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 | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 22 | 21 | 18 | 21 | 22 | 25 | 22 | 0 |
N.S. |
1 | 0.00 | 0.79 | 0.75 | 0.64 | 0.75 | 0.79 | 0.89 | 0.79 | 0.00 |
time (sec) |
N/A | 0.000 | 0.094 | 0.273 | 0.080 | 0.074 | 0.167 | 0.125 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 319 | 19 | 19 | 303 | 18 | 15 | 18 | 57 | 18 |
N.S. |
1 | 15.19 | 0.90 | 0.90 | 14.43 | 0.86 | 0.71 | 0.86 | 2.71 | 0.86 |
time (sec) |
N/A | 1.323 | 0.061 | 0.542 | 0.106 | 0.090 | 0.117 | 0.126 | 0.250 | 4.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 52 | 20 | 24 | 30 | 23 | 26 | 27 | 20 | 23 |
N.S. |
1 | 2.36 | 0.91 | 1.09 | 1.36 | 1.05 | 1.18 | 1.23 | 0.91 | 1.05 |
time (sec) |
N/A | 0.698 | 0.099 | 0.250 | 0.063 | 0.087 | 0.055 | 0.119 | 0.265 | 4.212 |
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 | 25 | 32 | 28 | 26 | 25 | 23 | 24 | 25 | 23 | 22 |
N.S. |
1 | 1.28 | 1.12 | 1.04 | 1.00 | 0.92 | 0.96 | 1.00 | 0.92 | 0.88 |
time (sec) |
N/A | 0.174 | 0.020 | 0.144 | 0.044 | 0.084 | 0.103 | 0.125 | 0.240 | 4.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 64 | 27 | 41 | 34 | 42 | 36 | 41 | 38 | 34 |
N.S. |
1 | 2.21 | 0.93 | 1.41 | 1.17 | 1.45 | 1.24 | 1.41 | 1.31 | 1.17 |
time (sec) |
N/A | 0.886 | 0.585 | 0.872 | 0.110 | 0.090 | 0.426 | 0.182 | 0.227 | 4.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 22 | 0 | 45 | 19 | 49 | 50 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 1.80 | 0.76 | 1.96 | 2.00 | 0.92 |
time (sec) |
N/A | 0.610 | 0.546 | 0.479 | 0.000 | 0.074 | 0.118 | 0.121 | 0.295 | 0.141 |
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 | 22 | 22 | 23 | 23 | 20 | 24 | 23 | 22 | 23 |
N.S. |
1 | 1.10 | 1.10 | 1.15 | 1.15 | 1.00 | 1.20 | 1.15 | 1.10 | 1.15 |
time (sec) |
N/A | 0.187 | 0.005 | 0.063 | 0.028 | 0.074 | 0.060 | 0.108 | 0.285 | 3.926 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | C | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 32 | 79 | 72 | 42 | 27 | 56 | 45 | 157 |
N.S. |
1 | 0.00 | 0.91 | 2.26 | 2.06 | 1.20 | 0.77 | 1.60 | 1.29 | 4.49 |
time (sec) |
N/A | 0.000 | 0.551 | 0.898 | 0.240 | 0.086 | 0.211 | 1.310 | 0.296 | 4.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 44 | 105 | 90 | 94 | 122 | 114 | 122 | 0 |
N.S. |
1 | 0.00 | 1.47 | 3.50 | 3.00 | 3.13 | 4.07 | 3.80 | 4.07 | 0.00 |
time (sec) |
N/A | 0.000 | 5.072 | 0.041 | 0.216 | 0.090 | 0.153 | 0.181 | 0.260 | 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 | 21 | 11 | 15 | 7 | 9 | 9 | 8 | 9 | 8 | 6 |
N.S. |
1 | 0.52 | 0.71 | 0.33 | 0.43 | 0.43 | 0.38 | 0.43 | 0.38 | 0.29 |
time (sec) |
N/A | 0.129 | 0.001 | 0.024 | 0.030 | 0.070 | 0.015 | 0.112 | 0.278 | 0.030 |
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 | 21 | 20 | 18 | 19 | 19 | 17 | 19 | 16 | 15 |
N.S. |
1 | 0.81 | 0.77 | 0.69 | 0.73 | 0.73 | 0.65 | 0.73 | 0.62 | 0.58 |
time (sec) |
N/A | 0.158 | 0.000 | 0.064 | 0.041 | 0.064 | 0.020 | 0.108 | 0.267 | 0.033 |
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 | 24 | 22 | 31 | 28 | 19 | 21 | 37 | 21 |
N.S. |
1 | 0.00 | 1.09 | 1.00 | 1.41 | 1.27 | 0.86 | 0.95 | 1.68 | 0.95 |
time (sec) |
N/A | 0.000 | 0.290 | 0.128 | 0.121 | 0.079 | 0.756 | 0.116 | 0.243 | 4.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | B | A | F(-2) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 123 | 53 | 38 | 41 | 63 | 42 | 0 | 71 | 314 |
N.S. |
1 | 4.24 | 1.83 | 1.31 | 1.41 | 2.17 | 1.45 | 0.00 | 2.45 | 10.83 |
time (sec) |
N/A | 0.733 | 0.051 | 1.078 | 0.042 | 0.082 | 0.756 | 0.000 | 0.280 | 4.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 36 | 32 | 31 | 61 | 27 | 69 | 67 | 30 |
N.S. |
1 | 0.00 | 1.09 | 0.97 | 0.94 | 1.85 | 0.82 | 2.09 | 2.03 | 0.91 |
time (sec) |
N/A | 0.000 | 0.347 | 0.867 | 0.120 | 0.078 | 0.282 | 0.144 | 49.008 | 4.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 50 | 35 | 29 | 29 | 28 | 24 | 43 | 58 | 29 |
N.S. |
1 | 1.72 | 1.21 | 1.00 | 1.00 | 0.97 | 0.83 | 1.48 | 2.00 | 1.00 |
time (sec) |
N/A | 0.691 | 0.449 | 0.605 | 0.181 | 0.083 | 0.849 | 0.130 | 37.435 | 4.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 66 | 23 | 26 | 24 | 26 | 34 | 33 | 25 | 24 |
N.S. |
1 | 3.00 | 1.05 | 1.18 | 1.09 | 1.18 | 1.55 | 1.50 | 1.14 | 1.09 |
time (sec) |
N/A | 0.597 | 0.211 | 22.974 | 0.162 | 0.093 | 0.218 | 0.116 | 0.182 | 6.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 110 | 157 | 429 | 116 | 122 | 155 | 302 | 345 |
N.S. |
1 | 0.00 | 3.67 | 5.23 | 14.30 | 3.87 | 4.07 | 5.17 | 10.07 | 11.50 |
time (sec) |
N/A | 0.000 | 1.019 | 0.113 | 1.602 | 0.090 | 1.314 | 0.930 | 200.038 | 4.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 18 | 21 | 33 | 19 | 19 | 33 | 55 | 16 |
N.S. |
1 | 0.00 | 0.95 | 1.11 | 1.74 | 1.00 | 1.00 | 1.74 | 2.89 | 0.84 |
time (sec) |
N/A | 0.000 | 0.146 | 0.356 | 0.147 | 0.081 | 0.189 | 0.129 | 0.243 | 4.411 |
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 | 33 | 0 | 34 | 35 | 37 | 37 | 36 | 37 | 41 | 39 |
N.S. |
1 | 0.00 | 1.03 | 1.06 | 1.12 | 1.12 | 1.09 | 1.12 | 1.24 | 1.18 |
time (sec) |
N/A | 0.000 | 0.155 | 0.385 | 0.074 | 0.086 | 0.117 | 0.116 | 0.233 | 4.381 |
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 | 26 | 0 | 23 | 21 | 20 | 50 | 17 | 0 | 46 | 21 |
N.S. |
1 | 0.00 | 0.88 | 0.81 | 0.77 | 1.92 | 0.65 | 0.00 | 1.77 | 0.81 |
time (sec) |
N/A | 0.000 | 0.343 | 0.157 | 0.244 | 0.082 | 0.193 | 0.000 | 0.210 | 0.117 |
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 | 4 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 0.50 | 0.50 | 0.75 | 0.50 | 0.50 | 0.50 | 0.75 | 0.50 | 0.50 |
time (sec) |
N/A | 0.122 | 0.000 | 0.023 | 0.034 | 0.082 | 0.035 | 0.107 | 0.209 | 0.009 |
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 | 34 | 0 | 33 | 25 | 24 | 24 | 24 | 35 | 26 | 23 |
N.S. |
1 | 0.00 | 0.97 | 0.74 | 0.71 | 0.71 | 0.71 | 1.03 | 0.76 | 0.68 |
time (sec) |
N/A | 0.000 | 0.290 | 0.920 | 0.167 | 0.086 | 0.279 | 0.154 | 0.215 | 4.199 |
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 | 20 | 24 | 20 | 20 | 66 | 44 | 22 | 140 | 34 | 32 |
N.S. |
1 | 1.20 | 1.00 | 1.00 | 3.30 | 2.20 | 1.10 | 7.00 | 1.70 | 1.60 |
time (sec) |
N/A | 0.765 | 0.117 | 1.026 | 0.317 | 0.082 | 0.255 | 0.120 | 0.208 | 4.415 |
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 | 16 | 16 | 12 | 11 | 15 | 15 | 15 | 16 | 11 |
N.S. |
1 | 0.73 | 0.73 | 0.55 | 0.50 | 0.68 | 0.68 | 0.68 | 0.73 | 0.50 |
time (sec) |
N/A | 0.779 | 0.362 | 19.271 | 0.091 | 0.083 | 1.436 | 0.177 | 0.215 | 5.021 |
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 | 20 | 20 | 25 | 36 | 24 | 40 | 39 | 29 |
N.S. |
1 | 0.00 | 0.77 | 0.77 | 0.96 | 1.38 | 0.92 | 1.54 | 1.50 | 1.12 |
time (sec) |
N/A | 0.000 | 0.107 | 1.708 | 0.082 | 0.086 | 0.076 | 0.145 | 0.211 | 4.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 65 | 80 | 93 | 89 | 128 | 107 | 113 | 0 |
N.S. |
1 | 0.00 | 2.32 | 2.86 | 3.32 | 3.18 | 4.57 | 3.82 | 4.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.042 | 11.935 | 0.100 | 0.100 | 0.291 | 0.234 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 34 | 33 | 42 | 33 | 32 | 57 | 25 | 51 |
N.S. |
1 | 0.00 | 1.36 | 1.32 | 1.68 | 1.32 | 1.28 | 2.28 | 1.00 | 2.04 |
time (sec) |
N/A | 0.000 | 2.524 | 1.704 | 0.190 | 0.087 | 0.224 | 0.128 | 0.205 | 4.433 |
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 | 24 | 13 | 15 | 24 | 14 | 12 | 14 | 15 | 12 |
N.S. |
1 | 0.83 | 0.45 | 0.52 | 0.83 | 0.48 | 0.41 | 0.48 | 0.52 | 0.41 |
time (sec) |
N/A | 0.178 | 0.028 | 0.055 | 0.038 | 0.090 | 0.055 | 0.115 | 0.205 | 4.375 |
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 | 24 | 24 | 33 | 33 | 36 | 31 | 30 | 36 | 30 |
N.S. |
1 | 1.00 | 1.00 | 1.38 | 1.38 | 1.50 | 1.29 | 1.25 | 1.50 | 1.25 |
time (sec) |
N/A | 0.711 | 0.054 | 0.273 | 0.068 | 0.082 | 0.139 | 0.109 | 0.210 | 4.436 |
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 | 21 | 20 | 19 | 19 | 20 | 19 | 23 | 19 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.90 | 0.90 | 0.95 | 0.90 | 1.10 | 0.90 |
time (sec) |
N/A | 0.000 | 0.198 | 0.404 | 0.180 | 0.095 | 0.226 | 0.359 | 0.216 | 4.450 |
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 | 25 | 22 | 22 | 24 | 25 | 25 | 22 | 25 | 22 | 22 |
N.S. |
1 | 0.88 | 0.88 | 0.96 | 1.00 | 1.00 | 0.88 | 1.00 | 0.88 | 0.88 |
time (sec) |
N/A | 0.616 | 0.508 | 0.598 | 0.164 | 0.083 | 0.137 | 0.251 | 0.208 | 4.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 20 | 20 | 22 | 42 | 34 | 22 | 0 | 22 | 50 |
N.S. |
1 | 0.91 | 0.91 | 1.00 | 1.91 | 1.55 | 1.00 | 0.00 | 1.00 | 2.27 |
time (sec) |
N/A | 0.486 | 0.411 | 0.348 | 0.051 | 0.096 | 0.156 | 0.000 | 0.218 | 4.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 31 | 30 | 29 | 29 | 29 | 29 | 508 | 0 |
N.S. |
1 | 0.00 | 1.11 | 1.07 | 1.04 | 1.04 | 1.04 | 1.04 | 18.14 | 0.00 |
time (sec) |
N/A | 0.000 | 0.140 | 0.734 | 0.067 | 0.084 | 0.091 | 0.164 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 33 | 28 | 22 | 41 | 32 | 20 | 32 | 38 | 21 |
N.S. |
1 | 1.57 | 1.33 | 1.05 | 1.95 | 1.52 | 0.95 | 1.52 | 1.81 | 1.00 |
time (sec) |
N/A | 0.456 | 0.118 | 0.347 | 0.028 | 0.087 | 0.077 | 0.110 | 0.214 | 0.109 |
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 | 12 | 15 | 13 | 12 | 14 | 12 | 12 | 12 | 12 |
N.S. |
1 | 0.57 | 0.71 | 0.62 | 0.57 | 0.67 | 0.57 | 0.57 | 0.57 | 0.57 |
time (sec) |
N/A | 0.130 | 0.000 | 0.066 | 0.035 | 0.066 | 0.015 | 0.120 | 0.199 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 37 | 61 | 62 | 60 | 53 | 72 | 234 | 0 |
N.S. |
1 | 0.00 | 1.06 | 1.74 | 1.77 | 1.71 | 1.51 | 2.06 | 6.69 | 0.00 |
time (sec) |
N/A | 0.000 | 0.108 | 54.899 | 0.120 | 0.100 | 0.261 | 0.448 | 200.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 151 | 51 | 162 | 27 | 24 | 0 | 29 | 27 |
N.S. |
1 | 0.00 | 5.39 | 1.82 | 5.79 | 0.96 | 0.86 | 0.00 | 1.04 | 0.96 |
time (sec) |
N/A | 0.000 | 0.203 | 1.713 | 0.181 | 0.081 | 0.325 | 0.000 | 0.171 | 4.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 28 | 25 | 0 | 29 | 20 | 29 | 24 | 28 |
N.S. |
1 | 0.00 | 1.08 | 0.96 | 0.00 | 1.12 | 0.77 | 1.12 | 0.92 | 1.08 |
time (sec) |
N/A | 0.000 | 1.883 | 0.259 | 0.000 | 0.087 | 0.094 | 0.115 | 0.168 | 4.303 |
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 | 14 | 14 | 9 | 8 | 12 | 7 | 9 | 12 | 8 |
N.S. |
1 | 0.58 | 0.58 | 0.38 | 0.33 | 0.50 | 0.29 | 0.38 | 0.50 | 0.33 |
time (sec) |
N/A | 0.146 | 0.002 | 0.036 | 0.029 | 0.084 | 0.036 | 0.106 | 0.165 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 16 | 19 | 17 | 17 | 15 | 17 | 25 | 0 |
N.S. |
1 | 0.00 | 0.67 | 0.79 | 0.71 | 0.71 | 0.62 | 0.71 | 1.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.146 | 0.245 | 0.081 | 0.102 | 0.070 | 0.120 | 0.169 | 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 | 17 | 7 | 7 | 8 | 7 | 7 | 5 | 7 | 7 | 7 |
N.S. |
1 | 0.41 | 0.41 | 0.47 | 0.41 | 0.41 | 0.29 | 0.41 | 0.41 | 0.41 |
time (sec) |
N/A | 0.132 | 0.000 | 0.035 | 0.042 | 0.071 | 0.019 | 0.118 | 0.159 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-1) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 30 | 30 | 36 | 37 | 40 | 29 | 0 | 37 | 44 |
N.S. |
1 | 1.36 | 1.36 | 1.64 | 1.68 | 1.82 | 1.32 | 0.00 | 1.68 | 2.00 |
time (sec) |
N/A | 0.578 | 0.137 | 0.429 | 0.081 | 0.084 | 0.281 | 0.000 | 0.165 | 5.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 24 | 19 | 16 | 18 | 18 | 17 | 18 | 141 | 21 |
N.S. |
1 | 1.26 | 1.00 | 0.84 | 0.95 | 0.95 | 0.89 | 0.95 | 7.42 | 1.11 |
time (sec) |
N/A | 0.315 | 0.401 | 0.171 | 0.210 | 0.083 | 0.156 | 0.123 | 0.329 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 31 | 44 | 38 | 27 | 0 | 125 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.42 | 1.23 | 0.87 | 0.00 | 4.03 | 0.90 |
time (sec) |
N/A | 0.000 | 5.165 | 0.090 | 0.217 | 0.095 | 0.264 | 0.000 | 200.031 | 4.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | F | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 122 | 45 | 50 | 0 | 40 | 56 | 95 | 34 | 0 |
N.S. |
1 | 5.81 | 2.14 | 2.38 | 0.00 | 1.90 | 2.67 | 4.52 | 1.62 | 0.00 |
time (sec) |
N/A | 3.818 | 0.120 | 0.263 | 0.000 | 0.097 | 4.769 | 0.124 | 0.181 | 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 | 16 | 10 | 12 | 10 | 9 | 9 | 8 | 9 | 52 | 9 |
N.S. |
1 | 0.62 | 0.75 | 0.62 | 0.56 | 0.56 | 0.50 | 0.56 | 3.25 | 0.56 |
time (sec) |
N/A | 0.169 | 0.012 | 0.046 | 0.043 | 0.074 | 0.042 | 0.113 | 0.184 | 0.115 |
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 | 29 | 0 | 45 | 29 | 65 | 34 | 48 | 40 | 46 | 19 |
N.S. |
1 | 0.00 | 1.55 | 1.00 | 2.24 | 1.17 | 1.66 | 1.38 | 1.59 | 0.66 |
time (sec) |
N/A | 0.000 | 0.332 | 0.528 | 0.076 | 0.078 | 1.230 | 0.116 | 0.180 | 4.629 |
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 | 26 | 25 | 31 | 20 | 21 | 27 | 15 | 68 | 43 | 21 |
N.S. |
1 | 0.96 | 1.19 | 0.77 | 0.81 | 1.04 | 0.58 | 2.62 | 1.65 | 0.81 |
time (sec) |
N/A | 0.932 | 0.091 | 0.432 | 0.140 | 0.087 | 0.169 | 0.110 | 0.179 | 4.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 19 | 53 | 43 | 26 | 53 | 55 | 34 |
N.S. |
1 | 0.00 | 1.00 | 0.76 | 2.12 | 1.72 | 1.04 | 2.12 | 2.20 | 1.36 |
time (sec) |
N/A | 0.000 | 0.169 | 7.543 | 0.081 | 0.088 | 0.119 | 0.127 | 0.190 | 4.662 |
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 | 24 | 0 | 31 | 23 | 22 | 242 | 27 | 0 | 34 | 25 |
N.S. |
1 | 0.00 | 1.29 | 0.96 | 0.92 | 10.08 | 1.12 | 0.00 | 1.42 | 1.04 |
time (sec) |
N/A | 0.000 | 0.042 | 1.999 | 0.435 | 0.093 | 1.924 | 0.000 | 0.329 | 4.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 41 | 66 | 31 | 238 | 29 | 31 | 31 | 96 | 27 |
N.S. |
1 | 2.16 | 3.47 | 1.63 | 12.53 | 1.53 | 1.63 | 1.63 | 5.05 | 1.42 |
time (sec) |
N/A | 0.280 | 0.022 | 0.458 | 0.052 | 0.085 | 0.103 | 0.151 | 0.189 | 0.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 55 | 31 | 28 | 122 | 27 | 26 | 44 | 91 | 34 |
N.S. |
1 | 1.72 | 0.97 | 0.88 | 3.81 | 0.84 | 0.81 | 1.38 | 2.84 | 1.06 |
time (sec) |
N/A | 2.107 | 0.212 | 1.310 | 0.816 | 0.089 | 0.151 | 0.127 | 0.192 | 4.698 |
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 | 16 | 16 | 16 | 18 | 13 | 16 | 20 | 13 | 17 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 0.81 | 1.00 | 1.25 | 0.81 | 1.06 | 0.88 |
time (sec) |
N/A | 0.134 | 0.000 | 0.062 | 0.037 | 0.076 | 0.014 | 0.111 | 0.191 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 23 | 22 | 35 | 35 | 22 | 47 | 48 | 25 |
N.S. |
1 | 0.00 | 0.88 | 0.85 | 1.35 | 1.35 | 0.85 | 1.81 | 1.85 | 0.96 |
time (sec) |
N/A | 0.000 | 0.262 | 4.244 | 0.093 | 0.083 | 0.101 | 0.153 | 0.195 | 4.500 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | A | B | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 41 | 59 | 59 | 31 | 3224 | 126 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.37 | 1.97 | 1.97 | 1.03 | 107.47 | 4.20 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 4.898 | 0.121 | 0.110 | 0.222 | 0.910 | 0.427 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 41 | 56 | 55 | 122 | 66 | 42 | 113 | 165 | 44 |
N.S. |
1 | 1.64 | 2.24 | 2.20 | 4.88 | 2.64 | 1.68 | 4.52 | 6.60 | 1.76 |
time (sec) |
N/A | 1.203 | 0.129 | 5.422 | 0.181 | 0.098 | 0.278 | 0.134 | 0.730 | 4.429 |
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 | 17 | 34 | 35 | 30 | 28 | 28 | 31 | 30 | 35 | 31 |
N.S. |
1 | 2.00 | 2.06 | 1.76 | 1.65 | 1.65 | 1.82 | 1.76 | 2.06 | 1.82 |
time (sec) |
N/A | 0.355 | 0.140 | 0.294 | 0.034 | 0.086 | 0.070 | 0.106 | 0.178 | 0.165 |
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 | 24 | 27 | 28 | 27 | 27 | 27 | 24 | 23 |
N.S. |
1 | 0.00 | 0.96 | 1.08 | 1.12 | 1.08 | 1.08 | 1.08 | 0.96 | 0.92 |
time (sec) |
N/A | 0.000 | 0.281 | 3.689 | 0.157 | 0.084 | 0.190 | 0.125 | 0.181 | 4.880 |
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 | 21 | 16 | 16 | 19 | 19 | 19 | 19 | 25 | 20 |
N.S. |
1 | 1.24 | 0.94 | 0.94 | 1.12 | 1.12 | 1.12 | 1.12 | 1.47 | 1.18 |
time (sec) |
N/A | 0.277 | 0.202 | 0.216 | 63.098 | 0.084 | 0.113 | 0.116 | 0.540 | 4.299 |
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 | 7 | 8 | 9 | 7 | 8 | 7 | 9 | 7 |
N.S. |
1 | 0.00 | 0.33 | 0.38 | 0.43 | 0.33 | 0.38 | 0.33 | 0.43 | 0.33 |
time (sec) |
N/A | 0.000 | 0.017 | 0.139 | 0.081 | 0.079 | 0.085 | 0.109 | 0.185 | 4.621 |
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 | 19 | 20 | 20 | 20 | 15 | 21 | 38 | 36 |
N.S. |
1 | 0.00 | 0.86 | 0.91 | 0.91 | 0.91 | 0.68 | 0.95 | 1.73 | 1.64 |
time (sec) |
N/A | 0.000 | 0.180 | 0.771 | 0.069 | 0.089 | 0.120 | 0.123 | 0.182 | 5.235 |
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 | 13 | 13 | 12 | 13 | 13 | 14 | 13 | 14 | 13 |
N.S. |
1 | 0.59 | 0.59 | 0.55 | 0.59 | 0.59 | 0.64 | 0.59 | 0.64 | 0.59 |
time (sec) |
N/A | 0.141 | 0.002 | 0.166 | 0.023 | 0.079 | 0.058 | 0.107 | 0.180 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 49 | 57 | 44 | 53 | 63 | 54 | 48 | 69 | 55 |
N.S. |
1 | 1.81 | 2.11 | 1.63 | 1.96 | 2.33 | 2.00 | 1.78 | 2.56 | 2.04 |
time (sec) |
N/A | 0.339 | 0.031 | 0.234 | 0.024 | 0.084 | 0.150 | 0.116 | 0.186 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 40 | 18 | 16 | 158 | 15 | 15 | 15 | 26 | 15 |
N.S. |
1 | 1.82 | 0.82 | 0.73 | 7.18 | 0.68 | 0.68 | 0.68 | 1.18 | 0.68 |
time (sec) |
N/A | 0.178 | 0.349 | 0.154 | 0.153 | 0.083 | 0.111 | 0.117 | 0.202 | 0.095 |
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 | 17 | 20 | 10 | 11 | 19 | 7 | 11 | 14 | 11 |
N.S. |
1 | 0.89 | 1.05 | 0.53 | 0.58 | 1.00 | 0.37 | 0.58 | 0.74 | 0.58 |
time (sec) |
N/A | 0.166 | 0.006 | 0.161 | 0.025 | 0.069 | 0.031 | 0.116 | 0.185 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 20 | 49 | 19 | 17 | 74 | 19 | 219 |
N.S. |
1 | 0.00 | 1.00 | 1.11 | 2.72 | 1.06 | 0.94 | 4.11 | 1.06 | 12.17 |
time (sec) |
N/A | 0.000 | 0.123 | 1.510 | 0.080 | 0.079 | 0.079 | 0.137 | 0.185 | 4.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 22 | 26 | 31 | 24 | 0 | 37 | 27 |
N.S. |
1 | 0.00 | 0.92 | 0.85 | 1.00 | 1.19 | 0.92 | 0.00 | 1.42 | 1.04 |
time (sec) |
N/A | 0.000 | 0.767 | 0.297 | 0.166 | 0.095 | 0.143 | 0.000 | 0.196 | 4.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 47 | 52 | 214 | 55 | 51 | 83 | 86 | 221 |
N.S. |
1 | 0.00 | 1.52 | 1.68 | 6.90 | 1.77 | 1.65 | 2.68 | 2.77 | 7.13 |
time (sec) |
N/A | 0.000 | 0.089 | 4.028 | 0.260 | 0.099 | 0.175 | 0.760 | 0.179 | 4.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 24 | 22 | 35 | 45 | 22 | 25 | 47 | 43 |
N.S. |
1 | 0.00 | 0.89 | 0.81 | 1.30 | 1.67 | 0.81 | 0.93 | 1.74 | 1.59 |
time (sec) |
N/A | 0.000 | 1.659 | 0.392 | 0.185 | 0.095 | 0.143 | 0.191 | 0.184 | 4.144 |
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 | 37 | 33 | 30 | 27 | 35 | 31 | 31 | 36 | 30 |
N.S. |
1 | 1.28 | 1.14 | 1.03 | 0.93 | 1.21 | 1.07 | 1.07 | 1.24 | 1.03 |
time (sec) |
N/A | 0.209 | 0.007 | 0.139 | 0.026 | 0.070 | 0.053 | 0.119 | 0.174 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 301 | 23 | 51 | 130 | 46 | 46 | 101 | 86 | 69 |
N.S. |
1 | 13.09 | 1.00 | 2.22 | 5.65 | 2.00 | 2.00 | 4.39 | 3.74 | 3.00 |
time (sec) |
N/A | 0.698 | 0.127 | 10.294 | 0.116 | 0.091 | 0.157 | 0.131 | 0.173 | 4.002 |
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 | 20 | 35 | 30 | 25 | 22 | 22 | 24 | 22 | 29 | 26 |
N.S. |
1 | 1.75 | 1.50 | 1.25 | 1.10 | 1.10 | 1.20 | 1.10 | 1.45 | 1.30 |
time (sec) |
N/A | 0.160 | 0.027 | 0.257 | 0.029 | 0.081 | 0.049 | 0.110 | 0.199 | 0.050 |
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 | 13 | 11 | 12 | 11 | 11 | 12 | 11 | 11 | 11 |
N.S. |
1 | 0.87 | 0.73 | 0.80 | 0.73 | 0.73 | 0.80 | 0.73 | 0.73 | 0.73 |
time (sec) |
N/A | 0.368 | 0.004 | 0.148 | 0.066 | 0.094 | 0.061 | 0.114 | 0.181 | 4.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 28 | 28 | 24 | 63 | 23 | 22 | 23 | 25 | 23 |
N.S. |
1 | 1.27 | 1.27 | 1.09 | 2.86 | 1.05 | 1.00 | 1.05 | 1.14 | 1.05 |
time (sec) |
N/A | 0.199 | 0.025 | 0.198 | 0.081 | 0.088 | 0.142 | 0.120 | 0.181 | 4.105 |
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 | 15 | 16 | 16 | 15 | 15 | 12 | 17 | 16 | 15 |
N.S. |
1 | 0.88 | 0.94 | 0.94 | 0.88 | 0.88 | 0.71 | 1.00 | 0.94 | 0.88 |
time (sec) |
N/A | 0.173 | 0.005 | 0.197 | 0.036 | 0.092 | 0.049 | 0.113 | 0.194 | 4.011 |
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 | 45 | 34 | 34 | 33 | 33 | 32 | 33 | 40 | 36 |
N.S. |
1 | 1.88 | 1.42 | 1.42 | 1.38 | 1.38 | 1.33 | 1.38 | 1.67 | 1.50 |
time (sec) |
N/A | 0.213 | 0.020 | 0.889 | 0.105 | 0.105 | 0.082 | 0.112 | 0.178 | 4.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 67 | 23 | 22 | 22 | 22 | 19 | 0 | 24 | 20 |
N.S. |
1 | 2.48 | 0.85 | 0.81 | 0.81 | 0.81 | 0.70 | 0.00 | 0.89 | 0.74 |
time (sec) |
N/A | 0.745 | 0.037 | 0.312 | 0.127 | 0.090 | 0.115 | 0.000 | 0.176 | 4.390 |
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 | 38 | 37 | 33 | 37 | 37 | 54 | 37 | 34 | 32 |
N.S. |
1 | 1.31 | 1.28 | 1.14 | 1.28 | 1.28 | 1.86 | 1.28 | 1.17 | 1.10 |
time (sec) |
N/A | 0.172 | 0.002 | 0.120 | 0.026 | 0.083 | 0.025 | 0.115 | 0.203 | 4.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 186 | 35 | 40 | 64 | 51 | 82 | 82 | 74 | 95 |
N.S. |
1 | 6.20 | 1.17 | 1.33 | 2.13 | 1.70 | 2.73 | 2.73 | 2.47 | 3.17 |
time (sec) |
N/A | 4.401 | 0.128 | 1.628 | 0.103 | 0.106 | 0.231 | 0.148 | 0.188 | 5.111 |
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 | 16 | 31 | 16 | 16 | 25 | 15 | 15 | 15 | 16 | 15 |
N.S. |
1 | 1.94 | 1.00 | 1.00 | 1.56 | 0.94 | 0.94 | 0.94 | 1.00 | 0.94 |
time (sec) |
N/A | 0.185 | 0.007 | 0.235 | 0.032 | 0.085 | 0.052 | 0.110 | 0.174 | 4.199 |
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 | 27 | 27 | 24 | 23 | 30 | 24 | 23 | 29 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.85 | 1.11 | 0.89 | 0.85 | 1.07 | 0.96 |
time (sec) |
N/A | 0.541 | 0.030 | 1.191 | 0.172 | 0.098 | 0.105 | 0.120 | 0.182 | 4.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 36 | 36 | 28 | 143 | 23 | 27 | 28 | 22 | 23 |
N.S. |
1 | 1.71 | 1.71 | 1.33 | 6.81 | 1.10 | 1.29 | 1.33 | 1.05 | 1.10 |
time (sec) |
N/A | 0.223 | 0.009 | 0.474 | 0.108 | 0.091 | 0.087 | 0.113 | 0.173 | 4.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | F(-1) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 59 | 39 | 36 | 39 | 40 | 66 | 0 | 49 | 0 |
N.S. |
1 | 2.46 | 1.62 | 1.50 | 1.62 | 1.67 | 2.75 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 5.323 | 0.155 | 137.904 | 0.098 | 0.091 | 0.214 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 67 | 44 | 45 | 64 | 44 | 41 | 67 | 45 | 43 |
N.S. |
1 | 2.09 | 1.38 | 1.41 | 2.00 | 1.38 | 1.28 | 2.09 | 1.41 | 1.34 |
time (sec) |
N/A | 0.290 | 0.032 | 0.505 | 0.035 | 0.082 | 0.089 | 0.113 | 0.185 | 4.361 |
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 | 28 | 25 | 20 | 19 | 18 | 26 | 19 | 18 | 26 | 17 |
N.S. |
1 | 0.89 | 0.71 | 0.68 | 0.64 | 0.93 | 0.68 | 0.64 | 0.93 | 0.61 |
time (sec) |
N/A | 0.187 | 0.004 | 0.242 | 0.031 | 0.080 | 0.058 | 0.109 | 0.178 | 4.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 53 | 52 | 61 | 45 | 63 | 59 | 52 | 44 |
N.S. |
1 | 0.00 | 1.61 | 1.58 | 1.85 | 1.36 | 1.91 | 1.79 | 1.58 | 1.33 |
time (sec) |
N/A | 0.000 | 0.768 | 1.223 | 0.143 | 0.087 | 0.078 | 0.117 | 0.180 | 5.272 |
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 | 22 | 22 | 19 | 18 | 18 | 19 | 18 | 22 | 19 |
N.S. |
1 | 1.10 | 1.10 | 0.95 | 0.90 | 0.90 | 0.95 | 0.90 | 1.10 | 0.95 |
time (sec) |
N/A | 0.152 | 0.004 | 0.119 | 0.047 | 0.082 | 0.043 | 0.108 | 0.176 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 37 | 30 | 35 | 29 | 0 | 0 | 44 | 27 |
N.S. |
1 | 0.00 | 1.12 | 0.91 | 1.06 | 0.88 | 0.00 | 0.00 | 1.33 | 0.82 |
time (sec) |
N/A | 0.000 | 1.714 | 1.323 | 0.085 | 0.094 | 0.000 | 0.000 | 0.176 | 4.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-1) | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 44 | 127 | 40 | 0 | 39 | 39 | 0 | 45 | 182 |
N.S. |
1 | 1.63 | 4.70 | 1.48 | 0.00 | 1.44 | 1.44 | 0.00 | 1.67 | 6.74 |
time (sec) |
N/A | 5.359 | 0.256 | 40.013 | 0.000 | 0.094 | 0.904 | 0.000 | 0.316 | 4.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 21 | 20 | 26 | 19 | 46 | 28 | 20 |
N.S. |
1 | 0.00 | 0.93 | 0.75 | 0.71 | 0.93 | 0.68 | 1.64 | 1.00 | 0.71 |
time (sec) |
N/A | 0.000 | 0.016 | 0.156 | 0.075 | 0.103 | 0.070 | 0.111 | 0.172 | 0.110 |
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 | 25 | 32 | 33 | 33 | 30 | 30 | 32 | 30 | 34 | 84 |
N.S. |
1 | 1.28 | 1.32 | 1.32 | 1.20 | 1.20 | 1.28 | 1.20 | 1.36 | 3.36 |
time (sec) |
N/A | 0.503 | 0.023 | 1.343 | 0.076 | 0.095 | 0.097 | 0.422 | 0.176 | 13.032 |
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 | 23 | 34 | 22 | 21 | 0 | 20 | 22 | 29 | 21 | 19 |
N.S. |
1 | 1.48 | 0.96 | 0.91 | 0.00 | 0.87 | 0.96 | 1.26 | 0.91 | 0.83 |
time (sec) |
N/A | 0.524 | 0.049 | 0.368 | 0.000 | 0.091 | 0.163 | 0.133 | 0.194 | 4.613 |
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 | 13 | 13 | 15 | 16 | 10 | 16 | 17 | 15 |
N.S. |
1 | 0.00 | 0.57 | 0.57 | 0.65 | 0.70 | 0.43 | 0.70 | 0.74 | 0.65 |
time (sec) |
N/A | 0.000 | 0.535 | 0.125 | 0.069 | 0.091 | 0.061 | 0.107 | 0.173 | 0.089 |
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 | 25 | 27 | 27 | 25 | 23 | 40 | 20 | 52 | 53 | 27 |
N.S. |
1 | 1.08 | 1.08 | 1.00 | 0.92 | 1.60 | 0.80 | 2.08 | 2.12 | 1.08 |
time (sec) |
N/A | 0.799 | 0.026 | 0.019 | 0.210 | 0.080 | 0.130 | 0.214 | 0.181 | 4.404 |
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 | 37 | 26 | 20 | 18 | 31 | 22 | 18 | 27 | 31 |
N.S. |
1 | 1.54 | 1.08 | 0.83 | 0.75 | 1.29 | 0.92 | 0.75 | 1.12 | 1.29 |
time (sec) |
N/A | 0.200 | 0.010 | 0.154 | 0.037 | 0.080 | 0.103 | 0.109 | 0.185 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F(-1) | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 31 | 243 | 162 | 230 | 143 | 0 | 217 | 0 |
N.S. |
1 | 0.00 | 1.29 | 10.12 | 6.75 | 9.58 | 5.96 | 0.00 | 9.04 | 0.00 |
time (sec) |
N/A | 0.000 | 5.097 | 0.186 | 0.116 | 0.094 | 30.691 | 0.000 | 0.188 | 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 | 17 | 32 | 16 | 16 | 15 | 15 | 12 | 15 | 14 | 13 |
N.S. |
1 | 1.88 | 0.94 | 0.94 | 0.88 | 0.88 | 0.71 | 0.88 | 0.82 | 0.76 |
time (sec) |
N/A | 0.161 | 0.003 | 0.159 | 0.030 | 0.103 | 0.041 | 0.112 | 0.181 | 0.050 |
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 | 33 | 42 | 32 | 33 | 56 | 47 | 34 | 48 | 57 | 46 |
N.S. |
1 | 1.27 | 0.97 | 1.00 | 1.70 | 1.42 | 1.03 | 1.45 | 1.73 | 1.39 |
time (sec) |
N/A | 0.383 | 0.068 | 0.490 | 0.031 | 0.085 | 0.161 | 0.109 | 0.176 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 63 | 67 | 50 | 74 | 50 | 66 | 59 | 65 | 56 |
N.S. |
1 | 2.42 | 2.58 | 1.92 | 2.85 | 1.92 | 2.54 | 2.27 | 2.50 | 2.15 |
time (sec) |
N/A | 0.384 | 1.387 | 1.398 | 0.072 | 0.091 | 0.119 | 0.116 | 0.181 | 4.447 |
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 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 | 6 |
N.S. |
1 | 0.43 | 0.43 | 0.50 | 0.43 | 0.43 | 0.36 | 0.50 | 0.43 | 0.43 |
time (sec) |
N/A | 0.133 | 0.001 | 0.040 | 0.028 | 0.074 | 0.030 | 0.104 | 0.175 | 0.018 |