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 | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 86 | 95 | 82 | 170 | 167 | 284 | 82 |
N.S. |
1 | 1.00 | 0.95 | 1.04 | 0.90 | 1.87 | 1.84 | 3.12 | 0.90 |
time (sec) |
N/A | 0.495 | 1.074 | 0.197 | 0.390 | 0.250 | 0.349 | 0.482 | 7.343 |
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 | 69 | 69 | 70 | 72 | 68 | 109 | 109 | 194 | 59 |
N.S. |
1 | 1.00 | 1.01 | 1.04 | 0.99 | 1.58 | 1.58 | 2.81 | 0.86 |
time (sec) |
N/A | 0.365 | 0.331 | 0.050 | 0.337 | 0.239 | 0.282 | 0.337 | 7.891 |
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 | 46 | 46 | 66 | 50 | 50 | 64 | 53 | 103 | 38 |
N.S. |
1 | 1.00 | 1.43 | 1.09 | 1.09 | 1.39 | 1.15 | 2.24 | 0.83 |
time (sec) |
N/A | 0.251 | 0.033 | 0.038 | 0.327 | 0.252 | 0.234 | 0.299 | 7.802 |
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 | 40 | 42 | 54 | 43 | 49 | 36 | 94 | 74 | 36 |
N.S. |
1 | 1.05 | 1.35 | 1.08 | 1.22 | 0.90 | 2.35 | 1.85 | 0.90 |
time (sec) |
N/A | 0.397 | 0.052 | 0.559 | 0.305 | 0.251 | 1.031 | 0.400 | 7.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 46 | 97 | 59 | 64 | 62 | 53 | 104 | 39 |
N.S. |
1 | 1.05 | 2.20 | 1.34 | 1.45 | 1.41 | 1.20 | 2.36 | 0.89 |
time (sec) |
N/A | 0.374 | 0.041 | 0.172 | 0.282 | 0.244 | 0.257 | 0.495 | 7.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 70 | 76 | 73 | 84 | 111 | 109 | 162 | 60 |
N.S. |
1 | 1.03 | 1.12 | 1.07 | 1.24 | 1.63 | 1.60 | 2.38 | 0.88 |
time (sec) |
N/A | 0.491 | 0.419 | 0.168 | 0.286 | 0.246 | 0.314 | 0.609 | 7.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 91 | 102 | 101 | 103 | 166 | 168 | 221 | 80 |
N.S. |
1 | 1.02 | 1.15 | 1.13 | 1.16 | 1.87 | 1.89 | 2.48 | 0.90 |
time (sec) |
N/A | 0.619 | 0.795 | 0.175 | 0.288 | 0.251 | 0.369 | 0.706 | 7.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 113 | 96 | 106 | 116 | 206 | 218 | 282 | 100 |
N.S. |
1 | 1.02 | 0.86 | 0.95 | 1.05 | 1.86 | 1.96 | 2.54 | 0.90 |
time (sec) |
N/A | 0.764 | 0.909 | 0.198 | 0.294 | 0.250 | 0.722 | 0.853 | 8.460 |
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 | 141 | 147 | 101 | 121 | 112 | 236 | 236 | 408 | 153 |
N.S. |
1 | 1.04 | 0.72 | 0.86 | 0.79 | 1.67 | 1.67 | 2.89 | 1.09 |
time (sec) |
N/A | 0.774 | 1.357 | 0.091 | 0.293 | 0.265 | 0.464 | 0.590 | 7.248 |
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 | 107 | 99 | 82 | 99 | 92 | 175 | 178 | 312 | 111 |
N.S. |
1 | 0.93 | 0.77 | 0.93 | 0.86 | 1.64 | 1.66 | 2.92 | 1.04 |
time (sec) |
N/A | 0.492 | 0.824 | 0.077 | 0.299 | 0.253 | 0.346 | 0.435 | 7.653 |
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 | 80 | 70 | 58 | 76 | 71 | 121 | 122 | 214 | 76 |
N.S. |
1 | 0.88 | 0.72 | 0.95 | 0.89 | 1.51 | 1.52 | 2.68 | 0.95 |
time (sec) |
N/A | 0.355 | 0.490 | 0.055 | 0.293 | 0.252 | 0.327 | 0.384 | 7.257 |
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 | 75 | 77 | 46 | 63 | 67 | 97 | 109 | 174 | 70 |
N.S. |
1 | 1.03 | 0.61 | 0.84 | 0.89 | 1.29 | 1.45 | 2.32 | 0.93 |
time (sec) |
N/A | 0.600 | 0.502 | 0.174 | 0.293 | 0.248 | 1.218 | 0.636 | 8.131 |
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 | 79 | 81 | 54 | 74 | 74 | 102 | 109 | 155 | 87 |
N.S. |
1 | 1.03 | 0.68 | 0.94 | 0.94 | 1.29 | 1.38 | 1.96 | 1.10 |
time (sec) |
N/A | 0.633 | 0.753 | 0.231 | 0.293 | 0.256 | 1.325 | 0.857 | 7.685 |
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 | 94 | 100 | 111 | 77 | 94 | 123 | 119 | 186 | 67 |
N.S. |
1 | 1.06 | 1.18 | 0.82 | 1.00 | 1.31 | 1.27 | 1.98 | 0.71 |
time (sec) |
N/A | 0.628 | 0.500 | 0.245 | 0.301 | 0.245 | 0.331 | 1.084 | 7.399 |
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 | 117 | 126 | 143 | 104 | 111 | 181 | 182 | 255 | 93 |
N.S. |
1 | 1.08 | 1.22 | 0.89 | 0.95 | 1.55 | 1.56 | 2.18 | 0.79 |
time (sec) |
N/A | 0.781 | 0.655 | 0.247 | 0.325 | 0.238 | 0.570 | 1.343 | 8.035 |
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 | 139 | 152 | 174 | 109 | 132 | 227 | 235 | 322 | 113 |
N.S. |
1 | 1.09 | 1.25 | 0.78 | 0.95 | 1.63 | 1.69 | 2.32 | 0.81 |
time (sec) |
N/A | 0.940 | 1.134 | 0.268 | 0.300 | 0.256 | 0.536 | 1.102 | 7.918 |
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 | 182 | 192 | 123 | 146 | 132 | 291 | 292 | 504 | 230 |
N.S. |
1 | 1.05 | 0.68 | 0.80 | 0.73 | 1.60 | 1.60 | 2.77 | 1.26 |
time (sec) |
N/A | 1.058 | 1.589 | 0.115 | 0.296 | 0.249 | 0.494 | 0.683 | 7.270 |
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 | 138 | 128 | 105 | 123 | 114 | 227 | 235 | 408 | 176 |
N.S. |
1 | 0.93 | 0.76 | 0.89 | 0.83 | 1.64 | 1.70 | 2.96 | 1.28 |
time (sec) |
N/A | 0.596 | 1.017 | 0.097 | 0.302 | 0.252 | 0.468 | 0.535 | 7.564 |
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 | 110 | 99 | 73 | 100 | 96 | 175 | 184 | 312 | 125 |
N.S. |
1 | 0.90 | 0.66 | 0.91 | 0.87 | 1.59 | 1.67 | 2.84 | 1.14 |
time (sec) |
N/A | 0.450 | 0.869 | 0.090 | 0.279 | 0.249 | 0.390 | 0.463 | 7.862 |
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 | 107 | 109 | 70 | 87 | 89 | 172 | 224 | 264 | 87 |
N.S. |
1 | 1.02 | 0.65 | 0.81 | 0.83 | 1.61 | 2.09 | 2.47 | 0.81 |
time (sec) |
N/A | 0.811 | 0.876 | 0.211 | 0.294 | 0.259 | 1.597 | 0.859 | 7.336 |
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 | 116 | 118 | 94 | 84 | 84 | 141 | 219 | 257 | 76 |
N.S. |
1 | 1.02 | 0.81 | 0.72 | 0.72 | 1.22 | 1.89 | 2.22 | 0.66 |
time (sec) |
N/A | 0.878 | 1.016 | 0.240 | 0.278 | 0.262 | 1.013 | 1.193 | 7.925 |
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 | 123 | 125 | 75 | 92 | 96 | 179 | 226 | 223 | 88 |
N.S. |
1 | 1.02 | 0.61 | 0.75 | 0.78 | 1.46 | 1.84 | 1.81 | 0.72 |
time (sec) |
N/A | 0.904 | 1.097 | 0.207 | 0.294 | 0.265 | 1.029 | 1.143 | 8.115 |
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 | 134 | 145 | 89 | 104 | 115 | 181 | 182 | 254 | 93 |
N.S. |
1 | 1.08 | 0.66 | 0.78 | 0.86 | 1.35 | 1.36 | 1.90 | 0.69 |
time (sec) |
N/A | 0.919 | 1.045 | 0.196 | 0.289 | 0.250 | 0.471 | 0.757 | 7.336 |
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 | 157 | 172 | 111 | 109 | 134 | 228 | 235 | 322 | 114 |
N.S. |
1 | 1.10 | 0.71 | 0.69 | 0.85 | 1.45 | 1.50 | 2.05 | 0.73 |
time (sec) |
N/A | 1.087 | 1.448 | 0.245 | 0.296 | 0.265 | 1.186 | 0.827 | 7.967 |
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 | 180 | 195 | 207 | 130 | 151 | 287 | 296 | 391 | 140 |
N.S. |
1 | 1.08 | 1.15 | 0.72 | 0.84 | 1.59 | 1.64 | 2.17 | 0.78 |
time (sec) |
N/A | 1.291 | 1.212 | 0.267 | 0.295 | 0.244 | 0.726 | 0.912 | 8.236 |
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 | 225 | 240 | 138 | 168 | 150 | 345 | 348 | 600 | 308 |
N.S. |
1 | 1.07 | 0.61 | 0.75 | 0.67 | 1.53 | 1.55 | 2.67 | 1.37 |
time (sec) |
N/A | 1.422 | 1.827 | 0.193 | 0.282 | 0.251 | 0.818 | 0.821 | 7.544 |
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 | 168 | 157 | 119 | 145 | 132 | 279 | 291 | 504 | 240 |
N.S. |
1 | 0.93 | 0.71 | 0.86 | 0.79 | 1.66 | 1.73 | 3.00 | 1.43 |
time (sec) |
N/A | 0.721 | 1.164 | 0.162 | 0.296 | 0.254 | 0.498 | 0.633 | 7.503 |
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 | 128 | 86 | 122 | 114 | 227 | 241 | 408 | 181 |
N.S. |
1 | 0.91 | 0.61 | 0.87 | 0.81 | 1.62 | 1.72 | 2.91 | 1.29 |
time (sec) |
N/A | 0.559 | 1.019 | 0.111 | 0.279 | 0.249 | 0.442 | 0.543 | 7.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 144 | 89 | 109 | 107 | 246 | 289 | 332 | 133 |
N.S. |
1 | 1.01 | 0.63 | 0.77 | 0.75 | 1.73 | 2.04 | 2.34 | 0.94 |
time (sec) |
N/A | 1.071 | 1.206 | 0.231 | 0.281 | 0.247 | 1.854 | 1.234 | 7.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 146 | 121 | 91 | 102 | 254 | 260 | 336 | 110 |
N.S. |
1 | 1.01 | 0.84 | 0.63 | 0.71 | 1.76 | 1.81 | 2.33 | 0.76 |
time (sec) |
N/A | 1.133 | 1.373 | 0.244 | 0.282 | 0.267 | 1.302 | 0.792 | 8.384 |
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 | 156 | 162 | 122 | 105 | 108 | 255 | 252 | 317 | 102 |
N.S. |
1 | 1.04 | 0.78 | 0.67 | 0.69 | 1.63 | 1.62 | 2.03 | 0.65 |
time (sec) |
N/A | 1.190 | 4.851 | 0.237 | 0.295 | 0.272 | 1.175 | 0.904 | 7.671 |
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 | 163 | 165 | 143 | 115 | 117 | 249 | 292 | 291 | 113 |
N.S. |
1 | 1.01 | 0.88 | 0.71 | 0.72 | 1.53 | 1.79 | 1.79 | 0.69 |
time (sec) |
N/A | 1.198 | 1.148 | 0.234 | 0.292 | 0.250 | 2.472 | 0.975 | 7.625 |
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 | 177 | 193 | 91 | 111 | 136 | 228 | 235 | 322 | 114 |
N.S. |
1 | 1.09 | 0.51 | 0.63 | 0.77 | 1.29 | 1.33 | 1.82 | 0.64 |
time (sec) |
N/A | 1.246 | 1.107 | 0.267 | 0.291 | 0.246 | 0.654 | 1.123 | 7.899 |
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 | 200 | 219 | 120 | 130 | 153 | 287 | 296 | 391 | 140 |
N.S. |
1 | 1.10 | 0.60 | 0.65 | 0.76 | 1.44 | 1.48 | 1.96 | 0.70 |
time (sec) |
N/A | 1.457 | 1.650 | 0.266 | 0.290 | 0.243 | 2.522 | 1.216 | 7.938 |
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 | 223 | 245 | 150 | 143 | 172 | 332 | 347 | 459 | 162 |
N.S. |
1 | 1.10 | 0.67 | 0.64 | 0.77 | 1.49 | 1.56 | 2.06 | 0.73 |
time (sec) |
N/A | 1.655 | 3.744 | 0.296 | 0.277 | 0.247 | 1.087 | 1.292 | 9.452 |
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 | 129 | 122 | 137 | 146 | 0 | 186 | 196 | 122 | 141 |
N.S. |
1 | 0.95 | 1.06 | 1.13 | 0.00 | 1.44 | 1.52 | 0.95 | 1.09 |
time (sec) |
N/A | 0.599 | 2.048 | 0.098 | 0.000 | 0.249 | 0.411 | 0.606 | 7.479 |
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 | 101 | 99 | 103 | 125 | 0 | 127 | 151 | 99 | 95 |
N.S. |
1 | 0.98 | 1.02 | 1.24 | 0.00 | 1.26 | 1.50 | 0.98 | 0.94 |
time (sec) |
N/A | 0.469 | 1.393 | 0.070 | 0.000 | 0.254 | 0.310 | 0.471 | 7.770 |
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 | 67 | 64 | 75 | 86 | 0 | 66 | 119 | 79 | 81 |
N.S. |
1 | 0.96 | 1.12 | 1.28 | 0.00 | 0.99 | 1.78 | 1.18 | 1.21 |
time (sec) |
N/A | 0.379 | 0.503 | 0.058 | 0.000 | 0.242 | 0.215 | 0.357 | 7.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 56 | 54 | 0 | 42 | 87 | 83 | 45 |
N.S. |
1 | 1.00 | 1.19 | 1.15 | 0.00 | 0.89 | 1.85 | 1.77 | 0.96 |
time (sec) |
N/A | 0.220 | 0.297 | 0.056 | 0.000 | 0.234 | 0.135 | 0.340 | 7.149 |
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 | 62 | 67 | 86 | 85 | 0 | 68 | 116 | 97 | 98 |
N.S. |
1 | 1.08 | 1.39 | 1.37 | 0.00 | 1.10 | 1.87 | 1.56 | 1.58 |
time (sec) |
N/A | 0.419 | 0.824 | 0.141 | 0.000 | 0.253 | 0.196 | 0.428 | 7.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 98 | 140 | 0 | 129 | 158 | 133 | 126 |
N.S. |
1 | 1.00 | 0.96 | 1.37 | 0.00 | 1.26 | 1.55 | 1.30 | 1.24 |
time (sec) |
N/A | 0.580 | 1.257 | 0.142 | 0.000 | 0.259 | 0.325 | 0.550 | 7.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 127 | 111 | 159 | 0 | 188 | 199 | 160 | 153 |
N.S. |
1 | 0.97 | 0.85 | 1.21 | 0.00 | 1.44 | 1.52 | 1.22 | 1.17 |
time (sec) |
N/A | 0.737 | 1.816 | 0.149 | 0.000 | 0.259 | 0.415 | 0.691 | 7.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 150 | 114 | 185 | 0 | 249 | 253 | 184 | 174 |
N.S. |
1 | 0.97 | 0.74 | 1.19 | 0.00 | 1.61 | 1.63 | 1.19 | 1.12 |
time (sec) |
N/A | 0.907 | 1.898 | 0.155 | 0.000 | 0.255 | 0.403 | 0.890 | 7.950 |
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 | 142 | 147 | 197 | 173 | 0 | 150 | 262 | 120 | 141 |
N.S. |
1 | 1.04 | 1.39 | 1.22 | 0.00 | 1.06 | 1.85 | 0.85 | 0.99 |
time (sec) |
N/A | 0.730 | 1.506 | 0.104 | 0.000 | 0.259 | 0.437 | 0.684 | 7.780 |
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 | 103 | 106 | 158 | 122 | 0 | 84 | 223 | 107 | 114 |
N.S. |
1 | 1.03 | 1.53 | 1.18 | 0.00 | 0.82 | 2.17 | 1.04 | 1.11 |
time (sec) |
N/A | 0.602 | 0.850 | 0.078 | 0.000 | 0.251 | 0.309 | 0.549 | 7.154 |
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 | 76 | 82 | 92 | 73 | 0 | 52 | 167 | 105 | 106 |
N.S. |
1 | 1.08 | 1.21 | 0.96 | 0.00 | 0.68 | 2.20 | 1.38 | 1.39 |
time (sec) |
N/A | 0.374 | 0.670 | 0.068 | 0.000 | 0.242 | 0.195 | 0.427 | 8.132 |
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 | 80 | 79 | 89 | 73 | 0 | 54 | 162 | 110 | 70 |
N.S. |
1 | 0.99 | 1.11 | 0.91 | 0.00 | 0.68 | 2.02 | 1.38 | 0.88 |
time (sec) |
N/A | 0.303 | 0.851 | 0.060 | 0.000 | 0.235 | 0.191 | 0.405 | 7.442 |
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 | 95 | 109 | 105 | 122 | 0 | 86 | 219 | 121 | 129 |
N.S. |
1 | 1.15 | 1.11 | 1.28 | 0.00 | 0.91 | 2.31 | 1.27 | 1.36 |
time (sec) |
N/A | 0.649 | 1.755 | 0.161 | 0.000 | 0.244 | 0.274 | 0.604 | 7.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 147 | 130 | 177 | 0 | 152 | 267 | 161 | 164 |
N.S. |
1 | 1.04 | 0.92 | 1.26 | 0.00 | 1.08 | 1.89 | 1.14 | 1.16 |
time (sec) |
N/A | 0.924 | 2.196 | 0.175 | 0.000 | 0.273 | 0.474 | 0.825 | 8.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 181 | 143 | 209 | 0 | 215 | 323 | 176 | 188 |
N.S. |
1 | 1.06 | 0.84 | 1.23 | 0.00 | 1.26 | 1.90 | 1.04 | 1.11 |
time (sec) |
N/A | 1.096 | 2.711 | 0.174 | 0.000 | 0.254 | 0.481 | 1.132 | 7.914 |
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 | 191 | 203 | 270 | 214 | 0 | 174 | 337 | 142 | 184 |
N.S. |
1 | 1.06 | 1.41 | 1.12 | 0.00 | 0.91 | 1.76 | 0.74 | 0.96 |
time (sec) |
N/A | 1.058 | 1.779 | 0.124 | 0.000 | 0.258 | 0.601 | 1.080 | 8.027 |
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 | 148 | 159 | 166 | 160 | 0 | 104 | 296 | 127 | 146 |
N.S. |
1 | 1.07 | 1.12 | 1.08 | 0.00 | 0.70 | 2.00 | 0.86 | 0.99 |
time (sec) |
N/A | 0.860 | 2.135 | 0.099 | 0.000 | 0.251 | 0.562 | 0.817 | 7.688 |
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 | 124 | 135 | 147 | 128 | 0 | 78 | 258 | 129 | 111 |
N.S. |
1 | 1.09 | 1.19 | 1.03 | 0.00 | 0.63 | 2.08 | 1.04 | 0.90 |
time (sec) |
N/A | 0.630 | 1.130 | 0.085 | 0.000 | 0.246 | 0.288 | 0.694 | 7.723 |
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 | 110 | 116 | 148 | 128 | 0 | 74 | 260 | 127 | 147 |
N.S. |
1 | 1.05 | 1.35 | 1.16 | 0.00 | 0.67 | 2.36 | 1.15 | 1.34 |
time (sec) |
N/A | 0.471 | 1.530 | 0.083 | 0.000 | 0.246 | 0.294 | 0.559 | 7.124 |
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 | 112 | 111 | 109 | 128 | 0 | 76 | 258 | 129 | 111 |
N.S. |
1 | 0.99 | 0.97 | 1.14 | 0.00 | 0.68 | 2.30 | 1.15 | 0.99 |
time (sec) |
N/A | 0.393 | 1.114 | 0.080 | 0.000 | 0.244 | 0.270 | 0.541 | 7.608 |
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 | 131 | 153 | 132 | 159 | 0 | 104 | 292 | 143 | 164 |
N.S. |
1 | 1.17 | 1.01 | 1.21 | 0.00 | 0.79 | 2.23 | 1.09 | 1.25 |
time (sec) |
N/A | 0.898 | 1.601 | 0.193 | 0.000 | 0.264 | 0.392 | 0.947 | 8.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 183 | 197 | 164 | 214 | 0 | 173 | 340 | 182 | 197 |
N.S. |
1 | 1.08 | 0.90 | 1.17 | 0.00 | 0.95 | 1.86 | 0.99 | 1.08 |
time (sec) |
N/A | 1.251 | 2.579 | 0.175 | 0.000 | 0.269 | 0.532 | 0.907 | 7.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 216 | 233 | 173 | 246 | 0 | 235 | 398 | 207 | 221 |
N.S. |
1 | 1.08 | 0.80 | 1.14 | 0.00 | 1.09 | 1.84 | 0.96 | 1.02 |
time (sec) |
N/A | 1.480 | 3.572 | 0.188 | 0.000 | 0.262 | 0.920 | 1.298 | 8.252 |
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 | 185 | 203 | 264 | 197 | 0 | 120 | 359 | 154 | 178 |
N.S. |
1 | 1.10 | 1.43 | 1.06 | 0.00 | 0.65 | 1.94 | 0.83 | 0.96 |
time (sec) |
N/A | 1.169 | 1.349 | 0.116 | 0.000 | 0.247 | 1.151 | 1.201 | 8.087 |
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 | 159 | 181 | 158 | 147 | 0 | 88 | 301 | 149 | 178 |
N.S. |
1 | 1.14 | 0.99 | 0.92 | 0.00 | 0.55 | 1.89 | 0.94 | 1.12 |
time (sec) |
N/A | 0.911 | 1.693 | 0.096 | 0.000 | 0.239 | 0.403 | 0.924 | 7.392 |
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 | 145 | 153 | 144 | 109 | 0 | 78 | 241 | 151 | 135 |
N.S. |
1 | 1.06 | 0.99 | 0.75 | 0.00 | 0.54 | 1.66 | 1.04 | 0.93 |
time (sec) |
N/A | 0.713 | 1.635 | 0.109 | 0.000 | 0.233 | 0.490 | 0.767 | 7.612 |
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 | 143 | 148 | 141 | 109 | 0 | 78 | 246 | 149 | 172 |
N.S. |
1 | 1.03 | 0.99 | 0.76 | 0.00 | 0.55 | 1.72 | 1.04 | 1.20 |
time (sec) |
N/A | 0.584 | 0.788 | 0.095 | 0.000 | 0.241 | 0.309 | 0.636 | 8.424 |
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 | 145 | 143 | 132 | 147 | 0 | 88 | 299 | 154 | 143 |
N.S. |
1 | 0.99 | 0.91 | 1.01 | 0.00 | 0.61 | 2.06 | 1.06 | 0.99 |
time (sec) |
N/A | 0.495 | 1.341 | 0.086 | 0.000 | 0.232 | 0.351 | 0.607 | 7.672 |
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 | 162 | 191 | 152 | 196 | 0 | 122 | 359 | 165 | 196 |
N.S. |
1 | 1.18 | 0.94 | 1.21 | 0.00 | 0.75 | 2.22 | 1.02 | 1.21 |
time (sec) |
N/A | 1.171 | 1.721 | 0.203 | 0.000 | 0.254 | 0.450 | 0.913 | 7.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 220 | 241 | 191 | 251 | 0 | 190 | 406 | 205 | 226 |
N.S. |
1 | 1.10 | 0.87 | 1.14 | 0.00 | 0.86 | 1.85 | 0.93 | 1.03 |
time (sec) |
N/A | 1.565 | 3.578 | 0.206 | 0.000 | 0.246 | 0.906 | 1.287 | 8.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 255 | 279 | 204 | 283 | 0 | 253 | 466 | 228 | 251 |
N.S. |
1 | 1.09 | 0.80 | 1.11 | 0.00 | 0.99 | 1.83 | 0.89 | 0.98 |
time (sec) |
N/A | 1.877 | 4.603 | 0.247 | 0.000 | 0.257 | 0.734 | 1.076 | 9.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 213 | 130 | 163 | 153 | 440 | 0 | 0 | 216 |
N.S. |
1 | 1.10 | 0.67 | 0.84 | 0.79 | 2.27 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A | 1.098 | 2.110 | 0.305 | 0.323 | 0.277 | 0.000 | 0.000 | 1.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 150 | 111 | 124 | 130 | 383 | 0 | 0 | 168 |
N.S. |
1 | 1.05 | 0.78 | 0.87 | 0.91 | 2.68 | 0.00 | 0.00 | 1.17 |
time (sec) |
N/A | 0.705 | 1.275 | 0.179 | 0.315 | 0.257 | 0.000 | 0.000 | 8.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 107 | 92 | 82 | 107 | 332 | 0 | 0 | 120 |
N.S. |
1 | 1.02 | 0.88 | 0.78 | 1.02 | 3.16 | 0.00 | 0.00 | 1.14 |
time (sec) |
N/A | 0.445 | 0.704 | 0.130 | 0.304 | 0.263 | 0.000 | 0.000 | 7.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 77 | 75 | 63 | 87 | 272 | 0 | 0 | 96 |
N.S. |
1 | 1.03 | 1.00 | 0.84 | 1.16 | 3.63 | 0.00 | 0.00 | 1.28 |
time (sec) |
N/A | 0.310 | 0.300 | 0.135 | 0.314 | 0.261 | 0.000 | 0.000 | 7.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 89 | 79 | 72 | 113 | 447 | 0 | 0 | 493 |
N.S. |
1 | 1.03 | 0.92 | 0.84 | 1.31 | 5.20 | 0.00 | 0.00 | 5.73 |
time (sec) |
N/A | 0.547 | 1.106 | 0.371 | 0.305 | 0.257 | 0.000 | 0.000 | 8.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 134 | 118 | 114 | 145 | 649 | 0 | 0 | 168 |
N.S. |
1 | 1.09 | 0.96 | 0.93 | 1.18 | 5.28 | 0.00 | 0.00 | 1.37 |
time (sec) |
N/A | 0.806 | 2.058 | 0.289 | 0.331 | 0.269 | 0.000 | 0.000 | 8.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 184 | 138 | 146 | 202 | 730 | 0 | 0 | 702 |
N.S. |
1 | 1.09 | 0.82 | 0.86 | 1.20 | 4.32 | 0.00 | 0.00 | 4.15 |
time (sec) |
N/A | 1.103 | 2.937 | 0.275 | 0.309 | 0.266 | 0.000 | 0.000 | 7.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 236 | 157 | 171 | 249 | 823 | 0 | 0 | 735 |
N.S. |
1 | 1.12 | 0.75 | 0.81 | 1.19 | 3.92 | 0.00 | 0.00 | 3.50 |
time (sec) |
N/A | 1.441 | 4.705 | 0.289 | 0.311 | 0.282 | 0.000 | 0.000 | 8.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 213 | 133 | 164 | 153 | 467 | 0 | 0 | 211 |
N.S. |
1 | 1.08 | 0.68 | 0.83 | 0.78 | 2.37 | 0.00 | 0.00 | 1.07 |
time (sec) |
N/A | 1.077 | 1.946 | 0.125 | 0.328 | 0.269 | 0.000 | 0.000 | 9.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 114 | 123 | 130 | 415 | 0 | 0 | 163 |
N.S. |
1 | 1.00 | 0.83 | 0.90 | 0.95 | 3.03 | 0.00 | 0.00 | 1.19 |
time (sec) |
N/A | 0.565 | 1.045 | 0.130 | 0.297 | 0.265 | 0.000 | 0.000 | 7.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 106 | 98 | 99 | 111 | 359 | 0 | 0 | 139 |
N.S. |
1 | 0.99 | 0.92 | 0.93 | 1.04 | 3.36 | 0.00 | 0.00 | 1.30 |
time (sec) |
N/A | 0.394 | 0.556 | 0.103 | 0.312 | 0.254 | 0.000 | 0.000 | 7.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 115 | 108 | 87 | 130 | 514 | 0 | 0 | 553 |
N.S. |
1 | 1.02 | 0.96 | 0.77 | 1.15 | 4.55 | 0.00 | 0.00 | 4.89 |
time (sec) |
N/A | 0.769 | 0.638 | 0.306 | 0.309 | 0.258 | 0.000 | 0.000 | 8.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 132 | 122 | 111 | 145 | 685 | 0 | 0 | 2338 |
N.S. |
1 | 1.06 | 0.98 | 0.89 | 1.16 | 5.48 | 0.00 | 0.00 | 18.70 |
time (sec) |
N/A | 0.836 | 3.436 | 0.296 | 0.309 | 0.282 | 0.000 | 0.000 | 9.996 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 182 | 139 | 148 | 203 | 762 | 0 | 0 | 3027 |
N.S. |
1 | 1.06 | 0.81 | 0.87 | 1.19 | 4.46 | 0.00 | 0.00 | 17.70 |
time (sec) |
N/A | 1.127 | 3.154 | 0.288 | 0.322 | 0.266 | 0.000 | 0.000 | 9.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 234 | 158 | 179 | 253 | 856 | 0 | 0 | 3084 |
N.S. |
1 | 1.10 | 0.74 | 0.84 | 1.19 | 4.02 | 0.00 | 0.00 | 14.48 |
time (sec) |
N/A | 1.489 | 5.411 | 0.300 | 0.308 | 0.272 | 0.000 | 0.000 | 9.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 266 | 151 | 206 | 176 | 531 | 0 | 0 | 258 |
N.S. |
1 | 1.08 | 0.61 | 0.84 | 0.72 | 2.16 | 0.00 | 0.00 | 1.05 |
time (sec) |
N/A | 1.431 | 3.619 | 0.184 | 0.313 | 0.277 | 0.000 | 0.000 | 8.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 168 | 132 | 165 | 153 | 477 | 0 | 0 | 212 |
N.S. |
1 | 0.98 | 0.77 | 0.96 | 0.89 | 2.79 | 0.00 | 0.00 | 1.24 |
time (sec) |
N/A | 0.664 | 1.538 | 0.125 | 0.313 | 0.261 | 0.000 | 0.000 | 1.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 137 | 116 | 141 | 134 | 421 | 0 | 0 | 188 |
N.S. |
1 | 0.97 | 0.82 | 1.00 | 0.95 | 2.99 | 0.00 | 0.00 | 1.33 |
time (sec) |
N/A | 0.504 | 0.874 | 0.126 | 0.301 | 0.252 | 0.000 | 0.000 | 1.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 149 | 126 | 125 | 154 | 610 | 0 | 0 | 597 |
N.S. |
1 | 1.01 | 0.86 | 0.85 | 1.05 | 4.15 | 0.00 | 0.00 | 4.06 |
time (sec) |
N/A | 1.012 | 1.172 | 0.299 | 0.296 | 0.270 | 0.000 | 0.000 | 8.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 166 | 129 | 131 | 163 | 705 | 0 | 0 | 2947 |
N.S. |
1 | 1.05 | 0.82 | 0.83 | 1.03 | 4.46 | 0.00 | 0.00 | 18.65 |
time (sec) |
N/A | 1.103 | 1.436 | 0.304 | 0.301 | 0.264 | 0.000 | 0.000 | 8.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 173 | 181 | 141 | 143 | 206 | 774 | 0 | 0 | 2991 |
N.S. |
1 | 1.05 | 0.82 | 0.83 | 1.19 | 4.47 | 0.00 | 0.00 | 17.29 |
time (sec) |
N/A | 1.157 | 5.859 | 0.282 | 0.313 | 0.274 | 0.000 | 0.000 | 9.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 217 | 232 | 160 | 179 | 249 | 868 | 0 | 0 | 3048 |
N.S. |
1 | 1.07 | 0.74 | 0.82 | 1.15 | 4.00 | 0.00 | 0.00 | 14.05 |
time (sec) |
N/A | 1.468 | 5.542 | 0.326 | 0.304 | 0.275 | 0.000 | 0.000 | 9.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 285 | 177 | 206 | 293 | 944 | 0 | 0 | 3094 |
N.S. |
1 | 1.09 | 0.68 | 0.79 | 1.12 | 3.62 | 0.00 | 0.00 | 11.85 |
time (sec) |
N/A | 1.892 | 4.771 | 0.339 | 0.307 | 0.284 | 0.000 | 0.000 | 9.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 218 | 130 | 167 | 157 | 447 | 0 | 0 | 236 |
N.S. |
1 | 1.06 | 0.63 | 0.81 | 0.77 | 2.18 | 0.00 | 0.00 | 1.15 |
time (sec) |
N/A | 1.099 | 2.430 | 0.172 | 0.311 | 0.282 | 0.000 | 0.000 | 8.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 165 | 111 | 128 | 134 | 391 | 0 | 0 | 188 |
N.S. |
1 | 1.04 | 0.70 | 0.81 | 0.84 | 2.46 | 0.00 | 0.00 | 1.18 |
time (sec) |
N/A | 0.757 | 1.867 | 0.141 | 0.325 | 0.266 | 0.000 | 0.000 | 8.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 111 | 109 | 88 | 110 | 327 | 0 | 0 | 141 |
N.S. |
1 | 1.02 | 1.00 | 0.81 | 1.01 | 3.00 | 0.00 | 0.00 | 1.29 |
time (sec) |
N/A | 0.460 | 1.356 | 0.135 | 0.302 | 0.255 | 0.000 | 0.000 | 1.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 84 | 82 | 71 | 91 | 328 | 0 | 0 | 117 |
N.S. |
1 | 1.02 | 1.00 | 0.87 | 1.11 | 4.00 | 0.00 | 0.00 | 1.43 |
time (sec) |
N/A | 0.314 | 0.504 | 0.138 | 0.305 | 0.257 | 0.000 | 0.000 | 0.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 125 | 120 | 99 | 133 | 575 | 0 | 0 | 515 |
N.S. |
1 | 1.10 | 1.05 | 0.87 | 1.17 | 5.04 | 0.00 | 0.00 | 4.52 |
time (sec) |
N/A | 0.782 | 2.059 | 0.303 | 0.289 | 0.265 | 0.000 | 0.000 | 7.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 183 | 131 | 139 | 184 | 742 | 0 | 0 | 2961 |
N.S. |
1 | 1.10 | 0.78 | 0.83 | 1.10 | 4.44 | 0.00 | 0.00 | 17.73 |
time (sec) |
N/A | 1.134 | 3.644 | 0.316 | 0.305 | 0.274 | 0.000 | 0.000 | 9.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 219 | 237 | 150 | 171 | 232 | 835 | 0 | 0 | 3037 |
N.S. |
1 | 1.08 | 0.68 | 0.78 | 1.06 | 3.81 | 0.00 | 0.00 | 13.87 |
time (sec) |
N/A | 1.517 | 4.417 | 0.319 | 0.306 | 0.281 | 0.000 | 0.000 | 9.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 209 | 219 | 149 | 154 | 160 | 440 | 0 | 0 | 233 |
N.S. |
1 | 1.05 | 0.71 | 0.74 | 0.77 | 2.11 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A | 1.110 | 2.937 | 0.156 | 0.310 | 0.276 | 0.000 | 0.000 | 8.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 166 | 148 | 116 | 137 | 375 | 0 | 0 | 186 |
N.S. |
1 | 0.99 | 0.89 | 0.69 | 0.82 | 2.25 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A | 0.778 | 1.724 | 0.125 | 0.316 | 0.254 | 0.000 | 0.000 | 0.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 126 | 118 | 96 | 116 | 369 | 0 | 0 | 163 |
N.S. |
1 | 1.06 | 0.99 | 0.81 | 0.97 | 3.10 | 0.00 | 0.00 | 1.37 |
time (sec) |
N/A | 0.525 | 1.369 | 0.117 | 0.366 | 0.252 | 0.000 | 0.000 | 8.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 119 | 76 | 96 | 113 | 372 | 0 | 0 | 162 |
N.S. |
1 | 0.98 | 0.63 | 0.79 | 0.93 | 3.07 | 0.00 | 0.00 | 1.34 |
time (sec) |
N/A | 0.408 | 0.623 | 0.126 | 0.310 | 0.255 | 0.000 | 0.000 | 7.558 |