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 | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 40 | 39 | 105 | 41 | 39 | 56 | 113 |
N.S. |
1 | 0.00 | 1.21 | 1.18 | 3.18 | 1.24 | 1.18 | 1.70 | 3.42 |
time (sec) |
N/A | 0.000 | 0.166 | 2.712 | 0.457 | 0.268 | 11.140 | 1.049 | 0.713 |
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 | 26 | 26 | 35 | 20 | 38 | 31 | 34 | 34 |
N.S. |
1 | 0.96 | 0.96 | 1.30 | 0.74 | 1.41 | 1.15 | 1.26 | 1.26 |
time (sec) |
N/A | 1.623 | 0.179 | 0.300 | 0.213 | 0.282 | 0.153 | 0.289 | 7.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 28 | 26 | 26 | 37 | 78 | 32 | 91 | 36 |
N.S. |
1 | 0.85 | 0.79 | 0.79 | 1.12 | 2.36 | 0.97 | 2.76 | 1.09 |
time (sec) |
N/A | 0.696 | 0.046 | 13.881 | 0.421 | 0.274 | 0.192 | 0.724 | 7.328 |
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 | 33 | 33 | 28 | 32 | 32 | 29 | 32 | 31 |
N.S. |
1 | 1.22 | 1.22 | 1.04 | 1.19 | 1.19 | 1.07 | 1.19 | 1.15 |
time (sec) |
N/A | 0.174 | 0.004 | 0.019 | 0.203 | 0.270 | 0.022 | 0.291 | 7.097 |
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 | 24 | 42 | 18 | 26 | 0 | 27 | 20 | 27 | 23 |
N.S. |
1 | 1.75 | 0.75 | 1.08 | 0.00 | 1.12 | 0.83 | 1.12 | 0.96 |
time (sec) |
N/A | 0.376 | 0.107 | 0.047 | 0.000 | 0.274 | 0.097 | 0.271 | 7.142 |
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 | 26 | 17 | 13 | 11 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 0.65 | 0.50 | 0.42 | 0.38 | 0.38 | 0.38 | 0.38 | 0.38 |
time (sec) |
N/A | 0.159 | 0.006 | 0.011 | 0.169 | 0.263 | 0.044 | 0.290 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 23 | 125 | 25 | 26 | 0 | 29 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 5.21 | 1.04 | 1.08 | 0.00 | 1.21 |
time (sec) |
N/A | 0.000 | 1.191 | 2.684 | 0.575 | 0.248 | 0.314 | 0.000 | 7.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 75 | 65 | 108 | 98 | 0 | 70 | 0 |
N.S. |
1 | 0.00 | 2.27 | 1.97 | 3.27 | 2.97 | 0.00 | 2.12 | 0.00 |
time (sec) |
N/A | 0.000 | 55.714 | 1.895 | 0.254 | 0.269 | 0.000 | 0.529 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 23 | 23 | 82 | 0 | 45 | 41 | 0 | 0 |
N.S. |
1 | 0.96 | 0.96 | 3.42 | 0.00 | 1.88 | 1.71 | 0.00 | 0.00 |
time (sec) |
N/A | 0.539 | 0.032 | 0.849 | 0.000 | 0.260 | 0.337 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 20 | 23 | 23 | 22 | 25 | 19 |
N.S. |
1 | 0.00 | 0.92 | 0.83 | 0.96 | 0.96 | 0.92 | 1.04 | 0.79 |
time (sec) |
N/A | 0.000 | 0.052 | 0.138 | 0.212 | 0.260 | 0.074 | 0.280 | 7.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 87 | 53 | 58 | 155 | 86 | 743 |
N.S. |
1 | 0.00 | 0.97 | 3.00 | 1.83 | 2.00 | 5.34 | 2.97 | 25.62 |
time (sec) |
N/A | 0.000 | 0.091 | 3.196 | 0.229 | 0.274 | 0.257 | 0.340 | 7.954 |
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 | 23 | 13 | 13 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 0.57 | 0.57 | 0.61 | 0.57 | 0.57 | 0.52 | 0.57 | 0.57 |
time (sec) |
N/A | 0.590 | 0.032 | 0.056 | 0.260 | 0.282 | 0.075 | 0.249 | 7.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 42 | 0 | 131 | 217 | 148 | 1110 | 0 |
N.S. |
1 | 0.00 | 1.68 | 0.00 | 5.24 | 8.68 | 5.92 | 44.40 | 0.00 |
time (sec) |
N/A | 0.000 | 0.148 | 0.000 | 0.842 | 0.285 | 0.502 | 78.983 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 40 | 45 | 68 | 94 | 54 | 118 | 62 |
N.S. |
1 | 0.00 | 1.11 | 1.25 | 1.89 | 2.61 | 1.50 | 3.28 | 1.72 |
time (sec) |
N/A | 0.000 | 9.686 | 0.115 | 0.244 | 0.288 | 0.134 | 0.303 | 0.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 34 | 289 | 59 | 92 | 65 | 33 |
N.S. |
1 | 0.00 | 0.97 | 1.17 | 9.97 | 2.03 | 3.17 | 2.24 | 1.14 |
time (sec) |
N/A | 0.000 | 4.650 | 0.278 | 0.320 | 0.268 | 0.107 | 0.270 | 0.405 |
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 | 14 | 14 | 19 | 18 | 17 | 17 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.36 | 1.29 | 1.21 | 1.21 | 1.21 | 1.21 | 1.21 |
time (sec) |
N/A | 0.244 | 0.009 | 0.073 | 0.190 | 0.257 | 0.181 | 0.251 | 0.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 33 | 18 | 18 | 17 | 17 | 15 | 17 | 14 |
N.S. |
1 | 2.20 | 1.20 | 1.20 | 1.13 | 1.13 | 1.00 | 1.13 | 0.93 |
time (sec) |
N/A | 0.169 | 0.053 | 0.023 | 0.181 | 0.269 | 0.054 | 0.286 | 7.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 92 | 12 | 70 | 456 | 69 | 78 | 69 | 69 |
N.S. |
1 | 7.08 | 0.92 | 5.38 | 35.08 | 5.31 | 6.00 | 5.31 | 5.31 |
time (sec) |
N/A | 0.919 | 0.009 | 0.053 | 0.197 | 0.260 | 0.118 | 0.273 | 7.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 0 | 62 | 135 | 137 | 199 | 185 | 33454 |
N.S. |
1 | 0.00 | 0.00 | 2.21 | 4.82 | 4.89 | 7.11 | 6.61 | 1194.79 |
time (sec) |
N/A | 0.000 | 0.000 | 1.659 | 0.388 | 0.271 | 0.630 | 0.316 | 24.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 30 | 34 | 34 | 31 | 53 | 35 |
N.S. |
1 | 0.00 | 1.09 | 0.94 | 1.06 | 1.06 | 0.97 | 1.66 | 1.09 |
time (sec) |
N/A | 0.000 | 5.033 | 0.147 | 0.231 | 0.262 | 0.114 | 0.261 | 7.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | F(-2) | A | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 0 | 44 | 62 | 59 | 0 | 49 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.57 | 2.21 | 2.11 | 0.00 | 1.75 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.718 | 0.225 | 0.256 | 0.000 | 0.362 | 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 | 16 | 17 | 17 | 17 | 16 | 16 | 14 | 16 | 16 |
N.S. |
1 | 1.06 | 1.06 | 1.06 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 |
time (sec) |
N/A | 0.153 | 0.005 | 0.012 | 0.201 | 0.265 | 0.033 | 0.282 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 20 | 19 | 72 | 33 | 15 | 0 | 18 |
N.S. |
1 | 0.00 | 0.87 | 0.83 | 3.13 | 1.43 | 0.65 | 0.00 | 0.78 |
time (sec) |
N/A | 0.000 | 0.891 | 51.653 | 0.368 | 0.273 | 0.194 | 0.000 | 7.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 43 | 27 | 0 | 31 | 26 | 54 | 44 |
N.S. |
1 | 0.00 | 1.59 | 1.00 | 0.00 | 1.15 | 0.96 | 2.00 | 1.63 |
time (sec) |
N/A | 0.000 | 0.066 | 5.544 | 0.000 | 0.273 | 0.241 | 0.270 | 7.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 19 | 19 | 29 | 17 | 17 | 17 | 19 |
N.S. |
1 | 0.95 | 0.86 | 0.86 | 1.32 | 0.77 | 0.77 | 0.77 | 0.86 |
time (sec) |
N/A | 0.295 | 0.078 | 0.095 | 0.279 | 0.258 | 0.092 | 0.313 | 10.838 |
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 | 20 | 15 | 15 | 16 | 15 | 15 | 14 | 15 | 15 |
N.S. |
1 | 0.75 | 0.75 | 0.80 | 0.75 | 0.75 | 0.70 | 0.75 | 0.75 |
time (sec) |
N/A | 0.130 | 0.000 | 0.019 | 0.205 | 0.253 | 0.018 | 0.303 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 67 | 50 | 49 | 47 | 47 | 46 | 51 | 63 |
N.S. |
1 | 3.35 | 2.50 | 2.45 | 2.35 | 2.35 | 2.30 | 2.55 | 3.15 |
time (sec) |
N/A | 0.384 | 0.454 | 0.054 | 0.188 | 0.254 | 0.068 | 0.335 | 0.119 |
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 | 12 | 11 | 11 | 12 | 11 | 14 | 7 | 12 | 11 |
N.S. |
1 | 0.92 | 0.92 | 1.00 | 0.92 | 1.17 | 0.58 | 1.00 | 0.92 |
time (sec) |
N/A | 0.147 | 0.002 | 0.012 | 0.190 | 0.258 | 0.028 | 0.262 | 0.027 |
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 | 16 | 14 | 15 | 15 | 25 | 21 | 17 | 15 | 15 |
N.S. |
1 | 0.88 | 0.94 | 0.94 | 1.56 | 1.31 | 1.06 | 0.94 | 0.94 |
time (sec) |
N/A | 0.418 | 0.147 | 0.057 | 0.308 | 0.271 | 0.108 | 0.265 | 7.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 15 | 18 | 19 | 17 | 20 | 22 | 17 |
N.S. |
1 | 0.00 | 0.79 | 0.95 | 1.00 | 0.89 | 1.05 | 1.16 | 0.89 |
time (sec) |
N/A | 0.000 | 0.088 | 0.147 | 0.284 | 0.254 | 0.088 | 0.273 | 7.975 |
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 | 19 | 19 | 19 | 19 | 27 | 23 | 17 | 23 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.42 | 1.21 | 0.89 | 1.21 | 0.95 |
time (sec) |
N/A | 0.213 | 0.078 | 0.048 | 0.290 | 0.265 | 0.095 | 0.282 | 7.200 |
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 | 19 | 21 | 21 | 20 | 19 | 19 | 17 | 19 | 21 |
N.S. |
1 | 1.11 | 1.11 | 1.05 | 1.00 | 1.00 | 0.89 | 1.00 | 1.11 |
time (sec) |
N/A | 0.298 | 0.814 | 0.065 | 0.324 | 0.277 | 0.089 | 0.254 | 7.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 26 | 34 | 37 | 36 | 31 | 81 | 84 |
N.S. |
1 | 0.00 | 1.18 | 1.55 | 1.68 | 1.64 | 1.41 | 3.68 | 3.82 |
time (sec) |
N/A | 0.000 | 1.275 | 0.272 | 0.430 | 0.262 | 0.098 | 0.267 | 7.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 17 | 17 | 18 | 48 | 15 | 0 | 16 |
N.S. |
1 | 0.00 | 0.85 | 0.85 | 0.90 | 2.40 | 0.75 | 0.00 | 0.80 |
time (sec) |
N/A | 0.000 | 0.184 | 0.134 | 0.363 | 0.273 | 0.138 | 0.000 | 7.803 |
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 | 18 | 18 | 18 | 17 | 27 | 17 | 15 | 17 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.50 | 0.94 | 0.83 | 0.94 | 0.89 |
time (sec) |
N/A | 0.180 | 0.060 | 0.018 | 0.180 | 0.261 | 0.042 | 0.244 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 79 | 30 | 28 | 30 | 33 | 31 | 33 | 33 |
N.S. |
1 | 3.16 | 1.20 | 1.12 | 1.20 | 1.32 | 1.24 | 1.32 | 1.32 |
time (sec) |
N/A | 0.326 | 0.761 | 0.103 | 0.261 | 0.272 | 0.062 | 0.253 | 7.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 64 | 32 | 25 | 114 | 114 | 54 | 117 | 0 |
N.S. |
1 | 3.05 | 1.52 | 1.19 | 5.43 | 5.43 | 2.57 | 5.57 | 0.00 |
time (sec) |
