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 | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 711 | 207 | 603 | 610 | 374 | 442 | 627 | 547 | 309 |
N.S. |
1 | 24.52 | 7.14 | 20.79 | 21.03 | 12.90 | 15.24 | 21.62 | 18.86 | 10.66 |
time (sec) |
N/A | 0.982 | 0.058 | 0.122 | 0.049 | 0.091 | 0.430 | 0.129 | 0.255 | 3.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 27 | 30 | 30 | 24 | 29 | 30 | 28 |
N.S. |
1 | 0.00 | 1.00 | 0.90 | 1.00 | 1.00 | 0.80 | 0.97 | 1.00 | 0.93 |
time (sec) |
N/A | 0.000 | 3.444 | 0.132 | 0.070 | 0.082 | 0.134 | 0.120 | 0.263 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 149 | 24 | 24 | 157 | 32 | 0 | 0 | 30 | 71 |
N.S. |
1 | 5.73 | 0.92 | 0.92 | 6.04 | 1.23 | 0.00 | 0.00 | 1.15 | 2.73 |
time (sec) |
N/A | 1.750 | 0.065 | 88.858 | 0.306 | 0.076 | 0.000 | 0.000 | 0.260 | 2.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 16 | 15 | 17 | 14 | 17 | 16 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.83 | 0.94 | 0.78 | 0.94 | 0.89 | 0.94 |
time (sec) |
N/A | 0.302 | 0.004 | 0.260 | 0.036 | 0.080 | 0.083 | 0.113 | 0.217 | 2.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 13 | 13 | 27 | 12 | 10 | 12 | 10 | 10 |
N.S. |
1 | 1.00 | 0.65 | 0.65 | 1.35 | 0.60 | 0.50 | 0.60 | 0.50 | 0.50 |
time (sec) |
N/A | 0.329 | 0.007 | 0.227 | 0.046 | 0.076 | 0.118 | 0.113 | 0.218 | 2.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 47 | 44 | 65 | 68 | 71 | 82 | 88 | 0 |
N.S. |
1 | 0.00 | 1.57 | 1.47 | 2.17 | 2.27 | 2.37 | 2.73 | 2.93 | 0.00 |
time (sec) |
N/A | 0.000 | 0.122 | 55.962 | 0.146 | 0.093 | 0.645 | 0.226 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 |
time (sec) |
N/A | 0.130 | 0.000 | 0.023 | 0.029 | 0.083 | 0.097 | 0.117 | 0.230 | 0.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 29 | 73 | 28 | 100 | 47 | 98 | 0 |
N.S. |
1 | 0.00 | 0.97 | 1.00 | 2.52 | 0.97 | 3.45 | 1.62 | 3.38 | 0.00 |
time (sec) |
N/A | 0.000 | 0.244 | 1.140 | 0.134 | 0.088 | 0.587 | 0.422 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 7 | 7 | 7 | 6 | 6 | 3 | 6 | 7 | 6 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 0.67 | 0.67 | 0.33 | 0.67 | 0.78 | 0.67 |
time (sec) |
N/A | 0.241 | 0.001 | 0.040 | 0.026 | 0.070 | 0.056 | 0.107 | 0.238 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 13 | 12 | 12 | 19 | 14 | 8 | 11 | 15 | 9 |
N.S. |
1 | 0.65 | 0.60 | 0.60 | 0.95 | 0.70 | 0.40 | 0.55 | 0.75 | 0.45 |
time (sec) |
N/A | 0.514 | 0.027 | 0.117 | 0.033 | 0.077 | 0.119 | 0.112 | 0.222 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 23 | 23 | 38 | 37 | 55 | 0 | 0 | 44 | 38 |
N.S. |
1 | 0.92 | 0.92 | 1.52 | 1.48 | 2.20 | 0.00 | 0.00 | 1.76 | 1.52 |
time (sec) |
N/A | 0.949 | 0.047 | 0.499 | 0.089 | 0.085 | 0.000 | 0.000 | 0.242 | 2.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 220 | 129 | 303 | 249 | 275 | 326 | 423 | 489 | 205 |
N.S. |
1 | 7.86 | 4.61 | 10.82 | 8.89 | 9.82 | 11.64 | 15.11 | 17.46 | 7.32 |
time (sec) |
N/A | 2.095 | 0.668 | 1.882 | 0.161 | 0.096 | 0.217 | 0.346 | 0.226 | 2.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 127 | 25 | 21 | 22 | 39 | 26 | 0 | 65 | 22 |
N.S. |
1 | 5.08 | 1.00 | 0.84 | 0.88 | 1.56 | 1.04 | 0.00 | 2.60 | 0.88 |
time (sec) |
N/A | 0.748 | 0.429 | 49.931 | 0.240 | 0.084 | 4.565 | 0.000 | 200.023 | 2.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 21 | 20 | 20 | 19 | 20 | 27 | 21 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.91 | 0.91 | 0.86 | 0.91 | 1.23 | 0.95 |
time (sec) |
N/A | 0.000 | 0.033 | 0.065 | 0.038 | 0.103 | 0.117 | 0.116 | 0.248 | 2.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 55 | 64 | 32 | 53 | 55 | 56 | 58 | 66 | 73 |
N.S. |
1 | 2.50 | 2.91 | 1.45 | 2.41 | 2.50 | 2.55 | 2.64 | 3.00 | 3.32 |
time (sec) |
N/A | 0.320 | 0.023 | 0.245 | 0.028 | 0.081 | 0.228 | 0.112 | 0.219 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 103 | 16 | 34 | 33 | 33 | 37 | 33 | 45 | 36 |
N.S. |
1 | 5.72 | 0.89 | 1.89 | 1.83 | 1.83 | 2.06 | 1.83 | 2.50 | 2.00 |
time (sec) |
N/A | 0.336 | 1.039 | 0.388 | 0.158 | 0.082 | 0.091 | 0.148 | 0.224 | 2.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 20 | 21 | 20 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.18 | 1.24 | 1.18 | 1.18 | 1.12 | 1.18 | 1.18 | 1.18 |
time (sec) |
N/A | 0.570 | 0.218 | 0.174 | 0.068 | 0.082 | 0.124 | 0.126 | 0.227 | 0.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 8 | 6 |
N.S. |
1 | 0.73 | 0.73 | 0.64 | 0.55 | 0.55 | 0.64 | 0.55 | 0.73 | 0.55 |
time (sec) |
N/A | 0.132 | 0.000 | 0.014 | 0.033 | 0.073 | 0.016 | 0.113 | 0.234 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 10 | 9 | 9 | 8 | 9 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 0.82 | 0.73 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.164 | 0.004 | 0.109 | 0.036 | 0.081 | 0.053 | 0.116 | 0.241 | 2.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 28 | 30 | 30 | 30 | 26 | 30 | 29 | 29 |
N.S. |
1 | 0.00 | 1.22 | 1.30 | 1.30 | 1.30 | 1.13 | 1.30 | 1.26 | 1.26 |
time (sec) |
N/A | 0.000 | 0.010 | 0.078 | 0.028 | 0.070 | 0.328 | 0.116 | 0.289 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 17 | 16 | 15 | 16 | 17 | 16 | 17 | 16 |
N.S. |
1 | 1.00 | 0.89 | 0.84 | 0.79 | 0.84 | 0.89 | 0.84 | 0.89 | 0.84 |
time (sec) |
N/A | 0.296 | 0.018 | 0.119 | 0.178 | 0.072 | 0.103 | 0.112 | 0.255 | 2.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 15 | 15 | 12 | 16 | 22 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.00 | 1.00 | 0.80 | 1.07 | 1.47 | 0.73 |
time (sec) |
N/A | 0.193 | 0.004 | 0.125 | 0.027 | 0.070 | 0.051 | 0.115 | 0.270 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 33 | 25 | 33 | 24 | 33 | 65 | 213 |
N.S. |
1 | 0.00 | 0.93 | 1.22 | 0.93 | 1.22 | 0.89 | 1.22 | 2.41 | 7.89 |
time (sec) |
N/A | 0.000 | 0.051 | 2.378 | 0.095 | 0.084 | 0.132 | 0.310 | 0.219 | 11.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 11 | 11 | 9 | 9 | 9 | 10 | 9 | 8 | 8 |
N.S. |
1 | 0.52 | 0.52 | 0.43 | 0.43 | 0.43 | 0.48 | 0.43 | 0.38 | 0.38 |
time (sec) |
N/A | 0.140 | 0.001 | 0.018 | 0.037 | 0.066 | 0.019 | 0.111 | 0.247 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 23 | 26 | 23 | 22 | 22 | 17 | 22 | 23 | 22 |
N.S. |
1 | 0.96 | 1.08 | 0.96 | 0.92 | 0.92 | 0.71 | 0.92 | 0.96 | 0.92 |
time (sec) |
N/A | 0.591 | 0.043 | 0.346 | 0.033 | 0.078 | 0.113 | 0.121 | 0.235 | 2.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 46 | 42 | 82 | 46 | 45 | 0 | 45 |
N.S. |
1 | 0.00 | 0.00 | 1.44 | 1.31 | 2.56 | 1.44 | 1.41 | 0.00 | 1.41 |
time (sec) |
N/A | 0.000 | 0.000 | 11.043 | 0.420 | 0.106 | 0.434 | 0.152 | 122.772 | 3.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 66 | 59 | 56 | 0 | 77 | 48 | 105 | 99 | 71 |
N.S. |
1 | 2.06 | 1.84 | 1.75 | 0.00 | 2.41 | 1.50 | 3.28 | 3.09 | 2.22 |
time (sec) |
N/A | 1.290 | 0.043 | 1.694 | 0.000 | 0.076 | 0.114 | 0.142 | 0.438 | 2.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 20 | 23 | 63 | 26 | 24 | 48 | 27 | 49 |
N.S. |
1 | 0.00 | 0.74 | 0.85 | 2.33 | 0.96 | 0.89 | 1.78 | 1.00 | 1.81 |
time (sec) |
N/A | 0.000 | 0.136 | 1.086 | 0.155 | 0.073 | 0.075 | 0.133 | 0.475 | 2.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 29 | 28 | 28 | 35 | 28 | 27 | 35 | 30 | 28 |
N.S. |
1 | 1.12 | 1.08 | 1.08 | 1.35 | 1.08 | 1.04 | 1.35 | 1.15 | 1.08 |
time (sec) |
N/A | 19.373 | 0.082 | 19.806 | 0.211 | 0.091 | 13.790 | 0.350 | 0.508 | 3.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 238 | 28 | 54 | 80 | 45 | 51 | 38 | 103 | 34 |
N.S. |
1 | 8.50 | 1.00 | 1.93 | 2.86 | 1.61 | 1.82 | 1.36 | 3.68 | 1.21 |
time (sec) |
N/A | 1.371 | 0.064 | 0.922 | 0.161 | 0.079 | 0.352 | 0.122 | 0.508 | 2.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | F(-2) | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 63 | 47 | 70 | 51 | 0 | 51 | 53 | 0 |
N.S. |
1 | 0.00 | 2.17 | 1.62 | 2.41 | 1.76 | 0.00 | 1.76 | 1.83 | 0.00 |
time (sec) |
N/A | 0.000 | 0.211 | 271.266 | 0.118 | 0.123 | 0.000 | 0.289 | 0.482 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | F | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 152 | 37 | 0 | 24 | 37 | 0 | 106 | 24 |
N.S. |
1 | 0.00 | 4.11 | 1.00 | 0.00 | 0.65 | 1.00 | 0.00 | 2.86 | 0.65 |
time (sec) |
N/A | 0.000 | 0.143 | 1.335 | 0.000 | 0.089 | 0.960 | 0.000 | 200.024 | 0.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 37 | 32 | 44 | 71 | 49 | 70 | 96 | 34 |
N.S. |
1 | 0.00 | 1.42 | 1.23 | 1.69 | 2.73 | 1.88 | 2.69 | 3.69 | 1.31 |
time (sec) |
N/A | 0.000 | 11.876 | 3.254 | 0.140 | 0.112 | 0.103 | 0.217 | 0.208 | 2.551 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 253 | 45 | 77 | 431 | 60 | 129 | 142 | 88 | 140 |
N.S. |
1 | 9.04 | 1.61 | 2.75 | 15.39 | 2.14 | 4.61 | 5.07 | 3.14 | 5.00 |
time (sec) |
N/A | 2.793 | 0.638 | 14.844 | 0.150 | 0.076 | 13.182 | 0.123 | 0.193 | 3.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 17 | 23 | 18 | 15 | 15 | 19 | 15 | 17 | 15 |
N.S. |
1 | 1.31 | 1.77 | 1.38 | 1.15 | 1.15 | 1.46 | 1.15 | 1.31 | 1.15 |
time (sec) |
N/A | 0.163 | 0.003 | 0.067 | 0.035 | 0.076 | 0.070 | 0.118 | 0.207 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | B | A | F(-1) | F | F | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 0 | 29 | 45 | 26 | 0 | 0 | 93 | 25 |
N.S. |
1 | 1.18 | 0.00 | 1.32 | 2.05 | 1.18 | 0.00 | 0.00 | 4.23 | 1.14 |
time (sec) |
N/A | 0.774 | 0.000 | 0.901 | 0.260 | 0.108 | 0.000 | 0.000 | 200.028 | 2.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 8 | 7 | 7 | 14 | 8 | 8 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.88 | 0.88 | 1.75 | 1.00 | 1.00 | 0.88 |
time (sec) |
N/A | 0.210 | 0.001 | 0.042 | 0.025 | 0.076 | 0.028 | 0.116 | 0.190 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 30 | 26 | 20 | 26 | 19 | 22 | 18 | 41 | 18 |
N.S. |
1 | 1.11 | 0.96 | 0.74 | 0.96 | 0.70 | 0.81 | 0.67 | 1.52 | 0.67 |
time (sec) |
N/A | 0.537 | 0.128 | 0.155 | 0.100 | 0.089 | 0.125 | 0.123 | 0.186 | 2.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 25 | 22 | 16 | 25 | 25 | 31 | 25 | 32 | 15 |
N.S. |
1 | 1.39 | 1.22 | 0.89 | 1.39 | 1.39 | 1.72 | 1.39 | 1.78 | 0.83 |
time (sec) |
N/A | 0.258 | 0.002 | 0.061 | 0.040 | 0.067 | 0.024 | 0.118 | 0.177 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 19 | 29 | 16 | 28 | 26 | 30 | 23 | 39 |
N.S. |
1 | 0.00 | 0.79 | 1.21 | 0.67 | 1.17 | 1.08 | 1.25 | 0.96 | 1.62 |
time (sec) |
N/A | 0.000 | 0.398 | 0.007 | 0.100 | 0.080 | 99.272 | 0.179 | 0.189 | 2.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 30 | 28 | 105 | 30 | 26 | 30 | 32 | 35 |
N.S. |
1 | 0.00 | 1.07 | 1.00 | 3.75 | 1.07 | 0.93 | 1.07 | 1.14 | 1.25 |
time (sec) |
N/A | 0.000 | 0.064 | 1.066 | 0.130 | 0.081 | 0.132 | 0.198 | 0.205 | 2.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 23 | 28 | 34 | 27 | 31 | 34 | 28 | 35 |
N.S. |
1 | 0.00 | 0.92 | 1.12 | 1.36 | 1.08 | 1.24 | 1.36 | 1.12 | 1.40 |
time (sec) |
N/A | 0.000 | 0.255 | 0.262 | 0.186 | 0.084 | 0.095 | 0.127 | 0.204 | 2.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 37 | 37 | 37 | 37 | 35 | 34 | 35 | 37 | 36 |
N.S. |
1 | 1.61 | 1.61 | 1.61 | 1.61 | 1.52 | 1.48 | 1.52 | 1.61 | 1.57 |
time (sec) |
N/A | 0.605 | 0.071 | 0.125 | 0.083 | 0.093 | 0.126 | 0.123 | 0.183 | 2.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 61 | 22 | 56 | 53 | 53 | 60 | 53 | 54 | 20 |
N.S. |
1 | 2.35 | 0.85 | 2.15 | 2.04 | 2.04 | 2.31 | 2.04 | 2.08 | 0.77 |
time (sec) |
N/A | 0.455 | 2.377 | 0.595 | 0.028 | 0.079 | 0.071 | 0.103 | 0.201 | 2.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 36 | 102 | 24 | 23 | 23 | 24 | 24 | 24 | 23 |
N.S. |
1 | 1.44 | 4.08 | 0.96 | 0.92 | 0.92 | 0.96 | 0.96 | 0.96 | 0.92 |
time (sec) |
N/A | 0.326 | 0.016 | 0.129 | 0.040 | 0.077 | 0.699 | 0.113 | 0.203 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 20 | 20 | 25 | 77 | 31 | 42 | 72 | 26 | 16 |
N.S. |
1 | 0.91 | 0.91 | 1.14 | 3.50 | 1.41 | 1.91 | 3.27 | 1.18 | 0.73 |
time (sec) |
N/A | 0.177 | 0.004 | 0.083 | 0.028 | 0.083 | 0.085 | 0.112 | 0.204 | 2.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 29 | 29 | 34 | 52 | 59 | 41 | 74 | 71 | 38 |
N.S. |
1 | 0.94 | 0.94 | 1.10 | 1.68 | 1.90 | 1.32 | 2.39 | 2.29 | 1.23 |
time (sec) |
N/A | 3.832 | 0.244 | 0.950 | 0.195 | 0.091 | 0.278 | 0.122 | 0.201 | 2.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 96 | 96 | 120 | 90 | 100 | 0 | 201 | 99 |
N.S. |
1 | 0.00 | 3.43 | 3.43 | 4.29 | 3.21 | 3.57 | 0.00 | 7.18 | 3.54 |
time (sec) |
N/A | 0.000 | 0.112 | 0.455 | 0.141 | 0.091 | 0.195 | 0.000 | 0.229 | 2.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 67 | 102 | 22 | 26 | 20 | 24 | 29 | 22 | 21 |
N.S. |
1 | 2.39 | 3.64 | 0.79 | 0.93 | 0.71 | 0.86 | 1.04 | 0.79 | 0.75 |
time (sec) |
N/A | 0.639 | 0.029 | 1.116 | 0.165 | 0.084 | 0.163 | 0.116 | 0.219 | 2.790 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 119 | 43 | 42 | 41 | 41 | 41 | 0 | 117 | 47 |
N.S. |
1 | 4.25 | 1.54 | 1.50 | 1.46 | 1.46 | 1.46 | 0.00 | 4.18 | 1.68 |
time (sec) |
N/A | 0.650 | 0.099 | 1.582 | 0.121 | 0.099 | 0.122 | 0.000 | 200.035 | 2.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 24 | 24 | 23 | 23 | 24 | 25 | 24 | 23 |
N.S. |
1 | 0.00 | 0.86 | 0.86 | 0.82 | 0.82 | 0.86 | 0.89 | 0.86 | 0.82 |
time (sec) |
N/A | 0.000 | 0.428 | 0.797 | 0.162 | 0.087 | 0.102 | 0.116 | 0.218 | 2.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 34 | 56 | 35 | 36 | 36 | 31 | 34 | 36 | 34 |
N.S. |
1 | 1.13 | 1.87 | 1.17 | 1.20 | 1.20 | 1.03 | 1.13 | 1.20 | 1.13 |
time (sec) |
N/A | 0.930 | 0.033 | 0.448 | 0.078 | 0.075 | 0.155 | 0.116 | 0.238 | 2.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 34 | 17 | 19 | 0 | 19 | 15 | 19 | 25 | 20 |
N.S. |
1 | 1.70 | 0.85 | 0.95 | 0.00 | 0.95 | 0.75 | 0.95 | 1.25 | 1.00 |
time (sec) |
N/A | 0.248 | 0.308 | 0.180 | 0.000 | 0.074 | 0.054 | 0.120 | 0.241 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 22 | 44 | 60 | 48 | 0 | 39 | 34 |
N.S. |
1 | 0.00 | 0.93 | 0.81 | 1.63 | 2.22 | 1.78 | 0.00 | 1.44 | 1.26 |
time (sec) |
N/A | 0.000 | 0.316 | 0.777 | 0.177 | 0.077 | 0.122 | 0.000 | 0.456 | 2.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 16 | 19 | 13 | 14 | 14 | 14 | 14 | 13 | 13 |
N.S. |
1 | 0.84 | 1.00 | 0.68 | 0.74 | 0.74 | 0.74 | 0.74 | 0.68 | 0.68 |
time (sec) |
N/A | 0.226 | 0.001 | 0.041 | 0.026 | 0.067 | 0.021 | 0.110 | 0.233 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 25 | 24 | 24 | 26 | 24 | 26 | 24 |
N.S. |
1 | 0.00 | 1.04 | 1.00 | 0.96 | 0.96 | 1.04 | 0.96 | 1.04 | 0.96 |
time (sec) |
N/A | 0.000 | 5.031 | 0.292 | 0.180 | 0.084 | 0.088 | 0.123 | 0.209 | 1.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 0.33 | 0.33 | 0.50 | 0.33 | 0.33 | 0.33 | 0.50 | 0.33 | 0.33 |
time (sec) |
N/A | 0.206 | 0.000 | 0.013 | 0.032 | 0.075 | 0.017 | 0.108 | 0.212 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 53 | 27 | 41 | 38 | 38 | 44 | 38 | 49 | 25 |
N.S. |
1 | 1.83 | 0.93 | 1.41 | 1.31 | 1.31 | 1.52 | 1.31 | 1.69 | 0.86 |
time (sec) |
N/A | 0.392 | 0.162 | 0.350 | 0.027 | 0.099 | 0.060 | 0.111 | 0.227 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 44 | 24 | 26 | 25 | 25 | 32 | 25 | 21 | 25 |
N.S. |
1 | 2.75 | 1.50 | 1.62 | 1.56 | 1.56 | 2.00 | 1.56 | 1.31 | 1.56 |
time (sec) |
N/A | 10.473 | 0.007 | 0.069 | 0.034 | 0.078 | 0.173 | 0.114 | 0.212 | 2.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 23 | 23 | 10 | 10 | 7 | 10 | 22 | 164 |
N.S. |
1 | 0.00 | 1.10 | 1.10 | 0.48 | 0.48 | 0.33 | 0.48 | 1.05 | 7.81 |
time (sec) |
N/A | 0.000 | 0.142 | 2.435 | 0.090 | 0.085 | 0.050 | 0.141 | 0.225 | 2.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 344 | 152 | 149 | 308 | 106 | 124 | 188 | 137 | 21 |
N.S. |
1 | 14.33 | 6.33 | 6.21 | 12.83 | 4.42 | 5.17 | 7.83 | 5.71 | 0.88 |
time (sec) |
N/A | 0.651 | 0.153 | 0.010 | 0.044 | 0.084 | 0.153 | 0.117 | 0.207 | 2.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 17 | 13 | 13 | 0 | 12 | 14 | 15 | 14 | 12 |
N.S. |
1 | 0.89 | 0.68 | 0.68 | 0.00 | 0.63 | 0.74 | 0.79 | 0.74 | 0.63 |
time (sec) |
N/A | 0.326 | 0.039 | 0.182 | 0.000 | 0.086 | 0.103 | 0.116 | 0.218 | 2.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 22 | 28 | 19 | 19 | 17 | 21 | 25 | 21 |
N.S. |
1 | 0.00 | 1.10 | 1.40 | 0.95 | 0.95 | 0.85 | 1.05 | 1.25 | 1.05 |
time (sec) |
N/A | 0.000 | 0.153 | 1.496 | 0.087 | 0.085 | 0.198 | 0.127 | 0.214 | 2.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 20 | 24 | 19 | 19 | 0 | 28 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.14 | 0.90 | 0.90 | 0.00 | 1.33 | 0.90 |
time (sec) |
N/A | 1.284 | 0.471 | 20.579 | 0.177 | 0.082 | 0.212 | 0.000 | 0.242 | 0.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-1) | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 44 | 44 | 0 | 99 | 97 | 99 | 219 | 508 |
N.S. |
1 | 0.00 | 1.69 | 1.69 | 0.00 | 3.81 | 3.73 | 3.81 | 8.42 | 19.54 |
time (sec) |
N/A | 0.000 | 0.066 | 1.464 | 0.000 | 0.078 | 0.256 | 0.772 | 200.034 | 2.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 21 | 21 | 21 | 59 | 67 | 82 | 215 | 81 | 0 |
N.S. |
1 | 1.11 | 1.11 | 1.11 | 3.11 | 3.53 | 4.32 | 11.32 | 4.26 | 0.00 |
time (sec) |
N/A | 1.167 | 0.027 | 1.864 | 0.155 | 0.077 | 0.123 | 0.138 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 153 | 137 | 69 | 151 | 129 | 175 | 160 | 59 | 262 |
N.S. |
1 | 4.78 | 4.28 | 2.16 | 4.72 | 4.03 | 5.47 | 5.00 | 1.84 | 8.19 |
time (sec) |
N/A | 0.803 | 0.037 | 0.299 | 0.044 | 0.105 | 1.079 | 0.113 | 0.244 | 2.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 24 | 28 | 25 | 28 | 24 | 27 | 88 | 26 |
N.S. |
1 | 0.00 | 1.04 | 1.22 | 1.09 | 1.22 | 1.04 | 1.17 | 3.83 | 1.13 |
time (sec) |
N/A | 0.000 | 0.216 | 0.468 | 0.062 | 0.078 | 0.080 | 0.148 | 63.148 | 2.665 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 19 | 12 | 11 | 13 | 10 | 18 | 11 | 11 |
N.S. |
1 | 1.00 | 1.73 | 1.09 | 1.00 | 1.18 | 0.91 | 1.64 | 1.00 | 1.00 |
time (sec) |
N/A | 0.306 | 0.032 | 0.096 | 0.025 | 0.100 | 0.047 | 0.111 | 0.237 | 2.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 34 | 19 | 18 | 20 | 22 | 19 | 19 | 15 |
N.S. |
1 | 1.00 | 1.70 | 0.95 | 0.90 | 1.00 | 1.10 | 0.95 | 0.95 | 0.75 |
time (sec) |
N/A | 0.171 | 0.013 | 0.128 | 0.029 | 0.094 | 0.196 | 0.119 | 0.234 | 0.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 43 | 43 | 35 | 30 | 41 | 45 | 56 | 41 |
N.S. |
1 | 0.00 | 1.65 | 1.65 | 1.35 | 1.15 | 1.58 | 1.73 | 2.15 | 1.58 |
time (sec) |
N/A | 0.000 | 0.152 | 0.514 | 0.165 | 0.078 | 0.216 | 0.126 | 0.224 | 2.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 44 | 50 | 40 | 22 | 44 | 310 | 34 |
N.S. |
1 | 1.00 | 1.00 | 1.63 | 1.85 | 1.48 | 0.81 | 1.63 | 11.48 | 1.26 |
time (sec) |
N/A | 2.242 | 5.062 | 6.083 | 0.172 | 0.088 | 0.228 | 0.123 | 0.311 | 2.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 28 | 28 | 33 | 26 | 37 | 31 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.97 | 1.14 | 0.90 | 1.28 | 1.07 | 0.86 |
time (sec) |
N/A | 0.518 | 0.038 | 0.266 | 0.214 | 0.088 | 0.119 | 0.117 | 0.201 | 2.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 32 | 30 | 36 | 41 | 31 | 26 | 33 | 37 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 1.12 | 1.28 | 0.97 | 0.81 | 1.03 | 1.16 |
time (sec) |
N/A | 0.000 | 0.054 | 27.831 | 0.205 | 0.080 | 0.196 | 0.124 | 0.215 | 2.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 18 | 22 | 64 | 37 | 19 | 37 | 34 | 21 |
N.S. |
1 | 0.00 | 0.95 | 1.16 | 3.37 | 1.95 | 1.00 | 1.95 | 1.79 | 1.11 |
time (sec) |
N/A | 0.000 | 0.086 | 0.316 | 0.096 | 0.075 | 0.066 | 0.273 | 0.213 | 2.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 38 | 27 | 18 | 29 | 29 | 20 | 29 | 36 | 17 |
N.S. |
1 | 1.73 | 1.23 | 0.82 | 1.32 | 1.32 | 0.91 | 1.32 | 1.64 | 0.77 |
time (sec) |
N/A | 0.237 | 0.037 | 0.368 | 0.065 | 0.080 | 0.121 | 0.111 | 0.226 | 2.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 67 | 67 | 64 | 82 | 57 | 70 | 63 | 56 | 23 |
N.S. |
1 | 2.68 | 2.68 | 2.56 | 3.28 | 2.28 | 2.80 | 2.52 | 2.24 | 0.92 |
time (sec) |
N/A | 0.250 | 0.036 | 0.612 | 0.057 | 0.078 | 0.092 | 0.107 | 0.236 | 2.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 16 | 16 | 13 | 15 | 15 | 12 | 15 | 14 | 15 |
N.S. |
1 | 1.14 | 1.14 | 0.93 | 1.07 | 1.07 | 0.86 | 1.07 | 1.00 | 1.07 |
time (sec) |
N/A | 0.155 | 0.002 | 0.059 | 0.029 | 0.068 | 0.068 | 0.104 | 0.226 | 2.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 32 | 33 | 53 | 32 | 48 | 70 | 54 | 63 | 56 |
N.S. |
1 | 1.07 | 1.10 | 1.77 | 1.07 | 1.60 | 2.33 | 1.80 | 2.10 | 1.87 |
time (sec) |
N/A | 0.303 | 0.040 | 0.443 | 0.186 | 0.078 | 0.271 | 0.153 | 0.216 | 2.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | F(-2) | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 74 | 98 | 105 | 113 | 0 | 87 | 119 | 0 |
N.S. |
1 | 0.00 | 2.24 | 2.97 | 3.18 | 3.42 | 0.00 | 2.64 | 3.61 | 0.00 |
time (sec) |
N/A | 0.000 | 28.252 | 0.162 | 0.211 | 0.099 | 0.000 | 0.167 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 29 | 125 | 37 | 39 | 0 | 0 | 62 |
N.S. |
1 | 0.00 | 1.00 | 1.26 | 5.43 | 1.61 | 1.70 | 0.00 | 0.00 | 2.70 |
time (sec) |
N/A | 0.000 | 0.381 | 2.424 | 0.345 | 0.083 | 0.875 | 0.000 | 1.646 | 4.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 35 | 14 | 12 | 25 | 19 | 8 | 12 | 18 | 11 |
N.S. |
1 | 1.35 | 0.54 | 0.46 | 0.96 | 0.73 | 0.31 | 0.46 | 0.69 | 0.42 |
time (sec) |
N/A | 0.260 | 0.043 | 0.087 | 0.037 | 0.074 | 0.041 | 0.112 | 0.214 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 26 | 24 | 24 | 25 | 25 | 22 | 26 | 28 | 22 |
N.S. |
1 | 1.13 | 1.04 | 1.04 | 1.09 | 1.09 | 0.96 | 1.13 | 1.22 | 0.96 |
time (sec) |
N/A | 0.201 | 0.010 | 0.109 | 0.030 | 0.071 | 0.228 | 0.114 | 0.242 | 2.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 30 | 29 | 25 | 25 | 26 | 29 | 30 | 25 |
N.S. |
1 | 0.00 | 1.03 | 1.00 | 0.86 | 0.86 | 0.90 | 1.00 | 1.03 | 0.86 |
time (sec) |
N/A | 0.000 | 0.094 | 0.849 | 0.194 | 0.106 | 0.124 | 0.117 | 0.241 | 2.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 0 | 59 | 80 | 102 | 71 | 94 | 67 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.11 | 2.86 | 3.64 | 2.54 | 3.36 | 2.39 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.823 | 0.183 | 0.093 | 1.814 | 0.173 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 27 | 19 | 21 | 21 | 22 | 21 | 21 | 20 |
N.S. |
1 | 0.00 | 1.23 | 0.86 | 0.95 | 0.95 | 1.00 | 0.95 | 0.95 | 0.91 |
time (sec) |
N/A | 0.000 | 0.222 | 0.163 | 0.109 | 0.088 | 0.087 | 0.122 | 0.219 | 2.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 17 | 17 | 77 | 34 | 31 | 56 | 61 | 35 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 4.05 | 1.79 | 1.63 | 2.95 | 3.21 | 1.84 |
time (sec) |
N/A | 0.000 | 0.436 | 0.224 | 2.904 | 0.082 | 0.102 | 0.115 | 0.211 | 2.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 11 | 11 | 10 | 11 | 11 | 10 | 12 | 11 | 11 |
N.S. |
1 | 0.58 | 0.58 | 0.53 | 0.58 | 0.58 | 0.53 | 0.63 | 0.58 | 0.58 |
time (sec) |
N/A | 0.158 | 0.004 | 0.033 | 0.026 | 0.076 | 0.037 | 0.119 | 0.211 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 23 | 16 | 22 | 22 | 16 | 19 | 16 |
N.S. |
1 | 0.00 | 1.00 | 1.05 | 0.73 | 1.00 | 1.00 | 0.73 | 0.86 | 0.73 |
time (sec) |
N/A | 0.000 | 0.292 | 0.542 | 0.233 | 0.093 | 0.199 | 0.114 | 0.194 | 2.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 25 | 23 | 29 | 24 | 22 | 21 | 23 | 23 |
N.S. |
1 | 0.00 | 1.14 | 1.05 | 1.32 | 1.09 | 1.00 | 0.95 | 1.05 | 1.05 |
time (sec) |
N/A | 0.000 | 0.064 | 0.263 | 0.142 | 0.084 | 0.063 | 0.118 | 0.205 | 2.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 30 | 30 | 39 | 39 | 0 | 29 | 42 | 28 |
N.S. |
1 | 0.00 | 1.11 | 1.11 | 1.44 | 1.44 | 0.00 | 1.07 | 1.56 | 1.04 |
time (sec) |
N/A | 0.000 | 0.180 | 0.492 | 0.085 | 0.084 | 0.000 | 0.135 | 0.215 | 2.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 29 | 27 | 27 | 28 | 26 | 20 | 37 | 27 | 26 |
N.S. |
1 | 1.21 | 1.12 | 1.12 | 1.17 | 1.08 | 0.83 | 1.54 | 1.12 | 1.08 |
time (sec) |
N/A | 5.143 | 1.368 | 1.433 | 0.109 | 0.089 | 0.326 | 0.222 | 0.216 | 0.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 64 | 74 | 175 | 73 | 70 | 68 | 78 | 71 |
N.S. |
1 | 0.00 | 2.67 | 3.08 | 7.29 | 3.04 | 2.92 | 2.83 | 3.25 | 2.96 |
time (sec) |
N/A | 0.000 | 0.098 | 72.083 | 0.524 | 0.095 | 0.355 | 0.449 | 0.230 | 2.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 42 | 124 | 60 | 60 | 65 | 108 | 64 | 0 |
N.S. |
1 | 0.00 | 1.27 | 3.76 | 1.82 | 1.82 | 1.97 | 3.27 | 1.94 | 0.00 |
time (sec) |
N/A | 0.000 | 0.095 | 0.038 | 0.188 | 0.098 | 0.366 | 0.252 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 37 | 34 | 34 | 46 | 37 | 29 | 38 | 41 | 33 |
N.S. |
1 | 1.95 | 1.79 | 1.79 | 2.42 | 1.95 | 1.53 | 2.00 | 2.16 | 1.74 |
time (sec) |
N/A | 0.265 | 0.029 | 0.488 | 0.039 | 0.079 | 0.065 | 0.109 | 0.207 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 23 | 25 | 25 | 22 | 42 | 26 | 23 |
N.S. |
1 | 0.00 | 1.04 | 0.92 | 1.00 | 1.00 | 0.88 | 1.68 | 1.04 | 0.92 |
time (sec) |
N/A | 0.000 | 1.459 | 0.168 | 0.118 | 0.085 | 0.120 | 0.122 | 0.244 | 2.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 24 | 17 | 17 | 22 | 15 | 14 | 50 | 24 | 31 |
N.S. |
1 | 1.14 | 0.81 | 0.81 | 1.05 | 0.71 | 0.67 | 2.38 | 1.14 | 1.48 |
time (sec) |
N/A | 0.218 | 0.062 | 0.093 | 0.118 | 0.083 | 0.087 | 0.118 | 0.238 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | B | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 32 | 49 | 0 | 45 | 19 | 326 | 138 | 21 |
N.S. |
1 | 0.00 | 1.10 | 1.69 | 0.00 | 1.55 | 0.66 | 11.24 | 4.76 | 0.72 |
time (sec) |
N/A | 0.000 | 0.060 | 3.273 | 0.000 | 0.092 | 0.170 | 0.194 | 200.022 | 2.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 18 | 26 | 25 | 27 | 25 | 26 | 28 |
N.S. |
1 | 0.00 | 1.00 | 0.90 | 1.30 | 1.25 | 1.35 | 1.25 | 1.30 | 1.40 |
time (sec) |
N/A | 0.000 | 0.159 | 0.315 | 0.163 | 0.087 | 0.078 | 0.114 | 0.247 | 2.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 24 | 23 | 29 | 24 | 22 | 22 | 25 | 22 |
N.S. |
1 | 0.00 | 0.83 | 0.79 | 1.00 | 0.83 | 0.76 | 0.76 | 0.86 | 0.76 |
time (sec) |
N/A | 0.000 | 5.064 | 3.253 | 0.125 | 0.079 | 0.237 | 0.158 | 0.252 | 0.418 |