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 | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 27 | 25 | 60 | 24 | 22 | 5629 | 25 |
N.S. |
1 | 0.93 | 0.93 | 0.86 | 2.07 | 0.83 | 0.76 | 194.10 | 0.86 |
time (sec) |
N/A | 0.358 | 0.271 | 0.314 | 0.395 | 0.264 | 0.316 | 0.375 | 7.984 |
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 | 46 | 23 | 25 | 31 | 35 | 20 | 43 | 24 |
N.S. |
1 | 1.70 | 0.85 | 0.93 | 1.15 | 1.30 | 0.74 | 1.59 | 0.89 |
time (sec) |
N/A | 0.969 | 1.948 | 0.165 | 0.237 | 0.262 | 0.183 | 0.261 | 8.275 |
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 | 12 | 12 | 11 | 12 | 12 | 8 | 13 | 10 |
N.S. |
1 | 0.50 | 0.50 | 0.46 | 0.50 | 0.50 | 0.33 | 0.54 | 0.42 |
time (sec) |
N/A | 0.144 | 0.003 | 0.128 | 0.175 | 0.256 | 0.029 | 0.254 | 0.069 |
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 | 25 | 0 | 43 | 37 | 59 | 48 | 54 | 62 | 51 |
N.S. |
1 | 0.00 | 1.72 | 1.48 | 2.36 | 1.92 | 2.16 | 2.48 | 2.04 |
time (sec) |
N/A | 0.000 | 0.268 | 0.330 | 0.226 | 0.261 | 0.161 | 0.261 | 8.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 56 | 20 | 21 | 24 | 19 | 19 | 0 | 25 |
N.S. |
1 | 2.80 | 1.00 | 1.05 | 1.20 | 0.95 | 0.95 | 0.00 | 1.25 |
time (sec) |
N/A | 0.233 | 0.044 | 0.145 | 0.252 | 0.274 | 0.098 | 0.000 | 8.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 38 | 20 | 32 | 29 | 19 | 19 | 0 | 0 |
N.S. |
1 | 1.90 | 1.00 | 1.60 | 1.45 | 0.95 | 0.95 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 0.098 | 0.595 | 0.296 | 0.261 | 0.130 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 54 | 25 | 53 | 27 | 59 | 0 |
N.S. |
1 | 0.00 | 0.93 | 1.93 | 0.89 | 1.89 | 0.96 | 2.11 | 0.00 |
time (sec) |
N/A | 0.000 | 0.066 | 1.306 | 0.272 | 0.266 | 73.190 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 14 | 17 | 13 | 21 | 19 | 16 | 14 |
N.S. |
1 | 0.00 | 1.00 | 1.21 | 0.93 | 1.50 | 1.36 | 1.14 | 1.00 |
time (sec) |
N/A | 0.000 | 0.037 | 0.058 | 0.231 | 0.262 | 0.097 | 0.258 | 8.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 73 | 21 | 24 | 60 | 21 | 272 | 67 | 29 |
N.S. |
1 | 2.61 | 0.75 | 0.86 | 2.14 | 0.75 | 9.71 | 2.39 | 1.04 |
time (sec) |
N/A | 0.250 | 0.018 | 0.258 | 0.174 | 0.262 | 0.453 | 0.252 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 132 | 324 | 196 | 196 | 218 | 0 | 117946 |
N.S. |
1 | 0.00 | 5.08 | 12.46 | 7.54 | 7.54 | 8.38 | 0.00 | 4536.38 |
time (sec) |
N/A | 0.000 | 0.217 | 239.630 | 1.115 | 0.312 | 2.228 | 0.000 | 142.247 |
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 | 25 | 18 | 17 | 41 | 16 | 17 | 16 | 16 |
N.S. |
1 | 0.86 | 0.62 | 0.59 | 1.41 | 0.55 | 0.59 | 0.55 | 0.55 |
time (sec) |
N/A | 0.222 | 0.035 | 0.025 | 0.175 | 0.261 | 0.051 | 0.265 | 8.295 |
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 | 36 | 0 | 53 | 120 | 73 | 119 | 109 | 0 | 386 |
N.S. |
1 | 0.00 | 1.47 | 3.33 | 2.03 | 3.31 | 3.03 | 0.00 | 10.72 |
time (sec) |
N/A | 0.000 | 0.886 | 14.348 | 0.249 | 0.270 | 0.537 | 0.000 | 8.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 1682 | 42 | 53 | 161 | 45 | 112 | 53 | 0 |
N.S. |
