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2.2.2 Integrals 101 to 174

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 A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 136 112 127 117 441 0 126 158

N.S.

1 1.01 0.83 0.94 0.87 3.27 0.00 0.93 1.17

time (sec)

N/A 0.473 0.065 3.450 0.285 0.319 0.000 0.285 6.127

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 186 139 140 165 574 357 157 232

N.S.

1 1.01 0.75 0.76 0.89 3.10 1.93 0.85 1.25

time (sec)

N/A 0.577 0.070 3.463 0.290 0.283 98.075 0.295 6.166

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 161 126 115 136 480 282 122 0

N.S.

1 1.04 0.81 0.74 0.88 3.10 1.82 0.79 0.00

time (sec)

N/A 0.500 0.049 3.471 0.286 0.281 87.259 0.302 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 148 122 123 146 447 304 128 195

N.S.

1 1.09 0.90 0.90 1.07 3.29 2.24 0.94 1.43

time (sec)

N/A 0.468 0.062 3.421 0.289 0.279 74.789 0.291 6.034

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 127 99 97 111 357 178 97 0

N.S.

1 1.07 0.83 0.82 0.93 3.00 1.50 0.82 0.00

time (sec)

N/A 0.355 0.070 3.493 0.284 0.285 7.835 0.281 0.000

Problem 106

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

116 127 104 98 122 346 184 106 163

N.S.

1 1.09 0.90 0.84 1.05 2.98 1.59 0.91 1.41

time (sec)

N/A 0.266 0.067 3.433 0.279 0.281 3.412 0.293 5.960

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 144 117 130 133 488 0 128 0

N.S.

1 1.11 0.90 1.00 1.02 3.75 0.00 0.98 0.00

time (sec)

N/A 0.382 0.070 3.450 0.284 0.317 0.000 0.297 0.000

Problem 108

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

144 157 141 125 152 524 0 141 202

N.S.

1 1.09 0.98 0.87 1.06 3.64 0.00 0.98 1.40

time (sec)

N/A 0.569 0.062 3.416 0.299 0.311 0.000 0.303 6.257

Problem 109

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

174 188 147 169 172 696 0 162 229

N.S.

1 1.08 0.84 0.97 0.99 4.00 0.00 0.93 1.32

time (sec)

N/A 0.646 0.096 3.595 0.287 0.338 0.000 0.307 6.387

Problem 110

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

20 22 20 19 18 24 15 25 20

N.S.

1 1.10 1.00 0.95 0.90 1.20 0.75 1.25 1.00

time (sec)

N/A 0.187 0.006 3.472 0.199 0.300 0.035 0.290 0.038

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 29 18 15 22 14 22 17 14

N.S.

1 1.26 0.78 0.65 0.96 0.61 0.96 0.74 0.61

time (sec)

N/A 0.187 0.017 3.495 0.199 0.271 0.110 0.288 0.105

Problem 112

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 33 25 21 20 20 20 20 20

N.S.

1 1.32 1.00 0.84 0.80 0.80 0.80 0.80 0.80

time (sec)

N/A 0.177 0.012 3.491 0.289 0.280 0.037 0.285 0.041

Problem 113

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

30 30 30 25 24 24 22 24 24

N.S.

1 1.00 1.00 0.83 0.80 0.80 0.73 0.80 0.80

time (sec)

N/A 0.181 0.006 3.444 0.293 0.277 0.041 0.288 0.038

Problem 114

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

210 210 210 233 213 452 384 244 289

N.S.

1 1.00 1.00 1.11 1.01 2.15 1.83 1.16 1.38

time (sec)

N/A 0.405 0.097 3.470 0.274 0.274 0.463 0.281 5.914

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 172 162 185 172 368 337 195 243

N.S.

1 1.00 0.94 1.08 1.00 2.14 1.96 1.13 1.41

time (sec)

N/A 0.358 0.076 3.557 0.277 0.280 0.446 0.288 5.924

Problem 116

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

136 136 128 137 133 286 185 148 193

N.S.

1 1.00 0.94 1.01 0.98 2.10 1.36 1.09 1.42

time (sec)

N/A 0.322 0.065 3.491 0.285 0.292 0.405 0.284 5.576

Problem 117

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

100 100 98 94 94 236 160 103 96

N.S.

1 1.00 0.98 0.94 0.94 2.36 1.60 1.03 0.96

time (sec)

N/A 0.264 0.052 3.501 0.284 0.296 0.365 0.301 5.724

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 84 83 79 80 211 150 84 76

N.S.

1 1.00 0.99 0.94 0.95 2.51 1.79 1.00 0.90

time (sec)

N/A 0.285 0.045 3.468 0.278 0.284 0.515 0.301 5.758

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 83 79 79 216 151 80 80

N.S.

