Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 27 | 27 | 20 | 21 | 23 | 20 | 21 | 21 |
N.S. |
1 | 1.23 | 1.23 | 0.91 | 0.95 | 1.05 | 0.91 | 0.95 | 0.95 |
time (sec) |
N/A | 0.006 | 0.007 | 1.320 | 0.188 | 0.251 | 0.039 | 0.252 | 0.096 |
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 | 18 | 17 | 17 | 15 | 17 | 18 |
N.S. |
1 | 0.00 | 0.75 | 0.75 | 0.71 | 0.71 | 0.62 | 0.71 | 0.75 |
time (sec) |
N/A | 0.000 | 0.129 | 2.840 | 0.219 | 0.249 | 0.058 | 0.251 | 9.194 |
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 | 27 | 0 | 29 | 29 | 27 | 26 | 27 | 0 | 29 |
N.S. |
1 | 0.00 | 1.07 | 1.07 | 1.00 | 0.96 | 1.00 | 0.00 | 1.07 |
time (sec) |
N/A | 0.000 | 5.125 | 3.616 | 0.278 | 0.256 | 7.341 | 0.000 | 9.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 51 | 22 | 22 | 28 | 21 | 20 | 21 | 0 |
N.S. |
1 | 2.22 | 0.96 | 0.96 | 1.22 | 0.91 | 0.87 | 0.91 | 0.00 |
time (sec) |
N/A | 1.116 | 1.109 | 2.065 | 0.354 | 0.269 | 0.200 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 23 | 22 | 23 | 31 | 17 | 23 | 22 |
N.S. |
1 | 1.04 | 1.00 | 0.96 | 1.00 | 1.35 | 0.74 | 1.00 | 0.96 |
time (sec) |
N/A | 0.032 | 0.028 | 3.392 | 0.197 | 0.245 | 0.240 | 0.251 | 0.240 |
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 | 19 | 19 | 19 | 101 | 26 | 17 | 26 | 18 |
N.S. |
1 | 0.79 | 0.79 | 0.79 | 4.21 | 1.08 | 0.71 | 1.08 | 0.75 |
time (sec) |
N/A | 0.473 | 0.349 | 1.694 | 0.258 | 0.250 | 0.089 | 0.265 | 9.219 |
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 | 18 | 18 | 16 | 19 | 15 | 15 | 17 | 15 |
N.S. |
1 | 0.90 | 0.90 | 0.80 | 0.95 | 0.75 | 0.75 | 0.85 | 0.75 |
time (sec) |
N/A | 0.121 | 0.301 | 0.758 | 0.309 | 0.253 | 0.072 | 0.260 | 9.369 |
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 | 23 | 32 | 26 | 22 | 88 | 28 | 32 | 45 | 19 |
N.S. |
1 | 1.39 | 1.13 | 0.96 | 3.83 | 1.22 | 1.39 | 1.96 | 0.83 |
time (sec) |
N/A | 0.034 | 0.058 | 0.474 | 0.278 | 0.260 | 0.071 | 0.249 | 9.318 |
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 | 31 | 0 | 38 | 87 | 103 | 91 | 85 | 0 | 117 |
N.S. |
1 | 0.00 | 1.23 | 2.81 | 3.32 | 2.94 | 2.74 | 0.00 | 3.77 |
time (sec) |
N/A | 0.000 | 0.222 | 2.068 | 1.258 | 0.258 | 0.354 | 0.000 | 9.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | F(-1) | A | A | F(-1) | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 143 | 0 | 54 | 46 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 3.76 | 0.00 | 1.42 | 1.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.399 | 0.000 | 17.446 | 0.268 | 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 | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.90 | 0.80 |
time (sec) |
N/A | 0.004 | 0.004 | 1.624 | 0.186 | 0.250 | 0.033 | 0.259 | 10.057 |
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 | 29 | 0 | 31 | 32 | 51 | 49 | 29 | 34 | 66 |
N.S. |
1 | 0.00 | 1.07 | 1.10 | 1.76 | 1.69 | 1.00 | 1.17 | 2.28 |
time (sec) |
N/A | 0.000 | 0.087 | 3.352 | 0.320 | 0.244 | 0.125 | 0.301 | 10.345 |
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 | 12 | 0 | 12 | 11 | 10 | 10 | 24 | 10 | 10 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.83 | 0.83 | 2.00 | 0.83 | 0.83 |
time (sec) |
N/A | 0.000 | 0.136 | 2.928 | 0.229 | 0.258 | 0.267 | 0.264 | 10.259 |
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 | 11 | 11 | 11 | 9 | 11 | 11 | 12 | 11 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.00 | 1.00 | 1.09 | 1.00 | 1.18 |
time (sec) |
N/A | 0.015 | 0.018 | 1.171 | 0.192 | 0.255 | 0.041 | 0.257 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 113 | 82 | 99 | 100 | 116 | 100 | 101 |
N.S. |
1 | 0.00 | 3.65 | 2.65 | 3.19 | 3.23 | 3.74 | 3.23 | 3.26 |
time (sec) |
N/A | 0.000 | 4.335 | 2.488 | 0.286 | 0.256 | 0.231 | 0.366 | 10.252 |
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 | 10 | 10 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 0.59 | 0.59 | 0.65 | 0.59 | 0.59 | 0.47 | 0.59 | 0.59 |
time (sec) |
N/A | 0.008 | 0.006 | 0.694 | 0.196 | 0.249 | 0.038 | 0.253 | 9.777 |
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 | 15 | 18 | 19 | 20 | 22 | 17 | 17 | 22 | 15 |
N.S. |
1 | 1.20 | 1.27 | 1.33 | 1.47 | 1.13 | 1.13 | 1.47 | 1.00 |
time (sec) |
N/A | 0.004 | 0.001 | 0.487 | 0.184 | 0.253 | 0.022 | 0.258 | 9.839 |
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 | 25 | 0 | 23 | 22 | 21 | 21 | 20 | 21 | 101 |
N.S. |
1 | 0.00 | 0.92 | 0.88 | 0.84 | 0.84 | 0.80 | 0.84 | 4.04 |
time (sec) |
N/A | 0.000 | 0.648 | 2.274 | 0.264 | 0.244 | 0.127 | 0.272 | 9.937 |
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 | 20 | 19 | 22 | 22 | 24 | 20 | 18 |
N.S. |
1 | 0.00 | 0.83 | 0.79 | 0.92 | 0.92 | 1.00 | 0.83 | 0.75 |
time (sec) |
N/A | 0.000 | 0.249 | 1.438 | 0.227 | 0.247 | 0.077 | 0.255 | 10.146 |
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 | 17 | 18 | 17 | 29 | 22 | 27 | 29 | 18 |
N.S. |
1 | 0.59 | 0.62 | 0.59 | 1.00 | 0.76 | 0.93 | 1.00 | 0.62 |
time (sec) |
N/A | 0.016 | 0.018 | 0.555 | 0.179 | 0.254 | 0.047 | 0.248 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 19 | 20 | 54 | 20 | 17 | 0 | 21 |
N.S. |
1 | 0.00 | 0.86 | 0.91 | 2.45 | 0.91 | 0.77 | 0.00 | 0.95 |
time (sec) |
N/A | 0.000 | 0.480 | 2.850 | 0.380 | 0.264 | 0.249 | 0.000 | 10.257 |
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 | 22 | 22 | 22 | 77 | 21 | 20 | 21 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 3.50 | 0.95 | 0.91 | 0.95 | 1.00 |
time (sec) |
N/A | 0.028 | 0.071 | 0.459 | 0.216 | 0.264 | 0.096 | 0.257 | 9.657 |
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 | 13 | 7 | 7 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 0.54 | 0.54 | 0.54 | 0.46 | 0.46 | 0.54 | 0.46 | 0.46 |
time (sec) |
N/A | 0.001 | 0.001 | 0.414 | 0.196 | 0.228 | 0.033 | 0.253 | 0.017 |
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 | 5 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 |
N.S. |
1 | 0.60 | 0.60 | 0.60 | 0.40 | 0.40 | 0.40 | 0.40 | 0.40 |
time (sec) |
N/A | 0.001 | 0.000 | 0.304 | 0.184 | 0.230 | 0.034 | 0.244 | 0.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 24 | 21 | 37 | 60 | 40 | 74 |
N.S. |
1 | 0.00 | 0.91 | 1.09 | 0.95 | 1.68 | 2.73 | 1.82 | 3.36 |
time (sec) |
N/A | 0.000 | 0.057 | 3.435 | 0.190 | 0.243 | 0.184 | 0.264 | 10.071 |
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 | 6 | 6 | 5 | 4 | 4 | 5 | 5 | 4 |
N.S. |
1 | 0.46 | 0.46 | 0.38 | 0.31 | 0.31 | 0.38 | 0.38 | 0.31 |
time (sec) |
N/A | 0.000 | 0.000 | 0.049 | 0.192 | 0.233 | 0.018 | 0.255 | 9.576 |
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 | 14 | 12 | 12 | 10 | 19 | 9 | 12 | 9 | 9 |
N.S. |
1 | 0.86 | 0.86 | 0.71 | 1.36 | 0.64 | 0.86 | 0.64 | 0.64 |
time (sec) |
N/A | 0.017 | 0.038 | 1.304 | 0.214 | 0.246 | 0.053 | 0.247 | 0.056 |
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 | 21 | 21 | 19 | 19 | 19 | 14 | 19 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 0.90 | 0.67 | 0.90 | 0.76 |
time (sec) |
N/A | 0.014 | 0.004 | 0.111 | 0.188 | 0.252 | 0.073 | 0.253 | 9.687 |
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 | 8 | 12 | 13 | 10 | 12 | 12 | 10 | 12 | 9 |
N.S. |
1 | 1.50 | 1.62 | 1.25 | 1.50 | 1.50 | 1.25 | 1.50 | 1.12 |
time (sec) |
N/A | 0.003 | 0.000 | 0.383 | 0.175 | 0.236 | 0.024 | 0.250 | 9.860 |
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 | 27 | 0 | 19 | 19 | 29 | 20 | 26 | 19 | 0 |
N.S. |
1 | 0.00 | 0.70 | 0.70 | 1.07 | 0.74 | 0.96 | 0.70 | 0.00 |
time (sec) |
N/A | 0.000 | 1.323 | 0.362 | 0.297 | 0.240 | 0.166 | 0.252 | 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 | 31 | 49 | 33 | 44 | 34 | 28 | 29 | 43 | 32 |
N.S. |
1 | 1.58 | 1.06 | 1.42 | 1.10 | 0.90 | 0.94 | 1.39 | 1.03 |
time (sec) |
N/A | 1.223 | 0.447 | 1.240 | 0.229 | 0.256 | 0.231 | 0.306 | 10.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 25 | 25 | 23 | 67 | 39 | 24 | 23 | 20 |
N.S. |
1 | 1.04 | 1.04 | 0.96 | 2.79 | 1.62 | 1.00 | 0.96 | 0.83 |
time (sec) |
N/A | 0.101 | 0.035 | 1.633 | 0.233 | 0.259 | 0.101 | 0.255 | 9.850 |
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 | 22 | 38 | 33 | 33 | 37 | 18 | 27 | 32 | 33 |
N.S. |
1 | 1.73 | 1.50 | 1.50 | 1.68 | 0.82 | 1.23 | 1.45 | 1.50 |
time (sec) |
N/A | 0.193 | 0.059 | 0.349 | 0.405 | 0.265 | 0.093 | 0.259 | 10.022 |
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 | 18 | 16 | 16 | 15 | 15 | 19 | 29 | 16 |
N.S. |
1 | 0.86 | 0.76 | 0.76 | 0.71 | 0.71 | 0.90 | 1.38 | 0.76 |
time (sec) |
N/A | 0.135 | 0.105 | 1.607 | 0.225 | 0.263 | 0.093 | 0.252 | 0.217 |
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 | 6 | 6 | 7 | 6 | 6 | 3 | 7 | 6 |
N.S. |
1 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 | 0.33 | 0.78 | 0.67 |
time (sec) |
N/A | 0.001 | 0.001 | 0.275 | 0.191 | 0.245 | 0.026 | 0.250 | 0.015 |
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 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 |
N.S. |
1 | 0.22 | 0.22 | 0.33 | 0.22 | 0.22 | 0.22 | 0.33 | 0.22 |
time (sec) |
N/A | 0.000 | 0.000 | 0.033 | 0.180 | 0.246 | 0.016 | 0.269 | 0.002 |
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 | 29 | 165 | 28 | 54 | 63 | 53 | 70 | 53 | 23 |
N.S. |
1 | 5.69 | 0.97 | 1.86 | 2.17 | 1.83 | 2.41 | 1.83 | 0.79 |
time (sec) |
N/A | 0.054 | 0.684 | 0.377 | 0.197 | 0.250 | 0.119 | 0.250 | 9.789 |
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 | 21 | 79 | 24 | 80 | 155 | 119 | 78 | 187 | 75 |
N.S. |
1 | 3.76 | 1.14 | 3.81 | 7.38 | 5.67 | 3.71 | 8.90 | 3.57 |
time (sec) |
N/A | 0.199 | 0.447 | 2.253 | 0.358 | 0.273 | 0.274 | 0.274 | 10.914 |
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 | 17 | 18 | 30 | 30 | 15 | 20 | 17 |
N.S. |
1 | 0.00 | 0.81 | 0.86 | 1.43 | 1.43 | 0.71 | 0.95 | 0.81 |
time (sec) |
N/A | 0.000 | 0.217 | 2.563 | 0.251 | 0.262 | 0.059 | 0.257 | 9.890 |
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 | 17 | 17 | 18 | 17 | 15 | 17 | 17 | 19 |
N.S. |
1 | 0.89 | 0.89 | 0.95 | 0.89 | 0.79 | 0.89 | 0.89 | 1.00 |
time (sec) |
N/A | 0.007 | 0.003 | 0.222 | 0.181 | 0.245 | 0.052 | 0.252 | 9.609 |
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 | 23 | 23 | 24 | 18 | 23 | 20 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 0.78 | 1.00 | 0.87 | 1.00 | 1.00 |
time (sec) |
N/A | 0.377 | 0.308 | 1.172 | 0.223 | 0.243 | 0.165 | 0.288 | 9.963 |
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 | 32 | 26 | 27 | 25 | 24 | 41 | 44 |
N.S. |
1 | 0.00 | 1.03 | 0.84 | 0.87 | 0.81 | 0.77 | 1.32 | 1.42 |
time (sec) |
N/A | 0.000 | 0.217 | 3.050 | 0.381 | 0.276 | 0.461 | 0.443 | 0.255 |
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 | 25 | 0 | 22 | 21 | 87 | 32 | 19 | 28 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.84 | 3.48 | 1.28 | 0.76 | 1.12 | 0.80 |
time (sec) |
N/A | 0.000 | 2.795 | 491.872 | 0.307 | 0.252 | 0.072 | 0.261 | 9.652 |
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 | 17 | 17 | 19 | 22 | 21 | 15 | 21 | 16488 |
N.S. |
1 | 0.81 | 0.81 | 0.90 | 1.05 | 1.00 | 0.71 | 1.00 | 785.14 |
time (sec) |
N/A | 0.054 | 0.027 | 0.977 | 0.180 | 0.246 | 0.413 | 0.262 | 27.578 |
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 | 7 | 7 | 8 | 13 | 7 | 5 | 7 | 7 |
N.S. |
1 | 0.35 | 0.35 | 0.40 | 0.65 | 0.35 | 0.25 | 0.35 | 0.35 |
time (sec) |
N/A | 0.005 | 0.001 | 0.224 | 0.190 | 0.252 | 0.041 | 0.252 | 10.208 |
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 | 23 | 0 | 23 | 28 | 25 | 27 | 19 | 21 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.22 | 1.09 | 1.17 | 0.83 | 0.91 | 0.91 |
time (sec) |
N/A | 0.000 | 0.658 | 7.096 | 0.304 | 0.258 | 0.069 | 0.292 | 10.302 |
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 | 14 | 14 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.08 | 1.08 | 1.08 | 1.00 | 1.00 | 0.92 | 1.00 | 1.00 |
time (sec) |
N/A | 0.003 | 0.004 | 0.473 | 0.183 | 0.258 | 0.039 | 0.250 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 23 | 30 | 23 | 19 | 24 | 0 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 1.25 | 0.96 | 0.79 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.090 | 38.347 | 0.326 | 0.263 | 0.251 | 0.459 | 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 | 22 | 20 | 20 | 20 | 19 | 19 | 15 | 27 | 18 |
N.S. |
1 | 0.91 | 0.91 | 0.91 | 0.86 | 0.86 | 0.68 | 1.23 | 0.82 |
time (sec) |
N/A | 0.016 | 0.013 | 1.821 | 0.183 | 0.250 | 0.085 | 0.267 | 0.118 |
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 | 28 | 0 | 31 | 35 | 32 | 46 | 26 | 58 | 60 |
N.S. |
1 | 0.00 | 1.11 | 1.25 | 1.14 | 1.64 | 0.93 | 2.07 | 2.14 |
time (sec) |
N/A | 0.000 | 0.091 | 0.877 | 0.250 | 0.258 | 0.132 | 0.281 | 10.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 35 | 48 | 19 | 0 | 23 | 0 | 30 | 23 |
N.S. |
1 | 1.67 | 2.29 | 0.90 | 0.00 | 1.10 | 0.00 | 1.43 | 1.10 |
time (sec) |
N/A | 0.710 | 0.699 | 3.270 | 0.000 | 0.251 | 0.000 | 0.263 | 10.899 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 129 | 18 | 14 | 88 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 7.59 | 1.06 | 0.82 | 5.18 | 1.12 |
time (sec) |
N/A | 0.124 | 0.446 | 4.770 | 0.276 | 0.254 | 0.153 | 0.267 | 0.730 |
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 | 17 | 33 | 19 | 24 | 74 | 28 | 27 | 30 | 24 |
N.S. |
1 | 1.94 | 1.12 | 1.41 | 4.35 | 1.65 | 1.59 | 1.76 | 1.41 |
time (sec) |
N/A | 0.141 | 0.027 | 0.463 | 0.188 | 0.253 | 0.067 | 0.254 | 10.284 |
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 | 28 | 62 | 48 | 28 | 57 | 56 | 61 | 122 | 55 |
N.S. |
1 | 2.21 | 1.71 | 1.00 | 2.04 | 2.00 | 2.18 | 4.36 | 1.96 |
time (sec) |
N/A | 0.325 | 0.911 | 1.012 | 0.219 | 0.254 | 0.131 | 0.250 | 10.306 |
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 | 71 | 28 | 31 | 29 | 26 | 34 | 29 | 27 |
N.S. |
1 | 2.96 | 1.17 | 1.29 | 1.21 | 1.08 | 1.42 | 1.21 | 1.12 |
time (sec) |
N/A | 0.059 | 0.978 | 0.630 | 0.272 | 0.250 | 0.140 | 0.299 | 10.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | A | A | A | B | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 58 | 49 | 49 | 159 | 0 | 0 | 90 |
N.S. |
1 | 0.00 | 1.53 | 1.29 | 1.29 | 4.18 | 0.00 | 0.00 | 2.37 |
time (sec) |
N/A | 0.000 | 0.916 | 121.008 | 0.773 | 0.269 | 0.000 | 0.000 | 11.186 |
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 | 26 | 0 | 33 | 55 | 63 | 59 | 68 | 349 | 79 |
N.S. |
1 | 0.00 | 1.27 | 2.12 | 2.42 | 2.27 | 2.62 | 13.42 | 3.04 |
time (sec) |
N/A | 0.000 | 0.162 | 6.512 | 0.236 | 0.262 | 0.179 | 0.323 | 11.266 |
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 | 24 | 41 | 22 | 31 | 27 | 37 |
N.S. |
1 | 0.00 | 1.08 | 0.92 | 1.58 | 0.85 | 1.19 | 1.04 | 1.42 |
time (sec) |
N/A | 0.000 | 2.578 | 1.208 | 0.262 | 0.256 | 0.186 | 0.269 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 23 | 21 | 31 | 25 | 0 | 31 | 25 |
N.S. |
1 | 0.00 | 1.28 | 1.17 | 1.72 | 1.39 | 0.00 | 1.72 | 1.39 |
time (sec) |
N/A | 0.000 | 0.157 | 3.240 | 0.324 | 0.249 | 0.000 | 0.684 | 10.311 |
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 | 18 | 16 | 16 | 15 | 15 | 14 | 15 | 16 |
N.S. |
1 | 0.86 | 0.76 | 0.76 | 0.71 | 0.71 | 0.67 | 0.71 | 0.76 |
time (sec) |
N/A | 0.022 | 0.009 | 0.286 | 0.190 | 0.235 | 0.087 | 0.264 | 10.223 |
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 | 20 | 0 | 31 | 20 | 23 | 22 | 20 | 23 | 23 |
N.S. |
1 | 0.00 | 1.55 | 1.00 | 1.15 | 1.10 | 1.00 | 1.15 | 1.15 |
time (sec) |
N/A | 0.000 | 0.108 | 2.231 | 0.215 | 0.239 | 0.100 | 0.269 | 10.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 19 | 18 | 102 | 0 | 0 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 0.82 | 4.64 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.000 | 0.116 | 0.184 | 0.513 | 0.257 | 0.000 | 0.000 | 11.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | F | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 83 | 45 | 0 | 57 | 60 | 0 | 74 |
