Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 38 | 25 | 26 | 37 | 22 | 25 | 18 |
N.S. |
1 | 1.00 | 1.36 | 0.89 | 0.93 | 1.32 | 0.79 | 0.89 | 0.64 |
time (sec) |
N/A | 0.010 | 0.011 | 1.793 | 0.202 | 0.226 | 0.052 | 0.275 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 35 | 32 | 36 | 55 | 32 | 33 | 25 |
N.S. |
1 | 1.00 | 0.95 | 0.86 | 0.97 | 1.49 | 0.86 | 0.89 | 0.68 |
time (sec) |
N/A | 0.012 | 0.017 | 1.915 | 0.216 | 0.215 | 0.059 | 0.278 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 40 | 36 | 46 | 75 | 42 | 38 | 35 |
N.S. |
1 | 1.00 | 0.83 | 0.75 | 0.96 | 1.56 | 0.88 | 0.79 | 0.73 |
time (sec) |
N/A | 0.014 | 0.021 | 1.816 | 0.201 | 0.227 | 0.065 | 0.271 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 45 | 41 | 56 | 95 | 53 | 52 | 45 |
N.S. |
1 | 1.00 | 0.76 | 0.69 | 0.95 | 1.61 | 0.90 | 0.88 | 0.76 |
time (sec) |
N/A | 0.016 | 0.022 | 2.226 | 0.199 | 0.220 | 0.070 | 0.284 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 50 | 46 | 66 | 115 | 63 | 48 | 55 |
N.S. |
1 | 1.00 | 0.71 | 0.66 | 0.94 | 1.64 | 0.90 | 0.69 | 0.79 |
time (sec) |
N/A | 0.019 | 0.026 | 0.734 | 0.209 | 0.216 | 0.079 | 0.278 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 75 | 51 | 76 | 135 | 73 | 53 | 65 |
N.S. |
1 | 1.00 | 0.93 | 0.63 | 0.94 | 1.67 | 0.90 | 0.65 | 0.80 |
time (sec) |
N/A | 0.022 | 0.033 | 2.245 | 0.206 | 0.225 | 0.086 | 0.301 | 1.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 85 | 50 | 51 | 62 | 61 | 93 | 49 |
N.S. |
1 | 1.00 | 1.23 | 0.72 | 0.74 | 0.90 | 0.88 | 1.35 | 0.71 |
time (sec) |
N/A | 0.026 | 0.027 | 0.754 | 0.204 | 0.225 | 0.052 | 0.284 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 59 | 45 | 46 | 57 | 54 | 84 | 44 |
N.S. |
1 | 1.00 | 0.95 | 0.73 | 0.74 | 0.92 | 0.87 | 1.35 | 0.71 |
time (sec) |
N/A | 0.020 | 0.015 | 0.735 | 0.206 | 0.214 | 0.049 | 0.289 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 48 | 40 | 41 | 52 | 48 | 75 | 39 |
N.S. |
1 | 1.00 | 0.87 | 0.73 | 0.75 | 0.95 | 0.87 | 1.36 | 0.71 |
time (sec) |
N/A | 0.017 | 0.016 | 2.230 | 0.224 | 0.221 | 0.049 | 0.284 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 49 | 35 | 36 | 47 | 41 | 66 | 34 |
N.S. |
1 | 1.00 | 1.02 | 0.73 | 0.75 | 0.98 | 0.85 | 1.38 | 0.71 |
time (sec) |
N/A | 0.016 | 0.014 | 2.203 | 0.204 | 0.223 | 0.049 | 0.274 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 46 | 30 | 31 | 42 | 34 | 57 | 29 |
N.S. |
1 | 1.00 | 1.12 | 0.73 | 0.76 | 1.02 | 0.83 | 1.39 | 0.71 |
time (sec) |
N/A | 0.014 | 0.014 | 0.727 | 0.197 | 0.215 | 0.044 | 0.288 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 41 | 25 | 26 | 37 | 27 | 48 | 24 |
N.S. |
1 | 1.00 | 1.21 | 0.74 | 0.76 | 1.09 | 0.79 | 1.41 | 0.71 |
time (sec) |
N/A | 0.011 | 0.012 | 2.221 | 0.222 | 0.231 | 0.042 | 0.292 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 26 | 20 | 21 | 32 | 20 | 32 | 19 |
N.S. |
1 | 1.00 | 0.96 | 0.74 | 0.78 | 1.19 | 0.74 | 1.19 | 0.70 |
