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 | 34 | 36 | 32 | 25 | 26 | 26 | 32 | 26 | 26 |
N.S. |
1 | 1.06 | 0.94 | 0.74 | 0.76 | 0.76 | 0.94 | 0.76 | 0.76 |
time (sec) |
N/A | 0.173 | 0.029 | 6.025 | 0.206 | 0.292 | 0.269 | 0.316 | 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 | 34 | 36 | 32 | 25 | 26 | 26 | 32 | 26 | 26 |
N.S. |
1 | 1.06 | 0.94 | 0.74 | 0.76 | 0.76 | 0.94 | 0.76 | 0.76 |
time (sec) |
N/A | 0.178 | 0.027 | 10.464 | 0.211 | 0.260 | 0.333 | 0.278 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 49 | 43 | 36 | 251 | 35 | 42 | 35 | 35 |
N.S. |
1 | 1.04 | 0.91 | 0.77 | 5.34 | 0.74 | 0.89 | 0.74 | 0.74 |
time (sec) |
N/A | 0.192 | 0.025 | 3.586 | 0.201 | 0.266 | 0.549 | 0.295 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 49 | 43 | 36 | 200 | 35 | 42 | 35 | 35 |
N.S. |
1 | 1.04 | 0.91 | 0.77 | 4.26 | 0.74 | 0.89 | 0.74 | 0.74 |
time (sec) |
N/A | 0.195 | 0.024 | 3.588 | 0.199 | 0.267 | 0.474 | 0.310 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 49 | 41 | 36 | 149 | 35 | 42 | 35 | 35 |
N.S. |
1 | 1.04 | 0.87 | 0.77 | 3.17 | 0.74 | 0.89 | 0.74 | 0.74 |
time (sec) |
N/A | 0.189 | 0.025 | 6.006 | 0.203 | 0.272 | 0.410 | 0.306 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 49 | 43 | 36 | 98 | 35 | 42 | 35 | 35 |
N.S. |
1 | 1.04 | 0.91 | 0.77 | 2.09 | 0.74 | 0.89 | 0.74 | 0.74 |
time (sec) |
N/A | 0.184 | 0.022 | 5.790 | 0.205 | 0.267 | 0.363 | 0.274 | 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 | 42 | 47 | 41 | 33 | 32 | 32 | 39 | 32 | 32 |
N.S. |
1 | 1.12 | 0.98 | 0.79 | 0.76 | 0.76 | 0.93 | 0.76 | 0.76 |
time (sec) |
N/A | 0.188 | 0.019 | 5.920 | 0.200 | 0.288 | 0.295 | 0.305 | 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 | 36 | 45 | 36 | 31 | 30 | 33 | 36 | 31 | 33 |
N.S. |
1 | 1.25 | 1.00 | 0.86 | 0.83 | 0.92 | 1.00 | 0.86 | 0.92 |
time (sec) |
N/A | 0.185 | 0.028 | 3.632 | 0.198 | 0.279 | 0.086 | 0.278 | 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 | 39 | 47 | 40 | 34 | 36 | 39 | 36 | 37 | 37 |
N.S. |
1 | 1.21 | 1.03 | 0.87 | 0.92 | 1.00 | 0.92 | 0.95 | 0.95 |
time (sec) |
N/A | 0.187 | 0.044 | 5.922 | 0.221 | 0.286 | 0.197 | 0.265 | 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 | 45 | 49 | 41 | 36 | 35 | 35 | 41 | 35 | 35 |
N.S. |
1 | 1.09 | 0.91 | 0.80 | 0.78 | 0.78 | 0.91 | 0.78 | 0.78 |
time (sec) |
N/A | 0.186 | 0.033 | 3.613 | 0.200 | 0.292 | 0.255 | 0.270 | 5.572 |
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 | 49 | 41 | 36 | 35 | 35 | 44 | 35 | 35 |
N.S. |
1 | 1.04 | 0.87 | 0.77 | 0.74 | 0.74 | 0.94 | 0.74 | 0.74 |
time (sec) |
N/A | 0.183 | 0.033 | 5.983 | 0.205 | 0.264 | 0.344 | 0.269 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 79 | 69 | 58 | 251 | 69 | 75 | 57 | 57 |
N.S. |
1 | 1.03 | 0.90 | 0.75 | 3.26 | 0.90 | 0.97 | 0.74 | 0.74 |
time (sec) |
N/A | 0.217 | 0.029 | 3.705 | 0.206 | 0.260 | 0.683 | 0.263 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 79 | 69 | 58 | 200 | 69 | 73 | 57 | 57 |
N.S. |
1 | 1.05 | 0.92 | 0.77 | 2.67 | 0.92 | 0.97 | 0.76 | 0.76 |
time (sec) |
