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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 86 99 86 85 139 1017 84

N.S.

1 1.00 0.99 1.14 0.99 0.98 1.60 11.69 0.97

time (sec)

N/A 0.096 0.410 0.083 0.501 4.634 0.115 1.045 8.825

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 67 74 66 66 105 616 63

N.S.

1 1.00 1.02 1.12 1.00 1.00 1.59 9.33 0.95

time (sec)

N/A 0.035 0.225 0.070 0.516 4.076 0.096 0.818 8.838

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 59 53 50 50 82 50 58

N.S.

1 1.00 1.40 1.26 1.19 1.19 1.95 1.19 1.38

time (sec)

N/A 0.050 0.046 0.237 0.501 4.456 0.348 0.803 8.791

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 44 43 52 59 85 53 69

N.S.

1 1.00 1.19 1.16 1.41 1.59 2.30 1.43 1.86

time (sec)

N/A 0.080 0.056 0.280 0.495 3.687 0.523 0.967 8.956

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 78 53 68 73 122 119 87

N.S.

1 1.00 1.81 1.23 1.58 1.70 2.84 2.77 2.02

time (sec)

N/A 0.090 0.114 0.216 0.515 3.563 0.925 1.134 8.875

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 77 77 86 95 150 179 108

N.S.

1 1.00 1.17 1.17 1.30 1.44 2.27 2.71 1.64

time (sec)

N/A 0.118 0.328 0.302 0.502 4.566 1.375 1.395 8.944

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 101 95 104 121 180 237 127

N.S.

1 1.00 1.16 1.09 1.20 1.39 2.07 2.72 1.46

time (sec)

N/A 0.146 0.723 0.277 0.518 3.568 2.231 1.634 8.888

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 100 108 122 138 211 299 145

N.S.

1 1.00 0.93 1.00 1.13 1.28 1.95 2.77 1.34

time (sec)

N/A 0.170 0.785 0.277 0.496 3.605 3.031 1.436 8.821

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

148 148 221 176 147 146 250 2228 151

N.S.

1 1.00 1.49 1.19 0.99 0.99 1.69 15.05 1.02

time (sec)

N/A 0.211 6.162 0.100 0.507 2.305 0.171 1.916 8.844

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 172 135 120 119 194 1509 121

N.S.

1 1.00 1.54 1.21 1.07 1.06 1.73 13.47 1.08

time (sec)

N/A 0.083 1.246 0.071 0.513 1.375 0.132 1.254 8.795

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 96 102 91 91 151 95 91

N.S.

1 1.00 1.10 1.17 1.05 1.05 1.74 1.09 1.05

time (sec)

N/A 0.100 0.320 0.309 0.492 1.418 0.564 1.151 8.848

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 91 82 85 92 136 86 90

N.S.

1 1.00 1.30 1.17 1.21 1.31 1.94 1.23 1.29

time (sec)

N/A 0.135 0.192 0.270 0.490 2.608 0.846 1.410 8.853

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 100 84 93 112 165 118 100

N.S.

1 1.00 1.39 1.17 1.29 1.56 2.29 1.64 1.39

time (sec)

N/A 0.149 0.172 0.262 0.492 2.404 1.345 1.695 8.999

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 123 107 120 122 212 237 127

N.S.

1 1.00 1.40 1.22 1.36 1.39 2.41 2.69 1.44

time (sec)

N/A 0.184 0.235 0.296 0.537 3.354 2.213 0.998 8.979

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 152 136 149 157 258 334 156

N.S.

1 1.00 1.29 1.15 1.26 1.33 2.19 2.83 1.32

time (sec)

N/A 0.221 0.781 0.271 0.511 4.867 3.052 1.063 9.078

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 180 162 175 191 311 435 182

N.S.

1 1.00 1.19 1.07 1.16 1.26 2.06 2.88 1.21

time (sec)

N/A 0.260 1.901 0.296 0.527 3.472 5.024 1.098 8.860

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 209 213 179 178 313 2870 181

N.S.

1 1.00 1.27 1.29 1.08 1.08 1.90 17.39 1.10

time (sec)

N/A 0.132 1.095 0.093 0.499 4.127 0.165 2.470 8.835

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 130 161 143 142 248 158 142

N.S.

1 1.00 0.93 1.15 1.02 1.01 1.77 1.13 1.01

time (sec)

N/A 0.144 0.709 0.287 0.507 6.586 0.894 1.653 8.963

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 113 131 124 133 211 129 118

N.S.

1 1.00 0.97 1.12 1.06 1.14 1.80 1.10 1.01

time (sec)

N/A 0.233 0.324 0.296 0.501 3.194 1.243 1.790 8.963

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 113 123 125 145 221 152 114

N.S.

1 1.00 0.95 1.03 1.05 1.22 1.86 1.28 0.96

time (sec)

N/A 0.234 0.327 0.272 0.500 5.318 2.228 1.296 8.860

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 126 138 142 162 260 193 135

N.S.

1 1.00 0.99 1.09 1.12 1.28 2.05 1.52 1.06

time (sec)

N/A 0.248 0.308 0.355 0.494 3.151 2.983 1.416 8.967

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

154 154 164 166 180 181 330 390 169

N.S.

1 1.00 1.06 1.08 1.17 1.18 2.14 2.53 1.10

time (sec)

N/A 0.300 0.839 0.316 0.507 2.886 4.910 1.537 8.999

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

191 191 199 203 215 225 398 528 204

N.S.

1 1.00 1.04 1.06 1.13 1.18 2.08 2.76 1.07

time (sec)

N/A 0.362 0.505 0.310 0.493 4.021 6.512 1.596 8.941

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

233 233 237 244 250 266 469 670 238

N.S.

1 1.00 1.02 1.05 1.07 1.14 2.01 2.88 1.02

time (sec)

N/A 0.389 0.780 0.345 0.502 3.010 10.142 1.663 9.120

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 138 127 130 190 1306 135 144

N.S.

1 1.00 1.09 1.00 1.02 1.50 10.28 1.06 1.13

time (sec)

N/A 0.316 0.986 0.194 0.512 4.860 0.823 0.787 9.071

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 118 101 109 149 1020 110 117

N.S.

1 1.00 1.17 1.00 1.08 1.48 10.10 1.09 1.16

time (sec)

N/A 0.174 0.492 0.177 0.511 4.217 0.641 0.686 8.768

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 98 87 94 110 711 95 100

N.S.

1 1.00 1.15 1.02 1.11 1.29 8.36 1.12 1.18

time (sec)

N/A 0.120 0.135 0.179 0.492 2.356 0.519 0.647 9.065

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 67 82 88 76 541 94 93

N.S.

1 1.00 1.16 1.41 1.52 1.31 9.33 1.62 1.60

time (sec)

N/A 0.095 0.089 0.369 0.518 1.651 1.415 0.801 9.125

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 113 101 107 118 966 113 115

N.S.

1 1.00 1.41 1.26 1.34 1.48 12.08 1.41 1.44

time (sec)

N/A 0.138 0.250 0.493 0.520 1.145 2.497 0.930 9.457

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 138 123 131 177 2064 157 140

N.S.

1 1.00 1.34 1.19 1.27 1.72 20.04 1.52 1.36

time (sec)

N/A 0.232 0.610 0.477 0.513 1.192 5.022 1.137 10.339

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 163 152 158 234 2592 214 175

N.S.

1 1.00 1.19 1.11 1.15 1.71 18.92 1.56 1.28

time (sec)

N/A 0.434 0.950 0.482 0.507 3.995 8.454 1.469 10.929

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

208 208 444 172 220 434 4541 290 210

N.S.

1 1.00 2.13 0.83 1.06 2.09 21.83 1.39 1.01

time (sec)

N/A 0.363 2.817 0.229 0.510 3.062 1.198 0.863 9.648

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 324 155 197 311 3497 244 165

N.S.

1 1.00 2.06 0.99 1.25 1.98 22.27 1.55 1.05

time (sec)

N/A 0.223 1.486 0.258 0.493 3.889 1.050 0.708 9.107

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 140 145 185 221 2995 241 163

N.S.

1 1.00 1.22 1.26 1.61 1.92 26.04 2.10 1.42

time (sec)

N/A 0.103 1.515 0.165 0.517 3.609 0.857 0.705 9.011

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 190 141 177 222 2895 234 153

N.S.

1 1.00 1.71 1.27 1.59 2.00 26.08 2.11 1.38

time (sec)

N/A 0.146 1.516 0.429 0.503 4.127 2.228 0.953 9.094

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 159 163 208 323 4461 279 180

N.S.

1 1.00 1.16 1.19 1.52 2.36 32.56 2.04 1.31

time (sec)

N/A 0.280 1.653 0.504 0.506 8.037 4.024 1.297 10.693

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 193 196 262 465 8097 362 230

N.S.

1 1.00 1.01 1.02 1.36 2.42 42.17 1.89 1.20

time (sec)

N/A 0.427 2.355 0.564 0.509 9.190 7.367 1.324 12.148

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

331 331 1146 263 389 890 0 505 335

N.S.

1 1.00 3.46 0.79 1.18 2.69 0.00 1.53 1.01

time (sec)

N/A 0.606 6.615 0.386 0.516 8.004 0.000 1.105 10.428

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

250 250 462 242 366 666 0 458 307

N.S.

1 1.00 1.85 0.97 1.46 2.66 0.00 1.83 1.23

time (sec)

N/A 0.374 3.225 0.302 0.515 5.069 0.000 0.967 9.316

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 288 223 333 478 0 410 280

N.S.

1 1.00 1.52 1.18 1.76 2.53 0.00 2.17 1.48

time (sec)

N/A 0.280 3.578 0.235 0.519 3.728 0.000 0.837 9.181

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

179 179 188 213 330 488 0 410 282

N.S.

1 1.00 1.05 1.19 1.84 2.73 0.00 2.29 1.58

time (sec)

N/A 0.179 2.735 0.224 0.499 4.126 0.000 0.839 9.280

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

175 175 243 208 321 482 0 409 279

N.S.

1 1.00 1.39 1.19 1.83 2.75 0.00 2.34 1.59

time (sec)

N/A 0.224 2.793 0.509 0.506 2.766 0.000 1.295 8.941

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

215 215 223 243 372 683 0 479 315

N.S.

1 1.00 1.04 1.13 1.73 3.18 0.00 2.23 1.47

time (sec)

N/A 0.474 2.081 0.651 0.518 2.346 0.000 1.281 10.976

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

287 287 288 289 454 917 0 560 380

N.S.

1 1.00 1.00 1.01 1.58 3.20 0.00 1.95 1.32

time (sec)

N/A 0.653 6.281 0.684 0.510 3.219 0.000 1.621 13.986

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 110 0 0 0 0 0 -1

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.120 0.307 0.423 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

154 154 115 0 0 0 0 0 -1

N.S.

1 1.00 0.75 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.104 0.274 0.504 0.000 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F(-1) F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

170 170 133 0 0 0 0 0 -1

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.108 0.378 0.650 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F(-1) F F F(-1) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

170 170 133 0 0 0 0 0 -1

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.099 0.376 0.625 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F(-1) F

verified

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

size

328 328 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.135 45.839 0.787 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

353 353 280 639 423 421 1001 11805 477

N.S.

1 1.00 0.79 1.81 1.20 1.19 2.84 33.44 1.35

time (sec)

N/A 0.554 5.855 0.206 0.511 1.481 0.351 8.909 8.997

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

248 248 243 386 280 278 617 6502 300

N.S.

1 1.00 0.98 1.56 1.13 1.12 2.49 26.22 1.21

time (sec)

N/A 0.309 2.268 0.118 0.497 3.354 0.229 3.760 8.982

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 161 187 156 154 326 2918 153

N.S.

