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 | B | B | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 98 | 88 | 88 | 88 | 97 | 15 | 88 |
N.S. |
1 | 1.00 | 7.00 | 6.29 | 6.29 | 6.29 | 6.93 | 1.07 | 6.29 |
time (sec) |
N/A | 0.136 | 0.002 | 0.718 | 0.195 | 0.235 | 0.035 | 0.281 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 115 | 17 | 458 | 458 | 484 | 488 | 440 |
N.S. |
1 | 1.00 | 6.39 | 0.94 | 25.44 | 25.44 | 26.89 | 27.11 | 24.44 |
time (sec) |
N/A | 0.225 | 0.007 | 0.068 | 0.185 | 0.246 | 0.074 | 0.290 | 0.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 98 | 13 | 88 | 88 | 97 | 88 | 88 |
N.S. |
1 | 1.00 | 7.00 | 0.93 | 6.29 | 6.29 | 6.93 | 6.29 | 6.29 |
time (sec) |
N/A | 0.134 | 0.002 | 0.722 | 0.186 | 0.241 | 0.035 | 0.266 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 14 | 98 | 13 | 88 | 88 | 97 | 88 | 88 |
N.S. |
1 | 0.78 | 5.44 | 0.72 | 4.89 | 4.89 | 5.39 | 4.89 | 4.89 |
time (sec) |
N/A | 0.133 | 0.002 | 0.734 | 0.190 | 0.256 | 0.036 | 0.294 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 98 | 89 | 88 | 88 | 97 | 88 | 88 |
N.S. |
1 | 1.00 | 7.00 | 6.36 | 6.29 | 6.29 | 6.93 | 6.29 | 6.29 |
time (sec) |
N/A | 0.129 | 0.002 | 0.683 | 0.192 | 0.250 | 0.034 | 0.274 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 30 | 80 | 25 | 66 | 66 | 70 | 24 | 66 |
N.S. |
1 | 1.07 | 2.86 | 0.89 | 2.36 | 2.36 | 2.50 | 0.86 | 2.36 |
time (sec) |
N/A | 0.196 | 0.004 | 0.724 | 0.186 | 0.244 | 0.034 | 0.293 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 32 | 108 | 27 | 187 | 187 | 194 | 88 | 180 |
N.S. |
1 | 1.03 | 3.48 | 0.87 | 6.03 | 6.03 | 6.26 | 2.84 | 5.81 |
time (sec) |
N/A | 0.222 | 0.025 | 0.882 | 0.186 | 0.264 | 0.048 | 0.281 | 0.077 |
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 | 34 | 34 | 34 | 31 | 52 | 48 | 228 | 30 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 1.53 | 1.41 | 6.71 | 0.88 | 0.91 |
time (sec) |
N/A | 0.163 | 0.340 | 0.818 | 0.300 | 0.262 | 18.289 | 0.267 | 9.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 36 | 73 | 33 | 54 | 52 | 0 | 32 | 58 |
N.S. |
1 | 1.03 | 2.09 | 0.94 | 1.54 | 1.49 | 0.00 | 0.91 | 1.66 |
time (sec) |
N/A | 0.169 | 0.212 | 1.041 | 0.336 | 0.269 | 0.000 | 0.286 | 9.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 93 | 25 | 77 | 77 | 87 | 24 | 77 |
N.S. |
1 | 1.00 | 3.10 | 0.83 | 2.57 | 2.57 | 2.90 | 0.80 | 2.57 |
time (sec) |
N/A | 0.210 | 0.006 | 0.801 | 0.191 | 0.248 | 0.036 | 0.276 | 9.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 32 | 140 | 27 | 280 | 280 | 314 | 105 | 266 |
N.S. |
1 | 1.03 | 4.52 | 0.87 | 9.03 | 9.03 | 10.13 | 3.39 | 8.58 |
time (sec) |
N/A | 0.263 | 0.030 | 0.196 | 0.188 | 0.256 | 0.060 | 0.267 | 9.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 40 | 98 | 31 | 80 | 80 | 90 | 30 | 80 |
N.S. |
1 | 1.18 | 2.88 | 0.91 | 2.35 | 2.35 | 2.65 | 0.88 | 2.35 |
time (sec) |
N/A | 0.206 | 0.006 | 0.732 | 0.195 | 0.266 | 0.038 | 0.281 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 42 | 146 | 33 | 289 | 289 | 321 | 126 | 273 |
N.S. |
1 | 1.02 | 3.56 | 0.80 | 7.05 | 7.05 | 7.83 | 3.07 | 6.66 |
