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 | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 31 | 17 | 17 | 95 | 22 | 19 | 22 | 20 | 16 |
N.S. |
1 | 1.55 | 0.85 | 0.85 | 4.75 | 1.10 | 0.95 | 1.10 | 1.00 | 0.80 |
time (sec) |
N/A | 0.367 | 0.067 | 0.051 | 0.031 | 0.079 | 0.050 | 0.115 | 0.191 | 2.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 27 | 43 | 130 | 44 | 0 | 194 | 24 |
N.S. |
1 | 0.00 | 1.00 | 0.93 | 1.48 | 4.48 | 1.52 | 0.00 | 6.69 | 0.83 |
time (sec) |
N/A | 0.000 | 0.097 | 3.563 | 0.918 | 0.134 | 0.284 | 0.000 | 0.202 | 0.386 |
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 | 18 | 17 | 16 | 13 | 19 | 12 | 15 | 18 | 15 |
N.S. |
1 | 0.95 | 0.89 | 0.84 | 0.68 | 1.00 | 0.63 | 0.79 | 0.95 | 0.79 |
time (sec) |
N/A | 0.394 | 0.042 | 0.185 | 0.060 | 0.098 | 0.044 | 0.111 | 0.173 | 2.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 18 | 18 | 15 | 14 | 35 | 14 | 33 | 18 | 15 |
N.S. |
1 | 0.95 | 0.95 | 0.79 | 0.74 | 1.84 | 0.74 | 1.74 | 0.95 | 0.79 |
time (sec) |
N/A | 0.594 | 0.092 | 0.136 | 0.246 | 0.096 | 0.115 | 0.119 | 0.170 | 2.526 |
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 | 14 | 14 | 15 | 14 | 14 | 14 | 14 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 | 1.00 | 1.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.153 | 0.002 | 0.036 | 0.034 | 0.069 | 0.043 | 0.111 | 0.172 | 2.501 |
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 | 19 | 21 | 23 | 39 | 19 | 25 | 41 | 22 |
N.S. |
1 | 0.00 | 0.83 | 0.91 | 1.00 | 1.70 | 0.83 | 1.09 | 1.78 | 0.96 |
time (sec) |
N/A | 0.000 | 0.278 | 0.438 | 0.123 | 0.091 | 54.480 | 0.749 | 0.171 | 2.737 |
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 | 20 | 20 | 21 | 20 | 20 | 22 | 20 | 28 | 18 |
N.S. |
1 | 0.87 | 0.87 | 0.91 | 0.87 | 0.87 | 0.96 | 0.87 | 1.22 | 0.78 |
time (sec) |
N/A | 0.446 | 0.037 | 0.079 | 0.065 | 0.089 | 0.106 | 0.107 | 0.167 | 2.565 |
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 | 19 | 32 | 32 | 15 | 23 | 16 | 29 | 25 | 17 | 10 |
N.S. |
1 | 1.68 | 1.68 | 0.79 | 1.21 | 0.84 | 1.53 | 1.32 | 0.89 | 0.53 |
time (sec) |
N/A | 0.176 | 0.004 | 0.054 | 0.034 | 0.077 | 0.095 | 0.108 | 0.170 | 2.664 |
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 | 28 | 20 | 17 | 16 | 16 | 24 | 16 | 26 | 24 |
N.S. |
1 | 1.40 | 1.00 | 0.85 | 0.80 | 0.80 | 1.20 | 0.80 | 1.30 | 1.20 |
time (sec) |
N/A | 2.187 | 1.069 | 11.932 | 0.151 | 0.076 | 1.760 | 0.113 | 0.225 | 3.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 40 | 44 | 38 | 75 | 70 | 44 | 39 |
N.S. |
1 | 0.00 | 1.00 | 1.29 | 1.42 | 1.23 | 2.42 | 2.26 | 1.42 | 1.26 |
time (sec) |
N/A | 0.000 | 0.136 | 7.043 | 0.181 | 0.091 | 1.366 | 0.503 | 0.226 | 3.293 |
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 | 15 | 15 | 17 | 16 | 16 | 17 | 16 | 15 | 16 |
N.S. |
1 | 1.07 | 1.07 | 1.21 | 1.14 | 1.14 | 1.21 | 1.14 | 1.07 | 1.14 |
time (sec) |
N/A | 0.629 | 0.120 | 0.217 | 0.071 | 0.079 | 0.083 | 0.113 | 0.176 | 2.719 |
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 | 23 | 0 | 29 | 25 | 70 | 33 | 20 | 33 | 31 | 79 |
N.S. |
1 | 0.00 | 1.26 | 1.09 | 3.04 | 1.43 | 0.87 | 1.43 | 1.35 | 3.43 |
time (sec) |
N/A | 0.000 | 0.453 | 0.271 | 0.197 | 0.089 | 0.099 | 0.209 | 0.184 | 2.758 |
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 | 25 | 28 | 27 | 25 | 28 | 26 | 30 | 28 | 26 |
N.S. |
1 | 1.19 | 1.33 | 1.29 | 1.19 | 1.33 | 1.24 | 1.43 | 1.33 | 1.24 |
time (sec) |
N/A | 0.449 | 0.015 | 0.085 | 0.041 | 0.068 | 0.679 | 0.115 | 0.182 | 0.199 |
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 | 22 | 36 | 32 | 34 | 35 | 27 | 29 | 33 | 36 | 33 |
N.S. |
1 | 1.64 | 1.45 | 1.55 | 1.59 | 1.23 | 1.32 | 1.50 | 1.64 | 1.50 |
time (sec) |
N/A | 0.348 | 0.154 | 0.734 | 0.063 | 0.090 | 0.139 | 0.110 | 0.189 | 2.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 51 | 41 | 49 | 34 | 32 | 59 | 39 | 0 |
N.S. |
1 | 0.00 | 1.82 | 1.46 | 1.75 | 1.21 | 1.14 | 2.11 | 1.39 | 0.00 |
time (sec) |
N/A | 0.000 | 0.099 | 0.533 | 0.084 | 0.103 | 0.185 | 1.504 | 0.179 | 0.000 |
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 | 18 | 0 | 17 | 20 | 103 | 20 | 14 | 39 | 22 | 18 |
N.S. |
1 | 0.00 | 0.94 | 1.11 | 5.72 | 1.11 | 0.78 | 2.17 | 1.22 | 1.00 |
time (sec) |
N/A | 0.000 | 0.168 | 0.109 | 0.090 | 0.100 | 0.080 | 0.123 | 0.180 | 3.408 |
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 | 26 | 0 | 25 | 21 | 20 | 34 | 0 | 0 | 25 | 20 |
N.S. |
1 | 0.00 | 0.96 | 0.81 | 0.77 | 1.31 | 0.00 | 0.00 | 0.96 | 0.77 |
time (sec) |
N/A | 0.000 | 3.618 | 1.049 | 0.110 | 0.104 | 0.000 | 0.000 | 0.176 | 2.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 22 | 22 | 22 | 22 | 22 | 19 | 26 | 22 | 0 |
N.S. |
1 | 0.96 | 0.96 | 0.96 | 0.96 | 0.96 | 0.83 | 1.13 | 0.96 | 0.00 |
time (sec) |
N/A | 0.778 | 0.119 | 0.234 | 0.086 | 0.083 | 0.138 | 0.117 | 0.171 | 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 | 26 | 28 | 36 | 18 | 28 | 20 | 19 | 28 | 43 | 27 |
N.S. |
1 | 1.08 | 1.38 | 0.69 | 1.08 | 0.77 | 0.73 | 1.08 | 1.65 | 1.04 |
time (sec) |
N/A | 0.650 | 0.038 | 0.247 | 0.211 | 0.092 | 0.157 | 0.110 | 0.178 | 0.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 65 | 57 | 31 | 46 | 53 | 46 | 48 | 31 | 48 |
N.S. |
1 | 2.10 | 1.84 | 1.00 | 1.48 | 1.71 | 1.48 | 1.55 | 1.00 | 1.55 |
time (sec) |
N/A | 0.501 | 0.023 | 0.226 | 0.039 | 0.081 | 3.185 | 0.124 | 0.179 | 2.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 32 | 39 | 35 | 36 | 36 | 105 | 38 |
N.S. |
1 | 0.00 | 0.00 | 1.19 | 1.44 | 1.30 | 1.33 | 1.33 | 3.89 | 1.41 |
time (sec) |
N/A | 0.000 | 0.000 | 0.931 | 0.290 | 0.087 | 0.397 | 0.413 | 200.017 | 2.648 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | F | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 47 | 42 | 0 | 53 | 36 | 96 | 93 | 42 |
N.S. |
1 | 0.00 | 2.04 | 1.83 | 0.00 | 2.30 | 1.57 | 4.17 | 4.04 | 1.83 |
time (sec) |
N/A | 0.000 | 0.776 | 0.177 | 0.000 | 0.091 | 3.056 | 0.137 | 0.160 | 2.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 126 | 25 | 28 | 31 | 26 | 26 | 0 | 35 | 0 |
N.S. |
1 | 5.73 | 1.14 | 1.27 | 1.41 | 1.18 | 1.18 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.713 | 0.311 | 0.449 | 0.186 | 0.089 | 0.276 | 0.000 | 0.165 | 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 | 22 | 23 | 26 | 21 | 26 | 25 | 30 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.05 | 1.18 | 0.95 | 1.18 | 1.14 | 1.36 | 0.95 |
time (sec) |
N/A | 0.000 | 0.032 | 0.122 | 0.152 | 0.082 | 0.104 | 0.111 | 0.157 | 2.762 |
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 | 25 | 0 | 20 | 19 | 18 | 30 | 17 | 0 | 20 | 18 |
N.S. |
1 | 0.00 | 0.80 | 0.76 | 0.72 | 1.20 | 0.68 | 0.00 | 0.80 | 0.72 |
time (sec) |
N/A | 0.000 | 1.379 | 0.609 | 0.080 | 0.089 | 0.189 | 0.000 | 0.163 | 2.632 |
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 | 26 | 124 | 32 | 24 | 34 | 24 | 20 | 24 | 94 | 26 |
N.S. |
1 | 4.77 | 1.23 | 0.92 | 1.31 | 0.92 | 0.77 | 0.92 | 3.62 | 1.00 |
time (sec) |
N/A | 0.805 | 0.068 | 0.425 | 0.189 | 0.076 | 0.091 | 0.124 | 0.168 | 0.235 |
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 | 17 | 13 | 21 | 14 | 13 | 18 | 10 | 13 | 18 | 13 |
N.S. |
1 | 0.76 | 1.24 | 0.82 | 0.76 | 1.06 | 0.59 | 0.76 | 1.06 | 0.76 |
time (sec) |
N/A | 0.353 | 0.010 | 0.071 | 0.028 | 0.078 | 0.043 | 0.110 | 0.157 | 0.056 |
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 | 32 | 0 | 33 | 32 | 70 | 31 | 27 | 1317 | 33 | 31 |
N.S. |
1 | 0.00 | 1.03 | 1.00 | 2.19 | 0.97 | 0.84 | 41.16 | 1.03 | 0.97 |
time (sec) |
N/A | 0.000 | 0.072 | 21.665 | 0.132 | 0.096 | 0.203 | 0.208 | 0.174 | 2.873 |
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 | 29 | 28 | 22 | 37 | 36 | 34 | 24 | 31 | 31 | 32 |
N.S. |
1 | 0.97 | 0.76 | 1.28 | 1.24 | 1.17 | 0.83 | 1.07 | 1.07 | 1.10 |
time (sec) |
N/A | 1.298 | 0.485 | 0.988 | 0.145 | 0.103 | 0.233 | 0.123 | 0.181 | 2.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | C | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 77 | 116 | 181 | 109 | 116 | 114 | 139 | 127 |
N.S. |
1 | 0.00 | 2.48 | 3.74 | 5.84 | 3.52 | 3.74 | 3.68 | 4.48 | 4.10 |
time (sec) |
N/A | 0.000 | 0.033 | 10.819 | 0.103 | 0.087 | 0.107 | 0.129 | 0.157 | 2.707 |
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 | 22 | 11 | 11 | 10 | 51 | 14 | 12 | 14 | 27 | 9 |
N.S. |
1 | 0.50 | 0.50 | 0.45 | 2.32 | 0.64 | 0.55 | 0.64 | 1.23 | 0.41 |
time (sec) |
N/A | 0.500 | 0.025 | 0.101 | 0.027 | 0.093 | 0.086 | 0.112 | 0.164 | 2.535 |
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 | 22 | 154 | 35 | 38 | 737 | 36 | 36 | 39 | 43 | 7411 |
N.S. |
1 | 7.00 | 1.59 | 1.73 | 33.50 | 1.64 | 1.64 | 1.77 | 1.95 | 336.86 |
time (sec) |
N/A | 1.208 | 0.106 | 0.359 | 0.052 | 0.103 | 0.256 | 0.120 | 0.157 | 12.645 |
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 | 6 | 6 | 5 | 6 | 6 | 5 | 7 | 6 | 4 |
N.S. |
1 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 | 0.62 | 0.88 | 0.75 | 0.50 |
time (sec) |
N/A | 0.134 | 0.001 | 0.028 | 0.026 | 0.072 | 0.019 | 0.112 | 0.185 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 22 | 1552 | 1114 | 17 | 1114 | 63 | 1773 |
N.S. |
1 | 0.00 | 0.88 | 0.92 | 64.67 | 46.42 | 0.71 | 46.42 | 2.62 | 73.88 |
time (sec) |
N/A | 0.000 | 7.633 | 94.909 | 89.899 | 0.573 | 103.280 | 0.202 | 200.027 | 3.684 |
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 | 19 | 18 | 16 | 19 | 17 | 18 | 21 | 14 |
N.S. |
1 | 0.00 | 0.90 | 0.86 | 0.76 | 0.90 | 0.81 | 0.86 | 1.00 | 0.67 |
time (sec) |
N/A | 0.000 | 0.147 | 0.191 | 0.143 | 0.079 | 0.083 | 0.110 | 0.166 | 2.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 30 | 27 | 0 | 23 | 22 | 63 | 49 | 24 |
N.S. |
1 | 0.00 | 1.03 | 0.93 | 0.00 | 0.79 | 0.76 | 2.17 | 1.69 | 0.83 |
time (sec) |
N/A | 0.000 | 5.100 | 0.220 | 0.000 | 0.088 | 0.790 | 0.121 | 0.179 | 2.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 17 | 16 | 0 | 30 | 0 | 0 | 89 | 15 |
N.S. |
1 | 0.00 | 0.89 | 0.84 | 0.00 | 1.58 | 0.00 | 0.00 | 4.68 | 0.79 |
time (sec) |
N/A | 0.000 | 0.163 | 0.209 | 0.000 | 0.095 | 0.000 | 0.000 | 0.177 | 2.614 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | 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 | 144 | 92 | 108 | 89 | 110 | 0 | 141 | 0 |
N.S. |
1 | 0.00 | 6.00 | 3.83 | 4.50 | 3.71 | 4.58 | 0.00 | 5.88 | 0.00 |
time (sec) |
N/A | 0.000 | 1.300 | 0.863 | 0.265 | 0.116 | 3.821 | 0.000 | 0.183 | 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 | 8 | 7 | 7 | 5 | 7 | 7 | 7 |
N.S. |
1 | 0.78 | 0.78 | 0.89 | 0.78 | 0.78 | 0.56 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.143 | 0.000 | 0.011 | 0.030 | 0.084 | 0.015 | 0.106 | 0.174 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 64 | 220 | 55 | 65 | 111 | 73 | 26 | 320 | 923 |
N.S. |
1 | 2.78 | 9.57 | 2.39 | 2.83 | 4.83 | 3.17 | 1.13 | 13.91 | 40.13 |
time (sec) |
N/A | 0.519 | 0.093 | 0.309 | 0.026 | 0.102 | 0.566 | 0.108 | 0.169 | 4.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 28 | 73 | 55 | 22 | 72 | 43 | 25 |
N.S. |
1 | 0.00 | 0.93 | 1.00 | 2.61 | 1.96 | 0.79 | 2.57 | 1.54 | 0.89 |
time (sec) |
N/A | 0.000 | 0.135 | 0.208 | 0.149 | 0.097 | 0.150 | 0.116 | 0.172 | 0.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 31 | 23 | 76 | 26 | 0 | 246 | 25 |
N.S. |
1 | 0.00 | 0.93 | 1.11 | 0.82 | 2.71 | 0.93 | 0.00 | 8.79 | 0.89 |
time (sec) |
N/A | 0.000 | 1.241 | 0.330 | 0.414 | 0.101 | 0.397 | 0.000 | 0.781 | 2.685 |
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 | 10 | 10 | 10 | 11 | 10 | 10 | 8 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.80 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.254 | 0.001 | 0.028 | 0.026 | 0.083 | 0.075 | 0.112 | 0.168 | 2.517 |
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 | 10 | 12 | 8 | 10 | 9 | 9 | 7 | 9 | 19 | 9 |
N.S. |
1 | 1.20 | 0.80 | 1.00 | 0.90 | 0.90 | 0.70 | 0.90 | 1.90 | 0.90 |
time (sec) |
N/A | 0.261 | 0.003 | 0.083 | 0.033 | 0.080 | 0.077 | 0.113 | 0.184 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F | B | B | F | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 169 | 0 | 0 | 173 | 141 | 0 | 288 | 0 |
N.S. |
1 | 0.00 | 5.63 | 0.00 | 0.00 | 5.77 | 4.70 | 0.00 | 9.60 | 0.00 |
time (sec) |
N/A | 0.000 | 0.056 | 0.000 | 0.000 | 0.099 | 0.693 | 0.000 | 0.191 | 0.000 |
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 | 23 | 28 | 25 | 21 | 32 | 24 | 17 | 26 | 28 | 24 |
N.S. |
1 | 1.22 | 1.09 | 0.91 | 1.39 | 1.04 | 0.74 | 1.13 | 1.22 | 1.04 |
time (sec) |
N/A | 0.612 | 0.049 | 0.134 | 0.068 | 0.085 | 0.063 | 0.119 | 0.176 | 2.454 |
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 | 33 | 184 | 29 | 144 | 127 | 124 | 165 | 122 | 139 | 147 |
N.S. |
1 | 5.58 | 0.88 | 4.36 | 3.85 | 3.76 | 5.00 | 3.70 | 4.21 | 4.45 |
time (sec) |
N/A | 1.384 | 1.597 | 0.731 | 0.031 | 0.105 | 0.176 | 0.122 | 0.178 | 0.183 |
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 | 9 | 14 | 13 | 14 | 14 | 12 | 14 | 12 | 14 |
N.S. |
1 | 0.64 | 1.00 | 0.93 | 1.00 | 1.00 | 0.86 | 1.00 | 0.86 | 1.00 |
time (sec) |
N/A | 0.228 | 0.000 | 0.026 | 0.027 | 0.067 | 0.021 | 0.122 | 0.174 | 2.410 |
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 | 34 | 22 | 20 | 21 | 23 | 20 | 21 | 23 | 21 |
N.S. |
1 | 1.17 | 0.76 | 0.69 | 0.72 | 0.79 | 0.69 | 0.72 | 0.79 | 0.72 |
time (sec) |
N/A | 0.347 | 0.013 | 0.154 | 0.185 | 0.085 | 0.089 | 0.153 | 0.990 | 2.603 |
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 | 29 | 0 | 27 | 23 | 43 | 65 | 22 | 0 | 28 | 22 |
N.S. |
1 | 0.00 | 0.93 | 0.79 | 1.48 | 2.24 | 0.76 | 0.00 | 0.97 | 0.76 |
time (sec) |
N/A | 0.000 | 3.538 | 3.309 | 0.215 | 0.111 | 0.502 | 0.000 | 0.186 | 2.633 |
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 | 18 | 24 | 19 | 22 | 22 | 24 | 22 | 25 | 22 |
N.S. |
1 | 1.06 | 1.41 | 1.12 | 1.29 | 1.29 | 1.41 | 1.29 | 1.47 | 1.29 |
time (sec) |
N/A | 0.283 | 0.005 | 0.066 | 0.042 | 0.086 | 0.053 | 0.115 | 0.183 | 2.547 |
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 | 27 | 27 | 21 | 18 | 23 | 32 | 20 | 38 | 38 | 23 |
N.S. |
1 | 1.00 | 0.78 | 0.67 | 0.85 | 1.19 | 0.74 | 1.41 | 1.41 | 0.85 |
time (sec) |
N/A | 0.438 | 0.238 | 0.145 | 0.031 | 0.097 | 0.158 | 0.135 | 200.025 | 0.227 |
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 | 31 | 0 | 90 | 66 | 287 | 76 | 114 | 114 | 121 | 89 |
N.S. |
1 | 0.00 | 2.90 | 2.13 | 9.26 | 2.45 | 3.68 | 3.68 | 3.90 | 2.87 |
time (sec) |
N/A | 0.000 | 0.069 | 1.560 | 0.096 | 0.092 | 0.585 | 0.169 | 0.190 | 3.015 |
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 | 24 | 16 | 16 | 16 | 21 | 30 | 37 | 16 | 30 | 20 |
N.S. |
1 | 0.67 | 0.67 | 0.67 | 0.88 | 1.25 | 1.54 | 0.67 | 1.25 | 0.83 |
time (sec) |
N/A | 0.220 | 0.008 | 0.058 | 0.037 | 0.074 | 0.114 | 0.121 | 0.180 | 0.063 |
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 | 27 | 0 | 23 | 33 | 22 | 31 | 29 | 32 | 35 | 0 |
N.S. |
1 | 0.00 | 0.85 | 1.22 | 0.81 | 1.15 | 1.07 | 1.19 | 1.30 | 0.00 |
time (sec) |
N/A | 0.000 | 0.054 | 0.717 | 0.116 | 0.097 | 0.237 | 0.246 | 0.182 | 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 | 26 | 37 | 26 | 27 | 82 | 28 | 22 | 35 | 39 | 27 |
N.S. |
1 | 1.42 | 1.00 | 1.04 | 3.15 | 1.08 | 0.85 | 1.35 | 1.50 | 1.04 |
time (sec) |
N/A | 0.462 | 0.064 | 2.733 | 0.038 | 0.079 | 0.125 | 0.129 | 0.180 | 2.659 |
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 | 39 | 36 | 35 | 36 | 36 | 36 | 35 | 65 |
N.S. |
1 | 0.00 | 1.18 | 1.09 | 1.06 | 1.09 | 1.09 | 1.09 | 1.06 | 1.97 |
time (sec) |
N/A | 0.000 | 0.103 | 1.173 | 0.218 | 0.083 | 0.289 | 0.997 | 0.183 | 2.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 76 | 74 | 30 | 29 | 29 | 37 | 29 | 25 | 27 |
N.S. |
1 | 2.71 | 2.64 | 1.07 | 1.04 | 1.04 | 1.32 | 1.04 | 0.89 | 0.96 |
time (sec) |
N/A | 0.396 | 0.066 | 0.170 | 0.027 | 0.100 | 0.080 | 0.121 | 0.182 | 0.062 |
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 | 29 | 0 | 20 | 21 | 48 | 46 | 49 | 47 | 48 | 0 |
N.S. |
1 | 0.00 | 0.69 | 0.72 | 1.66 | 1.59 | 1.69 | 1.62 | 1.66 | 0.00 |
time (sec) |
N/A | 0.000 | 5.015 | 0.874 | 0.185 | 0.089 | 0.174 | 0.130 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | A | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 70 | 38 | 46 | 45 | 0 | 34 | 36 | 34 |
N.S. |
1 | 0.00 | 2.41 | 1.31 | 1.59 | 1.55 | 0.00 | 1.17 | 1.24 | 1.17 |
time (sec) |
N/A | 0.000 | 8.201 | 0.296 | 0.085 | 0.097 | 0.000 | 0.130 | 0.189 | 2.795 |
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 | 15 | 15 | 16 | 15 | 15 | 10 | 16 | 15 | 15 |
N.S. |
1 | 0.94 | 0.94 | 1.00 | 0.94 | 0.94 | 0.62 | 1.00 | 0.94 | 0.94 |
time (sec) |
N/A | 0.477 | 0.051 | 0.102 | 0.114 | 0.091 | 0.077 | 0.120 | 0.189 | 2.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 35 | 38 | 56 | 49 | 54 | 69 | 69 | 0 |
N.S. |
1 | 0.00 | 1.06 | 1.15 | 1.70 | 1.48 | 1.64 | 2.09 | 2.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.154 | 57.860 | 0.816 | 0.096 | 0.337 | 0.780 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 104 | 86 | 86 | 291 | 113 | 121 | 217 |
N.S. |
1 | 0.00 | 0.97 | 3.59 | 2.97 | 2.97 | 10.03 | 3.90 | 4.17 | 7.48 |
time (sec) |
N/A | 0.000 | 0.793 | 0.740 | 0.101 | 0.100 | 0.373 | 0.132 | 0.212 | 2.918 |
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 | 37 | 41 | 34 | 33 | 37 | 31 | 34 | 37 | 33 |
N.S. |
1 | 1.23 | 1.37 | 1.13 | 1.10 | 1.23 | 1.03 | 1.13 | 1.23 | 1.10 |
time (sec) |
N/A | 0.214 | 0.004 | 0.029 | 0.033 | 0.086 | 0.052 | 0.121 | 0.191 | 2.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 72 | 55 | 171 | 30 | 24 | 48 | 45 | 30 |
N.S. |
1 | 0.00 | 2.18 | 1.67 | 5.18 | 0.91 | 0.73 | 1.45 | 1.36 | 0.91 |
time (sec) |
N/A | 0.000 | 0.092 | 0.402 | 0.056 | 0.098 | 0.178 | 0.123 | 0.193 | 2.531 |
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 | 25 | 24 | 25 | 23 | 24 | 26 | 24 | 26 | 45 |
N.S. |
1 | 1.09 | 1.04 | 1.09 | 1.00 | 1.04 | 1.13 | 1.04 | 1.13 | 1.96 |
time (sec) |
N/A | 0.569 | 0.028 | 0.359 | 0.163 | 0.091 | 0.123 | 0.145 | 0.231 | 0.382 |
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 | 25 | 27 | 20 | 21 | 22 | 31 | 20 | 17 | 25 | 17 |
N.S. |
1 | 1.08 | 0.80 | 0.84 | 0.88 | 1.24 | 0.80 | 0.68 | 1.00 | 0.68 |
time (sec) |
N/A | 0.517 | 0.167 | 0.187 | 0.063 | 0.078 | 0.071 | 0.124 | 0.198 | 0.076 |
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 | 28 | 20 | 20 | 25 | 20 | 22 | 25 | 22 | 20 |
N.S. |
1 | 1.40 | 1.00 | 1.00 | 1.25 | 1.00 | 1.10 | 1.25 | 1.10 | 1.00 |
time (sec) |
N/A | 0.842 | 0.031 | 0.119 | 0.043 | 0.089 | 0.107 | 0.127 | 0.193 | 2.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 42 | 56 | 50 | 53 | 53 | 60 | 70 | 98 |
N.S. |
1 | 0.00 | 1.11 | 1.47 | 1.32 | 1.39 | 1.39 | 1.58 | 1.84 | 2.58 |
time (sec) |
N/A | 0.000 | 0.147 | 59.773 | 0.400 | 0.089 | 0.747 | 0.324 | 0.209 | 2.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 95 | 50 | 59 | 80 | 59 | 60 | 78 | 84 | 69 |
N.S. |
1 | 3.28 | 1.72 | 2.03 | 2.76 | 2.03 | 2.07 | 2.69 | 2.90 | 2.38 |
time (sec) |
N/A | 0.489 | 0.697 | 0.637 | 0.075 | 0.095 | 0.102 | 0.122 | 0.228 | 0.090 |
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 | 17 | 16 | 17 | 17 | 19 | 17 | 16 | 20 |
N.S. |
1 | 0.00 | 0.81 | 0.76 | 0.81 | 0.81 | 0.90 | 0.81 | 0.76 | 0.95 |
time (sec) |
N/A | 0.000 | 0.068 | 0.406 | 0.147 | 0.083 | 0.076 | 0.118 | 0.189 | 2.787 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 17 | 17 | 25 | 26 | 24 | 54 | 24 | 495 | 24 |
N.S. |
1 | 0.65 | 0.65 | 0.96 | 1.00 | 0.92 | 2.08 | 0.92 | 19.04 | 0.92 |
time (sec) |
N/A | 1.461 | 0.844 | 0.386 | 0.093 | 0.086 | 0.421 | 0.153 | 0.213 | 2.905 |
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 | 22 | 0 | 21 | 18 | 23 | 20 | 22 | 23 | 134 | 19 |
N.S. |
1 | 0.00 | 0.95 | 0.82 | 1.05 | 0.91 | 1.00 | 1.05 | 6.09 | 0.86 |
time (sec) |
N/A | 0.000 | 0.104 | 1.416 | 0.141 | 0.101 | 0.749 | 0.176 | 0.210 | 2.652 |
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 | 37 | 21 | 21 | 20 | 20 | 19 | 20 | 17 | 16 |
N.S. |
1 | 1.42 | 0.81 | 0.81 | 0.77 | 0.77 | 0.73 | 0.77 | 0.65 | 0.62 |
time (sec) |
N/A | 0.282 | 0.014 | 0.106 | 0.033 | 0.088 | 0.050 | 0.125 | 0.220 | 0.043 |
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 | 31 | 62 | 28 | 28 | 27 | 27 | 24 | 27 | 28 | 29 |
N.S. |
1 | 2.00 | 0.90 | 0.90 | 0.87 | 0.87 | 0.77 | 0.87 | 0.90 | 0.94 |
time (sec) |
N/A | 0.949 | 0.242 | 1.431 | 0.168 | 0.096 | 0.162 | 0.125 | 0.192 | 2.824 |
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 | 15 | 16 | 15 | 15 | 14 | 15 | 15 | 15 |
N.S. |
1 | 0.00 | 0.54 | 0.57 | 0.54 | 0.54 | 0.50 | 0.54 | 0.54 | 0.54 |
time (sec) |
N/A | 0.000 | 0.063 | 0.166 | 0.070 | 0.081 | 0.057 | 0.139 | 0.192 | 2.661 |
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 | 21 | 21 | 29 | 27 | 33 | 29 | 20 | 25 | 22 |
N.S. |
1 | 0.95 | 0.95 | 1.32 | 1.23 | 1.50 | 1.32 | 0.91 | 1.14 | 1.00 |
time (sec) |
N/A | 1.035 | 0.663 | 0.332 | 0.203 | 0.096 | 0.118 | 0.205 | 0.197 | 2.620 |
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 | 30 | 0 | 37 | 29 | 41 | 36 | 26 | 0 | 38 | 34 |
N.S. |
1 | 0.00 | 1.23 | 0.97 | 1.37 | 1.20 | 0.87 | 0.00 | 1.27 | 1.13 |
time (sec) |
N/A | 0.000 | 2.015 | 0.328 | 0.081 | 0.088 | 3.568 | 0.000 | 0.230 | 2.532 |
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 | 34 | 70 | 36 | 33 | 49 | 48 | 31 | 61 | 66 | 32 |
N.S. |
1 | 2.06 | 1.06 | 0.97 | 1.44 | 1.41 | 0.91 | 1.79 | 1.94 | 0.94 |
time (sec) |
N/A | 0.793 | 0.100 | 0.329 | 0.148 | 0.087 | 0.077 | 0.122 | 0.204 | 0.370 |
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 | 23 | 26 | 23 | 20 | 19 | 19 | 20 | 19 | 434 | 22 |
N.S. |
1 | 1.13 | 1.00 | 0.87 | 0.83 | 0.83 | 0.87 | 0.83 | 18.87 | 0.96 |
time (sec) |
N/A | 2.810 | 0.194 | 1.751 | 0.194 | 0.086 | 0.923 | 0.176 | 0.516 | 2.819 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 18 | 37 | 15 | 14 | 34 | 17 | 15 | 33 | 14 |
N.S. |
1 | 1.12 | 2.31 | 0.94 | 0.88 | 2.12 | 1.06 | 0.94 | 2.06 | 0.88 |
time (sec) |
N/A | 0.456 | 0.102 | 0.056 | 0.027 | 0.094 | 0.064 | 0.123 | 0.220 | 0.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 55 | 52 | 57 | 32 | 44 | 53 | 129 | 49 |
N.S. |
1 | 0.00 | 1.67 | 1.58 | 1.73 | 0.97 | 1.33 | 1.61 | 3.91 | 1.48 |
time (sec) |
N/A | 0.000 | 0.102 | 4.106 | 0.158 | 0.093 | 0.584 | 0.153 | 200.016 | 2.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 628 | 27 | 272 | 211 | 212 | 237 | 320 | 0 |
N.S. |
1 | 0.00 | 25.12 | 1.08 | 10.88 | 8.44 | 8.48 | 9.48 | 12.80 | 0.00 |
time (sec) |
N/A | 0.000 | 0.489 | 0.164 | 0.296 | 0.101 | 0.321 | 0.518 | 1.131 | 0.000 |
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 | 17 | 38 | 16 | 20 | 22 | 22 | 20 | 22 | 50 | 18 |
N.S. |
1 | 2.24 | 0.94 | 1.18 | 1.29 | 1.29 | 1.18 | 1.29 | 2.94 | 1.06 |
time (sec) |
N/A | 0.189 | 0.072 | 0.158 | 0.027 | 0.078 | 0.066 | 0.119 | 0.165 | 0.079 |
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 | 15 | 16 | 16 | 12 | 0 | 28 | 10 | 28 | 26 | 13 |
N.S. |
1 | 1.07 | 1.07 | 0.80 | 0.00 | 1.87 | 0.67 | 1.87 | 1.73 | 0.87 |
time (sec) |
N/A | 0.303 | 0.082 | 0.207 | 0.000 | 0.083 | 0.062 | 0.123 | 0.165 | 0.090 |
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 | 21 | 19 | 23 | 23 | 22 | 23 | 26 | 18 |
N.S. |
1 | 0.00 | 0.88 | 0.79 | 0.96 | 0.96 | 0.92 | 0.96 | 1.08 | 0.75 |
time (sec) |
N/A | 0.000 | 0.443 | 0.716 | 0.082 | 0.076 | 0.094 | 0.130 | 0.189 | 0.126 |
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 | 28 | 0 | 21 | 15 | 14 | 24 | 20 | 28 | 79 | 14 |
N.S. |
1 | 0.00 | 0.75 | 0.54 | 0.50 | 0.86 | 0.71 | 1.00 | 2.82 | 0.50 |
time (sec) |
N/A | 0.000 | 0.196 | 0.151 | 0.144 | 0.090 | 0.205 | 0.137 | 0.201 | 2.800 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 44 | 23 | 0 | 22 | 22 | 0 | 0 | 52 |
N.S. |
1 | 0.00 | 1.69 | 0.88 | 0.00 | 0.85 | 0.85 | 0.00 | 0.00 | 2.00 |
time (sec) |
N/A | 0.000 | 2.703 | 0.334 | 0.000 | 0.080 | 0.314 | 0.000 | 0.242 | 2.868 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 135 | 584 | 119 | 126 | 123 | 68 | 594 |
N.S. |
1 | 0.00 | 1.00 | 5.87 | 25.39 | 5.17 | 5.48 | 5.35 | 2.96 | 25.83 |
time (sec) |
N/A | 0.000 | 0.929 | 0.227 | 0.736 | 0.111 | 1.630 | 2.502 | 0.286 | 5.385 |
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 | 31 | 0 | 44 | 43 | 39 | 39 | 31 | 39 | 43 | 42 |
N.S. |
1 | 0.00 | 1.42 | 1.39 | 1.26 | 1.26 | 1.00 | 1.26 | 1.39 | 1.35 |
time (sec) |
N/A | 0.000 | 0.070 | 9.986 | 0.078 | 0.091 | 0.101 | 0.140 | 0.213 | 2.743 |
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 | 19 | 21 | 18 | 21 | 21 | 29 | 21 | 18 | 18 |
N.S. |
1 | 1.19 | 1.31 | 1.12 | 1.31 | 1.31 | 1.81 | 1.31 | 1.12 | 1.12 |
time (sec) |
N/A | 0.193 | 0.002 | 0.046 | 0.030 | 0.070 | 0.023 | 0.118 | 0.189 | 2.526 |
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 | 17 | 17 | 18 | 17 | 22 | 12 | 17 | 25 | 17 |
N.S. |
1 | 0.94 | 0.94 | 1.00 | 0.94 | 1.22 | 0.67 | 0.94 | 1.39 | 0.94 |
time (sec) |
N/A | 0.412 | 0.031 | 0.082 | 0.095 | 0.082 | 0.047 | 0.123 | 0.196 | 2.538 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 24 | 28 | 23 | 20 | 288 | 24 | 0 |
N.S. |
1 | 0.00 | 0.92 | 0.92 | 1.08 | 0.88 | 0.77 | 11.08 | 0.92 | 0.00 |
time (sec) |
N/A | 0.000 | 0.097 | 144.512 | 0.209 | 0.092 | 1.917 | 0.530 | 0.219 | 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 | 36 | 0 | 29 | 27 | 26 | 26 | 24 | 26 | 27 | 26 |
N.S. |
1 | 0.00 | 0.81 | 0.75 | 0.72 | 0.72 | 0.67 | 0.72 | 0.75 | 0.72 |
time (sec) |
N/A | 0.000 | 0.224 | 0.248 | 0.153 | 0.086 | 0.103 | 0.121 | 0.209 | 0.146 |
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 | 23 | 25 | 22 | 22 | 19 | 22 | 23 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.09 | 0.96 | 0.96 | 0.83 | 0.96 | 1.00 | 1.04 |
time (sec) |
N/A | 0.000 | 1.134 | 0.600 | 0.151 | 0.098 | 0.073 | 0.127 | 0.200 | 2.724 |
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 | 26 | 27 | 33 | 33 | 27 | 42 | 37 | 26 |
N.S. |
1 | 0.00 | 0.93 | 0.96 | 1.18 | 1.18 | 0.96 | 1.50 | 1.32 | 0.93 |
time (sec) |
N/A | 0.000 | 0.058 | 3.049 | 0.086 | 0.082 | 0.156 | 0.248 | 0.198 | 2.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 27 | 31 | 25 | 46 | 25 | 24 | 27 |
N.S. |
1 | 0.00 | 0.96 | 1.08 | 1.24 | 1.00 | 1.84 | 1.00 | 0.96 | 1.08 |
time (sec) |
N/A | 0.000 | 0.042 | 5.368 | 0.097 | 0.110 | 0.728 | 0.484 | 0.237 | 3.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 74 | 42 | 46 | 0 | 43 | 92 | 83 | 54 | 50 |
N.S. |
1 | 2.24 | 1.27 | 1.39 | 0.00 | 1.30 | 2.79 | 2.52 | 1.64 | 1.52 |
time (sec) |
N/A | 0.801 | 1.650 | 0.799 | 0.000 | 0.096 | 0.611 | 0.130 | 0.208 | 0.362 |
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 | 24 | 93 | 40 | 22 | 68 | 50 | 21 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 3.72 | 1.60 | 0.88 | 2.72 | 2.00 | 0.84 |
time (sec) |
N/A | 0.000 | 0.135 | 0.563 | 0.085 | 0.086 | 0.213 | 0.129 | 0.196 | 2.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | C | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 88 | 81 | 133 | 77 | 83 | 107 | 118 | 66 |
N.S. |
1 | 0.00 | 3.26 | 3.00 | 4.93 | 2.85 | 3.07 | 3.96 | 4.37 | 2.44 |
time (sec) |
N/A | 0.000 | 0.339 | 22.098 | 0.102 | 0.090 | 3.288 | 0.130 | 1.657 | 3.002 |