N.S. |
1 | 0.00 | 2.86 | 1.55 | 0.00 | 1.97 | 2.07 | 0.00 | 2.55 |
time (sec) |
N/A | 0.000 | 10.286 | 3.017 | 0.000 | 0.268 | 116.663 | 0.000 | 11.125 |
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 | 32 | 0 | 37 | 27 | 26 | 26 | 29 | 28 | 60 |
N.S. |
1 | 0.00 | 1.16 | 0.84 | 0.81 | 0.81 | 0.91 | 0.88 | 1.88 |
time (sec) |
N/A | 0.000 | 0.099 | 2.174 | 0.257 | 0.246 | 0.177 | 0.354 | 11.050 |
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 | 10 | 10 | 9 | 8 | 8 | 12 | 9 | 8 |
N.S. |
1 | 0.59 | 0.59 | 0.53 | 0.47 | 0.47 | 0.71 | 0.53 | 0.47 |
time (sec) |
N/A | 0.001 | 0.002 | 1.633 | 0.184 | 0.238 | 0.025 | 0.258 | 10.535 |
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 | 16 | 16 | 15 | 17 | 17 | 17 | 17 | 17 |
N.S. |
1 | 1.23 | 1.23 | 1.15 | 1.31 | 1.31 | 1.31 | 1.31 | 1.31 |
time (sec) |
N/A | 0.003 | 0.003 | 0.478 | 0.191 | 0.237 | 0.023 | 0.258 | 0.075 |
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 | 31 | 43 | 31 | 68 | 79 | 85 | 60 | 85 | 50 |
N.S. |
1 | 1.39 | 1.00 | 2.19 | 2.55 | 2.74 | 1.94 | 2.74 | 1.61 |
time (sec) |
N/A | 0.118 | 0.044 | 2.400 | 0.191 | 0.245 | 0.102 | 0.262 | 10.707 |
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 | 28 | 21 | 27 | 26 | 26 | 26 | 26 | 18 |
N.S. |
1 | 1.12 | 0.84 | 1.08 | 1.04 | 1.04 | 1.04 | 1.04 | 0.72 |
time (sec) |
N/A | 0.018 | 0.038 | 0.566 | 0.182 | 0.253 | 0.105 | 0.259 | 10.442 |
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 | 20 | 0 | 28 | 24 | 29 | 29 | 20 | 24 | 31 |
N.S. |
1 | 0.00 | 1.40 | 1.20 | 1.45 | 1.45 | 1.00 | 1.20 | 1.55 |
time (sec) |
N/A | 0.000 | 0.136 | 2.503 | 0.217 | 0.267 | 0.061 | 0.271 | 9.809 |
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 | 26 | 24 | 25 | 20 | 24 | 19 | 24 | 22 |
N.S. |
1 | 1.08 | 1.00 | 1.04 | 0.83 | 1.00 | 0.79 | 1.00 | 0.92 |
time (sec) |
N/A | 0.356 | 0.091 | 4.719 | 0.293 | 0.247 | 0.177 | 0.375 | 9.895 |
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 | 15 | 10 | 10 | 9 | 10 | 12 | 8 | 12 | 10 |
N.S. |
1 | 0.67 | 0.67 | 0.60 | 0.67 | 0.80 | 0.53 | 0.80 | 0.67 |
time (sec) |
N/A | 0.013 | 0.007 | 1.332 | 0.192 | 0.247 | 0.045 | 0.261 | 9.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 78 | 44 | 30 | 189 | 30 | 26 | 30 | 27 |
N.S. |
1 | 4.11 | 2.32 | 1.58 | 9.95 | 1.58 | 1.37 | 1.58 | 1.42 |
time (sec) |
N/A | 0.138 | 0.122 | 3.080 | 0.323 | 0.275 | 0.114 | 0.284 | 10.104 |
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 | 35 | 0 | 33 | 34 | 34 | 36 | 37 | 43 | 106 |
N.S. |
1 | 0.00 | 0.94 | 0.97 | 0.97 | 1.03 | 1.06 | 1.23 | 3.03 |
time (sec) |
N/A | 0.000 | 0.818 | 5.498 | 0.237 | 0.251 | 0.101 | 0.487 | 9.911 |
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 | 7 | 10 | 9 | 9 | 10 | 9 | 7 |
N.S. |
1 | 0.00 | 0.47 | 0.67 | 0.60 | 0.60 | 0.67 | 0.60 | 0.47 |
time (sec) |
N/A | 0.000 | 0.032 | 0.359 | 0.223 | 0.258 | 0.071 | 0.274 | 10.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | C | B | C | C | C | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 1463 | 121 | 315 | 136 | 114 | 70 | 105 |
N.S. |
1 | 0.00 | 54.19 | 4.48 | 11.67 | 5.04 | 4.22 | 2.59 | 3.89 |