N/A | 1.577 | 0.046 | 0.207 | 0.220 | 0.260 | 0.104 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | B | A | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 39 | 40 | 83 | 39 | 57 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.18 | 1.21 | 2.52 | 1.18 | 1.73 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.085 | 0.542 | 0.267 | 1.110 | 0.846 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 26 | 25 | 54 | 76 | 31 | 108 | 24 |
N.S. |
1 | 0.00 | 0.90 | 0.86 | 1.86 | 2.62 | 1.07 | 3.72 | 0.83 |
time (sec) |
N/A | 0.000 | 0.098 | 1.936 | 0.258 | 0.259 | 0.133 | 0.301 | 8.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 19 | 18 | 26 | 17 | 17 | 17 | 17 |
N.S. |
1 | 0.00 | 0.90 | 0.86 | 1.24 | 0.81 | 0.81 | 0.81 | 0.81 |
time (sec) |
N/A | 0.000 | 0.101 | 0.223 | 0.226 | 0.264 | 0.073 | 0.279 | 8.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 25 | 25 | 23 | 0 | 41 | 19 | 0 | 0 |
N.S. |
1 | 0.89 | 0.89 | 0.82 | 0.00 | 1.46 | 0.68 | 0.00 | 0.00 |
time (sec) |
N/A | 1.604 | 0.232 | 0.146 | 0.000 | 0.270 | 0.093 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 23 | 15 | 61 | 20 | 0 | 18 |
N.S. |
1 | 0.00 | 1.00 | 1.28 | 0.83 | 3.39 | 1.11 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.680 | 0.056 | 0.492 | 0.255 | 0.116 | 0.000 | 8.827 |
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 | 9 | 9 | 9 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 0.78 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.168 | 0.009 | 0.015 | 0.183 | 0.258 | 0.061 | 0.250 | 0.062 |
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 | 26 | 21 | 19 | 22 | 24 | 35 | 24 | 23 | 24 |
N.S. |
1 | 0.81 | 0.73 | 0.85 | 0.92 | 1.35 | 0.92 | 0.88 | 0.92 |
time (sec) |
N/A | 0.438 | 0.042 | 0.070 | 0.204 | 0.254 | 0.085 | 0.257 | 8.153 |
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 | 32 | 25 | 21 | 26 | 25 | 27 | 22 | 29 | 25 |
N.S. |
1 | 0.78 | 0.66 | 0.81 | 0.78 | 0.84 | 0.69 | 0.91 | 0.78 |
time (sec) |
N/A | 0.497 | 0.121 | 0.047 | 0.235 | 0.259 | 0.074 | 0.260 | 8.315 |
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 | 19 | 20 | 22 | 17 | 16 | 16 | 19 | 16 | 17 |
N.S. |
1 | 1.05 | 1.16 | 0.89 | 0.84 | 0.84 | 1.00 | 0.84 | 0.89 |
time (sec) |
N/A | 0.151 | 0.003 | 0.035 | 0.175 | 0.242 | 0.034 | 0.248 | 7.840 |
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 | 23 | 20 | 18 | 28 | 23 | 31 | 17 | 18 | 18 |
N.S. |
1 | 0.87 | 0.78 | 1.22 | 1.00 | 1.35 | 0.74 | 0.78 | 0.78 |
time (sec) |
N/A | 0.606 | 0.091 | 0.073 | 0.212 | 0.241 | 0.070 | 0.254 | 8.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 48 | 23 | 42 | 41 | 42 | 42 | 47 | 21 |
N.S. |
1 | 1.92 | 0.92 | 1.68 | 1.64 | 1.68 | 1.68 | 1.88 | 0.84 |
time (sec) |
N/A | 0.249 | 0.108 | 0.034 | 0.169 | 0.245 | 0.077 | 0.267 | 8.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 38 | 34 | 34 | 39 | 31 | 26 | 2943 | 0 |
N.S. |
1 | 1.12 | 1.00 | 1.00 | 1.15 | 0.91 | 0.76 | 86.56 | 0.00 |
time (sec) |
N/A | 1.518 | 0.090 | 1.676 | 0.460 | 0.250 | 0.647 | 0.820 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 42 | 34 | 36 | 39 | 39 | 32 | 39 | 33 |
N.S. |
1 | 2.21 | 1.79 | 1.89 | 2.05 | 2.05 | 1.68 | 2.05 | 1.74 |
time (sec) |
