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 | 30 | 30 | 29 | 71 | 27 | 37 | 27 | 29 |
N.S. |
1 | 1.58 | 1.58 | 1.53 | 3.74 | 1.42 | 1.95 | 1.42 | 1.53 |
time (sec) |
N/A | 0.151 | 0.072 | 0.431 | 0.239 | 0.249 | 0.388 | 0.250 | 9.203 |
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 | 16 | 14 | 18 | 17 | 16 | 17 | 16 | 16 |
N.S. |
1 | 0.84 | 0.74 | 0.95 | 0.89 | 0.84 | 0.89 | 0.84 | 0.84 |
time (sec) |
N/A | 0.695 | 0.199 | 0.859 | 0.272 | 0.240 | 0.215 | 0.312 | 9.601 |
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 | 51 | 51 | 50 | 49 | 49 | 49 | 50 | 49 |
N.S. |
1 | 1.50 | 1.50 | 1.47 | 1.44 | 1.44 | 1.44 | 1.47 | 1.44 |
time (sec) |
N/A | 0.260 | 0.035 | 0.039 | 0.210 | 0.247 | 0.114 | 0.277 | 0.169 |
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 | 33 | 20 | 22 | 25 | 25 | 22 | 33 | 24 |
N.S. |
1 | 1.43 | 0.87 | 0.96 | 1.09 | 1.09 | 0.96 | 1.43 | 1.04 |
time (sec) |
N/A | 0.049 | 0.023 | 0.140 | 0.213 | 0.244 | 0.274 | 0.254 | 8.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 16 | 16 | 17 | 16 | 18 | 14 | 16 | 16 |
N.S. |
1 | 0.94 | 0.94 | 1.00 | 0.94 | 1.06 | 0.82 | 0.94 | 0.94 |
time (sec) |
N/A | 0.083 | 0.029 | 0.124 | 0.221 | 0.242 | 0.068 | 0.251 | 8.820 |
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 | 24 | 0 | 20 | 27 | 23 | 23 | 20 | 26 | 0 |
N.S. |
1 | 0.00 | 0.83 | 1.12 | 0.96 | 0.96 | 0.83 | 1.08 | 0.00 |
time (sec) |
N/A | 0.000 | 1.477 | 0.076 | 0.262 | 0.252 | 0.131 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 32 | 56 | 42 | 41 | 0 | 41 | 39 |
N.S. |
1 | 0.00 | 0.86 | 1.51 | 1.14 | 1.11 | 0.00 | 1.11 | 1.05 |
time (sec) |
N/A | 0.000 | 1.164 | 5.247 | 0.289 | 0.247 | 0.000 | 0.276 | 9.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 27 | 33 | 1153 | 31 | 44 | 49 | 27 |
N.S. |
1 | 0.00 | 1.12 | 1.38 | 48.04 | 1.29 | 1.83 | 2.04 | 1.12 |
time (sec) |
N/A | 0.000 | 0.586 | 0.250 | 2.848 | 0.249 | 0.143 | 0.277 | 9.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | F | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 69 | 52 | 38 | 0 | 42 | 41 | 0 | 40 |
N.S. |
1 | 2.76 | 2.08 | 1.52 | 0.00 | 1.68 | 1.64 | 0.00 | 1.60 |
time (sec) |
N/A | 0.092 | 0.103 | 0.283 | 0.000 | 0.255 | 0.131 | 0.000 | 8.820 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 22 | 16 | 90 | 244 | 54 | 71 | 61 | 63 |
N.S. |
1 | 1.16 | 0.84 | 4.74 | 12.84 | 2.84 | 3.74 | 3.21 | 3.32 |
time (sec) |
N/A | 0.074 | 0.023 | 0.520 | 0.297 | 0.245 | 0.111 | 0.272 | 0.786 |
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 | 35 | 21 | 29 | 22 | 26 | 27 | 28 | 25 |
N.S. |
1 | 1.67 | 1.00 | 1.38 | 1.05 | 1.24 | 1.29 | 1.33 | 1.19 |
time (sec) |
N/A | 0.116 | 0.129 | 0.166 | 0.334 | 0.250 | 0.128 | 0.284 | 9.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 33 | 106 | 40 | 41 | 0 | 110 |
N.S. |
1 | 0.00 | 0.93 | 1.22 | 3.93 | 1.48 | 1.52 | 0.00 | 4.07 |
time (sec) |
N/A | 0.000 | 0.148 | 8.719 | 0.374 | 0.246 | 0.422 | 0.000 | 9.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 23 | 53 | 31 | 34 | 72 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.00 | 2.30 | 1.35 | 1.48 | 3.13 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 2.154 | 0.319 | 0.249 | 0.328 | 0.396 | 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 | 21 | 20 | 23 | 22 | 36 | 21 | 17 | 21 | 19 |
N.S. |
1 | 0.95 | 1.10 | 1.05 | 1.71 | 1.00 | 0.81 | 1.00 | 0.90 |
time (sec) |
N/A | 0.117 | 0.036 | 0.410 | 0.222 | 0.251 | 0.075 | 0.253 | 8.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F(-1) | A | A | A | B | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 0 | 36 | 32 | 26 | 697 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 1.57 | 1.39 | 1.13 | 30.30 | 0.96 |
time (sec) |
N/A | 0.000 | 0.340 | 0.000 | 0.379 | 0.258 | 0.271 | 0.673 | 9.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 25 | 19 | 0 | 26 | 14 | 22 | 33 |
N.S. |
1 | 1.00 | 0.93 | 0.70 | 0.00 | 0.96 | 0.52 | 0.81 | 1.22 |
time (sec) |
N/A | 0.151 | 0.201 | 0.698 | 0.000 | 0.242 | 0.088 | 0.251 | 0.127 |
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 | 26 | 26 | 21 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.44 | 1.44 | 1.17 | 1.11 | 1.11 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.043 | 0.051 | 0.171 | 0.192 | 0.249 | 0.083 | 0.255 | 8.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 79 | 69 | 97 | 97 | 0 | 71 | 0 |
N.S. |
1 | 0.00 | 2.26 | 1.97 | 2.77 | 2.77 | 0.00 | 2.03 | 0.00 |
time (sec) |
N/A | 0.000 | 0.107 | 0.785 | 0.333 | 0.278 | 0.000 | 0.476 | 0.000 |
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 | 23 | 48 | 39 | 37 | 36 | 36 | 37 | 36 | 38 |
N.S. |
1 | 2.09 | 1.70 | 1.61 | 1.57 | 1.57 | 1.61 | 1.57 | 1.65 |
time (sec) |
N/A | 0.029 | 0.053 | 0.105 | 0.222 | 0.240 | 0.080 | 0.249 | 8.889 |
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 | 16 | 16 | 19 | 18 | 19 | 14 | 19 | 18 |
N.S. |
1 | 0.57 | 0.57 | 0.68 | 0.64 | 0.68 | 0.50 | 0.68 | 0.64 |
time (sec) |
N/A | 0.024 | 0.011 | 0.542 | 0.206 | 0.237 | 0.176 | 0.252 | 9.084 |
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 | 21 | 18 | 18 | 18 | 17 | 17 | 15 | 17 | 13 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 0.81 | 0.81 | 0.71 | 0.81 | 0.62 |
time (sec) |
N/A | 0.034 | 0.009 | 0.125 | 0.204 | 0.243 | 0.045 | 0.254 | 0.053 |
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 | 25 | 31 | 26 | 24 | 31 | 22 | 25 | 25 |
N.S. |
1 | 0.83 | 1.03 | 0.87 | 0.80 | 1.03 | 0.73 | 0.83 | 0.83 |
time (sec) |
N/A | 0.476 | 0.046 | 0.843 | 0.319 | 0.243 | 0.183 | 0.270 | 9.322 |
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 | 15 | 0 | 15 | 16 | 39 | 15 | 14 | 102 | 15 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 2.60 | 1.00 | 0.93 | 6.80 | 1.00 |
time (sec) |
N/A | 0.000 | 0.195 | 22.207 | 0.325 | 0.248 | 0.099 | 0.279 | 8.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 28 | 34 | 30 | 27 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.93 | 1.13 | 1.00 | 0.90 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 2.507 | 6.348 | 0.323 | 0.250 | 0.355 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 51 | 57 | 119 | 73 | 60 | 0 | 0 |
N.S. |
1 | 0.00 | 1.96 | 2.19 | 4.58 | 2.81 | 2.31 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.685 | 0.886 | 0.270 | 0.274 | 0.306 | 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 | 17 | 20 | 20 | 15 | 14 | 14 | 12 | 16 | 10 |
N.S. |
1 | 1.18 | 1.18 | 0.88 | 0.82 | 0.82 | 0.71 | 0.94 | 0.59 |
time (sec) |
N/A | 0.016 | 0.007 | 0.471 | 0.203 | 0.251 | 0.054 | 0.253 | 8.433 |
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 | 16 | 32 | 17 | 15 | 21 | 15 | 14 | 21 | 14 |
N.S. |
1 | 2.00 | 1.06 | 0.94 | 1.31 | 0.94 | 0.88 | 1.31 | 0.88 |
time (sec) |
N/A | 0.099 | 0.042 | 0.081 | 0.207 | 0.255 | 0.115 | 0.249 | 8.834 |
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 | 22 | 35 | 22 | 33 | 116 | 24 | 24 | 217 | 20 |
N.S. |
1 | 1.59 | 1.00 | 1.50 | 5.27 | 1.09 | 1.09 | 9.86 | 0.91 |
time (sec) |
N/A | 0.421 | 0.295 | 0.104 | 0.264 | 0.246 | 0.203 | 0.267 | 9.256 |
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 | 17 | 18 | 12 | 11 | 17 | 9 | 10 | 9 | 9 |
N.S. |
1 | 1.06 | 0.71 | 0.65 | 1.00 | 0.53 | 0.59 | 0.53 | 0.53 |
time (sec) |
N/A | 0.023 | 0.047 | 0.027 | 0.235 | 0.235 | 0.062 | 0.255 | 0.054 |
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 | 34 | 0 | 68 | 54 | 80 | 86 | 48 | 103 | 89 |
N.S. |
1 | 0.00 | 2.00 | 1.59 | 2.35 | 2.53 | 1.41 | 3.03 | 2.62 |
time (sec) |
N/A | 0.000 | 0.160 | 0.250 | 0.328 | 0.254 | 0.145 | 0.270 | 9.178 |
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 | 18 | 19 | 13 | 14 | 14 | 15 | 14 | 15 |
N.S. |
1 | 0.75 | 0.79 | 0.54 | 0.58 | 0.58 | 0.62 | 0.58 | 0.62 |
time (sec) |
N/A | 0.002 | 0.004 | 0.046 | 0.197 | 0.240 | 0.021 | 0.247 | 0.046 |
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 | 23 | 23 | 22 | 25 | 21 | 19 | 21 | 21 |
N.S. |
1 | 0.88 | 0.88 | 0.85 | 0.96 | 0.81 | 0.73 | 0.81 | 0.81 |
time (sec) |
N/A | 0.710 | 0.330 | 1.628 | 0.324 | 0.249 | 0.153 | 0.262 | 9.026 |
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 | 25 | 31 | 20 | 30 | 32 | 30 | 30 |
N.S. |
1 | 0.00 | 1.14 | 1.41 | 0.91 | 1.36 | 1.45 | 1.36 | 1.36 |
time (sec) |
N/A | 0.000 | 0.161 | 1.094 | 0.220 | 0.248 | 0.168 | 0.295 | 9.795 |
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 | 21 | 20 | 20 | 20 | 0 | 25 | 10 | 34 | 29 |
N.S. |
1 | 0.95 | 0.95 | 0.95 | 0.00 | 1.19 | 0.48 | 1.62 | 1.38 |
time (sec) |
N/A | 0.146 | 0.021 | 0.444 | 0.000 | 0.264 | 0.087 | 0.257 | 8.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 42 | 35 | 54 | 0 | 32 | 54 | 65 | 0 |
N.S. |
1 | 1.62 | 1.35 | 2.08 | 0.00 | 1.23 | 2.08 | 2.50 | 0.00 |
time (sec) |
N/A | 0.598 | 0.127 | 40.610 | 0.000 | 0.243 | 9.794 | 0.263 | 0.000 |
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 | 32 | 168 | 33 | 88 | 400 | 79 | 87 | 147 | 81 |
N.S. |
1 | 5.25 | 1.03 | 2.75 | 12.50 | 2.47 | 2.72 | 4.59 | 2.53 |
time (sec) |
N/A | 0.487 | 0.056 | 0.232 | 0.328 | 0.249 | 0.872 | 0.262 | 9.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 30 | 83 | 43 | 44 | 24 | 96 | 29 |
N.S. |
1 | 0.00 | 0.86 | 2.37 | 1.23 | 1.26 | 0.69 | 2.74 | 0.83 |
time (sec) |
N/A | 0.000 | 0.484 | 0.510 | 0.378 | 0.264 | 3.153 | 0.383 | 9.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 59 | 35 | 20 | 23 | 39 | 19 | 61 | 25 |
N.S. |
1 | 2.46 | 1.46 | 0.83 | 0.96 | 1.62 | 0.79 | 2.54 | 1.04 |
time (sec) |
N/A | 0.066 | 0.032 | 0.165 | 0.214 | 0.245 | 0.286 | 0.251 | 0.148 |
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 | 30 | 0 | 41 | 50 | 131 | 218 | 87 | 316 | 40 |
N.S. |
1 | 0.00 | 1.37 | 1.67 | 4.37 | 7.27 | 2.90 | 10.53 | 1.33 |
time (sec) |
N/A | 0.000 | 0.169 | 98.229 | 0.401 | 0.255 | 0.242 | 0.310 | 9.573 |
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 | 26 | 24 | 24 | 26 | 25 | 25 | 0 | 23 | 25 |
N.S. |
1 | 0.92 | 0.92 | 1.00 | 0.96 | 0.96 | 0.00 | 0.88 | 0.96 |
time (sec) |
N/A | 0.662 | 0.178 | 0.268 | 0.433 | 0.251 | 0.000 | 0.541 | 10.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 7 | 7 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 |
time (sec) |
N/A | 0.001 | 0.000 | 0.097 | 0.200 | 0.235 | 0.018 | 0.248 | 0.004 |
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 | 25 | 33 | 25 | 24 | 138 | 25 | 17 | 31 | 19 |
N.S. |
1 | 1.32 | 1.00 | 0.96 | 5.52 | 1.00 | 0.68 | 1.24 | 0.76 |
time (sec) |
N/A | 0.550 | 0.261 | 0.089 | 0.212 | 0.248 | 0.063 | 0.255 | 8.711 |
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 | 27 | 30 | 30 | 30 | 27 | 36 | 33 | 31 |
N.S. |
1 | 1.12 | 1.25 | 1.25 | 1.25 | 1.12 | 1.50 | 1.38 | 1.29 |
time (sec) |
N/A | 0.064 | 0.022 | 0.150 | 0.197 | 0.238 | 0.418 | 0.265 | 0.241 |
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 | 33 | 26 | 23 | 28 | 28 | 24 | 28 | 22 |
N.S. |
1 | 1.74 | 1.37 | 1.21 | 1.47 | 1.47 | 1.26 | 1.47 | 1.16 |
time (sec) |
N/A | 0.023 | 0.023 | 0.072 | 0.201 | 0.247 | 0.074 | 0.248 | 8.338 |
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 | 26 | 0 | 37 | 42 | 33 | 43 | 42 | 86 | 101 |
N.S. |
1 | 0.00 | 1.42 | 1.62 | 1.27 | 1.65 | 1.62 | 3.31 | 3.88 |
time (sec) |
N/A | 0.000 | 5.183 | 0.456 | 0.397 | 0.247 | 0.110 | 0.358 | 8.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 52 | 57 | 54 | 65 | 58 | 0 | 0 |
N.S. |
1 | 0.00 | 1.68 | 1.84 | 1.74 | 2.10 | 1.87 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.170 | 0.313 | 0.260 | 0.269 | 14.509 | 0.000 | 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 | 30 | 0 | 38 | 22 | 54 | 48 | 66 | 96 | 123 |
N.S. |
1 | 0.00 | 1.27 | 0.73 | 1.80 | 1.60 | 2.20 | 3.20 | 4.10 |
time (sec) |
N/A | 0.000 | 5.048 | 5.775 | 0.340 | 0.259 | 0.118 | 0.267 | 9.617 |
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 | 26 | 0 | 36 | 25 | 51 | 24 | 19 | 24 | 23 |
N.S. |
1 | 0.00 | 1.38 | 0.96 | 1.96 | 0.92 | 0.73 | 0.92 | 0.88 |
time (sec) |
N/A | 0.000 | 0.133 | 0.129 | 0.254 | 0.253 | 0.190 | 0.282 | 9.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 89 | 81 | 27 | 62 | 62 | 70 | 62 | 53 |
N.S. |
1 | 3.71 | 3.38 | 1.12 | 2.58 | 2.58 | 2.92 | 2.58 | 2.21 |
time (sec) |
N/A | 0.017 | 0.012 | 0.243 | 0.197 | 0.275 | 0.039 | 0.249 | 0.079 |
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 | 10 | 10 | 10 | 9 | 9 | 8 | 9 | 11 |
N.S. |
1 | 0.91 | 0.91 | 0.91 | 0.82 | 0.82 | 0.73 | 0.82 | 1.00 |
time (sec) |
N/A | 0.008 | 0.018 | 0.191 | 0.195 | 0.243 | 0.042 | 0.246 | 0.069 |
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 | 31 | 32 | 28 | 27 | 39 | 27 | 27 | 32 |
N.S. |
1 | 0.91 | 0.94 | 0.82 | 0.79 | 1.15 | 0.79 | 0.79 | 0.94 |
time (sec) |
N/A | 0.120 | 0.061 | 0.796 | 0.246 | 0.240 | 0.087 | 0.272 | 9.332 |
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 | 10 | 10 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 0.62 | 0.62 | 0.50 | 0.44 | 0.44 | 0.44 | 0.44 | 0.44 |
time (sec) |
N/A | 0.006 | 0.001 | 0.437 | 0.205 | 0.235 | 0.032 | 0.250 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 53 | 40 | 51 | 69 | 41 | 0 | 0 |
N.S. |
1 | 0.00 | 2.52 | 1.90 | 2.43 | 3.29 | 1.95 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.516 | 25.661 | 0.252 | 0.258 | 0.492 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 34 | 52 | 65 | 62 | 80 | 72 | 31 |
N.S. |
1 | 0.00 | 1.03 | 1.58 | 1.97 | 1.88 | 2.42 | 2.18 | 0.94 |
time (sec) |
N/A | 0.000 | 0.198 | 1.683 | 0.548 | 0.262 | 0.186 | 0.399 | 11.816 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 137 | 249 | 258 | 241 | 248 | 0 | 299 |
N.S. |
1 | 0.00 | 4.57 | 8.30 | 8.60 | 8.03 | 8.27 | 0.00 | 9.97 |
time (sec) |
N/A | 0.000 | 2.396 | 203.006 | 5.300 | 3.206 | 2.883 | 0.000 | 10.997 |
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 | 13 | 21 | 15 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 1.24 | 0.88 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.206 | 0.017 | 0.092 | 0.329 | 0.232 | 0.088 | 0.256 | 9.648 |
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 | 33 | 22 | 27 | 27 | 39 | 29 | 29 | 18 |
N.S. |
1 | 1.65 | 1.10 | 1.35 | 1.35 | 1.95 | 1.45 | 1.45 | 0.90 |
time (sec) |
N/A | 0.035 | 0.045 | 0.118 | 0.188 | 0.240 | 0.083 | 0.248 | 0.068 |
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 | 30 | 17 | 15 | 14 | 14 | 17 | 14 | 14 |
N.S. |
1 | 1.58 | 0.89 | 0.79 | 0.74 | 0.74 | 0.89 | 0.74 | 0.74 |
time (sec) |
N/A | 0.008 | 0.006 | 0.080 | 0.192 | 0.234 | 0.056 | 0.243 | 0.054 |
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 | 13 | 13 | 12 | 11 | 11 | 12 | 11 | 11 |
N.S. |
1 | 1.18 | 1.18 | 1.09 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 |
time (sec) |
N/A | 0.004 | 0.002 | 0.085 | 0.190 | 0.240 | 0.050 | 0.256 | 9.430 |
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 | 22 | 20 | 20 | 18 | 17 | 49 | 17 | 54 | 19 |
N.S. |
1 | 0.91 | 0.91 | 0.82 | 0.77 | 2.23 | 0.77 | 2.45 | 0.86 |
time (sec) |
N/A | 0.203 | 0.132 | 0.715 | 0.195 | 0.255 | 0.136 | 0.290 | 0.262 |
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 | 19 | 17 | 16 | 39 | 15 | 14 | 15 | 15 |
N.S. |
1 | 0.83 | 0.74 | 0.70 | 1.70 | 0.65 | 0.61 | 0.65 | 0.65 |
time (sec) |
N/A | 0.012 | 0.005 | 0.083 | 0.194 | 0.249 | 0.094 | 0.262 | 9.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 55 | 20 | 15 | 0 | 35 | 22 | 68 | 14 |
N.S. |
1 | 3.06 | 1.11 | 0.83 | 0.00 | 1.94 | 1.22 | 3.78 | 0.78 |
time (sec) |
N/A | 0.205 | 0.086 | 0.763 | 0.000 | 0.249 | 0.069 | 0.260 | 9.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 18 | 18 | 18 | 19 | 17 | 14 | 19 | 17 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 0.90 | 0.81 | 0.67 | 0.90 | 0.81 |
time (sec) |
N/A | 0.100 | 0.167 | 2.637 | 0.313 | 0.246 | 0.072 | 0.262 | 8.995 |
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 | 18 | 38 | 19 | 18 | 31 | 17 | 19 | 17 | 19 |
N.S. |
1 | 2.11 | 1.06 | 1.00 | 1.72 | 0.94 | 1.06 | 0.94 | 1.06 |
time (sec) |
N/A | 0.015 | 0.045 | 0.281 | 0.202 | 0.237 | 0.064 | 0.251 | 9.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | A | B | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 124 | 57 | 61 | 64 | 0 | 67 | 0 |
N.S. |
1 | 0.00 | 3.76 | 1.73 | 1.85 | 1.94 | 0.00 | 2.03 | 0.00 |
time (sec) |
N/A | 0.000 | 0.216 | 2.339 | 0.683 | 0.271 | 0.000 | 0.715 | 0.000 |
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 | 34 | 0 | 29 | 36 | 43 | 41 | 29 | 0 | 63 |
N.S. |
1 | 0.00 | 0.85 | 1.06 | 1.26 | 1.21 | 0.85 | 0.00 | 1.85 |
time (sec) |
N/A | 0.000 | 0.260 | 10.550 | 0.387 | 0.254 | 100.059 | 0.000 | 9.765 |
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 | 30 | 26 | 25 | 23 | 25 | 24 | 24 | 24 |
N.S. |
1 | 1.15 | 1.00 | 0.96 | 0.88 | 0.96 | 0.92 | 0.92 | 0.92 |
time (sec) |
N/A | 0.012 | 0.005 | 0.098 | 0.191 | 0.227 | 0.050 | 0.258 | 0.052 |
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 | 20 | 20 | 25 | 20 | 26 | 22 | 24 | 27 |
N.S. |
1 | 0.83 | 0.83 | 1.04 | 0.83 | 1.08 | 0.92 | 1.00 | 1.12 |
time (sec) |
N/A | 0.155 | 0.246 | 1.036 | 0.255 | 0.229 | 0.227 | 0.274 | 9.869 |
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 | 30 | 41 | 54 | 38 | 26 | 38 | 0 |
N.S. |
1 | 0.00 | 0.94 | 1.28 | 1.69 | 1.19 | 0.81 | 1.19 | 0.00 |
time (sec) |
N/A | 0.000 | 5.498 | 0.681 | 0.321 | 0.242 | 0.099 | 0.292 | 0.000 |
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 | 33 | 93 | 31 | 23 | 60 | 33 | 19 | 32 | 23 |
N.S. |
1 | 2.82 | 0.94 | 0.70 | 1.82 | 1.00 | 0.58 | 0.97 | 0.70 |
time (sec) |
N/A | 0.232 | 0.361 | 0.186 | 0.229 | 0.242 | 0.074 | 0.261 | 9.069 |
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 | 24 | 24 | 20 | 21 | 21 | 20 | 21 | 22 |
N.S. |
1 | 1.09 | 1.09 | 0.91 | 0.95 | 0.95 | 0.91 | 0.95 | 1.00 |
time (sec) |
N/A | 0.208 | 2.434 | 0.265 | 0.255 | 0.244 | 1.210 | 0.308 | 9.486 |
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 | 18 | 170 | 51 | 51 | 1044 | 50 | 51 | 50 | 50 |
N.S. |
1 | 9.44 | 2.83 | 2.83 | 58.00 | 2.78 | 2.83 | 2.78 | 2.78 |
time (sec) |
N/A | 1.295 | 0.127 | 0.480 | 0.227 | 0.250 | 0.102 | 0.284 | 9.239 |
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 | 41 | 36 | 37 | 52 | 37 | 37 | 39 | 32 |
N.S. |
1 | 1.46 | 1.29 | 1.32 | 1.86 | 1.32 | 1.32 | 1.39 | 1.14 |
time (sec) |
N/A | 0.080 | 1.190 | 0.084 | 0.241 | 0.252 | 0.095 | 0.259 | 0.089 |
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 | 21 | 22 | 30 | 18 | 0 | 19 | 22 | 19 | 17 |
N.S. |
1 | 1.05 | 1.43 | 0.86 | 0.00 | 0.90 | 1.05 | 0.90 | 0.81 |
time (sec) |
N/A | 0.087 | 0.028 | 0.398 | 0.000 | 0.246 | 0.093 | 0.253 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 23 | 27 | 25 | 25 | 34 | 42 | 25 |
N.S. |
1 | 0.00 | 1.05 | 1.23 | 1.14 | 1.14 | 1.55 | 1.91 | 1.14 |
time (sec) |
N/A | 0.000 | 1.407 | 16.314 | 0.325 | 0.250 | 16.399 | 1.067 | 9.745 |
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 | 75 | 75 | 59 | 59 | 59 | 71 | 59 | 63 |
N.S. |
1 | 2.42 | 2.42 | 1.90 | 1.90 | 1.90 | 2.29 | 1.90 | 2.03 |
time (sec) |
N/A | 4.793 | 0.242 | 0.678 | 0.705 | 0.252 | 0.244 | 0.388 | 10.041 |
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 | 4 | 4 | 5 | 4 | 4 | 5 | 5 | 4 |
N.S. |
1 | 0.22 | 0.22 | 0.28 | 0.22 | 0.22 | 0.28 | 0.28 | 0.22 |
time (sec) |
N/A | 0.000 | 0.000 | 0.010 | 0.190 | 0.224 | 0.018 | 0.250 | 0.013 |
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 | 9 | 9 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 0.36 | 0.36 | 0.28 | 0.24 | 0.24 | 0.20 | 0.24 | 0.24 |
time (sec) |
N/A | 0.002 | 0.001 | 0.108 | 0.194 | 0.250 | 0.032 | 0.250 | 0.031 |
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 | 20 | 200 | 20 | 18 | 216 | 17 | 17 | 17 | 17 |
N.S. |
1 | 10.00 | 1.00 | 0.90 | 10.80 | 0.85 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.320 | 0.052 | 0.454 | 0.632 | 0.252 | 0.089 | 0.313 | 0.247 |
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 | 22 | 18 | 18 | 17 | 18 | 18 | 17 | 19 | 18 |
N.S. |
1 | 0.82 | 0.82 | 0.77 | 0.82 | 0.82 | 0.77 | 0.86 | 0.82 |
time (sec) |
N/A | 0.012 | 0.009 | 0.098 | 0.195 | 0.240 | 0.056 | 0.256 | 0.105 |
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 | 21 | 0 | 21 | 23 | 32 | 25 | 24 | 555 | 25 |
N.S. |
1 | 0.00 | 1.00 | 1.10 | 1.52 | 1.19 | 1.14 | 26.43 | 1.19 |
time (sec) |
N/A | 0.000 | 0.646 | 0.751 | 0.258 | 0.251 | 0.075 | 0.272 | 10.838 |
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 | 27 | 0 | 24 | 24 | 49 | 49 | 54 | 51 | 0 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 1.81 | 1.81 | 2.00 | 1.89 | 0.00 |
time (sec) |
N/A | 0.000 | 0.342 | 0.448 | 0.236 | 0.242 | 0.172 | 0.271 | 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 | 20 | 0 | 19 | 23 | 26 | 26 | 20 | 29 | 25 |
N.S. |
1 | 0.00 | 0.95 | 1.15 | 1.30 | 1.30 | 1.00 | 1.45 | 1.25 |
time (sec) |
N/A | 0.000 | 0.125 | 5.504 | 0.225 | 0.253 | 0.084 | 0.263 | 10.073 |
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 | 27 | 0 | 22 | 32 | 26 | 30 | 26 | 61 | 39 |
N.S. |
1 | 0.00 | 0.81 | 1.19 | 0.96 | 1.11 | 0.96 | 2.26 | 1.44 |
time (sec) |
N/A | 0.000 | 0.784 | 0.295 | 0.319 | 0.253 | 0.249 | 0.269 | 10.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 43 | 0 | 40 | 20 | 46 | 42 |
N.S. |
1 | 0.00 | 1.00 | 1.72 | 0.00 | 1.60 | 0.80 | 1.84 | 1.68 |
time (sec) |
N/A | 0.000 | 0.110 | 0.215 | 0.000 | 0.259 | 0.137 | 0.298 | 10.087 |
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 | 28 | 154 | 26 | 27 | 26 | 37 | 27 | 0 | 29 |
N.S. |
1 | 5.50 | 0.93 | 0.96 | 0.93 | 1.32 | 0.96 | 0.00 | 1.04 |
time (sec) |
N/A | 0.223 | 0.251 | 8.308 | 0.266 | 0.250 | 54.402 | 0.000 | 11.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 46 | 31 | 25 | 23 | 24 | 22 | 29 | 25 |
N.S. |
1 | 1.48 | 1.00 | 0.81 | 0.74 | 0.77 | 0.71 | 0.94 | 0.81 |
time (sec) |
N/A | 4.911 | 0.305 | 0.224 | 0.286 | 0.278 | 0.093 | 0.280 | 10.656 |
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 | 17 | 15 | 15 | 14 | 18 | 12 | 15 | 14 |
N.S. |
1 | 0.74 | 0.65 | 0.65 | 0.61 | 0.78 | 0.52 | 0.65 | 0.61 |
time (sec) |
N/A | 0.020 | 0.013 | 0.114 | 0.187 | 0.248 | 0.094 | 0.252 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 22 | 21 | 0 | 20 | 19 | 37 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.84 | 0.00 | 0.80 | 0.76 | 1.48 | 0.80 |
time (sec) |
N/A | 0.000 | 2.503 | 0.202 | 0.000 | 0.259 | 0.387 | 0.321 | 9.938 |
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 | 18 | 18 | 19 | 18 | 21 | 22 | 21 | 19 |
N.S. |
1 | 0.72 | 0.72 | 0.76 | 0.72 | 0.84 | 0.88 | 0.84 | 0.76 |
time (sec) |
N/A | 0.024 | 0.045 | 0.145 | 0.206 | 0.250 | 0.060 | 0.258 | 10.019 |
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 | 27 | 26 | 24 | 28 | 24 | 31 | 28 |
N.S. |
1 | 0.00 | 1.04 | 1.00 | 0.92 | 1.08 | 0.92 | 1.19 | 1.08 |
time (sec) |
N/A | 0.000 | 0.132 | 159.300 | 0.405 | 0.257 | 20.952 | 0.800 | 11.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 71 | 20 | 41 | 98 | 147 | 143 | 38 | 120 |
N.S. |
1 | 3.23 | 0.91 | 1.86 | 4.45 | 6.68 | 6.50 | 1.73 | 5.45 |
time (sec) |
N/A | 0.133 | 0.028 | 0.462 | 0.211 | 0.276 | 3.282 | 0.265 | 10.979 |
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 | 27 | 26 | 33 | 27 | 26 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.23 | 1.18 | 1.50 | 1.23 | 1.18 | 1.05 |
time (sec) |
N/A | 0.015 | 0.008 | 0.504 | 0.187 | 0.258 | 0.077 | 0.255 | 11.231 |
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 | 24 | 31 | 25 | 22 | 60 | 23 | 22 | 33 | 26 |
N.S. |
1 | 1.29 | 1.04 | 0.92 | 2.50 | 0.96 | 0.92 | 1.38 | 1.08 |
time (sec) |
N/A | 0.210 | 0.211 | 0.386 | 0.235 | 0.260 | 0.059 | 0.265 | 10.174 |
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 | 19 | 19 | 18 | 19 | 17 | 15 | 19 | 17 |
N.S. |
1 | 0.95 | 0.95 | 0.90 | 0.95 | 0.85 | 0.75 | 0.95 | 0.85 |
time (sec) |
N/A | 0.167 | 0.110 | 0.079 | 0.230 | 0.253 | 0.067 | 0.256 | 10.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 20 | 18 | 17 | 15 | 16 | 15 | 22 | 17 |
N.S. |
1 | 0.80 | 0.72 | 0.68 | 0.60 | 0.64 | 0.60 | 0.88 | 0.68 |
time (sec) |
N/A | 0.175 | 0.206 | 6.551 | 0.218 | 0.246 | 0.062 | 0.264 | 9.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 943 | 28 | 27 | 42 | 40 | 24 | 156 | 26 |
N.S. |
1 | 33.68 | 1.00 | 0.96 | 1.50 | 1.43 | 0.86 | 5.57 | 0.93 |
time (sec) |
N/A | 1.220 | 0.527 | 0.827 | 0.255 | 0.252 | 0.126 | 0.344 | 10.693 |
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 | 21 | 62 | 37 | 26 | 24 | 23 | 26 | 24 | 28 |
N.S. |
1 | 2.95 | 1.76 | 1.24 | 1.14 | 1.10 | 1.24 | 1.14 | 1.33 |
time (sec) |
N/A | 0.097 | 0.581 | 0.184 | 0.399 | 0.255 | 0.073 | 0.273 | 0.130 |
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 | 9 | 8 | 8 | 8 | 7 | 8 | 8 | 25 | 8 |
N.S. |
1 | 0.89 | 0.89 | 0.89 | 0.78 | 0.89 | 0.89 | 2.78 | 0.89 |
time (sec) |
N/A | 0.011 | 0.062 | 0.126 | 0.198 | 0.256 | 0.051 | 0.260 | 10.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 58 | 65 | 65 | 94 | 60 | 0 | 62 |
N.S. |
1 | 0.00 | 1.76 | 1.97 | 1.97 | 2.85 | 1.82 | 0.00 | 1.88 |
time (sec) |
N/A | 0.000 | 0.600 | 0.444 | 0.402 | 0.258 | 0.165 | 0.000 | 9.729 |