0 0

N.S.

1 0.00 0.72 0.00 0.00 0.72 0.00 0.00 0.00

time (sec)

N/A 0.000 0.096 0.000 0.000 0.260 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 F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 459 171 324 0 184 0 0 0

N.S.

1 1.92 0.72 1.36 0.00 0.77 0.00 0.00 0.00

time (sec)

N/A 2.225 0.213 0.585 0.000 0.272 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

265 357 0 0 0 0 0 0 0

N.S.

1 1.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.180 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

177 292 137 208 0 149 0 0 0

N.S.

1 1.65 0.77 1.18 0.00 0.84 0.00 0.00 0.00

time (sec)

N/A 1.224 0.101 0.544 0.000 0.263 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

140 180 113 0 0 117 0 0 0

N.S.

1 1.29 0.81 0.00 0.00 0.84 0.00 0.00 0.00

time (sec)

N/A 1.037 0.038 0.000 0.000 0.259 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 169 100 122 0 111 0 0 0

N.S.

1 1.36 0.81 0.98 0.00 0.90 0.00 0.00 0.00

time (sec)

N/A 0.629 0.088 0.466 0.000 0.279 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

143 149 0 0 0 0 0 0 0

N.S.

1 1.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.511 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 61 55 49 0 60 0 0 0

N.S.

1 1.11 1.00 0.89 0.00 1.09 0.00 0.00 0.00

time (sec)

N/A 0.290 0.012 0.513 0.000 0.264 0.000 0.000 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

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 0.184 0.014 0.025 0.227 0.247 1.082 0.260 4.655

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 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 0.261 0.019 0.070 0.221 0.265 1.185 0.262 4.673

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

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 0.265 0.017 0.066 0.226 0.256 1.066 0.257 4.833

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

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 0.506 0.021 0.091 0.225 0.250 1.123 0.253 4.805

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

127 142 127 0 0 111 0 0 0

N.S.

1 1.12 1.00 0.00 0.00 0.87 0.00 0.00 0.00

time (sec)

N/A 0.881 0.005 0.000 0.000 0.261 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

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 0.951 0.021 0.075 0.214 0.257 1.401 0.259 4.802

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 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 1.407 0.016 0.068 0.214 0.259 1.327 0.261 4.848

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 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 1.629 0.025 0.066 0.221 0.261 1.618 0.257 4.746

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

242 0 242 0 0 187 0 0 0

N.S.

1 0.00 1.00 0.00 0.00 0.77 0.00 0.00 0.00

time (sec)

N/A 0.000 0.008 0.000 0.000 0.264 0.000 0.000 0.000

Problem 48

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 2.629 0.024 0.072 0.213 0.247 2.499 0.255 4.848

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

497 460 0 0 0 0 0 0 0

N.S.

1 0.93 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.561 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

279 256 0 0 0 0 0 0 0

N.S.

1 0.92 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.401 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 72 67 60 0 89 0 0 0

N.S.

1 1.03 0.96 0.86 0.00 1.27 0.00 0.00 0.00

time (sec)

N/A 0.454 0.011 0.470 0.000 0.259 0.000 0.000 0.000

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 18 18 14 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.88 1.12 1.12

time (sec)

N/A 0.205 0.027 0.189 0.222 0.249 0.422 0.263 4.877

Problem 53

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 29 15 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.81 0.94 1.12 1.12

time (sec)

N/A 0.201 0.062 0.261 0.227 0.255 0.596 0.262 4.847

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

231 257 319 0 0 448 0 0 0

N.S.

1 1.11 1.38 0.00 0.00 1.94 0.00 0.00 0.00

time (sec)

N/A 0.905 4.568 0.000 0.000 0.292 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

227 253 319 0 0 448 0 0 0

N.S.

1 1.11 1.41 0.00 0.00 1.97 0.00 0.00 0.00

time (sec)

N/A 0.834 4.337 0.000 0.000 0.279 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

214 238 316 0 0 445 0 0 0

N.S.

1 1.11 1.48 0.00 0.00 2.08 0.00 0.00 0.00

time (sec)

N/A 0.779 4.386 0.000 0.000 0.281 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 64 164 63 81 119 0 0 0

N.S.

1 0.98 2.52 0.97 1.25 1.83 0.00 0.00 0.00

time (sec)

N/A 0.283 0.084 2.163 0.197 0.268 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

217 240 195 0 0 444 0 0 0

N.S.

1 1.11 0.90 0.00 0.00 2.05 0.00 0.00 0.00

time (sec)

N/A 0.833 2.622 0.000 0.000 0.285 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

228 254 200 0 0 460 0 0 0

N.S.

1 1.11 0.88 0.00 0.00 2.02 0.00 0.00 0.00

time (sec)

N/A 0.828 2.626 0.000 0.000 0.281 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

280 343 244 0 0 691 0 0 0

N.S.

1 1.22 0.87 0.00 0.00 2.47 0.00 0.00 0.00

time (sec)

N/A 1.025 3.683 0.000 0.000 0.285 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

64 64 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.395 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

64 64 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.398 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

101 99 0 0 0 0 0 0 0

N.S.

1 0.98 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.360 0.000 0.000 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 F F F F F F F(-1)

verified

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

size

101 99 0 0 0 0 0 0 0

N.S.

1 0.98 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.359 0.000 0.000 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 A A A A A F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 12 11 11 10 0 0

N.S.

1 1.00 1.00 0.92 0.85 0.85 0.77 0.00 0.00

time (sec)

N/A 0.185 0.005 0.296 0.188 0.238 0.220 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 12 11 11 10 0 0

N.S.

1 1.00 1.00 0.92 0.85 0.85 0.77 0.00 0.00

time (sec)

N/A 0.177 0.003 0.270 0.180 0.256 0.155 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 10 9 9 8 0 0

N.S.

1 1.00 1.00 1.11 1.00 1.00 0.89 0.00 0.00

time (sec)

N/A 0.179 0.012 0.332 0.191 0.243 0.162 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 11 11 10 0 0

N.S.

1 1.00 1.00 1.09 1.00 1.00 0.91 0.00 0.00

time (sec)

N/A 0.185 0.004 0.384 0.184 0.248 0.351 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 12 11 11 14 0 0

N.S.

1 1.00 1.00 0.92 0.85 0.85 1.08 0.00 0.00

time (sec)

N/A 0.183 0.005 0.535 0.177 0.244 0.443 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 18 17 18 31 0 0

N.S.

1 1.00 1.00 1.06 1.00 1.06 1.82 0.00 0.00

time (sec)

N/A 0.188 0.007 0.381 0.187 0.257 0.573 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

232 0 232 0 0 169 301 0 0

N.S.

1 0.00 1.00 0.00 0.00 0.73 1.30 0.00 0.00

time (sec)

N/A 0.000 0.010 0.000 0.000 0.256 13.508 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

216 440 153 318 0 167 0 0 0

N.S.

1 2.04 0.71 1.47 0.00 0.77 0.00 0.00 0.00

time (sec)

N/A 2.023 0.185 4.317 0.000 0.289 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

248 338 0 0 0 0 0 0 0

N.S.

1 1.36 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.985 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 273 120 202 0 132 0 0 0

N.S.

1 1.73 0.76 1.28 0.00 0.84 0.00 0.00 0.00

time (sec)

N/A 1.083 0.119 1.492 0.000 0.269 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

120 161 120 0 0 105 151 0 0

N.S.

1 1.34 1.00 0.00 0.00 0.88 1.26 0.00 0.00

time (sec)

N/A 0.938 0.006 0.000 0.000 0.261 1.270 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 150 83 115 0 94 0 0 0

N.S.

1 1.43 0.79 1.10 0.00 0.90 0.00 0.00 0.00

time (sec)

N/A 0.528 0.076 0.818 0.000 0.265 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

137 132 0 0 0 0 0 0 0

N.S.

1 0.96 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.431 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 44 46 0 47 0 0 0

N.S.

1 1.00 0.90 0.94 0.00 0.96 0.00 0.00 0.00

time (sec)

N/A 0.223 0.019 0.645 0.000 0.260 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 12 11 11 10 0 0

N.S.

1 1.00 1.00 0.92 0.85 0.85 0.77 0.00 0.00

time (sec)

N/A 0.170 0.000 0.309 0.191 0.262 0.104 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 18 20 20 19 20 20

N.S.

1 1.00 1.10 0.90 1.00 1.00 0.95 1.00 1.00

time (sec)

N/A 0.185 0.023 0.137 0.281 0.274 1.065 0.275 4.784

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 18 20 20 20 20 20

N.S.

1 1.00 1.10 0.90 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.185 0.023 0.133 0.275 0.258 1.009 0.274 4.875

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 18 20 20 20 20 20

N.S.

1 1.00 1.10 0.90 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.409 0.024 0.147 0.275 0.250 1.265 0.286 4.837

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

109 123 109 0 0 98 0 0 0

N.S.

1 1.13 1.00 0.00 0.00 0.90 0.00 0.00 0.00

time (sec)

N/A 0.750 0.007 0.000 0.000 0.277 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 18 20 20 20 20 20

N.S.

1 1.00 1.10 0.90 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.796 0.026 0.135 0.270 0.251 3.134 0.279 4.821

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 18 20 20 20 20 20

N.S.

1 1.00 1.10 0.90 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 1.253 0.026 0.125 0.280 0.258 5.694 0.286 4.831

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 18 20 20 20 20 20

N.S.

1 1.00 1.10 0.90 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 1.449 0.023 0.137 0.263 0.251 11.356 0.281 4.774

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

224 0 224 0 0 172 0 0 0

N.S.

1 0.00 1.00 0.00 0.00 0.77 0.00 0.00 0.00

time (sec)

N/A 0.000 0.014 0.000 0.000 0.264 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 18 20 20 20 20 20

N.S.

1 1.00 1.10 0.90 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 2.419 0.030 0.125 0.279 0.252 36.284 0.264 4.976

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 18 20 20 20 20 20

N.S.

1 1.00 1.10 0.90 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 2.190 0.027 0.141 0.262 0.256 66.992 0.270 4.938

Problem 90

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

19 19 21 17 19 19 19 19 19

N.S.

1 1.00 1.11 0.89 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.180 0.053 0.151 0.290 0.258 1.106 0.298 4.832

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

307 0 0 0 0 0 0 0 0

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

217 439 163 321 0 169 0 0 0

N.S.

1 2.02 0.75 1.48 0.00 0.78 0.00 0.00 0.00

time (sec)

N/A 1.994 0.127 7.636 0.000 0.281 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

184 284 184 0 0 141 264 0 0

N.S.

1 1.54 1.00 0.00 0.00 0.77 1.43 0.00 0.00

time (sec)

N/A 1.882 0.008 0.000 0.000 0.265 4.604 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

166 283 126 212 0 139 0 0 0

N.S.

1 1.70 0.76 1.28 0.00 0.84 0.00 0.00 0.00

time (sec)

N/A 1.111 0.133 2.594 0.000 0.258 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

195 227 0 0 0 0 0 0 0

N.S.

1 1.16 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.033 0.000 0.000 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 A A F A F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 149 90 119 0 97 0 0 0

N.S.

1 1.38 0.83 1.10 0.00 0.90 0.00 0.00 0.00

time (sec)

N/A 0.562 0.064 1.129 0.000 0.258 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

73 78 73 0 0 58 114 0 0

N.S.

1 1.07 1.00 0.00 0.00 0.79 1.56 0.00 0.00

time (sec)

N/A 0.414 0.005 0.000 0.000 0.261 0.474 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 48 52 0 53 0 0 0

N.S.

1 1.00 0.81 0.88 0.00 0.90 0.00 0.00 0.00

time (sec)

N/A 0.254 0.021 0.754 0.000 0.256 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

80 80 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.196 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 18 20 20 19 20 20

N.S.

1 1.00 1.10 0.90 1.00 1.00 0.95 1.00 1.00

time (sec)

N/A 0.185 0.026 0.136 0.266 0.242 1.077 0.273 4.795

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