N/A | 0.176 | 0.006 | 0.019 | 0.194 | 0.236 | 0.022 | 0.265 | 8.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 25 | 17 | 19 | 16 | 14 | 19 | 19 |
N.S. |
1 | 0.00 | 1.47 | 1.00 | 1.12 | 0.94 | 0.82 | 1.12 | 1.12 |
time (sec) |
N/A | 0.000 | 0.137 | 0.099 | 0.218 | 0.245 | 0.114 | 0.275 | 8.975 |
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 | 22 | 36 | 28 | 29 | 36 | 36 | 37 | 37 | 28 |
N.S. |
1 | 1.64 | 1.27 | 1.32 | 1.64 | 1.64 | 1.68 | 1.68 | 1.27 |
time (sec) |
N/A | 0.212 | 0.004 | 0.028 | 0.186 | 0.233 | 0.044 | 0.245 | 0.061 |
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 | 24 | 20 | 20 | 24 | 24 | 24 | 24 | 105 | 24 |
N.S. |
1 | 0.83 | 0.83 | 1.00 | 1.00 | 1.00 | 1.00 | 4.38 | 1.00 |
time (sec) |
N/A | 0.538 | 0.139 | 0.451 | 0.329 | 0.260 | 0.121 | 0.323 | 10.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 34 | 22 | 28 | 63 | 26 | 29 | 30 | 33 |
N.S. |
1 | 1.13 | 0.73 | 0.93 | 2.10 | 0.87 | 0.97 | 1.00 | 1.10 |
time (sec) |
N/A | 0.549 | 1.089 | 0.171 | 0.258 | 0.246 | 0.133 | 0.365 | 8.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 43 | 25 | 22 | 171 | 26 | 22 | 26 | 22 |
N.S. |
1 | 1.59 | 0.93 | 0.81 | 6.33 | 0.96 | 0.81 | 0.96 | 0.81 |
time (sec) |
N/A | 0.612 | 0.154 | 0.051 | 0.291 | 0.253 | 0.042 | 0.254 | 8.458 |
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 | 20 | 21 | 21 | 37 | 36 | 36 | 39 | 42 | 42 |
N.S. |
1 | 1.05 | 1.05 | 1.85 | 1.80 | 1.80 | 1.95 | 2.10 | 2.10 |
time (sec) |
N/A | 0.280 | 1.430 | 0.117 | 0.176 | 0.242 | 0.119 | 0.254 | 8.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 267 | 70 | 57 | 0 | 80 | 48 | 96 | 67 |
N.S. |
1 | 9.54 | 2.50 | 2.04 | 0.00 | 2.86 | 1.71 | 3.43 | 2.39 |
time (sec) |
N/A | 1.377 | 0.127 | 0.151 | 0.000 | 0.244 | 0.159 | 0.252 | 8.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 18 | 18 | 38 | 30 | 20 | 38 | 212 |
N.S. |
1 | 0.00 | 0.95 | 0.95 | 2.00 | 1.58 | 1.05 | 2.00 | 11.16 |
time (sec) |
N/A | 0.000 | 0.269 | 0.066 | 0.223 | 0.259 | 0.057 | 0.264 | 8.321 |
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 | 26 | 29 | 29 | 30 | 29 | 29 | 29 | 30 | 29 |
N.S. |
1 | 1.12 | 1.12 | 1.15 | 1.12 | 1.12 | 1.12 | 1.15 | 1.12 |
time (sec) |
N/A | 0.684 | 0.015 | 0.027 | 0.174 | 0.248 | 0.066 | 0.259 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 18 | 25 | 17 | 24 | 26 | 26 | 19 |
N.S. |
1 | 0.00 | 0.75 | 1.04 | 0.71 | 1.00 | 1.08 | 1.08 | 0.79 |
time (sec) |
N/A | 0.000 | 0.119 | 0.245 | 0.210 | 0.246 | 0.103 | 0.291 | 8.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 43 | 58 | 42 | 49 | 49 | 49 | 49 | 42 |
N.S. |
1 | 1.23 | 1.66 | 1.20 | 1.40 | 1.40 | 1.40 | 1.40 | 1.20 |
time (sec) |
N/A | 0.170 | 0.017 | 0.023 | 0.182 | 0.252 | 0.052 | 0.257 | 0.077 |
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 | 18 | 18 | 22 | 11 | 14 | 14 | 17 | 14 | 10 |
N.S. |
1 | 1.00 | 1.22 | 0.61 | 0.78 | 0.78 | 0.94 | 0.78 | 0.56 |
time (sec) |
N/A | 0.128 | 0.002 | 0.008 | 0.196 | 0.244 | 0.018 | 0.265 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 19 | 21 | 25 | 25 | 22 | 52 | 37 |