N/A | 0.216 | 0.029 | 3.472 | 0.235 | 0.271 | 0.535 | 0.278 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 79 | 69 | 58 | 149 | 69 | 75 | 57 | 57 |
N.S. |
1 | 1.03 | 0.90 | 0.75 | 1.94 | 0.90 | 0.97 | 0.74 | 0.74 |
time (sec) |
N/A | 0.214 | 0.029 | 3.628 | 0.212 | 0.275 | 0.470 | 0.311 | 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 | 77 | 79 | 69 | 58 | 98 | 69 | 75 | 57 | 57 |
N.S. |
1 | 1.03 | 0.90 | 0.75 | 1.27 | 0.90 | 0.97 | 0.74 | 0.74 |
time (sec) |
N/A | 0.208 | 0.025 | 5.902 | 0.214 | 0.271 | 0.399 | 0.274 | 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 | 59 | 61 | 67 | 55 | 54 | 61 | 68 | 54 | 54 |
N.S. |
1 | 1.03 | 1.14 | 0.93 | 0.92 | 1.03 | 1.15 | 0.92 | 0.92 |
time (sec) |
N/A | 0.194 | 0.024 | 3.587 | 0.204 | 0.257 | 0.328 | 0.281 | 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 | 65 | 73 | 65 | 54 | 53 | 56 | 71 | 54 | 56 |
N.S. |
1 | 1.12 | 1.00 | 0.83 | 0.82 | 0.86 | 1.09 | 0.83 | 0.86 |
time (sec) |
N/A | 0.202 | 0.033 | 3.751 | 0.205 | 0.259 | 0.628 | 0.287 | 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 | 68 | 76 | 69 | 57 | 59 | 62 | 66 | 60 | 59 |
N.S. |
1 | 1.12 | 1.01 | 0.84 | 0.87 | 0.91 | 0.97 | 0.88 | 0.87 |
time (sec) |
N/A | 0.204 | 0.042 | 3.597 | 0.214 | 0.261 | 0.215 | 0.273 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 67 | 58 | 55 | 57 | 70 | 55 | 55 |
N.S. |
1 | 1.00 | 3.19 | 2.76 | 2.62 | 2.71 | 3.33 | 2.62 | 2.62 |
time (sec) |
N/A | 0.147 | 0.036 | 3.726 | 0.205 | 0.259 | 0.266 | 0.274 | 5.462 |
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 | 77 | 67 | 58 | 57 | 59 | 73 | 57 | 57 |
N.S. |
1 | 1.05 | 0.92 | 0.79 | 0.78 | 0.81 | 1.00 | 0.78 | 0.78 |
time (sec) |
N/A | 0.209 | 0.042 | 3.705 | 0.348 | 0.255 | 0.351 | 0.275 | 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 | 75 | 77 | 67 | 58 | 57 | 58 | 75 | 57 | 57 |
N.S. |
1 | 1.03 | 0.89 | 0.77 | 0.76 | 0.77 | 1.00 | 0.76 | 0.76 |
time (sec) |
N/A | 0.212 | 0.044 | 3.698 | 0.275 | 0.267 | 0.480 | 0.268 | 5.552 |
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 | 79 | 67 | 58 | 57 | 59 | 76 | 57 | 57 |
N.S. |
1 | 1.03 | 0.87 | 0.75 | 0.74 | 0.77 | 0.99 | 0.74 | 0.74 |
time (sec) |
N/A | 0.205 | 0.044 | 3.592 | 0.199 | 0.273 | 0.616 | 0.273 | 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 | 75 | 79 | 67 | 58 | 57 | 59 | 75 | 57 | 57 |
N.S. |
1 | 1.05 | 0.89 | 0.77 | 0.76 | 0.79 | 1.00 | 0.76 | 0.76 |
time (sec) |
N/A | 0.204 | 0.045 | 3.655 | 0.205 | 0.270 | 0.799 | 0.280 | 5.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 148 | 130 | 113 | 251 | 124 | 144 | 112 | 112 |
N.S. |
1 | 1.03 | 0.90 | 0.78 | 1.74 | 0.86 | 1.00 | 0.78 | 0.78 |
time (sec) |
N/A | 0.288 | 0.042 | 3.619 | 0.200 | 0.280 | 0.967 | 0.266 | 0.074 |
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 | 144 | 148 | 130 | 113 | 200 | 124 | 144 | 112 | 112 |
N.S. |
1 | 1.03 | 0.90 | 0.78 | 1.39 | 0.86 | 1.00 | 0.78 | 0.78 |
time (sec) |
N/A | 0.280 | 0.040 | 3.609 | 0.208 | 0.258 | 0.798 | 0.265 | 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 | 179 | 185 | 130 | 113 | 149 | 124 | 141 | 112 | 112 |
N.S. |
