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 | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 76 | 50 | 69 | 68 | 61 | 70 | 0 | 0 |
N.S. |
1 | 1.06 | 0.69 | 0.96 | 0.94 | 0.85 | 0.97 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 0.027 | 0.191 | 0.197 | 0.263 | 0.369 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 81 | 49 | 58 | 59 | 59 | 61 | 0 | 0 |
N.S. |
1 | 1.21 | 0.73 | 0.87 | 0.88 | 0.88 | 0.91 | 0.00 | 0.00 |
time (sec) |
N/A | 0.209 | 0.015 | 0.008 | 0.181 | 0.249 | 0.273 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 56 | 41 | 50 | 48 | 52 | 48 | 0 | 0 |
N.S. |
1 | 1.08 | 0.79 | 0.96 | 0.92 | 1.00 | 0.92 | 0.00 | 0.00 |
time (sec) |
N/A | 0.212 | 0.019 | 0.009 | 0.202 | 0.260 | 0.224 | 0.000 | 0.000 |
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 | 50 | 40 | 39 | 39 | 48 | 37 | 68 | 36 |
N.S. |
1 | 1.14 | 0.91 | 0.89 | 0.89 | 1.09 | 0.84 | 1.55 | 0.82 |
time (sec) |
N/A | 0.184 | 0.009 | 0.008 | 0.183 | 0.267 | 0.161 | 0.259 | 2.288 |
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 | 25 | 25 | 25 | 24 | 25 | 37 | 20 | 35 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.00 | 1.48 | 0.80 | 1.40 | 0.92 |
time (sec) |
N/A | 0.159 | 0.008 | 0.007 | 0.198 | 0.254 | 0.083 | 0.256 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 57 | 43 | 94 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.33 | 1.00 | 2.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.330 | 0.005 | 0.260 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 26 | 22 | 90 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.81 | 3.33 | 0.00 | 2.07 | 0.00 |
time (sec) |
N/A | 0.195 | 0.004 | 0.008 | 0.182 | 0.259 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 28 | 28 | 27 | 36 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.85 | 0.82 | 1.09 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.180 | 0.008 | 0.009 | 0.184 | 0.263 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 48 | 43 | 117 | 0 | 84 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.80 | 2.17 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.203 | 0.010 | 0.007 | 0.187 | 0.265 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 40 | 50 | 49 | 49 | 0 | 77 | 0 |
N.S. |
1 | 1.09 | 0.71 | 0.89 | 0.88 | 0.88 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.191 | 0.011 | 0.008 | 0.200 | 0.269 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 82 | 49 | 70 | 63 | 129 | 0 | 107 | 0 |
N.S. |
1 | 1.06 | 0.64 | 0.91 | 0.82 | 1.68 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.212 | 0.012 | 0.008 | 0.203 | 0.263 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 137 | 75 | 103 | 99 | 99 | 114 | 0 | 0 |
N.S. |
1 | 1.17 | 0.64 | 0.88 | 0.85 | 0.85 | 0.97 | 0.00 | 0.00 |
time (sec) |
N/A | 0.557 | 0.049 | 0.255 | 0.189 | 0.254 | 0.523 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 113 | 72 | 87 | 109 | 92 | 90 | 0 | 0 |
N.S. |
1 | 1.18 | 0.75 | 0.91 | 1.14 | 0.96 | 0.94 | 0.00 | 0.00 |
time (sec) |
N/A | 0.537 | 0.035 | 0.200 | 0.196 | 0.253 | 0.374 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 92 | 59 | 72 | 70 | 82 | 76 | 0 | 0 |
N.S. |
1 | 1.15 | 0.74 | 0.90 | 0.88 | 1.02 | 0.95 | 0.00 | 0.00 |
time (sec) |
N/A | 0.404 | 0.052 | 0.211 | 0.194 | 0.261 | 0.290 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 66 | 53 | 59 | 81 | 73 | 51 | 0 | 0 |
N.S. |
1 | 1.12 | 0.90 | 1.00 | 1.37 | 1.24 | 0.86 | 0.00 | 0.00 |
time (sec) |
N/A | 0.359 | 0.024 | 0.033 | 0.196 | 0.261 | 0.206 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 40 | 34 | 36 | 32 | 59 | 32 | 62 | 0 |
N.S. |
1 | 1.18 | 1.00 | 1.06 | 0.94 | 1.74 | 0.94 | 1.82 | 0.00 |
time (sec) |
N/A | 0.248 | 0.017 | 0.031 | 0.205 | 0.252 | 0.099 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 77 | 60 | 151 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 1.00 | 2.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.442 | 0.007 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 59 | 75 | 108 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 1.50 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.402 | 0.168 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 72 | 39 | 67 | 0 | 98 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 0.91 | 1.56 | 0.00 | 2.28 | 0.00 |
time (sec) |
N/A | 0.282 | 0.025 | 0.060 | 0.194 | 0.252 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 103 | 125 | 136 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.26 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.571 | 0.416 | 0.060 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 86 | 64 | 112 | 71 | 85 | 0 | 148 | 0 |
N.S. |
1 | 1.01 | 0.75 | 1.32 | 0.84 | 1.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.410 | 0.052 | 0.062 | 0.191 | 0.266 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 293 | 120 | 172 | 165 | 151 | 196 | 0 | 0 |
N.S. |
1 | 1.50 | 0.62 | 0.88 | 0.85 | 0.77 | 1.01 | 0.00 | 0.00 |
time (sec) |
N/A | 1.343 | 0.063 | 0.040 | 0.191 | 0.257 | 0.635 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 240 | 110 | 141 | 0 | 142 | 160 | 0 | 0 |
N.S. |
1 | 1.47 | 0.67 | 0.87 | 0.00 | 0.87 | 0.98 | 0.00 | 0.00 |
time (sec) |
N/A | 1.053 | 0.061 | 0.039 | 0.000 | 0.273 | 0.506 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 171 | 93 | 116 | 116 | 124 | 128 | 0 | 0 |
N.S. |
1 | 1.30 | 0.70 | 0.88 | 0.88 | 0.94 | 0.97 | 0.00 | 0.00 |
time (sec) |
N/A | 0.770 | 0.046 | 0.033 | 0.197 | 0.257 | 0.388 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 115 | 80 | 88 | 0 | 112 | 92 | 0 | 0 |
N.S. |
1 | 1.19 | 0.82 | 0.91 | 0.00 | 1.15 | 0.95 | 0.00 | 0.00 |
time (sec) |
N/A | 0.539 | 0.038 | 0.032 | 0.000 | 0.257 | 0.262 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 66 | 58 | 55 | 57 | 90 | 54 | 98 | 0 |
N.S. |
1 | 1.14 | 1.00 | 0.95 | 0.98 | 1.55 | 0.93 | 1.69 | 0.00 |
time (sec) |
N/A | 0.334 | 0.017 | 0.027 | 0.198 | 0.250 | 0.119 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 102 | 83 | 204 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 1.00 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.534 | 0.007 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 93 | 117 | 161 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.39 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.546 | 0.099 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 102 | 80 | 146 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.86 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.598 | 0.288 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 157 | 268 | 212 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.77 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.037 | 1.694 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 174 | 107 | 213 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.67 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.022 | 0.561 | 0.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 276 | 492 | 165 | 242 | 0 | 208 | 269 | 0 | 0 |
N.S. |
1 | 1.78 | 0.60 | 0.88 | 0.00 | 0.75 | 0.97 | 0.00 | 0.00 |
time (sec) |
N/A | 2.750 | 0.077 | 0.219 | 0.000 | 0.275 | 1.320 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 244 | 403 | 148 | 210 | 201 | 189 | 241 | 0 | 0 |
N.S. |
1 | 1.65 | 0.61 | 0.86 | 0.82 | 0.77 | 0.99 | 0.00 | 0.00 |
time (sec) |
N/A | 2.390 | 0.076 | 0.040 | 0.207 | 0.260 | 0.880 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 288 | 133 | 172 | 0 | 176 | 190 | 0 | 0 |
N.S. |
1 | 1.48 | 0.69 | 0.89 | 0.00 | 0.91 | 0.98 | 0.00 | 0.00 |
time (sec) |
N/A | 1.716 | 0.054 | 0.041 | 0.000 | 0.268 | 0.651 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 222 | 112 | 140 | 143 | 154 | 158 | 0 | 0 |
N.S. |
1 | 1.37 | 0.69 | 0.86 | 0.88 | 0.95 | 0.98 | 0.00 | 0.00 |
time (sec) |
N/A | 1.324 | 0.060 | 0.039 | 0.207 | 0.258 | 0.519 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 131 | 94 | 105 | 0 | 138 | 104 | 0 | 0 |
N.S. |
1 | 1.19 | 0.85 | 0.95 | 0.00 | 1.25 | 0.95 | 0.00 | 0.00 |
time (sec) |
N/A | 0.823 | 0.041 | 0.029 | 0.000 | 0.257 | 0.350 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 81 | 67 | 65 | 73 | 112 | 65 | 125 | 0 |
N.S. |
1 | 1.21 | 1.00 | 0.97 | 1.09 | 1.67 | 0.97 | 1.87 | 0.00 |
time (sec) |
N/A | 0.450 | 0.019 | 0.027 | 0.200 | 0.250 | 0.190 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 125 | 97 | 257 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.29 | 1.00 | 2.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.659 | 0.009 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 135 | 161 | 214 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 1.34 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.708 | 0.186 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 120 | 113 | 199 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.05 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.739 | 0.262 | 0.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 237 | 355 | 340 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.59 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.393 | 1.861 | 0.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 47 | 40 | 40 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.73 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 0.011 | 0.063 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 38 | 33 | 33 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.77 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.290 | 0.122 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 36 | 31 | 31 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.76 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.293 | 0.009 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 24 | 24 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.83 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 0.098 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 22 | 22 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.81 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.272 | 0.008 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.270 | 0.032 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.215 | 0.014 | 0.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.177 | 0.146 | 0.030 | 0.237 | 0.244 | 0.324 | 0.273 | 2.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.176 | 0.840 | 0.051 | 0.237 | 0.266 | 0.329 | 0.275 | 2.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 75 | 85 | 104 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 1.04 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.279 | 0.431 | 0.065 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 66 | 78 | 78 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 1.11 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.265 | 0.031 | 0.062 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 64 | 60 | 80 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.88 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.260 | 0.328 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 55 | 56 | 54 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.246 | 0.021 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 53 | 49 | 56 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.91 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.245 | 0.247 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 29 | 28 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.256 | 0.010 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 31 | 30 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.347 | 0.071 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 200 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 20.00 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.173 | 0.771 | 0.032 | 0.319 | 0.253 | 0.387 | 0.269 | 2.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 237 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 23.70 | 1.20 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.177 | 5.279 | 0.043 | 0.361 | 0.250 | 0.465 | 0.276 | 2.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 133 | 102 | 120 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.37 | 1.05 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.747 | 0.111 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 109 | 69 | 82 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.33 | 0.84 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.790 | 0.190 | 0.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 102 | 64 | 81 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.26 | 0.79 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.833 | 0.139 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 69 | 62 | 43 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.98 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.727 | 0.051 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 54 | 47 | 42 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.94 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.417 | 0.022 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 697 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 69.70 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.173 | 0.473 | 0.033 | 0.625 | 0.248 | 0.464 | 0.274 | 2.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 822 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 82.20 | 1.20 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.172 | 4.652 | 0.044 | 0.728 | 0.258 | 0.576 | 0.282 | 2.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 207 | 156 | 169 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.34 | 1.01 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.668 | 0.413 | 0.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 174 | 105 | 114 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 0.74 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.788 | 0.302 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 172 | 99 | 115 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 0.72 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.051 | 0.347 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 104 | 84 | 60 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.88 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.694 | 0.109 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 88 | 69 | 61 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.91 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.578 | 0.086 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 1611 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 161.10 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.173 | 1.987 | 0.031 | 1.292 | 0.262 | 0.607 | 0.270 | 2.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 1885 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 188.50 | 1.20 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.173 | 7.511 | 0.046 | 1.505 | 0.253 | 0.803 | 0.272 | 2.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 182 | 186 | 152 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.590 | 0.093 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 139 | 132 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.525 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 120 | 126 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.519 | 0.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 90 | 52 | 75 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.56 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.454 | 0.029 | 0.135 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 61 | 45 | 42 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 0.85 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.442 | 0.046 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 12 | 0 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 1.00 | 0.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.176 | 0.163 | 0.039 | 0.350 | 0.000 | 0.412 | 0.425 | 2.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 330 | 421 | 152 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.475 | 0.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 199 | 279 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.40 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.941 | 0.063 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 179 | 230 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.300 | 0.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 136 | 52 | 102 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.43 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.985 | 0.021 | 0.089 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 86 | 47 | 65 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.58 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.525 | 0.026 | 0.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 12 | 0 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 1.00 | 0.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.173 | 0.136 | 0.040 | 0.367 | 0.000 | 1.666 | 0.572 | 2.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 379 | 519 | 152 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.37 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.796 | 0.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 247 | 341 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.38 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.854 | 0.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 210 | 287 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.37 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.646 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 163 | 52 | 136 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.34 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.932 | 0.029 | 0.097 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 110 | 45 | 78 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 0.48 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.664 | 0.040 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 12 | 0 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 1.00 | 0.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.168 | 0.140 | 0.041 | 0.352 | 0.000 | 19.286 | 0.600 | 2.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 163 | 149 | 151 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.415 | 0.081 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 109 | 101 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.350 | 0.065 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 105 | 97 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 0.062 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 70 | 52 | 37 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.83 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.377 | 0.018 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 41 | 47 | 24 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.09 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.303 | 0.027 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 12 | 0 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.170 | 0.166 | 0.042 | 0.354 | 0.000 | 0.434 | 0.423 | 2.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 12 | 0 | 14 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 1.00 | 0.00 | 1.17 | 1.00 | 1.00 |
time (sec) |
N/A | 0.172 | 1.337 | 0.053 | 0.357 | 0.000 | 0.553 | 0.444 | 2.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 188 | 176 | 265 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.379 | 0.118 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 138 | 132 | 126 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.326 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |