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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.359 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 73 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.352 | 0.427 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 75 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.352 | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 113 | 62 | 81 | 63 | 71 | 92 | 69 | 78 |
N.S. |
1 | 1.18 | 0.65 | 0.84 | 0.66 | 0.74 | 0.96 | 0.72 | 0.81 |
time (sec) |
N/A | 0.374 | 0.042 | 0.254 | 0.202 | 0.261 | 0.397 | 0.271 | 4.950 |
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 | 71 | 85 | 54 | 64 | 55 | 63 | 68 | 61 | 58 |
N.S. |
1 | 1.20 | 0.76 | 0.90 | 0.77 | 0.89 | 0.96 | 0.86 | 0.82 |
time (sec) |
N/A | 0.301 | 0.037 | 0.158 | 0.205 | 0.256 | 0.233 | 0.282 | 4.885 |
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 | 46 | 54 | 43 | 44 | 44 | 50 | 42 | 49 | 38 |
N.S. |
1 | 1.17 | 0.93 | 0.96 | 0.96 | 1.09 | 0.91 | 1.07 | 0.83 |
time (sec) |
N/A | 0.240 | 0.029 | 0.114 | 0.208 | 0.246 | 0.149 | 0.282 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 45 | 0 | 0 | 0 | 36 | 0 | 0 |
N.S. |
1 | 1.00 | 1.29 | 0.00 | 0.00 | 0.00 | 1.03 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 0.008 | 0.000 | 0.000 | 0.000 | 0.377 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 48 | 40 | 42 | 35 | 43 | 34 | 0 | 38 |
N.S. |
1 | 1.20 | 1.00 | 1.05 | 0.88 | 1.08 | 0.85 | 0.00 | 0.95 |
time (sec) |
N/A | 0.245 | 0.030 | 0.173 | 0.259 | 0.258 | 0.187 | 0.000 | 4.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 75 | 53 | 62 | 35 | 58 | 60 | 0 | 71 |
N.S. |
1 | 1.06 | 0.75 | 0.87 | 0.49 | 0.82 | 0.85 | 0.00 | 1.00 |
time (sec) |
N/A | 0.294 | 0.026 | 0.237 | 0.238 | 0.253 | 0.284 | 0.000 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 100 | 62 | 81 | 35 | 66 | 87 | 0 | 0 |
N.S. |
1 | 1.04 | 0.65 | 0.84 | 0.36 | 0.69 | 0.91 | 0.00 | 0.00 |
time (sec) |
N/A | 0.356 | 0.036 | 0.471 | 0.256 | 0.252 | 0.478 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 112 | 73 | 86 | 52 | 68 | 102 | 57 | 90 |
N.S. |
1 | 1.03 | 0.67 | 0.79 | 0.48 | 0.62 | 0.94 | 0.52 | 0.83 |
time (sec) |
N/A | 0.372 | 0.015 | 0.387 | 0.207 | 0.249 | 0.525 | 0.270 | 4.978 |
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 | 84 | 86 | 66 | 69 | 44 | 60 | 78 | 49 | 70 |
N.S. |
1 | 1.02 | 0.79 | 0.82 | 0.52 | 0.71 | 0.93 | 0.58 | 0.83 |
time (sec) |
N/A | 0.324 | 0.013 | 0.181 | 0.206 | 0.252 | 0.295 | 0.271 | 5.098 |
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 | 60 | 42 | 49 | 36 | 52 | 54 | 41 | 50 |
N.S. |
1 | 1.02 | 0.71 | 0.83 | 0.61 | 0.88 | 0.92 | 0.69 | 0.85 |
time (sec) |
N/A | 0.257 | 0.019 | 0.410 | 0.205 | 0.243 | 0.188 | 0.287 | 5.367 |
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 | 27 | 27 | 27 | 25 | 26 | 35 | 24 | 26 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.96 | 1.30 | 0.89 | 0.96 | 0.89 |
time (sec) |
N/A | 0.166 | 0.003 | 0.324 | 0.200 | 0.254 | 0.124 | 0.280 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 25 | 25 | 32 | 20 | 0 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.93 | 1.19 | 0.74 | 0.00 | 0.93 |
time (sec) |
N/A | 0.211 | 0.013 | 0.714 | 0.244 | 0.253 | 0.671 | 0.000 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 49 | 46 | 27 | 51 | 48 | 0 | 46 |
N.S. |
1 | 1.00 | 0.88 | 0.82 | 0.48 | 0.91 | 0.86 | 0.00 | 0.82 |
time (sec) |
N/A | 0.257 | 0.032 | 0.361 | 0.246 | 0.246 | 1.117 | 0.000 | 4.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 73 | 66 | 27 | 62 | 70 | 0 | 66 |
N.S. |
1 | 1.00 | 0.90 | 0.81 | 0.33 | 0.77 | 0.86 | 0.00 | 0.81 |
time (sec) |
N/A | 0.308 | 0.022 | 0.658 | 0.258 | 0.253 | 1.841 | 0.000 | 4.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 292 | 291 | 268 | 483 | 0 | 314 | 746 | 435 | 352 |
