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
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 | 92 | 92 | 92 | 86 | 88 | 207 | 138 | 101 | 135 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.96 | 2.25 | 1.50 | 1.10 | 1.47 |
time (sec) |
N/A | 0.057 | 0.104 | 2.895 | 0.206 | 0.269 | 7.219 | 0.304 | 5.279 |
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 | 109 | 109 | 87 | 87 | 109 | 211 | 165 | 89 | 103 |
N.S. |
1 | 1.00 | 0.80 | 0.80 | 1.00 | 1.94 | 1.51 | 0.82 | 0.94 |
time (sec) |
N/A | 0.065 | 0.147 | 2.956 | 0.199 | 0.266 | 18.275 | 0.300 | 5.564 |
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 | 143 | 140 | 104 | 98 | 173 | 225 | 219 | 153 | 137 |
N.S. |
1 | 0.98 | 0.73 | 0.69 | 1.21 | 1.57 | 1.53 | 1.07 | 0.96 |
time (sec) |
N/A | 0.113 | 0.205 | 2.970 | 0.200 | 0.250 | 53.203 | 0.299 | 5.645 |
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 | 149 | 149 | 126 | 117 | 247 | 276 | 291 | 222 | 193 |
N.S. |
1 | 1.00 | 0.85 | 0.79 | 1.66 | 1.85 | 1.95 | 1.49 | 1.30 |
time (sec) |
N/A | 0.105 | 0.210 | 2.907 | 0.199 | 0.266 | 65.945 | 0.291 | 6.238 |
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 | 191 | 188 | 164 | 141 | 237 | 341 | 250 | 174 | 0 |
N.S. |
1 | 0.98 | 0.86 | 0.74 | 1.24 | 1.79 | 1.31 | 0.91 | 0.00 |
time (sec) |
N/A | 0.125 | 0.591 | 3.014 | 0.203 | 0.297 | 0.377 | 0.290 | 0.000 |
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 | 149 | 149 | 121 | 106 | 168 | 262 | 189 | 128 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.71 | 1.13 | 1.76 | 1.27 | 0.86 | 0.00 |
time (sec) |
N/A | 0.065 | 0.145 | 2.971 | 0.195 | 0.291 | 0.318 | 0.306 | 0.000 |
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 | 133 | 130 | 115 | 96 | 120 | 215 | 233 | 121 | 0 |
N.S. |
1 | 0.98 | 0.86 | 0.72 | 0.90 | 1.62 | 1.75 | 0.91 | 0.00 |
time (sec) |
N/A | 0.067 | 0.303 | 2.917 | 0.201 | 0.274 | 1.399 | 0.297 | 0.000 |
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 | 111 | 111 | 90 | 82 | 86 | 210 | 190 | 183 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.77 | 1.89 | 1.71 | 1.65 | 0.00 |
time (sec) |
N/A | 0.048 | 0.172 | 2.935 | 0.194 | 0.264 | 1.525 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 104 | 101 | 94 | 221 | 199 | 403 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.98 | 0.91 | 2.15 | 1.93 | 3.91 | 0.00 |
time (sec) |
N/A | 0.048 | 0.159 | 2.945 | 0.201 | 0.281 | 1.829 | 0.300 | 0.000 |
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 | 99 | 100 | 76 | 69 | 124 | 107 | 510 | 490 | 181 |
N.S. |
1 | 1.01 | 0.77 | 0.70 | 1.25 | 1.08 | 5.15 | 4.95 | 1.83 |
time (sec) |
N/A | 0.051 | 0.150 | 2.882 | 0.211 | 0.274 | 1.743 | 0.306 | 6.223 |
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 | 143 | 144 | 108 | 95 | 190 | 147 | 1061 | 579 | 249 |
N.S. |
1 | 1.01 | 0.76 | 0.66 | 1.33 | 1.03 | 7.42 | 4.05 | 1.74 |
time (sec) |
N/A | 0.116 | 0.186 | 2.945 | 0.218 | 0.315 | 2.343 | 0.307 | 7.098 |
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 | 190 | 141 | 129 | 258 | 185 | 1856 | 668 | 317 |
N.S. |
1 | 1.01 | 0.75 | 0.68 | 1.37 | 0.98 | 9.82 | 3.53 | 1.68 |
time (sec) |
N/A | 0.153 | 0.215 | 2.980 | 0.204 | 0.374 | 3.039 | 0.316 | 7.598 |
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 | 281 | 278 | 259 | 201 | 367 | 494 | 534 | 263 | 0 |
N.S. |
1 | 0.99 | 0.92 | 0.72 | 1.31 | 1.76 | 1.90 | 0.94 | 0.00 |
time (sec) |
N/A | 0.189 | 0.946 | 3.050 | 0.232 | 0.415 | 0.510 | 0.309 | 0.000 |
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 | 114 | 114 | 100 | 91 | 181 | 179 | 384 | 150 | 170 |
N.S. |
1 | 1.00 | 0.88 | 0.80 | 1.59 | 1.57 | 3.37 | 1.32 | 1.49 |
time (sec) |
N/A | 0.064 | 0.073 | 2.882 | 0.233 | 0.255 | 0.449 | 0.288 | 5.520 |
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 | 235 | 232 | 200 | 173 | 299 | 419 | 432 | 219 | 0 |
N.S. |
1 | 0.99 | 0.85 | 0.74 | 1.27 | 1.78 | 1.84 | 0.93 | 0.00 |
time (sec) |
N/A | 0.145 | 0.807 | 2.983 | 0.211 | 0.332 | 0.451 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 67 | 60 | 115 | 141 | 303 | 98 | 136 |
N.S. |
1 | 1.00 | 0.87 | 0.78 | 1.49 | 1.83 | 3.94 | 1.27 | 1.77 |
time (sec) |
N/A | 0.041 | 0.054 | 2.953 | 0.198 | 0.262 | 0.361 | 0.294 | 5.353 |
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 | 196 | 196 | 158 | 144 | 227 | 344 | 330 | 175 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.73 | 1.16 | 1.76 | 1.68 | 0.89 | 0.00 |
time (sec) |
N/A | 0.082 | 0.215 | 2.938 | 0.195 | 0.299 | 0.386 | 0.311 | 0.000 |
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 | 111 | 111 | 103 | 111 | 103 | 282 | 158 | 121 | 191 |
N.S. |
1 | 1.00 | 0.93 | 1.00 | 0.93 | 2.54 | 1.42 | 1.09 | 1.72 |
time (sec) |
N/A | 0.078 | 0.135 | 2.903 | 0.194 | 0.266 | 15.913 | 0.293 | 5.299 |
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 | 175 | 172 | 145 | 127 | 178 | 293 | 529 | 168 | 0 |
N.S. |
1 | 0.98 | 0.83 | 0.73 | 1.02 | 1.67 | 3.02 | 0.96 | 0.00 |
time (sec) |
N/A | 0.079 | 0.554 | 2.918 | 0.199 | 0.275 | 1.965 | 0.323 | 0.000 |
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 | 108 | 117 | 138 | 267 | 337 | 126 | 201 |
N.S. |
1 | 1.00 | 0.79 | 0.86 | 1.01 | 1.96 | 2.48 | 0.93 | 1.48 |
time (sec) |
N/A | 0.082 | 0.171 | 2.919 | 0.192 | 0.268 | 21.315 | 0.297 | 5.763 |
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 | 184 | 181 | 127 | 108 | 177 | 266 | 435 | 257 | 0 |
N.S. |
1 | 0.98 | 0.69 | 0.59 | 0.96 | 1.45 | 2.36 | 1.40 | 0.00 |
time (sec) |
N/A | 0.099 | 0.333 | 2.910 | 0.194 | 0.265 | 2.554 | 0.324 | 0.000 |
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 | 181 | 178 | 116 | 113 | 222 | 267 | 348 | 182 | 208 |
N.S. |
1 | 0.98 | 0.64 | 0.62 | 1.23 | 1.48 | 1.92 | 1.01 | 1.15 |
time (sec) |
N/A | 0.147 | 0.200 | 2.907 | 0.201 | 0.273 | 59.380 | 0.309 | 6.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 112 | 120 | 147 | 266 | 347 | 407 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.82 | 1.00 | 1.81 | 2.36 | 2.77 | 0.00 |
time (sec) |
N/A | 0.062 | 0.261 | 2.965 | 0.193 | 0.281 | 3.001 | 0.353 | 0.000 |
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 | 187 | 184 | 133 | 128 | 301 | 301 | 367 | 259 | 215 |
N.S. |
1 | 0.98 | 0.71 | 0.68 | 1.61 | 1.61 | 1.96 | 1.39 | 1.15 |
time (sec) |
N/A | 0.151 | 0.237 | 2.943 | 0.203 | 0.267 | 84.178 | 0.309 | 6.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 99 | 91 | 181 | 216 | 468 | 150 | 207 |
