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 | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 135 | 137 | 93 | 191 | 224 | 0 | 200 | 0 |
N.S. |
1 | 0.86 | 0.87 | 0.59 | 1.22 | 1.43 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.344 | 0.362 | 0.207 | 0.185 | 0.266 | 0.000 | 0.291 | 0.000 |
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 | 155 | 132 | 136 | 97 | 244 | 224 | 0 | 293 | 0 |
N.S. |
1 | 0.85 | 0.88 | 0.63 | 1.57 | 1.45 | 0.00 | 1.89 | 0.00 |
time (sec) |
N/A | 0.307 | 0.302 | 0.234 | 0.199 | 0.274 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 120 | 113 | 95 | 258 | 238 | 0 | 379 | 0 |
N.S. |
1 | 1.01 | 0.95 | 0.80 | 2.17 | 2.00 | 0.00 | 3.18 | 0.00 |
time (sec) |
N/A | 0.282 | 0.274 | 0.242 | 0.204 | 0.264 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 36 | 39 | 258 | 102 | 0 | 431 | 188 |
N.S. |
1 | 1.00 | 0.63 | 0.68 | 4.53 | 1.79 | 0.00 | 7.56 | 3.30 |
time (sec) |
N/A | 0.200 | 0.259 | 0.276 | 0.192 | 0.272 | 0.000 | 0.285 | 11.843 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 89 | 63 | 56 | 304 | 127 | 0 | 491 | 234 |
N.S. |
1 | 0.99 | 0.70 | 0.62 | 3.38 | 1.41 | 0.00 | 5.46 | 2.60 |
time (sec) |
N/A | 0.228 | 0.297 | 0.346 | 0.195 | 0.296 | 0.000 | 0.280 | 12.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 121 | 87 | 73 | 350 | 153 | 0 | 551 | 280 |
N.S. |
1 | 0.97 | 0.70 | 0.58 | 2.80 | 1.22 | 0.00 | 4.41 | 2.24 |
time (sec) |
N/A | 0.264 | 0.387 | 0.412 | 0.206 | 0.265 | 0.000 | 0.277 | 13.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 153 | 107 | 90 | 396 | 177 | 0 | 611 | 326 |
N.S. |
1 | 0.96 | 0.67 | 0.56 | 2.48 | 1.11 | 0.00 | 3.82 | 2.04 |
time (sec) |
N/A | 0.306 | 0.093 | 0.509 | 0.198 | 0.260 | 0.000 | 0.278 | 13.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 185 | 130 | 107 | 442 | 202 | 0 | 671 | 372 |
N.S. |
1 | 0.95 | 0.67 | 0.55 | 2.27 | 1.04 | 0.00 | 3.44 | 1.91 |
time (sec) |
N/A | 0.347 | 0.105 | 0.651 | 0.200 | 0.277 | 0.000 | 0.293 | 14.682 |
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 | 197 | 182 | 163 | 116 | 252 | 303 | 228 | 163 | 0 |
N.S. |
1 | 0.92 | 0.83 | 0.59 | 1.28 | 1.54 | 1.16 | 0.83 | 0.00 |
time (sec) |
N/A | 0.352 | 0.634 | 0.260 | 0.189 | 0.284 | 0.502 | 0.294 | 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 | 162 | 150 | 188 | 99 | 206 | 256 | 204 | 135 | 0 |
N.S. |
1 | 0.93 | 1.16 | 0.61 | 1.27 | 1.58 | 1.26 | 0.83 | 0.00 |
time (sec) |
N/A | 0.318 | 0.470 | 0.174 | 0.181 | 0.290 | 0.501 | 0.294 | 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 | 127 | 118 | 125 | 82 | 160 | 207 | 180 | 107 | 0 |
N.S. |
1 | 0.93 | 0.98 | 0.65 | 1.26 | 1.63 | 1.42 | 0.84 | 0.00 |
time (sec) |
N/A | 0.266 | 0.406 | 0.155 | 0.189 | 0.280 | 0.491 | 0.288 | 0.000 |
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 | 75 | 75 | 108 | 64 | 115 | 158 | 151 | 81 | 0 |
N.S. |
1 | 1.00 | 1.44 | 0.85 | 1.53 | 2.11 | 2.01 | 1.08 | 0.00 |
time (sec) |
N/A | 0.202 | 0.273 | 0.125 | 0.188 | 0.284 | 0.595 | 0.291 | 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 | 55 | 55 | 86 | 46 | 75 | 115 | 122 | 58 | 77 |
N.S. |
1 | 1.00 | 1.56 | 0.84 | 1.36 | 2.09 | 2.22 | 1.05 | 1.40 |
time (sec) |
N/A | 0.187 | 0.184 | 0.113 | 0.180 | 0.264 | 0.360 | 0.288 | 10.779 |
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 | 52 | 52 | 74 | 49 | 49 | 116 | 0 | 59 | 50 |
N.S. |
1 | 1.00 | 1.42 | 0.94 | 0.94 | 2.23 | 0.00 | 1.13 | 0.96 |
time (sec) |
N/A | 0.185 | 0.087 | 0.095 | 0.182 | 0.260 | 0.000 | 0.294 | 10.584 |
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 | 57 | 57 | 35 | 32 | 62 | 34 | 0 | 76 | 33 |
N.S. |
1 | 1.00 | 0.61 | 0.56 | 1.09 | 0.60 | 0.00 | 1.33 | 0.58 |
time (sec) |
N/A | 0.193 | 0.090 | 0.102 | 0.182 | 0.257 | 0.000 | 0.286 | 10.060 |
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 | 89 | 54 | 49 | 106 | 57 | 0 | 133 | 56 |
N.S. |
1 | 0.99 | 0.60 | 0.54 | 1.18 | 0.63 | 0.00 | 1.48 | 0.62 |
time (sec) |
N/A | 0.225 | 0.117 | 0.115 | 0.181 | 0.248 | 0.000 | 0.271 | 10.068 |
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 | 125 | 121 | 79 | 66 | 152 | 82 | 0 | 191 | 113 |
N.S. |
1 | 0.97 | 0.63 | 0.53 | 1.22 | 0.66 | 0.00 | 1.53 | 0.90 |
time (sec) |
N/A | 0.257 | 0.139 | 0.154 | 0.184 | 0.259 | 0.000 | 0.291 | 10.080 |
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 | 160 | 153 | 100 | 83 | 198 | 106 | 0 | 251 | 146 |
N.S. |
1 | 0.96 | 0.62 | 0.52 | 1.24 | 0.66 | 0.00 | 1.57 | 0.91 |
time (sec) |
N/A | 0.298 | 0.164 | 0.157 | 0.186 | 0.265 | 0.000 | 0.282 | 10.119 |
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 | 195 | 185 | 123 | 100 | 244 | 130 | 0 | 311 | 177 |
N.S. |
1 | 0.95 | 0.63 | 0.51 | 1.25 | 0.67 | 0.00 | 1.59 | 0.91 |
time (sec) |
N/A | 0.335 | 0.183 | 0.220 | 0.179 | 0.258 | 0.000 | 0.278 | 10.120 |
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 | 170 | 168 | 148 | 107 | 212 | 313 | 0 | 164 | 0 |
N.S. |
1 | 0.99 | 0.87 | 0.63 | 1.25 | 1.84 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.523 | 0.471 | 0.241 | 0.188 | 0.260 | 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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 121 | 125 | 87 | 163 | 262 | 0 | 136 | 0 |
N.S. |
1 | 0.90 | 0.93 | 0.64 | 1.21 | 1.94 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.363 | 0.354 | 0.184 | 0.184 | 0.275 | 0.000 | 0.292 | 0.000 |
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 | 99 | 86 | 103 | 74 | 115 | 202 | 0 | 107 | 0 |
N.S. |
1 | 0.87 | 1.04 | 0.75 | 1.16 | 2.04 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.250 | 0.222 | 0.175 | 0.182 | 0.267 | 0.000 | 0.298 | 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 | 60 | 60 | 77 | 63 | 65 | 164 | 0 | 80 | 64 |
N.S. |
1 | 1.00 | 1.28 | 1.05 | 1.08 | 2.73 | 0.00 | 1.33 | 1.07 |
time (sec) |
N/A | 0.198 | 0.102 | 0.111 | 0.187 | 0.262 | 0.000 | 0.296 | 10.688 |
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 | 33 | 33 | 30 | 30 | 55 | 44 | 0 | 33 | 31 |
N.S. |
1 | 1.00 | 0.91 | 0.91 | 1.67 | 1.33 | 0.00 | 1.00 | 0.94 |
time (sec) |
N/A | 0.158 | 0.085 | 0.108 | 0.267 | 0.269 | 0.000 | 0.275 | 10.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 52 | 49 | 96 | 68 | 0 | 0 | 62 |
N.S. |
1 | 1.00 | 0.87 | 0.82 | 1.60 | 1.13 | 0.00 | 0.00 | 1.03 |
time (sec) |
N/A | 0.192 | 0.126 | 0.122 | 0.251 | 0.271 | 0.000 | 0.000 | 10.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 92 | 75 | 66 | 142 | 93 | 0 | 0 | 87 |
N.S. |
1 | 0.99 | 0.81 | 0.71 | 1.53 | 1.00 | 0.00 | 0.00 | 0.94 |
time (sec) |
N/A | 0.232 | 0.153 | 0.142 | 0.220 | 0.248 | 0.000 | 0.000 | 10.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 124 | 98 | 83 | 188 | 117 | 0 | 0 | 161 |
N.S. |
1 | 0.97 | 0.77 | 0.65 | 1.47 | 0.91 | 0.00 | 0.00 | 1.26 |
time (sec) |
N/A | 0.263 | 0.181 | 0.143 | 0.214 | 0.256 | 0.000 | 0.000 | 10.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 156 | 123 | 102 | 234 | 142 | 0 | 0 | 191 |
N.S. |
1 | 0.96 | 0.75 | 0.63 | 1.44 | 0.87 | 0.00 | 0.00 | 1.17 |
time (sec) |
N/A | 0.295 | 0.206 | 0.192 | 0.211 | 0.263 | 0.000 | 0.000 | 10.645 |
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 | 172 | 149 | 180 | 120 | 362 | 380 | 0 | 246 | 0 |
N.S. |
1 | 0.87 | 1.05 | 0.70 | 2.10 | 2.21 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.366 | 0.463 | 0.275 | 0.198 | 0.288 | 0.000 | 0.308 | 0.000 |
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 | 136 | 123 | 125 | 103 | 310 | 321 | 0 | 217 | 0 |
N.S. |
1 | 0.90 | 0.92 | 0.76 | 2.28 | 2.36 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.288 | 0.322 | 0.236 | 0.258 | 0.259 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 88 | 93 | 88 | 221 | 239 | 0 | 188 | 0 |
N.S. |
1 | 1.05 | 1.11 | 1.05 | 2.63 | 2.85 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.240 | 0.150 | 0.151 | 0.245 | 0.269 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 35 | 37 | 134 | 51 | 0 | 119 | 37 |
N.S. |
1 | 1.00 | 0.52 | 0.55 | 2.00 | 0.76 | 0.00 | 1.78 | 0.55 |
time (sec) |
N/A | 0.211 | 0.091 | 0.109 | 0.192 | 0.261 | 0.000 | 0.298 | 10.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 55 | 53 | 111 | 77 | 0 | 0 | 63 |
N.S. |
1 | 1.00 | 0.79 | 0.76 | 1.59 | 1.10 | 0.00 | 0.00 | 0.90 |
time (sec) |
N/A | 0.199 | 0.128 | 0.128 | 0.187 | 0.258 | 0.000 | 0.000 | 10.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 72 | 73 | 130 | 101 | 0 | 82 | 76 |
N.S. |
1 | 1.00 | 1.03 | 1.04 | 1.86 | 1.44 | 0.00 | 1.17 | 1.09 |
time (sec) |
N/A | 0.184 | 0.144 | 0.143 | 0.189 | 0.266 | 0.000 | 0.288 | 10.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 95 | 98 | 92 | 176 | 128 | 0 | 0 | 111 |
N.S. |
1 | 0.99 | 1.02 | 0.96 | 1.83 | 1.33 | 0.00 | 0.00 | 1.16 |
time (sec) |
N/A | 0.224 | 0.194 | 0.161 | 0.188 | 0.255 | 0.000 | 0.000 | 10.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 127 | 123 | 109 | 224 | 153 | 0 | 0 | 235 |
N.S. |
1 | 0.97 | 0.94 | 0.83 | 1.71 | 1.17 | 0.00 | 0.00 | 1.79 |
time (sec) |
N/A | 0.259 | 0.222 | 0.187 | 0.182 | 0.261 | 0.000 | 0.000 | 10.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 159 | 145 | 126 | 270 | 177 | 0 | 0 | 266 |
N.S. |
1 | 0.96 | 0.87 | 0.76 | 1.63 | 1.07 | 0.00 | 0.00 | 1.60 |
time (sec) |
N/A | 0.299 | 0.261 | 0.211 | 0.190 | 0.280 | 0.000 | 0.000 | 10.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 106 | 105 | 109 | 210 | 164 | 0 | 142 | 125 |
N.S. |
1 | 0.99 | 0.98 | 1.02 | 1.96 | 1.53 | 0.00 | 1.33 | 1.17 |
time (sec) |
N/A | 0.215 | 0.207 | 0.193 | 0.185 | 0.260 | 0.000 | 0.294 | 10.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 141 | 150 | 180 | 292 | 223 | 0 | 198 | 185 |