1 | 54.26 | 1.35 | 1.71 | 5.19 | 1.45 | 3.61 | 1.71 | 0.00 |
time (sec) |
N/A | 5.495 | 0.138 | 0.480 | 0.305 | 0.273 | 0.254 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 39 | 74 | 38 | 54 | 39 | 0 | 48 |
N.S. |
1 | 0.00 | 1.50 | 2.85 | 1.46 | 2.08 | 1.50 | 0.00 | 1.85 |
time (sec) |
N/A | 0.000 | 0.152 | 4.413 | 0.231 | 0.299 | 0.975 | 0.000 | 8.902 |
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 | 24 | 35 | 25 | 19 | 25 | 22 |
N.S. |
1 | 0.00 | 1.07 | 0.83 | 1.21 | 0.86 | 0.66 | 0.86 | 0.76 |
time (sec) |
N/A | 0.000 | 0.483 | 0.159 | 0.218 | 0.261 | 0.092 | 0.279 | 8.438 |
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 | 17 | 17 | 16 | 18 | 18 | 19 | 18 | 18 |
N.S. |
1 | 0.71 | 0.71 | 0.67 | 0.75 | 0.75 | 0.79 | 0.75 | 0.75 |
time (sec) |
N/A | 0.494 | 0.139 | 0.240 | 0.214 | 0.256 | 0.065 | 0.270 | 8.693 |
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 | 25 | 114 | 91 | 101 | 86 | 89 | 92 | 94 | 99 |
N.S. |
1 | 4.56 | 3.64 | 4.04 | 3.44 | 3.56 | 3.68 | 3.76 | 3.96 |
time (sec) |
N/A | 0.560 | 0.827 | 0.100 | 0.181 | 0.259 | 0.092 | 0.262 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 19 | 19 | 19 | 18 | 18 | 17 | 18 | 20 |
N.S. |
1 | 0.68 | 0.68 | 0.68 | 0.64 | 0.64 | 0.61 | 0.64 | 0.71 |
time (sec) |
N/A | 0.162 | 0.039 | 0.026 | 0.177 | 0.267 | 0.038 | 0.264 | 7.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 23 | 21 | 17 | 17 | 0 | 33 | 17 |
N.S. |
1 | 0.00 | 1.05 | 0.95 | 0.77 | 0.77 | 0.00 | 1.50 | 0.77 |
time (sec) |
N/A | 0.000 | 0.843 | 36.653 | 0.225 | 0.269 | 0.000 | 0.298 | 8.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 20 | 18 | 22 | 36 | 34 | 19 | 21 | 21 |
N.S. |
1 | 1.05 | 0.95 | 1.16 | 1.89 | 1.79 | 1.00 | 1.11 | 1.11 |
time (sec) |
N/A | 1.005 | 0.231 | 0.735 | 0.293 | 0.260 | 0.081 | 0.326 | 8.593 |
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 | 16 | 16 | 11 | 16 | 16 | 12 | 16 | 10 |
N.S. |
1 | 0.70 | 0.70 | 0.48 | 0.70 | 0.70 | 0.52 | 0.70 | 0.43 |
time (sec) |
N/A | 0.141 | 0.000 | 0.009 | 0.183 | 0.247 | 0.016 | 0.272 | 0.034 |
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 | 32 | 0 | 59 | 42 | 112 | 40 | 37 | 0 | 92 |
N.S. |
1 | 0.00 | 1.84 | 1.31 | 3.50 | 1.25 | 1.16 | 0.00 | 2.88 |
time (sec) |
N/A | 0.000 | 0.298 | 2.129 | 0.459 | 0.258 | 0.622 | 0.000 | 9.211 |
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 | 24 | 0 | 48 | 64 | 51 | 51 | 46 | 73 | 0 |
N.S. |
1 | 0.00 | 2.00 | 2.67 | 2.12 | 2.12 | 1.92 | 3.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.083 | 0.326 | 0.230 | 0.263 | 0.133 | 0.333 | 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 | 25 | 13 | 13 | 14 | 13 | 13 | 10 | 14 | 13 |
N.S. |
1 | 0.52 | 0.52 | 0.56 | 0.52 | 0.52 | 0.40 | 0.56 | 0.52 |
time (sec) |
N/A | 0.150 | 0.002 | 0.016 | 0.172 | 0.241 | 0.027 | 0.259 | 7.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 350 | 34 | 95 | 105 | 88 | 326 | 0 | 173 |
N.S. |
1 | 10.29 | 1.00 | 2.79 | 3.09 | 2.59 | 9.59 | 0.00 | 5.09 |
time (sec) |
N/A | 5.545 | 0.299 | 4.435 | 0.264 | 0.271 | 0.434 | 0.000 | 8.794 |