time (sec) |
N/A | 0.229 | 0.035 | 0.082 | 0.198 | 0.269 | 0.062 | 0.279 | 9.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 244 | 37 | 289 | 289 | 323 | 37 | 270 |
N.S. |
1 | 1.00 | 5.30 | 0.80 | 6.28 | 6.28 | 7.02 | 0.80 | 5.87 |
time (sec) |
N/A | 0.244 | 0.045 | 0.356 | 0.188 | 0.383 | 0.068 | 0.283 | 9.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 48 | 248 | 39 | 773 | 773 | 930 | 153 | 753 |
N.S. |
1 | 1.02 | 5.28 | 0.83 | 16.45 | 16.45 | 19.79 | 3.26 | 16.02 |
time (sec) |
N/A | 0.340 | 0.076 | 0.530 | 0.203 | 0.252 | 0.116 | 0.436 | 9.340 |
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 | 34 | 34 | 36 | 31 | 54 | 48 | 190 | 30 | 33 |
N.S. |
1 | 1.00 | 1.06 | 0.91 | 1.59 | 1.41 | 5.59 | 0.88 | 0.97 |
time (sec) |
N/A | 0.180 | 0.195 | 0.803 | 0.303 | 0.274 | 40.139 | 0.288 | 9.163 |
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 | 44 | 44 | 42 | 37 | 71 | 57 | 189 | 36 | 37 |
N.S. |
1 | 1.00 | 0.95 | 0.84 | 1.61 | 1.30 | 4.30 | 0.82 | 0.84 |
time (sec) |
N/A | 0.174 | 0.174 | 0.817 | 0.310 | 0.257 | 73.303 | 0.340 | 9.485 |
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 | 50 | 50 | 49 | 43 | 83 | 72 | 0 | 42 | 73 |
N.S. |
1 | 1.00 | 0.98 | 0.86 | 1.66 | 1.44 | 0.00 | 0.84 | 1.46 |
time (sec) |
N/A | 0.177 | 0.267 | 0.162 | 0.316 | 0.259 | 0.000 | 0.271 | 9.204 |
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 | 33 | 18 | 17 | 29 | 29 | 30 | 29 |
N.S. |
1 | 1.00 | 1.74 | 0.95 | 0.89 | 1.53 | 1.53 | 1.58 | 1.53 |
time (sec) |
N/A | 0.160 | 0.002 | 0.062 | 0.191 | 0.245 | 0.019 | 0.276 | 0.014 |
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 | 16 | 21 | 15 | 14 | 17 | 17 | 22 | 17 |
N.S. |
1 | 1.00 | 1.31 | 0.94 | 0.88 | 1.06 | 1.06 | 1.38 | 1.06 |
time (sec) |
N/A | 0.151 | 0.002 | 0.106 | 0.189 | 0.239 | 0.018 | 0.273 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 96 | 96 | 29 | 86 | 86 | 94 | 28 | 86 |
N.S. |
1 | 2.91 | 2.91 | 0.88 | 2.61 | 2.61 | 2.85 | 0.85 | 2.61 |
time (sec) |
N/A | 0.483 | 0.006 | 0.783 | 0.185 | 0.254 | 0.032 | 0.293 | 9.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 96 | 96 | 86 | 86 | 86 | 94 | 28 | 86 |
N.S. |
1 | 2.91 | 2.91 | 2.61 | 2.61 | 2.61 | 2.85 | 0.85 | 2.61 |
time (sec) |
N/A | 0.420 | 0.004 | 0.786 | 0.191 | 0.255 | 0.035 | 0.313 | 0.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 57 | 56 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 4.07 | 4.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.150 | 0.005 | 0.049 | 0.192 | 0.234 | 0.080 | 0.291 | 9.369 |
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 | 15 | 15 | 14 | 13 | 13 | 12 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.80 | 0.93 | 0.87 |
time (sec) |
N/A | 0.154 | 0.005 | 0.031 | 0.184 | 0.234 | 0.037 | 0.289 | 0.030 |
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 | 17 | 20 | 14 | 15 | 15 | 14 | 18 | 13 |
N.S. |
1 | 1.00 | 1.18 | 0.82 | 0.88 | 0.88 | 0.82 | 1.06 | 0.76 |
time (sec) |
N/A | 0.154 | 0.005 | 0.035 | 0.187 | 0.231 | 0.041 | 0.311 | 0.043 |
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 | 40 | 40 | 23 | 24 | 23 | 23 | 22 | 23 | 23 |
N.S. |
1 | 1.00 | 0.58 | 0.60 | 0.58 | 0.58 | 0.55 | 0.58 | 0.58 |
time (sec) |
N/A | 0.283 | 0.040 | 0.067 | 0.196 | 0.267 | 12.989 | 0.328 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 605 | 597 | 98 | 535 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.16 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.852 | 0.040 | 0.157 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 55 | 53 | 0 | 83 | 58 | 58 | 75 |
N.S. |
1 | 1.00 | 0.87 | 0.84 | 0.00 | 1.32 | 0.92 | 0.92 | 1.19 |
time (sec) |
N/A | 0.301 | 0.022 | 0.091 | 0.000 | 0.317 | 0.056 | 0.287 | 0.111 |
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 | 14 | 14 | 14 | 13 | 22 | 38 | 20 | 13 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.57 | 2.71 | 1.43 | 0.93 | 0.86 |
time (sec) |
N/A | 0.206 | 0.006 | 0.039 | 0.191 | 0.305 | 0.036 | 0.301 | 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 | 28 | 28 | 24 | 22 | 32 | 46 | 29 | 23 | 21 |
N.S. |
1 | 1.00 | 0.86 | 0.79 | 1.14 | 1.64 | 1.04 | 0.82 | 0.75 |
time (sec) |
N/A | 0.223 | 0.011 | 0.036 | 0.193 | 0.294 | 0.044 | 0.291 | 0.022 |
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 | 59 | 59 | 28 | 29 | 38 | 38 | 36 | 28 | 28 |
N.S. |
1 | 1.00 | 0.47 | 0.49 | 0.64 | 0.64 | 0.61 | 0.47 | 0.47 |
time (sec) |
N/A | 0.456 | 0.009 | 0.050 | 0.215 | 0.323 | 0.061 | 0.569 | 0.029 |
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 | 12 | 11 | 11 | 8 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.73 | 1.00 | 1.00 |
time (sec) |
N/A | 0.156 | 0.005 | 0.054 | 0.188 | 0.300 | 0.043 | 0.285 | 9.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 245 | 132 | 116 | 114 | 223 | 272 | 134 | 124 |
N.S. |
1 | 2.69 | 1.45 | 1.27 | 1.25 | 2.45 | 2.99 | 1.47 | 1.36 |
time (sec) |
N/A | 0.458 | 0.065 | 0.113 | 0.278 | 0.340 | 0.804 | 0.290 | 9.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 26 | 44 | 40 | 0 | 99 | 49 |
N.S. |
1 | 1.00 | 0.92 | 1.04 | 1.76 | 1.60 | 0.00 | 3.96 | 1.96 |
time (sec) |
N/A | 0.189 | 1.358 | 4.232 | 0.244 | 0.509 | 0.000 | 0.543 | 9.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 21 | 24 | 39 | 39 | 0 | 89 | 39 |
N.S. |
1 | 1.00 | 0.91 | 1.04 | 1.70 | 1.70 | 0.00 | 3.87 | 1.70 |
time (sec) |
N/A | 0.222 | 2.163 | 0.260 | 0.229 | 0.327 | 0.000 | 0.531 | 9.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 21 | 24 | 39 | 39 | 0 | 89 | 39 |
N.S. |
1 | 1.00 | 0.91 | 1.04 | 1.70 | 1.70 | 0.00 | 3.87 | 1.70 |
time (sec) |
N/A | 0.206 | 1.065 | 0.218 | 0.224 | 0.294 | 0.000 | 0.394 | 9.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 22 | 37 | 37 | 0 | 87 | 37 |
N.S. |
1 | 1.00 | 0.90 | 1.05 | 1.76 | 1.76 | 0.00 | 4.14 | 1.76 |
time (sec) |
N/A | 0.189 | 0.803 | 0.174 | 0.221 | 0.313 | 0.000 | 0.400 | 9.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 17 | 20 | 33 | 33 | 0 | 52 | 19 |
N.S. |
1 | 1.00 | 0.89 | 1.05 | 1.74 | 1.74 | 0.00 | 2.74 | 1.00 |
time (sec) |
N/A | 0.183 | 0.062 | 0.151 | 0.230 | 0.306 | 0.000 | 0.270 | 9.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 21 | 24 | 36 | 36 | 0 | 0 | 23 |
N.S. |
1 | 1.00 | 0.91 | 1.04 | 1.57 | 1.57 | 0.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.187 | 0.798 | 0.203 | 0.221 | 0.343 | 0.000 | 0.000 | 9.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 21 | 24 | 36 | 36 | 0 | 0 | 23 |
N.S. |
1 | 1.00 | 0.91 | 1.04 | 1.57 | 1.57 | 0.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.192 | 0.853 | 0.205 | 0.266 | 0.341 | 0.000 | 0.000 | 10.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 21 | 24 | 36 | 36 | 0 | 0 | 23 |
N.S. |
1 | 1.00 | 0.91 | 1.04 | 1.57 | 1.57 | 0.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.187 | 1.013 | 0.207 | 0.233 | 0.331 | 0.000 | 0.000 | 9.856 |
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 | 97 | 97 | 83 | 74 | 73 | 79 | 97 | 73 | 97 |
N.S. |
1 | 1.00 | 0.86 | 0.76 | 0.75 | 0.81 | 1.00 | 0.75 | 1.00 |
time (sec) |
N/A | 0.311 | 0.025 | 0.092 | 0.272 | 0.332 | 0.117 | 0.299 | 0.120 |
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 | 90 | 90 | 78 | 69 | 68 | 74 | 92 | 68 | 92 |
N.S. |
1 | 1.00 | 0.87 | 0.77 | 0.76 | 0.82 | 1.02 | 0.76 | 1.02 |
time (sec) |
N/A | 0.296 | 0.017 | 0.073 | 0.270 | 0.336 | 0.121 | 0.277 | 0.102 |
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 | 77 | 77 | 72 | 62 | 61 | 67 | 78 | 61 | 85 |
N.S. |
1 | 1.00 | 0.94 | 0.81 | 0.79 | 0.87 | 1.01 | 0.79 | 1.10 |
time (sec) |
N/A | 0.278 | 0.021 | 0.072 | 0.273 | 0.274 | 0.113 | 0.308 | 9.259 |
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 | 72 | 72 | 69 | 57 | 56 | 62 | 75 | 56 | 80 |
N.S. |
1 | 1.00 | 0.96 | 0.79 | 0.78 | 0.86 | 1.04 | 0.78 | 1.11 |
time (sec) |
N/A | 0.262 | 0.018 | 0.063 | 0.291 | 0.303 | 0.128 | 0.282 | 9.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 65 | 56 | 55 | 61 | 75 | 55 | 79 |
N.S. |
1 | 1.00 | 0.92 | 0.79 | 0.77 | 0.86 | 1.06 | 0.77 | 1.11 |
time (sec) |
N/A | 0.250 | 0.013 | 0.059 | 0.275 | 0.274 | 0.116 | 0.307 | 0.084 |
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 | 75 | 75 | 69 | 60 | 59 | 65 | 78 | 60 | 83 |
N.S. |
1 | 1.00 | 0.92 | 0.80 | 0.79 | 0.87 | 1.04 | 0.80 | 1.11 |
time (sec) |
N/A | 0.282 | 0.016 | 0.080 | 0.286 | 0.293 | 0.142 | 0.337 | 9.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 78 | 65 | 64 | 76 | 87 | 65 | 88 |
N.S. |
1 | 1.00 | 0.93 | 0.77 | 0.76 | 0.90 | 1.04 | 0.77 | 1.05 |
time (sec) |
N/A | 0.291 | 0.023 | 0.091 | 0.283 | 0.298 | 0.160 | 0.291 | 9.087 |
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 | 91 | 91 | 82 | 70 | 69 | 89 | 94 | 70 | 92 |
N.S. |
1 | 1.00 | 0.90 | 0.77 | 0.76 | 0.98 | 1.03 | 0.77 | 1.01 |
time (sec) |
N/A | 0.297 | 0.037 | 0.082 | 0.271 | 0.275 | 0.164 | 0.280 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 307 | 228 | 109 | 74 | 0 | 1202 | 61 | 0 | 128 |
N.S. |
1 | 0.74 | 0.36 | 0.24 | 0.00 | 3.92 | 0.20 | 0.00 | 0.42 |
time (sec) |
N/A | 0.734 | 0.014 | 0.054 | 0.000 | 1.058 | 0.580 | 0.000 | 9.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 269 | 216 | 101 | 67 | 0 | 1145 | 3662 | 0 | 188 |
N.S. |
1 | 0.80 | 0.38 | 0.25 | 0.00 | 4.26 | 13.61 | 0.00 | 0.70 |
time (sec) |
N/A | 0.581 | 0.012 | 0.046 | 0.000 | 1.024 | 1.587 | 0.000 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 230 | 217 | 94 | 62 | 0 | 1190 | 48 | 0 | 183 |
N.S. |
1 | 0.94 | 0.41 | 0.27 | 0.00 | 5.17 | 0.21 | 0.00 | 0.80 |
time (sec) |
N/A | 0.506 | 0.013 | 0.041 | 0.000 | 0.996 | 0.519 | 0.000 | 9.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 214 | 90 | 58 | 0 | 1189 | 46 | 0 | 181 |
N.S. |
1 | 1.08 | 0.45 | 0.29 | 0.00 | 6.01 | 0.23 | 0.00 | 0.91 |
time (sec) |
N/A | 0.510 | 0.010 | 0.037 | 0.000 | 0.998 | 0.529 | 0.000 | 9.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 245 | 214 | 101 | 51 | 0 | 1143 | 60 | 0 | 237 |
N.S. |
1 | 0.87 | 0.41 | 0.21 | 0.00 | 4.67 | 0.24 | 0.00 | 0.97 |
time (sec) |
N/A | 0.571 | 0.013 | 0.058 | 0.000 | 1.022 | 8.492 | 0.000 | 9.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 281 | 226 | 109 | 58 | 0 | 1245 | 25507 | 0 | 242 |
N.S. |
1 | 0.80 | 0.39 | 0.21 | 0.00 | 4.43 | 90.77 | 0.00 | 0.86 |
time (sec) |
N/A | 0.601 | 0.013 | 0.066 | 0.000 | 1.011 | 18.687 | 0.000 | 9.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 317 | 235 | 116 | 62 | 0 | 1274 | 70 | 0 | 246 |
N.S. |
1 | 0.74 | 0.37 | 0.20 | 0.00 | 4.02 | 0.22 | 0.00 | 0.78 |
time (sec) |
N/A | 0.637 | 0.014 | 0.064 | 0.000 | 0.977 | 1.748 | 0.000 | 9.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 87 | 49 | 0 | 83 | 44 | 0 | 252 |
N.S. |
1 | 1.00 | 4.58 | 2.58 | 0.00 | 4.37 | 2.32 | 0.00 | 13.26 |
time (sec) |
N/A | 0.263 | 0.031 | 0.265 | 0.000 | 0.258 | 0.609 | 0.000 | 9.547 |
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 | 43 | 48 | 57 | 33 | 33 | 47 | 37 | 34 | 38 |
N.S. |
1 | 1.12 | 1.33 | 0.77 | 0.77 | 1.09 | 0.86 | 0.79 | 0.88 |
time (sec) |
N/A | 0.279 | 0.018 | 0.842 | 0.267 | 0.267 | 0.081 | 0.309 | 0.034 |
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 | 15 | 15 | 14 | 18 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.82 | 1.06 | 1.24 |
time (sec) |
N/A | 0.217 | 0.005 | 0.788 | 0.240 | 0.249 | 0.060 | 0.289 | 10.429 |
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 | 25 | 25 | 22 | 21 | 21 | 20 | 24 | 30 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.80 | 0.96 | 1.20 |
time (sec) |
N/A | 0.222 | 0.005 | 0.800 | 0.191 | 0.253 | 0.058 | 0.295 | 9.754 |
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 | 22 | 20 | 19 | 18 | 24 | 14 | 28 | 18 |
N.S. |
1 | 1.00 | 0.91 | 0.86 | 0.82 | 1.09 | 0.64 | 1.27 | 0.82 |
time (sec) |
N/A | 0.167 | 0.007 | 0.790 | 0.183 | 0.247 | 0.048 | 0.318 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 38 | 22 | 21 | 21 | 26 | 22 | 25 |
N.S. |
1 | 1.00 | 1.41 | 0.81 | 0.78 | 0.78 | 0.96 | 0.81 | 0.93 |
time (sec) |
N/A | 0.210 | 0.010 | 0.810 | 0.281 | 0.257 | 0.068 | 0.274 | 0.036 |
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 | 18 | 17 | 17 | 15 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.81 | 0.81 | 0.71 | 0.81 | 0.81 |
time (sec) |
N/A | 0.181 | 0.004 | 0.783 | 0.275 | 0.251 | 0.037 | 0.292 | 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 | 27 | 27 | 27 | 24 | 23 | 23 | 22 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.85 | 0.85 | 0.81 | 0.85 | 0.85 |
time (sec) |
N/A | 0.225 | 0.006 | 1.069 | 0.268 | 0.244 | 0.052 | 0.313 | 9.439 |
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 | 39 | 39 | 39 | 26 | 25 | 25 | 26 | 29 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.64 | 0.64 | 0.67 | 0.74 | 0.64 |
time (sec) |
N/A | 0.196 | 0.005 | 0.057 | 0.191 | 0.261 | 0.127 | 0.297 | 9.283 |
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 | 22 | 23 | 19 | 18 | 18 | 17 | 19 | 18 |
N.S. |
1 | 1.00 | 1.05 | 0.86 | 0.82 | 0.82 | 0.77 | 0.86 | 0.82 |
time (sec) |
N/A | 0.175 | 0.003 | 0.738 | 0.195 | 0.254 | 0.030 | 0.282 | 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 | 15 | 15 | 15 | 14 | 13 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.93 | 0.87 | 0.87 |
time (sec) |
N/A | 0.202 | 0.005 | 0.793 | 0.269 | 0.245 | 0.037 | 0.278 | 9.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 24 | 21 | 20 | 26 | 17 | 22 | 10 |
N.S. |
1 | 1.00 | 2.00 | 1.75 | 1.67 | 2.17 | 1.42 | 1.83 | 0.83 |
time (sec) |
N/A | 0.176 | 0.010 | 0.038 | 0.186 | 0.262 | 0.044 | 0.294 | 0.044 |
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 | 25 | 25 | 22 | 21 | 22 | 19 | 23 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.88 | 0.76 | 0.92 | 0.76 |
time (sec) |
N/A | 0.218 | 0.006 | 0.834 | 0.189 | 0.263 | 0.047 | 0.296 | 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 | 13 | 13 | 13 | 12 | 11 | 11 | 10 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.189 | 0.006 | 0.069 | 0.264 | 0.263 | 0.050 | 0.318 | 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 | 35 | 35 | 35 | 31 | 35 | 55 | 36 | 30 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.00 | 1.57 | 1.03 | 0.86 | 1.00 |
time (sec) |
N/A | 0.218 | 0.012 | 0.817 | 0.284 | 0.251 | 0.061 | 0.303 | 9.521 |
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 | 18 | 17 | 17 | 17 | 20 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.74 | 0.74 | 0.74 | 0.87 | 0.74 |
time (sec) |
N/A | 0.215 | 0.005 | 0.046 | 0.190 | 0.251 | 0.085 | 0.290 | 9.588 |
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 | 20 | 19 | 19 | 19 | 20 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.83 | 0.83 | 0.83 | 0.87 | 0.83 |
time (sec) |
N/A | 0.237 | 0.007 | 0.046 | 0.197 | 0.238 | 0.051 | 0.273 | 0.035 |
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 | 28 | 25 | 24 | 23 | 32 | 20 | 23 | 25 |
N.S. |
1 | 0.97 | 0.86 | 0.83 | 0.79 | 1.10 | 0.69 | 0.79 | 0.86 |
time (sec) |
N/A | 0.174 | 0.008 | 0.833 | 0.272 | 0.250 | 0.054 | 0.295 | 0.019 |
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 | 44 | 44 | 44 | 42 | 41 | 58 | 49 | 43 | 55 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.93 | 1.32 | 1.11 | 0.98 | 1.25 |
time (sec) |
N/A | 0.438 | 0.019 | 0.798 | 0.278 | 0.265 | 0.097 | 0.294 | 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 | 46 | 46 | 46 | 39 | 38 | 38 | 51 | 38 | 88 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.83 | 0.83 | 1.11 | 0.83 | 1.91 |
