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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 B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

42 34 37 37 37 45 60 37 230

N.S.

1 0.81 0.88 0.88 0.88 1.07 1.43 0.88 5.48

time (sec)

N/A 0.274 0.015 0.286 0.171 0.289 0.562 0.271 0.787

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

45 36 40 140 40 58 0 40 58

N.S.

1 0.80 0.89 3.11 0.89 1.29 0.00 0.89 1.29

time (sec)

N/A 0.306 0.027 6.573 0.172 0.276 0.000 0.272 0.739

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 149 86 260 0 76 138 94 0

N.S.

1 1.03 0.60 1.81 0.00 0.53 0.96 0.65 0.00

time (sec)

N/A 0.290 0.055 0.031 0.000 0.280 0.895 0.333 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 119 74 212 0 65 107 80 0

N.S.

1 1.03 0.64 1.83 0.00 0.56 0.92 0.69 0.00

time (sec)

N/A 0.269 0.038 0.025 0.000 0.277 0.389 0.349 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 89 59 164 0 49 73 63 0

N.S.

1 1.01 0.67 1.86 0.00 0.56 0.83 0.72 0.00

time (sec)

N/A 0.242 0.028 0.023 0.000 0.275 0.126 0.327 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

288 189 171 0 0 0 0 0 0

N.S.

1 0.66 0.59 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.734 1.852 0.000 0.000 0.000 0.000 0.000 0.000

Problem 7

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

57 57 54 122 58 44 53 104 0

N.S.

1 1.00 0.95 2.14 1.02 0.77 0.93 1.82 0.00

time (sec)

N/A 0.215 0.028 0.023 0.216 0.274 1.872 0.351 0.000

Problem 8

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

85 84 67 69 68 58 83 198 0

N.S.

1 0.99 0.79 0.81 0.80 0.68 0.98 2.33 0.00

time (sec)

N/A 0.237 0.036 0.026 0.191 0.301 2.186 0.338 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 114 78 117 109 68 352 275 0

N.S.

1 1.01 0.69 1.04 0.96 0.60 3.12 2.43 0.00

time (sec)

N/A 0.257 0.043 0.024 0.197 0.295 2.676 0.354 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 144 89 165 132 80 575 353 0

N.S.

1 1.02 0.63 1.17 0.94 0.57 4.08 2.50 0.00

time (sec)

N/A 0.278 0.053 0.027 0.186 0.331 3.466 0.352 0.000

Problem 11

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

124 116 83 231 167 79 136 137 0

N.S.

1 0.94 0.67 1.86 1.35 0.64 1.10 1.10 0.00

time (sec)

N/A 0.286 0.076 0.038 0.190 0.270 1.434 0.322 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

99 97 72 183 139 68 105 101 0

N.S.

1 0.98 0.73 1.85 1.40 0.69 1.06 1.02 0.00

time (sec)

N/A 0.267 0.067 0.026 0.185 0.266 0.589 0.347 0.000

Problem 13

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

74 76 60 135 111 56 75 64 0

N.S.

1 1.03 0.81 1.82 1.50 0.76 1.01 0.86 0.00

time (sec)

N/A 0.255 0.070 0.023 0.192 0.266 0.276 0.342 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 47 43 86 77 41 41 40 35

N.S.

1 1.09 1.00 2.00 1.79 0.95 0.95 0.93 0.81

time (sec)

N/A 0.212 0.013 0.021 0.201 0.269 0.129 0.534 0.773

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 86 90 0 148 66 53 0

N.S.

1 1.00 1.46 1.53 0.00 2.51 1.12 0.90 0.00

time (sec)

N/A 0.242 0.042 0.023 0.000 0.295 1.930 0.367 0.000

Problem 16

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

91 85 101 130 0 198 82 87 0

N.S.

1 0.93 1.11 1.43 0.00 2.18 0.90 0.96 0.00

time (sec)

N/A 0.246 0.063 0.022 0.000 0.304 3.887 0.343 0.000

Problem 17

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

119 115 114 178 0 228 148 116 0

N.S.

1 0.97 0.96 1.50 0.00 1.92 1.24 0.97 0.00

time (sec)

N/A 0.261 0.083 0.027 0.000 0.312 6.188 0.338 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

211 218 170 0 0 96 0 0 0

N.S.

1 1.03 0.81 0.00 0.00 0.45 0.00 0.00 0.00

time (sec)

N/A 0.337 11.410 0.000 0.000 0.132 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

181 186 158 0 0 85 75 0 0

N.S.

1 1.03 0.87 0.00 0.00 0.47 0.41 0.00 0.00

time (sec)

N/A 0.298 0.312 0.000 0.000 0.112 43.609 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

153 154 147 0 0 71 75 0 0

N.S.

1 1.01 0.96 0.00 0.00 0.46 0.49 0.00 0.00

time (sec)

N/A 0.280 0.213 0.000 0.000 0.100 8.640 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

122 122 115 0 0 52 71 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.43 0.58 0.00 0.00

time (sec)

N/A 0.250 0.093 0.000 0.000 0.093 7.972 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

156 154 150 0 0 73 78 0 0

N.S.

1 0.99 0.96 0.00 0.00 0.47 0.50 0.00 0.00

time (sec)

N/A 0.283 0.196 0.000 0.000 0.095 44.905 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

186 186 162 0 0 86 0 0 0

N.S.

1 1.00 0.87 0.00 0.00 0.46 0.00 0.00 0.00

time (sec)

N/A 0.308 0.223 0.000 0.000 0.097 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

216 218 171 0 0 97 0 0 0

N.S.

1 1.01 0.79 0.00 0.00 0.45 0.00 0.00 0.00

time (sec)

N/A 0.335 0.419 0.000 0.000 0.095 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

326 321 139 0 0 94 0 0 0

N.S.

1 0.98 0.43 0.00 0.00 0.29 0.00 0.00 0.00

time (sec)

N/A 0.432 10.120 0.000 0.000 0.120 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

296 289 119 0 0 79 75 0 0

N.S.

1 0.98 0.40 0.00 0.00 0.27 0.25 0.00 0.00

time (sec)

N/A 0.409 0.083 0.000 0.000 0.109 9.881 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

260 253 89 0 0 55 71 0 0

N.S.

1 0.97 0.34 0.00 0.00 0.21 0.27 0.00 0.00

time (sec)

N/A 0.368 0.081 0.000 0.000 0.106 9.308 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

298 285 121 0 0 80 78 0 0

N.S.

1 0.96 0.41 0.00 0.00 0.27 0.26 0.00 0.00

time (sec)

N/A 0.386 0.098 0.000 0.000 0.101 10.110 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

331 317 137 0 0 94 0 0 0

N.S.

1 0.96 0.41 0.00 0.00 0.28 0.00 0.00 0.00

time (sec)

N/A 0.419 0.086 0.000 0.000 0.094 0.000 0.000 0.000

Problem 30

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

50 50 50 43 42 47 41 43 42

N.S.

1 1.00 1.00 0.86 0.84 0.94 0.82 0.86 0.84

time (sec)

N/A 0.295 0.014 0.361 0.319 0.274 0.286 0.279 0.901

Problem 31

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

40 40 42 36 39 38 34 38 39

N.S.

1 1.00 1.05 0.90 0.98 0.95 0.85 0.95 0.98

time (sec)

N/A 0.250 0.135 0.415 0.963 0.292 3.748 0.387 1.017

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

431 429 0 1664 0 0 0 0 0

N.S.

1 1.00 0.00 3.86 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.142 0.000 0.580 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

283 285 0 916 0 0 0 0 0

N.S.

1 1.01 0.00 3.24 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.799 0.000 0.476 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 B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 93 93 368 0 0 0 0 0

N.S.

1 0.95 0.95 3.76 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.329 0.029 0.324 0.000 0.000 0.000 0.000 0.000

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

40 40 42 36 39 48 61 38 39

N.S.

1 1.00 1.05 0.90 0.98 1.20 1.52 0.95 0.98

time (sec)

N/A 0.263 0.224 0.279 0.426 0.243 2.756 0.371 0.804

Problem 36

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

40 40 42 36 163 91 126 38 39

N.S.

1 1.00 1.05 0.90 4.08 2.28 3.15 0.95 0.98

time (sec)

N/A 0.250 1.019 0.296 0.536 0.245 6.120 0.517 1.553

Problem 37

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

37 37 34 41 38 33 158 0 0

N.S.

1 1.00 0.92 1.11 1.03 0.89 4.27 0.00 0.00

time (sec)

N/A 0.184 0.047 0.270 0.213 0.278 0.665 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 20 20 81 13 32 0 19

N.S.

1 1.00 0.87 0.87 3.52 0.57 1.39 0.00 0.83

time (sec)

N/A 0.162 0.014 0.114 0.186 0.253 0.102 0.000 0.137

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 20 20 57 13 76 0 19

N.S.

1 1.00 0.87 0.87 2.48 0.57 3.30 0.00 0.83

time (sec)

N/A 0.178 0.012 0.110 0.185 0.251 0.167 0.000 0.072

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 18 15 12 10 42 26 16

N.S.

1 1.00 1.12 0.94 0.75 0.62 2.62 1.62 1.00

time (sec)

N/A 0.156 0.006 0.101 0.182 0.260 0.066 0.289 0.047

Problem 41

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

21 21 19 23 42 8 34 0 0

N.S.

1 1.00 0.90 1.10 2.00 0.38 1.62 0.00 0.00

time (sec)

N/A 0.187 0.014 0.127 0.280 0.263 0.335 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 31 56 40 42 160 62 0

N.S.

1 1.00 0.86 1.56 1.11 1.17 4.44 1.72 0.00

time (sec)

N/A 0.187 0.035 0.317 0.191 0.261 1.857 0.279 0.000

Problem 43

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

23 23 20 26 17 17 26 19 25

N.S.

1 1.00 0.87 1.13 0.74 0.74 1.13 0.83 1.09

time (sec)

N/A 0.171 0.014 0.247 0.191 0.231 0.104 0.282 0.650

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 20 26 17 17 49 19 25

N.S.

1 1.00 0.87 1.13 0.74 0.74 2.13 0.83 1.09

time (sec)

N/A 0.180 0.014 0.221 0.184 0.236 0.162 0.273 0.078

Problem 45

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

16 16 18 22 15 15 24 15 21

N.S.

1 1.00 1.12 1.38 0.94 0.94 1.50 0.94 1.31

time (sec)

N/A 0.163 0.007 0.118 0.188 0.236 0.059 0.279 0.073

Problem 46

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

19 19 19 27 14 14 27 15 0

N.S.

1 1.00 1.00 1.42 0.74 0.74 1.42 0.79 0.00

time (sec)

N/A 0.185 0.014 0.168 0.191 0.258 1.351 0.262 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 18 15 12 10 42 26 16

N.S.

1 1.00 1.12 0.94 0.75 0.62 2.62 1.62 1.00

time (sec)

N/A 0.155 0.000 0.040 0.193 0.255 0.066 0.288 0.002

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

403 519 371 8039 0 1965 0 0 0

N.S.

1 1.29 0.92 19.95 0.00 4.88 0.00 0.00 0.00

time (sec)

N/A 1.598 3.162 27.782 0.000 0.351 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

305 396 281 7647 0 1545 0 0 0

N.S.

1 1.30 0.92 25.07 0.00 5.07 0.00 0.00 0.00

time (sec)

N/A 1.120 2.847 2.852 0.000 0.339 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

198 277 549 1001 433 1101 0 0 0

N.S.

1 1.40 2.77 5.06 2.19 5.56 0.00 0.00 0.00

time (sec)

N/A 0.675 5.607 2.408 0.342 0.343 0.000 0.000 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 F(-1) N/A N/A

verified

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

size

15 15 17 15 17 17 0 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.00 1.13 1.13

time (sec)

N/A 0.293 2.147 0.082 232.907 0.264 0.000 1.319 0.733

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

154 198 140 1487 310 322 0 0 0

N.S.

1 1.29 0.91 9.66 2.01 2.09 0.00 0.00 0.00

time (sec)

N/A 0.805 0.310 1.445 0.206 0.270 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

123 155 110 1452 218 271 0 0 0

N.S.

1 1.26 0.89 11.80 1.77 2.20 0.00 0.00 0.00

time (sec)

N/A 0.623 0.181 1.071 0.204 0.279 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

85 107 967 563 448 202 0 0 0

N.S.

1 1.26 11.38 6.62 5.27 2.38 0.00 0.00 0.00

time (sec)

N/A 0.454 11.097 1.112 0.281 0.271 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A F(-2) 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 0 37 0 21 22

N.S.

1 1.00 1.10 0.90 0.00 1.76 0.00 1.00 1.05

time (sec)

N/A 0.301 0.575 0.080 0.000 0.256 0.000 1.005 0.868

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

155 199 137 1488 310 322 0 0 0

N.S.

1 1.28 0.88 9.60 2.00 2.08 0.00 0.00 0.00

time (sec)

N/A 0.827 0.315 1.480 0.214 0.285 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

124 156 111 1453 218 271 0 0 0

N.S.

1 1.26 0.90 11.72 1.76 2.19 0.00 0.00 0.00

time (sec)

N/A 0.649 0.211 0.981 0.222 0.269 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

86 108 847 594 448 200 0 0 0

N.S.

1 1.26 9.85 6.91 5.21 2.33 0.00 0.00 0.00

time (sec)

N/A 0.440 8.388 1.169 0.293 0.294 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A F(-2) 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 0 37 0 21 22

N.S.

1 1.00 1.10 0.90 0.00 1.76 0.00 1.00 1.05

time (sec)

N/A 0.317 0.876 0.082 0.000 0.260 0.000 1.170 1.074

Problem 60

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

16 16 18 22 15 15 24 15 21

N.S.

1 1.00 1.12 1.38 0.94 0.94 1.50 0.94 1.31

time (sec)

N/A 0.160 0.001 0.054 0.174 0.235 0.059 0.288 0.002

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

399 515 360 7869 0 1589 0 0 0

N.S.

1 1.29 0.90 19.72 0.00 3.98 0.00 0.00 0.00

time (sec)

N/A 1.586 3.069 30.662 0.000 0.433 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

303 394 275 7501 0 1289 0 0 0

N.S.

1 1.30 0.91 24.76 0.00 4.25 0.00 0.00 0.00

time (sec)

N/A 1.110 2.469 3.151 0.000 0.411 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

198 277 1648 1145 532 965 0 0 0

N.S.

1 1.40 8.32 5.78 2.69 4.87 0.00 0.00 0.00

time (sec)

N/A 0.683 21.134 2.872 0.342 0.399 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 15 17 15 0 17 0 17 17

N.S.

1 1.00 1.13 1.00 0.00 1.13 0.00 1.13 1.13

time (sec)

N/A 0.286 1.983 0.138 0.000 0.257 0.000 3.784 0.785

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

154 198 136 1487 309 166 0 0 0

N.S.

1 1.29 0.88 9.66 2.01 1.08 0.00 0.00 0.00

time (sec)

N/A 0.799 0.282 1.420 0.210 0.263 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

123 155 110 1452 217 144 0 0 0

N.S.

1 1.26 0.89 11.80 1.76 1.17 0.00 0.00 0.00

time (sec)

N/A 0.638 0.195 1.101 0.191 0.264 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

85 107 929 584 458 112 0 0 0

N.S.

1 1.26 10.93 6.87 5.39 1.32 0.00 0.00 0.00

time (sec)

N/A 0.443 11.672 1.070 0.360 0.265 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A F(-2) 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 23 0 37 0 25 23

N.S.

1 1.00 1.10 1.10 0.00 1.76 0.00 1.19 1.10

time (sec)

N/A 0.292 0.539 0.125 0.000 0.260 0.000 1.798 1.062

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

155 199 140 1488 311 166 0 0 0

N.S.

1 1.28 0.90 9.60 2.01 1.07 0.00 0.00 0.00

time (sec)

N/A 0.824 0.291 1.497 0.223 0.263 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

124 156 110 1453 219 144 0 0 0

N.S.

1 1.26 0.89 11.72 1.77 1.16 0.00 0.00 0.00

time (sec)

N/A 0.633 0.191 1.098 0.197 0.270 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

86 108 872 625 458 112 0 0 0

N.S.

1 1.26 10.14 7.27 5.33 1.30 0.00 0.00 0.00

time (sec)

N/A 0.448 6.715 1.186 0.295 0.265 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A F(-2) 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 23 0 37 0 25 23

N.S.

1 1.00 1.10 1.10 0.00 1.76 0.00 1.19 1.10

time (sec)

N/A 0.305 0.540 0.135 0.000 0.259 0.000 2.043 1.121

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 56 52 0 58 0 0 0

N.S.

1 1.00 1.44 1.33 0.00 1.49 0.00 0.00 0.00

time (sec)

N/A 0.310 0.046 0.652 0.000 0.270 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

74 77 93 632 0 93 0 0 0

N.S.

1 1.04 1.26 8.54 0.00 1.26 0.00 0.00 0.00

time (sec)

N/A 0.445 0.042 0.561 0.000 0.265 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

108 113 121 658 0 125 0 0 0

N.S.

1 1.05 1.12 6.09 0.00 1.16 0.00 0.00 0.00

time (sec)

N/A 0.590 0.072 0.744 0.000 0.359 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

299 327 600 3570 0 1460 0 0 0

N.S.

1 1.09 2.01 11.94 0.00 4.88 0.00 0.00 0.00

time (sec)

N/A 1.150 0.785 15.921 0.000 0.349 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

229 251 375 2668 0 1002 0 0 0

N.S.

1 1.10 1.64 11.65 0.00 4.38 0.00 0.00 0.00

time (sec)

N/A 0.869 0.427 10.447 0.000 0.326 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

159 175 237 1776 0 600 0 0 0

N.S.

1 1.10 1.49 11.17 0.00 3.77 0.00 0.00 0.00

time (sec)

N/A 0.601 0.235 1.237 0.000 0.329 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 80 91 160 0 334 0 0 0

N.S.

1 1.08 1.23 2.16 0.00 4.51 0.00 0.00 0.00

time (sec)

N/A 0.356 0.024 0.825 0.000 0.312 0.000 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

15 15 17 15 17 17 14 3 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.93 0.20 1.13

time (sec)

N/A 0.217 11.143 0.129 1.555 0.271 2.953 105.119 0.696

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

355 441 438 6917 0 1289 0 0 0

N.S.

1 1.24 1.23 19.48 0.00 3.63 0.00 0.00 0.00

time (sec)

N/A 1.441 0.990 26.221 0.000 0.370 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

267 343 330 6567 0 1067 0 0 0

N.S.

1 1.28 1.24 24.60 0.00 4.00 0.00 0.00 0.00

time (sec)

N/A 1.046 0.783 3.002 0.000 0.357 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 237 288 352 0 825 0 0 0

N.S.

1 1.36 1.66 2.02 0.00 4.74 0.00 0.00 0.00

time (sec)

N/A 0.637 2.551 2.177 0.000 0.390 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 F(-1) N/A N/A

verified

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

size

15 15 17 15 17 17 0 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.00 1.13 1.13

time (sec)

N/A 0.289 6.491 0.108 1.060 0.264 0.000 0.495 0.777

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

142 167 134 1406 129 293 0 0 0

N.S.

1 1.18 0.94 9.90 0.91 2.06 0.00 0.00 0.00

time (sec)

N/A 0.810 0.168 1.599 1.316 0.273 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

113 132 103 1370 106 247 0 0 0

N.S.

1 1.17 0.91 12.12 0.94 2.19 0.00 0.00 0.00

time (sec)

N/A 0.635 0.073 0.908 1.257 0.274 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 92 71 545 80 187 0 0 0

N.S.

1 1.16 0.90 6.90 1.01 2.37 0.00 0.00 0.00

time (sec)

N/A 0.453 1.656 1.027 1.229 0.296 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 F(-1) N/A N/A

verified

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

size

19 19 21 17 72 37 0 19 20

N.S.

1 1.00 1.11 0.89 3.79 1.95 0.00 1.00 1.05

time (sec)

N/A 0.283 3.373 0.146 0.590 0.264 0.000 0.337 1.215

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

145 170 134 1409 129 293 0 0 0

N.S.

1 1.17 0.92 9.72 0.89 2.02 0.00 0.00 0.00

time (sec)

N/A 0.817 0.163 1.619 1.278 0.270 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

116 136 103 1373 107 247 0 0 0

N.S.

1 1.17 0.89 11.84 0.92 2.13 0.00 0.00 0.00

time (sec)

N/A 0.635 0.089 0.968 1.279 0.282 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 96 71 516 80 187 0 0 0

N.S.

1 1.17 0.87 6.29 0.98 2.28 0.00 0.00 0.00

time (sec)

N/A 0.451 1.679 1.015 1.274 0.269 0.000 0.000 0.000

Problem 92

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

22 22 24 20 77 37 0 19 20

N.S.

1 1.00 1.09 0.91 3.50 1.68 0.00 0.86 0.91

time (sec)

N/A 0.293 3.306 0.141 0.614 0.254 0.000 0.341 1.093

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

299 327 600 3570 0 1460 0 0 0

N.S.

1 1.09 2.01 11.94 0.00 4.88 0.00 0.00 0.00

time (sec)

N/A 1.222 0.299 15.857 0.000 0.358 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

229 251 375 2668 0 1002 0 0 0

N.S.

1 1.10 1.64 11.65 0.00 4.38 0.00 0.00 0.00

time (sec)

N/A 0.834 0.176 10.369 0.000 0.342 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

159 175 237 1777 0 600 0 0 0

N.S.

1 1.10 1.49 11.18 0.00 3.77 0.00 0.00 0.00

time (sec)

N/A 0.588 0.116 1.340 0.000 0.337 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 79 91 160 0 334 0 0 0

N.S.

1 1.08 1.25 2.19 0.00 4.58 0.00 0.00 0.00

time (sec)

N/A 0.352 0.021 0.837 0.000 0.293 0.000 0.000 0.000

Problem 97

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

15 15 17 15 17 17 0 3 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.00 0.20 1.13

time (sec)

N/A 0.216 3.179 0.135 1.554 0.251 0.000 90.476 0.713

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

351 437 442 6845 0 1269 0 0 0

N.S.

1 1.25 1.26 19.50 0.00 3.62 0.00 0.00 0.00

time (sec)

N/A 1.436 0.940 24.977 0.000 0.361 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

265 339 334 6495 0 1051 0 0 0

N.S.

1 1.28 1.26 24.51 0.00 3.97 0.00 0.00 0.00

time (sec)

N/A 1.053 0.682 3.421 0.000 0.368 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 237 287 352 0 813 0 0 0

N.S.

1 1.36 1.65 2.02 0.00 4.67 0.00 0.00 0.00

time (sec)

N/A 0.645 2.203 2.573 0.000 0.386 0.000 0.000 0.000

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