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 | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 81 | 173 | 78 | 75 | 0 | 302 |
N.S. |
1 | 0.00 | 1.00 | 2.89 | 6.18 | 2.79 | 2.68 | 0.00 | 10.79 |
time (sec) |
N/A | 0.000 | 0.671 | 13.171 | 0.758 | 0.246 | 0.337 | 0.000 | 9.324 |
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 | 24 | 24 | 22 | 23 | 24 | 24 | 23 | 24 |
N.S. |
1 | 0.92 | 0.92 | 0.85 | 0.88 | 0.92 | 0.92 | 0.88 | 0.92 |
time (sec) |
N/A | 0.382 | 0.139 | 0.570 | 0.375 | 0.240 | 0.154 | 0.286 | 9.405 |
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 | 30 | 0 | 33 | 34 | 49 | 49 | 31 | 35 | 32 |
N.S. |
1 | 0.00 | 1.10 | 1.13 | 1.63 | 1.63 | 1.03 | 1.17 | 1.07 |
time (sec) |
N/A | 0.000 | 0.048 | 0.436 | 0.226 | 0.249 | 0.078 | 0.258 | 9.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 17 | 17 | 81 | 1368 | 101 | 112 | 112 | 109 |
N.S. |
1 | 0.89 | 0.89 | 4.26 | 72.00 | 5.32 | 5.89 | 5.89 | 5.74 |
time (sec) |
N/A | 0.477 | 0.033 | 0.349 | 0.301 | 0.246 | 0.224 | 0.277 | 10.038 |
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 | 28 | 26 | 26 | 28 | 36 | 41 | 36 | 198 | 25 |
N.S. |
1 | 0.93 | 0.93 | 1.00 | 1.29 | 1.46 | 1.29 | 7.07 | 0.89 |
time (sec) |
N/A | 1.985 | 0.347 | 0.275 | 0.354 | 0.242 | 0.143 | 0.555 | 0.237 |
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 | 31 | 32 | 23 | 24 | 38 | 20 | 23 | 22 |
N.S. |
1 | 1.03 | 1.07 | 0.77 | 0.80 | 1.27 | 0.67 | 0.77 | 0.73 |
time (sec) |
N/A | 0.333 | 0.032 | 0.071 | 0.201 | 0.238 | 0.094 | 0.250 | 0.109 |
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 | 38 | 27 | 37 | 38 | 40 | 32 | 40 | 36 |
N.S. |
1 | 1.36 | 0.96 | 1.32 | 1.36 | 1.43 | 1.14 | 1.43 | 1.29 |
time (sec) |
N/A | 0.914 | 0.217 | 0.535 | 0.237 | 0.256 | 0.164 | 0.283 | 9.773 |
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 | 33 | 0 | 43 | 29 | 50 | 42 | 27 | 88 | 187 |
N.S. |
1 | 0.00 | 1.30 | 0.88 | 1.52 | 1.27 | 0.82 | 2.67 | 5.67 |
time (sec) |
N/A | 0.000 | 0.141 | 0.773 | 0.322 | 0.257 | 0.158 | 0.310 | 10.896 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 39 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 2.17 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.369 | 0.063 | 0.936 | 0.210 | 0.248 | 0.098 | 0.257 | 9.311 |
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 | 28 | 30 | 33 | 25 | 79 | 34 | 20 | 40 | 22 |
N.S. |
1 | 1.07 | 1.18 | 0.89 | 2.82 | 1.21 | 0.71 | 1.43 | 0.79 |
time (sec) |
N/A | 0.558 | 0.060 | 0.262 | 0.307 | 0.238 | 0.094 | 0.255 | 9.548 |
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 | 14 | 13 | 12 | 16 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 1.14 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.188 | 0.013 | 0.073 | 0.226 | 0.246 | 0.078 | 0.253 | 9.405 |
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 | 29 | 0 | 28 | 28 | 32 | 78 | 22 | 0 | 25 |
N.S. |
1 | 0.00 | 0.97 | 0.97 | 1.10 | 2.69 | 0.76 | 0.00 | 0.86 |
time (sec) |
N/A | 0.000 | 1.106 | 0.526 | 0.449 | 0.244 | 0.153 | 0.000 | 9.265 |
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 | 25 | 25 | 17 | 15 | 25 | 14 | 20 | 14 | 14 |
N.S. |
1 | 1.00 | 0.68 | 0.60 | 1.00 | 0.56 | 0.80 | 0.56 | 0.56 |
time (sec) |
N/A | 0.197 | 0.066 | 0.040 | 0.219 | 0.237 | 0.062 | 0.253 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 55 | 52 | 110 | 110 | 109 | 128 | 0 |
N.S. |
1 | 0.00 | 2.62 | 2.48 | 5.24 | 5.24 | 5.19 | 6.10 | 0.00 |
time (sec) |
N/A | 0.000 | 3.761 | 0.162 | 0.292 | 0.249 | 0.139 | 0.658 | 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 | 35 | 138 | 105 | 116 | 119 | 149 | 116 | 114 | 116 |
N.S. |
1 | 3.94 | 3.00 | 3.31 | 3.40 | 4.26 | 3.31 | 3.26 | 3.31 |
time (sec) |
N/A | 1.121 | 0.092 | 0.250 | 0.190 | 0.241 | 2.028 | 0.256 | 0.313 |
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 | 28 | 27 | 26 | 23 | 25 | 22 | 22 | 0 | 28 |
N.S. |
1 | 0.96 | 0.93 | 0.82 | 0.89 | 0.79 | 0.79 | 0.00 | 1.00 |
time (sec) |
N/A | 3.360 | 0.151 | 0.739 | 0.282 | 0.243 | 0.246 | 0.000 | 10.158 |
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 | 17 | 17 | 14 | 14 | 14 | 14 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.82 | 0.82 | 0.82 | 0.76 | 0.82 |
time (sec) |
N/A | 0.169 | 0.008 | 0.381 | 0.196 | 0.240 | 0.044 | 0.252 | 9.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 111 | 35 | 84 | 97 | 216 | 0 | 0 | 100 |
N.S. |
1 | 3.26 | 1.03 | 2.47 | 2.85 | 6.35 | 0.00 | 0.00 | 2.94 |
time (sec) |
N/A | 5.291 | 0.511 | 33.218 | 0.494 | 0.271 | 0.000 | 0.000 | 10.010 |
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 | 18 | 20 | 17 | 16 | 16 | 15 | 18 | 16 |
N.S. |
1 | 0.82 | 0.91 | 0.77 | 0.73 | 0.73 | 0.68 | 0.82 | 0.73 |
time (sec) |
N/A | 0.212 | 0.007 | 0.031 | 0.193 | 0.236 | 0.050 | 0.254 | 9.306 |
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 | 12 | 12 | 12 | 12 | 0 | 11 | 10 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.92 | 0.83 | 0.92 | 0.92 |
time (sec) |
N/A | 0.335 | 0.079 | 0.138 | 0.000 | 0.240 | 0.066 | 0.254 | 9.362 |
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 | 30 | 125 | 39 | 46 | 60 | 53 | 56 | 53 | 0 |
N.S. |
1 | 4.17 | 1.30 | 1.53 | 2.00 | 1.77 | 1.87 | 1.77 | 0.00 |
time (sec) |
N/A | 0.534 | 0.149 | 0.352 | 0.275 | 0.244 | 15.719 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 0 | 33 | 37 | 124 | 38 | 32 | 91 | 0 |
N.S. |
1 | 0.00 | 0.85 | 0.95 | 3.18 | 0.97 | 0.82 | 2.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.092 | 8.441 | 0.531 | 0.237 | 0.202 | 0.639 | 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 | 19 | 20 | 24 | 20 | 23 | 27 | 24 | 27 | 27 |
N.S. |
1 | 1.05 | 1.26 | 1.05 | 1.21 | 1.42 | 1.26 | 1.42 | 1.42 |
time (sec) |
N/A | 0.343 | 0.108 | 0.283 | 0.289 | 0.237 | 0.068 | 0.261 | 9.566 |
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 | 18 | 24 | 17 | 14 | 19 | 18 |
N.S. |
1 | 0.84 | 0.84 | 0.72 | 0.96 | 0.68 | 0.56 | 0.76 | 0.72 |
time (sec) |
N/A | 0.821 | 0.091 | 0.214 | 0.314 | 0.242 | 0.062 | 0.253 | 0.158 |
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 | 30 | 0 | 30 | 21 | 23 | 24 | 19 | 26 | 27 |
N.S. |
1 | 0.00 | 1.00 | 0.70 | 0.77 | 0.80 | 0.63 | 0.87 | 0.90 |
time (sec) |
N/A | 0.000 | 2.469 | 0.166 | 0.224 | 0.240 | 0.201 | 0.256 | 9.588 |