time (sec) |
N/A | 0.328 | 0.016 | 1.439 | 0.275 | 0.260 | 0.102 | 0.274 | 0.099 |
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 | 33 | 33 | 33 | 34 | 44 | 72 | 41 | 44 | 56 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.33 | 2.18 | 1.24 | 1.33 | 1.70 |
time (sec) |
N/A | 0.372 | 0.014 | 1.328 | 0.190 | 0.280 | 0.073 | 0.309 | 9.390 |
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 | 12 | 11 | 11 | 10 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.65 | 0.65 | 0.59 | 0.65 | 0.65 |
time (sec) |
N/A | 0.143 | 0.005 | 0.809 | 0.262 | 0.277 | 0.064 | 0.301 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 22 | 21 | 20 | 20 | 34 | 20 | 20 |
N.S. |
1 | 1.00 | 0.92 | 0.88 | 0.83 | 0.83 | 1.42 | 0.83 | 0.83 |
time (sec) |
N/A | 0.187 | 0.008 | 0.822 | 0.287 | 0.277 | 0.081 | 0.292 | 9.343 |
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 | 15 | 23 | 18 | 17 | 17 | 17 | 20 | 19 |
N.S. |
1 | 1.00 | 1.53 | 1.20 | 1.13 | 1.13 | 1.13 | 1.33 | 1.27 |
time (sec) |
N/A | 0.225 | 0.008 | 0.788 | 0.268 | 0.265 | 0.069 | 0.283 | 0.037 |
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 | 18 | 17 | 17 | 19 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.85 | 0.85 | 0.95 | 0.85 | 0.85 |
time (sec) |
N/A | 0.144 | 0.008 | 0.774 | 0.262 | 0.272 | 0.070 | 0.275 | 0.031 |
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 | 37 | 37 | 33 | 28 | 27 | 44 | 29 | 60 | 35 |
N.S. |
1 | 1.00 | 0.89 | 0.76 | 0.73 | 1.19 | 0.78 | 1.62 | 0.95 |
time (sec) |
N/A | 0.216 | 0.018 | 0.838 | 0.280 | 0.276 | 0.077 | 0.280 | 9.419 |
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 | 22 | 21 | 21 | 26 | 21 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.81 | 0.81 | 1.00 | 0.81 | 0.81 |
time (sec) |
N/A | 0.165 | 0.008 | 0.766 | 0.279 | 0.288 | 0.039 | 0.281 | 0.019 |
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 | 12 | 12 | 11 | 10 | 16 | 10 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 1.33 | 0.83 | 0.92 | 0.83 |
time (sec) |
N/A | 0.203 | 0.004 | 0.790 | 0.177 | 0.274 | 0.037 | 0.284 | 9.458 |
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 | 18 | 17 | 17 | 15 | 20 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.81 | 0.81 | 0.71 | 0.95 | 1.00 |
time (sec) |
N/A | 0.196 | 0.005 | 0.043 | 0.182 | 0.271 | 0.066 | 0.271 | 0.032 |
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 | 22 | 22 | 21 | 20 | 34 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 1.55 | 0.77 | 0.91 | 0.91 |
time (sec) |
N/A | 0.185 | 0.007 | 0.063 | 0.267 | 0.265 | 0.051 | 0.288 | 0.020 |
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 | 24 | 24 | 21 | 20 | 32 | 19 | 20 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 1.33 | 0.79 | 0.83 | 0.92 |
time (sec) |
N/A | 0.184 | 0.008 | 0.057 | 0.265 | 0.259 | 0.049 | 0.268 | 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 | 36 | 38 | 36 | 34 | 33 | 33 | 39 | 33 | 56 |
N.S. |
1 | 1.06 | 1.00 | 0.94 | 0.92 | 0.92 | 1.08 | 0.92 | 1.56 |
time (sec) |
N/A | 0.182 | 0.012 | 0.813 | 0.276 | 0.295 | 0.099 | 0.265 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 45 | 37 | 28 | 27 | 27 | 29 | 27 | 37 |
N.S. |
1 | 1.22 | 1.00 | 0.76 | 0.73 | 0.73 | 0.78 | 0.73 | 1.00 |
time (sec) |
N/A | 0.179 | 0.007 | 0.819 | 0.272 | 0.267 | 0.084 | 0.290 | 9.555 |
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 | 29 | 29 | 22 | 21 | 21 | 22 | 23 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.72 | 0.72 | 0.76 | 0.79 | 0.72 |
time (sec) |
N/A | 0.179 | 0.005 | 0.873 | 0.176 | 0.255 | 0.056 | 0.270 | 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 | 19 | 19 | 19 | 16 | 15 | 15 | 14 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 0.79 | 0.74 | 0.84 | 0.79 |
time (sec) |
N/A | 0.173 | 0.004 | 0.802 | 0.185 | 0.287 | 0.031 | 0.270 | 9.674 |
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 | 41 | 41 | 41 | 35 | 34 | 34 | 46 | 34 | 36 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.83 | 0.83 | 1.12 | 0.83 | 0.88 |
time (sec) |
N/A | 0.200 | 0.010 | 1.190 | 0.261 | 0.250 | 0.052 | 0.278 | 0.026 |
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 | 41 | 41 | 39 | 32 | 31 | 31 | 34 | 31 | 31 |
N.S. |
1 | 1.00 | 0.95 | 0.78 | 0.76 | 0.76 | 0.83 | 0.76 | 0.76 |
time (sec) |
N/A | 0.204 | 0.006 | 1.073 | 0.267 | 0.245 | 0.060 | 0.269 | 9.570 |
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 | 30 | 24 | 21 | 20 | 20 | 24 | 23 | 20 |
N.S. |
1 | 1.00 | 0.80 | 0.70 | 0.67 | 0.67 | 0.80 | 0.77 | 0.67 |
time (sec) |
N/A | 0.211 | 0.012 | 0.849 | 0.188 | 0.278 | 0.069 | 0.272 | 9.509 |
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 | 35 | 35 | 28 | 27 | 27 | 31 | 30 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.77 | 0.77 | 0.89 | 0.86 | 0.77 |
time (sec) |
N/A | 0.207 | 0.006 | 0.055 | 0.178 | 0.277 | 0.071 | 0.275 | 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 | 34 | 34 | 32 | 25 | 24 | 34 | 27 | 34 | 26 |
N.S. |
1 | 1.00 | 0.94 | 0.74 | 0.71 | 1.00 | 0.79 | 1.00 | 0.76 |
time (sec) |
N/A | 0.219 | 0.010 | 0.787 | 0.182 | 0.246 | 0.065 | 0.258 | 9.382 |
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 | 42 | 43 | 42 | 35 | 33 | 44 | 36 | 33 | 39 |
N.S. |
1 | 1.02 | 1.00 | 0.83 | 0.79 | 1.05 | 0.86 | 0.79 | 0.93 |
time (sec) |
N/A | 0.186 | 0.015 | 0.763 | 0.265 | 0.256 | 0.058 | 0.272 | 9.210 |
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 | 49 | 49 | 49 | 38 | 37 | 37 | 46 | 37 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.76 | 0.76 | 0.94 | 0.76 | 0.84 |
time (sec) |
N/A | 0.347 | 0.010 | 1.382 | 0.268 | 0.266 | 0.104 | 0.301 | 0.045 |
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 | 29 | 29 | 20 | 19 | 19 | 24 | 22 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.69 | 0.66 | 0.66 | 0.83 | 0.76 | 0.66 |
time (sec) |
N/A | 0.215 | 0.007 | 0.852 | 0.190 | 0.255 | 0.064 | 0.266 | 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 | 46 | 52 | 43 | 34 | 33 | 33 | 41 | 34 | 50 |
N.S. |
1 | 1.13 | 0.93 | 0.74 | 0.72 | 0.72 | 0.89 | 0.74 | 1.09 |
time (sec) |
N/A | 0.238 | 0.014 | 0.799 | 0.262 | 0.253 | 0.068 | 0.281 | 0.053 |