time (sec) |
N/A | 0.008 | 0.008 | 1.815 | 0.207 | 0.221 | 0.040 | 0.291 | 1.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 17 | 18 | 24 | 17 | 28 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.82 | 1.09 | 0.77 | 1.27 | 0.73 |
time (sec) |
N/A | 0.006 | 0.005 | 1.796 | 0.188 | 0.223 | 0.037 | 0.272 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 25 | 26 | 37 | 22 | 25 | 18 |
N.S. |
1 | 1.00 | 1.07 | 0.89 | 0.93 | 1.32 | 0.79 | 0.89 | 0.64 |
time (sec) |
N/A | 0.008 | 0.016 | 0.718 | 0.206 | 0.217 | 0.051 | 0.268 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 37 | 36 | 36 | 55 | 31 | 38 | 26 |
N.S. |
1 | 1.00 | 1.06 | 1.03 | 1.03 | 1.57 | 0.89 | 1.09 | 0.74 |
time (sec) |
N/A | 0.012 | 0.018 | 2.219 | 0.200 | 0.222 | 0.059 | 0.284 | 1.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 48 | 44 | 46 | 75 | 41 | 49 | 36 |
N.S. |
1 | 1.00 | 1.04 | 0.96 | 1.00 | 1.63 | 0.89 | 1.07 | 0.78 |
time (sec) |
N/A | 0.017 | 0.018 | 1.826 | 0.207 | 0.223 | 0.078 | 0.280 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 57 | 48 | 56 | 95 | 51 | 58 | 46 |
N.S. |
1 | 1.00 | 1.04 | 0.87 | 1.02 | 1.73 | 0.93 | 1.05 | 0.84 |
time (sec) |
N/A | 0.020 | 0.014 | 2.234 | 0.201 | 0.224 | 0.075 | 0.285 | 1.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 70 | 53 | 66 | 115 | 61 | 67 | 56 |
N.S. |
1 | 1.00 | 1.03 | 0.78 | 0.97 | 1.69 | 0.90 | 0.99 | 0.82 |
time (sec) |
N/A | 0.023 | 0.020 | 2.235 | 0.243 | 0.212 | 0.078 | 0.281 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 77 | 58 | 76 | 135 | 71 | 76 | 66 |
N.S. |
1 | 1.00 | 1.03 | 0.77 | 1.01 | 1.80 | 0.95 | 1.01 | 0.88 |
time (sec) |
N/A | 0.025 | 0.021 | 2.206 | 0.238 | 0.221 | 0.089 | 0.293 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 92 | 63 | 86 | 155 | 82 | 85 | 76 |
N.S. |
1 | 1.00 | 1.02 | 0.70 | 0.96 | 1.72 | 0.91 | 0.94 | 0.84 |
time (sec) |
N/A | 0.032 | 0.026 | 2.223 | 0.208 | 0.222 | 0.090 | 0.285 | 1.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 64 | 52 | 56 | 72 | 63 | 52 | 52 |
N.S. |
1 | 1.00 | 0.88 | 0.71 | 0.77 | 0.99 | 0.86 | 0.71 | 0.71 |
time (sec) |
N/A | 0.027 | 0.019 | 2.256 | 0.204 | 0.217 | 0.061 | 0.281 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 61 | 47 | 51 | 67 | 56 | 47 | 47 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.77 | 1.02 | 0.85 | 0.71 | 0.71 |
time (sec) |
N/A | 0.022 | 0.015 | 0.719 | 0.225 | 0.248 | 0.058 | 0.278 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 58 | 42 | 46 | 62 | 49 | 42 | 42 |
N.S. |
1 | 1.00 | 0.98 | 0.71 | 0.78 | 1.05 | 0.83 | 0.71 | 0.71 |
time (sec) |
N/A | 0.021 | 0.014 | 2.247 | 0.220 | 0.216 | 0.059 | 0.278 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 51 | 37 | 41 | 57 | 42 | 37 | 37 |
N.S. |
1 | 1.00 | 0.98 | 0.71 | 0.79 | 1.10 | 0.81 | 0.71 | 0.71 |
time (sec) |
N/A | 0.023 | 0.014 | 2.960 | 0.200 | 0.218 | 0.054 | 0.274 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 48 | 32 | 36 | 52 | 36 | 32 | 32 |
N.S. |
1 | 1.00 | 1.07 | 0.71 | 0.80 | 1.16 | 0.80 | 0.71 | 0.71 |
time (sec) |
N/A | 0.015 | 0.012 | 0.733 | 0.193 | 0.220 | 0.053 | 0.264 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 39 | 27 | 31 | 47 | 29 | 27 | 27 |
N.S. |
1 | 1.00 | 1.03 | 0.71 | 0.82 | 1.24 | 0.76 | 0.71 | 0.71 |
time (sec) |
N/A | 0.015 | 0.015 | 2.223 | 0.201 | 0.209 | 0.053 | 0.263 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 24 | 28 | 37 | 26 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.85 | 1.12 | 0.79 | 0.73 | 0.73 |
time (sec) |
N/A | 0.009 | 0.007 | 2.232 | 0.208 | 0.216 | 0.050 | 0.275 | 1.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 16 | 15 | 19 | 19 | 17 | 14 | 14 |
N.S. |
1 | 1.00 | 0.89 | 0.83 | 1.06 | 1.06 | 0.94 | 0.78 | 0.78 |
time (sec) |
N/A | 0.002 | 0.004 | 1.823 | 0.195 | 0.216 | 0.043 | 0.286 | 1.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 48 | 32 | 36 | 55 | 32 | 33 | 25 |
N.S. |
1 | 1.00 | 1.30 | 0.86 | 0.97 | 1.49 | 0.86 | 0.89 | 0.68 |
time (sec) |
N/A | 0.013 | 0.011 | 0.730 | 0.213 | 0.226 | 0.060 | 0.292 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 48 | 44 | 46 | 75 | 42 | 49 | 35 |
N.S. |
1 | 1.00 | 1.04 | 0.96 | 1.00 | 1.63 | 0.91 | 1.07 | 0.76 |
time (sec) |
N/A | 0.019 | 0.016 | 2.246 | 0.228 | 0.216 | 0.066 | 0.289 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 59 | 48 | 56 | 95 | 53 | 48 | 45 |
N.S. |
1 | 1.00 | 1.04 | 0.84 | 0.98 | 1.67 | 0.93 | 0.84 | 0.79 |
time (sec) |
N/A | 0.019 | 0.025 | 2.246 | 0.202 | 0.225 | 0.073 | 0.288 | 1.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 68 | 53 | 66 | 115 | 63 | 55 | 55 |
N.S. |
1 | 1.00 | 1.03 | 0.80 | 1.00 | 1.74 | 0.95 | 0.83 | 0.83 |
time (sec) |
N/A | 0.024 | 0.018 | 2.232 | 0.216 | 0.230 | 0.082 | 0.286 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 77 | 58 | 76 | 135 | 73 | 76 | 65 |
N.S. |
1 | 1.00 | 1.03 | 0.77 | 1.01 | 1.80 | 0.97 | 1.01 | 0.87 |
time (sec) |
N/A | 0.027 | 0.023 | 2.251 | 0.214 | 0.222 | 0.085 | 0.273 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 88 | 63 | 86 | 155 | 83 | 65 | 75 |
N.S. |
1 | 1.00 | 1.02 | 0.73 | 1.00 | 1.80 | 0.97 | 0.76 | 0.87 |
time (sec) |
N/A | 0.030 | 0.023 | 2.240 | 0.232 | 0.227 | 0.096 | 0.274 | 1.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 67 | 59 | 59 | 59 | 65 | 59 | 59 |
N.S. |
1 | 1.00 | 1.49 | 1.31 | 1.31 | 1.31 | 1.44 | 1.31 | 1.31 |
time (sec) |
N/A | 0.017 | 0.004 | 0.734 | 0.213 | 0.218 | 0.027 | 0.300 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 64 | 54 | 54 | 54 | 61 | 54 | 54 |
N.S. |
1 | 1.00 | 1.42 | 1.20 | 1.20 | 1.20 | 1.36 | 1.20 | 1.20 |
time (sec) |
N/A | 0.016 | 0.003 | 2.246 | 0.200 | 0.212 | 0.026 | 0.278 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 53 | 49 | 49 | 49 | 51 | 49 | 49 |
N.S. |
1 | 1.00 | 1.18 | 1.09 | 1.09 | 1.09 | 1.13 | 1.09 | 1.09 |
time (sec) |
N/A | 0.015 | 0.002 | 2.245 | 0.195 | 0.215 | 0.025 | 0.269 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 48 | 44 | 44 | 44 | 46 | 44 | 44 |
N.S. |
1 | 1.00 | 1.07 | 0.98 | 0.98 | 0.98 | 1.02 | 0.98 | 0.98 |
time (sec) |
N/A | 0.014 | 0.002 | 2.215 | 0.192 | 0.212 | 0.023 | 0.271 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 49 | 39 | 39 | 39 | 46 | 39 | 39 |
N.S. |
1 | 1.00 | 1.09 | 0.87 | 0.87 | 0.87 | 1.02 | 0.87 | 0.87 |
time (sec) |
N/A | 0.013 | 0.001 | 1.844 | 0.195 | 0.213 | 0.022 | 0.263 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 34 | 34 | 34 | 39 | 34 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.81 | 0.81 | 0.93 | 0.81 | 0.81 |
time (sec) |
N/A | 0.011 | 0.001 | 1.845 | 0.198 | 0.213 | 0.020 | 0.259 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 29 | 29 | 29 | 32 | 29 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.91 | 0.83 | 0.83 |
time (sec) |
N/A | 0.009 | 0.001 | 1.836 | 0.213 | 0.212 | 0.019 | 0.270 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 24 | 24 | 24 | 26 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.86 | 0.86 | 0.93 | 0.86 | 0.86 |
time (sec) |
N/A | 0.008 | 0.001 | 1.841 | 0.192 | 0.216 | 0.018 | 0.296 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 19 | 19 | 19 | 20 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.87 | 0.83 | 0.83 |
time (sec) |
N/A | 0.006 | 0.001 | 1.840 | 0.220 | 0.216 | 0.019 | 0.264 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 27 | 21 | 22 | 22 | 27 | 23 | 20 |
N.S. |
1 | 1.00 | 0.90 | 0.70 | 0.73 | 0.73 | 0.90 | 0.77 | 0.67 |
time (sec) |
N/A | 0.008 | 0.012 | 0.737 | 0.200 | 0.211 | 0.036 | 0.273 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 39 | 25 | 26 | 37 | 27 | 48 | 24 |
N.S. |
1 | 1.00 | 1.15 | 0.74 | 0.76 | 1.09 | 0.79 | 1.41 | 0.71 |
time (sec) |
N/A | 0.010 | 0.012 | 2.256 | 0.232 | 0.219 | 0.043 | 0.275 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 41 | 27 | 31 | 47 | 31 | 27 | 27 |
N.S. |
1 | 1.00 | 1.08 | 0.71 | 0.82 | 1.24 | 0.82 | 0.71 | 0.71 |
time (sec) |
N/A | 0.011 | 0.012 | 2.222 | 0.209 | 0.220 | 0.052 | 0.283 | 1.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 36 | 29 | 38 | 52 | 34 | 29 | 33 |
N.S. |
1 | 1.00 | 0.82 | 0.66 | 0.86 | 1.18 | 0.77 | 0.66 | 0.75 |
time (sec) |
N/A | 0.012 | 0.012 | 2.259 | 0.197 | 0.218 | 0.057 | 0.269 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 26 | 25 | 39 | 39 | 36 | 37 | 37 |
N.S. |
1 | 1.00 | 0.70 | 0.68 | 1.05 | 1.05 | 0.97 | 1.00 | 1.00 |
time (sec) |
N/A | 0.004 | 0.011 | 2.223 | 0.202 | 0.217 | 0.058 | 0.286 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 26 | 24 | 44 | 44 | 39 | 24 | 37 |
N.S. |
1 | 1.00 | 0.58 | 0.53 | 0.98 | 0.98 | 0.87 | 0.53 | 0.82 |
time (sec) |
N/A | 0.011 | 0.010 | 2.266 | 0.195 | 0.219 | 0.062 | 0.261 | 1.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 26 | 24 | 49 | 49 | 44 | 24 | 37 |
N.S. |
1 | 1.00 | 0.58 | 0.53 | 1.09 | 1.09 | 0.98 | 0.53 | 0.82 |
time (sec) |
N/A | 0.012 | 0.012 | 0.740 | 0.198 | 0.219 | 0.066 | 0.278 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 26 | 24 | 54 | 54 | 49 | 24 | 37 |
N.S. |
1 | 1.00 | 0.58 | 0.53 | 1.20 | 1.20 | 1.09 | 0.53 | 0.82 |
time (sec) |
N/A | 0.012 | 0.010 | 2.269 | 0.197 | 0.211 | 0.071 | 0.262 | 1.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 74 | 64 | 64 | 64 | 71 | 64 | 64 |
N.S. |
1 | 1.00 | 1.32 | 1.14 | 1.14 | 1.14 | 1.27 | 1.14 | 1.14 |
time (sec) |
N/A | 0.021 | 0.003 | 2.263 | 0.208 | 0.219 | 0.028 | 0.259 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 69 | 59 | 59 | 59 | 66 | 59 | 59 |
N.S. |
1 | 1.00 | 1.23 | 1.05 | 1.05 | 1.05 | 1.18 | 1.05 | 1.05 |
time (sec) |
N/A | 0.019 | 0.002 | 2.267 | 0.198 | 0.216 | 0.027 | 0.270 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 60 | 54 | 54 | 54 | 58 | 54 | 54 |
N.S. |
1 | 1.00 | 1.07 | 0.96 | 0.96 | 0.96 | 1.04 | 0.96 | 0.96 |
time (sec) |
N/A | 0.019 | 0.002 | 2.272 | 0.210 | 0.213 | 0.026 | 0.280 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 55 | 49 | 49 | 49 | 53 | 49 | 49 |
N.S. |
1 | 1.00 | 0.98 | 0.88 | 0.88 | 0.88 | 0.95 | 0.88 | 0.88 |
time (sec) |
N/A | 0.019 | 0.002 | 2.268 | 0.200 | 0.230 | 0.024 | 0.269 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 52 | 44 | 44 | 44 | 49 | 44 | 44 |
N.S. |
1 | 1.00 | 0.93 | 0.79 | 0.79 | 0.79 | 0.88 | 0.79 | 0.79 |
time (sec) |
N/A | 0.016 | 0.002 | 0.742 | 0.204 | 0.219 | 0.023 | 0.308 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 39 | 39 | 39 | 48 | 39 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.76 | 0.76 | 0.94 | 0.76 | 0.76 |
time (sec) |
N/A | 0.013 | 0.002 | 2.271 | 0.215 | 0.222 | 0.021 | 0.276 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 34 | 34 | 34 | 39 | 34 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.81 | 0.81 | 0.93 | 0.81 | 0.81 |
time (sec) |
N/A | 0.012 | 0.001 | 2.275 | 0.196 | 0.217 | 0.020 | 0.261 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 29 | 29 | 29 | 32 | 29 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.91 | 0.83 | 0.83 |
time (sec) |
N/A | 0.010 | 0.001 | 1.863 | 0.189 | 0.213 | 0.024 | 0.278 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 24 | 24 | 24 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 0.92 | 0.92 | 0.92 | 0.92 |
time (sec) |
N/A | 0.007 | 0.002 | 1.837 | 0.199 | 0.224 | 0.019 | 0.272 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 32 | 26 | 27 | 27 | 34 | 28 | 25 |
N.S. |
1 | 1.00 | 0.86 | 0.70 | 0.73 | 0.73 | 0.92 | 0.76 | 0.68 |
time (sec) |
N/A | 0.011 | 0.008 | 1.857 | 0.188 | 0.229 | 0.038 | 0.284 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 44 | 30 | 31 | 42 | 34 | 57 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.73 | 0.76 | 1.02 | 0.83 | 1.39 | 0.71 |
time (sec) |
N/A | 0.013 | 0.011 | 2.285 | 0.195 | 0.225 | 0.045 | 0.275 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 42 | 32 | 36 | 52 | 36 | 32 | 31 |
N.S. |
1 | 1.00 | 0.93 | 0.71 | 0.80 | 1.16 | 0.80 | 0.71 | 0.69 |
time (sec) |
N/A | 0.014 | 0.013 | 2.293 | 0.195 | 0.219 | 0.054 | 0.292 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 46 | 32 | 41 | 62 | 41 | 32 | 37 |
N.S. |
1 | 1.00 | 0.94 | 0.65 | 0.84 | 1.27 | 0.84 | 0.65 | 0.76 |
time (sec) |
N/A | 0.014 | 0.013 | 2.290 | 0.219 | 0.214 | 0.061 | 0.298 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 41 | 34 | 48 | 67 | 44 | 55 | 43 |
N.S. |
1 | 1.00 | 0.75 | 0.62 | 0.87 | 1.22 | 0.80 | 1.00 | 0.78 |
time (sec) |
N/A | 0.015 | 0.011 | 2.293 | 0.265 | 0.224 | 0.063 | 0.293 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 31 | 29 | 49 | 49 | 46 | 29 | 46 |
N.S. |
1 | 1.00 | 0.55 | 0.52 | 0.88 | 0.88 | 0.82 | 0.52 | 0.82 |
time (sec) |
N/A | 0.015 | 0.011 | 2.293 | 0.208 | 0.219 | 0.067 | 0.282 | 1.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 31 | 29 | 54 | 54 | 51 | 29 | 46 |
N.S. |
1 | 1.00 | 0.55 | 0.52 | 0.96 | 0.96 | 0.91 | 0.52 | 0.82 |
time (sec) |
N/A | 0.016 | 0.010 | 2.300 | 0.229 | 0.215 | 0.069 | 0.294 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 31 | 29 | 59 | 59 | 54 | 29 | 46 |
N.S. |
1 | 1.00 | 0.55 | 0.52 | 1.05 | 1.05 | 0.96 | 0.52 | 0.82 |
time (sec) |
N/A | 0.014 | 0.010 | 2.297 | 0.211 | 0.216 | 0.074 | 0.276 | 1.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 93 | 79 | 79 | 79 | 90 | 79 | 79 |
N.S. |
1 | 1.00 | 1.39 | 1.18 | 1.18 | 1.18 | 1.34 | 1.18 | 1.18 |
time (sec) |
N/A | 0.027 | 0.003 | 2.267 | 0.214 | 0.219 | 0.035 | 0.284 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 90 | 74 | 74 | 74 | 87 | 74 | 74 |
N.S. |
1 | 1.00 | 1.34 | 1.10 | 1.10 | 1.10 | 1.30 | 1.10 | 1.10 |
time (sec) |
N/A | 0.024 | 0.003 | 2.283 | 0.193 | 0.212 | 0.031 | 0.283 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 85 | 69 | 69 | 69 | 82 | 69 | 69 |
N.S. |
1 | 1.00 | 1.27 | 1.03 | 1.03 | 1.03 | 1.22 | 1.03 | 1.03 |
time (sec) |
N/A | 0.022 | 0.002 | 2.288 | 0.194 | 0.210 | 0.031 | 0.271 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 76 | 64 | 64 | 64 | 73 | 64 | 64 |
N.S. |
1 | 1.00 | 1.13 | 0.96 | 0.96 | 0.96 | 1.09 | 0.96 | 0.96 |
time (sec) |
N/A | 0.020 | 0.002 | 2.287 | 0.195 | 0.224 | 0.031 | 0.259 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 67 | 59 | 59 | 59 | 65 | 59 | 59 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.88 | 0.88 | 0.97 | 0.88 | 0.88 |
time (sec) |
N/A | 0.020 | 0.002 | 2.289 | 0.202 | 0.208 | 0.027 | 0.277 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 60 | 54 | 54 | 54 | 58 | 54 | 54 |
N.S. |
1 | 1.00 | 0.90 | 0.81 | 0.81 | 0.81 | 0.87 | 0.81 | 0.81 |
time (sec) |
N/A | 0.019 | 0.002 | 2.272 | 0.190 | 0.209 | 0.026 | 0.264 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 57 | 49 | 49 | 49 | 54 | 49 | 49 |
N.S. |
1 | 1.00 | 0.85 | 0.73 | 0.73 | 0.73 | 0.81 | 0.73 | 0.73 |
time (sec) |
N/A | 0.018 | 0.002 | 2.293 | 0.192 | 0.213 | 0.024 | 0.272 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 44 | 44 | 44 | 49 | 44 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.85 | 0.85 | 0.94 | 0.85 | 0.85 |
time (sec) |
N/A | 0.015 | 0.002 | 2.291 | 0.191 | 0.216 | 0.022 | 0.277 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 39 | 39 | 39 | 46 | 39 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 0.80 | 0.94 | 0.80 | 0.80 |
time (sec) |
N/A | 0.012 | 0.002 | 2.299 | 0.204 | 0.215 | 0.022 | 0.264 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 34 | 34 | 34 | 39 | 34 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.81 | 0.81 | 0.93 | 0.81 | 0.81 |
time (sec) |
N/A | 0.011 | 0.001 | 2.286 | 0.205 | 0.223 | 0.020 | 0.283 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 35 | 29 | 29 | 29 | 32 | 29 | 29 |
N.S. |
1 | 1.00 | 1.03 | 0.85 | 0.85 | 0.85 | 0.94 | 0.85 | 0.85 |
time (sec) |
N/A | 0.009 | 0.001 | 1.873 | 0.209 | 0.210 | 0.020 | 0.277 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 37 | 31 | 32 | 32 | 41 | 33 | 30 |
N.S. |
1 | 1.00 | 0.84 | 0.70 | 0.73 | 0.73 | 0.93 | 0.75 | 0.68 |
time (sec) |
N/A | 0.013 | 0.009 | 1.905 | 0.285 | 0.210 | 0.041 | 0.268 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 49 | 35 | 36 | 47 | 41 | 66 | 34 |
N.S. |
1 | 1.00 | 1.02 | 0.73 | 0.75 | 0.98 | 0.85 | 1.38 | 0.71 |
time (sec) |
N/A | 0.014 | 0.026 | 2.311 | 0.187 | 0.217 | 0.048 | 0.284 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 51 | 37 | 41 | 57 | 44 | 37 | 37 |
N.S. |
1 | 1.00 | 0.98 | 0.71 | 0.79 | 1.10 | 0.85 | 0.71 | 0.71 |
time (sec) |
N/A | 0.015 | 0.027 | 2.333 | 0.201 | 0.211 | 0.056 | 0.270 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 51 | 37 | 46 | 67 | 46 | 37 | 41 |
N.S. |
1 | 1.00 | 0.91 | 0.66 | 0.82 | 1.20 | 0.82 | 0.66 | 0.73 |
time (sec) |
N/A | 0.017 | 0.029 | 2.334 | 0.205 | 0.223 | 0.064 | 0.268 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 51 | 37 | 51 | 77 | 51 | 59 | 47 |
N.S. |
1 | 1.00 | 0.85 | 0.62 | 0.85 | 1.28 | 0.85 | 0.98 | 0.78 |
time (sec) |
N/A | 0.017 | 0.027 | 2.455 | 0.196 | 0.217 | 0.075 | 0.276 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 38 | 58 | 82 | 54 | 39 | 53 |
N.S. |
1 | 1.00 | 0.70 | 0.58 | 0.88 | 1.24 | 0.82 | 0.59 | 0.80 |
time (sec) |
N/A | 0.018 | 0.027 | 2.340 | 0.202 | 0.219 | 0.071 | 0.298 | 1.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 36 | 34 | 59 | 59 | 56 | 34 | 55 |
N.S. |
1 | 1.00 | 0.54 | 0.51 | 0.88 | 0.88 | 0.84 | 0.51 | 0.82 |
time (sec) |
N/A | 0.016 | 0.023 | 2.345 | 0.218 | 0.218 | 0.072 | 0.267 | 1.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 36 | 34 | 64 | 64 | 61 | 34 | 55 |
N.S. |
1 | 1.00 | 0.54 | 0.51 | 0.96 | 0.96 | 0.91 | 0.51 | 0.82 |
time (sec) |
N/A | 0.017 | 0.022 | 2.292 | 0.205 | 0.223 | 0.081 | 0.272 | 1.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 57 | 51 | 52 | 52 | 68 | 53 | 50 |
N.S. |
1 | 1.00 | 0.79 | 0.71 | 0.72 | 0.72 | 0.94 | 0.74 | 0.69 |
time (sec) |
N/A | 0.021 | 0.012 | 2.347 | 0.213 | 0.219 | 0.048 | 0.281 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 52 | 46 | 47 | 47 | 61 | 48 | 45 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.72 | 0.72 | 0.94 | 0.74 | 0.69 |
time (sec) |
N/A | 0.019 | 0.011 | 0.803 | 0.199 | 0.220 | 0.047 | 0.290 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 47 | 41 | 42 | 42 | 54 | 43 | 40 |
N.S. |
1 | 1.00 | 0.81 | 0.71 | 0.72 | 0.72 | 0.93 | 0.74 | 0.69 |
time (sec) |
N/A | 0.019 | 0.011 | 0.768 | 0.201 | 0.217 | 0.045 | 0.287 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 42 | 36 | 37 | 37 | 48 | 38 | 35 |
N.S. |
1 | 1.00 | 0.82 | 0.71 | 0.73 | 0.73 | 0.94 | 0.75 | 0.69 |
time (sec) |
N/A | 0.018 | 0.010 | 2.327 | 0.201 | 0.216 | 0.042 | 0.271 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 37 | 31 | 32 | 32 | 41 | 33 | 30 |
N.S. |
1 | 1.00 | 0.84 | 0.70 | 0.73 | 0.73 | 0.93 | 0.75 | 0.68 |
time (sec) |
N/A | 0.013 | 0.009 | 2.327 | 0.203 | 0.222 | 0.040 | 0.275 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 35 | 26 | 27 | 27 | 34 | 28 | 25 |
N.S. |
1 | 1.00 | 0.95 | 0.70 | 0.73 | 0.73 | 0.92 | 0.76 | 0.68 |
time (sec) |
N/A | 0.011 | 0.009 | 2.337 | 0.193 | 0.214 | 0.039 | 0.269 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 27 | 21 | 22 | 22 | 27 | 23 | 20 |
N.S. |
1 | 1.00 | 0.90 | 0.70 | 0.73 | 0.73 | 0.90 | 0.77 | 0.67 |
time (sec) |
N/A | 0.008 | 0.009 | 2.302 | 0.195 | 0.216 | 0.035 | 0.273 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 22 | 16 | 17 | 17 | 20 | 18 | 15 |
N.S. |
1 | 1.00 | 0.96 | 0.70 | 0.74 | 0.74 | 0.87 | 0.78 | 0.65 |
time (sec) |
N/A | 0.006 | 0.007 | 2.309 | 0.204 | 0.221 | 0.033 | 0.273 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 27 | 17 | 20 | 20 | 24 | 22 | 16 |
N.S. |
1 | 1.00 | 1.04 | 0.65 | 0.77 | 0.77 | 0.92 | 0.85 | 0.62 |
time (sec) |
N/A | 0.009 | 0.009 | 1.903 | 0.198 | 0.212 | 0.054 | 0.257 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 25 | 26 | 37 | 26 | 43 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.81 | 1.16 | 0.81 | 1.34 | 0.69 |
time (sec) |
N/A | 0.011 | 0.016 | 1.911 | 0.207 | 0.221 | 0.062 | 0.267 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 48 | 32 | 36 | 55 | 31 | 33 | 25 |
N.S. |
1 | 1.00 | 1.23 | 0.82 | 0.92 | 1.41 | 0.79 | 0.85 | 0.64 |
time (sec) |
N/A | 0.012 | 0.013 | 2.331 | 0.199 | 0.222 | 0.059 | 0.276 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 40 | 36 | 46 | 75 | 41 | 38 | 35 |
N.S. |
1 | 1.00 | 0.83 | 0.75 | 0.96 | 1.56 | 0.85 | 0.79 | 0.73 |
time (sec) |
N/A | 0.014 | 0.020 | 2.324 | 0.194 | 0.220 | 0.067 | 0.283 | 0.047 |