N.S. |
1 | 0.00 | 0.90 | 1.00 | 1.19 | 1.19 | 1.05 | 2.48 | 1.76 |
time (sec) |
N/A | 0.000 | 0.156 | 0.161 | 0.296 | 0.242 | 0.063 | 0.260 | 8.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 16 | 20 | 19 | 19 | 26 | 19 | 14 |
N.S. |
1 | 0.00 | 0.84 | 1.05 | 1.00 | 1.00 | 1.37 | 1.00 | 0.74 |
time (sec) |
N/A | 0.000 | 0.037 | 0.487 | 0.223 | 0.255 | 0.144 | 0.261 | 8.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 26 | 21 | 25 | 24 | 24 | 0 | 24 | 24 |
N.S. |
1 | 1.24 | 1.00 | 1.19 | 1.14 | 1.14 | 0.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.441 | 0.232 | 0.066 | 0.331 | 0.248 | 0.000 | 0.349 | 9.962 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 30 | 24 | 25 | 24 | 24 | 22 | 24 | 0 |
N.S. |
1 | 1.15 | 0.92 | 0.96 | 0.92 | 0.92 | 0.85 | 0.92 | 0.00 |
time (sec) |
N/A | 0.463 | 0.137 | 0.148 | 0.232 | 0.239 | 0.075 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 55 | 91 | 51 | 61 | 66 | 100 | 0 |
N.S. |
1 | 0.00 | 1.49 | 2.46 | 1.38 | 1.65 | 1.78 | 2.70 | 0.00 |
time (sec) |
N/A | 0.000 | 0.083 | 0.259 | 0.227 | 0.250 | 0.236 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 65 | 32 | 34 | 100 | 39 | 37 | 43 | 38 |
N.S. |
1 | 2.41 | 1.19 | 1.26 | 3.70 | 1.44 | 1.37 | 1.59 | 1.41 |
time (sec) |
N/A | 0.287 | 0.030 | 0.061 | 0.172 | 0.250 | 0.107 | 0.264 | 8.245 |
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 | 26 | 17 | 17 | 10 | 9 | 17 | 8 | 9 | 9 |
N.S. |
1 | 0.65 | 0.65 | 0.38 | 0.35 | 0.65 | 0.31 | 0.35 | 0.35 |
time (sec) |
N/A | 0.171 | 0.007 | 0.069 | 0.168 | 0.239 | 0.032 | 0.260 | 8.093 |
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 | 22 | 18 | 15 | 20 | 0 | 22 | 15 | 17 | 14 |
N.S. |
1 | 0.82 | 0.68 | 0.91 | 0.00 | 1.00 | 0.68 | 0.77 | 0.64 |
time (sec) |
N/A | 0.431 | 0.176 | 0.071 | 0.000 | 0.243 | 0.107 | 0.255 | 7.990 |
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 | 30 | 40 | 30 | 20 | 22 | 22 | 37 | 22 | 22 |
N.S. |
1 | 1.33 | 1.00 | 0.67 | 0.73 | 0.73 | 1.23 | 0.73 | 0.73 |
time (sec) |
N/A | 0.246 | 0.034 | 0.060 | 0.183 | 0.241 | 0.871 | 0.260 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 33 | 32 | 33 | 33 | 29 | 33 | 0 |
N.S. |
1 | 0.00 | 1.10 | 1.07 | 1.10 | 1.10 | 0.97 | 1.10 | 0.00 |
time (sec) |
N/A | 0.000 | 5.285 | 0.306 | 0.296 | 0.223 | 0.075 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 60 | 81 | 80 | 97 | 90 | 112 | 95 | 99 |
N.S. |
1 | 2.31 | 3.12 | 3.08 | 3.73 | 3.46 | 4.31 | 3.65 | 3.81 |
time (sec) |
N/A | 0.321 | 0.047 | 0.097 | 0.202 | 0.231 | 0.326 | 0.246 | 0.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 30 | 37 | 0 | 36 | 36 | 0 | 36 |
N.S. |
1 | 0.00 | 0.94 | 1.16 | 0.00 | 1.12 | 1.12 | 0.00 | 1.12 |
time (sec) |
N/A | 0.000 | 0.130 | 34.749 | 0.000 | 0.240 | 2.583 | 0.000 | 9.484 |
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 | 23 | 7 | 7 | 8 | 7 | 9 | 3 | 7 | 7 |
N.S. |
1 | 0.30 | 0.30 | 0.35 | 0.30 | 0.39 | 0.13 | 0.30 | 0.30 |
time (sec) |
N/A | 0.137 | 0.001 | 0.016 | 0.180 | 0.219 | 0.023 | 0.250 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 54 | 27 | 28 | 28 | 27 | 28 | 26 |
N.S. |
1 | 1.08 | 2.16 | 1.08 | 1.12 | 1.12 | 1.08 | 1.12 | 1.04 |
time (sec) |
N/A | 0.335 | 0.019 | 0.189 | 0.238 | 0.233 | 0.776 | 0.259 | 8.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 58 | 31 | 65 | 41 | 80 | 50 | 0 |
N.S. |
1 | 0.00 | 2.00 | 1.07 | 2.24 | 1.41 | 2.76 | 1.72 | 0.00 |
time (sec) |
N/A | 0.000 | 5.058 | 0.706 | 0.315 | 0.240 | 9.372 | 0.259 | 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 | 17 | 16 | 14 | 11 | 10 | 10 | 12 | 10 | 10 |
N.S. |
1 | 0.94 | 0.82 | 0.65 | 0.59 | 0.59 | 0.71 | 0.59 | 0.59 |
time (sec) |
N/A | 0.165 | 0.003 | 0.021 | 0.188 | 0.232 | 0.046 | 0.256 | 8.478 |
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 | 28 | 33 | 35 | 27 | 25 | 25 | 29 | 26 | 22 |
N.S. |
1 | 1.18 | 1.25 | 0.96 | 0.89 | 0.89 | 1.04 | 0.93 | 0.79 |
time (sec) |
N/A | 0.171 | 0.006 | 0.028 | 0.172 | 0.231 | 0.054 | 0.259 | 8.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 249 | 50 | 50 | 53 | 63 | 51 | 57 | 72 |
N.S. |
1 | 7.55 | 1.52 | 1.52 | 1.61 | 1.91 | 1.55 | 1.73 | 2.18 |
time (sec) |
N/A | 3.082 | 0.271 | 0.329 | 0.240 | 0.241 | 1.490 | 0.257 | 8.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 28 | 25 | 23 | 24 | 22 | 24 | 98 |
N.S. |
1 | 0.00 | 1.27 | 1.14 | 1.05 | 1.09 | 1.00 | 1.09 | 4.45 |
time (sec) |
N/A | 0.000 | 3.412 | 0.304 | 0.265 | 0.232 | 0.107 | 0.276 | 8.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | C | F | A | A | A | B |
verified |
N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 44 | 0 | 0 | 169 | 0 | 59 | 44 | 43 | 157 |
N.S. |
1 | 0.00 | 0.00 | 3.84 | 0.00 | 1.34 | 1.00 | 0.98 | 3.57 |
time (sec) |
N/A | 0.000 | 0.000 | 0.295 | 0.000 | 0.254 | 8.118 | 4.083 | 9.112 |
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 | 21 | 27 | 19 | 18 | 25 | 17 | 20 | 18 |
N.S. |
1 | 0.78 | 1.00 | 0.70 | 0.67 | 0.93 | 0.63 | 0.74 | 0.67 |
time (sec) |
N/A | 0.235 | 0.010 | 0.070 | 0.193 | 0.228 | 0.164 | 0.254 | 8.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 28 | 28 | 27 | 24 | 31 | 29 | 26 | 25 |
N.S. |
1 | 0.82 | 0.82 | 0.79 | 0.71 | 0.91 | 0.85 | 0.76 | 0.74 |
time (sec) |
N/A | 0.368 | 0.238 | 0.237 | 0.316 | 0.240 | 0.114 | 0.329 | 8.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 22 | 21 | 18 | 21 | 17 | 24 | 21 | 0 |
N.S. |
1 | 0.96 | 0.91 | 0.78 | 0.91 | 0.74 | 1.04 | 0.91 | 0.00 |
time (sec) |
N/A | 0.437 | 0.972 | 0.916 | 0.347 | 0.224 | 0.187 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 15 | 15 | 0 | 19 | 0 | 19 | 14 |
N.S. |
1 | 0.00 | 0.56 | 0.56 | 0.00 | 0.70 | 0.00 | 0.70 | 0.52 |
time (sec) |
N/A | 0.000 | 0.101 | 0.277 | 0.000 | 0.236 | 0.000 | 0.275 | 7.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 72 | 19 | 46 | 44 | 45 | 58 | 49 | 24 |
N.S. |
1 | 3.79 | 1.00 | 2.42 | 2.32 | 2.37 | 3.05 | 2.58 | 1.26 |
time (sec) |
N/A | 0.280 | 0.018 | 0.033 | 0.200 | 0.232 | 0.087 | 0.279 | 7.893 |
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 | 25 | 23 | 23 | 18 | 18 | 18 | 19 | 18 | 18 |
N.S. |
1 | 0.92 | 0.92 | 0.72 | 0.72 | 0.72 | 0.76 | 0.72 | 0.72 |
time (sec) |
N/A | 0.154 | 0.003 | 0.100 | 0.185 | 0.227 | 0.047 | 0.279 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 31 | 20 | 20 | 0 | 22 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.35 | 0.87 | 0.87 | 0.00 | 0.96 | 0.87 |
time (sec) |
N/A | 0.000 | 0.469 | 57.569 | 0.236 | 0.240 | 0.000 | 0.310 | 8.417 |
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 | 26 | 27 | 29 | 21 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.04 | 1.12 | 0.81 | 0.77 | 0.77 | 0.77 | 0.77 | 0.77 |
time (sec) |
N/A | 0.161 | 0.018 | 0.020 | 0.177 | 0.227 | 0.040 | 0.271 | 7.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 27 | 64 | 45 | 19 | 40 | 712 |
N.S. |
1 | 0.00 | 0.00 | 1.08 | 2.56 | 1.80 | 0.76 | 1.60 | 28.48 |
time (sec) |
N/A | 0.000 | 0.000 | 0.331 | 0.316 | 0.231 | 0.079 | 0.330 | 9.623 |
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 | 25 | 21 | 21 | 21 | 20 | 20 | 17 | 20 | 20 |
N.S. |
1 | 0.84 | 0.84 | 0.84 | 0.80 | 0.80 | 0.68 | 0.80 | 0.80 |
time (sec) |
N/A | 0.537 | 0.025 | 13.005 | 0.242 | 0.246 | 0.115 | 0.334 | 8.476 |
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 | 28 | 21 | 21 | 21 | 20 | 23 | 17 | 23 | 20 |
N.S. |
1 | 0.75 | 0.75 | 0.75 | 0.71 | 0.82 | 0.61 | 0.82 | 0.71 |
time (sec) |
N/A | 0.182 | 0.021 | 0.036 | 0.186 | 0.231 | 0.069 | 0.270 | 7.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | B | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 56 | 74 | 188 | 69 | 0 | 72 | 3724 |
N.S. |
1 | 0.00 | 1.60 | 2.11 | 5.37 | 1.97 | 0.00 | 2.06 | 106.40 |
time (sec) |
N/A | 0.000 | 0.090 | 2.773 | 0.446 | 0.238 | 0.000 | 0.335 | 11.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 35 | 18 | 30 | 0 | 19 | 65 |
N.S. |
1 | 0.00 | 1.00 | 1.59 | 0.82 | 1.36 | 0.00 | 0.86 | 2.95 |
time (sec) |
N/A | 0.000 | 0.492 | 2.301 | 0.292 | 0.225 | 0.000 | 0.378 | 7.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 26 | 37 | 24 | 24 | 0 | 38 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 1.54 | 1.00 | 1.00 | 0.00 | 1.58 |
time (sec) |
N/A | 0.000 | 2.000 | 180.234 | 0.537 | 0.294 | 0.306 | 0.000 | 7.689 |
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 | 22 | 13 | 13 | 12 | 11 | 11 | 8 | 11 | 11 |
N.S. |
1 | 0.59 | 0.59 | 0.55 | 0.50 | 0.50 | 0.36 | 0.50 | 0.50 |
time (sec) |
N/A | 0.308 | 0.053 | 0.042 | 0.220 | 0.236 | 0.049 | 0.303 | 7.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 77 | 21 | 24 | 17 | 28 | 27 | 27 | 17 |
N.S. |
1 | 3.21 | 0.88 | 1.00 | 0.71 | 1.17 | 1.12 | 1.12 | 0.71 |
time (sec) |
N/A | 0.267 | 0.029 | 0.864 | 0.274 | 0.236 | 0.131 | 0.275 | 7.999 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 70 | 52 | 64 | 65 | 0 | 53 | 0 |
N.S. |
1 | 0.00 | 2.33 | 1.73 | 2.13 | 2.17 | 0.00 | 1.77 | 0.00 |
time (sec) |
N/A | 0.000 | 0.166 | 0.371 | 0.268 | 0.259 | 0.000 | 0.499 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 24 | 21 | 22 | 0 | 25 | 26 | 25 | 20 |
N.S. |
1 | 1.09 | 0.95 | 1.00 | 0.00 | 1.14 | 1.18 | 1.14 | 0.91 |
time (sec) |
N/A | 0.430 | 1.139 | 0.060 | 0.000 | 0.249 | 0.082 | 0.260 | 8.679 |