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 | 34 | 36 | 29 | 29 | 22 | 29 | 30 |
N.S. |
1 | 0.00 | 1.06 | 1.12 | 0.91 | 0.91 | 0.69 | 0.91 | 0.94 |
time (sec) |
N/A | 0.000 | 0.095 | 0.326 | 0.239 | 0.263 | 0.092 | 0.296 | 9.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 17 | 15 | 14 | 49 | 12 | 0 | 14 |
N.S. |
1 | 0.00 | 0.85 | 0.75 | 0.70 | 2.45 | 0.60 | 0.00 | 0.70 |
time (sec) |
N/A | 0.000 | 0.049 | 0.092 | 0.186 | 0.260 | 0.097 | 0.000 | 0.124 |
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 | 30 | 0 | 0 | 35 | 59 | 37 | 36 | 57 | 58 |
N.S. |
1 | 0.00 | 0.00 | 1.17 | 1.97 | 1.23 | 1.20 | 1.90 | 1.93 |
time (sec) |
N/A | 0.000 | 0.000 | 0.488 | 0.430 | 0.269 | 0.508 | 0.270 | 11.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 49 | 28 | 20 | 25 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.96 | 1.12 | 0.80 | 1.00 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.257 | 0.040 | 0.109 | 0.215 | 0.270 | 0.091 | 0.262 | 8.231 |
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 | 18 | 16 | 18 | 44 | 17 | 14 | 17 | 16 |
N.S. |
1 | 1.00 | 0.89 | 1.00 | 2.44 | 0.94 | 0.78 | 0.94 | 0.89 |
time (sec) |
N/A | 0.383 | 0.038 | 0.139 | 0.230 | 0.256 | 0.065 | 0.274 | 8.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 27 | 42 | 37 | 43 | 78 | 77 | 0 |
N.S. |
1 | 0.00 | 1.29 | 2.00 | 1.76 | 2.05 | 3.71 | 3.67 | 0.00 |
time (sec) |
N/A | 0.000 | 18.131 | 0.227 | 0.283 | 0.261 | 0.192 | 0.279 | 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 | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.118 | 0.000 | 0.006 | 0.198 | 0.241 | 0.037 | 0.258 | 0.008 |
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 | 26 | 25 | 32 | 24 | 22 | 25 | 25 |
N.S. |
1 | 1.39 | 1.13 | 1.09 | 1.39 | 1.04 | 0.96 | 1.09 | 1.09 |
time (sec) |
N/A | 0.298 | 0.102 | 0.382 | 0.289 | 0.259 | 0.114 | 0.306 | 8.399 |
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 | 32 | 35 | 30 | 30 | 36 | 30 | 33 |
N.S. |
1 | 0.00 | 1.10 | 1.21 | 1.03 | 1.03 | 1.24 | 1.03 | 1.14 |
time (sec) |
N/A | 0.000 | 0.162 | 0.930 | 0.292 | 0.277 | 1.085 | 30.184 | 8.946 |
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 | 28 | 30 | 24 | 21 | 156 | 37 | 34 | 74 | 81 |
N.S. |
1 | 1.07 | 0.86 | 0.75 | 5.57 | 1.32 | 1.21 | 2.64 | 2.89 |
time (sec) |
N/A | 0.409 | 0.031 | 0.113 | 0.349 | 0.281 | 0.061 | 0.259 | 0.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 40 | 18 | 18 | 23 | 21 | 22 | 23 | 17 |
N.S. |
1 | 1.25 | 0.56 | 0.56 | 0.72 | 0.66 | 0.69 | 0.72 | 0.53 |
time (sec) |
N/A | 0.265 | 0.035 | 0.127 | 0.178 | 0.259 | 0.410 | 0.259 | 0.140 |
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 | 29 | 85 | 55 | 75 | 78 | 60 | 87 |
N.S. |
1 | 0.00 | 1.12 | 3.27 | 2.12 | 2.88 | 3.00 | 2.31 | 3.35 |
time (sec) |
N/A | 0.000 | 0.531 | 1.724 | 0.309 | 0.267 | 0.205 | 0.317 | 8.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 40 | 27 | 25 | 24 | 24 | 24 | 24 | 28 |
N.S. |
1 | 1.33 | 0.90 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.93 |
time (sec) |
N/A | 0.168 | 0.008 | 0.045 | 0.198 | 0.268 | 0.056 | 0.253 | 8.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 24 | 25 | 80 | 32 | 22 | 36 | 25 |
N.S. |
1 | 0.00 | 0.86 | 0.89 | 2.86 | 1.14 | 0.79 | 1.29 | 0.89 |
time (sec) |
N/A | 0.000 | 0.762 | 1.713 | 0.312 | 0.256 | 0.100 | 0.276 | 8.121 |
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 | 34 | 36 | 25 | 22 | 22 | 20 | 22 | 23 |
N.S. |
1 | 1.31 | 1.38 | 0.96 | 0.85 | 0.85 | 0.77 | 0.85 | 0.88 |
time (sec) |
N/A | 0.867 | 0.066 | 0.235 | 0.329 | 0.257 | 0.068 | 0.257 | 0.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 85 | 45 | 39 | 42 | 48 | 39 | 71 | 39 |
N.S. |
1 | 2.93 | 1.55 | 1.34 | 1.45 | 1.66 | 1.34 | 2.45 | 1.34 |
time (sec) |
N/A | 0.369 | 0.033 | 0.142 | 0.185 | 0.264 | 1.729 | 0.261 | 0.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 35 | 26 | 0 | 32 | 20 | 58 | 20 |
N.S. |
1 | 0.00 | 1.46 | 1.08 | 0.00 | 1.33 | 0.83 | 2.42 | 0.83 |
time (sec) |
N/A | 0.000 | 0.195 | 0.098 | 0.000 | 0.256 | 0.106 | 0.259 | 8.441 |
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 | 20 | 22 | 17 | 22 | 16 | 22 | 16 | 11 |
N.S. |
1 | 1.33 | 1.47 | 1.13 | 1.47 | 1.07 | 1.47 | 1.07 | 0.73 |
time (sec) |
N/A | 0.148 | 0.007 | 0.026 | 0.168 | 0.270 | 0.043 | 0.259 | 7.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 20 | 17 | 19 | 19 | 18 | 15 | 16 | 18 |
N.S. |
1 | 0.87 | 0.74 | 0.83 | 0.83 | 0.78 | 0.65 | 0.70 | 0.78 |
time (sec) |
N/A | 0.336 | 0.335 | 0.147 | 0.235 | 0.260 | 0.119 | 0.325 | 8.345 |
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 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 0.46 | 0.46 | 0.54 | 0.46 | 0.46 | 0.38 | 0.46 | 0.46 |
time (sec) |
N/A | 0.127 | 0.000 | 0.031 | 0.190 | 0.257 | 0.031 | 0.267 | 8.313 |
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 | 21 | 0 | 136 | 85 | 87 | 135 | 95 | 84 | 132 |
N.S. |
1 | 0.00 | 6.48 | 4.05 | 4.14 | 6.43 | 4.52 | 4.00 | 6.29 |
time (sec) |
N/A | 0.000 | 5.156 | 85.990 | 0.276 | 0.300 | 0.552 | 0.855 | 8.636 |
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 | 20 | 14 | 14 | 20 | 20 | 15 | 20 | 16 |
N.S. |
1 | 0.95 | 0.67 | 0.67 | 0.95 | 0.95 | 0.71 | 0.95 | 0.76 |
time (sec) |
N/A | 0.146 | 0.003 | 0.022 | 0.172 | 0.251 | 0.020 | 0.261 | 8.394 |
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 | 34 | 27 | 25 | 30 | 24 | 26 | 24 | 24 |
N.S. |
1 | 1.62 | 1.29 | 1.19 | 1.43 | 1.14 | 1.24 | 1.14 | 1.14 |
time (sec) |
N/A | 0.210 | 0.070 | 0.045 | 0.190 | 0.268 | 0.087 | 0.263 | 0.107 |
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 | 23 | 0 | 28 | 36 | 25 | 37 | 31 | 37 | 37 |
N.S. |
1 | 0.00 | 1.22 | 1.57 | 1.09 | 1.61 | 1.35 | 1.61 | 1.61 |
time (sec) |
N/A | 0.000 | 0.092 | 0.521 | 0.222 | 0.278 | 0.192 | 0.347 | 8.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 27 | 149 | 27 | 46 | 42 | 182 |
N.S. |
1 | 0.00 | 0.00 | 1.00 | 5.52 | 1.00 | 1.70 | 1.56 | 6.74 |
time (sec) |
N/A | 0.000 | 0.000 | 19.125 | 0.457 | 0.272 | 1.050 | 1.259 | 8.692 |
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 | 37 | 0 | 34 | 34 | 96 | 96 | 42 | 104 | 45 |