time (sec) |
N/A | 0.000 | 5.867 | 7.316 | 0.335 | 0.274 | 4.915 | 0.291 | 10.069 |
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 | 26 | 0 | 51 | 51 | 46 | 43 | 53 | 62 | 0 |
N.S. |
1 | 0.00 | 1.96 | 1.96 | 1.77 | 1.65 | 2.04 | 2.38 | 0.00 |
time (sec) |
N/A | 0.000 | 0.255 | 14.221 | 0.234 | 0.261 | 0.861 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 27 | 60 | 63 | 48 | 63 | 93 | 25 |
N.S. |
1 | 0.00 | 0.82 | 1.82 | 1.91 | 1.45 | 1.91 | 2.82 | 0.76 |
time (sec) |
N/A | 0.000 | 0.337 | 3.615 | 0.195 | 0.255 | 0.414 | 0.277 | 10.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 16 | 15 | 21 | 17 | 20 | 0 | 0 |
N.S. |
1 | 0.00 | 0.89 | 0.83 | 1.17 | 0.94 | 1.11 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.449 | 144.780 | 0.335 | 0.269 | 39.186 | 0.000 | 0.000 |
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 | 28 | 0 | 25 | 34 | 34 | 33 | 36 | 32 | 0 |
N.S. |
1 | 0.00 | 0.89 | 1.21 | 1.21 | 1.18 | 1.29 | 1.14 | 0.00 |
time (sec) |
N/A | 0.000 | 5.073 | 13.396 | 0.334 | 0.258 | 0.173 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 19 | 19 | 20 | 46 | 29 | 20 | 87 | 19 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 2.30 | 1.45 | 1.00 | 4.35 | 0.95 |
time (sec) |
N/A | 0.056 | 0.067 | 1.659 | 0.208 | 0.231 | 0.044 | 0.266 | 10.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 47 | 48 | 141 | 43 | 39 | 0 | 0 |
N.S. |
1 | 0.00 | 1.38 | 1.41 | 4.15 | 1.26 | 1.15 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.223 | 4.005 | 0.469 | 0.243 | 0.809 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 42 | 84 | 66 | 36 | 130 | 165 |
N.S. |
1 | 0.00 | 1.00 | 1.35 | 2.71 | 2.13 | 1.16 | 4.19 | 5.32 |
time (sec) |
N/A | 0.000 | 0.108 | 7.644 | 0.258 | 0.262 | 0.279 | 0.753 | 10.874 |
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 | 33 | 64 | 50 | 38 | 53 | 41 | 37 | 54 | 46 |
N.S. |
1 | 1.94 | 1.52 | 1.15 | 1.61 | 1.24 | 1.12 | 1.64 | 1.39 |
time (sec) |
N/A | 0.116 | 0.088 | 1.684 | 0.214 | 0.260 | 0.082 | 0.277 | 9.792 |
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 | 18 | 0 | 17 | 32 | 1148 | 26 | 26 | 27 | 27 |
N.S. |
1 | 0.00 | 0.94 | 1.78 | 63.78 | 1.44 | 1.44 | 1.50 | 1.50 |
time (sec) |
N/A | 0.000 | 0.499 | 0.486 | 0.490 | 0.259 | 0.233 | 0.268 | 10.710 |
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 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 0.92 | 0.92 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.83 |
time (sec) |
N/A | 0.002 | 0.000 | 0.223 | 0.180 | 0.238 | 0.018 | 0.269 | 0.023 |
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 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. |
1 | 0.44 | 0.44 | 0.50 | 0.44 | 0.44 | 0.39 | 0.50 | 0.44 |
time (sec) |
N/A | 0.002 | 0.001 | 0.331 | 0.179 | 0.252 | 0.034 | 0.259 | 0.019 |
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 | 12 | 18 | 15 | 18 | 44 | 17 | 17 | 19 | 54 |
N.S. |
1 | 1.50 | 1.25 | 1.50 | 3.67 | 1.42 | 1.42 | 1.58 | 4.50 |
time (sec) |
N/A | 0.232 | 0.031 | 1.763 | 0.306 | 0.248 | 0.074 | 0.267 | 9.883 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 52 | 85 | 70 | 53 | 0 | 84 | 49 |
N.S. |
1 | 0.00 | 1.93 | 3.15 | 2.59 | 1.96 | 0.00 | 3.11 | 1.81 |
time (sec) |
N/A | 0.000 | 0.250 | 77.584 | 0.239 | 0.255 | 0.000 | 0.600 | 10.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 42 | 37 | 38 | 0 | 72 | 37 | 0 | 42 |
N.S. |
1 | 1.45 | 1.28 | 1.31 | 0.00 | 2.48 | 1.28 | 0.00 | 1.45 |
time (sec) |
N/A | 0.271 | 0.102 | 4.862 | 0.000 | 0.265 | 0.543 | 0.000 | 10.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 47 | 47 | 45 | 48 | 42 | 42 | 44 | 36 |
N.S. |
1 | 2.04 | 2.04 | 1.96 | 2.09 | 1.83 | 1.83 | 1.91 | 1.57 |
time (sec) |
N/A | 0.017 | 0.009 | 0.459 | 0.182 | 0.248 | 0.073 | 0.263 | 9.883 |
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 | 29 | 25 | 51 | 59 | 26 | 68 | 26 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 1.76 | 2.03 | 0.90 | 2.34 | 0.90 |
time (sec) |
N/A | 0.000 | 0.501 | 12.373 | 0.387 | 0.264 | 0.541 | 0.292 | 10.238 |
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 | 29 | 18 | 18 | 17 | 17 | 17 | 17 | 14 |
N.S. |
1 | 1.38 | 0.86 | 0.86 | 0.81 | 0.81 | 0.81 | 0.81 | 0.67 |
time (sec) |
N/A | 0.009 | 0.010 | 0.418 | 0.176 | 0.244 | 0.044 | 0.263 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 84 | 23 | 22 | 97 | 141 | 79 | 122 |
N.S. |
1 | 1.18 | 3.82 | 1.05 | 1.00 | 4.41 | 6.41 | 3.59 | 5.55 |
time (sec) |
N/A | 0.026 | 0.048 | 2.238 | 0.184 | 0.249 | 0.053 | 0.273 | 9.927 |
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 | 26 | 26 | 23 | 31 | 28 | 22 | 26 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.19 | 1.08 | 0.85 | 1.00 | 1.00 |
time (sec) |
N/A | 0.262 | 0.218 | 3.056 | 0.293 | 0.256 | 0.104 | 0.278 | 9.960 |
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 | 30 | 36 | 35 | 32 | 31 | 31 | 37 | 74 | 29 |
N.S. |
1 | 1.20 | 1.17 | 1.07 | 1.03 | 1.03 | 1.23 | 2.47 | 0.97 |
time (sec) |
N/A | 0.017 | 0.007 | 1.159 | 0.178 | 0.246 | 0.078 | 0.261 | 9.883 |
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 | 28 | 32 | 21 | 21 | 27 | 17 | 21 | 20 |
N.S. |
1 | 1.17 | 1.33 | 0.88 | 0.88 | 1.12 | 0.71 | 0.88 | 0.83 |
time (sec) |
N/A | 0.039 | 0.014 | 0.604 | 0.176 | 0.231 | 0.064 | 0.260 | 9.857 |
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 | 14 | 0 | 17 | 12 | 11 | 11 | 14 | 11 | 11 |
N.S. |
1 | 0.00 | 1.21 | 0.86 | 0.79 | 0.79 | 1.00 | 0.79 | 0.79 |
time (sec) |
N/A | 0.000 | 0.211 | 0.691 | 0.220 | 0.267 | 0.389 | 1.244 | 10.478 |
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 | 14 | 12 | 12 | 10 | 9 | 9 | 12 | 9 | 9 |
N.S. |
1 | 0.86 | 0.86 | 0.71 | 0.64 | 0.64 | 0.86 | 0.64 | 0.64 |
time (sec) |
N/A | 0.001 | 0.001 | 0.627 | 0.176 | 0.238 | 0.020 | 0.271 | 9.757 |
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 | 31 | 30 | 19 | 40 | 25 | 26 | 40 | 33 |
N.S. |
1 | 1.15 | 1.11 | 0.70 | 1.48 | 0.93 | 0.96 | 1.48 | 1.22 |
time (sec) |
N/A | 0.071 | 0.070 | 1.250 | 0.338 | 0.253 | 0.079 | 0.267 | 0.198 |
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 | 24 | 37 | 30 | 35 | 27 | 34 | 34 | 27 | 31 |
N.S. |
1 | 1.54 | 1.25 | 1.46 | 1.12 | 1.42 | 1.42 | 1.12 | 1.29 |
time (sec) |
N/A | 0.427 | 0.692 | 0.852 | 0.390 | 0.259 | 0.131 | 0.283 | 10.061 |