1 | 1.03 | 0.73 | 0.63 | 0.83 | 0.69 | 0.79 | 0.63 | 0.63 |
time (sec) |
N/A | 0.297 | 0.042 | 3.610 | 0.200 | 0.257 | 0.695 | 0.271 | 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 | 120 | 124 | 130 | 113 | 98 | 124 | 143 | 112 | 112 |
N.S. |
1 | 1.03 | 1.08 | 0.94 | 0.82 | 1.03 | 1.19 | 0.93 | 0.93 |
time (sec) |
N/A | 0.250 | 0.047 | 3.668 | 0.200 | 0.275 | 0.585 | 0.276 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 61 | 128 | 110 | 47 | 117 | 136 | 109 | 109 |
N.S. |
1 | 1.03 | 2.17 | 1.86 | 0.80 | 1.98 | 2.31 | 1.85 | 1.85 |
time (sec) |
N/A | 0.202 | 0.036 | 3.684 | 0.215 | 0.270 | 0.481 | 0.268 | 0.074 |
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 | 136 | 142 | 132 | 109 | 108 | 113 | 144 | 109 | 111 |
N.S. |
1 | 1.04 | 0.97 | 0.80 | 0.79 | 0.83 | 1.06 | 0.80 | 0.82 |
time (sec) |
N/A | 0.267 | 0.050 | 3.723 | 0.205 | 0.288 | 1.168 | 0.285 | 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 | 125 | 135 | 125 | 110 | 110 | 116 | 131 | 111 | 112 |
N.S. |
1 | 1.08 | 1.00 | 0.88 | 0.88 | 0.93 | 1.05 | 0.89 | 0.90 |
time (sec) |
N/A | 0.267 | 0.083 | 3.679 | 0.192 | 0.282 | 1.167 | 0.269 | 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 | 131 | 139 | 132 | 110 | 110 | 117 | 136 | 111 | 112 |
N.S. |
1 | 1.06 | 1.01 | 0.84 | 0.84 | 0.89 | 1.04 | 0.85 | 0.85 |
time (sec) |
N/A | 0.260 | 0.068 | 3.710 | 0.196 | 0.269 | 1.177 | 0.316 | 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 | 131 | 136 | 132 | 112 | 112 | 118 | 133 | 113 | 113 |
N.S. |
1 | 1.04 | 1.01 | 0.85 | 0.85 | 0.90 | 1.02 | 0.86 | 0.86 |
time (sec) |
N/A | 0.258 | 0.115 | 3.682 | 0.190 | 0.284 | 0.398 | 0.300 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 48 | 128 | 113 | 112 | 114 | 139 | 112 | 112 |
N.S. |
1 | 1.04 | 2.78 | 2.46 | 2.43 | 2.48 | 3.02 | 2.43 | 2.43 |
time (sec) |
N/A | 0.159 | 0.068 | 3.671 | 0.198 | 0.276 | 0.523 | 0.278 | 0.096 |
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 | 122 | 142 | 128 | 113 | 112 | 114 | 143 | 112 | 112 |
N.S. |
1 | 1.16 | 1.05 | 0.93 | 0.92 | 0.93 | 1.17 | 0.92 | 0.92 |
time (sec) |
N/A | 0.201 | 0.082 | 3.609 | 0.194 | 0.284 | 0.676 | 0.292 | 5.577 |
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 | 144 | 146 | 128 | 113 | 112 | 114 | 146 | 112 | 112 |
N.S. |
1 | 1.01 | 0.89 | 0.78 | 0.78 | 0.79 | 1.01 | 0.78 | 0.78 |
time (sec) |
N/A | 0.269 | 0.086 | 3.702 | 0.200 | 0.263 | 0.857 | 0.278 | 5.694 |
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 | 144 | 148 | 128 | 113 | 112 | 114 | 146 | 112 | 112 |
N.S. |
1 | 1.03 | 0.89 | 0.78 | 0.78 | 0.79 | 1.01 | 0.78 | 0.78 |
time (sec) |
N/A | 0.275 | 0.089 | 3.492 | 0.204 | 0.276 | 1.088 | 0.269 | 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 | 144 | 150 | 128 | 113 | 112 | 114 | 146 | 112 | 112 |
N.S. |
1 | 1.04 | 0.89 | 0.78 | 0.78 | 0.79 | 1.01 | 0.78 | 0.78 |
time (sec) |
N/A | 0.270 | 0.086 | 3.568 | 0.209 | 0.272 | 1.400 | 0.286 | 0.103 |
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 | 142 | 144 | 128 | 113 | 112 | 114 | 144 | 112 | 112 |
N.S. |
1 | 1.01 | 0.90 | 0.80 | 0.79 | 0.80 | 1.01 | 0.79 | 0.79 |
time (sec) |
N/A | 0.277 | 0.087 | 3.694 | 0.206 | 0.267 | 1.764 | 0.284 | 5.948 |
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 | 217 | 221 | 191 | 168 | 302 | 179 | 218 | 167 | 167 |
N.S. |
1 | 1.02 | 0.88 | 0.77 | 1.39 | 0.82 | 1.00 | 0.77 | 0.77 |
time (sec) |
N/A | 0.368 | 0.055 | 3.442 | 0.212 | 0.265 | 1.686 | 0.265 | 0.175 |
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 | 217 | 221 | 191 | 168 | 251 | 179 | 218 | 167 | 167 |
N.S. |
1 | 1.02 | 0.88 | 0.77 | 1.16 | 0.82 | 1.00 | 0.77 | 0.77 |
time (sec) |
N/A | 0.346 | 0.052 | 3.498 | 0.201 | 0.265 | 1.376 | 0.270 | 0.181 |
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 | 244 | 246 | 191 | 168 | 200 | 179 | 216 | 167 | 167 |
N.S. |
1 | 1.01 | 0.78 | 0.69 | 0.82 | 0.73 | 0.89 | 0.68 | 0.68 |
time (sec) |
N/A | 0.363 | 0.052 | 3.541 | 0.200 | 0.284 | 1.161 | 0.272 | 0.219 |
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 | 183 | 187 | 191 | 168 | 149 | 179 | 214 | 167 | 167 |
N.S. |
1 | 1.02 | 1.04 | 0.92 | 0.81 | 0.98 | 1.17 | 0.91 | 0.91 |
time (sec) |
N/A | 0.304 | 0.052 | 3.738 | 0.213 | 0.286 | 0.966 | 0.275 | 0.169 |
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 | 122 | 124 | 191 | 168 | 98 | 179 | 214 | 167 | 167 |
N.S. |
1 | 1.02 | 1.57 | 1.38 | 0.80 | 1.47 | 1.75 | 1.37 | 1.37 |
time (sec) |
N/A | 0.254 | 0.050 | 3.686 | 0.206 | 0.272 | 0.814 | 0.271 | 0.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 61 | 189 | 165 | 47 | 172 | 207 | 164 | 164 |
N.S. |
1 | 1.03 | 3.20 | 2.80 | 0.80 | 2.92 | 3.51 | 2.78 | 2.78 |
time (sec) |
N/A | 0.214 | 0.047 | 3.681 | 0.202 | 0.265 | 0.663 | 0.279 | 0.170 |
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 | 209 | 217 | 193 | 164 | 163 | 168 | 212 | 164 | 166 |
N.S. |
1 | 1.04 | 0.92 | 0.78 | 0.78 | 0.80 | 1.01 | 0.78 | 0.79 |
time (sec) |
N/A | 0.330 | 0.067 | 3.710 | 0.209 | 0.270 | 0.433 | 0.284 | 0.180 |
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 | 202 | 212 | 195 | 165 | 167 | 173 | 204 | 168 | 167 |
N.S. |
1 | 1.05 | 0.97 | 0.82 | 0.83 | 0.86 | 1.01 | 0.83 | 0.83 |
time (sec) |
N/A | 0.338 | 0.108 | 3.431 | 0.211 | 0.267 | 0.476 | 0.270 | 5.967 |
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 | 200 | 210 | 193 | 165 | 165 | 173 | 202 | 166 | 167 |
N.S. |
1 | 1.05 | 0.96 | 0.82 | 0.82 | 0.86 | 1.01 | 0.83 | 0.84 |
time (sec) |
N/A | 0.335 | 0.119 | 3.586 | 0.194 | 0.269 | 0.505 | 0.296 | 5.967 |
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 | 200 | 210 | 193 | 165 | 165 | 173 | 202 | 166 | 167 |
N.S. |
1 | 1.05 | 0.96 | 0.82 | 0.82 | 0.86 | 1.01 | 0.83 | 0.84 |
time (sec) |
N/A | 0.344 | 0.142 | 3.651 | 0.233 | 0.282 | 0.504 | 0.271 | 5.832 |
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 | 211 | 219 | 193 | 166 | 166 | 173 | 212 | 167 | 168 |
N.S. |
1 | 1.04 | 0.91 | 0.79 | 0.79 | 0.82 | 1.00 | 0.79 | 0.80 |
time (sec) |
N/A | 0.336 | 0.196 | 3.612 | 0.204 | 0.276 | 0.677 | 0.271 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 80 | 189 | 168 | 167 | 169 | 209 | 167 | 166 |
N.S. |
1 | 1.11 | 2.62 | 2.33 | 2.32 | 2.35 | 2.90 | 2.32 | 2.31 |