N.S. |
1 | 1.00 | 0.92 | 1.65 | 0.00 | 1.08 | 2.55 | 1.49 | 1.21 |
time (sec) |
N/A | 0.560 | 0.247 | 1.121 | 0.000 | 0.247 | 1.819 | 0.443 | 0.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 204 | 159 | 272 | 0 | 197 | 398 | 280 | 220 |
N.S. |
1 | 1.05 | 0.82 | 1.40 | 0.00 | 1.02 | 2.05 | 1.44 | 1.13 |
time (sec) |
N/A | 0.452 | 0.183 | 0.906 | 0.000 | 0.276 | 0.883 | 0.389 | 4.971 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 132 | 104 | 124 | 0 | 110 | 178 | 158 | 119 |
N.S. |
1 | 1.11 | 0.87 | 1.04 | 0.00 | 0.92 | 1.50 | 1.33 | 1.00 |
time (sec) |
N/A | 0.350 | 0.090 | 0.345 | 0.000 | 0.241 | 0.433 | 0.349 | 5.188 |
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 | 42 | 33 | 32 | 53 | 53 | 60 | 49 |
N.S. |
1 | 1.00 | 1.14 | 0.89 | 0.86 | 1.43 | 1.43 | 1.62 | 1.32 |
time (sec) |
N/A | 0.184 | 0.017 | 0.304 | 0.208 | 0.246 | 0.217 | 0.263 | 0.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 19 | 12 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.36 | 0.86 | 1.14 | 1.14 |
time (sec) |
N/A | 0.189 | 0.095 | 0.188 | 0.305 | 0.248 | 1.017 | 0.280 | 4.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 30 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 2.14 | 1.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.245 | 0.321 | 0.267 | 0.292 | 0.253 | 10.724 | 0.310 | 5.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 41 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 2.93 | 1.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.386 | 0.593 | 0.260 | 0.299 | 0.245 | 76.545 | 0.277 | 4.983 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 272 | 155 | 160 | 0 | 149 | 172 | 0 | 143 |
N.S. |
1 | 1.53 | 0.87 | 0.90 | 0.00 | 0.84 | 0.97 | 0.00 | 0.80 |
time (sec) |
N/A | 1.253 | 0.164 | 0.583 | 0.000 | 0.247 | 0.552 | 0.000 | 4.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 164 | 144 | 116 | 0 | 124 | 121 | 0 | 102 |
N.S. |
1 | 1.30 | 1.14 | 0.92 | 0.00 | 0.98 | 0.96 | 0.00 | 0.81 |
time (sec) |
N/A | 0.770 | 0.170 | 0.374 | 0.000 | 0.249 | 0.325 | 0.000 | 4.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 85 | 99 | 72 | 0 | 91 | 68 | 0 | 68 |
N.S. |
1 | 1.18 | 1.38 | 1.00 | 0.00 | 1.26 | 0.94 | 0.00 | 0.94 |
time (sec) |
N/A | 0.409 | 0.099 | 0.373 | 0.000 | 0.241 | 0.198 | 0.000 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 20 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 2.00 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.182 | 0.116 | 0.031 | 0.230 | 0.248 | 1.074 | 0.270 | 4.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 67 | 75 | 63 | 0 | 0 | 98 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 0.94 | 0.00 | 0.00 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.411 | 0.023 | 0.000 | 0.000 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 125 | 146 | 97 | 0 | 0 | 141 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 0.78 | 0.00 | 0.00 | 1.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.733 | 0.057 | 0.000 | 0.000 | 0.260 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 177 | 242 | 133 | 0 | 0 | 168 | 0 | 0 | 0 |
N.S. |
1 | 1.37 | 0.75 | 0.00 | 0.00 | 0.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.238 | 0.030 | 0.000 | 0.000 | 0.253 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 262 | 108 | 205 | 0 | 154 | 0 | 218 | 0 |
N.S. |
1 | 1.59 | 0.65 | 1.24 | 0.00 | 0.93 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 1.050 | 0.099 | 0.537 | 0.000 | 0.266 | 0.000 | 0.343 | 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 | 113 | 150 | 88 | 151 | 0 | 123 | 0 | 151 | 0 |
N.S. |
1 | 1.33 | 0.78 | 1.34 | 0.00 | 1.09 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.595 | 0.075 | 0.536 | 0.000 | 0.258 | 0.000 | 0.332 | 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 | 56 | 60 | 56 | 48 | 0 | 85 | 0 | 73 | 0 |
