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 | 59 | 59 | 45 | 41 | 56 | 95 | 51 | 52 | 45 |
N.S. |
1 | 1.00 | 0.76 | 0.69 | 0.95 | 1.61 | 0.86 | 0.88 | 0.76 |
time (sec) |
N/A | 0.190 | 0.022 | 2.318 | 0.197 | 0.219 | 0.071 | 0.294 | 1.198 |
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 | 57 | 46 | 66 | 115 | 61 | 48 | 55 |
N.S. |
1 | 1.00 | 0.81 | 0.66 | 0.94 | 1.64 | 0.87 | 0.69 | 0.79 |
time (sec) |
N/A | 0.200 | 0.025 | 2.287 | 0.191 | 0.233 | 0.079 | 0.281 | 1.394 |
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 | 55 | 51 | 76 | 135 | 71 | 53 | 65 |
N.S. |
1 | 1.00 | 0.68 | 0.63 | 0.94 | 1.67 | 0.88 | 0.65 | 0.80 |
time (sec) |
N/A | 0.206 | 0.035 | 2.337 | 0.203 | 0.224 | 0.084 | 0.281 | 1.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 84 | 56 | 86 | 155 | 82 | 58 | 75 |
N.S. |
1 | 1.00 | 0.91 | 0.61 | 0.93 | 1.68 | 0.89 | 0.63 | 0.82 |
time (sec) |
N/A | 0.215 | 0.045 | 2.340 | 0.194 | 0.234 | 0.092 | 0.279 | 1.244 |
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 | 76 | 76 | 69 | 55 | 56 | 67 | 68 | 102 | 54 |
N.S. |
1 | 1.00 | 0.91 | 0.72 | 0.74 | 0.88 | 0.89 | 1.34 | 0.71 |
time (sec) |
N/A | 0.197 | 0.022 | 2.352 | 0.198 | 0.217 | 0.054 | 0.275 | 0.058 |
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 | 66 | 50 | 51 | 62 | 61 | 93 | 49 |
N.S. |
1 | 1.00 | 0.96 | 0.72 | 0.74 | 0.90 | 0.88 | 1.35 | 0.71 |
time (sec) |
N/A | 0.195 | 0.030 | 0.780 | 0.196 | 0.217 | 0.054 | 0.272 | 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 | 62 | 62 | 61 | 45 | 46 | 57 | 54 | 84 | 44 |
N.S. |
1 | 1.00 | 0.98 | 0.73 | 0.74 | 0.92 | 0.87 | 1.35 | 0.71 |
time (sec) |
N/A | 0.191 | 0.027 | 0.779 | 0.193 | 0.225 | 0.052 | 0.291 | 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 | 55 | 55 | 56 | 40 | 41 | 52 | 48 | 75 | 39 |
N.S. |
1 | 1.00 | 1.02 | 0.73 | 0.75 | 0.95 | 0.87 | 1.36 | 0.71 |
time (sec) |
N/A | 0.180 | 0.026 | 0.778 | 0.190 | 0.214 | 0.051 | 0.273 | 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 | 48 | 48 | 51 | 35 | 36 | 47 | 41 | 66 | 34 |
N.S. |
1 | 1.00 | 1.06 | 0.73 | 0.75 | 0.98 | 0.85 | 1.38 | 0.71 |
time (sec) |
N/A | 0.175 | 0.025 | 2.344 | 0.196 | 0.218 | 0.053 | 0.279 | 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 | 41 | 41 | 42 | 30 | 31 | 42 | 34 | 57 | 29 |
N.S. |
1 | 1.00 | 1.02 | 0.73 | 0.76 | 1.02 | 0.83 | 1.39 | 0.71 |
time (sec) |
N/A | 0.171 | 0.013 | 2.343 | 0.206 | 0.211 | 0.046 | 0.287 | 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 | 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 | 0.164 | 0.013 | 2.318 | 0.195 | 0.216 | 0.042 | 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 | 27 | 27 | 34 | 20 | 21 | 32 | 20 | 32 | 19 |
N.S. |
1 | 1.00 | 1.26 | 0.74 | 0.78 | 1.19 | 0.74 | 1.19 | 0.70 |
time (sec) |
N/A | 0.159 | 0.010 | 2.338 | 0.199 | 0.225 | 0.039 | 0.287 | 1.182 |
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 | 0.167 | 0.017 | 3.069 | 0.208 | 0.228 | 0.063 | 0.288 | 1.253 |
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 | 61 | 36 | 36 | 55 | 32 | 38 | 26 |
N.S. |
1 | 1.00 | 1.56 | 0.92 | 0.92 | 1.41 | 0.82 | 0.97 | 0.67 |
time (sec) |
N/A | 0.170 | 0.027 | 0.763 | 0.206 | 0.211 | 0.065 | 0.282 | 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 | 46 | 46 | 48 | 44 | 46 | 75 | 42 | 49 | 36 |
N.S. |
1 | 1.00 | 1.04 | 0.96 | 1.00 | 1.63 | 0.91 | 1.07 | 0.78 |
time (sec) |
N/A | 0.178 | 0.020 | 2.342 | 0.202 | 0.222 | 0.070 | 0.277 | 1.261 |
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 | 53 | 58 | 46 |
N.S. |
1 | 1.00 | 1.04 | 0.87 | 1.02 | 1.73 | 0.96 | 1.05 | 0.84 |
time (sec) |
N/A | 0.191 | 0.024 | 2.346 | 0.211 | 0.223 | 0.076 | 0.289 | 1.189 |
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 | 57 | 53 | 66 | 115 | 63 | 67 | 56 |
N.S. |
1 | 1.00 | 0.84 | 0.78 | 0.97 | 1.69 | 0.93 | 0.99 | 0.82 |
time (sec) |
N/A | 0.198 | 0.058 | 2.334 | 0.190 | 0.221 | 0.084 | 0.269 | 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 | 77 | 77 | 62 | 58 | 76 | 135 | 73 | 76 | 66 |
N.S. |
1 | 1.00 | 0.81 | 0.75 | 0.99 | 1.75 | 0.95 | 0.99 | 0.86 |
time (sec) |
N/A | 0.207 | 0.047 | 2.347 | 0.196 | 0.229 | 0.086 | 0.281 | 1.344 |
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 | 83 | 85 | 76 |
N.S. |
1 | 1.00 | 1.02 | 0.70 | 0.96 | 1.72 | 0.92 | 0.94 | 0.84 |
time (sec) |
N/A | 0.223 | 0.068 | 2.352 | 0.203 | 0.223 | 0.093 | 0.286 | 1.179 |
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 | 97 | 97 | 99 | 68 | 96 | 175 | 94 | 94 | 86 |
N.S. |
1 | 1.00 | 1.02 | 0.70 | 0.99 | 1.80 | 0.97 | 0.97 | 0.89 |
time (sec) |
N/A | 0.229 | 0.053 | 2.357 | 0.218 | 0.224 | 0.102 | 0.293 | 1.369 |
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 | 87 | 87 | 76 | 62 | 66 | 82 | 78 | 62 | 62 |
N.S. |
1 | 1.00 | 0.87 | 0.71 | 0.76 | 0.94 | 0.90 | 0.71 | 0.71 |
time (sec) |
N/A | 0.211 | 0.024 | 2.382 | 0.200 | 0.217 | 0.066 | 0.301 | 1.194 |
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 | 80 | 80 | 71 | 57 | 61 | 77 | 71 | 57 | 57 |
N.S. |
1 | 1.00 | 0.89 | 0.71 | 0.76 | 0.96 | 0.89 | 0.71 | 0.71 |
time (sec) |
N/A | 0.203 | 0.022 | 0.784 | 0.200 | 0.228 | 0.063 | 0.273 | 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 | 73 | 73 | 68 | 52 | 56 | 72 | 65 | 52 | 52 |
N.S. |
1 | 1.00 | 0.93 | 0.71 | 0.77 | 0.99 | 0.89 | 0.71 | 0.71 |
time (sec) |
N/A | 0.196 | 0.032 | 0.783 | 0.196 | 0.228 | 0.059 | 0.283 | 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 | 66 | 66 | 63 | 47 | 51 | 67 | 58 | 47 | 47 |
N.S. |
1 | 1.00 | 0.95 | 0.71 | 0.77 | 1.02 | 0.88 | 0.71 | 0.71 |
time (sec) |
N/A | 0.193 | 0.030 | 0.779 | 0.216 | 0.214 | 0.062 | 0.299 | 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 | 59 | 59 | 58 | 42 | 46 | 62 | 51 | 42 | 42 |
N.S. |
1 | 1.00 | 0.98 | 0.71 | 0.78 | 1.05 | 0.86 | 0.71 | 0.71 |
time (sec) |
N/A | 0.186 | 0.029 | 0.776 | 0.212 | 0.229 | 0.060 | 0.288 | 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 | 52 | 52 | 48 | 37 | 41 | 52 | 44 | 37 | 37 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.79 | 1.00 | 0.85 | 0.71 | 0.71 |
time (sec) |
N/A | 0.179 | 0.027 | 2.359 | 0.201 | 0.218 | 0.057 | 0.282 | 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 | 42 | 32 | 36 | 52 | 37 | 32 | 32 |
N.S. |
1 | 1.00 | 0.93 | 0.71 | 0.80 | 1.16 | 0.82 | 0.71 | 0.71 |
time (sec) |
N/A | 0.174 | 0.013 | 2.370 | 0.200 | 0.216 | 0.056 | 0.297 | 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 | 38 | 38 | 37 | 27 | 31 | 47 | 31 | 27 | 27 |
N.S. |
1 | 1.00 | 0.97 | 0.71 | 0.82 | 1.24 | 0.82 | 0.71 | 0.71 |
time (sec) |
N/A | 0.168 | 0.015 | 2.357 | 0.210 | 0.223 | 0.052 | 0.284 | 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 | 33 | 33 | 31 | 24 | 28 | 37 | 24 | 24 | 23 |
N.S. |
1 | 1.00 | 0.94 | 0.73 | 0.85 | 1.12 | 0.73 | 0.73 | 0.70 |
time (sec) |
N/A | 0.161 | 0.011 | 2.303 | 0.212 | 0.215 | 0.046 | 0.290 | 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 | 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 | 0.174 | 0.014 | 2.369 | 0.200 | 0.224 | 0.062 | 0.289 | 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 | 46 | 46 | 48 | 44 | 46 | 75 | 41 | 49 | 35 |
N.S. |
1 | 1.00 | 1.04 | 0.96 | 1.00 | 1.63 | 0.89 | 1.07 | 0.76 |
time (sec) |
N/A | 0.184 | 0.020 | 2.365 | 0.226 | 0.220 | 0.067 | 0.286 | 1.167 |
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 | 51 | 48 | 45 |
N.S. |
1 | 1.00 | 1.04 | 0.84 | 0.98 | 1.67 | 0.89 | 0.84 | 0.79 |
time (sec) |
N/A | 0.193 | 0.020 | 2.367 | 0.208 | 0.226 | 0.072 | 0.275 | 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 | 68 | 68 | 70 | 53 | 66 | 115 | 61 | 55 | 55 |
N.S. |
1 | 1.00 | 1.03 | 0.78 | 0.97 | 1.69 | 0.90 | 0.81 | 0.81 |
time (sec) |
N/A | 0.204 | 0.034 | 2.364 | 0.213 | 0.218 | 0.080 | 0.282 | 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 | 77 | 77 | 79 | 58 | 76 | 135 | 71 | 76 | 65 |
N.S. |
1 | 1.00 | 1.03 | 0.75 | 0.99 | 1.75 | 0.92 | 0.99 | 0.84 |
time (sec) |
N/A | 0.214 | 0.040 | 2.366 | 0.215 | 0.219 | 0.091 | 0.281 | 1.493 |
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 | 88 | 88 | 90 | 63 | 86 | 155 | 82 | 65 | 75 |
N.S. |
1 | 1.00 | 1.02 | 0.72 | 0.98 | 1.76 | 0.93 | 0.74 | 0.85 |
time (sec) |
N/A | 0.225 | 0.045 | 2.375 | 0.220 | 0.229 | 0.093 | 0.266 | 1.367 |
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 | 101 | 101 | 103 | 68 | 96 | 175 | 92 | 70 | 85 |
N.S. |
1 | 1.00 | 1.02 | 0.67 | 0.95 | 1.73 | 0.91 | 0.69 | 0.84 |
time (sec) |
N/A | 0.236 | 0.049 | 2.338 | 0.216 | 0.219 | 0.097 | 0.284 | 1.439 |
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 | 110 | 110 | 112 | 73 | 106 | 195 | 102 | 75 | 95 |
N.S. |
1 | 1.00 | 1.02 | 0.66 | 0.96 | 1.77 | 0.93 | 0.68 | 0.86 |
time (sec) |
N/A | 0.246 | 0.056 | 2.369 | 0.201 | 0.228 | 0.103 | 0.269 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 72 | 64 | 64 | 64 | 70 | 64 | 64 |
N.S. |
1 | 1.00 | 1.29 | 1.14 | 1.14 | 1.14 | 1.25 | 1.14 | 1.14 |
time (sec) |
N/A | 0.226 | 0.002 | 2.322 | 0.205 | 0.215 | 0.028 | 0.276 | 0.081 |
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 | 67 | 59 | 59 | 59 | 65 | 59 | 59 |
N.S. |
1 | 1.00 | 1.20 | 1.05 | 1.05 | 1.05 | 1.16 | 1.05 | 1.05 |
time (sec) |
N/A | 0.207 | 0.002 | 2.360 | 0.200 | 0.218 | 0.030 | 0.280 | 0.065 |
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 | 62 | 54 | 54 | 54 | 60 | 54 | 54 |
N.S. |
1 | 1.00 | 1.11 | 0.96 | 0.96 | 0.96 | 1.07 | 0.96 | 0.96 |
time (sec) |
N/A | 0.215 | 0.002 | 2.358 | 0.222 | 0.218 | 0.026 | 0.281 | 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 | 56 | 56 | 53 | 49 | 49 | 49 | 51 | 49 | 49 |
N.S. |
1 | 1.00 | 0.95 | 0.88 | 0.88 | 0.88 | 0.91 | 0.88 | 0.88 |
time (sec) |
N/A | 0.200 | 0.002 | 2.359 | 0.206 | 0.216 | 0.025 | 0.257 | 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 | 50 | 44 | 44 | 44 | 48 | 44 | 44 |
N.S. |
1 | 1.00 | 0.89 | 0.79 | 0.79 | 0.79 | 0.86 | 0.79 | 0.79 |
time (sec) |
N/A | 0.205 | 0.004 | 2.354 | 0.192 | 0.209 | 0.022 | 0.269 | 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 | 45 | 45 | 45 | 39 | 39 | 39 | 42 | 39 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.87 | 0.87 | 0.93 | 0.87 | 0.87 |
time (sec) |
N/A | 0.183 | 0.001 | 2.364 | 0.191 | 0.217 | 0.021 | 0.268 | 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 | 40 | 40 | 40 | 34 | 34 | 34 | 37 | 34 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.85 | 0.85 | 0.92 | 0.85 | 0.85 |
time (sec) |
N/A | 0.185 | 0.001 | 2.359 | 0.208 | 0.214 | 0.020 | 0.275 | 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 | 0.169 | 0.001 | 1.927 | 0.205 | 0.218 | 0.022 | 0.279 | 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 | 23 | 23 | 26 | 24 | 24 | 24 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.13 | 1.04 | 1.04 | 1.04 | 1.04 | 1.04 | 1.04 |
time (sec) |
N/A | 0.163 | 0.001 | 1.929 | 0.195 | 0.215 | 0.021 | 0.280 | 0.020 |
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 | 0.164 | 0.013 | 1.958 | 0.201 | 0.213 | 0.038 | 0.278 | 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 | 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 | 0.165 | 0.013 | 2.382 | 0.195 | 0.217 | 0.046 | 0.284 | 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 | 45 | 45 | 46 | 32 | 36 | 52 | 36 | 32 | 32 |
N.S. |
1 | 1.00 | 1.02 | 0.71 | 0.80 | 1.16 | 0.80 | 0.71 | 0.71 |
time (sec) |
N/A | 0.181 | 0.018 | 2.377 | 0.198 | 0.215 | 0.055 | 0.277 | 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 | 49 | 49 | 46 | 32 | 41 | 62 | 41 | 32 | 36 |
N.S. |
1 | 1.00 | 0.94 | 0.65 | 0.84 | 1.27 | 0.84 | 0.65 | 0.73 |
time (sec) |
N/A | 0.178 | 0.014 | 2.384 | 0.206 | 0.229 | 0.060 | 0.282 | 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 | 55 | 55 | 41 | 34 | 48 | 67 | 46 | 55 | 44 |
N.S. |
1 | 1.00 | 0.75 | 0.62 | 0.87 | 1.22 | 0.84 | 1.00 | 0.80 |
time (sec) |
N/A | 0.180 | 0.015 | 2.389 | 0.198 | 0.220 | 0.075 | 0.287 | 1.348 |
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 | 31 | 29 | 49 | 49 | 48 | 29 | 46 |
N.S. |
1 | 1.00 | 0.84 | 0.78 | 1.32 | 1.32 | 1.30 | 0.78 | 1.24 |
time (sec) |
N/A | 0.154 | 0.011 | 2.393 | 0.200 | 0.216 | 0.064 | 0.268 | 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 | 55 | 60 | 31 | 29 | 54 | 54 | 51 | 29 | 46 |
N.S. |
1 | 1.09 | 0.56 | 0.53 | 0.98 | 0.98 | 0.93 | 0.53 | 0.84 |
time (sec) |
N/A | 0.167 | 0.012 | 2.381 | 0.194 | 0.216 | 0.069 | 0.296 | 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 | 56 | 56 | 31 | 29 | 59 | 59 | 56 | 29 | 46 |
N.S. |
1 | 1.00 | 0.55 | 0.52 | 1.05 | 1.05 | 1.00 | 0.52 | 0.82 |
time (sec) |
N/A | 0.199 | 0.010 | 2.391 | 0.202 | 0.215 | 0.083 | 0.289 | 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 | 67 | 67 | 87 | 69 | 69 | 69 | 83 | 69 | 69 |
N.S. |
1 | 1.00 | 1.30 | 1.03 | 1.03 | 1.03 | 1.24 | 1.03 | 1.03 |
time (sec) |
N/A | 0.229 | 0.003 | 2.388 | 0.192 | 0.218 | 0.030 | 0.283 | 0.098 |
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 | 78 | 64 | 64 | 64 | 75 | 64 | 64 |
N.S. |
1 | 1.00 | 1.16 | 0.96 | 0.96 | 0.96 | 1.12 | 0.96 | 0.96 |
time (sec) |
N/A | 0.241 | 0.003 | 2.377 | 0.205 | 0.212 | 0.029 | 0.279 | 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 | 67 | 67 | 71 | 59 | 59 | 59 | 68 | 59 | 59 |
N.S. |
1 | 1.00 | 1.06 | 0.88 | 0.88 | 0.88 | 1.01 | 0.88 | 0.88 |
time (sec) |
N/A | 0.214 | 0.003 | 2.388 | 0.198 | 0.216 | 0.028 | 0.296 | 0.065 |
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 | 62 | 54 | 54 | 54 | 60 | 54 | 54 |
N.S. |
1 | 1.00 | 0.93 | 0.81 | 0.81 | 0.81 | 0.90 | 0.81 | 0.81 |
time (sec) |
N/A | 0.226 | 0.002 | 2.381 | 0.214 | 0.220 | 0.035 | 0.282 | 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 | 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 | 0.208 | 0.002 | 2.394 | 0.194 | 0.208 | 0.024 | 0.280 | 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 | 56 | 56 | 56 | 44 | 44 | 44 | 53 | 44 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.79 | 0.79 | 0.95 | 0.79 | 0.79 |
time (sec) |
N/A | 0.195 | 0.002 | 2.395 | 0.197 | 0.217 | 0.023 | 0.296 | 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 | 47 | 47 | 47 | 39 | 39 | 39 | 44 | 39 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.94 | 0.83 | 0.83 |
time (sec) |
N/A | 0.180 | 0.002 | 2.396 | 0.195 | 0.213 | 0.022 | 0.278 | 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 | 46 | 46 | 46 | 34 | 34 | 34 | 42 | 34 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.74 | 0.74 | 0.91 | 0.74 | 0.74 |
time (sec) |
N/A | 0.183 | 0.002 | 2.408 | 0.200 | 0.213 | 0.020 | 0.275 | 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 | 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 | 0.174 | 0.001 | 2.398 | 0.195 | 0.219 | 0.022 | 0.279 | 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 | 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 | 0.168 | 0.010 | 2.415 | 0.195 | 0.225 | 0.041 | 0.281 | 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 | 0.173 | 0.028 | 2.414 | 0.217 | 0.227 | 0.049 | 0.288 | 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 | 52 | 52 | 51 | 37 | 41 | 57 | 44 | 37 | 36 |
N.S. |
1 | 1.00 | 0.98 | 0.71 | 0.79 | 1.10 | 0.85 | 0.71 | 0.69 |
time (sec) |
N/A | 0.178 | 0.030 | 2.413 | 0.194 | 0.219 | 0.059 | 0.282 | 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 | 42 |
N.S. |
1 | 1.00 | 0.91 | 0.66 | 0.82 | 1.20 | 0.82 | 0.66 | 0.75 |
time (sec) |
N/A | 0.181 | 0.030 | 2.416 | 0.199 | 0.222 | 0.066 | 0.278 | 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 | 60 | 60 | 51 | 37 | 51 | 77 | 51 | 59 | 46 |
N.S. |
1 | 1.00 | 0.85 | 0.62 | 0.85 | 1.28 | 0.85 | 0.98 | 0.77 |
time (sec) |
N/A | 0.187 | 0.027 | 2.413 | 0.197 | 0.218 | 0.069 | 0.281 | 1.167 |
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 | 56 | 39 | 54 |
N.S. |
1 | 1.00 | 0.70 | 0.58 | 0.88 | 1.24 | 0.85 | 0.59 | 0.82 |
time (sec) |
N/A | 0.189 | 0.030 | 2.414 | 0.210 | 0.221 | 0.095 | 0.292 | 1.307 |
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 | 58 | 34 | 55 |
N.S. |
1 | 1.00 | 0.54 | 0.51 | 0.88 | 0.88 | 0.87 | 0.51 | 0.82 |
time (sec) |
N/A | 0.189 | 0.023 | 2.400 | 0.209 | 0.215 | 0.077 | 0.280 | 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 | 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 | 0.189 | 0.024 | 2.413 | 0.206 | 0.218 | 0.079 | 0.288 | 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 | 78 | 78 | 85 | 69 | 69 | 69 | 82 | 69 | 69 |
N.S. |
1 | 1.00 | 1.09 | 0.88 | 0.88 | 0.88 | 1.05 | 0.88 | 0.88 |
time (sec) |
N/A | 0.227 | 0.003 | 2.403 | 0.200 | 0.218 | 0.030 | 0.286 | 0.166 |
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 | 78 | 78 | 74 | 64 | 64 | 64 | 71 | 64 | 64 |
N.S. |
1 | 1.00 | 0.95 | 0.82 | 0.82 | 0.82 | 0.91 | 0.82 | 0.82 |
time (sec) |
N/A | 0.236 | 0.003 | 2.412 | 0.198 | 0.206 | 0.030 | 0.280 | 0.136 |
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 | 78 | 78 | 65 | 59 | 59 | 59 | 63 | 59 | 59 |
N.S. |
1 | 1.00 | 0.83 | 0.76 | 0.76 | 0.76 | 0.81 | 0.76 | 0.76 |
time (sec) |
N/A | 0.223 | 0.003 | 2.408 | 0.208 | 0.219 | 0.026 | 0.269 | 0.104 |
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 | 62 | 54 | 54 | 54 | 60 | 54 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.87 | 0.87 | 0.97 | 0.87 | 0.87 |
time (sec) |
N/A | 0.218 | 0.003 | 2.408 | 0.205 | 0.218 | 0.025 | 0.283 | 0.081 |
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 | 59 | 49 | 49 | 49 | 56 | 49 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.95 | 0.83 | 0.83 |
time (sec) |
N/A | 0.196 | 0.002 | 2.396 | 0.206 | 0.210 | 0.023 | 0.286 | 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 | 54 | 54 | 54 | 44 | 44 | 44 | 51 | 44 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.81 | 0.81 | 0.94 | 0.81 | 0.81 |
time (sec) |
N/A | 0.212 | 0.002 | 2.393 | 0.202 | 0.222 | 0.031 | 0.289 | 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 | 47 | 47 | 47 | 39 | 39 | 39 | 44 | 39 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.94 | 0.83 | 0.83 |
time (sec) |
N/A | 0.182 | 0.001 | 2.413 | 0.200 | 0.222 | 0.023 | 0.279 | 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 | 40 | 40 | 40 | 34 | 34 | 34 | 37 | 34 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.85 | 0.85 | 0.92 | 0.85 | 0.85 |
time (sec) |
N/A | 0.180 | 0.002 | 2.405 | 0.213 | 0.215 | 0.021 | 0.270 | 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 | 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 | 0.174 | 0.010 | 2.430 | 0.206 | 0.229 | 0.043 | 0.290 | 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 | 55 | 55 | 54 | 40 | 41 | 52 | 48 | 75 | 39 |
N.S. |
1 | 1.00 | 0.98 | 0.73 | 0.75 | 0.95 | 0.87 | 1.36 | 0.71 |
time (sec) |
N/A | 0.176 | 0.011 | 2.426 | 0.205 | 0.215 | 0.052 | 0.281 | 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 | 59 | 59 | 56 | 42 | 46 | 62 | 49 | 42 | 42 |
N.S. |
1 | 1.00 | 0.95 | 0.71 | 0.78 | 1.05 | 0.83 | 0.71 | 0.71 |
time (sec) |
N/A | 0.185 | 0.014 | 2.437 | 0.199 | 0.215 | 0.058 | 0.290 | 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 | 63 | 63 | 52 | 42 | 51 | 72 | 54 | 42 | 46 |
N.S. |
1 | 1.00 | 0.83 | 0.67 | 0.81 | 1.14 | 0.86 | 0.67 | 0.73 |
time (sec) |
N/A | 0.186 | 0.014 | 2.422 | 0.222 | 0.226 | 0.064 | 0.277 | 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 | 67 | 67 | 56 | 42 | 56 | 82 | 56 | 75 | 52 |
N.S. |
1 | 1.00 | 0.84 | 0.63 | 0.84 | 1.22 | 0.84 | 1.12 | 0.78 |
time (sec) |
N/A | 0.191 | 0.015 | 2.438 | 0.219 | 0.214 | 0.068 | 0.283 | 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 | 71 | 71 | 56 | 42 | 61 | 92 | 61 | 42 | 56 |
N.S. |
1 | 1.00 | 0.79 | 0.59 | 0.86 | 1.30 | 0.86 | 0.59 | 0.79 |
time (sec) |
N/A | 0.193 | 0.017 | 2.445 | 0.207 | 0.214 | 0.073 | 0.278 | 1.251 |
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 | 77 | 77 | 51 | 43 | 68 | 97 | 66 | 44 | 64 |
N.S. |
1 | 1.00 | 0.66 | 0.56 | 0.88 | 1.26 | 0.86 | 0.57 | 0.83 |
time (sec) |
N/A | 0.199 | 0.013 | 2.442 | 0.220 | 0.222 | 0.078 | 0.259 | 0.075 |
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 | 78 | 78 | 41 | 39 | 69 | 69 | 68 | 39 | 64 |
N.S. |
1 | 1.00 | 0.53 | 0.50 | 0.88 | 0.88 | 0.87 | 0.50 | 0.82 |
time (sec) |
N/A | 0.202 | 0.011 | 2.438 | 0.231 | 0.214 | 0.079 | 0.278 | 1.298 |
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 | 0.189 | 0.013 | 2.452 | 0.216 | 0.223 | 0.050 | 0.274 | 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 | 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 | 0.187 | 0.011 | 0.807 | 0.212 | 0.225 | 0.048 | 0.267 | 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 | 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 | 0.176 | 0.010 | 0.800 | 0.210 | 0.219 | 0.043 | 0.294 | 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 | 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 | 0.175 | 0.009 | 2.434 | 0.222 | 0.214 | 0.043 | 0.265 | 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 | 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 | 0.169 | 0.010 | 2.444 | 0.193 | 0.215 | 0.040 | 0.277 | 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 | 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 | 0.160 | 0.013 | 2.434 | 0.195 | 0.217 | 0.046 | 0.282 | 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 | 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 | 0.155 | 0.008 | 2.433 | 0.199 | 0.218 | 0.034 | 0.272 | 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 | 33 | 33 | 35 | 22 | 25 | 25 | 31 | 27 | 21 |
N.S. |
1 | 1.00 | 1.06 | 0.67 | 0.76 | 0.76 | 0.94 | 0.82 | 0.64 |
time (sec) |
N/A | 0.160 | 0.011 | 2.426 | 0.193 | 0.224 | 0.056 | 0.269 | 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 | 37 | 37 | 36 | 28 | 29 | 45 | 31 | 47 | 25 |
N.S. |
1 | 1.00 | 0.97 | 0.76 | 0.78 | 1.22 | 0.84 | 1.27 | 0.68 |
time (sec) |
N/A | 0.163 | 0.017 | 2.439 | 0.207 | 0.213 | 0.063 | 0.275 | 1.162 |
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 | 43 | 43 | 39 | 32 | 36 | 55 | 36 | 33 | 29 |
N.S. |
1 | 1.00 | 0.91 | 0.74 | 0.84 | 1.28 | 0.84 | 0.77 | 0.67 |
time (sec) |
N/A | 0.170 | 0.021 | 2.441 | 0.218 | 0.224 | 0.072 | 0.271 | 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 | 50 | 50 | 40 | 36 | 46 | 75 | 42 | 38 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.72 | 0.92 | 1.50 | 0.84 | 0.76 | 0.70 |
time (sec) |
N/A | 0.182 | 0.023 | 2.445 | 0.198 | 0.219 | 0.074 | 0.267 | 1.293 |
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 | 0.203 | 0.023 | 2.445 | 0.234 | 0.223 | 0.081 | 0.286 | 0.073 |
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 | 0.196 | 0.033 | 2.442 | 0.271 | 0.232 | 0.086 | 0.275 | 0.047 |