time (sec) |
N/A | 0.185 | 0.099 | 3.637 | 0.200 | 0.277 | 0.877 | 0.282 | 6.038 |
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 | 148 | 174 | 189 | 168 | 167 | 169 | 216 | 167 | 167 |
N.S. |
1 | 1.18 | 1.28 | 1.14 | 1.13 | 1.14 | 1.46 | 1.13 | 1.13 |
time (sec) |
N/A | 0.225 | 0.118 | 3.740 | 0.194 | 0.278 | 1.133 | 0.266 | 6.144 |
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 | 224 | 268 | 189 | 168 | 167 | 169 | 216 | 167 | 167 |
N.S. |
1 | 1.20 | 0.84 | 0.75 | 0.75 | 0.75 | 0.96 | 0.75 | 0.75 |
time (sec) |
N/A | 0.273 | 0.122 | 3.646 | 0.220 | 0.275 | 1.420 | 0.280 | 6.046 |
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 | 215 | 221 | 189 | 168 | 167 | 169 | 218 | 167 | 167 |
N.S. |
1 | 1.03 | 0.88 | 0.78 | 0.78 | 0.79 | 1.01 | 0.78 | 0.78 |
time (sec) |
N/A | 0.344 | 0.122 | 3.640 | 0.201 | 0.298 | 1.778 | 0.277 | 0.217 |
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 | 217 | 221 | 189 | 168 | 167 | 169 | 219 | 167 | 167 |
N.S. |
1 | 1.02 | 0.87 | 0.77 | 0.77 | 0.78 | 1.01 | 0.77 | 0.77 |
time (sec) |
N/A | 0.344 | 0.124 | 3.694 | 0.204 | 0.303 | 2.246 | 0.272 | 5.976 |
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 | 217 | 221 | 189 | 168 | 167 | 169 | 219 | 167 | 167 |
N.S. |
1 | 1.02 | 0.87 | 0.77 | 0.77 | 0.78 | 1.01 | 0.77 | 0.77 |
time (sec) |
N/A | 0.343 | 0.132 | 3.670 | 0.196 | 0.280 | 2.840 | 0.279 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 170 | 152 | 132 | 197 | 133 | 0 | 133 | 130 |
N.S. |
1 | 1.02 | 0.92 | 0.80 | 1.19 | 0.80 | 0.00 | 0.80 | 0.78 |
time (sec) |
N/A | 0.311 | 0.141 | 3.681 | 0.204 | 0.281 | 0.000 | 0.269 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 127 | 115 | 99 | 146 | 100 | 0 | 100 | 98 |
N.S. |
1 | 1.02 | 0.93 | 0.80 | 1.18 | 0.81 | 0.00 | 0.81 | 0.79 |
time (sec) |
N/A | 0.260 | 0.093 | 3.695 | 0.193 | 0.275 | 0.000 | 0.264 | 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 | 80 | 84 | 78 | 66 | 95 | 66 | 80 | 67 | 64 |
N.S. |
1 | 1.05 | 0.98 | 0.82 | 1.19 | 0.82 | 1.00 | 0.84 | 0.80 |
time (sec) |
N/A | 0.222 | 0.043 | 5.960 | 0.194 | 0.264 | 147.925 | 0.283 | 0.061 |
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 | 43 | 42 | 35 | 44 | 33 | 42 | 35 | 34 |
N.S. |
1 | 1.02 | 1.00 | 0.83 | 1.05 | 0.79 | 1.00 | 0.83 | 0.81 |
time (sec) |
N/A | 0.184 | 0.030 | 6.044 | 0.194 | 0.259 | 0.140 | 0.273 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 28 | 30 | 21 | 20 | 20 | 37 | 22 | 17 |
N.S. |
1 | 1.27 | 1.36 | 0.95 | 0.91 | 0.91 | 1.68 | 1.00 | 0.77 |
time (sec) |
N/A | 0.158 | 0.026 | 12.852 | 0.207 | 0.267 | 0.171 | 0.265 | 5.891 |
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 | 70 | 62 | 56 | 56 | 56 | 83 | 61 | 50 |
N.S. |
1 | 1.11 | 0.98 | 0.89 | 0.89 | 0.89 | 1.32 | 0.97 | 0.79 |
time (sec) |
N/A | 0.210 | 0.050 | 12.776 | 0.197 | 0.274 | 0.542 | 0.273 | 0.071 |
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 | 104 | 112 | 95 | 87 | 86 | 93 | 129 | 91 | 83 |
N.S. |
1 | 1.08 | 0.91 | 0.84 | 0.83 | 0.89 | 1.24 | 0.88 | 0.80 |
time (sec) |
N/A | 0.242 | 0.086 | 3.514 | 0.199 | 0.263 | 1.148 | 0.271 | 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 | 149 | 156 | 132 | 122 | 120 | 126 | 172 | 125 | 116 |
N.S. |
1 | 1.05 | 0.89 | 0.82 | 0.81 | 0.85 | 1.15 | 0.84 | 0.78 |
time (sec) |
N/A | 0.279 | 0.112 | 5.974 | 0.195 | 0.293 | 2.205 | 0.275 | 5.811 |
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 | 21 | 27 | 25 | 16 | 15 | 17 | 22 | 17 | 10 |
N.S. |
1 | 1.29 | 1.19 | 0.76 | 0.71 | 0.81 | 1.05 | 0.81 | 0.48 |
time (sec) |
N/A | 0.149 | 0.021 | 3.899 | 0.192 | 0.258 | 0.144 | 0.285 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 174 | 171 | 139 | 197 | 181 | 0 | 144 | 143 |
N.S. |
1 | 1.02 | 1.00 | 0.81 | 1.15 | 1.06 | 0.00 | 0.84 | 0.84 |
time (sec) |
N/A | 0.328 | 0.117 | 3.524 | 0.199 | 0.276 | 0.000 | 0.267 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 128 | 134 | 106 | 146 | 147 | 0 | 111 | 110 |
N.S. |
1 | 1.05 | 1.10 | 0.87 | 1.20 | 1.20 | 0.00 | 0.91 | 0.90 |
time (sec) |
N/A | 0.282 | 0.092 | 3.673 | 0.201 | 0.291 | 0.000 | 0.278 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 88 | 97 | 73 | 95 | 114 | 243 | 78 | 77 |
N.S. |
1 | 1.04 | 1.14 | 0.86 | 1.12 | 1.34 | 2.86 | 0.92 | 0.91 |
time (sec) |
N/A | 0.238 | 0.067 | 5.997 | 0.192 | 0.277 | 45.750 | 0.309 | 5.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 47 | 56 | 41 | 44 | 68 | 109 | 41 | 43 |
N.S. |
1 | 1.02 | 1.22 | 0.89 | 0.96 | 1.48 | 2.37 | 0.89 | 0.93 |
time (sec) |
N/A | 0.191 | 0.055 | 6.011 | 0.207 | 0.280 | 0.187 | 0.267 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 43 | 37 | 35 | 34 | 70 | 160 | 36 | 32 |
N.S. |
1 | 1.13 | 0.97 | 0.92 | 0.89 | 1.84 | 4.21 | 0.95 | 0.84 |
time (sec) |
N/A | 0.186 | 0.061 | 3.853 | 0.224 | 0.285 | 0.382 | 0.296 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 87 | 77 | 73 | 73 | 122 | 272 | 77 | 67 |
N.S. |
1 | 1.09 | 0.96 | 0.91 | 0.91 | 1.52 | 3.40 | 0.96 | 0.84 |
time (sec) |
N/A | 0.231 | 0.137 | 3.753 | 0.208 | 0.283 | 0.987 | 0.287 | 5.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 132 | 117 | 106 | 110 | 164 | 405 | 112 | 103 |
N.S. |
1 | 1.06 | 0.94 | 0.85 | 0.88 | 1.31 | 3.24 | 0.90 | 0.82 |
time (sec) |
N/A | 0.269 | 0.156 | 6.013 | 0.197 | 0.303 | 2.520 | 0.276 | 5.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 172 | 154 | 139 | 143 | 196 | 505 | 145 | 136 |
N.S. |
1 | 1.06 | 0.95 | 0.86 | 0.88 | 1.21 | 3.12 | 0.90 | 0.84 |
time (sec) |
N/A | 0.319 | 0.264 | 3.656 | 0.207 | 0.290 | 5.456 | 0.288 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 177 | 171 | 145 | 197 | 225 | 624 | 145 | 154 |
N.S. |
1 | 1.04 | 1.00 | 0.85 | 1.15 | 1.32 | 3.65 | 0.85 | 0.90 |
time (sec) |
N/A | 0.344 | 0.119 | 3.648 | 0.222 | 0.286 | 1.174 | 0.271 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 138 | 134 | 112 | 146 | 192 | 493 | 112 | 120 |
N.S. |
1 | 1.03 | 1.00 | 0.84 | 1.09 | 1.43 | 3.68 | 0.84 | 0.90 |
time (sec) |
N/A | 0.295 | 0.095 | 12.847 | 0.198 | 0.277 | 0.557 | 0.274 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 95 | 97 | 79 | 94 | 159 | 362 | 79 | 87 |
N.S. |
1 | 1.06 | 1.08 | 0.88 | 1.04 | 1.77 | 4.02 | 0.88 | 0.97 |
time (sec) |
N/A | 0.236 | 0.080 | 6.073 | 0.206 | 0.266 | 0.322 | 0.281 | 5.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 55 | 47 | 47 | 46 | 113 | 228 | 44 | 53 |
N.S. |
1 | 1.02 | 0.87 | 0.87 | 0.85 | 2.09 | 4.22 | 0.81 | 0.98 |
time (sec) |
N/A | 0.197 | 0.059 | 3.775 | 0.188 | 0.296 | 0.302 | 0.274 | 5.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 51 | 49 | 57 | 129 | 386 | 49 | 54 |
N.S. |
1 | 1.09 | 0.91 | 0.88 | 1.02 | 2.30 | 6.89 | 0.88 | 0.96 |
time (sec) |
N/A | 0.197 | 0.093 | 3.497 | 0.206 | 0.292 | 0.599 | 0.286 | 5.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 111 | 93 | 90 | 97 | 191 | 561 | 90 | 89 |
N.S. |
1 | 1.08 | 0.90 | 0.87 | 0.94 | 1.85 | 5.45 | 0.87 | 0.86 |
time (sec) |
N/A | 0.247 | 0.203 | 6.038 | 0.209 | 0.314 | 1.472 | 0.280 | 6.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 154 | 130 | 123 | 132 | 230 | 706 | 123 | 125 |
N.S. |
1 | 1.05 | 0.89 | 0.84 | 0.90 | 1.58 | 4.84 | 0.84 | 0.86 |
time (sec) |
N/A | 0.292 | 0.188 | 5.963 | 0.205 | 0.298 | 3.676 | 0.264 | 6.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 183 | 193 | 167 | 156 | 165 | 263 | 847 | 156 | 159 |
N.S. |
1 | 1.05 | 0.91 | 0.85 | 0.90 | 1.44 | 4.63 | 0.85 | 0.87 |
time (sec) |
N/A | 0.346 | 0.305 | 5.970 | 0.215 | 0.311 | 7.666 | 0.273 | 6.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 46 | 31 | 29 | 28 | 21 | 359 | 28 | 12 |
N.S. |
1 | 1.10 | 0.74 | 0.69 | 0.67 | 0.50 | 8.55 | 0.67 | 0.29 |
time (sec) |
N/A | 0.172 | 0.022 | 3.613 | 0.206 | 0.288 | 0.759 | 0.280 | 5.906 |
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 | 27 | 25 | 18 | 19 | 23 | 20 | 19 | 18 |
N.S. |
1 | 1.17 | 1.09 | 0.78 | 0.83 | 1.00 | 0.87 | 0.83 | 0.78 |
time (sec) |
N/A | 0.156 | 0.045 | 3.777 | 0.283 | 0.290 | 0.692 | 0.268 | 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 | 39 | 41 | 39 | 28 | 42 | 25 | 34 | 27 | 27 |
N.S. |
1 | 1.05 | 1.00 | 0.72 | 1.08 | 0.64 | 0.87 | 0.69 | 0.69 |
time (sec) |
N/A | 0.175 | 0.022 | 3.712 | 0.215 | 0.284 | 0.075 | 0.269 | 0.024 |
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 | 16 | 16 | 16 | 13 | 12 | 12 | 14 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A | 0.149 | 0.020 | 3.690 | 0.293 | 0.279 | 0.066 | 0.265 | 5.777 |
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 | 12 | 12 | 12 | 9 | 8 | 8 | 10 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.67 | 0.67 | 0.83 | 0.67 | 0.67 |
time (sec) |
N/A | 0.143 | 0.015 | 5.982 | 0.230 | 0.280 | 0.069 | 0.283 | 5.840 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A | 0.147 | 0.015 | 6.110 | 0.283 | 0.276 | 0.096 | 0.268 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 8 | 7 | 7 | 24 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.64 | 0.64 | 2.18 | 0.64 | 0.64 |
time (sec) |
N/A | 0.137 | 0.026 | 6.042 | 0.214 | 0.833 | 0.084 | 0.273 | 6.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 10 | 9 | 19 | 49 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.60 | 1.27 | 3.27 | 0.60 | 0.60 |
time (sec) |
N/A | 0.137 | 0.033 | 3.735 | 0.202 | 0.836 | 0.204 | 0.271 | 6.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | C | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 131 | 71 | 71 | 88 | 79 | 187 | 88 | 47 |
N.S. |
1 | 1.12 | 0.61 | 0.61 | 0.75 | 0.68 | 1.60 | 0.75 | 0.40 |
time (sec) |
N/A | 0.317 | 0.124 | 3.807 | 0.285 | 0.309 | 0.778 | 0.267 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 188 | 205 | 126 | 124 | 272 | 638 | 462 | 139 | 223 |
N.S. |
1 | 1.09 | 0.67 | 0.66 | 1.45 | 3.39 | 2.46 | 0.74 | 1.19 |
time (sec) |
N/A | 0.436 | 0.016 | 3.545 | 0.281 | 0.978 | 15.997 | 0.347 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 67 | 79 | 52 | 75 | 78 | 63 | 165 | 59 | 31 |
N.S. |
1 | 1.18 | 0.78 | 1.12 | 1.16 | 0.94 | 2.46 | 0.88 | 0.46 |
time (sec) |
N/A | 0.196 | 0.143 | 3.845 | 0.292 | 0.276 | 1.845 | 0.480 | 6.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 56 | 45 | 38 | 62 | 55 | 60 | 42 | 27 |
N.S. |
1 | 1.12 | 0.90 | 0.76 | 1.24 | 1.10 | 1.20 | 0.84 | 0.54 |
time (sec) |
N/A | 0.183 | 0.084 | 3.667 | 0.195 | 0.279 | 2.219 | 0.293 | 5.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | A | F(-1) | C | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 95 | 107 | 280 | 0 | 109 | 0 | 46 | 0 | 37 |
N.S. |
1 | 1.13 | 2.95 | 0.00 | 1.15 | 0.00 | 0.48 | 0.00 | 0.39 |
time (sec) |
N/A | 0.226 | 7.348 | 0.000 | 0.283 | 0.000 | 1.737 | 0.000 | 6.100 |
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 | 19 | 19 | 21 | 14 | 15 | 13 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.11 | 0.74 | 0.79 | 0.68 | 0.79 | 0.68 | 0.68 |
time (sec) |
N/A | 0.157 | 0.030 | 0.027 | 0.203 | 0.273 | 0.257 | 0.273 | 5.951 |
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 | 19 | 19 | 19 | 14 | 15 | 13 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.79 | 0.68 | 0.79 | 0.68 | 0.68 |
time (sec) |
N/A | 0.156 | 0.003 | 0.027 | 0.198 | 0.299 | 0.181 | 0.266 | 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 | 19 | 19 | 19 | 14 | 15 | 13 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.79 | 0.68 | 0.79 | 0.68 | 0.68 |
time (sec) |
N/A | 0.156 | 0.004 | 0.025 | 0.221 | 0.284 | 0.117 | 0.268 | 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 | 19 | 19 | 19 | 14 | 15 | 13 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.79 | 0.68 | 0.79 | 0.68 | 0.68 |
time (sec) |
N/A | 0.154 | 0.003 | 0.024 | 0.201 | 0.260 | 0.075 | 0.278 | 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 | 14 | 14 | 14 | 11 | 10 | 10 | 12 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.86 | 0.71 | 0.71 |
time (sec) |
N/A | 0.141 | 0.002 | 0.022 | 0.200 | 0.270 | 0.016 | 0.263 | 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 | 13 | 13 | 13 | 12 | 11 | 19 | 12 | 12 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.46 | 0.92 | 0.92 | 1.08 |
time (sec) |
N/A | 0.151 | 0.022 | 0.040 | 0.216 | 0.336 | 0.154 | 0.287 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 47 | 16 | 14 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 2.76 | 0.94 | 0.82 | 0.88 | 0.76 |
time (sec) |
N/A | 0.152 | 0.022 | 0.029 | 0.189 | 0.342 | 0.201 | 0.275 | 5.998 |