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 | 18 | 18 | 14 | 0 | 13 | 14 | 13 | 12 |
N.S. |
1 | 0.75 | 0.75 | 0.58 | 0.00 | 0.54 | 0.58 | 0.54 | 0.50 |
time (sec) |
N/A | 0.197 | 0.033 | 0.232 | 0.000 | 0.243 | 0.094 | 0.253 | 9.328 |
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 | 20 | 17 | 20 | 15 | 12 | 14 | 15 | 14 | 14 |
N.S. |
1 | 0.85 | 1.00 | 0.75 | 0.60 | 0.70 | 0.75 | 0.70 | 0.70 |
time (sec) |
N/A | 0.260 | 0.005 | 0.217 | 0.221 | 0.257 | 0.058 | 0.251 | 9.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 21 | 52 | 21 | 19 | 21 | 28 |
N.S. |
1 | 0.00 | 0.92 | 0.88 | 2.17 | 0.88 | 0.79 | 0.88 | 1.17 |
time (sec) |
N/A | 0.000 | 0.100 | 0.044 | 0.224 | 0.244 | 0.047 | 0.255 | 9.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 39 | 83 | 77 | 82 | 41 | 94 | 45 |
N.S. |
1 | 0.00 | 1.39 | 2.96 | 2.75 | 2.93 | 1.46 | 3.36 | 1.61 |
time (sec) |
N/A | 0.000 | 0.100 | 26.559 | 0.403 | 0.253 | 0.247 | 2.151 | 9.862 |
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 | 24 | 15 | 19 | 15 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 0.62 | 0.79 | 0.62 | 0.58 | 0.58 | 0.58 | 0.58 | 0.58 |
time (sec) |
N/A | 0.179 | 0.009 | 0.248 | 0.194 | 0.231 | 0.062 | 0.250 | 9.290 |
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 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | 3 |
N.S. |
1 | 0.17 | 0.17 | 0.22 | 0.17 | 0.17 | 0.11 | 0.17 | 0.17 |
time (sec) |
N/A | 0.117 | 0.000 | 0.013 | 0.182 | 0.227 | 0.019 | 0.253 | 0.018 |
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 | 45 | 28 | 27 | 28 | 30 | 26 | 30 | 26 |
N.S. |
1 | 1.73 | 1.08 | 1.04 | 1.08 | 1.15 | 1.00 | 1.15 | 1.00 |
time (sec) |
N/A | 0.352 | 0.025 | 0.151 | 0.190 | 0.231 | 0.359 | 0.252 | 8.956 |
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 | 14 | 15 | 15 | 15 | 15 | 28 | 14 |
N.S. |
1 | 0.00 | 0.82 | 0.88 | 0.88 | 0.88 | 0.88 | 1.65 | 0.82 |
time (sec) |
N/A | 0.000 | 0.108 | 1.161 | 0.240 | 0.237 | 0.131 | 0.255 | 9.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 46 | 39 | 40 | 58 | 63 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.70 | 1.44 | 1.48 | 2.15 | 2.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.663 | 0.315 | 0.249 | 0.080 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 41 | 46 | 48 | 48 | 73 | 89 | 49 |
N.S. |
1 | 0.00 | 1.71 | 1.92 | 2.00 | 2.00 | 3.04 | 3.71 | 2.04 |
time (sec) |
N/A | 0.000 | 0.353 | 1.668 | 0.225 | 0.250 | 0.134 | 0.261 | 9.307 |
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 | 16 | 16 | 17 | 22 | 16 | 15 | 25 | 14 |
N.S. |
1 | 0.80 | 0.80 | 0.85 | 1.10 | 0.80 | 0.75 | 1.25 | 0.70 |
time (sec) |
N/A | 0.212 | 0.010 | 0.283 | 0.183 | 0.230 | 0.044 | 0.247 | 0.063 |
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 | 30 | 43 | 36 | 31 | 0 | 32 | 32 | 46 | 47 |
N.S. |
1 | 1.43 | 1.20 | 1.03 | 0.00 | 1.07 | 1.07 | 1.53 | 1.57 |
time (sec) |
N/A | 0.444 | 0.159 | 0.479 | 0.000 | 0.240 | 0.137 | 0.259 | 9.158 |
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 | 25 | 33 | 22 | 25 | 25 | 24 | 27 | 23 |
N.S. |