N.S. |
1 | 1.07 | 1.00 | 0.86 | 0.00 | 1.52 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.289 | 0.031 | 0.330 | 0.000 | 0.252 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 20 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 2.00 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.183 | 0.098 | 0.026 | 0.224 | 0.247 | 0.958 | 0.251 | 4.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 20 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 2.00 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.183 | 0.106 | 0.024 | 0.227 | 0.246 | 1.083 | 0.266 | 4.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 20 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 2.00 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.183 | 0.109 | 0.029 | 0.223 | 0.254 | 1.361 | 0.259 | 4.914 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 375 | 343 | 610 | 0 | 0 | 472 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 1.63 | 0.00 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.543 | 3.525 | 0.000 | 0.000 | 0.281 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 189 | 172 | 301 | 0 | 0 | 273 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 1.59 | 0.00 | 0.00 | 1.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.371 | 2.317 | 0.000 | 0.000 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 66 | 59 | 0 | 141 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.83 | 0.00 | 1.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.466 | 0.069 | 0.378 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 18 | 28 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.75 | 0.88 | 1.12 | 1.12 |
time (sec) |
N/A | 0.209 | 0.446 | 0.188 | 0.223 | 0.251 | 2.551 | 0.281 | 4.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 18 | 39 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 2.44 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.219 | 0.284 | 0.233 | 0.226 | 0.258 | 11.429 | 0.317 | 4.917 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 87 | 0 | 0 | 130 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 1.27 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.469 | 0.207 | 0.000 | 0.000 | 0.262 | 0.000 | 0.361 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 94 | 111 | 80 | 0 | 0 | 126 | 0 | 88 | 0 |
N.S. |
1 | 1.18 | 0.85 | 0.00 | 0.00 | 1.34 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.469 | 0.198 | 0.000 | 0.000 | 0.264 | 0.000 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 77 | 0 | 0 | 123 | 0 | 82 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 1.34 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.417 | 0.171 | 0.000 | 0.000 | 0.280 | 0.000 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 65 | 93 | 63 | 59 | 128 | 0 | 83 | 100 |
N.S. |
1 | 0.98 | 1.41 | 0.95 | 0.89 | 1.94 | 0.00 | 1.26 | 1.52 |
time (sec) |
N/A | 0.279 | 0.100 | 1.140 | 0.203 | 0.255 | 0.000 | 0.274 | 5.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 81 | 0 | 0 | 128 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 1.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.444 | 0.182 | 0.000 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 95 | 110 | 79 | 0 | 0 | 125 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.83 | 0.00 | 0.00 | 1.32 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.466 | 0.183 | 0.000 | 0.000 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 126 | 142 | 126 | 0 | 0 | 194 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.00 | 0.00 | 0.00 | 1.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.524 | 0.338 | 0.000 | 0.000 | 0.264 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 43 | 0 | 31 | 24 | 0 | 16 |
N.S. |
1 | 1.00 | 1.00 | 2.05 | 0.00 | 1.48 | 1.14 | 0.00 | 0.76 |
