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2.2.2 Integrals 101 to 200

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 101

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 131 109 303 99 222 0 322 0

N.S.

1 1.00 0.83 2.31 0.76 1.69 0.00 2.46 0.00

time (sec)

N/A 0.459 0.605 1.074 0.253 0.260 0.000 0.267 0.000

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 232 220 191 525 596 1134 580 393

N.S.

1 0.95 0.90 0.78 2.14 2.43 4.63 2.37 1.60

time (sec)

N/A 0.542 0.937 1.191 0.233 0.259 0.617 0.288 1.883

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 174 189 141 326 351 694 333 217

N.S.

1 1.00 1.09 0.81 1.87 2.02 3.99 1.91 1.25

time (sec)

N/A 0.429 0.523 1.029 0.194 0.261 0.454 0.272 1.491

Problem 104

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

122 102 86 84 167 164 357 155 104

N.S.

1 0.84 0.70 0.69 1.37 1.34 2.93 1.27 0.85

time (sec)

N/A 0.307 12.522 0.812 0.198 0.250 0.322 0.267 0.418

Problem 105

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

149 143 117 193 150 149 0 135 0

N.S.

1 0.96 0.79 1.30 1.01 1.00 0.00 0.91 0.00

time (sec)

N/A 0.581 0.770 2.357 0.249 0.253 0.000 0.272 0.000

Problem 106

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

170 173 214 313 183 266 0 1134 0

N.S.

1 1.02 1.26 1.84 1.08 1.56 0.00 6.67 0.00

time (sec)

N/A 0.566 0.804 2.410 0.251 0.248 0.000 0.335 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

236 327 198 625 205 454 0 682 0

N.S.

1 1.39 0.84 2.65 0.87 1.92 0.00 2.89 0.00

time (sec)

N/A 0.895 2.062 2.530 0.263 0.262 0.000 0.270 0.000

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 146 206 435 238 364 0 0 0

N.S.

1 1.11 1.56 3.30 1.80 2.76 0.00 0.00 0.00

time (sec)

N/A 0.793 0.994 1.445 0.309 0.254 0.000 0.000 0.000

Problem 109

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

101 115 152 227 0 201 0 0 0

N.S.

1 1.14 1.50 2.25 0.00 1.99 0.00 0.00 0.00

time (sec)

N/A 0.604 0.723 1.338 0.000 0.236 0.000 0.000 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 65 185 66 75 60 56 67 56

N.S.

1 1.03 2.94 1.05 1.19 0.95 0.89 1.06 0.89

time (sec)

N/A 0.363 0.378 1.526 0.181 0.237 0.111 0.267 1.091

Problem 111

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

23 23 25 21 102 126 117 23 24

N.S.

1 1.00 1.09 0.91 4.43 5.48 5.09 1.00 1.04

time (sec)

N/A 0.237 26.868 0.343 0.298 0.249 3.311 0.268 0.942

Problem 112

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

23 23 25 21 158 204 187 23 24

N.S.

1 1.00 1.09 0.91 6.87 8.87 8.13 1.00 1.04

time (sec)

N/A 0.235 26.722 0.342 0.333 0.257 10.174 0.317 0.995

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

305 308 473 723 635 917 0 0 0

N.S.

1 1.01 1.55 2.37 2.08 3.01 0.00 0.00 0.00

time (sec)

N/A 1.281 2.885 1.941 0.377 0.263 0.000 0.000 0.000

Problem 114

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

241 241 269 374 0 482 0 0 0

N.S.

1 1.00 1.12 1.55 0.00 2.00 0.00 0.00 0.00

time (sec)

N/A 0.978 1.688 1.411 0.000 0.237 0.000 0.000 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 154 241 113 255 160 167 195 160

N.S.

1 0.97 1.53 0.72 1.61 1.01 1.06 1.23 1.01

time (sec)

N/A 0.532 1.282 1.205 0.209 0.245 0.217 0.272 1.346

Problem 116

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

23 23 25 21 606 793 0 23 24

N.S.

1 1.00 1.09 0.91 26.35 34.48 0.00 1.00 1.04

time (sec)

N/A 0.242 25.917 0.509 0.527 0.259 0.000 0.286 1.061

Problem 117

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

23 23 25 21 723 965 0 23 24

N.S.

1 1.00 1.09 0.91 31.43 41.96 0.00 1.00 1.04

time (sec)

N/A 0.236 26.605 0.501 0.725 0.257 0.000 0.390 1.165

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

181 204 141 174 0 0 0 0 149

N.S.

1 1.13 0.78 0.96 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.773 0.266 0.901 0.000 0.000 0.000 0.000 0.799

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 164 125 151 0 0 0 0 126

N.S.

1 1.21 0.92 1.11 0.00 0.00 0.00 0.00 0.93

time (sec)

N/A 0.648 2.143 0.546 0.000 0.000 0.000 0.000 1.121

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 130 105 128 0 0 0 0 92

N.S.

1 1.17 0.95 1.15 0.00 0.00 0.00 0.00 0.83

time (sec)

N/A 0.527 0.764 0.467 0.000 0.000 0.000 0.000 1.072

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 90 87 105 0 0 0 0 80

N.S.

1 1.36 1.32 1.59 0.00 0.00 0.00 0.00 1.21

time (sec)

N/A 0.375 0.361 0.483 0.000 0.000 0.000 0.000 1.058

Problem 122

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

125 89 96 0 0 0 0 0 0

N.S.

1 0.71 0.77 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.503 0.312 0.000 0.000 0.000 0.000 0.000 0.000

Problem 123

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

149 122 133 0 0 0 0 0 0

N.S.

1 0.82 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.609 0.479 0.000 0.000 0.000 0.000 0.000 0.000

Problem 124

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

204 159 170 0 0 0 0 0 0

N.S.

1 0.78 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.744 0.587 0.000 0.000 0.000 0.000 0.000 0.000

Problem 125

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

377 398 269 0 0 0 0 0 0

N.S.

1 1.06 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.462 7.661 0.000 0.000 0.000 0.000 0.000 0.000

Problem 126

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

303 281 173 0 0 0 0 0 0

N.S.

1 0.93 0.57 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.881 7.465 0.000 0.000 0.000 0.000 0.000 0.000

Problem 127

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

185 176 138 0 0 0 0 0 0

N.S.

1 0.95 0.75 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.558 3.405 0.000 0.000 0.000 0.000 0.000 0.000

Problem 128

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

261 149 146 0 0 0 0 0 0

N.S.

1 0.57 0.56 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.538 1.721 0.000 0.000 0.000 0.000 0.000 0.000

Problem 129

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

302 184 243 0 0 0 0 0 0

N.S.

1 0.61 0.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.525 2.023 0.000 0.000 0.000 0.000 0.000 0.000

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

638 0 2918 0 0 0 0 0 0

N.S.

1 0.00 4.57 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 15.617 0.000 0.000 0.000 0.000 0.000 0.000

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

506 460 300 0 0 0 0 0 0

N.S.

1 0.91 0.59 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.289 9.753 0.000 0.000 0.000 0.000 0.000 0.000

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

312 262 218 0 0 0 0 0 0

N.S.

1 0.84 0.70 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.687 9.433 0.000 0.000 0.000 0.000 0.000 0.000

Problem 133

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

403 205 242 0 0 0 0 0 0

N.S.

1 0.51 0.60 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.635 4.701 0.000 0.000 0.000 0.000 0.000 0.000

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

444 240 347 0 0 0 0 0 0

N.S.

1 0.54 0.78 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.617 5.362 0.000 0.000 0.000 0.000 0.000 0.000

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

536 408 4751 0 0 0 0 0 0

N.S.

1 0.76 8.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.856 10.656 0.000 0.000 0.000 0.000 0.000 0.000

Problem 136

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

493 288 331 0 0 0 0 0 0

N.S.