1 | 1.47 | 1.94 | 1.29 | 1.47 | 1.47 | 1.41 | 1.59 | 1.35 |
time (sec) |
N/A | 0.295 | 0.015 | 0.044 | 0.277 | 0.239 | 0.062 | 0.256 | 0.117 |
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 | 42 | 23 | 30 | 33 | 23 | 20 | 41 | 25 |
N.S. |
1 | 1.40 | 0.77 | 1.00 | 1.10 | 0.77 | 0.67 | 1.37 | 0.83 |
time (sec) |
N/A | 1.368 | 11.609 | 0.163 | 0.325 | 0.256 | 0.120 | 0.276 | 8.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F(-2) | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 81 | 20 | 18 | 0 | 19 | 0 | 19 | 17 |
N.S. |
1 | 3.38 | 0.83 | 0.75 | 0.00 | 0.79 | 0.00 | 0.79 | 0.71 |
time (sec) |
N/A | 0.673 | 0.200 | 0.422 | 0.000 | 0.245 | 0.000 | 0.279 | 8.736 |
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 | 28 | 38 | 29 | 34 | 27 | 32 | 31 | 0 | 28 |
N.S. |
1 | 1.36 | 1.04 | 1.21 | 0.96 | 1.14 | 1.11 | 0.00 | 1.00 |
time (sec) |
N/A | 0.250 | 1.010 | 0.781 | 0.374 | 0.252 | 0.217 | 0.000 | 9.190 |
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 | 24 | 22 | 22 | 24 | 21 | 22 | 23 | 21 |
N.S. |
1 | 1.20 | 1.10 | 1.10 | 1.20 | 1.05 | 1.10 | 1.15 | 1.05 |
time (sec) |
N/A | 0.249 | 0.010 | 0.076 | 0.183 | 0.249 | 0.221 | 0.259 | 8.980 |
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 | 27 | 44 | 29 | 24 | 0 | 26 | 20 | 26 | 24 |
N.S. |
1 | 1.63 | 1.07 | 0.89 | 0.00 | 0.96 | 0.74 | 0.96 | 0.89 |
time (sec) |
N/A | 0.250 | 0.079 | 0.089 | 0.000 | 0.243 | 0.101 | 0.253 | 9.082 |
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 | 25 | 25 | 23 | 23 | 23 | 22 | 19 | 0 | 22 |
N.S. |
1 | 1.00 | 0.92 | 0.92 | 0.92 | 0.88 | 0.76 | 0.00 | 0.88 |
time (sec) |
N/A | 0.286 | 0.426 | 7.463 | 0.201 | 0.238 | 0.181 | 0.000 | 32.350 |
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 | 17 | 17 | 16 | 17 | 17 | 15 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 |
time (sec) |
N/A | 0.169 | 0.006 | 2.026 | 0.178 | 0.232 | 0.047 | 0.259 | 0.052 |
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 | 11 | 30 | 30 | 31 | 30 | 29 | 29 | 29 | 11 |
N.S. |
1 | 2.73 | 2.73 | 2.82 | 2.73 | 2.64 | 2.64 | 2.64 | 1.00 |
time (sec) |
N/A | 0.200 | 0.004 | 0.054 | 0.191 | 0.249 | 0.060 | 0.256 | 8.463 |
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 | 17 | 0 | 18 | 15 | 14 | 20 | 10 | 33 | 15 |
N.S. |
1 | 0.00 | 1.06 | 0.88 | 0.82 | 1.18 | 0.59 | 1.94 | 0.88 |
time (sec) |
N/A | 0.000 | 0.187 | 0.366 | 0.232 | 0.247 | 0.074 | 0.253 | 8.910 |
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 | 26 | 17 | 13 | 17 | 14 | 13 | 14 |
N.S. |
1 | 1.00 | 1.44 | 0.94 | 0.72 | 0.94 | 0.78 | 0.72 | 0.78 |
time (sec) |
N/A | 0.132 | 0.000 | 0.040 | 0.188 | 0.236 | 0.023 | 0.256 | 8.535 |
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 | 20 | 24 | 24 | 27 | 26 | 26 | 24 | 26 | 0 |
N.S. |
1 | 1.20 | 1.20 | 1.35 | 1.30 | 1.30 | 1.20 | 1.30 | 0.00 |
time (sec) |
N/A | 0.467 | 0.028 | 0.732 | 0.307 | 0.236 | 0.091 | 0.262 | 0.000 |
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 | 27 | 43 | 35 | 30 | 41 | 36 | 27 | 40 | 30 |
N.S. |
1 | 1.59 | 1.30 | 1.11 | 1.52 | 1.33 | 1.00 | 1.48 | 1.11 |
time (sec) |
N/A | 0.411 | 0.132 | 0.111 | 0.224 | 0.273 | 0.091 | 0.252 | 8.714 |