time (sec) |
N/A | 0.202 | 0.009 | 0.542 | 0.000 | 0.251 | 0.374 | 0.000 | 4.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 30 | 0 | 23 | 24 | 0 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.43 | 0.00 | 1.10 | 1.14 | 0.00 | 0.76 |
time (sec) |
N/A | 0.194 | 0.006 | 0.313 | 0.000 | 0.247 | 0.154 | 0.000 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 0 | 0 | 17 | 24 | 0 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.85 | 1.20 | 0.00 | 0.75 |
time (sec) |
N/A | 0.198 | 0.012 | 0.000 | 0.000 | 0.247 | 0.217 | 0.000 | 4.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 0 | 0 | 19 | 20 | 0 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.90 | 0.95 | 0.00 | 0.76 |
time (sec) |
N/A | 0.202 | 0.007 | 0.000 | 0.000 | 0.254 | 0.355 | 0.000 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 0 | 0 | 26 | 22 | 0 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.24 | 1.05 | 0.00 | 0.76 |
time (sec) |
N/A | 0.196 | 0.006 | 0.000 | 0.000 | 0.254 | 0.647 | 0.000 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | B | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 0 | 0 | 30 | 60 | 0 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.07 | 2.14 | 0.00 | 0.82 |
time (sec) |
N/A | 0.199 | 0.010 | 0.000 | 0.000 | 0.262 | 1.494 | 0.000 | 4.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 317 | 138 | 376 | 0 | 356 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 0.49 | 1.33 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.281 | 0.276 | 5.430 | 0.000 | 0.279 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 164 | 99 | 206 | 0 | 190 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.64 | 1.33 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.616 | 0.219 | 1.471 | 0.000 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 50 | 92 | 0 | 70 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.61 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.248 | 0.033 | 0.625 | 0.000 | 0.253 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 19 | 16 | 18 | 21 | 17 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 1.06 | 1.24 | 1.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.210 | 0.355 | 0.102 | 0.279 | 0.246 | 2.898 | 0.259 | 4.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 19 | 16 | 18 | 21 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 1.06 | 1.24 | 1.12 | 1.06 | 1.06 |
time (sec) |
N/A | 0.541 | 0.446 | 0.234 | 0.270 | 0.244 | 6.145 | 0.268 | 4.800 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 19 | 16 | 18 | 21 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 1.06 | 1.24 | 1.12 | 1.06 | 1.06 |
time (sec) |
N/A | 1.105 | 0.551 | 0.246 | 0.263 | 0.237 | 32.348 | 0.263 | 4.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 19 | 16 | 18 | 26 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 1.06 | 1.53 | 1.12 | 1.06 | 1.06 |
time (sec) |
N/A | 0.817 | 0.580 | 0.071 | 0.268 | 0.263 | 41.921 | 0.259 | 4.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 19 | 16 | 18 | 26 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 1.06 | 1.53 | 1.12 | 1.06 | 1.06 |
time (sec) |
N/A | 0.391 | 0.464 | 0.138 | 0.264 | 0.255 | 8.158 | 0.270 | 4.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 13 | 15 | 18 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.14 | 0.93 | 1.07 | 1.29 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.183 | 0.025 | 0.066 | 0.255 | 0.238 | 2.116 | 0.266 | 4.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 19 | 16 | 18 | 21 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 1.06 | 1.24 | 1.12 | 1.06 | 1.06 |
time (sec) |
N/A | 0.380 | 0.486 | 0.082 | 0.252 | 0.239 | 2.921 | 0.261 | 4.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 19 | 16 | 18 | 21 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 1.06 | 1.24 | 1.12 | 1.06 | 1.06 |
