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 | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 18 | 18 | 14 | 41 | 16 | 15 | 13 | 13 |
N.S. |
1 | 0.95 | 0.95 | 0.74 | 2.16 | 0.84 | 0.79 | 0.68 | 0.68 |
time (sec) |
N/A | 0.203 | 0.014 | 0.436 | 0.181 | 0.263 | 0.051 | 0.264 | 17.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 17 | 14 | 14 | 16 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.94 | 0.78 | 0.78 | 0.89 | 0.78 |
time (sec) |
N/A | 0.572 | 0.045 | 0.806 | 0.311 | 0.271 | 0.058 | 0.271 | 16.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 32 | 26 | 68 | 55 | 27 | 41 | 30 |
N.S. |
1 | 0.00 | 1.14 | 0.93 | 2.43 | 1.96 | 0.96 | 1.46 | 1.07 |
time (sec) |
N/A | 0.000 | 10.118 | 1.209 | 0.334 | 0.276 | 0.137 | 0.268 | 16.703 |
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 | 24 | 35 | 33 | 35 | 36 | 36 | 34 |
N.S. |
1 | 0.00 | 1.00 | 1.46 | 1.38 | 1.46 | 1.50 | 1.50 | 1.42 |
time (sec) |
N/A | 0.000 | 0.048 | 2.125 | 0.212 | 0.297 | 152.565 | 0.338 | 27.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 34 | 24 | 0 | 25 | 29 | 0 | 20 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.86 | 1.00 | 0.00 | 0.69 |
time (sec) |
N/A | 0.425 | 0.992 | 2.119 | 0.000 | 0.262 | 83.307 | 0.000 | 15.627 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 26 | 36 | 56 | 36 | 32 | 41 | 64 |
N.S. |
1 | 0.00 | 0.79 | 1.09 | 1.70 | 1.09 | 0.97 | 1.24 | 1.94 |
time (sec) |
N/A | 0.000 | 1.472 | 0.304 | 0.351 | 0.251 | 0.221 | 1.239 | 16.843 |
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 | 22 | 24 | 21 | 19 | 24 | 21 |
N.S. |
1 | 1.10 | 1.10 | 1.05 | 1.14 | 1.00 | 0.90 | 1.14 | 1.00 |
time (sec) |
N/A | 1.160 | 0.228 | 2.981 | 0.328 | 0.266 | 0.190 | 0.422 | 16.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 17 | 17 | 17 | 15 | 15 | 14 | 0 | 16 |
N.S. |
1 | 0.94 | 0.94 | 0.94 | 0.83 | 0.83 | 0.78 | 0.00 | 0.89 |
time (sec) |
N/A | 0.154 | 0.012 | 1.117 | 0.215 | 0.258 | 0.117 | 0.000 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 25 | 23 | 20 | 30 | 40 | 42 | 42 | 19 |
N.S. |
1 | 0.89 | 0.82 | 0.71 | 1.07 | 1.43 | 1.50 | 1.50 | 0.68 |
time (sec) |
N/A | 0.404 | 0.441 | 0.609 | 0.329 | 0.278 | 0.072 | 0.267 | 16.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F(-1) | B | B | B | F(-1) | F(-1) | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 0 | 0 | 225 | 192 | 211 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 5.77 | 4.92 | 5.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 4.198 | 22.653 | 0.438 | 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 | 23 | 32 | 32 | 29 | 28 | 30 | 27 | 31 | 28 |
N.S. |
1 | 1.39 | 1.39 | 1.26 | 1.22 | 1.30 | 1.17 | 1.35 | 1.22 |
time (sec) |
N/A | 0.335 | 0.016 | 0.081 | 0.218 | 0.246 | 0.089 | 0.270 | 0.153 |
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 | 24 | 21 | 24 | 24 | 20 | 26 | 20 |
N.S. |
1 | 0.00 | 1.04 | 0.91 | 1.04 | 1.04 | 0.87 | 1.13 | 0.87 |
time (sec) |
N/A | 0.000 | 0.167 | 2.037 | 0.229 | 0.303 | 0.062 | 0.272 | 15.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 26 | 58 | 45 | 24 | 0 | 49 |
N.S. |
1 | 0.00 | 0.00 | 0.79 | 1.76 | 1.36 | 0.73 | 0.00 | 1.48 |
time (sec) |
N/A | 0.000 | 0.000 | 1.776 | 0.366 | 0.267 | 0.138 | 0.000 | 15.783 |
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 | 7 | 7 | 7 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.126 | 0.000 | 0.053 | 0.212 | 0.238 | 0.021 | 0.258 | 0.003 |
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 | 21 | 24 | 23 | 24 | 27 | 27 | 32 | 27 | 24 |
N.S. |
1 | 1.14 | 1.10 | 1.14 | 1.29 | 1.29 | 1.52 | 1.29 | 1.14 |
time (sec) |
N/A | 0.158 | 0.007 | 1.461 | 0.214 | 0.264 | 0.102 | 0.249 | 0.121 |
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 | 21 | 57 | 33 | 28 | 27 | 39 | 31 | 27 | 27 |
N.S. |
1 | 2.71 | 1.57 | 1.33 | 1.29 | 1.86 | 1.48 | 1.29 | 1.29 |
time (sec) |
N/A | 0.188 | 0.031 | 0.044 | 0.214 | 0.243 | 0.082 | 0.253 | 0.109 |
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 | 24 | 34 | 24 | 23 | 28 | 55 | 19 | 28 | 21 |
N.S. |
1 | 1.42 | 1.00 | 0.96 | 1.17 | 2.29 | 0.79 | 1.17 | 0.88 |
time (sec) |
N/A | 0.177 | 0.040 | 0.327 | 0.280 | 0.263 | 0.116 | 0.253 | 0.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 20 | 264 | 19 | 0 | 0 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 12.00 | 0.86 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A | 1.118 | 0.084 | 0.182 | 0.414 | 0.254 | 0.000 | 0.000 | 16.271 |
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 | 22 | 21 | 19 | 33 | 16 | 19 | 27 | 18 |
N.S. |
1 | 1.16 | 1.11 | 1.00 | 1.74 | 0.84 | 1.00 | 1.42 | 0.95 |
time (sec) |
N/A | 0.231 | 0.021 | 0.809 | 0.304 | 0.261 | 0.066 | 0.260 | 0.267 |
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 | 13 | 17 | 17 | 29 | 12 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.65 | 0.85 | 0.85 | 1.45 | 0.60 | 0.95 |
time (sec) |
N/A | 0.152 | 0.004 | 0.222 | 0.205 | 0.291 | 0.056 | 0.261 | 15.648 |
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 | 32 | 70 | 70 | 73 | 72 | 72 | 76 | 72 | 71 |
N.S. |
1 | 2.19 | 2.19 | 2.28 | 2.25 | 2.25 | 2.38 | 2.25 | 2.22 |
time (sec) |
N/A | 0.222 | 0.000 | 0.145 | 0.203 | 0.254 | 0.036 | 0.262 | 16.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 23 | 32 | 24 | 22 | 50 | 49 | 24 | 50 |
N.S. |
1 | 0.92 | 1.28 | 0.96 | 0.88 | 2.00 | 1.96 | 0.96 | 2.00 |
time (sec) |
N/A | 0.147 | 0.017 | 0.360 | 0.214 | 0.266 | 0.045 | 0.258 | 14.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 68 | 64 | 57 | 80 | 56 | 53 | 0 | 56 |
N.S. |
1 | 2.72 | 2.56 | 2.28 | 3.20 | 2.24 | 2.12 | 0.00 | 2.24 |
time (sec) |
N/A | 1.198 | 5.452 | 2.293 | 0.269 | 0.278 | 1.391 | 0.000 | 13.693 |
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 | 18 | 34 | 27 | 28 | 27 | 27 | 29 | 27 | 0 |
N.S. |
1 | 1.89 | 1.50 | 1.56 | 1.50 | 1.50 | 1.61 | 1.50 | 0.00 |
time (sec) |
N/A | 0.848 | 0.226 | 1.539 | 0.245 | 0.280 | 0.145 | 0.272 | 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 | 28 | 19 | 19 | 23 | 25 | 22 | 24 | 23 | 17 |
N.S. |
1 | 0.68 | 0.68 | 0.82 | 0.89 | 0.79 | 0.86 | 0.82 | 0.61 |
time (sec) |
N/A | 0.409 | 0.140 | 3.477 | 0.340 | 0.260 | 0.271 | 0.331 | 15.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | B | F(-1) | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 71 | 25 | 120 | 0 | 0 | 28 |
N.S. |
1 | 0.00 | 0.92 | 2.73 | 0.96 | 4.62 | 0.00 | 0.00 | 1.08 |
time (sec) |
N/A | 0.000 | 0.350 | 1.027 | 0.828 | 0.275 | 0.000 | 0.000 | 15.588 |
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 | 32 | 0 | 31 | 39 | 40 | 48 | 34 | 50 | 0 |
N.S. |
1 | 0.00 | 0.97 | 1.22 | 1.25 | 1.50 | 1.06 | 1.56 | 0.00 |
time (sec) |
N/A | 0.000 | 0.198 | 0.296 | 0.290 | 0.268 | 0.194 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 32 | 130 | 37 | 32 | 0 | 0 | 37 |
N.S. |
1 | 0.00 | 1.00 | 4.06 | 1.16 | 1.00 | 0.00 | 0.00 | 1.16 |
time (sec) |
N/A | 0.000 | 0.204 | 0.539 | 0.428 | 0.283 | 0.000 | 0.000 | 15.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | C | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 46 | 47 | 91 | 72 | 65 | 145 | 0 |
N.S. |
1 | 0.00 | 1.31 | 1.34 | 2.60 | 2.06 | 1.86 | 4.14 | 0.00 |
time (sec) |
N/A | 0.000 | 5.069 | 2.181 | 0.378 | 0.261 | 0.174 | 0.408 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 46 | 45 | 81 | 57 | 54 | 175 | 183 |
N.S. |
1 | 0.00 | 1.92 | 1.88 | 3.38 | 2.38 | 2.25 | 7.29 | 7.62 |
time (sec) |
N/A | 0.000 | 0.083 | 15.859 | 0.659 | 0.267 | 0.247 | 0.290 | 15.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 0 | 30 | 96 | 58 | 22 | 74 | 123 |
N.S. |
1 | 0.00 | 0.00 | 1.03 | 3.31 | 2.00 | 0.76 | 2.55 | 4.24 |
time (sec) |
N/A | 0.000 | 0.000 | 1.352 | 0.332 | 0.266 | 0.267 | 0.674 | 16.163 |
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 | 27 | 36 | 38 | 36 | 34 | 35 | 37 | 35 | 0 |
N.S. |
1 | 1.33 | 1.41 | 1.33 | 1.26 | 1.30 | 1.37 | 1.30 | 0.00 |
time (sec) |
N/A | 0.961 | 0.060 | 8.255 | 0.241 | 0.267 | 0.191 | 0.360 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 0 | 13 | 14 | 0 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 0.87 | 0.93 | 0.00 | 0.87 |
time (sec) |
N/A | 0.167 | 0.127 | 1.429 | 0.000 | 0.259 | 0.533 | 0.000 | 15.413 |
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 | 14 | 19 | 13 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.36 | 0.93 | 0.79 | 0.71 | 0.71 | 0.57 | 0.71 | 0.71 |
time (sec) |
N/A | 0.146 | 0.027 | 0.030 | 0.219 | 0.258 | 0.050 | 0.286 | 0.072 |
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 | 31 | 6532 | 633 | 961 | 6363 | 793 | 1146 | 1952 | 772 |
N.S. |
1 | 210.71 | 20.42 | 31.00 | 205.26 | 25.58 | 36.97 | 62.97 | 24.90 |
time (sec) |
N/A | 34.127 | 3.015 | 1.598 | 0.411 | 0.288 | 2.331 | 0.388 | 18.689 |
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 | 17 | 15 | 15 | 17 | 13 | 16 | 19 | 18 | 0 |
N.S. |
1 | 0.88 | 0.88 | 1.00 | 0.76 | 0.94 | 1.12 | 1.06 | 0.00 |
time (sec) |
N/A | 0.279 | 0.095 | 0.328 | 0.319 | 0.255 | 0.114 | 0.284 | 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 | 38 | 0 | 37 | 54 | 64 | 64 | 60 | 71 | 81 |
N.S. |
1 | 0.00 | 0.97 | 1.42 | 1.68 | 1.68 | 1.58 | 1.87 | 2.13 |
time (sec) |
N/A | 0.000 | 0.073 | 2.051 | 0.263 | 0.252 | 0.137 | 0.347 | 14.336 |
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 | 19 | 23 | 22 | 25 | 21 | 19 | 28 | 19 |
N.S. |
1 | 0.68 | 0.82 | 0.79 | 0.89 | 0.75 | 0.68 | 1.00 | 0.68 |
time (sec) |
N/A | 0.890 | 0.441 | 0.710 | 0.256 | 0.274 | 0.108 | 0.284 | 15.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 35 | 11 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 2.33 | 0.73 | 0.73 | 0.67 | 0.67 | 0.53 | 0.67 | 0.67 |
time (sec) |
N/A | 0.203 | 0.003 | 0.172 | 0.202 | 0.255 | 0.076 | 0.278 | 15.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 43 | 97 | 45 | 28 | 44 | 41 | 27 |
N.S. |
1 | 0.00 | 1.54 | 3.46 | 1.61 | 1.00 | 1.57 | 1.46 | 0.96 |
time (sec) |
N/A | 0.000 | 0.372 | 2.646 | 0.338 | 0.259 | 0.272 | 0.654 | 15.783 |
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 | 23 | 26 | 25 | 24 | 22 | 25 | 22 |
N.S. |
1 | 0.00 | 0.88 | 1.00 | 0.96 | 0.92 | 0.85 | 0.96 | 0.85 |
time (sec) |
N/A | 0.000 | 0.378 | 0.411 | 0.318 | 0.250 | 0.092 | 0.302 | 0.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 295 | 31 | 27 | 391 | 24 | 24 | 120 | 23 |
N.S. |
1 | 11.35 | 1.19 | 1.04 | 15.04 | 0.92 | 0.92 | 4.62 | 0.88 |
time (sec) |
N/A | 1.266 | 0.072 | 0.979 | 0.399 | 0.263 | 0.161 | 0.506 | 14.929 |
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 | 26 | 26 | 27 | 40 | 19 | 24 | 24 | 19 |
N.S. |
1 | 1.18 | 1.18 | 1.23 | 1.82 | 0.86 | 1.09 | 1.09 | 0.86 |
time (sec) |
N/A | 0.199 | 0.027 | 0.185 | 0.216 | 0.267 | 0.078 | 0.267 | 13.410 |
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 | 28 | 29 | 28 | 27 | 24 | 28 | 27 |
N.S. |
1 | 0.00 | 1.12 | 1.16 | 1.12 | 1.08 | 0.96 | 1.12 | 1.08 |
time (sec) |
N/A | 0.000 | 0.133 | 26.854 | 0.297 | 0.268 | 0.831 | 0.642 | 14.273 |
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 | 25 | 0 | 32 | 26 | 68 | 52 | 26 | 83 | 192 |
N.S. |
1 | 0.00 | 1.28 | 1.04 | 2.72 | 2.08 | 1.04 | 3.32 | 7.68 |
time (sec) |
N/A | 0.000 | 0.157 | 2.030 | 0.467 | 0.270 | 0.188 | 0.683 | 13.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 33 | 81 | 38 | 34 | 72 | 200 |
N.S. |
1 | 0.00 | 0.90 | 1.10 | 2.70 | 1.27 | 1.13 | 2.40 | 6.67 |
time (sec) |
N/A | 0.000 | 0.364 | 38.872 | 0.332 | 0.254 | 0.106 | 0.289 | 14.321 |
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 | 27 | 0 | 30 | 27 | 34 | 34 | 36 | 27 | 34 |
N.S. |
1 | 0.00 | 1.11 | 1.00 | 1.26 | 1.26 | 1.33 | 1.00 | 1.26 |
time (sec) |
N/A | 0.000 | 0.368 | 1.390 | 0.241 | 0.274 | 0.243 | 0.270 | 14.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 58 | 56 | 32 | 858 | 30 | 34 | 30 | 32 |
N.S. |
1 | 3.22 | 3.11 | 1.78 | 47.67 | 1.67 | 1.89 | 1.67 | 1.78 |
time (sec) |
N/A | 0.330 | 0.078 | 1.830 | 0.313 | 0.275 | 0.098 | 0.305 | 1.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | F | A | F(-2) | A | F(-2) | A | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 99 | 0 | 28 | 0 | 29 | 0 | 29 | 0 |
N.S. |
1 | 3.96 | 0.00 | 1.12 | 0.00 | 1.16 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 2.248 | 0.000 | 4.137 | 0.000 | 0.291 | 0.000 | 0.948 | 0.000 |
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 | 24 | 0 | 21 | 21 | 20 | 28 | 24 | 51 | 52 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 0.83 | 1.17 | 1.00 | 2.12 | 2.17 |
time (sec) |
N/A | 0.000 | 1.130 | 0.698 | 0.358 | 0.273 | 0.201 | 0.279 | 0.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | C | A | A | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 41 | 111 | 112 | 61 | 44 | 0 | 0 |
N.S. |
1 | 0.00 | 1.08 | 2.92 | 2.95 | 1.61 | 1.16 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.273 | 30.555 | 0.481 | 0.265 | 0.433 | 0.000 | 0.000 |
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 | 15 | 15 | 15 | 24 | 57 | 23 | 20 | 47 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.60 | 3.80 | 1.53 | 1.33 | 3.13 | 0.93 |
time (sec) |
N/A | 3.464 | 0.589 | 2.353 | 1.141 | 0.263 | 0.106 | 0.447 | 15.629 |
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 | 29 | 22 | 47 | 32 | 34 | 32 | 32 |
N.S. |
1 | 1.39 | 1.26 | 0.96 | 2.04 | 1.39 | 1.48 | 1.39 | 1.39 |
time (sec) |
N/A | 0.248 | 0.027 | 0.845 | 0.212 | 0.268 | 0.104 | 0.277 | 0.243 |
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 | 22 | 20 | 19 | 18 | 25 | 19 | 25 | 16 |
N.S. |
1 | 1.10 | 1.00 | 0.95 | 0.90 | 1.25 | 0.95 | 1.25 | 0.80 |
time (sec) |
N/A | 0.176 | 0.029 | 0.203 | 0.207 | 0.265 | 0.060 | 0.269 | 0.096 |
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 | 36 | 0 | 58 | 36 | 55 | 43 | 37 | 14225 | 274 |
N.S. |
1 | 0.00 | 1.61 | 1.00 | 1.53 | 1.19 | 1.03 | 395.14 | 7.61 |
time (sec) |
N/A | 0.000 | 0.194 | 5.110 | 0.274 | 0.259 | 0.280 | 0.467 | 13.807 |
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 | 7 | 7 | 8 | 7 | 9 | 3 | 7 | 7 |
N.S. |
1 | 0.28 | 0.28 | 0.32 | 0.28 | 0.36 | 0.12 | 0.28 | 0.28 |
time (sec) |
N/A | 0.136 | 0.001 | 0.063 | 0.218 | 0.259 | 0.026 | 0.262 | 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 | 36 | 51 | 44 | 32 | 37 | 37 | 39 | 37 | 31 |
N.S. |
1 | 1.42 | 1.22 | 0.89 | 1.03 | 1.03 | 1.08 | 1.03 | 0.86 |
time (sec) |
N/A | 0.201 | 0.011 | 0.191 | 0.204 | 0.248 | 0.031 | 0.269 | 0.043 |
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 | 18 | 14 | 14 | 11 | 39 | 10 | 12 | 14 | 10 |
N.S. |
1 | 0.78 | 0.78 | 0.61 | 2.17 | 0.56 | 0.67 | 0.78 | 0.56 |
time (sec) |
N/A | 0.310 | 0.043 | 1.005 | 0.250 | 0.261 | 0.078 | 0.265 | 14.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 22 | 22 | 23 | 22 | 22 | 22 | 22 | 22 |
N.S. |
1 | 1.22 | 1.22 | 1.28 | 1.22 | 1.22 | 1.22 | 1.22 | 1.22 |
time (sec) |
N/A | 0.285 | 0.010 | 0.100 | 0.232 | 0.266 | 0.125 | 0.266 | 14.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | F | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 92 | 166 | 0 | 99 | 150 | 165 | 150 |
N.S. |
1 | 0.00 | 3.54 | 6.38 | 0.00 | 3.81 | 5.77 | 6.35 | 5.77 |
time (sec) |
N/A | 0.000 | 0.434 | 10.951 | 0.000 | 0.269 | 0.432 | 0.330 | 14.668 |
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 | 26 | 22 | 25 | 25 | 22 | 25 | 21 |
N.S. |
1 | 0.00 | 1.04 | 0.88 | 1.00 | 1.00 | 0.88 | 1.00 | 0.84 |
time (sec) |
N/A | 0.000 | 0.131 | 4.071 | 0.269 | 0.276 | 0.207 | 0.280 | 14.739 |
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 | 33 | 0 | 37 | 41 | 46 | 39 | 39 | 47 | 113 |
N.S. |
1 | 0.00 | 1.12 | 1.24 | 1.39 | 1.18 | 1.18 | 1.42 | 3.42 |
time (sec) |
N/A | 0.000 | 0.072 | 1.637 | 0.350 | 0.276 | 0.184 | 0.279 | 15.433 |
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 | 31 | 34 | 23 | 22 | 22 | 31 | 22 | 25 |
N.S. |
1 | 1.29 | 1.42 | 0.96 | 0.92 | 0.92 | 1.29 | 0.92 | 1.04 |
time (sec) |
N/A | 0.160 | 0.006 | 0.166 | 0.200 | 0.251 | 0.034 | 0.272 | 0.055 |
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 | 16 | 16 | 15 | 14 | 14 | 12 | 21 | 15 |
N.S. |
1 | 0.73 | 0.73 | 0.68 | 0.64 | 0.64 | 0.55 | 0.95 | 0.68 |
time (sec) |
N/A | 0.171 | 0.030 | 0.388 | 0.219 | 0.262 | 0.063 | 0.263 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 32 | 30 | 45 | 47 | 51 | 52 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.97 | 1.45 | 1.52 | 1.65 | 1.68 | 0.00 |
time (sec) |
N/A | 0.000 | 0.086 | 1.278 | 0.342 | 0.248 | 0.207 | 0.297 | 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 | 15 | 22 | 20 | 15 | 18 | 18 | 20 | 18 | 15 |
N.S. |
1 | 1.47 | 1.33 | 1.00 | 1.20 | 1.20 | 1.33 | 1.20 | 1.00 |
time (sec) |
N/A | 0.135 | 0.002 | 0.106 | 0.201 | 0.239 | 0.023 | 0.261 | 14.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 202 | 23 | 22 | 29 | 21 | 22 | 21 | 21 |
N.S. |
1 | 10.10 | 1.15 | 1.10 | 1.45 | 1.05 | 1.10 | 1.05 | 1.05 |
time (sec) |
N/A | 0.872 | 0.200 | 0.452 | 0.287 | 0.247 | 0.091 | 0.288 | 0.288 |
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 | 35 | 0 | 59 | 50 | 66 | 52 | 46 | 58 | 89 |
N.S. |
1 | 0.00 | 1.69 | 1.43 | 1.89 | 1.49 | 1.31 | 1.66 | 2.54 |
time (sec) |
N/A | 0.000 | 0.375 | 0.821 | 0.362 | 0.250 | 0.270 | 0.893 | 15.170 |
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 | 14 | 15 | 22 | 22 | 20 | 14 | 14 |
N.S. |
1 | 0.00 | 0.93 | 1.00 | 1.47 | 1.47 | 1.33 | 0.93 | 0.93 |
time (sec) |
N/A | 0.000 | 0.073 | 1.237 | 0.240 | 0.258 | 0.162 | 0.267 | 14.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 26 | 23 | 23 | 23 | 20 | 23 | 23 |
N.S. |
1 | 0.00 | 1.18 | 1.05 | 1.05 | 1.05 | 0.91 | 1.05 | 1.05 |
time (sec) |
N/A | 0.000 | 2.068 | 0.069 | 0.244 | 0.245 | 0.112 | 0.274 | 14.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 1678 | 36 | 24 | 119 | 38 | 20 | 38 | 23 |
N.S. |
1 | 67.12 | 1.44 | 0.96 | 4.76 | 1.52 | 0.80 | 1.52 | 0.92 |
time (sec) |
N/A | 6.711 | 0.577 | 0.188 | 0.315 | 0.291 | 0.075 | 0.271 | 15.575 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 60 | 83 | 55 | 58 | 58 | 53 | 58 | 49 |
N.S. |
1 | 3.00 | 4.15 | 2.75 | 2.90 | 2.90 | 2.65 | 2.90 | 2.45 |
time (sec) |
N/A | 0.193 | 0.008 | 0.176 | 0.199 | 0.255 | 0.028 | 0.264 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 37 | 24 | 31 | 0 | 40 | 20 | 55 | 29 |
N.S. |
1 | 1.48 | 0.96 | 1.24 | 0.00 | 1.60 | 0.80 | 2.20 | 1.16 |
time (sec) |
N/A | 0.736 | 0.292 | 0.204 | 0.000 | 0.275 | 0.137 | 0.268 | 15.269 |
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 | 33 | 221 | 98 | 128 | 294 | 122 | 133 | 153 | 143 |
N.S. |
1 | 6.70 | 2.97 | 3.88 | 8.91 | 3.70 | 4.03 | 4.64 | 4.33 |
time (sec) |
N/A | 0.791 | 0.493 | 0.317 | 0.214 | 0.268 | 0.178 | 0.257 | 15.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 29 | 25 | 0 | 24 | 0 | 0 | 24 |
N.S. |
1 | 0.96 | 1.16 | 1.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.96 |
time (sec) |
N/A | 1.482 | 4.770 | 2.388 | 0.000 | 0.247 | 0.000 | 0.000 | 15.993 |
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 | 46 | 34 | 43 | 42 | 39 | 43 | 42 |
N.S. |
1 | 1.00 | 1.70 | 1.26 | 1.59 | 1.56 | 1.44 | 1.59 | 1.56 |
time (sec) |
N/A | 3.057 | 5.160 | 7.400 | 0.319 | 0.266 | 0.502 | 0.271 | 16.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 30 | 0 | 22 | 29 | 24 | 0 | 22 | 21 |
N.S. |
1 | 0.91 | 0.00 | 0.67 | 0.88 | 0.73 | 0.00 | 0.67 | 0.64 |
time (sec) |
N/A | 4.654 | 0.000 | 5.941 | 0.386 | 0.266 | 0.000 | 0.572 | 15.657 |
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 | 16 | 16 | 16 | 14 | 13 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.81 | 0.81 | 0.88 | 0.81 | 0.81 |
time (sec) |
N/A | 0.137 | 0.002 | 0.479 | 0.211 | 0.252 | 0.031 | 0.260 | 14.555 |
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 | 31 | 0 | 32 | 20 | 28 | 41 | 31 | 0 | 28 |
N.S. |
1 | 0.00 | 1.03 | 0.65 | 0.90 | 1.32 | 1.00 | 0.00 | 0.90 |
time (sec) |
N/A | 0.000 | 6.159 | 13.316 | 0.334 | 0.262 | 7.188 | 0.000 | 15.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 77 | 24 | 23 | 38 | 38 | 22 | 38 | 42 |
N.S. |
1 | 3.21 | 1.00 | 0.96 | 1.58 | 1.58 | 0.92 | 1.58 | 1.75 |
time (sec) |
N/A | 1.447 | 0.092 | 2.566 | 0.376 | 0.286 | 0.208 | 0.419 | 15.355 |
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 | 15 | 20 | 15 | 17 | 14 | 14 | 14 | 15 |
N.S. |
1 | 1.07 | 1.43 | 1.07 | 1.21 | 1.00 | 1.00 | 1.00 | 1.07 |
time (sec) |
N/A | 0.261 | 0.127 | 2.169 | 0.229 | 0.255 | 0.068 | 0.262 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 53 | 68 | 58 | 58 | 102 | 131 | 0 |
N.S. |
1 | 0.00 | 1.71 | 2.19 | 1.87 | 1.87 | 3.29 | 4.23 | 0.00 |
time (sec) |
N/A | 0.000 | 0.095 | 2.093 | 0.275 | 0.261 | 0.459 | 0.494 | 0.000 |
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 | 29 | 0 | 38 | 185 | 458 | 90 | 85 | 0 | 522 |
N.S. |
1 | 0.00 | 1.31 | 6.38 | 15.79 | 3.10 | 2.93 | 0.00 | 18.00 |
time (sec) |
N/A | 0.000 | 1.046 | 12.648 | 2.609 | 0.277 | 7.140 | 0.000 | 16.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 95 | 32 | 58 | 31 | 26 | 0 | 28 |
N.S. |
1 | 0.00 | 2.97 | 1.00 | 1.81 | 0.97 | 0.81 | 0.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.460 | 84.620 | 0.344 | 0.262 | 0.495 | 0.000 | 15.872 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 35 | 26 | 120 | 25 | 85 | 0 | 34 |
N.S. |
1 | 0.00 | 1.03 | 0.76 | 3.53 | 0.74 | 2.50 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 5.308 | 3.450 | 0.384 | 0.265 | 1.133 | 0.000 | 16.707 |
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 | 30 | 100 | 48 | 44 | 81 | 35 | 39 | 39 | 42 |
N.S. |
1 | 3.33 | 1.60 | 1.47 | 2.70 | 1.17 | 1.30 | 1.30 | 1.40 |
time (sec) |
N/A | 0.608 | 0.087 | 0.960 | 0.240 | 0.253 | 0.124 | 0.256 | 16.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 24 | 23 | 19 | 18 | 18 | 20 | 18 | 18 |
N.S. |
1 | 1.33 | 1.28 | 1.06 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 |
time (sec) |
N/A | 0.180 | 0.006 | 0.151 | 0.196 | 0.265 | 0.107 | 0.263 | 15.936 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 25 | 16 | 0 | 23 | 12 | 0 | 21 |
N.S. |
1 | 0.00 | 1.32 | 0.84 | 0.00 | 1.21 | 0.63 | 0.00 | 1.11 |
time (sec) |
N/A | 0.000 | 0.825 | 1.183 | 0.000 | 0.252 | 0.102 | 0.000 | 16.490 |
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 | 20 | 18 | 13 | 12 | 26 | 15 | 12 | 12 |
N.S. |
1 | 0.71 | 0.64 | 0.46 | 0.43 | 0.93 | 0.54 | 0.43 | 0.43 |
time (sec) |
N/A | 0.150 | 0.006 | 0.074 | 0.190 | 0.252 | 0.083 | 0.256 | 17.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 38 | 58 | 194 | 227 | 139 | 264 | 0 |
N.S. |
1 | 0.00 | 1.73 | 2.64 | 8.82 | 10.32 | 6.32 | 12.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.221 | 2.878 | 0.601 | 0.270 | 0.397 | 0.702 | 0.000 |
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 | 26 | 44 | 39 | 29 | 32 | 47 | 49 | 57 | 32 |
N.S. |
1 | 1.69 | 1.50 | 1.12 | 1.23 | 1.81 | 1.88 | 2.19 | 1.23 |
time (sec) |
N/A | 0.218 | 0.020 | 0.162 | 0.196 | 0.260 | 0.131 | 0.262 | 0.148 |
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 | 19 | 16 | 15 | 21 | 14 | 15 | 13 |
N.S. |
1 | 1.00 | 1.19 | 1.00 | 0.94 | 1.31 | 0.88 | 0.94 | 0.81 |
time (sec) |
N/A | 0.133 | 0.002 | 0.504 | 0.187 | 0.267 | 0.028 | 0.261 | 16.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 122 | 63 | 121 | 121 | 99 | 968 | 1087 |
N.S. |
1 | 0.00 | 3.94 | 2.03 | 3.90 | 3.90 | 3.19 | 31.23 | 35.06 |
time (sec) |
N/A | 0.000 | 10.083 | 4.629 | 0.327 | 0.250 | 0.122 | 0.315 | 16.680 |
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 | 42 | 24 | 38 | 37 | 38 | 34 | 38 | 37 |
N.S. |
1 | 1.62 | 0.92 | 1.46 | 1.42 | 1.46 | 1.31 | 1.46 | 1.42 |
time (sec) |
N/A | 0.225 | 0.012 | 0.158 | 0.180 | 0.230 | 0.143 | 0.267 | 16.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | C | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 40 | 22 | 27 | 37 | 39 | 0 | 0 |
N.S. |
1 | 0.00 | 1.90 | 1.05 | 1.29 | 1.76 | 1.86 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.723 | 3.190 | 0.349 | 0.250 | 0.374 | 0.000 | 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 | 20 | 107 | 60 | 43 | 45 | 42 | 51 | 107 | 33 |
N.S. |
1 | 5.35 | 3.00 | 2.15 | 2.25 | 2.10 | 2.55 | 5.35 | 1.65 |
time (sec) |
N/A | 0.364 | 0.266 | 0.453 | 0.195 | 0.250 | 0.146 | 0.271 | 0.134 |
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 | 19 | 20 | 16 | 16 | 17 | 15 | 15 | 153 | 15 |
N.S. |
1 | 1.05 | 0.84 | 0.84 | 0.89 | 0.79 | 0.79 | 8.05 | 0.79 |
time (sec) |
N/A | 0.307 | 0.024 | 1.496 | 0.198 | 0.244 | 0.080 | 0.280 | 15.258 |
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 | 20 | 49 | 86 | 21 | 44 | 20 | 20 | 20 | 20 |
N.S. |
1 | 2.45 | 4.30 | 1.05 | 2.20 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.462 | 0.157 | 1.070 | 0.326 | 0.259 | 0.095 | 0.290 | 16.413 |
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 | 23 | 50 | 19 | 26 | 68 | 22 | 24 | 22 | 24 |
N.S. |
1 | 2.17 | 0.83 | 1.13 | 2.96 | 0.96 | 1.04 | 0.96 | 1.04 |
time (sec) |
N/A | 0.311 | 0.007 | 1.134 | 0.206 | 0.244 | 0.085 | 0.273 | 15.477 |
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 | 53 | 37 | 37 | 42 | 46 | 34 | 42 | 38 |
N.S. |
1 | 1.89 | 1.32 | 1.32 | 1.50 | 1.64 | 1.21 | 1.50 | 1.36 |
time (sec) |
N/A | 0.587 | 2.094 | 0.510 | 0.463 | 0.251 | 0.167 | 0.278 | 15.946 |