N.S. |
1 | 0.97 | 1.03 | 1.24 | 2.01 | 1.54 | 0.00 | 1.37 | 1.28 |
time (sec) |
N/A | 0.239 | 0.282 | 0.194 | 0.190 | 0.270 | 0.000 | 0.293 | 10.485 |
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 | 39 | 39 | 31 | 28 | 27 | 32 | 46 | 29 | 27 |
N.S. |
1 | 1.00 | 0.79 | 0.72 | 0.69 | 0.82 | 1.18 | 0.74 | 0.69 |
time (sec) |
N/A | 0.159 | 0.022 | 0.139 | 0.186 | 0.252 | 0.452 | 0.278 | 0.052 |
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 | 39 | 39 | 31 | 28 | 27 | 32 | 46 | 29 | 27 |
N.S. |
1 | 1.00 | 0.79 | 0.72 | 0.69 | 0.82 | 1.18 | 0.74 | 0.69 |
time (sec) |
N/A | 0.157 | 0.021 | 0.122 | 0.184 | 0.248 | 0.289 | 0.274 | 0.046 |
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 | 39 | 39 | 31 | 28 | 27 | 32 | 46 | 29 | 27 |
N.S. |
1 | 1.00 | 0.79 | 0.72 | 0.69 | 0.82 | 1.18 | 0.74 | 0.69 |
time (sec) |
N/A | 0.162 | 0.018 | 0.119 | 0.183 | 0.244 | 0.186 | 0.256 | 10.129 |
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 | 39 | 39 | 33 | 28 | 27 | 32 | 37 | 29 | 27 |
N.S. |
1 | 1.00 | 0.85 | 0.72 | 0.69 | 0.82 | 0.95 | 0.74 | 0.69 |
time (sec) |
N/A | 0.162 | 0.018 | 0.113 | 0.187 | 0.258 | 0.580 | 0.268 | 0.045 |
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 | 39 | 39 | 33 | 28 | 27 | 30 | 46 | 29 | 27 |
N.S. |
1 | 1.00 | 0.85 | 0.72 | 0.69 | 0.77 | 1.18 | 0.74 | 0.69 |
time (sec) |
N/A | 0.165 | 0.018 | 0.118 | 0.191 | 0.273 | 0.109 | 0.282 | 0.045 |
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 | 37 | 37 | 31 | 27 | 27 | 27 | 44 | 29 | 27 |
N.S. |
1 | 1.00 | 0.84 | 0.73 | 0.73 | 0.73 | 1.19 | 0.78 | 0.73 |
time (sec) |
N/A | 0.161 | 0.020 | 0.119 | 0.182 | 0.250 | 0.120 | 0.267 | 0.046 |
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 | 35 | 31 | 28 | 27 | 26 | 41 | 29 | 27 |
N.S. |
1 | 1.00 | 0.89 | 0.80 | 0.77 | 0.74 | 1.17 | 0.83 | 0.77 |
time (sec) |
N/A | 0.162 | 0.021 | 0.040 | 0.179 | 0.269 | 0.198 | 0.271 | 10.215 |
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 | 35 | 28 | 27 | 27 | 27 | 41 | 27 | 27 |
N.S. |
1 | 1.00 | 0.80 | 0.77 | 0.77 | 0.77 | 1.17 | 0.77 | 0.77 |
time (sec) |
N/A | 0.161 | 0.022 | 0.043 | 0.191 | 0.251 | 0.258 | 0.261 | 10.303 |
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 | 37 | 37 | 31 | 28 | 27 | 27 | 46 | 27 | 28 |
N.S. |
1 | 1.00 | 0.84 | 0.76 | 0.73 | 0.73 | 1.24 | 0.73 | 0.76 |
time (sec) |
N/A | 0.160 | 0.024 | 0.043 | 0.189 | 0.263 | 0.373 | 0.257 | 0.037 |
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 | 63 | 63 | 55 | 52 | 51 | 56 | 80 | 53 | 51 |
N.S. |
1 | 1.00 | 0.87 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.81 |
time (sec) |
N/A | 0.189 | 0.030 | 0.139 | 0.181 | 0.259 | 0.689 | 0.286 | 10.276 |
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 | 63 | 63 | 55 | 52 | 51 | 56 | 80 | 53 | 51 |
N.S. |
1 | 1.00 | 0.87 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.81 |
time (sec) |
N/A | 0.186 | 0.029 | 0.137 | 0.189 | 0.251 | 0.463 | 0.273 | 0.052 |
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 | 63 | 63 | 55 | 52 | 51 | 56 | 80 | 53 | 51 |
N.S. |
1 | 1.00 | 0.87 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.81 |
time (sec) |
N/A | 0.185 | 0.031 | 0.140 | 0.188 | 0.254 | 0.304 | 0.263 | 0.050 |
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 | 63 | 63 | 55 | 52 | 51 | 56 | 66 | 53 | 51 |
N.S. |
1 | 1.00 | 0.87 | 0.83 | 0.81 | 0.89 | 1.05 | 0.84 | 0.81 |
time (sec) |
N/A | 0.188 | 0.029 | 0.133 | 0.189 | 0.258 | 0.693 | 0.273 | 0.051 |
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 | 63 | 63 | 55 | 52 | 51 | 56 | 80 | 53 | 51 |
N.S. |
1 | 1.00 | 0.87 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.81 |
time (sec) |
N/A | 0.185 | 0.027 | 0.124 | 0.181 | 0.257 | 0.199 | 0.270 | 0.052 |
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 | 63 | 63 | 54 | 52 | 51 | 54 | 80 | 53 | 51 |
N.S. |
1 | 1.00 | 0.86 | 0.83 | 0.81 | 0.86 | 1.27 | 0.84 | 0.81 |
time (sec) |
N/A | 0.194 | 0.028 | 0.121 | 0.188 | 0.248 | 0.227 | 0.262 | 0.057 |
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 | 61 | 61 | 54 | 51 | 51 | 51 | 78 | 53 | 51 |
N.S. |
1 | 1.00 | 0.89 | 0.84 | 0.84 | 0.84 | 1.28 | 0.87 | 0.84 |
time (sec) |
N/A | 0.186 | 0.031 | 0.123 | 0.193 | 0.253 | 0.234 | 0.273 | 0.051 |
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 | 59 | 59 | 55 | 52 | 51 | 51 | 75 | 53 | 51 |
N.S. |
1 | 1.00 | 0.93 | 0.88 | 0.86 | 0.86 | 1.27 | 0.90 | 0.86 |
time (sec) |
N/A | 0.183 | 0.034 | 0.050 | 0.189 | 0.260 | 0.357 | 0.272 | 0.053 |
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 | 59 | 59 | 54 | 51 | 51 | 50 | 73 | 51 | 51 |
N.S. |
1 | 1.00 | 0.92 | 0.86 | 0.86 | 0.85 | 1.24 | 0.86 | 0.86 |
time (sec) |
N/A | 0.184 | 0.042 | 0.059 | 0.189 | 0.278 | 0.426 | 0.256 | 0.053 |
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 | 85 | 85 | 77 | 76 | 73 | 78 | 114 | 77 | 69 |
N.S. |
1 | 1.00 | 0.91 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.81 |
time (sec) |
N/A | 0.212 | 0.040 | 0.167 | 0.187 | 0.259 | 1.016 | 0.269 | 9.870 |
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 | 85 | 85 | 77 | 76 | 73 | 78 | 114 | 77 | 69 |
N.S. |
1 | 1.00 | 0.91 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.81 |
time (sec) |
N/A | 0.204 | 0.037 | 0.167 | 0.182 | 0.253 | 0.686 | 0.269 | 0.035 |
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 | 85 | 85 | 77 | 76 | 73 | 78 | 114 | 77 | 69 |
N.S. |
1 | 1.00 | 0.91 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.81 |
time (sec) |
N/A | 0.208 | 0.040 | 0.160 | 0.193 | 0.262 | 0.471 | 0.269 | 0.035 |
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 | 85 | 85 | 77 | 76 | 73 | 78 | 95 | 77 | 69 |
N.S. |
1 | 1.00 | 0.91 | 0.89 | 0.86 | 0.92 | 1.12 | 0.91 | 0.81 |
time (sec) |
N/A | 0.206 | 0.038 | 0.156 | 0.182 | 0.278 | 0.817 | 0.269 | 0.034 |
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 | 85 | 85 | 77 | 76 | 73 | 78 | 114 | 77 | 69 |
N.S. |
1 | 1.00 | 0.91 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.81 |
time (sec) |
N/A | 0.213 | 0.040 | 0.155 | 0.189 | 0.256 | 0.320 | 0.275 | 0.034 |
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 | 85 | 85 | 77 | 76 | 73 | 78 | 114 | 77 | 69 |
N.S. |
1 | 1.00 | 0.91 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.81 |
time (sec) |
N/A | 0.206 | 0.037 | 0.131 | 0.182 | 0.263 | 0.331 | 0.259 | 0.034 |
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 | 85 | 85 | 77 | 76 | 73 | 76 | 114 | 77 | 69 |
N.S. |
1 | 1.00 | 0.91 | 0.89 | 0.86 | 0.89 | 1.34 | 0.91 | 0.81 |
time (sec) |
N/A | 0.207 | 0.036 | 0.126 | 0.188 | 0.266 | 0.351 | 0.262 | 0.035 |
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 | 83 | 83 | 76 | 75 | 73 | 73 | 110 | 77 | 69 |
N.S. |
1 | 1.00 | 0.92 | 0.90 | 0.88 | 0.88 | 1.33 | 0.93 | 0.83 |
time (sec) |
N/A | 0.204 | 0.037 | 0.125 | 0.183 | 0.316 | 0.437 | 0.272 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 75 | 76 | 73 | 73 | 105 | 77 | 69 |
N.S. |
1 | 1.00 | 0.95 | 0.96 | 0.92 | 0.92 | 1.33 | 0.97 | 0.87 |
time (sec) |
N/A | 0.211 | 0.051 | 0.052 | 0.188 | 0.325 | 0.617 | 0.268 | 0.037 |
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 | 81 | 81 | 74 | 75 | 73 | 73 | 105 | 75 | 70 |
N.S. |
1 | 1.00 | 0.91 | 0.93 | 0.90 | 0.90 | 1.30 | 0.93 | 0.86 |
time (sec) |
N/A | 0.208 | 0.051 | 0.060 | 0.183 | 0.328 | 0.751 | 0.278 | 0.061 |
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 | 113 | 105 | 101 | 100 | 105 | 229 | 294 | 115 | 125 |
N.S. |
1 | 0.93 | 0.89 | 0.88 | 0.93 | 2.03 | 2.60 | 1.02 | 1.11 |
time (sec) |
N/A | 0.207 | 0.113 | 0.082 | 0.272 | 0.367 | 15.794 | 0.287 | 9.883 |
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 | 90 | 86 | 81 | 76 | 82 | 180 | 260 | 91 | 101 |
N.S. |
1 | 0.96 | 0.90 | 0.84 | 0.91 | 2.00 | 2.89 | 1.01 | 1.12 |
time (sec) |
N/A | 0.190 | 0.101 | 0.065 | 0.266 | 0.393 | 7.028 | 0.268 | 10.240 |
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 | 69 | 67 | 63 | 53 | 58 | 129 | 221 | 64 | 76 |
N.S. |
1 | 0.97 | 0.91 | 0.77 | 0.84 | 1.87 | 3.20 | 0.93 | 1.10 |
time (sec) |
N/A | 0.175 | 0.062 | 0.063 | 0.273 | 0.377 | 2.326 | 0.259 | 0.084 |
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 | 49 | 49 | 49 | 40 | 39 | 102 | 180 | 39 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.80 | 2.08 | 3.67 | 0.80 | 0.76 |
time (sec) |
N/A | 0.167 | 0.044 | 0.063 | 0.278 | 0.619 | 0.718 | 0.265 | 0.065 |
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 | 49 | 49 | 49 | 40 | 39 | 112 | 178 | 39 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.80 | 2.29 | 3.63 | 0.80 | 1.02 |
time (sec) |
N/A | 0.167 | 0.053 | 0.069 | 0.267 | 0.287 | 0.968 | 0.274 | 0.074 |
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 | 69 | 66 | 64 | 54 | 56 | 146 | 218 | 55 | 54 |
N.S. |
1 | 0.96 | 0.93 | 0.78 | 0.81 | 2.12 | 3.16 | 0.80 | 0.78 |
time (sec) |
N/A | 0.177 | 0.080 | 0.075 | 0.270 | 0.283 | 2.309 | 0.270 | 10.295 |
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 | 90 | 85 | 83 | 76 | 80 | 195 | 262 | 80 | 71 |
N.S. |
1 | 0.94 | 0.92 | 0.84 | 0.89 | 2.17 | 2.91 | 0.89 | 0.79 |
time (sec) |
N/A | 0.187 | 0.104 | 0.079 | 0.271 | 0.270 | 7.521 | 0.275 | 10.258 |
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 | 113 | 104 | 107 | 95 | 103 | 246 | 299 | 104 | 90 |
N.S. |
1 | 0.92 | 0.95 | 0.84 | 0.91 | 2.18 | 2.65 | 0.92 | 0.80 |
time (sec) |
N/A | 0.197 | 0.128 | 0.085 | 0.272 | 0.303 | 20.534 | 0.274 | 10.071 |
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 | 123 | 129 | 114 | 126 | 291 | 333 | 128 | 109 |
N.S. |
1 | 0.90 | 0.95 | 0.84 | 0.93 | 2.14 | 2.45 | 0.94 | 0.80 |
time (sec) |
N/A | 0.207 | 0.145 | 0.088 | 0.279 | 0.284 | 48.484 | 0.271 | 10.212 |
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 | 131 | 126 | 110 | 99 | 115 | 290 | 0 | 122 | 146 |
N.S. |
1 | 0.96 | 0.84 | 0.76 | 0.88 | 2.21 | 0.00 | 0.93 | 1.11 |
time (sec) |
N/A | 0.213 | 0.139 | 0.115 | 0.269 | 0.368 | 0.000 | 0.273 | 10.146 |
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 | 109 | 107 | 88 | 77 | 88 | 231 | 762 | 95 | 107 |
N.S. |
1 | 0.98 | 0.81 | 0.71 | 0.81 | 2.12 | 6.99 | 0.87 | 0.98 |
time (sec) |
N/A | 0.203 | 0.112 | 0.096 | 0.270 | 0.306 | 125.736 | 0.266 | 10.173 |
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 | 88 | 88 | 67 | 62 | 65 | 198 | 634 | 65 | 62 |
N.S. |
1 | 1.00 | 0.76 | 0.70 | 0.74 | 2.25 | 7.20 | 0.74 | 0.70 |
time (sec) |
N/A | 0.192 | 0.080 | 0.089 | 0.267 | 0.281 | 54.808 | 0.268 | 0.100 |
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 | 64 | 64 | 63 | 57 | 58 | 177 | 615 | 60 | 51 |
N.S. |
1 | 1.00 | 0.98 | 0.89 | 0.91 | 2.77 | 9.61 | 0.94 | 0.80 |
time (sec) |
N/A | 0.177 | 0.077 | 0.070 | 0.270 | 0.283 | 24.967 | 0.282 | 10.174 |
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 | 85 | 87 | 67 | 64 | 65 | 215 | 794 | 60 | 65 |
N.S. |
1 | 1.02 | 0.79 | 0.75 | 0.76 | 2.53 | 9.34 | 0.71 | 0.76 |
time (sec) |
N/A | 0.191 | 0.083 | 0.096 | 0.270 | 0.300 | 12.677 | 0.266 | 9.928 |
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 | 107 | 92 | 77 | 93 | 262 | 882 | 85 | 81 |
N.S. |
1 | 0.97 | 0.84 | 0.70 | 0.85 | 2.38 | 8.02 | 0.77 | 0.74 |
time (sec) |
N/A | 0.204 | 0.113 | 0.110 | 0.270 | 0.356 | 21.151 | 0.273 | 9.977 |
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 | 130 | 126 | 115 | 101 | 118 | 319 | 1017 | 110 | 103 |
N.S. |
1 | 0.97 | 0.88 | 0.78 | 0.91 | 2.45 | 7.82 | 0.85 | 0.79 |
time (sec) |
N/A | 0.219 | 0.138 | 0.118 | 0.275 | 0.415 | 44.452 | 0.286 | 10.127 |
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 | 156 | 145 | 136 | 121 | 143 | 372 | 1142 | 136 | 121 |
N.S. |
1 | 0.93 | 0.87 | 0.78 | 0.92 | 2.38 | 7.32 | 0.87 | 0.78 |
time (sec) |
N/A | 0.228 | 0.159 | 0.116 | 0.270 | 0.350 | 116.540 | 0.264 | 10.144 |
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 | 169 | 153 | 129 | 120 | 151 | 408 | 0 | 146 | 183 |
N.S. |
1 | 0.91 | 0.76 | 0.71 | 0.89 | 2.41 | 0.00 | 0.86 | 1.08 |
time (sec) |
N/A | 0.226 | 0.175 | 0.155 | 0.266 | 0.383 | 0.000 | 0.264 | 10.160 |
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 | 147 | 134 | 110 | 98 | 124 | 349 | 0 | 119 | 143 |
N.S. |
1 | 0.91 | 0.75 | 0.67 | 0.84 | 2.37 | 0.00 | 0.81 | 0.97 |
time (sec) |
N/A | 0.219 | 0.164 | 0.146 | 0.274 | 0.437 | 0.000 | 0.276 | 10.235 |
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 | 126 | 115 | 94 | 83 | 99 | 319 | 0 | 87 | 96 |
N.S. |
1 | 0.91 | 0.75 | 0.66 | 0.79 | 2.53 | 0.00 | 0.69 | 0.76 |
time (sec) |
N/A | 0.205 | 0.139 | 0.102 | 0.266 | 0.575 | 0.000 | 0.271 | 0.118 |
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 | 100 | 95 | 86 | 79 | 94 | 291 | 0 | 82 | 84 |
N.S. |
1 | 0.95 | 0.86 | 0.79 | 0.94 | 2.91 | 0.00 | 0.82 | 0.84 |
time (sec) |
N/A | 0.194 | 0.138 | 0.076 | 0.266 | 0.322 | 0.000 | 0.266 | 10.108 |
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 | 100 | 94 | 86 | 80 | 94 | 291 | 0 | 82 | 84 |
N.S. |
1 | 0.94 | 0.86 | 0.80 | 0.94 | 2.91 | 0.00 | 0.82 | 0.84 |
time (sec) |
N/A | 0.193 | 0.125 | 0.074 | 0.276 | 0.279 | 0.000 | 0.280 | 10.109 |
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 | 123 | 113 | 96 | 84 | 98 | 331 | 1598 | 86 | 116 |
N.S. |
1 | 0.92 | 0.78 | 0.68 | 0.80 | 2.69 | 12.99 | 0.70 | 0.94 |
time (sec) |
N/A | 0.206 | 0.132 | 0.099 | 0.266 | 0.312 | 164.323 | 0.269 | 10.196 |
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 | 147 | 133 | 117 | 98 | 128 | 380 | 1703 | 108 | 114 |
N.S. |
1 | 0.90 | 0.80 | 0.67 | 0.87 | 2.59 | 11.59 | 0.73 | 0.78 |
time (sec) |
N/A | 0.226 | 0.162 | 0.128 | 0.279 | 0.264 | 87.014 | 0.276 | 10.243 |
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 | 169 | 152 | 140 | 121 | 154 | 437 | 1882 | 135 | 135 |
N.S. |
1 | 0.90 | 0.83 | 0.72 | 0.91 | 2.59 | 11.14 | 0.80 | 0.80 |
time (sec) |
N/A | 0.234 | 0.174 | 0.135 | 0.273 | 0.281 | 122.822 | 0.284 | 10.295 |
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 | 193 | 171 | 161 | 141 | 178 | 490 | 0 | 159 | 154 |
N.S. |
1 | 0.89 | 0.83 | 0.73 | 0.92 | 2.54 | 0.00 | 0.82 | 0.80 |
time (sec) |
N/A | 0.240 | 0.201 | 0.137 | 0.273 | 0.307 | 0.000 | 0.271 | 10.269 |
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 | 207 | 197 | 113 | 129 | 142 | 150 | 0 | 158 | 0 |
N.S. |
1 | 0.95 | 0.55 | 0.62 | 0.69 | 0.72 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.354 | 0.067 | 0.110 | 0.205 | 0.310 | 0.000 | 0.274 | 0.000 |
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 | 170 | 163 | 94 | 105 | 120 | 126 | 0 | 134 | 0 |
N.S. |
1 | 0.96 | 0.55 | 0.62 | 0.71 | 0.74 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.309 | 0.056 | 0.099 | 0.211 | 0.324 | 0.000 | 0.277 | 0.000 |
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 | 133 | 129 | 72 | 81 | 98 | 102 | 0 | 110 | 0 |
N.S. |
1 | 0.97 | 0.54 | 0.61 | 0.74 | 0.77 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.268 | 0.046 | 0.100 | 0.199 | 0.298 | 0.000 | 0.267 | 0.000 |
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 | 96 | 95 | 56 | 57 | 75 | 78 | 0 | 86 | 0 |
N.S. |
1 | 0.99 | 0.58 | 0.59 | 0.78 | 0.81 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.230 | 0.036 | 0.099 | 0.204 | 0.287 | 0.000 | 0.280 | 0.000 |
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 | 61 | 61 | 37 | 37 | 45 | 53 | 0 | 60 | 0 |
N.S. |
1 | 1.00 | 0.61 | 0.61 | 0.74 | 0.87 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.198 | 0.027 | 0.084 | 0.205 | 0.286 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 82 | 80 | 79 | 0 | 148 | 0 | 103 | 0 |
N.S. |
1 | 1.01 | 0.99 | 0.98 | 0.00 | 1.83 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.222 | 0.060 | 0.076 | 0.000 | 0.298 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 93 | 80 | 78 | 0 | 157 | 0 | 61 | 0 |
N.S. |
1 | 0.98 | 0.84 | 0.82 | 0.00 | 1.65 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.238 | 0.090 | 0.070 | 0.000 | 0.357 | 0.000 | 0.293 | 0.000 |