N.S. |
1 | 1.00 | 0.87 | 0.80 | 1.59 | 1.89 | 4.11 | 1.32 | 1.82 |
time (sec) |
N/A | 0.069 | 0.076 | 2.938 | 0.202 | 0.254 | 0.656 | 0.306 | 5.553 |
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 | 281 | 278 | 259 | 203 | 361 | 495 | 665 | 265 | 0 |
N.S. |
1 | 0.99 | 0.92 | 0.72 | 1.28 | 1.76 | 2.37 | 0.94 | 0.00 |
time (sec) |
N/A | 0.177 | 1.037 | 3.029 | 0.201 | 0.398 | 0.574 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 67 | 60 | 115 | 178 | 384 | 98 | 98 |
N.S. |
1 | 1.00 | 0.87 | 0.78 | 1.49 | 2.31 | 4.99 | 1.27 | 1.27 |
time (sec) |
N/A | 0.040 | 0.054 | 2.887 | 0.196 | 0.250 | 0.520 | 0.294 | 5.337 |
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 | 240 | 240 | 191 | 170 | 286 | 420 | 520 | 221 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 1.19 | 1.75 | 2.17 | 0.92 | 0.00 |
time (sec) |
N/A | 0.104 | 0.285 | 3.002 | 0.208 | 0.327 | 0.478 | 0.343 | 0.000 |
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 | 132 | 132 | 115 | 125 | 120 | 360 | 178 | 141 | 249 |
N.S. |
1 | 1.00 | 0.87 | 0.95 | 0.91 | 2.73 | 1.35 | 1.07 | 1.89 |
time (sec) |
N/A | 0.092 | 0.139 | 2.941 | 0.197 | 0.265 | 22.113 | 0.295 | 5.362 |
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 | 217 | 214 | 175 | 161 | 235 | 375 | 915 | 214 | 0 |
N.S. |
1 | 0.99 | 0.81 | 0.74 | 1.08 | 1.73 | 4.22 | 0.99 | 0.00 |
time (sec) |
N/A | 0.101 | 0.298 | 2.984 | 0.220 | 0.299 | 2.580 | 0.343 | 0.000 |
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 | 162 | 162 | 133 | 153 | 170 | 349 | 570 | 165 | 274 |
N.S. |
1 | 1.00 | 0.82 | 0.94 | 1.05 | 2.15 | 3.52 | 1.02 | 1.69 |
time (sec) |
N/A | 0.095 | 0.196 | 2.997 | 0.215 | 0.268 | 24.117 | 0.301 | 5.835 |
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 | 223 | 219 | 163 | 146 | 234 | 346 | 750 | 302 | 0 |
N.S. |
1 | 0.98 | 0.73 | 0.65 | 1.05 | 1.55 | 3.36 | 1.35 | 0.00 |
time (sec) |
N/A | 0.134 | 0.463 | 2.975 | 0.198 | 0.280 | 3.116 | 0.421 | 0.000 |
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 | 222 | 219 | 153 | 144 | 271 | 319 | 507 | 242 | 262 |
N.S. |
1 | 0.99 | 0.69 | 0.65 | 1.22 | 1.44 | 2.28 | 1.09 | 1.18 |
time (sec) |
N/A | 0.171 | 0.204 | 3.002 | 0.218 | 0.258 | 62.050 | 0.314 | 6.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 225 | 164 | 148 | 285 | 318 | 607 | 510 | 0 |
N.S. |
1 | 0.99 | 0.72 | 0.65 | 1.25 | 1.39 | 2.66 | 2.24 | 0.00 |
time (sec) |
N/A | 0.134 | 0.399 | 2.976 | 0.207 | 0.296 | 4.008 | 0.363 | 0.000 |
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 | 222 | 219 | 152 | 144 | 353 | 347 | 484 | 286 | 301 |
N.S. |
1 | 0.99 | 0.68 | 0.65 | 1.59 | 1.56 | 2.18 | 1.29 | 1.36 |
time (sec) |
N/A | 0.183 | 0.259 | 2.942 | 0.212 | 0.276 | 89.314 | 0.319 | 7.165 |
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 | 194 | 166 | 144 | 243 | 344 | 219 | 178 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.74 | 1.25 | 1.77 | 1.13 | 0.92 | 0.00 |
time (sec) |
N/A | 0.139 | 0.577 | 2.990 | 0.209 | 0.298 | 0.379 | 0.342 | 0.000 |
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 | 112 | 112 | 99 | 91 | 181 | 103 | 240 | 137 | 105 |
N.S. |
1 | 1.00 | 0.88 | 0.81 | 1.62 | 0.92 | 2.14 | 1.22 | 0.94 |
time (sec) |
N/A | 0.081 | 0.058 | 2.856 | 0.198 | 0.262 | 0.297 | 0.316 | 5.259 |
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 | 146 | 146 | 131 | 109 | 175 | 267 | 177 | 135 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.75 | 1.20 | 1.83 | 1.21 | 0.92 | 0.00 |
time (sec) |
N/A | 0.109 | 0.453 | 2.922 | 0.196 | 0.276 | 0.340 | 0.331 | 0.000 |
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 | 74 | 74 | 66 | 60 | 114 | 68 | 158 | 84 | 68 |
N.S. |
1 | 1.00 | 0.89 | 0.81 | 1.54 | 0.92 | 2.14 | 1.14 | 0.92 |
time (sec) |
N/A | 0.050 | 0.043 | 2.866 | 0.182 | 0.263 | 0.229 | 0.299 | 5.150 |
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 | 107 | 107 | 90 | 78 | 109 | 194 | 134 | 91 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.73 | 1.02 | 1.81 | 1.25 | 0.85 | 0.00 |
time (sec) |
N/A | 0.042 | 0.092 | 2.925 | 0.209 | 0.270 | 0.305 | 0.305 | 0.000 |
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 | 75 | 75 | 63 | 63 | 75 | 157 | 109 | 82 | 77 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 1.00 | 2.09 | 1.45 | 1.09 | 1.03 |
time (sec) |
N/A | 0.050 | 0.069 | 2.859 | 0.194 | 0.274 | 5.288 | 0.317 | 5.273 |
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 | 82 | 82 | 79 | 69 | 73 | 165 | 151 | 88 | 125 |
N.S. |
1 | 1.00 | 0.96 | 0.84 | 0.89 | 2.01 | 1.84 | 1.07 | 1.52 |
time (sec) |
N/A | 0.044 | 0.113 | 2.967 | 0.202 | 0.261 | 0.829 | 0.290 | 6.208 |
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 | 80 | 80 | 77 | 72 | 77 | 175 | 99 | 81 | 65 |
N.S. |
1 | 1.00 | 0.96 | 0.90 | 0.96 | 2.19 | 1.24 | 1.01 | 0.81 |
time (sec) |
N/A | 0.051 | 0.120 | 2.910 | 0.211 | 0.272 | 15.943 | 0.287 | 5.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 73 | 61 | 77 | 173 | 129 | 156 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.73 | 0.92 | 2.06 | 1.54 | 1.86 | 0.00 |
time (sec) |
N/A | 0.036 | 0.118 | 2.914 | 0.200 | 0.262 | 1.047 | 0.320 | 0.000 |
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 | 106 | 106 | 92 | 87 | 123 | 204 | 178 | 140 | 129 |
N.S. |
1 | 1.00 | 0.87 | 0.82 | 1.16 | 1.92 | 1.68 | 1.32 | 1.22 |
time (sec) |
N/A | 0.087 | 0.166 | 2.876 | 0.213 | 0.272 | 42.370 | 0.289 | 5.571 |
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 | 99 | 100 | 74 | 69 | 124 | 73 | 391 | 312 | 77 |
N.S. |
1 | 1.01 | 0.75 | 0.70 | 1.25 | 0.74 | 3.95 | 3.15 | 0.78 |
time (sec) |
N/A | 0.051 | 0.114 | 2.915 | 0.199 | 0.270 | 1.549 | 0.289 | 5.441 |
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 | 151 | 151 | 128 | 117 | 190 | 279 | 301 | 241 | 207 |
N.S. |
1 | 1.00 | 0.85 | 0.77 | 1.26 | 1.85 | 1.99 | 1.60 | 1.37 |
time (sec) |
N/A | 0.110 | 0.305 | 2.939 | 0.197 | 0.287 | 50.925 | 0.284 | 5.960 |
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 | 197 | 197 | 162 | 146 | 241 | 431 | 0 | 175 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.74 | 1.22 | 2.19 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.117 | 0.568 | 3.009 | 0.217 | 0.307 | 0.000 | 0.318 | 0.000 |
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 | 108 | 108 | 97 | 92 | 180 | 115 | 236 | 149 | 107 |
N.S. |
1 | 1.00 | 0.90 | 0.85 | 1.67 | 1.06 | 2.19 | 1.38 | 0.99 |