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 | 13 | 13 | 14 | 13 | 15 | 10 | 13 | 16 |
N.S. |
1 | 0.81 | 0.81 | 0.88 | 0.81 | 0.94 | 0.62 | 0.81 | 1.00 |
time (sec) |
N/A | 0.167 | 0.005 | 0.044 | 0.189 | 0.245 | 0.047 | 0.248 | 8.341 |
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 | 27 | 104 | 96 | 107 | 201 | 253 | 202 | 181 | 67153 |
N.S. |
1 | 3.85 | 3.56 | 3.96 | 7.44 | 9.37 | 7.48 | 6.70 | 2487.15 |
time (sec) |
N/A | 0.966 | 0.282 | 0.261 | 0.205 | 0.243 | 5.490 | 0.271 | 30.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 163 | 26 | 152 | 385 | 156 | 153 | 164 | 156 |
N.S. |
1 | 6.79 | 1.08 | 6.33 | 16.04 | 6.50 | 6.38 | 6.83 | 6.50 |
time (sec) |
N/A | 1.375 | 3.629 | 0.901 | 0.321 | 0.255 | 0.314 | 0.274 | 8.837 |
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 | 20 | 20 | 19 | 18 | 18 | 17 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 0.85 | 0.90 | 0.95 |
time (sec) |
N/A | 0.273 | 1.027 | 0.075 | 0.306 | 0.234 | 0.116 | 0.267 | 0.114 |
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 | 28 | 71 | 59 | 57 | 67 | 98 | 66 | 51 | 66 |
N.S. |
1 | 2.54 | 2.11 | 2.04 | 2.39 | 3.50 | 2.36 | 1.82 | 2.36 |
time (sec) |
N/A | 0.348 | 0.039 | 0.095 | 0.195 | 0.237 | 0.181 | 0.252 | 8.159 |
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 | 25 | 40 | 28 | 34 | 34 | 38 | 38 |
N.S. |
1 | 0.00 | 1.04 | 1.67 | 1.17 | 1.42 | 1.42 | 1.58 | 1.58 |
time (sec) |
N/A | 0.000 | 0.039 | 25.194 | 0.327 | 0.239 | 1.348 | 0.342 | 10.124 |
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 | 27 | 18 | 14 | 23 | 21 | 14 | 16 | 13 |
N.S. |
1 | 1.35 | 0.90 | 0.70 | 1.15 | 1.05 | 0.70 | 0.80 | 0.65 |
time (sec) |
N/A | 0.321 | 0.043 | 0.038 | 0.184 | 0.247 | 0.057 | 0.250 | 8.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 47 | 123 | 46 | 42 | 46 | 116 |
N.S. |
1 | 0.00 | 0.92 | 1.81 | 4.73 | 1.77 | 1.62 | 1.77 | 4.46 |
time (sec) |
N/A | 0.000 | 0.766 | 3.833 | 0.359 | 0.237 | 0.122 | 0.438 | 9.474 |
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 | 29 | 27 | 18 | 17 | 17 | 19 | 17 | 17 |
N.S. |
1 | 1.61 | 1.50 | 1.00 | 0.94 | 0.94 | 1.06 | 0.94 | 0.94 |
time (sec) |
N/A | 0.263 | 0.049 | 0.085 | 0.195 | 0.251 | 0.062 | 0.255 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 18 | 18 | 18 | 15 | 15 | 112 | 16 | 15 |
N.S. |
1 | 0.82 | 0.82 | 0.82 | 0.68 | 0.68 | 5.09 | 0.73 | 0.68 |
time (sec) |
N/A | 0.149 | 0.006 | 0.304 | 0.187 | 0.250 | 1.577 | 0.263 | 0.107 |
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 | 18 | 15 | 15 | 17 | 17 | 14 | 17 | 17 |
N.S. |
1 | 0.95 | 0.79 | 0.79 | 0.89 | 0.89 | 0.74 | 0.89 | 0.89 |
time (sec) |
N/A | 0.465 | 0.447 | 0.245 | 0.241 | 0.252 | 0.065 | 0.252 | 8.330 |
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 | 22 | 29 | 26 | 30 | 29 | 29 | 29 | 46 | 19 |
N.S. |
1 | 1.32 | 1.18 | 1.36 | 1.32 | 1.32 | 1.32 | 2.09 | 0.86 |
time (sec) |
N/A | 0.176 | 0.041 | 0.210 | 0.192 | 0.258 | 0.084 | 0.254 | 8.400 |
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 | 29 | 34 | 35 | 33 | 41 | 35 | 0 |
N.S. |
1 | 0.00 | 0.97 | 1.13 | 1.17 | 1.10 | 1.37 | 1.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.117 | 24.518 | 0.250 | 0.253 | 0.297 | 0.357 | 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 | 30 | 37 | 28 | 27 | 27 | 27 | 22 | 22 | 26 |
N.S. |
1 | 1.23 | 0.93 | 0.90 | 0.90 | 0.90 | 0.73 | 0.73 | 0.87 |
time (sec) |
N/A | 2.032 | 0.212 | 0.130 | 0.700 | 0.252 | 0.116 | 0.259 | 0.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 50 | 50 | 48 | 44 | 44 | 46 | 44 | 48 |
N.S. |
1 | 2.17 | 2.17 | 2.09 | 1.91 | 1.91 | 2.00 | 1.91 | 2.09 |
time (sec) |
N/A | 0.195 | 0.011 | 0.061 | 0.190 | 0.233 | 0.024 | 0.251 | 8.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 22 | 26 | 24 | 29 | 61 | 25 | 21 |
N.S. |
1 | 1.17 | 0.96 | 1.13 | 1.04 | 1.26 | 2.65 | 1.09 | 0.91 |
time (sec) |
N/A | 0.188 | 0.005 | 0.083 | 0.191 | 0.240 | 0.103 | 0.253 | 0.065 |
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 | 28 | 936 | 25 | 31 | 763 | 22 | 31 | 27 | 24 |
N.S. |
1 | 33.43 | 0.89 | 1.11 | 27.25 | 0.79 | 1.11 | 0.96 | 0.86 |
time (sec) |
N/A | 1.936 | 0.552 | 0.293 | 1.205 | 0.276 | 0.130 | 0.286 | 0.413 |
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 | 38 | 23 | 20 | 20 | 21 | 36 | 21 | 19 |
N.S. |
1 | 1.41 | 0.85 | 0.74 | 0.74 | 0.78 | 1.33 | 0.78 | 0.70 |
time (sec) |
N/A | 0.798 | 0.158 | 0.325 | 0.231 | 0.251 | 0.065 | 0.268 | 9.041 |
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 | 15 | 0 | 18 | 19 | 18 | 16 | 19 | 18 | 18 |
N.S. |
1 | 0.00 | 1.20 | 1.27 | 1.20 | 1.07 | 1.27 | 1.20 | 1.20 |
time (sec) |
N/A | 0.000 | 0.006 | 0.054 | 0.193 | 0.242 | 0.054 | 0.256 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 18 | 12 | 13 | 12 | 16 | 10 | 12 | 12 |
N.S. |
1 | 0.82 | 0.55 | 0.59 | 0.55 | 0.73 | 0.45 | 0.55 | 0.55 |
time (sec) |
N/A | 0.353 | 0.005 | 0.027 | 0.197 | 0.247 | 0.033 | 0.254 | 8.030 |
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 | 15 | 14 | 17 | 13 | 14 | 17 | 13 |
N.S. |
1 | 0.94 | 0.88 | 0.82 | 1.00 | 0.76 | 0.82 | 1.00 | 0.76 |
time (sec) |
N/A | 0.250 | 0.223 | 1.003 | 0.326 | 0.250 | 0.232 | 0.274 | 9.269 |
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 | 26 | 23 | 21 | 19 | 25 | 21 |
N.S. |
1 | 0.00 | 0.92 | 1.08 | 0.96 | 0.88 | 0.79 | 1.04 | 0.88 |
time (sec) |
N/A | 0.000 | 0.282 | 0.816 | 0.229 | 0.242 | 0.113 | 0.285 | 8.657 |
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 | 39 | 39 | 36 | 37 | 37 | 36 | 40 | 35 |
N.S. |
1 | 1.44 | 1.44 | 1.33 | 1.37 | 1.37 | 1.33 | 1.48 | 1.30 |
time (sec) |
N/A | 0.419 | 0.021 | 0.062 | 0.199 | 0.240 | 0.083 | 0.266 | 0.173 |
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 | 29 | 21 | 23 | 22 | 21 | 38 | 19 | 22 | 21 |
N.S. |
1 | 0.72 | 0.79 | 0.76 | 0.72 | 1.31 | 0.66 | 0.76 | 0.72 |
time (sec) |
N/A | 0.305 | 0.019 | 0.048 | 0.188 | 0.249 | 0.053 | 0.255 | 7.962 |
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 | 31 | 0 | 34 | 34 | 47 | 33 | 27 | 39 | 33 |
N.S. |
1 | 0.00 | 1.10 | 1.10 | 1.52 | 1.06 | 0.87 | 1.26 | 1.06 |
time (sec) |
N/A | 0.000 | 0.331 | 0.814 | 0.339 | 0.257 | 0.132 | 0.370 | 8.782 |