time (sec) |
N/A | 0.786 | 0.586 | 0.187 | 0.274 | 0.251 | 13.979 | 0.266 | 4.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 134 | 73 | 135 | 0 | 97 | 126 | 0 | 94 |
N.S. |
1 | 1.14 | 0.62 | 1.14 | 0.00 | 0.82 | 1.07 | 0.00 | 0.80 |
time (sec) |
N/A | 0.480 | 0.035 | 2.596 | 0.000 | 0.251 | 33.428 | 0.000 | 4.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 85 | 58 | 99 | 0 | 68 | 83 | 0 | 63 |
N.S. |
1 | 1.06 | 0.72 | 1.24 | 0.00 | 0.85 | 1.04 | 0.00 | 0.79 |
time (sec) |
N/A | 0.336 | 0.026 | 1.014 | 0.000 | 0.254 | 6.417 | 0.000 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 51 | 0 | 38 | 41 | 0 | 30 |
N.S. |
1 | 1.00 | 1.00 | 1.42 | 0.00 | 1.06 | 1.14 | 0.00 | 0.83 |
time (sec) |
N/A | 0.211 | 0.016 | 0.159 | 0.000 | 0.257 | 1.179 | 0.000 | 4.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 45 | 0 | 0 | 0 | 39 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 | 0.00 |
time (sec) |
N/A | 0.373 | 0.110 | 0.000 | 0.000 | 0.000 | 5.227 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 65 | 0 | 0 | 0 | 61 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 | 0.00 |
time (sec) |
N/A | 0.501 | 0.159 | 0.000 | 0.000 | 0.000 | 28.845 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 83 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.661 | 0.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 138 | 150 | 147 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.610 | 0.285 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 104 | 0 | 0 | 0 | 65 | 0 | 0 |
N.S. |
1 | 1.04 | 1.09 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 | 0.00 |
time (sec) |
N/A | 0.450 | 0.219 | 0.000 | 0.000 | 0.000 | 28.601 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 0 | 0 | 0 | 0 | 44 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 | 0.00 |
time (sec) |
N/A | 0.294 | 0.000 | 0.000 | 0.000 | 0.000 | 4.023 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 80 | 89 | 99 | 0 | 0 | 0 | 80 | 0 | 0 |
N.S. |
1 | 1.11 | 1.24 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.429 | 0.215 | 0.000 | 0.000 | 0.000 | 10.182 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 135 | 151 | 0 | 0 | 0 | 22 | 0 | 0 |
N.S. |
1 | 1.01 | 1.13 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 | 0.00 |
time (sec) |
N/A | 0.590 | 0.296 | 0.000 | 0.000 | 0.000 | 80.525 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 238 | 87 | 172 | 0 | 121 | 0 | 0 | 0 |
N.S. |
1 | 1.76 | 0.64 | 1.27 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.918 | 0.099 | 2.273 | 0.000 | 0.243 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 126 | 69 | 118 | 0 | 90 | 0 | 0 | 0 |
N.S. |
1 | 1.40 | 0.77 | 1.31 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.459 | 0.058 | 0.969 | 0.000 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 39 | 53 | 0 | 47 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.23 | 0.00 | 1.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.216 | 0.017 | 0.441 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 19 | 22 | 15 | 19 | 19 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.06 | 1.22 | 0.83 | 1.06 | 1.06 |
time (sec) |
N/A | 0.195 | 0.163 | 0.072 | 0.236 | 0.240 | 1.714 | 0.276 | 4.706 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 19 | 22 | 17 | 19 | 19 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.06 | 1.22 | 0.94 | 1.06 | 1.06 |
time (sec) |
N/A | 0.428 | 0.216 | 0.211 | 0.251 | 0.247 | 3.629 | 0.265 | 4.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 19 | 22 | 17 | 19 | 19 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.06 | 1.22 | 0.94 | 1.06 | 1.06 |
time (sec) |
N/A | 0.832 | 0.222 | 0.224 | 0.235 | 0.260 | 16.093 | 0.261 | 4.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 143 | 112 | 0 | 0 | 97 | 112 | 0 | 90 |