1 1.00 1.00 1.16 0.97 0.96 2.02 18.12 0.95

time (sec)

N/A 0.168 1.066 0.118 0.507 2.700 0.143 1.698 8.842

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 76 80 78 77 131 918 75

N.S.

1 1.00 1.04 1.10 1.07 1.05 1.79 12.58 1.03

time (sec)

N/A 0.045 0.329 0.071 0.494 3.153 0.100 0.856 8.679

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 155 148 173 187 231 2387 186 186

N.S.

1 0.99 0.95 1.11 1.20 1.48 15.30 1.19 1.19

time (sec)

N/A 0.237 0.787 0.209 0.505 5.584 1.022 0.669 10.127

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

265 265 589 321 342 564 9721 531 1875

N.S.

1 1.00 2.22 1.21 1.29 2.13 36.68 2.00 7.08

time (sec)

N/A 0.324 4.486 0.323 0.516 6.443 1.653 0.764 21.136

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

320 320 331 494 580 996 0 1037 502

N.S.

1 1.00 1.03 1.54 1.81 3.11 0.00 3.24 1.57

time (sec)

N/A 0.497 4.619 0.303 0.528 7.206 0.000 0.954 15.885

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

661 661 573 1239 699 697 1819 24014 891

N.S.

1 1.00 0.87 1.87 1.06 1.05 2.75 36.33 1.35

time (sec)

N/A 1.434 6.452 0.238 0.513 7.551 0.500 18.531 9.287

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

443 443 352 770 470 468 1134 13549 561

N.S.

1 1.00 0.79 1.74 1.06 1.06 2.56 30.58 1.27

time (sec)

N/A 0.826 5.179 0.181 0.512 5.084 0.347 9.574 9.119

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

266 264 241 386 266 264 617 6502 300

N.S.

1 0.99 0.91 1.45 1.00 0.99 2.32 24.44 1.13

time (sec)

N/A 0.317 1.768 0.123 0.520 5.501 0.230 3.877 9.006

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 176 162 140 138 241 2128 141

N.S.

1 1.00 1.34 1.24 1.07 1.05 1.84 16.24 1.08

time (sec)

N/A 0.105 0.726 0.077 0.515 5.627 0.135 1.411 8.808

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

254 252 190 317 295 403 4444 338 325

N.S.

1 0.99 0.75 1.25 1.16 1.59 17.50 1.33 1.28

time (sec)

N/A 0.549 1.960 0.253 0.510 4.500 2.639 0.849 11.275

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

415 415 2640 552 501 973 16225 912 2500

N.S.

1 1.00 6.36 1.33 1.21 2.34 39.10 2.20 6.02

time (sec)

N/A 0.733 7.394 0.372 0.550 5.958 3.496 0.916 34.031

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

597 597 2499 865 845 1711 0 1714 807

N.S.

1 1.00 4.19 1.45 1.42 2.87 0.00 2.87 1.35

time (sec)

N/A 0.883 7.513 0.584 0.549 3.946 0.000 1.203 29.277

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

603 603 419 1239 688 686 1819 24014 891

N.S.

1 1.00 0.69 2.05 1.14 1.14 3.02 39.82 1.48

time (sec)

N/A 1.079 6.412 0.355 0.516 2.448 0.491 20.705 9.310

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

389 387 297 639 394 392 1001 11805 478

N.S.

1 0.99 0.76 1.64 1.01 1.01 2.57 30.35 1.23

time (sec)

N/A 0.521 6.258 0.161 0.517 1.589 0.349 8.913 9.038

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

191 191 212 265 208 206 410 4300 221

N.S.

1 1.00 1.11 1.39 1.09 1.08 2.15 22.51 1.16

time (sec)

N/A 0.174 1.613 0.103 0.523 0.994 0.180 2.887 8.789

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

363 363 255 542 442 630 7096 573 508

N.S.

1 1.00 0.70 1.49 1.22 1.74 19.55 1.58 1.40

time (sec)

N/A 1.040 3.035 0.342 0.520 2.580 25.439 1.097 13.004

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

574 574 2467 829 691 1522 24300 1357 701

N.S.

1 1.00 4.30 1.44 1.20 2.65 42.33 2.36 1.22

time (sec)

N/A 1.524 7.750 0.623 0.542 4.128 33.116 1.238 15.699

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F(-2) B B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

798 798 1451 1271 1126 2562 0 2505 1172

N.S.

1 1.00 1.82 1.59 1.41 3.21 0.00 3.14 1.47

time (sec)

N/A 1.846 13.872 0.895 0.569 4.554 0.000 1.495 19.238

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

337 337 258 542 451 634 7096 573 508

N.S.

1 1.00 0.77 1.61 1.34 1.88 21.06 1.70 1.51

time (sec)

N/A 1.011 2.857 0.430 0.558 4.203 25.846 1.119 13.392

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

236 236 190 317 299 396 4444 338 325

N.S.

1 1.00 0.81 1.34 1.27 1.68 18.83 1.43 1.38

time (sec)

N/A 0.519 1.917 0.249 0.544 6.800 2.681 0.825 11.200

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 148 173 182 217 2387 186 186

N.S.

1 1.00 0.95 1.11 1.17 1.39 15.30 1.19 1.19

time (sec)

N/A 0.226 0.720 0.219 0.549 3.878 1.024 0.709 10.246

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 117 100 109 122 966 109 109

N.S.

1 1.00 1.18 1.01 1.10 1.23 9.76 1.10 1.10

time (sec)

N/A 0.069 0.140 0.186 0.591 4.741 0.609 0.635 9.898

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 164 313 197 247 307 24052 272 196

N.S.

1 0.99 1.90 1.19 1.50 1.86 145.77 1.65 1.19

time (sec)

N/A 0.177 0.974 0.335 0.597 10.941 43.033 0.765 21.398

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

281 281 543 364 525 1355 0 846 393

N.S.

1 1.00 1.93 1.30 1.87 4.82 0.00 3.01 1.40

time (sec)

N/A 0.524 4.377 0.840 0.538 11.323 0.000 0.893 63.656

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

477 477 898 647 1103 3657 0 2127 2500

N.S.

1 1.00 1.88 1.36 2.31 7.67 0.00 4.46 5.24

time (sec)

N/A 1.166 7.952 1.596 0.632 12.067 0.000 1.224 24.034

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

579 579 2463 829 690 1487 24300 1355 701

N.S.

1 1.00 4.25 1.43 1.19 2.57 41.97 2.34 1.21

time (sec)

N/A 1.403 7.740 0.464 0.535 12.852 33.483 1.235 16.677

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

417 417 2636 552 498 948 16225 912 2500

N.S.

1 1.00 6.32 1.32 1.19 2.27 38.91 2.19 6.00

time (sec)

N/A 0.729 7.352 0.351 0.558 4.403 3.737 0.940 35.258

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

292 288 606 321 323 513 9721 528 1875

N.S.

1 0.99 2.08 1.10 1.11 1.76 33.29 1.81 6.42

time (sec)

N/A 0.360 4.457 0.359 0.531 3.104 1.691 0.774 22.014

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 207 173 209 262 4396 299 184

N.S.

1 1.00 1.48 1.24 1.49 1.87 31.40 2.14 1.31

time (sec)

N/A 0.143 1.776 0.206 0.514 3.288 0.986 0.713 11.345

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

293 293 561 365 518 1285 0 846 430

N.S.

1 1.00 1.91 1.25 1.77 4.39 0.00 2.89 1.47

time (sec)

N/A 0.543 4.920 0.758 0.531 10.131 0.000 0.938 85.865

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

509 508 984 577 1192 4188 0 2893 2500

N.S.

1 1.00 1.93 1.13 2.34 8.23 0.00 5.68 4.91

time (sec)

N/A 1.402 7.841 1.601 0.616 13.104 0.000 1.227 31.511

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

841 841 1758 951 2528 9612 0 3176 2500

N.S.

1 1.00 2.09 1.13 3.01 11.43 0.00 3.78 2.97

time (sec)

N/A 2.715 7.698 3.594 0.717 20.927 0.000 1.233 58.468

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F(-2) B B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

804 804 1445 1271 1117 2503 0 2505 1172

N.S.

1 1.00 1.80 1.58 1.39 3.11 0.00 3.12 1.46

time (sec)

N/A 1.790 13.708 1.010 0.603 4.638 0.000 1.487 20.600

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

597 597 2499 865 833 1630 0 1709 807

N.S.

1 1.00 4.19 1.45 1.40 2.73 0.00 2.86 1.35

time (sec)

N/A 0.947 7.493 0.587 0.548 3.365 0.000 1.144 30.686

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

352 349 331 493 549 906 0 1037 502

N.S.

1 0.99 0.94 1.40 1.56 2.57 0.00 2.95 1.43

time (sec)

N/A 0.509 4.617 0.319 0.551 4.610 0.000 0.950 16.535

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 261 262 373 575 0 548 327

N.S.

1 1.00 1.25 1.25 1.78 2.75 0.00 2.62 1.56

time (sec)

N/A 0.250 3.485 0.281 0.547 5.260 0.000 0.893 11.877

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

487 487 912 649 1085 3510 0 2125 2500

N.S.

1 1.00 1.87 1.33 2.23 7.21 0.00 4.36 5.13

time (sec)

N/A 1.230 8.125 1.829 0.597 48.335 0.000 1.190 24.606

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F(-2) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

861 860 1732 949 2546 9585 0 3176 2500

N.S.

1 1.00 2.01 1.10 2.96 11.13 0.00 3.69 2.90

time (sec)

N/A 2.888 7.754 3.471 0.707 71.528 0.000 1.161 47.926

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

464 464 1232 3066 0 0 0 0 -1

N.S.

1 1.00 2.66 6.61 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.415 6.286 0.684 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

325 325 314 2208 0 0 0 0 -1

N.S.

1 1.00 0.97 6.79 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.863 3.185 0.491 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

224 224 220 1398 0 0 0 0 2500

N.S.

1 1.00 0.98 6.24 0.00 0.00 0.00 0.00 11.16

time (sec)

N/A 0.416 1.316 0.479 0.000 0.000 0.000 0.000 60.113

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 150 846 0 0 0 0 1199

N.S.

1 1.00 0.97 5.46 0.00 0.00 0.00 0.00 7.74

time (sec)

N/A 0.206 0.388 0.425 0.000 0.000 0.000 0.000 17.403

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

234 234 233 1394 0 0 0 0 2500

N.S.

1 1.00 1.00 5.96 0.00 0.00 0.00 0.00 10.68

time (sec)

N/A 0.720 0.458 0.618 0.000 0.000 0.000 0.000 36.224

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

317 317 362 2143 0 0 0 0 2500

N.S.

1 1.00 1.14 6.76 0.00 0.00 0.00 0.00 7.89

time (sec)

N/A 0.981 4.112 0.580 0.000 0.000 0.000 0.000 45.420

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

543 543 2819 3102 0 0 0 0 -1

N.S.

1 1.00 5.19 5.71 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.869 6.278 0.629 0.000 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

550 550 1290 5095 0 0 0 0 -1

N.S.

1 1.00 2.35 9.26 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.841 6.286 0.559 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

396 396 350 3689 0 0 0 0 -1

N.S.

1 1.00 0.88 9.32 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.128 3.955 0.523 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

273 273 260 2315 0 0 0 0 -1

N.S.

1 1.00 0.95 8.48 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.597 3.029 0.489 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

187 187 202 1293 0 0 0 0 2500

N.S.

1 1.00 1.08 6.91 0.00 0.00 0.00 0.00 13.37

time (sec)

N/A 0.290 0.870 0.498 0.000 0.000 0.000 0.000 44.865

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