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 | 26 | 0 | 28 | 27 | 29 | 29 | 19 | 26 | 29 |
N.S. |
1 | 0.00 | 1.08 | 1.04 | 1.12 | 1.12 | 0.73 | 1.00 | 1.12 |
time (sec) |
N/A | 0.000 | 0.298 | 0.414 | 0.223 | 0.240 | 0.092 | 0.264 | 7.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 25 | 81 | 102 | 0 | 104 | 79 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 2.89 | 3.64 | 0.00 | 3.71 | 2.82 |
time (sec) |
N/A | 0.000 | 0.263 | 20.454 | 0.286 | 0.260 | 0.000 | 1.101 | 8.819 |
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 | 21 | 23 | 23 | 19 | 23 | 18 | 20 | 18 | 18 |
N.S. |
1 | 1.10 | 1.10 | 0.90 | 1.10 | 0.86 | 0.95 | 0.86 | 0.86 |
time (sec) |
N/A | 0.500 | 0.217 | 0.117 | 0.321 | 0.252 | 0.134 | 0.291 | 8.425 |
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 | 17 | 0 | 17 | 14 | 13 | 46 | 14 | 0 | 14 |
N.S. |
1 | 0.00 | 1.00 | 0.82 | 0.76 | 2.71 | 0.82 | 0.00 | 0.82 |
time (sec) |
N/A | 0.000 | 0.880 | 0.302 | 0.303 | 0.257 | 0.804 | 0.000 | 8.213 |
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 | 35 | 29 | 25 | 26 | 31 | 31 | 21 | 25 |
N.S. |
1 | 1.30 | 1.07 | 0.93 | 0.96 | 1.15 | 1.15 | 0.78 | 0.93 |
time (sec) |
N/A | 0.218 | 0.013 | 0.063 | 0.181 | 0.240 | 0.088 | 0.251 | 8.124 |
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 | 19 | 19 | 19 | 19 | 75 | 21 | 15 | 19 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 3.95 | 1.11 | 0.79 | 1.00 | 0.95 |
time (sec) |
N/A | 0.199 | 0.023 | 0.054 | 0.310 | 0.243 | 0.060 | 0.268 | 8.060 |
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 | 29 | 31 | 30 | 33 | 32 | 43 | 39 | 38 | 36 |
N.S. |
1 | 1.07 | 1.03 | 1.14 | 1.10 | 1.48 | 1.34 | 1.31 | 1.24 |
time (sec) |
N/A | 0.224 | 0.015 | 0.075 | 0.187 | 0.234 | 0.070 | 0.255 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 56 | 26 | 84 | 0 | 23 | 36 | 37 | 0 |
N.S. |
1 | 2.15 | 1.00 | 3.23 | 0.00 | 0.88 | 1.38 | 1.42 | 0.00 |
time (sec) |
N/A | 0.870 | 0.337 | 0.119 | 0.000 | 0.259 | 10.184 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 35 | 32 | 38 | 32 | 32 | 35 |
N.S. |
1 | 0.00 | 1.00 | 1.67 | 1.52 | 1.81 | 1.52 | 1.52 | 1.67 |
time (sec) |
N/A | 0.000 | 1.604 | 0.753 | 0.353 | 0.245 | 0.174 | 0.319 | 8.334 |
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 | 39 | 323 | 1272 | 532 | 648 | 668 | 728 | 785 | 655 |
N.S. |
1 | 8.28 | 32.62 | 13.64 | 16.62 | 17.13 | 18.67 | 20.13 | 16.79 |
time (sec) |
N/A | 3.088 | 1.326 | 0.766 | 0.229 | 0.257 | 25.590 | 0.327 | 9.087 |
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 | 38 | 38 | 31 | 70 | 29 | 26 | 33 | 31 |
N.S. |
1 | 1.27 | 1.27 | 1.03 | 2.33 | 0.97 | 0.87 | 1.10 | 1.03 |
time (sec) |
N/A | 1.631 | 0.117 | 0.114 | 0.710 | 0.259 | 0.113 | 0.275 | 8.286 |
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 | 31 | 0 | 28 | 33 | 27 | 31 | 24 | 31 | 27 |
N.S. |
1 | 0.00 | 0.90 | 1.06 | 0.87 | 1.00 | 0.77 | 1.00 | 0.87 |
time (sec) |
N/A | 0.000 | 0.139 | 0.197 | 0.266 | 0.246 | 0.135 | 0.350 | 8.500 |
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 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 |
time (sec) |