N.S. |
1 | 0.00 | 0.92 | 0.92 | 2.59 | 2.59 | 1.14 | 2.81 | 1.22 |
time (sec) |
N/A | 0.000 | 5.489 | 0.174 | 0.242 | 0.260 | 0.104 | 0.271 | 8.651 |
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 | 28 | 0 | 30 | 32 | 56 | 56 | 26 | 75 | 29 |
N.S. |
1 | 0.00 | 1.07 | 1.14 | 2.00 | 2.00 | 0.93 | 2.68 | 1.04 |
time (sec) |
N/A | 0.000 | 0.096 | 11.725 | 0.273 | 0.280 | 1.225 | 1.146 | 8.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | A | C | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 75 | 59 | 68 | 120 | 34 | 44 | 44 | 28 |
N.S. |
1 | 2.34 | 1.84 | 2.12 | 3.75 | 1.06 | 1.38 | 1.38 | 0.88 |
time (sec) |
N/A | 0.322 | 0.065 | 0.183 | 0.270 | 0.257 | 0.107 | 0.265 | 8.368 |
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 | 16 | 35 | 28 | 22 | 31 | 24 | 24 | 25 | 23 |
N.S. |
1 | 2.19 | 1.75 | 1.38 | 1.94 | 1.50 | 1.50 | 1.56 | 1.44 |
time (sec) |
N/A | 0.207 | 0.148 | 0.051 | 0.189 | 0.250 | 0.061 | 0.263 | 0.097 |
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 | 23 | 31 | 27 | 72 | 55 | 55 | 88 | 74 | 74 |
N.S. |
1 | 1.35 | 1.17 | 3.13 | 2.39 | 2.39 | 3.83 | 3.22 | 3.22 |
time (sec) |
N/A | 0.655 | 0.054 | 0.230 | 0.232 | 0.281 | 0.217 | 0.364 | 10.297 |
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 | 32 | 28 | 28 | 27 | 35 | 28 |
N.S. |
1 | 0.00 | 1.18 | 1.45 | 1.27 | 1.27 | 1.23 | 1.59 | 1.27 |
time (sec) |
N/A | 0.000 | 0.272 | 0.366 | 0.205 | 0.261 | 0.168 | 0.267 | 8.747 |
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 | 30 | 27 | 21 | 20 | 22 | 19 | 22 | 21 |
N.S. |
1 | 1.11 | 1.00 | 0.78 | 0.74 | 0.81 | 0.70 | 0.81 | 0.78 |
time (sec) |
N/A | 0.351 | 0.652 | 0.149 | 0.259 | 0.255 | 0.162 | 0.267 | 8.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 21 | 25 | 29 | 27 | 34 | 26 | 24 | 0 |
N.S. |
1 | 1.05 | 1.25 | 1.45 | 1.35 | 1.70 | 1.30 | 1.20 | 0.00 |
time (sec) |
N/A | 0.249 | 0.041 | 0.184 | 0.177 | 0.240 | 0.096 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 20 | 0 | 19 | 0 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.95 | 0.00 | 0.95 | 0.95 |
time (sec) |
N/A | 0.499 | 0.246 | 0.285 | 0.000 | 0.263 | 0.000 | 0.365 | 9.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 55 | 26 | 26 | 66 | 25 | 22 | 25 | 25 |
N.S. |
1 | 1.83 | 0.87 | 0.87 | 2.20 | 0.83 | 0.73 | 0.83 | 0.83 |
time (sec) |
N/A | 0.306 | 0.271 | 0.037 | 0.181 | 0.272 | 0.045 | 0.260 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 57 | 28 | 25 | 30 | 39 | 53 | 25 | 24 |
N.S. |
1 | 2.04 | 1.00 | 0.89 | 1.07 | 1.39 | 1.89 | 0.89 | 0.86 |
time (sec) |
N/A | 0.870 | 0.349 | 2.778 | 0.318 | 0.270 | 0.391 | 0.285 | 9.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 33 | 22 | 27 | 35 | 38 | 20 | 41 | 32 |
N.S. |
1 | 1.18 | 0.79 | 0.96 | 1.25 | 1.36 | 0.71 | 1.46 | 1.14 |
time (sec) |
N/A | 1.775 | 3.181 | 0.096 | 0.215 | 0.254 | 0.057 | 0.262 | 8.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 51 | 45 | 37 | 39 | 41 | 56 | 39 | 39 |
N.S. |
1 | 2.43 | 2.14 | 1.76 | 1.86 | 1.95 | 2.67 | 1.86 | 1.86 |
time (sec) |