1 0.58 0.67 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.902 0.811 0.000 0.000 0.000 0.000 0.000 0.000

Problem 137

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

349 210 276 0 0 0 0 0 0

N.S.

1 0.60 0.79 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.675 0.604 0.000 0.000 0.000 0.000 0.000 0.000

Problem 138

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

207 134 178 0 0 0 0 0 0

N.S.

1 0.65 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.429 0.448 0.000 0.000 0.000 0.000 0.000 0.000

Problem 139

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

21 21 23 17 19 40 19 19 20

N.S.

1 1.00 1.10 0.81 0.90 1.90 0.90 0.90 0.95

time (sec)

N/A 0.247 3.740 0.175 0.336 0.245 2.573 0.425 1.116

Problem 140

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

21 21 23 17 19 44 20 19 20

N.S.

1 1.00 1.10 0.81 0.90 2.10 0.95 0.90 0.95

time (sec)

N/A 0.256 3.883 0.175 0.340 0.252 4.811 0.433 1.108

Problem 141

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

807 475 546 0 0 0 0 0 0

N.S.

1 0.59 0.68 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.601 2.131 0.000 0.000 0.000 0.000 0.000 0.000

Problem 142

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

506 320 384 0 0 0 0 0 0

N.S.

1 0.63 0.76 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.996 1.162 0.000 0.000 0.000 0.000 0.000 0.000

Problem 143

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

288 215 258 0 0 0 0 0 0

N.S.

1 0.75 0.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.596 0.766 0.000 0.000 0.000 0.000 0.000 0.000

Problem 144

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

21 21 23 17 19 209 19 19 20

N.S.

1 1.00 1.10 0.81 0.90 9.95 0.90 0.90 0.95

time (sec)

N/A 0.261 21.864 0.180 0.351 0.244 28.433 0.455 1.665

Problem 145

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

21 21 23 17 19 209 20 19 20

N.S.

1 1.00 1.10 0.81 0.90 9.95 0.95 0.90 0.95

time (sec)

N/A 0.257 23.838 0.178 0.357 0.253 52.714 0.445 1.649

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1016 737 1200 0 0 0 0 0 0

N.S.

1 0.73 1.18 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.711 2.993 0.000 0.000 0.000 0.000 0.000 0.000

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

689 484 482 0 0 0 0 0 0

N.S.

1 0.70 0.70 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.598 1.477 0.000 0.000 0.000 0.000 0.000 0.000

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

416 299 337 0 0 0 0 0 0

N.S.

1 0.72 0.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.792 1.056 0.000 0.000 0.000 0.000 0.000 0.000

Problem 149

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

21 21 23 17 19 396 0 19 20

N.S.

1 1.00 1.10 0.81 0.90 18.86 0.00 0.90 0.95

time (sec)

N/A 0.257 36.544 0.193 0.354 0.251 0.000 0.490 2.069

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 23 17 19 0 17 19 20

N.S.

1 1.00 1.10 0.81 0.90 0.00 0.81 0.90 0.95

time (sec)

N/A 0.245 4.245 0.168 0.354 0.000 2.278 0.361 0.910

Problem 151

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

23 23 25 21 23 48 0 23 24

N.S.

1 1.00 1.09 0.91 1.00 2.09 0.00 1.00 1.04

time (sec)

N/A 0.240 3.029 0.391 0.352 0.266 0.000 0.362 1.065

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

410 394 410 0 375 374 0 0 0

N.S.

1 0.96 1.00 0.00 0.91 0.91 0.00 0.00 0.00

time (sec)

N/A 0.861 1.044 0.000 0.144 0.105 0.000 0.000 0.000

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

268 262 229 0 210 259 0 0 0

N.S.

1 0.98 0.85 0.00 0.78 0.97 0.00 0.00 0.00

time (sec)

N/A 0.629 0.525 0.000 0.090 0.094 0.000 0.000 0.000

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

135 135 207 0 101 134 0 0 0

N.S.

1 1.00 1.53 0.00 0.75 0.99 0.00 0.00 0.00

time (sec)

N/A 0.378 0.385 0.000 0.072 0.087 0.000 0.000 0.000

Problem 155

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

23 23 25 21 23 86 20 23 24

N.S.

1 1.00 1.09 0.91 1.00 3.74 0.87 1.00 1.04

time (sec)

N/A 0.237 3.559 0.305 0.289 0.264 11.915 0.272 0.967

Problem 156

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

23 23 25 21 23 696 0 23 24

N.S.

1 1.00 1.09 0.91 1.00 30.26 0.00 1.00 1.04

time (sec)

N/A 0.231 13.664 0.556 0.310 0.254 0.000 0.285 1.154

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 123 110 234 168 264 258 187

N.S.

1 1.00 1.38 1.24 2.63 1.89 2.97 2.90 2.10

time (sec)

N/A 0.340 0.260 1.238 0.196 0.248 0.295 0.269 0.204

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 83 83 139 102 151 146 110

N.S.

1 1.00 1.24 1.24 2.07 1.52 2.25 2.18 1.64

time (sec)

N/A 0.292 0.189 1.279 0.195 0.244 0.216 0.284 0.117

Problem 159

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

45 45 43 46 65 51 68 64 49

N.S.

1 1.00 0.96 1.02 1.44 1.13 1.51 1.42 1.09

time (sec)

N/A 0.231 0.127 0.968 0.195 0.234 0.169 0.292 0.822

Problem 160

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

64 64 57 94 71 111 0 68 0

N.S.

1 1.00 0.89 1.47 1.11 1.73 0.00 1.06 0.00

time (sec)

N/A 0.334 0.102 1.006 0.224 0.248 0.000 0.278 0.000

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 71 149 88 162 0 630 0

N.S.

1 1.00 0.82 1.71 1.01 1.86 0.00 7.24 0.00

time (sec)

N/A 0.375 0.272 1.097 0.232 0.245 0.000 0.309 0.000

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 123 95 296 99 274 0 319 0

N.S.

1 1.00 0.77 2.41 0.80 2.23 0.00 2.59 0.00

time (sec)

N/A 0.437 0.408 1.079 0.232 0.251 0.000 0.270 0.000

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

250 237 235 213 520 418 779 598 481

N.S.

1 0.95 0.94 0.85 2.08 1.67 3.12 2.39 1.92

time (sec)

N/A 0.542 0.692 1.482 0.220 0.256 0.427 0.289 2.613

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 182 249 157 322 247 456 344 281

N.S.

1 1.00 1.37 0.86 1.77 1.36 2.51 1.89 1.54

time (sec)

N/A 0.436 0.416 1.354 0.204 0.249 0.328 0.273 1.295

Problem 165

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

116 113 98 111 164 128 219 159 135

N.S.

1 0.97 0.84 0.96 1.41 1.10 1.89 1.37 1.16

time (sec)

N/A 0.315 4.399 1.053 0.195 0.245 0.226 0.285 0.161

Problem 166

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

156 156 134 201 148 232 0 144 0

N.S.

1 1.00 0.86 1.29 0.95 1.49 0.00 0.92 0.00

time (sec)

N/A 0.550 0.223 4.197 0.243 0.259 0.000 0.270 0.000

Problem 167

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

183 183 232 319 181 357 0 1135 0

N.S.

1 1.00 1.27 1.74 0.99 1.95 0.00 6.20 0.00

time (sec)

N/A 0.593 0.444 4.282 0.249 0.258 0.000 0.354 0.000

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

242 242 395 626 203 590 0 678 0

N.S.

1 1.00 1.63 2.59 0.84 2.44 0.00 2.80 0.00

time (sec)

N/A 0.719 0.615 4.362 0.257 0.249 0.000 0.280 0.000

Problem 169

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

404 377 318 0 0 1004 0 0 0

N.S.

1 0.93 0.79 0.00 0.00 2.49 0.00 0.00 0.00

time (sec)

N/A 1.673 0.184 0.000 0.000 0.278 0.000 0.000 0.000

Problem 170

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

296 283 233 0 0 708 0 0 0

N.S.

1 0.96 0.79 0.00 0.00 2.39 0.00 0.00 0.00

time (sec)

N/A 1.230 0.093 0.000 0.000 0.263 0.000 0.000 0.000

Problem 171

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

187 189 142 393 0 455 0 0 0

N.S.

1 1.01 0.76 2.10 0.00 2.43 0.00 0.00 0.00

time (sec)

N/A 0.753 0.028 1.281 0.000 0.263 0.000 0.000 0.000

Problem 172

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 27 17 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.35 0.85 1.10 1.10

time (sec)

N/A 0.237 0.892 0.518 0.308 0.246 10.270 0.286 0.877

Problem 173

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 51 19 22 22

N.S.

1 1.00 1.10 1.00 1.10 2.55 0.95 1.10 1.10

time (sec)

N/A 0.235 0.830 0.575 0.365 0.236 59.085 0.468 0.911

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

549 520 428 0 0 3957 0 0 0

N.S.

1 0.95 0.78 0.00 0.00 7.21 0.00 0.00 0.00

time (sec)

N/A 2.683 1.043 0.000 0.000 0.329 0.000 0.000 0.000

Problem 175

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

254 263 194 519 0 1717 0 0 0

N.S.

1 1.04 0.76 2.04 0.00 6.76 0.00 0.00 0.00

time (sec)

N/A 1.060 0.617 1.527 0.000 0.274 0.000 0.000 0.000

Problem 176

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

20 20 22 20 406 55 0 22 22

N.S.

1 1.00 1.10 1.00 20.30 2.75 0.00 1.10 1.10

time (sec)

N/A 0.238 26.611 0.575 0.620 0.244 0.000 0.592 1.001

Problem 177

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

20 20 22 20 606 96 0 22 22

N.S.

1 1.00 1.10 1.00 30.30 4.80 0.00 1.10 1.10

time (sec)

N/A 0.229 26.977 0.501 0.857 0.257 0.000 1.487 1.128

Problem 178

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

544 834 773 1232 0 6396 0 0 0

N.S.

1 1.53 1.42 2.26 0.00 11.76 0.00 0.00 0.00

time (sec)

N/A 3.631 5.029 2.046 0.000 0.354 0.000 0.000 0.000

Problem 179

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

20 20 22 20 1651 83 0 22 22

N.S.

1 1.00 1.10 1.00 82.55 4.15 0.00 1.10 1.10

time (sec)

N/A 0.232 46.764 0.745 2.412 0.264 0.000 1.471 0.980

Problem 180

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

20 20 22 20 2122 141 0 22 22

N.S.

1 1.00 1.10 1.00 106.10 7.05 0.00 1.10 1.10

time (sec)

N/A 0.236 46.118 0.852 3.622 0.288 0.000 60.711 1.092

Problem 181

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

20 20 22 20 22 22 0 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.00 1.10 1.10

time (sec)

N/A 0.235 3.174 0.435 0.343 0.261 0.000 0.408 0.979

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

543 543 448 0 377 829 0 0 0

N.S.

1 1.00 0.83 0.00 0.69 1.53 0.00 0.00 0.00

time (sec)

N/A 1.101 1.107 0.000 0.143 0.107 0.000 0.000 0.000

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

281 281 254 0 208 517 0 0 0

N.S.

1 1.00 0.90 0.00 0.74 1.84 0.00 0.00 0.00

time (sec)

N/A 0.622 0.464 0.000 0.088 0.088 0.000 0.000 0.000

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

131 131 118 0 101 249 0 0 0

N.S.

1 1.00 0.90 0.00 0.77 1.90 0.00 0.00 0.00

time (sec)

N/A 0.357 0.122 0.000 0.070 0.094 0.000 0.000 0.000

Problem 185

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 0.225 1.180 0.393 0.279 0.247 1.227 0.276 0.860

Problem 186

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 38 19 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.90 0.95 1.10 1.10

time (sec)

N/A 0.224 4.845 0.610 0.304 0.246 27.363 0.326 0.931

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 168 214 579 318 456 0 0 0

N.S.

1 1.03 1.31 3.55 1.95 2.80 0.00 0.00 0.00

time (sec)

N/A 0.949 1.609 1.984 0.290 0.262 0.000 0.000 0.000

Problem 188

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

130 137 187 321 0 261 0 0 0

N.S.

1 1.05 1.44 2.47 0.00 2.01 0.00 0.00 0.00

time (sec)

N/A 0.721 1.087 1.665 0.000 0.265 0.000 0.000 0.000

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 87 239 86 108 96 73 111 74

N.S.

1 0.97 2.66 0.96 1.20 1.07 0.81 1.23 0.82

time (sec)

N/A 0.473 0.752 1.888 0.223 0.252 0.150 0.268 1.298

Problem 190

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

35 38 61 28 36 33 24 33 27

N.S.

1 1.09 1.74 0.80 1.03 0.94 0.69 0.94 0.77

time (sec)

N/A 0.262 0.155 0.960 0.190 0.244 0.076 0.267 0.937

Problem 191

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

29 29 31 27 116 154 425 29 30

N.S.

1 1.00 1.07 0.93 4.00 5.31 14.66 1.00 1.03

time (sec)

N/A 0.226 37.760 0.463 0.264 0.263 12.079 0.297 1.006

Problem 192

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

29 29 31 27 194 232 631 29 30

N.S.

1 1.00 1.07 0.93 6.69 8.00 21.76 1.00 1.03

time (sec)

N/A 0.229 29.545 0.464 0.296 0.237 22.541 0.372 1.019

Problem 193

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 Yes Yes TBD TBD TBD TBD TBD

size

241 266 2619 699 671 823 0 0 0

N.S.

1 1.10 10.87 2.90 2.78 3.41 0.00 0.00 0.00

time (sec)

N/A 1.967 3.576 2.896 0.377 0.265 0.000 0.000 0.000

Problem 194

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

184 204 260 385 0 474 0 0 0

N.S.

1 1.11 1.41 2.09 0.00 2.58 0.00 0.00 0.00

time (sec)

N/A 1.474 1.952 2.503 0.000 0.263 0.000 0.000 0.000

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 130 238 134 238 172 224 251 143

N.S.

1 1.09 2.00 1.13 2.00 1.45 1.88 2.11 1.20

time (sec)

N/A 0.880 2.454 2.062 0.254 0.248 0.277 0.280 1.307

Problem 196

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

52 50 59 60 74 69 99 61 59

N.S.

1 0.96 1.13 1.15 1.42 1.33 1.90 1.17 1.13

time (sec)

N/A 0.364 0.174 1.177 0.190 0.243 0.140 0.279 1.063

Problem 197

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

31 31 33 29 177 203 950 31 32

N.S.

1 1.00 1.06 0.94 5.71 6.55 30.65 1.00 1.03

time (sec)

N/A 0.256 21.378 1.082 0.327 0.232 74.643 0.307 1.086

Problem 198

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

31 31 33 29 270 281 0 31 32

N.S.

1 1.00 1.06 0.94 8.71 9.06 0.00 1.00 1.03

time (sec)

N/A 0.255 22.822 1.062 0.364 0.257 0.000 0.414 1.098

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

393 0 376 1006 0 1044 0 0 0

N.S.

1 0.00 0.96 2.56 0.00 2.66 0.00 0.00 0.00

time (sec)

N/A 0.000 4.700 2.530 0.000 0.310 0.000 0.000 0.000

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

287 0 1661 560 0 595 0 0 0

N.S.

1 0.00 5.79 1.95 0.00 2.07 0.00 0.00 0.00

time (sec)

N/A 0.000 3.722 2.425 0.000 0.255 0.000 0.000 0.000

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