N/A | 0.151 | 0.019 | 0.090 | 0.185 | 0.241 | 0.038 | 0.250 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 32 | 35 | 31 | 31 | 31 | 34 | 28 | 28 |
N.S. |
1 | 1.45 | 1.59 | 1.41 | 1.41 | 1.41 | 1.55 | 1.27 | 1.27 |
time (sec) |
N/A | 0.171 | 0.009 | 0.457 | 0.192 | 0.242 | 0.140 | 0.252 | 0.209 |
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 | 22 | 0 | 21 | 31 | 25 | 21 | 24 | 38 | 19 |
N.S. |
1 | 0.00 | 0.95 | 1.41 | 1.14 | 0.95 | 1.09 | 1.73 | 0.86 |
time (sec) |
N/A | 0.000 | 1.092 | 0.111 | 0.306 | 0.255 | 0.131 | 0.257 | 8.305 |
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 | 18 | 18 | 18 | 17 | 17 | 15 | 17 | 18 |
N.S. |
1 | 0.82 | 0.82 | 0.82 | 0.77 | 0.77 | 0.68 | 0.77 | 0.82 |
time (sec) |
N/A | 0.155 | 0.035 | 0.025 | 0.193 | 0.250 | 0.047 | 0.253 | 0.108 |
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 | 36 | 0 | 25 | 26 | 34 | 25 | 24 | 31 | 29 |
N.S. |
1 | 0.00 | 0.69 | 0.72 | 0.94 | 0.69 | 0.67 | 0.86 | 0.81 |
time (sec) |
N/A | 0.000 | 0.127 | 0.181 | 0.258 | 0.244 | 0.129 | 0.269 | 8.308 |
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 | 13 | 13 | 13 | 11 | 10 | 10 | 8 | 16 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.77 | 0.77 | 0.62 | 1.23 | 0.77 |
time (sec) |
N/A | 0.161 | 0.010 | 0.159 | 0.192 | 0.249 | 0.044 | 0.255 | 7.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F(-1) | C | A | A | F(-1) | F | B |
verified |
N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 152 | 42 | 40 | 0 | 0 | 40 |
N.S. |
1 | 0.00 | 0.00 | 4.90 | 1.35 | 1.29 | 0.00 | 0.00 | 1.29 |
time (sec) |
N/A | 0.000 | 0.000 | 0.266 | 0.391 | 0.255 | 0.000 | 0.000 | 10.025 |
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 | 24 | 45 | 41 | 32 | 40 | 39 | 44 | 40 | 23 |
N.S. |
1 | 1.88 | 1.71 | 1.33 | 1.67 | 1.62 | 1.83 | 1.67 | 0.96 |
time (sec) |
N/A | 0.167 | 0.004 | 0.077 | 0.182 | 0.238 | 0.028 | 0.249 | 7.564 |
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 | 27 | 22 | 22 | 19 | 93 | 18 | 20 | 18 | 20 |
N.S. |
1 | 0.81 | 0.81 | 0.70 | 3.44 | 0.67 | 0.74 | 0.67 | 0.74 |
time (sec) |
N/A | 0.296 | 0.045 | 0.080 | 0.315 | 0.246 | 0.095 | 0.255 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 50 | 29 | 31 | 53 | 59 | 60 | 53 | 42 |
N.S. |
1 | 2.27 | 1.32 | 1.41 | 2.41 | 2.68 | 2.73 | 2.41 | 1.91 |
time (sec) |
N/A | 0.175 | 0.005 | 0.057 | 0.199 | 0.238 | 0.026 | 0.247 | 0.098 |
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 | 10 | 8 | 8 | 9 | 8 | 8 | 5 | 8 | 8 |
N.S. |
1 | 0.80 | 0.80 | 0.90 | 0.80 | 0.80 | 0.50 | 0.80 | 0.80 |
time (sec) |
N/A | 0.187 | 0.005 | 0.263 | 0.198 | 0.232 | 0.034 | 0.250 | 0.131 |
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 | 17 | 17 | 18 | 17 | 15 | 15 | 16 | 15 |
N.S. |
1 | 0.63 | 0.63 | 0.67 | 0.63 | 0.56 | 0.56 | 0.59 | 0.56 |
time (sec) |
N/A | 0.187 | 0.006 | 0.059 | 0.198 | 0.244 | 0.056 | 0.253 | 8.219 |
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 | 24 | 30 | 30 | 19 | 42 | 18 | 24 | 18 | 18 |
N.S. |
1 | 1.25 | 1.25 | 0.79 | 1.75 | 0.75 | 1.00 | 0.75 | 0.75 |
time (sec) |
N/A | 0.585 | 0.074 | 0.419 | 0.333 | 0.240 | 0.461 | 0.412 | 12.427 |