time (sec) |
N/A | 0.063 | 0.064 | 2.912 | 0.219 | 0.263 | 0.323 | 0.287 | 5.635 |
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 | 152 | 152 | 129 | 117 | 170 | 350 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.77 | 1.12 | 2.30 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.082 | 0.363 | 2.984 | 0.208 | 0.285 | 0.000 | 0.308 | 0.000 |
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 | 73 | 73 | 65 | 61 | 115 | 79 | 155 | 92 | 75 |
N.S. |
1 | 1.00 | 0.89 | 0.84 | 1.58 | 1.08 | 2.12 | 1.26 | 1.03 |
time (sec) |
N/A | 0.039 | 0.048 | 2.896 | 0.195 | 0.263 | 0.252 | 0.323 | 5.519 |
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 | 106 | 106 | 92 | 92 | 108 | 275 | 0 | 92 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.87 | 1.02 | 2.59 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.039 | 0.146 | 2.950 | 0.211 | 0.279 | 0.000 | 0.323 | 0.000 |
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 | 75 | 75 | 75 | 86 | 90 | 232 | 102 | 82 | 76 |
N.S. |
1 | 1.00 | 1.00 | 1.15 | 1.20 | 3.09 | 1.36 | 1.09 | 1.01 |
time (sec) |
N/A | 0.056 | 0.085 | 2.885 | 0.233 | 0.271 | 6.749 | 0.279 | 5.601 |
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 | 91 | 87 | 88 | 97 | 91 | 239 | 0 | 104 | 0 |
N.S. |
1 | 0.96 | 0.97 | 1.07 | 1.00 | 2.63 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.045 | 0.132 | 3.010 | 0.226 | 0.273 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 106 | 97 | 98 | 112 | 292 | 0 | 140 | 119 |
N.S. |
1 | 1.03 | 0.94 | 0.95 | 1.09 | 2.83 | 0.00 | 1.36 | 1.16 |
time (sec) |
N/A | 0.077 | 0.203 | 2.914 | 0.202 | 0.284 | 0.000 | 0.275 | 5.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 98 | 74 | 69 | 117 | 85 | 0 | 199 | 76 |
N.S. |
1 | 1.01 | 0.76 | 0.71 | 1.21 | 0.88 | 0.00 | 2.05 | 0.78 |
time (sec) |
N/A | 0.051 | 0.117 | 2.943 | 0.200 | 0.273 | 0.000 | 0.298 | 5.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 125 | 123 | 177 | 364 | 0 | 163 | 179 |
N.S. |
1 | 1.00 | 0.86 | 0.85 | 1.22 | 2.51 | 0.00 | 1.12 | 1.23 |
time (sec) |
N/A | 0.123 | 0.289 | 2.958 | 0.206 | 0.281 | 0.000 | 0.297 | 5.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 103 | 101 | 184 | 121 | 0 | 452 | 116 |
N.S. |
1 | 1.00 | 0.73 | 0.72 | 1.30 | 0.86 | 0.00 | 3.21 | 0.82 |
time (sec) |
N/A | 0.081 | 0.155 | 2.914 | 0.199 | 0.290 | 0.000 | 0.307 | 5.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 190 | 191 | 158 | 156 | 247 | 447 | 0 | 267 | 246 |
N.S. |
1 | 1.01 | 0.83 | 0.82 | 1.30 | 2.35 | 0.00 | 1.41 | 1.29 |
time (sec) |
N/A | 0.151 | 0.274 | 2.986 | 0.206 | 0.283 | 0.000 | 0.288 | 6.328 |
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 | 202 | 202 | 163 | 147 | 296 | 522 | 0 | 190 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.73 | 1.47 | 2.58 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.120 | 0.414 | 3.033 | 0.242 | 0.303 | 0.000 | 0.307 | 0.000 |
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 | 110 | 110 | 98 | 91 | 181 | 124 | 454 | 140 | 107 |
N.S. |
1 | 1.00 | 0.89 | 0.83 | 1.65 | 1.13 | 4.13 | 1.27 | 0.97 |
time (sec) |
N/A | 0.066 | 0.061 | 2.928 | 0.214 | 0.284 | 0.419 | 0.291 | 5.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 122 | 116 | 211 | 409 | 0 | 130 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.96 | 1.74 | 3.38 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.076 | 0.396 | 3.012 | 0.207 | 0.283 | 0.000 | 0.308 | 0.000 |
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 | 72 | 72 | 67 | 60 | 114 | 91 | 303 | 79 | 76 |
N.S. |
1 | 1.00 | 0.93 | 0.83 | 1.58 | 1.26 | 4.21 | 1.10 | 1.06 |
time (sec) |
N/A | 0.039 | 0.049 | 2.918 | 0.202 | 0.250 | 0.355 | 0.272 | 5.532 |
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 | 105 | 105 | 91 | 104 | 147 | 321 | 0 | 105 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.99 | 1.40 | 3.06 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.037 | 0.170 | 2.932 | 0.205 | 0.261 | 0.000 | 0.317 | 0.000 |
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 | 88 | 88 | 87 | 97 | 108 | 316 | 119 | 102 | 90 |
N.S. |
1 | 1.00 | 0.99 | 1.10 | 1.23 | 3.59 | 1.35 | 1.16 | 1.02 |
time (sec) |
N/A | 0.070 | 0.134 | 2.914 | 0.195 | 0.271 | 9.129 | 0.290 | 5.875 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 76 | 70 | 132 | 92 | 0 | 117 | 77 |
N.S. |
1 | 1.00 | 0.84 | 0.78 | 1.47 | 1.02 | 0.00 | 1.30 | 0.86 |
time (sec) |
N/A | 0.039 | 0.136 | 2.900 | 0.195 | 0.250 | 0.000 | 0.297 | 5.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 134 | 120 | 119 | 146 | 426 | 0 | 128 | 147 |
N.S. |
1 | 1.02 | 0.92 | 0.91 | 1.11 | 3.25 | 0.00 | 0.98 | 1.12 |
time (sec) |
N/A | 0.096 | 0.202 | 2.979 | 0.193 | 0.257 | 0.000 | 0.308 | 5.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 130 | 107 | 99 | 175 | 130 | 0 | 258 | 187 |
N.S. |
1 | 0.99 | 0.82 | 0.76 | 1.34 | 0.99 | 0.00 | 1.97 | 1.43 |
time (sec) |
N/A | 0.084 | 0.148 | 2.919 | 0.219 | 0.260 | 0.000 | 0.298 | 5.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 185 | 159 | 154 | 231 | 537 | 0 | 210 | 216 |
N.S. |
1 | 1.00 | 0.86 | 0.83 | 1.25 | 2.90 | 0.00 | 1.14 | 1.17 |
time (sec) |
N/A | 0.157 | 0.220 | 3.001 | 0.186 | 0.271 | 0.000 | 0.290 | 6.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 183 | 183 | 142 | 131 | 244 | 171 | 0 | 509 | 298 |
N.S. |
1 | 1.00 | 0.78 | 0.72 | 1.33 | 0.93 | 0.00 | 2.78 | 1.63 |
time (sec) |
N/A | 0.114 | 0.212 | 2.982 | 0.204 | 0.286 | 0.000 | 0.313 | 5.883 |
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 | 72 | 72 | 71 | 54 | 67 | 147 | 75 | 56 | 51 |
N.S. |
1 | 1.00 | 0.99 | 0.75 | 0.93 | 2.04 | 1.04 | 0.78 | 0.71 |
time (sec) |
N/A | 0.018 | 0.068 | 3.040 | 0.308 | 0.246 | 1.423 | 0.273 | 5.231 |
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 | 52 | 60 | 38 | 49 | 126 | 54 | 40 | 37 |
N.S. |
1 | 1.00 | 1.15 | 0.73 | 0.94 | 2.42 | 1.04 | 0.77 | 0.71 |
time (sec) |
N/A | 0.010 | 0.047 | 2.889 | 0.334 | 0.238 | 1.382 | 0.276 | 5.382 |
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 | 34 | 34 | 42 | 24 | 23 | 94 | 32 | 22 | 23 |
N.S. |
1 | 1.00 | 1.24 | 0.71 | 0.68 | 2.76 | 0.94 | 0.65 | 0.68 |
time (sec) |
N/A | 0.006 | 0.022 | 2.889 | 0.345 | 0.246 | 0.997 | 0.302 | 5.318 |
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 | 50 | 50 | 63 | 36 | 35 | 132 | 49 | 43 | 38 |
N.S. |
1 | 1.00 | 1.26 | 0.72 | 0.70 | 2.64 | 0.98 | 0.86 | 0.76 |
time (sec) |
N/A | 0.012 | 0.063 | 2.879 | 0.310 | 0.257 | 1.288 | 0.285 | 5.336 |
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 | 68 | 68 | 70 | 57 | 52 | 157 | 70 | 54 | 53 |
N.S. |
1 | 1.00 | 1.03 | 0.84 | 0.76 | 2.31 | 1.03 | 0.79 | 0.78 |
time (sec) |
N/A | 0.016 | 0.075 | 2.968 | 0.319 | 0.255 | 1.138 | 0.296 | 5.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 395 | 136 | 0 | 857 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.52 | 0.87 | 0.00 | 5.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.169 | 1.905 | 3.025 | 0.000 | 0.368 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 85 | 83 | 0 | 295 | 119 | 96 | 86 |
N.S. |
1 | 1.00 | 0.97 | 0.94 | 0.00 | 3.35 | 1.35 | 1.09 | 0.98 |
time (sec) |
N/A | 0.082 | 0.117 | 3.174 | 0.000 | 0.276 | 2.451 | 0.281 | 5.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 354 | 122 | 0 | 690 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.16 | 1.09 | 0.00 | 6.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.075 | 1.431 | 3.011 | 0.000 | 0.320 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 65 | 61 | 0 | 255 | 88 | 64 | 53 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 3.92 | 1.35 | 0.98 | 0.82 |
time (sec) |
N/A | 0.043 | 0.077 | 2.964 | 0.000 | 0.271 | 1.852 | 0.288 | 5.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 102 | 112 | 0 | 596 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.38 | 0.00 | 7.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.031 | 0.174 | 2.927 | 0.000 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 78 | 70 | 0 | 578 | 151 | 78 | 103 |
N.S. |
1 | 1.00 | 0.98 | 0.88 | 0.00 | 7.22 | 1.89 | 0.98 | 1.29 |
time (sec) |
N/A | 0.066 | 0.072 | 2.942 | 0.000 | 0.307 | 3.651 | 0.293 | 5.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 304 | 68 | 0 | 273 | 0 | 117 | 0 |
N.S. |
1 | 1.00 | 4.34 | 0.97 | 0.00 | 3.90 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 0.036 | 0.972 | 2.963 | 0.000 | 0.251 | 0.000 | 0.805 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 107 | 121 | 0 | 708 | 0 | 106 | 268 |
N.S. |
1 | 1.00 | 0.95 | 1.07 | 0.00 | 6.27 | 0.00 | 0.94 | 2.37 |
time (sec) |
N/A | 0.091 | 0.255 | 3.037 | 0.000 | 0.324 | 0.000 | 0.291 | 5.603 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 114 | 91 | 0 | 325 | 0 | 215 | 0 |
N.S. |
1 | 1.00 | 1.09 | 0.87 | 0.00 | 3.10 | 0.00 | 2.05 | 0.00 |
time (sec) |
N/A | 0.087 | 0.226 | 2.977 | 0.000 | 0.296 | 0.000 | 1.060 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 457 | 189 | 0 | 1119 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.18 | 0.90 | 0.00 | 5.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 1.993 | 3.061 | 0.000 | 1.357 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 109 | 117 | 0 | 397 | 143 | 151 | 179 |
N.S. |
1 | 1.00 | 0.95 | 1.02 | 0.00 | 3.45 | 1.24 | 1.31 | 1.56 |
time (sec) |
N/A | 0.080 | 0.196 | 3.093 | 0.000 | 0.285 | 7.893 | 0.280 | 5.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 401 | 133 | 0 | 894 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.54 | 0.84 | 0.00 | 5.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.179 | 1.638 | 2.984 | 0.000 | 0.566 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 82 | 94 | 0 | 303 | 116 | 112 | 98 |
N.S. |
1 | 1.00 | 0.90 | 1.03 | 0.00 | 3.33 | 1.27 | 1.23 | 1.08 |
time (sec) |
N/A | 0.057 | 0.157 | 2.958 | 0.000 | 0.267 | 5.157 | 0.289 | 5.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 129 | 117 | 0 | 721 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.04 | 0.00 | 6.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.072 | 0.270 | 2.997 | 0.000 | 0.369 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 103 | 103 | 0 | 682 | 172 | 110 | 711 |
N.S. |
1 | 1.00 | 1.07 | 1.07 | 0.00 | 7.10 | 1.79 | 1.15 | 7.41 |
time (sec) |
N/A | 0.079 | 0.154 | 2.982 | 0.000 | 0.440 | 5.450 | 0.313 | 5.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 129 | 114 | 0 | 718 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.12 | 0.00 | 7.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.066 | 0.216 | 3.005 | 0.000 | 0.328 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 108 | 117 | 0 | 732 | 0 | 120 | 560 |
N.S. |
1 | 1.00 | 0.95 | 1.03 | 0.00 | 6.42 | 0.00 | 1.05 | 4.91 |
time (sec) |
N/A | 0.107 | 0.241 | 2.992 | 0.000 | 0.450 | 0.000 | 0.309 | 5.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 343 | 104 | 0 | 331 | 0 | 256 | 0 |
N.S. |
1 | 1.00 | 3.36 | 1.02 | 0.00 | 3.25 | 0.00 | 2.51 | 0.00 |
time (sec) |
N/A | 0.092 | 1.174 | 2.999 | 0.000 | 0.281 | 0.000 | 1.105 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 291 | 291 | 519 | 259 | 0 | 1443 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.78 | 0.89 | 0.00 | 4.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.413 | 2.606 | 3.115 | 0.000 | 4.535 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 140 | 147 | 0 | 527 | 187 | 228 | 251 |
N.S. |
1 | 1.00 | 0.97 | 1.02 | 0.00 | 3.66 | 1.30 | 1.58 | 1.74 |
time (sec) |
N/A | 0.110 | 0.188 | 3.045 | 0.000 | 0.292 | 12.496 | 0.295 | 5.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 217 | 217 | 452 | 185 | 0 | 1161 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.08 | 0.85 | 0.00 | 5.35 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.292 | 2.364 | 3.051 | 0.000 | 1.691 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 116 | 123 | 0 | 405 | 156 | 184 | 137 |
N.S. |
1 | 1.00 | 0.97 | 1.03 | 0.00 | 3.40 | 1.31 | 1.55 | 1.15 |
time (sec) |
N/A | 0.074 | 0.130 | 3.110 | 0.000 | 0.274 | 9.033 | 0.292 | 5.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 160 | 135 | 0 | 931 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.87 | 0.00 | 5.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.132 | 0.361 | 3.053 | 0.000 | 0.852 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 114 | 122 | 0 | 837 | 201 | 163 | 2094 |
N.S. |
1 | 1.00 | 0.92 | 0.98 | 0.00 | 6.75 | 1.62 | 1.31 | 16.89 |
time (sec) |
N/A | 0.126 | 0.151 | 3.019 | 0.000 | 0.851 | 8.975 | 0.283 | 5.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 148 | 139 | 0 | 887 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.96 | 0.00 | 6.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.133 | 0.306 | 3.079 | 0.000 | 0.613 | 0.000 | 0.000 | 0.000 |