N/A | 0.168 | 0.027 | 0.063 | 0.179 | 0.252 | 0.683 | 0.261 | 0.058 |
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 | 19 | 19 | 23 | 28 | 17 | 23 | 23 |
N.S. |
1 | 1.17 | 0.79 | 0.79 | 0.96 | 1.17 | 0.71 | 0.96 | 0.96 |
time (sec) |
N/A | 0.194 | 0.012 | 0.195 | 0.184 | 0.239 | 0.068 | 0.266 | 8.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 27 | 21 | 531 | 531 | 275 | 713 | 0 |
N.S. |
1 | 0.00 | 1.04 | 0.81 | 20.42 | 20.42 | 10.58 | 27.42 | 0.00 |
time (sec) |
N/A | 0.000 | 20.209 | 0.564 | 1.195 | 0.284 | 0.682 | 0.769 | 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 | 22 | 76 | 84 | 59 | 100 | 51 | 61 | 58 | 62 |
N.S. |
1 | 3.45 | 3.82 | 2.68 | 4.55 | 2.32 | 2.77 | 2.64 | 2.82 |
time (sec) |
N/A | 0.386 | 0.074 | 0.027 | 0.182 | 0.246 | 0.117 | 0.264 | 8.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 27 | 27 | 26 | 53 | 21 | 32 | 27 | 25 |
N.S. |
1 | 1.59 | 1.59 | 1.53 | 3.12 | 1.24 | 1.88 | 1.59 | 1.47 |
time (sec) |
N/A | 0.549 | 0.064 | 0.158 | 0.208 | 0.247 | 0.236 | 0.269 | 9.333 |
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 | 1229 | 25 | 24 | 98 | 22 | 17 | 29 | 21 |
N.S. |
1 | 49.16 | 1.00 | 0.96 | 3.92 | 0.88 | 0.68 | 1.16 | 0.84 |
time (sec) |
N/A | 3.621 | 0.635 | 0.220 | 0.679 | 0.285 | 0.111 | 0.265 | 9.324 |
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 | 23 | 38 | 44 | 45 | 47 | 66 | 63 | 43 | 38 |
N.S. |
1 | 1.65 | 1.91 | 1.96 | 2.04 | 2.87 | 2.74 | 1.87 | 1.65 |
time (sec) |
N/A | 0.243 | 0.022 | 0.180 | 0.185 | 0.244 | 0.434 | 0.264 | 0.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 58 | 21 | 56 | 20 | 17 | 20 | 20 |
N.S. |
1 | 0.00 | 2.76 | 1.00 | 2.67 | 0.95 | 0.81 | 0.95 | 0.95 |
time (sec) |
N/A | 0.000 | 0.726 | 1.309 | 0.261 | 0.262 | 0.137 | 0.427 | 0.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 60 | 25 | 28 | 92 | 28 | 34 | 40 | 26 |
N.S. |
1 | 2.14 | 0.89 | 1.00 | 3.29 | 1.00 | 1.21 | 1.43 | 0.93 |
time (sec) |
N/A | 0.507 | 0.070 | 0.063 | 0.218 | 0.253 | 0.102 | 0.261 | 8.901 |
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 | 21 | 0 | 21 | 46 | 65 | 47 | 49 | 56 | 41 |
N.S. |
1 | 0.00 | 1.00 | 2.19 | 3.10 | 2.24 | 2.33 | 2.67 | 1.95 |
time (sec) |
N/A | 0.000 | 0.323 | 0.792 | 0.303 | 0.255 | 0.290 | 0.296 | 9.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 29 | 26 | 28 | 27 | 28 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.53 | 1.37 | 1.47 | 1.42 | 1.47 | 1.53 |
time (sec) |
N/A | 0.000 | 0.028 | 0.344 | 0.302 | 0.252 | 0.168 | 0.302 | 9.080 |
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 | 5 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 1.00 | 0.71 | 1.00 | 1.00 |
time (sec) |
N/A | 0.233 | 0.002 | 0.024 | 0.191 | 0.277 | 0.037 | 0.266 | 8.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 54 | 52 | 81 | 75 | 107 | 90 | 0 | 94 |
N.S. |
1 | 1.69 | 1.62 | 2.53 | 2.34 | 3.34 | 2.81 | 0.00 | 2.94 |
time (sec) |
N/A | 0.634 | 0.074 | 0.160 | 0.182 | 0.255 | 0.897 | 0.000 | 0.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 27 | 43 | 0 | 42 | 0 | 34 | 101 |
N.S. |
1 | 0.00 | 0.87 | 1.39 | 0.00 | 1.35 | 0.00 | 1.10 | 3.26 |
time (sec) |
N/A | 0.000 | 0.086 | 0.583 | 0.000 | 0.251 | 0.000 | 1.185 | 9.011 |
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 | 18 | 17 | 17 | 14 | 19 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.82 | 1.12 | 1.00 |
time (sec) |
N/A | 0.598 | 0.118 | 0.219 | 0.208 | 0.255 | 0.085 | 0.262 | 8.705 |
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 | 34 | 0 | 30 | 30 | 50 | 49 | 24 | 55 | 53 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 1.47 | 1.44 | 0.71 | 1.62 | 1.56 |
time (sec) |
N/A | 0.000 | 0.062 | 2.710 | 0.220 | 0.264 | 0.077 | 0.371 | 9.021 |
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 | 20 | 20 | 16 | 16 | 16 | 22 | 16 | 15 |
N.S. |
1 | 0.80 | 0.80 | 0.64 | 0.64 | 0.64 | 0.88 | 0.64 | 0.60 |
time (sec) |
N/A | 0.148 | 0.002 | 0.030 | 0.180 | 0.244 | 0.018 | 0.265 | 8.541 |
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 | 17 | 16 | 28 | 15 | 16 | 19 |
N.S. |
1 | 0.90 | 0.90 | 0.85 | 0.80 | 1.40 | 0.75 | 0.80 | 0.95 |
time (sec) |
N/A | 0.274 | 0.049 | 0.582 | 0.271 | 0.256 | 0.054 | 0.268 | 0.255 |
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 | 10 | 10 | 10 | 9 | 9 | 8 | 9 | 9 |
N.S. |
1 | 0.53 | 0.53 | 0.53 | 0.47 | 0.47 | 0.42 | 0.47 | 0.47 |
time (sec) |
N/A | 0.140 | 0.002 | 0.010 | 0.187 | 0.260 | 0.034 | 0.263 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 57 | 50 | 46 | 0 | 104 | 44 | 133 | 72 |
N.S. |
1 | 1.97 | 1.72 | 1.59 | 0.00 | 3.59 | 1.52 | 4.59 | 2.48 |
time (sec) |
N/A | 2.755 | 0.137 | 0.119 | 0.000 | 0.258 | 0.110 | 0.268 | 8.697 |
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 | 16 | 16 | 19 | 16 | 20 | 22 | 20 | 16 |
N.S. |
1 | 1.07 | 1.07 | 1.27 | 1.07 | 1.33 | 1.47 | 1.33 | 1.07 |
time (sec) |
N/A | 0.528 | 0.056 | 0.078 | 0.310 | 0.252 | 0.077 | 0.263 | 8.532 |
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 | 25 | 29 | 19 | 15 | 0 | 28 | 14 | 28 | 18 |
N.S. |
1 | 1.16 | 0.76 | 0.60 | 0.00 | 1.12 | 0.56 | 1.12 | 0.72 |
time (sec) |
N/A | 0.396 | 0.029 | 0.200 | 0.000 | 0.253 | 0.069 | 0.262 | 9.367 |
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 | 26 | 39 | 27 | 25 | 33 | 23 | 22 | 30 | 24 |
N.S. |
1 | 1.50 | 1.04 | 0.96 | 1.27 | 0.88 | 0.85 | 1.15 | 0.92 |
time (sec) |
N/A | 0.234 | 0.188 | 0.195 | 0.216 | 0.276 | 0.137 | 0.265 | 9.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 58 | 16 | 17 | 49 | 16 | 22 | 20 | 13 |
N.S. |
1 | 3.62 | 1.00 | 1.06 | 3.06 | 1.00 | 1.38 | 1.25 | 0.81 |
time (sec) |
N/A | 0.547 | 0.079 | 0.046 | 0.220 | 0.252 | 0.042 | 0.264 | 8.412 |
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 | 25 | 24 | 24 | 23 | 88 | 22 | 24 | 22 | 22 |
N.S. |
1 | 0.96 | 0.96 | 0.92 | 3.52 | 0.88 | 0.96 | 0.88 | 0.88 |
time (sec) |
N/A | 0.292 | 0.134 | 0.068 | 0.198 | 0.261 | 0.071 | 0.277 | 8.345 |
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 | 17 | 17 | 17 | 16 | 16 | 14 | 16 | 12 |
N.S. |
1 | 0.94 | 0.94 | 0.94 | 0.89 | 0.89 | 0.78 | 0.89 | 0.67 |
time (sec) |
N/A | 0.553 | 0.119 | 0.036 | 0.217 | 0.275 | 0.079 | 0.275 | 8.789 |
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 | 27 | 0 | 24 | 21 | 90 | 31 | 32 | 0 | 66 |
N.S. |
1 | 0.00 | 0.89 | 0.78 | 3.33 | 1.15 | 1.19 | 0.00 | 2.44 |
time (sec) |
N/A | 0.000 | 3.605 | 1.421 | 0.527 | 0.258 | 0.267 | 0.000 | 9.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 20 | 19 | 17 | 18 | 18 | 17 | 18 | 18 |
N.S. |
1 | 1.05 | 1.00 | 0.89 | 0.95 | 0.95 | 0.89 | 0.95 | 0.95 |
time (sec) |
N/A | 0.207 | 0.010 | 0.084 | 0.188 | 0.256 | 0.160 | 0.288 | 0.203 |
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 | 38 | 17 | 28 | 27 | 27 | 29 | 27 | 27 |
N.S. |
1 | 2.00 | 0.89 | 1.47 | 1.42 | 1.42 | 1.53 | 1.42 | 1.42 |
time (sec) |
N/A | 0.224 | 0.029 | 0.057 | 0.205 | 0.270 | 0.117 | 0.264 | 8.509 |
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 | 22 | 23 | 32 | 32 | 19 | 32 | 25 |
N.S. |
1 | 0.00 | 0.81 | 0.85 | 1.19 | 1.19 | 0.70 | 1.19 | 0.93 |
time (sec) |
N/A | 0.000 | 2.536 | 0.063 | 0.223 | 0.256 | 0.060 | 0.267 | 8.585 |
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 | 26 | 163 | 39 | 120 | 115 | 165 | 122 | 111 | 131 |
N.S. |
1 | 6.27 | 1.50 | 4.62 | 4.42 | 6.35 | 4.69 | 4.27 | 5.04 |
time (sec) |
N/A | 0.836 | 0.061 | 0.129 | 0.195 | 0.252 | 5.296 | 0.257 | 0.232 |
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 | 28 | 29 | 25 | 29 | 32 | 28 | 27 | 28 | 26 |
N.S. |
1 | 1.04 | 0.89 | 1.04 | 1.14 | 1.00 | 0.96 | 1.00 | 0.93 |
time (sec) |
N/A | 0.227 | 0.049 | 0.058 | 0.208 | 0.270 | 0.095 | 0.245 | 8.215 |
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 | 17 | 0 | 20 | 20 | 41 | 41 | 31 | 55 | 19 |
N.S. |
1 | 0.00 | 1.18 | 1.18 | 2.41 | 2.41 | 1.82 | 3.24 | 1.12 |
time (sec) |
N/A | 0.000 | 0.152 | 0.243 | 0.207 | 0.250 | 0.065 | 0.254 | 8.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | A | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 89 | 79 | 120 | 43 | 0 | 90 | 0 |
N.S. |
1 | 0.00 | 2.70 | 2.39 | 3.64 | 1.30 | 0.00 | 2.73 | 0.00 |
time (sec) |
N/A | 0.000 | 0.275 | 5.705 | 0.351 | 0.261 | 0.000 | 2.492 | 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 | 25 | 44 | 34 | 33 | 36 | 36 | 39 | 36 | 38 |
N.S. |
1 | 1.76 | 1.36 | 1.32 | 1.44 | 1.44 | 1.56 | 1.44 | 1.52 |
time (sec) |
N/A | 0.184 | 0.012 | 0.033 | 0.177 | 0.236 | 0.021 | 0.242 | 8.320 |
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 | 26 | 27 | 30 | 26 | 24 | 26 | 26 |
N.S. |
1 | 0.00 | 1.08 | 1.12 | 1.25 | 1.08 | 1.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.000 | 0.157 | 0.335 | 0.300 | 0.245 | 0.119 | 0.252 | 8.279 |
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 | 14 | 18 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.95 | 0.68 | 0.74 | 0.68 | 0.68 |
time (sec) |
N/A | 0.133 | 0.002 | 0.056 | 0.194 | 0.249 | 0.023 | 0.248 | 0.094 |
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 | 23 | 18 | 20 | 16 | 0 | 24 | 14 | 24 | 17 |
N.S. |
1 | 0.78 | 0.87 | 0.70 | 0.00 | 1.04 | 0.61 | 1.04 | 0.74 |
time (sec) |
N/A | 0.308 | 0.278 | 0.196 | 0.000 | 0.269 | 0.055 | 0.247 | 8.052 |