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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 Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 12 17 11 18 19 13 16

N.S.

1 1.00 1.00 1.42 0.92 1.50 1.58 1.08 1.33

time (sec)

N/A 0.154 0.011 0.035 0.270 0.258 0.063 0.313 2.944

Problem 2

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

14 14 23 15 18 17 15 226 14

N.S.

1 1.00 1.64 1.07 1.29 1.21 1.07 16.14 1.00

time (sec)

N/A 0.165 0.004 0.031 0.286 0.248 0.074 0.423 2.793

Problem 3

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

27 27 25 28 31 27 32 216 30

N.S.

1 1.00 0.93 1.04 1.15 1.00 1.19 8.00 1.11

time (sec)

N/A 0.220 0.036 0.050 0.191 0.249 0.082 0.588 2.797

Problem 4

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

28 28 38 27 29 26 27 585 24

N.S.

1 1.00 1.36 0.96 1.04 0.93 0.96 20.89 0.86

time (sec)

N/A 0.232 0.005 0.046 0.278 0.252 0.104 0.842 2.881

Problem 5

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

43 43 37 38 54 39 44 462 38

N.S.

1 1.00 0.86 0.88 1.26 0.91 1.02 10.74 0.88

time (sec)

N/A 0.292 0.041 0.088 0.322 0.231 0.125 1.373 2.739

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

44 44 53 39 41 38 39 989 35

N.S.

1 1.00 1.20 0.89 0.93 0.86 0.89 22.48 0.80

time (sec)

N/A 0.300 0.017 0.063 0.509 0.225 0.140 2.163 2.907

Problem 7

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

57 57 47 49 74 51 56 740 49

N.S.

1 1.00 0.82 0.86 1.30 0.89 0.98 12.98 0.86

time (sec)

N/A 0.360 0.076 0.104 0.590 0.237 0.172 3.112 2.561

Problem 8

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

58 58 68 49 51 48 51 1441 44

N.S.

1 1.00 1.17 0.84 0.88 0.83 0.88 24.84 0.76

time (sec)

N/A 0.358 0.011 0.086 0.277 0.231 0.196 5.001 2.986

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

232 227 174 169 186 203 0 0 93

N.S.

1 0.98 0.75 0.73 0.80 0.88 0.00 0.00 0.40

time (sec)

N/A 0.548 0.684 0.195 0.279 0.235 0.000 0.000 3.383

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

212 197 101 154 176 202 0 0 74

N.S.

1 0.93 0.48 0.73 0.83 0.95 0.00 0.00 0.35

time (sec)

N/A 0.457 0.195 0.056 0.284 0.240 0.000 0.000 3.150

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

210 201 160 149 170 177 0 0 73

N.S.

1 0.96 0.76 0.71 0.81 0.84 0.00 0.00 0.35

time (sec)

N/A 0.475 0.126 0.053 0.293 0.245 0.000 0.000 3.135

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

192 174 71 136 153 164 0 176 49

N.S.

1 0.91 0.37 0.71 0.80 0.85 0.00 0.92 0.26

time (sec)

N/A 0.386 0.059 0.168 0.299 0.232 0.000 0.369 2.773

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

192 180 131 138 155 152 0 184 59

N.S.

1 0.94 0.68 0.72 0.81 0.79 0.00 0.96 0.31

time (sec)

N/A 0.380 0.081 0.099 0.313 0.229 0.000 0.385 3.121

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

212 197 82 157 167 235 0 0 76

N.S.

1 0.93 0.39 0.74 0.79 1.11 0.00 0.00 0.36

time (sec)

N/A 0.465 0.099 0.057 0.316 0.235 0.000 0.000 2.971

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

214 205 86 157 168 236 0 0 75

N.S.

1 0.96 0.40 0.73 0.79 1.10 0.00 0.00 0.35

time (sec)

N/A 0.479 0.145 0.056 0.296 0.247 0.000 0.000 3.355

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

234 225 96 171 195 256 0 0 92

N.S.

1 0.96 0.41 0.73 0.83 1.09 0.00 0.00 0.39

time (sec)

N/A 0.563 0.221 0.055 0.309 0.248 0.000 0.000 3.328

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

243 217 205 215 185 312 0 209 247

N.S.

1 0.89 0.84 0.88 0.76 1.28 0.00 0.86 1.02

time (sec)

N/A 0.498 0.246 0.174 0.305 0.241 0.000 0.445 3.339

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

224 196 185 191 168 314 0 206 259

N.S.

1 0.88 0.83 0.85 0.75 1.40 0.00 0.92 1.16

time (sec)

N/A 0.412 0.156 0.163 0.316 0.233 0.000 0.397 3.778

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

131 112 106 108 98 124 0 127 146

N.S.

1 0.85 0.81 0.82 0.75 0.95 0.00 0.97 1.11

time (sec)

N/A 0.319 0.228 0.106 0.304 0.233 0.000 0.385 3.387

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

131 112 100 108 99 299 0 125 128

N.S.

1 0.85 0.76 0.82 0.76 2.28 0.00 0.95 0.98

time (sec)

N/A 0.334 0.098 0.095 0.308 0.272 0.000 0.362 3.174

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

224 196 189 203 170 282 0 0 230

N.S.

1 0.88 0.84 0.91 0.76 1.26 0.00 0.00 1.03

time (sec)

N/A 0.427 0.170 0.135 0.315 0.233 0.000 0.000 3.393

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

245 219 254 215 182 430 0 227 278

N.S.

1 0.89 1.04 0.88 0.74 1.76 0.00 0.93 1.13

time (sec)

N/A 0.482 0.229 0.098 0.305 0.247 0.000 0.477 3.166

Problem 23

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

50 50 51 0 0 0 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.215 0.154 0.000 0.000 0.000 0.000 0.000 0.000

Problem 24

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

98 67 56 58 47 74 0 646 0

N.S.

1 0.68 0.57 0.59 0.48 0.76 0.00 6.59 0.00

time (sec)

N/A 0.399 0.280 0.161 0.296 0.239 0.000 1.181 0.000

Problem 25

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

61 49 47 48 34 52 0 226 0

N.S.

1 0.80 0.77 0.79 0.56 0.85 0.00 3.70 0.00

time (sec)

N/A 0.315 0.117 0.065 0.288 0.241 0.000 0.611 0.000

Problem 26

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

32 32 32 37 19 38 0 23 0

N.S.

1 1.00 1.00 1.16 0.59 1.19 0.00 0.72 0.00

time (sec)

N/A 0.245 0.029 0.066 0.309 0.241 0.000 0.361 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 33 39 45 33 50 0 0 34

N.S.

1 1.06 1.26 1.45 1.06 1.61 0.00 0.00 1.10

time (sec)

N/A 0.242 0.066 0.072 0.364 0.233 0.000 0.000 3.136

Problem 28

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

66 54 56 63 46 69 0 169 0

N.S.

1 0.82 0.85 0.95 0.70 1.05 0.00 2.56 0.00

time (sec)

N/A 0.323 0.257 0.075 0.318 0.251 0.000 0.428 0.000

Problem 29

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

97 70 66 74 66 82 0 225 0

N.S.

1 0.72 0.68 0.76 0.68 0.85 0.00 2.32 0.00

time (sec)

N/A 0.414 0.194 0.083 0.322 0.237 0.000 0.440 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

364 232 204 263 178 332 0 291 0

N.S.

1 0.64 0.56 0.72 0.49 0.91 0.00 0.80 0.00

time (sec)

N/A 0.785 0.678 0.173 0.339 0.236 0.000 0.504 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

286 198 115 236 140 279 0 253 0

N.S.

1 0.69 0.40 0.83 0.49 0.98 0.00 0.88 0.00

time (sec)

N/A 0.582 0.480 0.072 0.331 0.239 0.000 0.391 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

255 178 162 205 133 272 0 195 0

N.S.

1 0.70 0.64 0.80 0.52 1.07 0.00 0.76 0.00

time (sec)

N/A 0.486 0.176 0.073 0.325 0.238 0.000 0.354 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

255 178 87 211 126 307 0 251 0

N.S.

1 0.70 0.34 0.83 0.49 1.20 0.00 0.98 0.00

time (sec)

N/A 0.489 0.263 0.075 0.359 0.240 0.000 0.465 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

298 200 98 233 163 320 0 279 0

N.S.

1 0.67 0.33 0.78 0.55 1.07 0.00 0.94 0.00

time (sec)

N/A 0.573 0.212 0.075 0.490 0.237 0.000 0.618 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

364 232 139 272 172 348 0 305 0

N.S.

1 0.64 0.38 0.75 0.47 0.96 0.00 0.84 0.00

time (sec)

N/A 0.741 0.401 0.079 0.421 0.256 0.000 0.860 0.000

Problem 36

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

182 100 86 84 79 96 0 960 0

N.S.

1 0.55 0.47 0.46 0.43 0.53 0.00 5.27 0.00

time (sec)

N/A 0.570 0.598 0.233 0.380 0.245 0.000 6.981 0.000

Problem 37

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

110 68 66 64 53 62 0 992 0

N.S.

1 0.62 0.60 0.58 0.48 0.56 0.00 9.02 0.00

time (sec)

N/A 0.387 0.547 0.062 0.325 0.234 0.000 2.937 0.000

Problem 38

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

50 37 41 42 26 37 0 229 0

N.S.

1 0.74 0.82 0.84 0.52 0.74 0.00 4.58 0.00

time (sec)

N/A 0.247 0.075 0.063 0.302 0.231 0.000 0.458 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 38 43 40 27 39 0 45 0

N.S.

1 0.75 0.84 0.78 0.53 0.76 0.00 0.88 0.00

time (sec)

N/A 0.241 0.048 0.069 0.293 0.238 0.000 0.472 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 71 45 63 50 62 0 114 0

N.S.

1 0.60 0.38 0.53 0.42 0.52 0.00 0.96 0.00

time (sec)

N/A 0.396 0.038 0.071 0.306 0.240 0.000 0.653 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 101 45 83 70 82 0 169 0

N.S.

1 0.55 0.25 0.45 0.38 0.45 0.00 0.92 0.00

time (sec)

N/A 0.563 0.036 0.094 0.459 0.259 0.000 1.280 0.000

Problem 42

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

59 59 59 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.289 0.098 0.000 0.000 0.000 0.000 0.000 0.000

Problem 43

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

59 59 51 0 0 0 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.290 0.077 0.000 0.000 0.000 0.000 0.000 0.000

Problem 44

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

57 57 57 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.284 0.073 0.000 0.000 0.000 0.000 0.000 0.000

Problem 45

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

59 59 55 0 0 0 0 0 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.279 0.081 0.000 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

71 71 63 0 0 0 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.293 0.102 0.000 0.000 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

65 65 61 0 0 0 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.283 0.085 0.000 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 70 56 0 0 0 0 0 0

N.S.

1 1.25 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.281 0.072 0.000 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 F F F(-2) F F F(-1)

verified

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

size

62 62 60 0 0 0 0 0 0

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.287 0.087 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 A F F F(-2) F F F(-1)

verified

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

size

71 71 61 0 0 0 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.288 0.098 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 F F F(-2) F F F(-1)

verified

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

size

71 71 63 0 0 0 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.285 0.098 0.000 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 A C F A F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

32 32 32 5979 0 23 0 0 0

N.S.

1 1.00 1.00 186.84 0.00 0.72 0.00 0.00 0.00

time (sec)

N/A 0.248 0.020 6.385 0.000 0.243 0.000 0.000 0.000

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

61 61 61 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.299 0.083 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 A A B A C F A F(-1)

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

257 251 122 619 225 947 0 245 0

N.S.

1 0.98 0.47 2.41 0.88 3.68 0.00 0.95 0.00

time (sec)

N/A 0.430 0.490 13.869 0.406 0.401 0.000 0.314 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

227 212 104 529 194 934 0 219 0

N.S.

1 0.93 0.46 2.33 0.85 4.11 0.00 0.96 0.00

time (sec)

N/A 0.424 0.324 0.920 0.353 0.383 0.000 0.309 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 17 23 37 0 16 48

N.S.

1 1.00 1.00 0.94 1.28 2.06 0.00 0.89 2.67

time (sec)

N/A 0.205 0.324 0.207 0.250 0.239 0.000 0.341 3.172

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 39 30 43 33 63 0 43 102

N.S.

1 0.95 0.73 1.05 0.80 1.54 0.00 1.05 2.49

time (sec)

N/A 0.238 0.322 0.800 0.276 0.243 0.000 0.336 8.404

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 58 50 52 48 82 0 58 356

N.S.

1 0.92 0.79 0.83 0.76 1.30 0.00 0.92 5.65

time (sec)

N/A 0.241 0.366 0.751 0.303 0.267 0.000 0.355 8.128

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

105 108 139 1740 0 0 0 0 0

N.S.

1 1.03 1.32 16.57 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.593 11.785 9.250 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 C B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 57 200 0 0 0 0 0

N.S.

1 1.00 0.76 2.67 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.440 3.786 0.740 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 C A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 73 108 0 54 0 0 0

N.S.

1 1.00 1.55 2.30 0.00 1.15 0.00 0.00 0.00

time (sec)

N/A 0.338 0.251 0.630 0.000 0.086 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 115 218 0 113 0 0 0

N.S.

1 1.00 1.49 2.83 0.00 1.47 0.00 0.00 0.00

time (sec)

N/A 0.450 0.667 0.750 0.000 0.090 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 110 124 345 0 157 0 0 0

N.S.

1 1.05 1.18 3.29 0.00 1.50 0.00 0.00 0.00

time (sec)

N/A 0.597 1.344 0.699 0.000 0.095 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

277 277 123 890 235 954 0 252 0

N.S.

1 1.00 0.44 3.21 0.85 3.44 0.00 0.91 0.00

time (sec)

N/A 0.467 0.769 3.462 0.366 0.386 0.000 0.378 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

247 238 113 1083 204 942 0 226 0

N.S.

1 0.96 0.46 4.38 0.83 3.81 0.00 0.91 0.00

time (sec)

N/A 0.454 0.464 2.329 0.385 0.383 0.000 0.330 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 17 23 24 0 16 43

N.S.

1 1.00 1.00 0.94 1.28 1.33 0.00 0.89 2.39

time (sec)

N/A 0.212 0.342 0.159 0.245 0.234 0.000 0.324 2.882

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 39 30 38 34 51 0 43 100

N.S.

1 0.95 0.73 0.93 0.83 1.24 0.00 1.05 2.44

time (sec)

N/A 0.242 0.287 0.638 0.252 0.249 0.000 0.359 3.741

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 58 42 47 58 71 0 64 292

N.S.

1 0.92 0.67 0.75 0.92 1.13 0.00 1.02 4.63

time (sec)

N/A 0.252 0.383 0.578 0.214 0.251 0.000 0.365 7.078

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 111 90 409 0 0 0 0 0

N.S.

1 1.01 0.82 3.72 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.635 4.041 0.815 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 F F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 58 395 0 0 0 0 0

N.S.

1 1.00 0.76 5.20 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.435 0.318 0.769 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 C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 61 381 0 136 0 0 0

N.S.

1 1.00 0.80 5.01 0.00 1.79 0.00 0.00 0.00

time (sec)

N/A 0.457 0.339 0.625 0.000 0.098 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 138 71 371 0 176 0 0 0

N.S.

1 1.35 0.70 3.64 0.00 1.73 0.00 0.00 0.00

time (sec)

N/A 0.613 0.643 0.668 0.000 0.096 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

277 273 142 526 240 1048 0 278 0

N.S.

1 0.99 0.51 1.90 0.87 3.78 0.00 1.00 0.00

time (sec)

N/A 0.464 0.830 48.450 0.315 0.416 0.000 0.354 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

247 234 126 500 209 1035 0 252 0

N.S.

1 0.95 0.51 2.02 0.85 4.19 0.00 1.02 0.00

time (sec)

N/A 0.452 0.461 3.589 0.323 0.387 0.000 0.352 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 17 23 40 0 24 56

N.S.

1 1.00 1.00 0.85 1.15 2.00 0.00 1.20 2.80

time (sec)

N/A 0.226 0.400 0.296 0.211 0.248 0.000 0.362 3.127

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 39 32 42 36 58 0 42 64

N.S.

1 0.95 0.78 1.02 0.88 1.41 0.00 1.02 1.56

time (sec)

N/A 0.248 0.378 4.887 0.215 0.254 0.000 0.421 3.612

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 58 42 55 56 82 0 70 134

N.S.

1 0.92 0.67 0.87 0.89 1.30 0.00 1.11 2.13

time (sec)

N/A 0.250 0.504 73.866 0.219 0.248 0.000 0.394 6.155

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

137 142 153 1840 0 0 0 0 0

N.S.

1 1.04 1.12 13.43 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.770 2.609 7.734 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 109 133 233 0 0 0 0 0

N.S.

1 1.01 1.23 2.16 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.565 1.773 5.351 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 C B F C F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 71 215 0 103 0 0 0

N.S.

1 1.00 0.89 2.69 0.00 1.29 0.00 0.00 0.00

time (sec)

N/A 0.453 0.509 1.633 0.000 0.087 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 71 215 0 103 0 0 0

N.S.

1 1.00 0.89 2.69 0.00 1.29 0.00 0.00 0.00

time (sec)

N/A 0.467 0.612 2.502 0.000 0.086 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 111 110 259 0 162 0 0 0

N.S.

1 1.01 1.00 2.35 0.00 1.47 0.00 0.00 0.00

time (sec)

N/A 0.614 0.697 20.387 0.000 0.093 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 146 130 456 0 209 0 0 0

N.S.

1 1.04 0.93 3.26 0.00 1.49 0.00 0.00 0.00

time (sec)

N/A 0.771 1.844 151.869 0.000 0.091 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

257 257 122 603 220 892 0 246 0

N.S.

1 1.00 0.47 2.35 0.86 3.47 0.00 0.96 0.00

time (sec)

N/A 0.444 0.616 9.156 0.316 0.352 0.000 0.351 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

227 218 109 524 188 877 0 218 0

N.S.

1 0.96 0.48 2.31 0.83 3.86 0.00 0.96 0.00

time (sec)

N/A 0.433 0.391 1.731 0.332 0.396 0.000 0.349 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 17 23 46 0 23 102

N.S.

1 1.00 1.00 0.85 1.15 2.30 0.00 1.15 5.10

time (sec)

N/A 0.213 0.290 0.158 0.238 0.246 0.000 0.322 3.431

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 41 40 43 35 70 0 45 530

N.S.

1 0.95 0.93 1.00 0.81 1.63 0.00 1.05 12.33

time (sec)

N/A 0.239 0.279 0.772 0.234 0.253 0.000 0.361 7.663

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 60 50 52 48 93 0 58 831

N.S.

1 0.92 0.77 0.80 0.74 1.43 0.00 0.89 12.78

time (sec)

N/A 0.244 0.310 0.865 0.270 0.271 0.000 0.349 12.236

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 112 86 390 0 0 0 0 0

N.S.

1 1.05 0.80 3.64 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.628 0.938 1.116 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 C B F F F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 79 98 377 0 0 0 0 0

N.S.

1 1.00 1.24 4.77 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.463 0.766 0.988 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 C B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 60 363 0 0 0 0 0

N.S.

1 1.00 1.28 7.72 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.337 0.233 0.829 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 C B F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 109 69 349 0 169 0 0 0

N.S.

1 1.51 0.96 4.85 0.00 2.35 0.00 0.00 0.00

time (sec)

N/A 0.489 0.319 0.885 0.000 0.095 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 139 104 370 0 237 0 0 0

N.S.

1 1.36 1.02 3.63 0.00 2.32 0.00 0.00 0.00

time (sec)

N/A 0.613 0.702 1.033 0.000 0.097 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

257 257 123 621 225 986 0 257 0

N.S.

1 1.00 0.48 2.42 0.88 3.84 0.00 1.00 0.00

time (sec)

N/A 0.459 0.589 10.056 0.368 0.397 0.000 0.428 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

227 218 105 529 193 971 0 228 0

N.S.

1 0.96 0.46 2.33 0.85 4.28 0.00 1.00 0.00

time (sec)

N/A 0.442 0.350 13.241 0.330 0.393 0.000 0.388 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 17 23 58 0 26 381

N.S.

1 1.00 1.00 0.85 1.15 2.90 0.00 1.30 19.05

time (sec)

N/A 0.226 0.329 0.150 0.229 0.252 0.000 0.405 7.067

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 41 42 48 35 84 0 45 684

N.S.

1 0.95 0.98 1.12 0.81 1.95 0.00 1.05 15.91

time (sec)

N/A 0.245 0.282 0.700 0.250 0.254 0.000 0.434 9.492

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 60 54 57 48 109 0 58 987

N.S.

1 0.92 0.83 0.88 0.74 1.68 0.00 0.89 15.18

time (sec)

N/A 0.252 0.314 0.769 0.270 0.275 0.000 0.500 14.657

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

112 113 102 1048 0 0 0 0 0

N.S.

1 1.01 0.91 9.36 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.633 0.498 3.034 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 113 126 151 0 0 0 0 0

N.S.

1 1.43 1.59 1.91 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.494 0.669 2.535 0.000 0.000 0.000 0.000 0.000

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