N.S. |
1 | 1.28 | 1.00 | 0.00 | 0.00 | 0.87 | 1.00 | 0.00 | 0.80 |
time (sec) |
N/A | 0.633 | 0.101 | 0.000 | 0.000 | 0.256 | 7.010 | 0.000 | 4.899 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 79 | 0 | 0 | 66 | 63 | 0 | 49 |
N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.00 | 1.05 | 1.00 | 0.00 | 0.78 |
time (sec) |
N/A | 0.345 | 0.089 | 0.000 | 0.000 | 0.251 | 1.319 | 0.000 | 4.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 22 | 14 | 21 | 17 | 0 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.22 | 0.78 | 1.17 | 0.94 | 0.00 | 0.78 |
time (sec) |
N/A | 0.188 | 0.005 | 0.172 | 0.195 | 0.249 | 0.350 | 0.000 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 53 | 0 | 0 | 77 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.45 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.335 | 0.015 | 0.000 | 0.000 | 0.256 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 108 | 124 | 85 | 0 | 0 | 122 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 0.79 | 0.00 | 0.00 | 1.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.612 | 0.049 | 0.000 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 342 | 378 | 256 | 0 | 0 | 328 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.75 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.587 | 3.215 | 0.000 | 0.000 | 0.266 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 95 | 81 | 179 | 0 | 108 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.94 | 2.08 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.323 | 0.082 | 0.905 | 0.000 | 0.250 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 18 | 20 | 23 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 0.95 | 1.05 | 1.21 | 1.00 | 1.05 | 1.05 |
time (sec) |
N/A | 0.218 | 0.531 | 0.089 | 0.252 | 0.255 | 6.352 | 0.276 | 4.830 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 18 | 20 | 23 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 0.95 | 1.05 | 1.21 | 1.05 | 1.05 | 1.05 |
time (sec) |
N/A | 1.303 | 0.666 | 0.248 | 0.251 | 0.263 | 27.556 | 0.276 | 4.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 18 | 20 | 28 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 0.95 | 1.05 | 1.47 | 0.00 | 1.05 | 1.05 |
time (sec) |
N/A | 3.691 | 0.790 | 0.078 | 0.247 | 0.246 | 0.000 | 0.279 | 5.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 18 | 20 | 28 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 0.95 | 1.05 | 1.47 | 1.05 | 1.05 | 1.05 |
time (sec) |
N/A | 0.663 | 0.635 | 0.144 | 0.259 | 0.272 | 61.485 | 0.276 | 4.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 15 | 17 | 20 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 1.06 | 1.25 | 1.06 | 1.06 | 1.06 |
time (sec) |
N/A | 0.188 | 0.035 | 0.073 | 0.253 | 0.243 | 5.279 | 0.264 | 4.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 18 | 20 | 23 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 0.95 | 1.05 | 1.21 | 1.05 | 1.05 | 1.05 |
time (sec) |
N/A | 0.501 | 0.688 | 0.099 | 0.273 | 0.242 | 7.839 | 0.270 | 4.843 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 18 | 20 | 23 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 0.95 | 1.05 | 1.21 | 1.05 | 1.05 | 1.05 |
time (sec) |
N/A | 2.458 | 0.835 | 0.201 | 0.246 | 0.250 | 87.830 | 0.272 | 4.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 60 | 84 | 0 | 71 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.40 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.273 | 0.066 | 1.714 | 0.000 | 0.260 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 91 | 92 | 94 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.520 | 0.320 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 91 | 92 | 101 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.512 | 2.196 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |