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 | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 71 | 211 | 64 | 71 | 368 | 0 | 83 | 318 | 69 |
N.S. |
1 | 0.97 | 2.89 | 0.88 | 0.97 | 5.04 | 0.00 | 1.14 | 4.36 | 0.95 |
time (sec) |
N/A | 0.250 | 1.879 | 0.516 | 0.107 | 0.099 | 0.000 | 0.164 | 0.170 | 15.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 111 | 240 | 90 | 106 | 435 | 0 | 114 | 562 | 2056 |
N.S. |
1 | 1.21 | 2.61 | 0.98 | 1.15 | 4.73 | 0.00 | 1.24 | 6.11 | 22.35 |
time (sec) |
N/A | 0.268 | 1.581 | 0.430 | 0.119 | 0.115 | 0.000 | 0.175 | 0.177 | 17.678 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 161 | 103 | 120 | 175 | 544 | 0 | 192 | 792 | 2401 |
N.S. |
1 | 1.13 | 0.73 | 0.85 | 1.23 | 3.83 | 0.00 | 1.35 | 5.58 | 16.91 |
time (sec) |
N/A | 0.368 | 1.091 | 1.454 | 0.130 | 0.125 | 0.000 | 0.163 | 0.201 | 18.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 232 | 138 | 160 | 268 | 656 | 0 | 195 | 963 | 2880 |
N.S. |
1 | 1.14 | 0.68 | 0.79 | 1.32 | 3.23 | 0.00 | 0.96 | 4.74 | 14.19 |
time (sec) |
N/A | 0.455 | 1.497 | 2.551 | 0.111 | 0.139 | 0.000 | 0.192 | 0.238 | 19.493 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 316 | 499 | 210 | 369 | 789 | 0 | 270 | 1142 | 3310 |
N.S. |
1 | 1.14 | 1.79 | 0.76 | 1.33 | 2.84 | 0.00 | 0.97 | 4.11 | 11.91 |
time (sec) |
N/A | 0.526 | 4.680 | 4.435 | 0.123 | 0.149 | 0.000 | 0.162 | 0.313 | 21.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 90 | 108 | 179 | 472 | 0 | 117 | 834 | 113 |
N.S. |
1 | 1.05 | 0.83 | 1.00 | 1.66 | 4.37 | 0.00 | 1.08 | 7.72 | 1.05 |
time (sec) |
N/A | 0.270 | 0.729 | 1.075 | 0.115 | 0.116 | 0.000 | 0.185 | 0.212 | 0.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 163 | 124 | 212 | 544 | 0 | 155 | 1184 | 129 |
N.S. |
1 | 1.00 | 1.30 | 0.99 | 1.70 | 4.35 | 0.00 | 1.24 | 9.47 | 1.03 |
time (sec) |
N/A | 0.285 | 0.670 | 1.266 | 0.112 | 0.112 | 0.000 | 0.229 | 0.211 | 16.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 156 | 927 | 142 | 233 | 613 | 0 | 178 | 1518 | 149 |
N.S. |
1 | 1.11 | 6.62 | 1.01 | 1.66 | 4.38 | 0.00 | 1.27 | 10.84 | 1.06 |
time (sec) |
N/A | 0.309 | 5.413 | 1.218 | 0.114 | 0.121 | 0.000 | 0.211 | 0.213 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 148 | 176 | 149 | 253 | 727 | 0 | 197 | 1649 | 175 |
N.S. |
1 | 0.95 | 1.13 | 0.96 | 1.62 | 4.66 | 0.00 | 1.26 | 10.57 | 1.12 |
time (sec) |
N/A | 0.377 | 1.061 | 2.219 | 0.115 | 0.126 | 0.000 | 0.243 | 0.271 | 17.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 170 | 194 | 177 | 272 | 856 | 0 | 229 | 1766 | 256 |
N.S. |
1 | 0.94 | 1.07 | 0.98 | 1.50 | 4.73 | 0.00 | 1.27 | 9.76 | 1.41 |
time (sec) |
N/A | 0.406 | 3.111 | 3.974 | 0.109 | 0.147 | 0.000 | 0.188 | 0.340 | 0.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 200 | 2670 | 214 | 303 | 995 | 0 | 271 | 1887 | 257 |
N.S. |
1 | 0.93 | 12.48 | 1.00 | 1.42 | 4.65 | 0.00 | 1.27 | 8.82 | 1.20 |
time (sec) |
N/A | 0.433 | 7.256 | 6.946 | 0.115 | 0.176 | 0.000 | 0.185 | 0.493 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 152 | 125 | 137 | 210 | 722 | 0 | 185 | 1296 | 149 |
N.S. |
1 | 1.10 | 0.91 | 0.99 | 1.52 | 5.23 | 0.00 | 1.34 | 9.39 | 1.08 |
time (sec) |
N/A | 0.320 | 0.718 | 1.118 | 0.119 | 0.121 | 0.000 | 0.176 | 0.250 | 17.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 283 | 118 | 187 | 654 | 0 | 163 | 1026 | 125 |
N.S. |
1 | 1.00 | 2.30 | 0.96 | 1.52 | 5.32 | 0.00 | 1.33 | 8.34 | 1.02 |
time (sec) |
N/A | 0.277 | 4.174 | 1.115 | 0.114 | 0.130 | 0.000 | 0.182 | 0.244 | 17.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 111 | 265 | 100 | 156 | 580 | 0 | 124 | 752 | 112 |
N.S. |
1 | 1.05 | 2.50 | 0.94 | 1.47 | 5.47 | 0.00 | 1.17 | 7.09 | 1.06 |
time (sec) |
N/A | 0.267 | 3.333 | 1.191 | 0.105 | 0.122 | 0.000 | 0.174 | 0.241 | 15.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 175 | 332 | 147 | 231 | 819 | 0 | 196 | 1496 | 3271 |
N.S. |
1 | 1.22 | 2.31 | 1.02 | 1.60 | 5.69 | 0.00 | 1.36 | 10.39 | 22.72 |
time (sec) |
N/A | 0.343 | 4.527 | 1.069 | 0.117 | 0.142 | 0.000 | 0.139 | 0.234 | 19.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 239 | 156 | 177 | 338 | 970 | 0 | 228 | 1949 | 3708 |
N.S. |
1 | 1.19 | 0.78 | 0.88 | 1.68 | 4.83 | 0.00 | 1.13 | 9.70 | 18.45 |
time (sec) |
N/A | 0.463 | 2.988 | 3.142 | 0.117 | 0.159 | 0.000 | 0.175 | 0.286 | 19.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 305 | 1134 | 215 | 464 | 1129 | 0 | 464 | 2166 | 4158 |
N.S. |
1 | 1.13 | 4.22 | 0.80 | 1.72 | 4.20 | 0.00 | 1.72 | 8.05 | 15.46 |
time (sec) |
N/A | 0.540 | 8.906 | 4.667 | 0.125 | 0.177 | 0.000 | 0.218 | 0.387 | 20.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 352 | 397 | 1770 | 267 | 611 | 1296 | 0 | 350 | 2455 | 4594 |
N.S. |
1 | 1.13 | 5.03 | 0.76 | 1.74 | 3.68 | 0.00 | 0.99 | 6.97 | 13.05 |
time (sec) |
N/A | 0.619 | 9.476 | 8.789 | 0.125 | 0.226 | 0.000 | 0.190 | 0.601 | 20.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 245 | 1411 | 229 | 401 | 1323 | 0 | 324 | 2880 | 4506 |
N.S. |
1 | 1.20 | 6.92 | 1.12 | 1.97 | 6.49 | 0.00 | 1.59 | 14.12 | 22.09 |
time (sec) |
N/A | 0.426 | 8.648 | 2.227 | 0.117 | 0.179 | 0.000 | 0.149 | 0.358 | 19.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 83 | 70 | 143 | 81 | 100 | 0 | 217 | 100 | 0 |
N.S. |
1 | 0.62 | 0.52 | 1.07 | 0.60 | 0.75 | 0.00 | 1.62 | 0.75 | 0.00 |
time (sec) |
N/A | 0.532 | 1.051 | 4.088 | 0.112 | 0.090 | 0.000 | 0.463 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 68 | 83 | 133 | 62 | 87 | 0 | 182 | 72 | 0 |
N.S. |
1 | 0.67 | 0.82 | 1.32 | 0.61 | 0.86 | 0.00 | 1.80 | 0.71 | 0.00 |
time (sec) |
N/A | 0.439 | 0.284 | 4.026 | 0.111 | 0.083 | 0.000 | 0.298 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 51 | 48 | 100 | 40 | 68 | 0 | 137 | 46 | 0 |
N.S. |
1 | 0.80 | 0.75 | 1.56 | 0.62 | 1.06 | 0.00 | 2.14 | 0.72 | 0.00 |
time (sec) |
N/A | 0.363 | 0.100 | 1.237 | 0.158 | 0.082 | 0.000 | 0.232 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 38 | 21 | 53 | 0 | 141 | 18 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.15 | 0.64 | 1.61 | 0.00 | 4.27 | 0.55 | 0.00 |
time (sec) |
N/A | 0.300 | 0.028 | 0.519 | 0.104 | 0.085 | 0.000 | 0.242 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 34 | 32 | 48 | 37 | 56 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.06 | 1.00 | 1.50 | 1.16 | 1.75 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.304 | 0.040 | 0.519 | 0.112 | 0.080 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 54 | 48 | 87 | 60 | 94 | 0 | 108 | 44 | 0 |
N.S. |
1 | 0.81 | 0.72 | 1.30 | 0.90 | 1.40 | 0.00 | 1.61 | 0.66 | 0.00 |
time (sec) |
N/A | 0.376 | 0.115 | 1.218 | 0.111 | 0.084 | 0.000 | 0.258 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 71 | 59 | 105 | 79 | 125 | 0 | 147 | 55 | 0 |
N.S. |
1 | 0.71 | 0.59 | 1.05 | 0.79 | 1.25 | 0.00 | 1.47 | 0.55 | 0.00 |
time (sec) |
N/A | 0.462 | 0.216 | 1.290 | 0.105 | 0.087 | 0.000 | 0.424 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 84 | 71 | 115 | 94 | 162 | 0 | 171 | 64 | 0 |
N.S. |
1 | 0.63 | 0.53 | 0.86 | 0.71 | 1.22 | 0.00 | 1.29 | 0.48 | 0.00 |
time (sec) |
N/A | 0.530 | 0.112 | 1.318 | 0.107 | 0.090 | 0.000 | 0.367 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 376 | 390 | 0 | 3376 | 0 | 887 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.04 | 0.00 | 8.98 | 0.00 | 2.36 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.686 | 0.000 | 36.366 | 0.000 | 0.152 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 305 | 0 | 2475 | 0 | 782 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.04 | 0.00 | 8.48 | 0.00 | 2.68 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.573 | 0.000 | 12.586 | 0.000 | 0.122 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 238 | 0 | 1831 | 0 | 603 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.07 | 0.00 | 8.25 | 0.00 | 2.72 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.488 | 0.000 | 7.983 | 0.000 | 0.113 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 90 | 69 | 1770 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.10 | 0.84 | 21.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.313 | 0.390 | 3.954 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 249 | 402 | 2386 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.61 | 9.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.501 | 9.131 | 9.783 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 328 | 0 | 3236 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.96 | 0.00 | 9.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.636 | 0.000 | 21.351 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 180 | 433 | 1106 | 317 | 468 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.01 | 2.43 | 6.21 | 1.78 | 2.63 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.342 | 12.226 | 47.892 | 0.040 | 0.842 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 117 | 349 | 797 | 173 | 390 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.96 | 2.86 | 6.53 | 1.42 | 3.20 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.294 | 9.291 | 31.992 | 0.033 | 0.239 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 74 | 210 | 509 | 69 | 320 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.97 | 2.76 | 6.70 | 0.91 | 4.21 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.259 | 1.217 | 23.766 | 0.048 | 0.138 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | C | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 77 | 284 | 353 | 3227 | 1227 | 0 | 0 | 15 | 0 |
N.S. |
1 | 0.97 | 3.59 | 4.47 | 40.85 | 15.53 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.247 | 0.321 | 4.978 | 0.594 | 0.296 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 86 | 136 | 278 | 0 | 499 | 0 | 78 | 24 | 0 |
N.S. |
1 | 1.05 | 1.66 | 3.39 | 0.00 | 6.09 | 0.00 | 0.95 | 0.29 | 0.00 |
time (sec) |
N/A | 0.270 | 0.488 | 5.560 | 0.000 | 0.235 | 0.000 | 0.247 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 143 | 152 | 441 | 0 | 567 | 0 | 117 | 24 | 0 |
N.S. |
1 | 1.02 | 1.09 | 3.15 | 0.00 | 4.05 | 0.00 | 0.84 | 0.17 | 0.00 |
time (sec) |
N/A | 0.305 | 0.897 | 9.616 | 0.000 | 0.337 | 0.000 | 0.239 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 215 | 1902 | 625 | 0 | 641 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.10 | 9.70 | 3.19 | 0.00 | 3.27 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.381 | 14.950 | 21.964 | 0.000 | 0.950 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 454 | 471 | 0 | 3995 | 0 | 981 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.04 | 0.00 | 8.80 | 0.00 | 2.16 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.819 | 0.000 | 45.559 | 0.000 | 0.177 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 375 | 389 | 0 | 3442 | 0 | 890 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.04 | 0.00 | 9.18 | 0.00 | 2.37 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.709 | 0.000 | 33.151 | 0.000 | 0.148 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 308 | 0 | 2743 | 0 | 798 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.05 | 0.00 | 9.33 | 0.00 | 2.71 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.586 | 0.000 | 22.911 | 0.000 | 0.135 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 244 | 0 | 1987 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.07 | 0.00 | 8.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.470 | 0.000 | 9.904 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 245 | 179 | 2625 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 0.73 | 10.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.517 | 1.836 | 4.511 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 323 | 356 | 3284 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 1.10 | 10.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.646 | 13.277 | 10.433 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 217 | 512 | 1474 | 415 | 566 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.92 | 2.16 | 6.22 | 1.75 | 2.39 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.361 | 9.117 | 63.987 | 0.038 | 3.536 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 152 | 400 | 1151 | 243 | 470 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.92 | 2.42 | 6.98 | 1.47 | 2.85 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.313 | 7.837 | 48.296 | 0.034 | 0.825 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 109 | 84 | 829 | 104 | 390 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.98 | 0.76 | 7.47 | 0.94 | 3.51 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.280 | 0.268 | 40.878 | 0.035 | 0.242 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 116 | 527 | 677 | 0 | 1457 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.98 | 4.47 | 5.74 | 0.00 | 12.35 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.287 | 1.294 | 10.138 | 0.000 | 0.433 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 128 | 466 | 507 | 0 | 1403 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.03 | 3.76 | 4.09 | 0.00 | 11.31 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.345 | 4.410 | 21.639 | 0.000 | 0.447 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 133 | 191 | 464 | 0 | 563 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.06 | 1.53 | 3.71 | 0.00 | 4.50 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.299 | 0.739 | 5.826 | 0.000 | 0.352 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 190 | 165 | 649 | 0 | 647 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.98 | 0.85 | 3.36 | 0.00 | 3.35 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.341 | 1.332 | 10.572 | 0.000 | 0.975 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 706 | 988 | 0 | 1611 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 4.25 | 5.95 | 0.00 | 9.70 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.342 | 5.777 | 33.528 | 0.000 | 1.055 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 109 | 181 | 0 | 160 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 2.60 | 4.31 | 0.00 | 3.81 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.204 | 0.134 | 9.306 | 0.000 | 0.099 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | C | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 57 | 135 | 1391 | 131 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 2.38 | 5.62 | 57.96 | 5.46 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.185 | 0.046 | 7.092 | 0.411 | 0.090 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 334 | 315 | 0 | 2359 | 0 | 784 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.94 | 0.00 | 7.06 | 0.00 | 2.35 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.585 | 0.000 | 13.509 | 0.000 | 0.137 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 201 | 0 | 1518 | 0 | 594 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.17 | 0.00 | 8.83 | 0.00 | 3.45 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.436 | 0.000 | 6.355 | 0.000 | 0.109 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 90 | 69 | 230 | 0 | 303 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.10 | 0.84 | 2.80 | 0.00 | 3.70 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.346 | 0.539 | 2.918 | 0.000 | 0.100 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 115 | 274 | 1526 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.07 | 2.56 | 14.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.327 | 7.270 | 5.539 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 258 | 0 | 2331 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.00 | 9.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.520 | 0.000 | 10.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 337 | 0 | 3198 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.97 | 0.00 | 9.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.616 | 0.000 | 14.443 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 142 | 326 | 879 | 160 | 396 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.07 | 2.45 | 6.61 | 1.20 | 2.98 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.320 | 7.282 | 29.715 | 0.041 | 0.252 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 79 | 326 | 572 | 74 | 324 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.98 | 4.02 | 7.06 | 0.91 | 4.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.277 | 9.193 | 23.800 | 0.033 | 0.164 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 87 | 241 | 23 | 215 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 2.23 | 6.18 | 0.59 | 5.51 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.256 | 0.079 | 9.138 | 0.034 | 0.129 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 87 | 138 | 992 | 408 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 2.23 | 3.54 | 25.44 | 10.46 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.213 | 0.046 | 3.508 | 0.262 | 0.195 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 91 | 126 | 295 | 0 | 502 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.05 | 1.45 | 3.39 | 0.00 | 5.77 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.285 | 0.183 | 6.211 | 0.000 | 0.228 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 156 | 1840 | 463 | 0 | 567 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.09 | 12.87 | 3.24 | 0.00 | 3.97 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.332 | 14.513 | 9.977 | 0.000 | 0.372 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 226 | 1739 | 636 | 0 | 643 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.11 | 8.52 | 3.12 | 0.00 | 3.15 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.394 | 14.130 | 22.079 | 0.000 | 0.923 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 316 | 0 | 3242 | 0 | 960 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.08 | 0.00 | 11.06 | 0.00 | 3.28 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.586 | 0.000 | 9.245 | 0.000 | 0.141 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 187 | 113 | 1783 | 0 | 894 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.23 | 0.74 | 11.73 | 0.00 | 5.88 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.435 | 2.720 | 5.399 | 0.000 | 0.137 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 247 | 206 | 1783 | 0 | 762 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.06 | 0.88 | 7.65 | 0.00 | 3.27 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.508 | 12.802 | 5.636 | 0.000 | 0.128 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 261 | 0 | 3227 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.07 | 0.00 | 13.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.490 | 0.000 | 7.560 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 336 | 0 | 4192 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.99 | 0.00 | 12.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.633 | 0.000 | 11.398 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 440 | 422 | 0 | 5206 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.96 | 0.00 | 11.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.736 | 0.000 | 23.532 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 143 | 259 | 1285 | 161 | 524 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.18 | 2.14 | 10.62 | 1.33 | 4.33 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.337 | 6.053 | 25.352 | 0.036 | 0.283 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 75 | 405 | 890 | 78 | 410 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.97 | 5.26 | 11.56 | 1.01 | 5.32 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.282 | 7.359 | 9.945 | 0.036 | 0.152 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 57 | 49 | 30 | 65 | 0 | 103 | 54 | 199 |
N.S. |
1 | 1.00 | 1.78 | 1.53 | 0.94 | 2.03 | 0.00 | 3.22 | 1.69 | 6.22 |
time (sec) |
N/A | 0.259 | 0.439 | 3.611 | 0.035 | 0.096 | 0.000 | 0.465 | 0.158 | 17.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 75 | 168 | 450 | 2055 | 601 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.97 | 2.18 | 5.84 | 26.69 | 7.81 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.236 | 1.000 | 4.488 | 0.375 | 0.261 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 134 | 2059 | 666 | 0 | 699 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.02 | 15.72 | 5.08 | 0.00 | 5.34 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.348 | 14.090 | 7.393 | 0.000 | 0.445 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 207 | 2046 | 858 | 0 | 811 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.07 | 10.55 | 4.42 | 0.00 | 4.18 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.399 | 14.329 | 11.561 | 0.000 | 1.248 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 293 | 2068 | 1099 | 0 | 941 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.08 | 7.63 | 4.06 | 0.00 | 3.47 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.482 | 16.034 | 24.627 | 0.000 | 3.808 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 327 | 167 | 4473 | 0 | 1374 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.01 | 0.51 | 13.76 | 0.00 | 4.23 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.618 | 3.088 | 7.739 | 0.000 | 0.210 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 323 | 1204 | 3241 | 0 | 1244 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 3.73 | 10.03 | 0.00 | 3.85 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.609 | 17.453 | 6.990 | 0.000 | 0.205 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 333 | 0 | 4473 | 0 | 1293 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.01 | 0.00 | 13.51 | 0.00 | 3.91 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.611 | 0.000 | 8.365 | 0.000 | 0.213 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 351 | 0 | 5176 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 0.99 | 0.00 | 14.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.587 | 0.000 | 9.842 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 430 | 0 | 6007 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.97 | 0.00 | 13.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.729 | 0.000 | 13.989 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 563 | 531 | 0 | 7179 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.94 | 0.00 | 12.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.824 | 0.000 | 26.633 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 145 | 592 | 1637 | 275 | 688 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.14 | 4.66 | 12.89 | 2.17 | 5.42 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.328 | 9.886 | 21.561 | 0.040 | 0.316 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 79 | 74 | 75 | 117 | 134 | 0 | 336 | 70 | 153 |
N.S. |
1 | 0.95 | 0.89 | 0.90 | 1.41 | 1.61 | 0.00 | 4.05 | 0.84 | 1.84 |
time (sec) |
N/A | 0.261 | 3.469 | 5.505 | 0.034 | 0.158 | 0.000 | 0.750 | 0.156 | 26.837 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 69 | 78 | 84 | 61 | 134 | 0 | 337 | 70 | 172 |
N.S. |
1 | 0.97 | 1.10 | 1.18 | 0.86 | 1.89 | 0.00 | 4.75 | 0.99 | 2.42 |
time (sec) |
N/A | 0.256 | 5.251 | 5.869 | 0.035 | 0.182 | 0.000 | 0.718 | 0.153 | 26.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 135 | 1927 | 861 | 0 | 881 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.08 | 15.42 | 6.89 | 0.00 | 7.05 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.288 | 6.346 | 6.880 | 0.000 | 0.532 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 204 | 1775 | 1107 | 0 | 1023 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.09 | 9.49 | 5.92 | 0.00 | 5.47 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.391 | 15.069 | 9.105 | 0.000 | 1.484 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 287 | 1777 | 1342 | 0 | 1187 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.10 | 6.81 | 5.14 | 0.00 | 4.55 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.480 | 16.133 | 13.797 | 0.000 | 4.798 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 367 | 1776 | 1602 | 0 | 1337 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.11 | 5.35 | 4.83 | 0.00 | 4.03 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.547 | 18.257 | 27.990 | 0.000 | 14.675 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 201 | 1777 | 1292 | 0 | 1241 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.12 | 9.93 | 7.22 | 0.00 | 6.93 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.351 | 15.037 | 11.174 | 0.000 | 1.855 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 37 | 76 | 388 | 53 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 2.64 | 5.43 | 27.71 | 3.79 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.178 | 0.019 | 1.388 | 0.188 | 0.082 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 0 | 2195 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.00 | 19.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.000 | 16.948 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 113 | 1392 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.08 | 13.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.348 | 15.469 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 113 | 1394 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.08 | 13.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.326 | 15.163 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |