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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 B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 57 51 47 47 51 65 128 53

N.S.

1 1.00 0.89 0.82 0.82 0.89 1.14 2.25 0.93

time (sec)

N/A 0.226 0.102 0.182 0.247 0.293 0.404 0.289 0.204

Problem 2

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

44 44 44 39 37 40 49 75 38

N.S.

1 1.00 1.00 0.89 0.84 0.91 1.11 1.70 0.86

time (sec)

N/A 0.197 0.005 0.135 0.236 0.267 0.231 0.286 0.115

Problem 3

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

25 25 41 22 21 23 31 26 21

N.S.

1 1.00 1.64 0.88 0.84 0.92 1.24 1.04 0.84

time (sec)

N/A 0.173 0.037 0.134 0.238 0.262 0.085 0.282 5.598

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 29 29 50 27 0 32 0

N.S.

1 1.00 0.94 0.94 1.61 0.87 0.00 1.03 0.00

time (sec)

N/A 0.186 0.068 0.145 0.299 0.273 0.000 0.305 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 48 47 57 49 0 99 0

N.S.

1 1.00 0.91 0.89 1.08 0.92 0.00 1.87 0.00

time (sec)

N/A 0.246 0.094 0.164 0.328 0.266 0.000 0.305 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 86 65 58 63 0 204 0

N.S.

1 1.00 1.16 0.88 0.78 0.85 0.00 2.76 0.00

time (sec)

N/A 0.273 0.114 0.191 0.330 0.289 0.000 0.305 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 121 125 89 92 103 488 165 0

N.S.

1 1.00 1.03 0.74 0.76 0.85 4.03 1.36 0.00

time (sec)

N/A 0.294 0.195 0.177 0.255 0.260 2.374 0.310 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 102 104 68 75 86 223 145 0

N.S.

1 1.00 1.02 0.67 0.74 0.84 2.19 1.42 0.00

time (sec)

N/A 0.232 0.154 0.140 0.257 0.290 1.868 0.294 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 61 48 53 67 66 100 56

N.S.

1 1.00 0.82 0.65 0.72 0.91 0.89 1.35 0.76

time (sec)

N/A 0.186 0.115 0.103 0.247 0.307 0.201 0.291 6.021

Problem 10

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

88 88 91 66 81 78 0 0 0

N.S.

1 1.00 1.03 0.75 0.92 0.89 0.00 0.00 0.00

time (sec)

N/A 0.234 0.146 0.155 0.401 0.276 0.000 0.000 0.000

Problem 11

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

114 114 119 83 82 98 0 0 0

N.S.

1 1.00 1.04 0.73 0.72 0.86 0.00 0.00 0.00

time (sec)

N/A 0.256 0.171 0.169 0.393 0.290 0.000 0.000 0.000

Problem 12

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

163 167 122 111 106 121 209 284 149

N.S.

1 1.02 0.75 0.68 0.65 0.74 1.28 1.74 0.91

time (sec)

N/A 0.437 0.248 0.254 0.264 0.290 0.547 0.283 0.478

Problem 13

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

102 107 92 89 87 84 136 165 95

N.S.

1 1.05 0.90 0.87 0.85 0.82 1.33 1.62 0.93

time (sec)

N/A 0.333 0.149 0.217 0.241 0.301 0.316 0.283 6.110

Problem 14

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

58 62 52 52 52 53 95 57 51

N.S.

1 1.07 0.90 0.90 0.90 0.91 1.64 0.98 0.88

time (sec)

N/A 0.247 0.176 0.216 0.238 0.270 0.128 0.277 5.861

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

74 74 71 157 108 68 0 77 0

N.S.

1 1.00 0.96 2.12 1.46 0.92 0.00 1.04 0.00

time (sec)

N/A 0.284 0.123 0.577 0.362 0.262 0.000 0.290 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

115 115 116 219 124 112 0 226 0

N.S.

1 1.00 1.01 1.90 1.08 0.97 0.00 1.97 0.00

time (sec)

N/A 0.418 0.190 0.573 0.368 0.274 0.000 0.286 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

169 169 158 271 128 156 0 448 0

N.S.

1 1.00 0.93 1.60 0.76 0.92 0.00 2.65 0.00

time (sec)

N/A 0.497 0.312 0.675 0.364 0.276 0.000 0.299 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

247 247 234 185 207 216 0 329 0

N.S.

1 1.00 0.95 0.75 0.84 0.87 0.00 1.33 0.00

time (sec)

N/A 0.460 0.377 0.279 0.349 0.308 0.000 0.302 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 198 191 138 171 176 0 283 0

N.S.

1 1.00 0.96 0.70 0.86 0.89 0.00 1.43 0.00

time (sec)

N/A 0.372 0.343 0.242 0.331 0.326 0.000 0.292 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 153 147 98 129 134 0 195 0

N.S.

1 1.00 0.96 0.64 0.84 0.88 0.00 1.27 0.00

time (sec)

N/A 0.302 0.217 0.181 0.336 0.282 0.000 0.294 0.000

Problem 21

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

187 187 184 134 170 159 0 0 0

N.S.

1 1.00 0.98 0.72 0.91 0.85 0.00 0.00 0.00

time (sec)

N/A 0.356 0.341 0.223 0.458 0.298 0.000 0.000 0.000

Problem 22

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

239 239 226 173 176 206 0 0 0

N.S.

1 1.00 0.95 0.72 0.74 0.86 0.00 0.00 0.00

time (sec)

N/A 0.405 0.455 0.254 0.455 0.278 0.000 0.000 0.000

Problem 23

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

117 130 75 85 79 79 143 138 94

N.S.

1 1.11 0.64 0.73 0.68 0.68 1.22 1.18 0.80

time (sec)

N/A 0.641 0.201 0.200 0.252 0.280 0.771 0.283 6.402

Problem 24

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

79 83 58 66 60 58 92 94 66

N.S.

1 1.05 0.73 0.84 0.76 0.73 1.16 1.19 0.84

time (sec)

N/A 0.402 0.115 0.312 0.250 0.305 0.396 0.276 0.234

Problem 25

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

33 23 33 26 27 26 46 26 28

N.S.

1 0.70 1.00 0.79 0.82 0.79 1.39 0.79 0.85

time (sec)

N/A 0.241 0.021 0.321 0.232 0.278 0.156 0.294 5.980

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

55 55 51 125 89 47 0 47 0

N.S.

1 1.00 0.93 2.27 1.62 0.85 0.00 0.85 0.00

time (sec)

N/A 0.269 0.054 0.618 0.376 0.311 0.000 0.286 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

91 91 90 185 97 90 0 186 0

N.S.

1 1.00 0.99 2.03 1.07 0.99 0.00 2.04 0.00

time (sec)

N/A 0.394 0.100 0.701 0.370 0.292 0.000 0.308 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 188 159 132 143 147 439 259 0

N.S.

1 1.00 0.85 0.70 0.76 0.78 2.34 1.38 0.00

time (sec)

N/A 0.398 0.303 0.182 0.338 0.313 1.888 0.295 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 153 117 99 112 120 129 185 0

N.S.

1 1.00 0.76 0.65 0.73 0.78 0.84 1.21 0.00

time (sec)

N/A 0.266 0.157 0.158 0.345 0.310 0.510 0.312 0.000

Problem 30

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

168 172 167 130 152 147 0 0 0

N.S.

1 1.02 0.99 0.77 0.90 0.88 0.00 0.00 0.00

time (sec)

N/A 0.345 0.300 0.253 0.463 0.320 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 63 58 97 51 116 97 0

N.S.

1 1.00 0.89 0.82 1.37 0.72 1.63 1.37 0.00

time (sec)

N/A 0.234 0.050 0.250 0.338 0.310 2.161 0.298 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 89 75 78 117 73 291 125 0

N.S.

1 1.06 0.89 0.93 1.39 0.87 3.46 1.49 0.00

time (sec)

N/A 0.288 0.112 0.367 0.334 0.323 2.106 0.285 0.000

Problem 33

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

67 35 67 50 55 52 95 52 55

N.S.

1 0.52 1.00 0.75 0.82 0.78 1.42 0.78 0.82

time (sec)

N/A 0.242 0.030 0.407 0.252 0.298 0.668 0.280 6.544

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 41 39 54 38 51 39 0

N.S.

1 1.00 0.93 0.89 1.23 0.86 1.16 0.89 0.00

time (sec)

N/A 0.262 0.079 0.322 0.294 0.321 2.184 0.281 0.000

Problem 35

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

362 341 289 0 0 1435 0 0 0

N.S.

1 0.94 0.80 0.00 0.00 3.96 0.00 0.00 0.00

time (sec)

N/A 1.398 0.157 0.000 0.000 0.455 0.000 0.000 0.000

Problem 36

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

245 237 188 0 0 1041 0 0 0

N.S.

1 0.97 0.77 0.00 0.00 4.25 0.00 0.00 0.00

time (sec)

N/A 0.874 0.053 0.000 0.000 0.419 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 54 48 48 8078 208 165 63 128

N.S.

1 1.12 1.00 1.00 168.29 4.33 3.44 1.31 2.67

time (sec)

N/A 0.272 0.063 0.161 24.834 0.324 3.557 0.293 8.488

Problem 38

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

18 18 20 18 20 19 15 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.06 0.83 1.11 1.11

time (sec)

N/A 0.186 1.089 0.044 0.441 0.347 2.380 0.305 6.103

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

18 18 20 18 20 23 17 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.28 0.94 1.11 1.11

time (sec)

N/A 0.189 0.985 0.049 0.447 0.274 3.219 0.324 6.112

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

18 18 20 18 20 20 15 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.83 1.11 1.11

time (sec)

N/A 0.185 0.555 0.045 0.470 0.287 1.856 0.301 5.963

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 16 16 14 16 16

N.S.

1 1.00 1.14 1.00 1.14 1.14 1.00 1.14 1.14

time (sec)

N/A 0.164 0.022 0.042 0.417 0.322 0.799 0.296 5.963

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

18 18 20 18 20 23 17 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.28 0.94 1.11 1.11

time (sec)

N/A 0.183 0.433 0.047 0.454 0.278 3.015 0.305 6.433

Problem 43

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

663 625 513 0 0 2469 0 0 0

N.S.

1 0.94 0.77 0.00 0.00 3.72 0.00 0.00 0.00

time (sec)

N/A 2.799 1.743 0.000 0.000 0.528 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

324 326 302 0 0 1509 0 0 0

N.S.

1 1.01 0.93 0.00 0.00 4.66 0.00 0.00 0.00

time (sec)

N/A 1.160 0.817 0.000 0.000 0.465 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 99 91 131 0 366 2116 144 178

N.S.

1 1.09 1.00 1.44 0.00 4.02 23.25 1.58 1.96

time (sec)

N/A 0.376 0.201 0.239 0.000 0.343 54.296 0.284 6.552

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

18 18 20 18 3466 45 17 20 20

N.S.

1 1.00 1.11 1.00 192.56 2.50 0.94 1.11 1.11

time (sec)

N/A 0.182 4.684 0.298 4.106 0.308 26.566 0.444 6.275

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

18 18 20 18 3475 51 19 20 20

N.S.

1 1.00 1.11 1.00 193.06 2.83 1.06 1.11 1.11

time (sec)

N/A 0.183 6.935 0.228 4.117 0.337 39.901 0.553 6.377

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

18 18 20 18 922 46 17 20 20

N.S.

1 1.00 1.11 1.00 51.22 2.56 0.94 1.11 1.11

time (sec)

N/A 0.183 3.026 0.208 0.600 0.296 40.495 0.363 6.016

Problem 49

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 3381 43 15 16 16

N.S.

1 1.00 1.14 1.00 241.50 3.07 1.07 1.14 1.14

time (sec)

N/A 0.160 3.122 0.223 4.013 0.296 18.265 0.344 5.979

Problem 50

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

18 18 20 18 3486 51 19 20 20

N.S.

1 1.00 1.11 1.00 193.67 2.83 1.06 1.11 1.11

time (sec)

N/A 0.183 5.365 0.288 4.145 0.327 44.262 0.372 6.085

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

20 20 22 20 22 22 19 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.10

time (sec)

N/A 0.186 0.796 0.059 0.723 0.359 16.095 0.558 6.386

Problem 52

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

444 444 373 0 0 323 0 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.73 0.00 0.00 0.00

time (sec)

N/A 0.663 1.397 0.000 0.000 0.113 0.000 0.000 0.000

Problem 53

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

279 279 551 0 0 198 0 0 0

N.S.

1 1.00 1.97 0.00 0.00 0.71 0.00 0.00 0.00

time (sec)

N/A 0.458 1.900 0.000 0.000 0.110 0.000 0.000 0.000

Problem 54

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

134 134 149 0 0 98 0 0 0

N.S.

1 1.00 1.11 0.00 0.00 0.73 0.00 0.00 0.00

time (sec)

N/A 0.287 0.345 0.000 0.000 0.106 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 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 20 22 22 17 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.85 1.10 1.10

time (sec)

N/A 0.183 0.687 0.062 0.521 0.285 0.434 0.302 6.101

Problem 56

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 20 3886 48 19 22 22

N.S.

1 1.00 1.10 1.00 194.30 2.40 0.95 1.10 1.10

time (sec)

N/A 0.182 1.192 0.233 8.109 0.290 1.445 0.342 6.202

Problem 57

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

44 44 44 39 37 40 49 75 38

N.S.

1 1.00 1.00 0.89 0.84 0.91 1.11 1.70 0.86

time (sec)

N/A 0.206 0.009 0.191 0.198 0.291 0.400 0.274 0.229

Problem 58

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

25 25 41 22 21 23 31 26 21

N.S.

1 1.00 1.64 0.88 0.84 0.92 1.24 1.04 0.84

time (sec)

N/A 0.180 0.038 0.137 0.289 0.288 0.113 0.270 5.909

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

31 31 29 0 50 27 0 32 0

N.S.

1 1.00 0.94 0.00 1.61 0.87 0.00 1.03 0.00

time (sec)

N/A 0.193 0.077 0.000 0.386 0.309 0.000 0.279 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

53 53 48 0 57 49 0 99 0

N.S.

1 1.00 0.91 0.00 1.08 0.92 0.00 1.87 0.00

time (sec)

N/A 0.255 0.094 0.000 0.391 0.316 0.000 0.287 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

112 112 124 0 109 82 0 0 0

N.S.

1 1.00 1.11 0.00 0.97 0.73 0.00 0.00 0.00

time (sec)

N/A 0.268 0.176 0.000 0.207 0.112 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

91 91 108 0 93 63 0 0 0

N.S.

1 1.00 1.19 0.00 1.02 0.69 0.00 0.00 0.00

time (sec)

N/A 0.229 0.113 0.000 0.198 0.109 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

101 101 120 0 89 72 0 0 0

N.S.

1 1.00 1.19 0.00 0.88 0.71 0.00 0.00 0.00

time (sec)

N/A 0.255 0.170 0.000 0.186 0.118 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

130 130 143 0 91 101 0 0 0

N.S.

1 1.00 1.10 0.00 0.70 0.78 0.00 0.00 0.00

time (sec)

N/A 0.282 0.291 0.000 0.185 0.127 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

106 106 124 0 110 80 0 0 0

N.S.

1 1.00 1.17 0.00 1.04 0.75 0.00 0.00 0.00

time (sec)

N/A 0.228 0.146 0.000 0.181 0.111 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

82 82 138 0 85 61 0 0 0

N.S.

1 1.00 1.68 0.00 1.04 0.74 0.00 0.00 0.00

time (sec)

N/A 0.177 0.084 0.000 0.175 0.116 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

101 101 120 0 90 80 0 0 0

N.S.

1 1.00 1.19 0.00 0.89 0.79 0.00 0.00 0.00

time (sec)

N/A 0.218 0.160 0.000 0.191 0.110 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

126 126 146 0 91 101 0 0 0

N.S.

1 1.00 1.16 0.00 0.72 0.80 0.00 0.00 0.00

time (sec)

N/A 0.243 0.290 0.000 0.181 0.101 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 A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 107 92 92 87 84 143 165 95

N.S.

1 1.00 0.86 0.86 0.81 0.79 1.34 1.54 0.89

time (sec)

N/A 0.337 0.178 0.525 0.206 0.305 0.538 0.283 5.864

Problem 70

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

60 62 52 52 52 53 99 57 51

N.S.

1 1.03 0.87 0.87 0.87 0.88 1.65 0.95 0.85

time (sec)

N/A 0.258 0.100 0.225 0.204 0.304 0.179 0.290 5.928

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

80 80 71 0 108 70 0 79 0

N.S.

1 1.00 0.89 0.00 1.35 0.88 0.00 0.99 0.00

time (sec)

N/A 0.279 0.131 0.000 0.323 0.286 0.000 0.292 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

122 122 116 0 124 112 0 226 0

N.S.

1 1.00 0.95 0.00 1.02 0.92 0.00 1.85 0.00

time (sec)

N/A 0.405 0.192 0.000 0.326 0.287 0.000 0.309 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

249 249 339 0 234 186 0 0 0

N.S.

1 1.00 1.36 0.00 0.94 0.75 0.00 0.00 0.00

time (sec)

N/A 0.417 0.610 0.000 0.232 0.108 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

193 193 251 0 199 141 0 0 0

N.S.

1 1.00 1.30 0.00 1.03 0.73 0.00 0.00 0.00

time (sec)

N/A 0.339 1.352 0.000 0.220 0.104 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

231 229 332 0 187 173 0 0 0

N.S.

1 0.99 1.44 0.00 0.81 0.75 0.00 0.00 0.00

time (sec)

N/A 0.398 0.695 0.000 0.226 0.128 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

285 283 292 0 194 232 0 0 0

N.S.

1 0.99 1.02 0.00 0.68 0.81 0.00 0.00 0.00

time (sec)

N/A 0.463 1.843 0.000 0.234 0.119 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

237 237 339 0 240 182 0 0 0

N.S.

1 1.00 1.43 0.00 1.01 0.77 0.00 0.00 0.00

time (sec)

N/A 0.371 0.598 0.000 0.218 0.114 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

183 183 228 0 192 139 0 0 0

N.S.

1 1.00 1.25 0.00 1.05 0.76 0.00 0.00 0.00

time (sec)

N/A 0.275 0.614 0.000 0.212 0.111 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

227 225 334 0 188 189 0 0 0

N.S.

1 0.99 1.47 0.00 0.83 0.83 0.00 0.00 0.00

time (sec)

N/A 0.342 0.535 0.000 0.225 0.116 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

277 275 294 0 193 233 0 0 0

N.S.

1 0.99 1.06 0.00 0.70 0.84 0.00 0.00 0.00

time (sec)

N/A 0.393 1.957 0.000 0.231 0.119 0.000 0.000 0.000

Problem 81

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

245 241 188 0 0 1041 0 0 0

N.S.

1 0.98 0.77 0.00 0.00 4.25 0.00 0.00 0.00

time (sec)

N/A 0.856 0.117 0.000 0.000 0.419 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 57 51 49 8078 208 172 64 136

N.S.

1 1.12 1.00 0.96 158.39 4.08 3.37 1.25 2.67

time (sec)

N/A 0.274 0.068 0.178 23.030 0.335 6.161 0.295 8.567

Problem 83

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

18 18 20 18 20 19 15 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.06 0.83 1.11 1.11

time (sec)

N/A 0.178 1.033 0.046 0.465 0.291 2.487 0.320 6.627

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

18 18 20 18 20 23 17 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.28 0.94 1.11 1.11

time (sec)

N/A 0.184 0.924 0.063 0.467 0.299 4.425 0.338 6.285

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

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 0.182 0.438 0.044 0.452 0.285 2.156 0.324 5.932

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

18 18 20 18 20 23 17 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.28 0.94 1.11 1.11

time (sec)

N/A 0.183 0.440 0.047 0.500 0.308 2.712 0.336 6.055

Problem 87

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 14 16 16

N.S.

1 1.00 1.14 1.00 1.14 1.14 1.00 1.14 1.14

time (sec)

N/A 0.160 0.015 0.045 0.457 0.311 0.742 0.302 5.898

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

18 18 20 18 20 23 17 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.28 0.94 1.11 1.11

time (sec)

N/A 0.182 0.465 0.049 0.491 0.344 3.987 0.307 6.041

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

324 326 302 0 0 1509 0 0 0

N.S.

1 1.01 0.93 0.00 0.00 4.66 0.00 0.00 0.00

time (sec)

N/A 1.167 0.846 0.000 0.000 0.468 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 99 91 131 0 366 2116 146 186

N.S.

1 1.05 0.97 1.39 0.00 3.89 22.51 1.55 1.98

time (sec)

N/A 0.389 0.144 0.240 0.000 0.326 73.187 0.294 6.595

Problem 91

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

18 18 20 18 2696 45 17 20 20

N.S.

1 1.00 1.11 1.00 149.78 2.50 0.94 1.11 1.11

time (sec)

N/A 0.184 6.888 0.289 4.214 0.309 25.038 0.442 6.334

Problem 92

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

18 18 20 18 2705 51 19 20 20

N.S.

1 1.00 1.11 1.00 150.28 2.83 1.06 1.11 1.11

time (sec)

N/A 0.183 10.075 0.289 4.242 0.316 50.273 0.598 6.527

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A F(-2) 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 0 44 15 18 18

N.S.

1 1.00 1.12 1.00 0.00 2.75 0.94 1.12 1.12

time (sec)

N/A 0.173 4.337 0.217 0.000 0.324 24.651 0.367 6.043

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

18 18 20 18 0 51 19 20 20

N.S.

1 1.00 1.11 1.00 0.00 2.83 1.06 1.11 1.11

time (sec)

N/A 0.181 7.519 0.327 0.000 0.309 35.661 0.371 6.203

Problem 95

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 2171 43 15 16 16

N.S.

1 1.00 1.14 1.00 155.07 3.07 1.07 1.14 1.14

time (sec)

N/A 0.160 5.192 0.235 1.840 0.323 16.636 0.315 5.957

Problem 96

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

18 18 20 18 2171 51 19 20 20

N.S.

1 1.00 1.11 1.00 120.61 2.83 1.06 1.11 1.11

time (sec)

N/A 0.183 8.380 0.297 1.958 0.324 49.111 0.358 6.369

Problem 97

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 20 22 22 19 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.10

time (sec)

N/A 0.183 0.770 0.053 0.727 0.331 17.069 0.539 6.377

Problem 98

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

442 442 373 0 0 347 0 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.79 0.00 0.00 0.00

time (sec)

N/A 0.652 1.524 0.000 0.000 0.142 0.000 0.000 0.000

Problem 99

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

285 285 556 0 0 214 0 0 0

N.S.

1 1.00 1.95 0.00 0.00 0.75 0.00 0.00 0.00

time (sec)

N/A 0.453 1.810 0.000 0.000 0.133 0.000 0.000 0.000

Problem 100

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

134 134 149 0 0 106 0 0 0

N.S.

1 1.00 1.11 0.00 0.00 0.79 0.00 0.00 0.00

time (sec)

N/A 0.281 0.319 0.000 0.000 0.143 0.000 0.000 0.000

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