1 1.00 1.01 0.96 0.96 2.63 1.84 0.98 0.98

time (sec)

N/A 0.283 0.055 3.493 0.281 0.287 0.989 0.274 0.109

Problem 120

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

104 104 103 94 97 246 167 103 94

N.S.

1 1.00 0.99 0.90 0.93 2.37 1.61 0.99 0.90

time (sec)

N/A 0.296 0.060 3.425 0.277 0.274 2.246 0.278 5.986

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 137 139 129 134 292 301 148 127

N.S.

1 1.00 1.01 0.94 0.98 2.13 2.20 1.08 0.93

time (sec)

N/A 0.349 0.078 3.480 0.291 0.283 5.860 0.311 6.017

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 175 174 163 175 374 354 197 161

N.S.

1 1.00 0.99 0.93 1.00 2.14 2.02 1.13 0.92

time (sec)

N/A 0.372 0.096 3.462 0.292 0.297 24.351 0.327 5.959

Problem 123

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

211 211 211 201 214 458 398 244 197

N.S.

1 1.00 1.00 0.95 1.01 2.17 1.89 1.16 0.93

time (sec)

N/A 0.422 0.113 3.505 0.288 0.281 38.915 0.296 5.863

Problem 124

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

240 248 227 229 227 572 444 246 413

N.S.

1 1.03 0.95 0.95 0.95 2.38 1.85 1.02 1.72

time (sec)

N/A 0.527 0.080 3.591 0.274 0.295 1.155 0.307 0.106

Problem 125

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

202 208 187 182 183 478 257 196 288

N.S.

1 1.03 0.93 0.90 0.91 2.37 1.27 0.97 1.43

time (sec)

N/A 0.472 0.069 3.441 0.294 0.291 1.078 0.279 5.778

Problem 126

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

163 165 148 139 140 418 221 148 153

N.S.

1 1.01 0.91 0.85 0.86 2.56 1.36 0.91 0.94

time (sec)

N/A 0.459 0.056 3.458 0.281 0.281 0.977 0.373 5.866

Problem 127

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

118 126 122 114 117 364 201 123 113

N.S.

1 1.07 1.03 0.97 0.99 3.08 1.70 1.04 0.96

time (sec)

N/A 0.351 0.058 3.465 0.275 0.305 0.804 0.393 0.104

Problem 128

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

112 120 115 107 117 354 197 120 112

N.S.

1 1.07 1.03 0.96 1.04 3.16 1.76 1.07 1.00

time (sec)

N/A 0.368 0.040 3.469 0.288 0.271 2.034 0.294 6.079

Problem 129

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

121 127 125 116 130 378 212 121 119

N.S.

1 1.05 1.03 0.96 1.07 3.12 1.75 1.00 0.98

time (sec)

N/A 0.388 0.051 3.462 0.282 0.281 5.298 0.288 0.149

Problem 130

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

152 158 151 137 151 438 226 148 145

N.S.

1 1.04 0.99 0.90 0.99 2.88 1.49 0.97 0.95

time (sec)

N/A 0.570 0.058 3.461 0.277 0.273 19.290 0.306 6.013

Problem 131

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

189 195 190 174 194 488 0 197 181

N.S.

1 1.03 1.01 0.92 1.03 2.58 0.00 1.04 0.96

time (sec)

N/A 0.668 0.070 3.460 0.303 0.261 0.000 0.285 5.964

Problem 132

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

230 236 230 210 238 582 0 247 219

N.S.

1 1.03 1.00 0.91 1.03 2.53 0.00 1.07 0.95

time (sec)

N/A 0.761 0.079 3.489 0.286 0.270 0.000 0.314 5.613

Problem 133

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

287 298 272 268 281 762 503 294 506

N.S.

1 1.04 0.95 0.93 0.98 2.66 1.75 1.02 1.76

time (sec)

N/A 0.859 0.110 3.619 0.281 0.267 19.388 0.310 5.587

Problem 134

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

247 258 232 219 237 668 316 244 348

N.S.

1 1.04 0.94 0.89 0.96 2.70 1.28 0.99 1.41

time (sec)

N/A 0.782 0.090 3.516 0.295 0.289 17.925 0.278 0.116

Problem 135

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

207 216 176 177 193 614 280 195 206

N.S.

1 1.04 0.85 0.86 0.93 2.97 1.35 0.94 1.00

time (sec)

N/A 0.643 0.105 3.503 0.298 0.273 15.945 0.286 5.616

Problem 136

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

167 178 156 151 169 555 260 169 163

N.S.

1 1.07 0.93 0.90 1.01 3.32 1.56 1.01 0.98

time (sec)

N/A 0.524 0.100 3.489 0.285 0.259 5.710 0.294 5.512

Problem 137

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

147 164 141 139 154 504 243 146 148

N.S.

1 1.12 0.96 0.95 1.05 3.43 1.65 0.99 1.01

time (sec)

N/A 0.367 0.076 3.499 0.282 0.286 3.400 0.278 5.543

Problem 138

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

153 170 155 140 161 517 250 150 149

N.S.

1 1.11 1.01 0.92 1.05 3.38 1.63 0.98 0.97

time (sec)

N/A 0.423 0.084 3.516 0.288 0.283 11.076 0.285 0.170

Problem 139

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

168 186 169 152 181 570 0 167 166

N.S.

1 1.11 1.01 0.90 1.08 3.39 0.00 0.99 0.99

time (sec)

N/A 0.511 0.098 3.513 0.275 0.277 0.000 0.316 5.715

Problem 140

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

196 210 196 176 202 628 0 194 192

N.S.

1 1.07 1.00 0.90 1.03 3.20 0.00 0.99 0.98

time (sec)

N/A 0.836 0.078 3.516 0.280 0.274 0.000 0.279 5.595

Problem 141

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

234 248 234 212 247 678 0 245 230

N.S.

1 1.06 1.00 0.91 1.06 2.90 0.00 1.05 0.98

time (sec)

N/A 1.056 0.090 3.639 0.289 0.270 0.000 0.299 5.612

Problem 142

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

277 291 276 248 291 772 0 295 268

N.S.

1 1.05 1.00 0.90 1.05 2.79 0.00 1.06 0.97

time (sec)

N/A 1.196 0.108 3.499 0.297 0.263 0.000 0.298 5.645

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

214 219 158 142 347 177 442 259 186

N.S.

1 1.02 0.74 0.66 1.62 0.83 2.07 1.21 0.87

time (sec)

N/A 0.503 0.126 3.515 0.204 0.295 0.461 0.290 5.823

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 171 122 111 263 134 340 193 146

N.S.

1 1.02 0.73 0.66 1.57 0.80 2.04 1.16 0.87

time (sec)

N/A 0.444 0.092 3.487 0.197 0.262 0.378 0.312 5.778

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 126 89 82 180 94 238 127 103

N.S.

1 1.04 0.74 0.68 1.49 0.78 1.97 1.05 0.85

time (sec)

N/A 0.348 0.071 3.470 0.275 0.254 0.294 0.269 5.721

Problem 146

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

103 108 86 82 122 205 134 125 99

N.S.

1 1.05 0.83 0.80 1.18 1.99 1.30 1.21 0.96

time (sec)

N/A 0.362 0.113 3.516 0.469 0.286 4.479 0.285 6.335

Problem 147

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

100 101 92 88 104 210 138 113 99

N.S.

1 1.01 0.92 0.88 1.04 2.10 1.38 1.13 0.99

time (sec)

N/A 0.440 0.182 3.537 0.206 0.309 12.825 0.295 6.423

Problem 148

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

114 145 102 95 128 221 194 140 133

N.S.

1 1.27 0.89 0.83 1.12 1.94 1.70 1.23 1.17

time (sec)

N/A 0.437 0.210 3.561 0.203 0.315 33.693 0.288 6.990

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

146 182 126 116 193 261 303 228 199

N.S.

1 1.25 0.86 0.79 1.32 1.79 2.08 1.56 1.36

time (sec)

N/A 0.463 0.243 3.572 0.196 0.294 40.705 0.288 7.622

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

195 218 159 148 275 341 444 356 277

N.S.

1 1.12 0.82 0.76 1.41 1.75 2.28 1.83 1.42

time (sec)

N/A 0.497 0.367 3.568 0.192 0.354 103.418 0.293 7.854

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 221 218 169 339 414 243 218 0

N.S.

1 0.90 0.89 0.69 1.38 1.69 0.99 0.89 0.00

time (sec)

N/A 0.443 0.977 3.699 0.201 0.360 0.613 0.316 0.000

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 191 159 137 255 329 199 170 0

N.S.

1 0.98 0.82 0.71 1.31 1.70 1.03 0.88 0.00

time (sec)

N/A 0.406 0.630 3.649 0.197 0.313 0.571 0.310 0.000

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 161 129 108 174 250 155 125 0

N.S.

1 1.11 0.89 0.74 1.20 1.72 1.07 0.86 0.00

time (sec)

N/A 0.333 0.335 3.685 0.200 0.297 0.407 0.307 0.000

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 132 105 93 118 216 246 113 0

N.S.

1 1.13 0.90 0.79 1.01 1.85 2.10 0.97 0.00

time (sec)

N/A 0.340 0.193 3.608 0.214 0.269 0.918 0.317 0.000

Problem 155

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

110 120 95 83 102 210 196 171 143

N.S.

1 1.09 0.86 0.75 0.93 1.91 1.78 1.55 1.30

time (sec)

N/A 0.336 0.194 3.605 0.196 0.284 1.088 0.363 7.205

Problem 156

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

118 136 98 90 128 221 427 319 105

N.S.

1 1.15 0.83 0.76 1.08 1.87 3.62 2.70 0.89

time (sec)

N/A 0.342 0.228 3.555 0.199 0.279 1.490 0.331 6.653

Problem 157

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

140 156 103 92 193 100 891 548 124

N.S.

1 1.11 0.74 0.66 1.38 0.71 6.36 3.91 0.89

time (sec)

N/A 0.438 0.205 3.583 0.197 0.313 2.123 0.324 6.072

Problem 158

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

189 186 134 123 275 141 1642 660 171

N.S.

1 0.98 0.71 0.65 1.46 0.75 8.69 3.49 0.90

time (sec)

N/A 0.464 0.295 3.677 0.192 0.396 2.922 0.336 6.136

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

381 310 259 236 1221 987 0 342 0

N.S.

1 0.81 0.68 0.62 3.20 2.59 0.00 0.90 0.00

time (sec)

N/A 0.650 1.262 3.750 0.224 0.529 0.000 0.312 0.000

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

279 245 215 196 986 816 0 265 0

N.S.

1 0.88 0.77 0.70 3.53 2.92 0.00 0.95 0.00

time (sec)

N/A 0.548 1.008 3.672 0.229 0.434 0.000 0.306 0.000

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

210 230 178 164 753 653 6467 203 0

N.S.

1 1.10 0.85 0.78 3.59 3.11 30.80 0.97 0.00

time (sec)

N/A 0.613 1.005 3.646 0.233 0.400 94.777 0.319 0.000

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 220 147 139 533 491 3803 160 0

N.S.

1 1.23 0.82 0.78 2.98 2.74 21.25 0.89 0.00

time (sec)

N/A 0.562 0.592 3.585 0.247 0.385 66.249 0.290 0.000

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 183 98 89 335 141 2088 131 0

N.S.

1 1.37 0.73 0.66 2.50 1.05 15.58 0.98 0.00

time (sec)

N/A 0.522 0.421 3.575 0.202 0.339 47.665 0.289 0.000

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 187 133 123 313 182 2392 211 0

N.S.

1 1.01 0.72 0.66 1.69 0.98 12.93 1.14 0.00

time (sec)

N/A 0.458 0.652 3.548 0.202 0.322 77.574 0.351 0.000

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

242 218 165 156 337 225 2861 349 0

N.S.

1 0.90 0.68 0.64 1.39 0.93 11.82 1.44 0.00

time (sec)

N/A 0.515 0.512 3.553 0.222 0.394 120.749 0.292 0.000

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

281 233 202 185 398 270 0 592 405

N.S.

1 0.83 0.72 0.66 1.42 0.96 0.00 2.11 1.44

time (sec)

N/A 0.514 0.565 3.641 0.212 0.523 0.000 0.304 7.412

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

334 261 234 218 489 311 0 938 421

N.S.

1 0.78 0.70 0.65 1.46 0.93 0.00 2.81 1.26

time (sec)

N/A 0.554 0.631 3.579 0.207 0.700 0.000 0.322 7.744

Problem 168

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

392 289 270 249 579 354 0 1162 0

N.S.

1 0.74 0.69 0.64 1.48 0.90 0.00 2.96 0.00

time (sec)

N/A 0.567 0.720 3.653 0.210 0.973 0.000 0.310 0.000

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

214 219 158 142 347 177 442 259 186

N.S.

1 1.02 0.74 0.66 1.62 0.83 2.07 1.21 0.87

time (sec)

N/A 0.527 0.029 3.685 0.200 0.293 0.458 0.291 6.072

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 171 122 111 263 134 340 193 146

N.S.

1 1.02 0.73 0.66 1.57 0.80 2.04 1.16 0.87

time (sec)

N/A 0.451 0.020 3.508 0.215 0.289 0.365 0.294 5.886

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 126 89 82 180 94 238 127 103

N.S.

1 1.04 0.74 0.68 1.49 0.78 1.97 1.05 0.85

time (sec)

N/A 0.374 0.016 3.550 0.211 0.294 0.291 0.282 5.992

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

261 285 205 193 826 705 6987 224 0

N.S.

1 1.09 0.79 0.74 3.16 2.70 26.77 0.86 0.00

time (sec)

N/A 1.097 1.183 3.640 0.228 0.430 108.770 0.296 0.000

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

214 269 176 167 597 567 5071 204 0

N.S.

1 1.26 0.82 0.78 2.79 2.65 23.70 0.95 0.00

time (sec)

N/A 0.806 0.640 3.594 0.245 0.429 74.123 0.315 0.000

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 246 138 131 421 187 2490 220 0

N.S.

1 1.27 0.72 0.68 2.18 0.97 12.90 1.14 0.00

time (sec)

N/A 0.641 0.498 3.607 0.207 0.342 98.387 0.310 0.000

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