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 | 58 | 58 | 57 | 51 | 54 | 129 | 90 | 58 | 70 |
N.S. |
1 | 1.00 | 0.98 | 0.88 | 0.93 | 2.22 | 1.55 | 1.00 | 1.21 |
time (sec) |
N/A | 0.023 | 0.026 | 2.706 | 0.294 | 0.303 | 0.184 | 0.273 | 5.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 31 | 32 | 31 | 29 | 27 | 32 | 31 |
N.S. |
1 | 1.00 | 0.89 | 0.91 | 0.89 | 0.83 | 0.77 | 0.91 | 0.89 |
time (sec) |
N/A | 0.026 | 0.008 | 2.577 | 0.200 | 0.256 | 0.131 | 0.291 | 0.052 |
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 | 39 | 39 | 40 | 34 | 33 | 98 | 82 | 33 | 32 |
N.S. |
1 | 1.00 | 1.03 | 0.87 | 0.85 | 2.51 | 2.10 | 0.85 | 0.82 |
time (sec) |
N/A | 0.011 | 0.016 | 2.621 | 0.273 | 0.246 | 0.156 | 0.294 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 33 | 35 | 33 | 26 | 36 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.03 | 0.97 | 0.76 | 1.06 | 0.94 |
time (sec) |
N/A | 0.023 | 0.010 | 2.566 | 0.203 | 0.252 | 0.423 | 0.276 | 0.080 |
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 | 43 | 43 | 42 | 37 | 37 | 105 | 82 | 37 | 34 |
N.S. |
1 | 1.00 | 0.98 | 0.86 | 0.86 | 2.44 | 1.91 | 0.86 | 0.79 |
time (sec) |
N/A | 0.017 | 0.018 | 2.641 | 0.290 | 0.270 | 0.168 | 0.271 | 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 | 50 | 50 | 49 | 46 | 48 | 48 | 41 | 72 | 45 |
N.S. |
1 | 1.00 | 0.98 | 0.92 | 0.96 | 0.96 | 0.82 | 1.44 | 0.90 |
time (sec) |
N/A | 0.040 | 0.015 | 2.645 | 0.206 | 0.248 | 0.407 | 0.294 | 0.092 |
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 | 59 | 59 | 60 | 55 | 56 | 136 | 129 | 57 | 53 |
N.S. |
1 | 1.00 | 1.02 | 0.93 | 0.95 | 2.31 | 2.19 | 0.97 | 0.90 |
time (sec) |
N/A | 0.026 | 0.035 | 2.636 | 0.306 | 0.250 | 0.234 | 0.292 | 5.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 116 | 126 | 137 | 138 | 122 | 148 | 146 |
N.S. |
1 | 1.00 | 1.13 | 1.22 | 1.33 | 1.34 | 1.18 | 1.44 | 1.42 |
time (sec) |
N/A | 0.095 | 0.036 | 2.729 | 0.197 | 0.249 | 0.262 | 0.283 | 5.090 |
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 | 105 | 105 | 105 | 142 | 140 | 304 | 246 | 153 | 169 |
N.S. |
1 | 1.00 | 1.00 | 1.35 | 1.33 | 2.90 | 2.34 | 1.46 | 1.61 |
time (sec) |
N/A | 0.052 | 0.062 | 2.711 | 0.272 | 0.252 | 0.305 | 0.302 | 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 | 80 | 80 | 82 | 94 | 101 | 102 | 83 | 107 | 106 |
N.S. |
1 | 1.00 | 1.02 | 1.18 | 1.26 | 1.28 | 1.04 | 1.34 | 1.32 |
time (sec) |
N/A | 0.061 | 0.026 | 2.653 | 0.188 | 0.243 | 0.226 | 0.279 | 5.144 |
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 | 84 | 84 | 84 | 102 | 105 | 230 | 194 | 113 | 128 |
N.S. |
1 | 1.00 | 1.00 | 1.21 | 1.25 | 2.74 | 2.31 | 1.35 | 1.52 |
time (sec) |
N/A | 0.044 | 0.048 | 2.652 | 0.290 | 0.246 | 0.270 | 0.290 | 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 | 61 | 61 | 49 | 63 | 66 | 67 | 49 | 67 | 68 |
N.S. |
1 | 1.00 | 0.80 | 1.03 | 1.08 | 1.10 | 0.80 | 1.10 | 1.11 |
time (sec) |
N/A | 0.037 | 0.015 | 2.677 | 0.195 | 0.233 | 0.234 | 0.286 | 0.069 |
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 | 63 | 63 | 59 | 64 | 69 | 181 | 172 | 72 | 90 |
N.S. |
1 | 1.00 | 0.94 | 1.02 | 1.10 | 2.87 | 2.73 | 1.14 | 1.43 |
time (sec) |
N/A | 0.027 | 0.036 | 2.712 | 0.299 | 0.243 | 0.250 | 0.273 | 5.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 50 | 59 | 61 | 59 | 41 | 62 | 58 |
N.S. |
1 | 1.00 | 0.98 | 1.16 | 1.20 | 1.16 | 0.80 | 1.22 | 1.14 |
time (sec) |
N/A | 0.036 | 0.015 | 2.647 | 0.192 | 0.237 | 0.715 | 0.282 | 5.313 |
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 | 55 | 55 | 55 | 65 | 63 | 164 | 165 | 63 | 80 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 1.15 | 2.98 | 3.00 | 1.15 | 1.45 |
time (sec) |
N/A | 0.035 | 0.035 | 2.671 | 0.283 | 0.251 | 0.302 | 0.284 | 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 | 58 | 58 | 60 | 66 | 69 | 73 | 49 | 90 | 67 |
N.S. |
1 | 1.00 | 1.03 | 1.14 | 1.19 | 1.26 | 0.84 | 1.55 | 1.16 |
time (sec) |
N/A | 0.044 | 0.019 | 2.654 | 0.209 | 0.241 | 0.817 | 0.277 | 0.128 |
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 | 64 | 64 | 66 | 70 | 70 | 190 | 172 | 72 | 90 |
N.S. |
1 | 1.00 | 1.03 | 1.09 | 1.09 | 2.97 | 2.69 | 1.12 | 1.41 |
time (sec) |
N/A | 0.041 | 0.041 | 2.764 | 0.284 | 0.249 | 0.368 | 0.287 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 128 | 204 | 219 | 220 | 201 | 238 | 236 |
N.S. |
1 | 1.00 | 0.93 | 1.48 | 1.59 | 1.59 | 1.46 | 1.72 | 1.71 |
time (sec) |
N/A | 0.130 | 0.049 | 2.759 | 0.196 | 0.240 | 0.354 | 0.291 | 5.249 |
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 | 140 | 140 | 140 | 231 | 222 | 468 | 343 | 241 | 260 |
N.S. |
1 | 1.00 | 1.00 | 1.65 | 1.59 | 3.34 | 2.45 | 1.72 | 1.86 |
time (sec) |
N/A | 0.069 | 0.032 | 2.695 | 0.281 | 0.251 | 0.403 | 0.295 | 5.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 125 | 157 | 168 | 169 | 144 | 180 | 178 |
N.S. |
1 | 1.00 | 1.09 | 1.37 | 1.46 | 1.47 | 1.25 | 1.57 | 1.55 |
time (sec) |
N/A | 0.095 | 0.037 | 2.594 | 0.206 | 0.232 | 0.333 | 0.272 | 5.315 |
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 | 119 | 119 | 118 | 173 | 172 | 364 | 274 | 184 | 199 |
N.S. |
1 | 1.00 | 0.99 | 1.45 | 1.45 | 3.06 | 2.30 | 1.55 | 1.67 |
time (sec) |
N/A | 0.059 | 0.027 | 2.688 | 0.280 | 0.251 | 0.372 | 0.278 | 5.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 82 | 112 | 119 | 120 | 94 | 124 | 123 |
N.S. |
1 | 1.00 | 0.94 | 1.29 | 1.37 | 1.38 | 1.08 | 1.43 | 1.41 |
time (sec) |
N/A | 0.058 | 0.021 | 2.663 | 0.195 | 0.235 | 0.285 | 0.282 | 0.075 |
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 | 98 | 98 | 92 | 116 | 122 | 292 | 238 | 129 | 146 |
N.S. |
1 | 1.00 | 0.94 | 1.18 | 1.24 | 2.98 | 2.43 | 1.32 | 1.49 |
time (sec) |
N/A | 0.043 | 0.043 | 2.646 | 0.289 | 0.249 | 0.327 | 0.289 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 65 | 86 | 98 | 101 | 65 | 99 | 97 |
N.S. |
1 | 1.00 | 0.89 | 1.18 | 1.34 | 1.38 | 0.89 | 1.36 | 1.33 |
time (sec) |
N/A | 0.054 | 0.024 | 2.708 | 0.199 | 0.246 | 1.013 | 0.277 | 5.384 |
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 | 77 | 77 | 76 | 95 | 101 | 253 | 221 | 104 | 118 |
N.S. |
1 | 1.00 | 0.99 | 1.23 | 1.31 | 3.29 | 2.87 | 1.35 | 1.53 |
time (sec) |
N/A | 0.046 | 0.026 | 2.696 | 0.281 | 0.246 | 0.438 | 0.282 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 75 | 94 | 97 | 105 | 63 | 120 | 95 |
N.S. |
1 | 1.00 | 1.03 | 1.29 | 1.33 | 1.44 | 0.86 | 1.64 | 1.30 |
time (sec) |
N/A | 0.055 | 0.028 | 2.687 | 0.209 | 0.239 | 1.283 | 0.279 | 5.382 |
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 | 74 | 74 | 74 | 98 | 98 | 256 | 221 | 100 | 122 |
N.S. |
1 | 1.00 | 1.00 | 1.32 | 1.32 | 3.46 | 2.99 | 1.35 | 1.65 |
time (sec) |
N/A | 0.048 | 0.028 | 2.713 | 0.299 | 0.261 | 0.630 | 0.296 | 0.097 |
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 | 70 | 70 | 66 | 65 | 68 | 72 | 0 | 70 | 68 |
N.S. |
1 | 1.00 | 0.94 | 0.93 | 0.97 | 1.03 | 0.00 | 1.00 | 0.97 |
time (sec) |
N/A | 0.055 | 0.020 | 2.708 | 0.201 | 0.250 | 0.000 | 0.286 | 5.383 |
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 | 78 | 78 | 74 | 73 | 72 | 391 | 921 | 72 | 343 |
N.S. |
1 | 1.00 | 0.95 | 0.94 | 0.92 | 5.01 | 11.81 | 0.92 | 4.40 |
time (sec) |
N/A | 0.061 | 0.059 | 2.693 | 0.290 | 0.274 | 157.189 | 0.280 | 5.714 |
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 | 53 | 53 | 43 | 43 | 49 | 42 | 144 | 51 | 51 |
N.S. |
1 | 1.00 | 0.81 | 0.81 | 0.92 | 0.79 | 2.72 | 0.96 | 0.96 |
time (sec) |
N/A | 0.035 | 0.014 | 2.711 | 0.202 | 0.245 | 1.354 | 0.291 | 5.479 |
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 | 70 | 70 | 61 | 55 | 54 | 309 | 570 | 54 | 133 |
N.S. |
1 | 1.00 | 0.87 | 0.79 | 0.77 | 4.41 | 8.14 | 0.77 | 1.90 |
time (sec) |
N/A | 0.024 | 0.029 | 2.826 | 0.296 | 0.258 | 1.816 | 0.288 | 5.462 |
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 | 45 | 45 | 31 | 32 | 41 | 31 | 138 | 51 | 148 |
N.S. |
1 | 1.00 | 0.69 | 0.71 | 0.91 | 0.69 | 3.07 | 1.13 | 3.29 |
time (sec) |
N/A | 0.022 | 0.012 | 2.700 | 0.199 | 0.233 | 0.535 | 0.307 | 5.293 |
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 | 70 | 70 | 61 | 55 | 54 | 292 | 712 | 54 | 135 |
N.S. |
1 | 1.00 | 0.87 | 0.79 | 0.77 | 4.17 | 10.17 | 0.77 | 1.93 |
time (sec) |
N/A | 0.019 | 0.027 | 2.777 | 0.288 | 0.264 | 2.734 | 0.294 | 0.312 |
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 | 62 | 62 | 54 | 55 | 61 | 54 | 0 | 73 | 58 |
N.S. |
1 | 1.00 | 0.87 | 0.89 | 0.98 | 0.87 | 0.00 | 1.18 | 0.94 |
time (sec) |
N/A | 0.047 | 0.018 | 2.641 | 0.201 | 0.279 | 0.000 | 0.295 | 5.439 |
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 | 81 | 81 | 76 | 76 | 75 | 384 | 1093 | 75 | 338 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.93 | 4.74 | 13.49 | 0.93 | 4.17 |
time (sec) |
N/A | 0.063 | 0.055 | 2.816 | 0.285 | 0.283 | 141.539 | 0.296 | 5.799 |
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 | 87 | 87 | 88 | 82 | 87 | 99 | 0 | 112 | 87 |
N.S. |
1 | 1.00 | 1.01 | 0.94 | 1.00 | 1.14 | 0.00 | 1.29 | 1.00 |
time (sec) |
N/A | 0.075 | 0.027 | 2.691 | 0.235 | 0.369 | 0.000 | 0.298 | 5.354 |
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 | 100 | 100 | 101 | 96 | 96 | 560 | 0 | 98 | 367 |
N.S. |
1 | 1.00 | 1.01 | 0.96 | 0.96 | 5.60 | 0.00 | 0.98 | 3.67 |
time (sec) |
N/A | 0.145 | 0.078 | 2.738 | 0.296 | 0.280 | 0.000 | 0.278 | 0.695 |
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 | 119 | 119 | 115 | 114 | 117 | 127 | 0 | 167 | 118 |
N.S. |
1 | 1.00 | 0.97 | 0.96 | 0.98 | 1.07 | 0.00 | 1.40 | 0.99 |
time (sec) |
N/A | 0.094 | 0.035 | 2.698 | 0.217 | 0.792 | 0.000 | 0.294 | 5.498 |
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 | 134 | 134 | 135 | 127 | 131 | 669 | 0 | 139 | 397 |
N.S. |
1 | 1.00 | 1.01 | 0.95 | 0.98 | 4.99 | 0.00 | 1.04 | 2.96 |
time (sec) |
N/A | 0.167 | 0.082 | 2.761 | 0.298 | 0.302 | 0.000 | 0.319 | 5.670 |
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 | 155 | 155 | 147 | 157 | 165 | 155 | 0 | 239 | 165 |
N.S. |
1 | 1.00 | 0.95 | 1.01 | 1.06 | 1.00 | 0.00 | 1.54 | 1.06 |
time (sec) |
N/A | 0.129 | 0.043 | 2.710 | 0.197 | 1.089 | 0.000 | 0.282 | 5.473 |
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 | 93 | 93 | 91 | 86 | 130 | 162 | 0 | 152 | 169 |
N.S. |
1 | 1.00 | 0.98 | 0.92 | 1.40 | 1.74 | 0.00 | 1.63 | 1.82 |
time (sec) |
N/A | 0.081 | 0.030 | 2.724 | 0.204 | 0.267 | 0.000 | 0.311 | 5.495 |
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 | 108 | 108 | 108 | 95 | 132 | 718 | 0 | 121 | 3572 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.22 | 6.65 | 0.00 | 1.12 | 33.07 |
time (sec) |
N/A | 0.072 | 0.081 | 2.752 | 0.284 | 0.302 | 0.000 | 0.298 | 6.068 |
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 | 74 | 74 | 74 | 68 | 105 | 117 | 253 | 91 | 173 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.42 | 1.58 | 3.42 | 1.23 | 2.34 |
time (sec) |
N/A | 0.048 | 0.023 | 2.659 | 0.203 | 0.248 | 1.016 | 0.296 | 5.272 |
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 | 104 | 104 | 90 | 85 | 119 | 705 | 0 | 110 | 3154 |
N.S. |
1 | 1.00 | 0.87 | 0.82 | 1.14 | 6.78 | 0.00 | 1.06 | 30.33 |
time (sec) |
N/A | 0.046 | 0.079 | 2.683 | 0.292 | 0.286 | 0.000 | 0.289 | 5.791 |
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 | 70 | 70 | 66 | 73 | 99 | 103 | 248 | 85 | 160 |
N.S. |
1 | 1.00 | 0.94 | 1.04 | 1.41 | 1.47 | 3.54 | 1.21 | 2.29 |
time (sec) |
N/A | 0.038 | 0.018 | 2.706 | 0.209 | 0.256 | 0.977 | 0.288 | 0.205 |
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 | 109 | 109 | 95 | 93 | 133 | 711 | 0 | 122 | 3637 |
N.S. |
1 | 1.00 | 0.87 | 0.85 | 1.22 | 6.52 | 0.00 | 1.12 | 33.37 |
time (sec) |
N/A | 0.061 | 0.104 | 2.658 | 0.283 | 0.319 | 0.000 | 0.292 | 6.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 98 | 99 | 138 | 219 | 0 | 185 | 127 |
N.S. |
1 | 1.00 | 0.98 | 0.99 | 1.38 | 2.19 | 0.00 | 1.85 | 1.27 |
time (sec) |
N/A | 0.079 | 0.059 | 2.737 | 0.216 | 0.686 | 0.000 | 0.290 | 5.653 |
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 | 144 | 144 | 123 | 109 | 178 | 1005 | 0 | 164 | 432 |
N.S. |
1 | 1.00 | 0.85 | 0.76 | 1.24 | 6.98 | 0.00 | 1.14 | 3.00 |
time (sec) |
N/A | 0.134 | 0.106 | 2.729 | 0.305 | 0.450 | 0.000 | 0.281 | 5.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 119 | 120 | 188 | 302 | 0 | 257 | 171 |
N.S. |
1 | 1.00 | 0.94 | 0.95 | 1.49 | 2.40 | 0.00 | 2.04 | 1.36 |
time (sec) |
N/A | 0.108 | 0.079 | 2.749 | 0.221 | 1.473 | 0.000 | 0.292 | 5.931 |
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 | 189 | 189 | 142 | 127 | 236 | 1281 | 0 | 165 | 469 |
N.S. |
1 | 1.00 | 0.75 | 0.67 | 1.25 | 6.78 | 0.00 | 0.87 | 2.48 |
time (sec) |
N/A | 0.200 | 0.255 | 2.732 | 0.299 | 0.918 | 0.000 | 0.282 | 6.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 115 | 124 | 236 | 290 | 418 | 232 | 370 |
N.S. |
1 | 1.00 | 0.99 | 1.07 | 2.03 | 2.50 | 3.60 | 2.00 | 3.19 |
time (sec) |
N/A | 0.084 | 0.041 | 2.683 | 0.201 | 0.252 | 3.166 | 0.278 | 5.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 133 | 154 | 264 | 1573 | 0 | 204 | 5754 |
N.S. |
1 | 1.00 | 0.85 | 0.98 | 1.68 | 10.02 | 0.00 | 1.30 | 36.65 |
time (sec) |
N/A | 0.125 | 0.218 | 2.791 | 0.293 | 0.482 | 0.000 | 0.283 | 6.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 97 | 105 | 217 | 256 | 411 | 174 | 343 |
N.S. |
1 | 1.00 | 0.97 | 1.05 | 2.17 | 2.56 | 4.11 | 1.74 | 3.43 |
time (sec) |
N/A | 0.084 | 0.038 | 2.721 | 0.204 | 0.251 | 2.536 | 0.279 | 5.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 147 | 151 | 266 | 1587 | 0 | 206 | 5898 |
N.S. |
1 | 1.00 | 0.95 | 0.97 | 1.72 | 10.24 | 0.00 | 1.33 | 38.05 |
time (sec) |
N/A | 0.101 | 0.169 | 2.735 | 0.287 | 0.491 | 0.000 | 0.280 | 6.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 93 | 111 | 211 | 254 | 391 | 174 | 340 |
N.S. |
1 | 1.00 | 0.95 | 1.13 | 2.15 | 2.59 | 3.99 | 1.78 | 3.47 |
time (sec) |
N/A | 0.054 | 0.027 | 2.713 | 0.207 | 0.247 | 2.405 | 0.283 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 151 | 158 | 277 | 1585 | 0 | 217 | 6033 |
N.S. |
1 | 1.00 | 0.94 | 0.99 | 1.73 | 9.91 | 0.00 | 1.36 | 37.71 |
time (sec) |
N/A | 0.130 | 0.191 | 2.658 | 0.308 | 0.722 | 0.000 | 0.293 | 7.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 149 | 126 | 165 | 278 | 520 | 0 | 315 | 246 |
N.S. |
1 | 1.00 | 0.85 | 1.11 | 1.87 | 3.49 | 0.00 | 2.11 | 1.65 |
time (sec) |
N/A | 0.114 | 0.171 | 2.769 | 0.215 | 2.386 | 0.000 | 0.296 | 6.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 211 | 172 | 170 | 352 | 1991 | 0 | 236 | 738 |
N.S. |
1 | 1.00 | 0.82 | 0.81 | 1.67 | 9.44 | 0.00 | 1.12 | 3.50 |
time (sec) |
N/A | 0.239 | 0.242 | 2.893 | 0.297 | 1.216 | 0.000 | 0.289 | 6.436 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 171 | 187 | 364 | 640 | 0 | 357 | 314 |
N.S. |
1 | 1.00 | 0.96 | 1.05 | 2.04 | 3.60 | 0.00 | 2.01 | 1.76 |
time (sec) |
N/A | 0.165 | 0.285 | 2.785 | 0.227 | 5.043 | 0.000 | 0.295 | 6.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 196 | 190 | 440 | 2397 | 0 | 256 | 785 |
N.S. |
1 | 1.00 | 0.73 | 0.70 | 1.63 | 8.88 | 0.00 | 0.95 | 2.91 |
time (sec) |
N/A | 0.325 | 0.273 | 2.789 | 0.299 | 3.318 | 0.000 | 0.279 | 6.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 21 | 21 | 18 | 17 | 17 | 15 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.81 | 0.81 | 0.71 | 0.81 | 0.81 |
time (sec) |
N/A | 0.009 | 0.003 | 2.652 | 0.203 | 0.225 | 0.042 | 0.279 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 89 | 76 | 84 | 240 | 129 | 88 | 104 |
N.S. |
1 | 1.00 | 1.02 | 0.87 | 0.97 | 2.76 | 1.48 | 1.01 | 1.20 |
time (sec) |
N/A | 0.060 | 0.049 | 2.673 | 0.281 | 0.250 | 0.367 | 0.283 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 50 | 59 | 59 | 78 | 56 | 90 | 63 |
N.S. |
1 | 1.00 | 0.83 | 0.98 | 0.98 | 1.30 | 0.93 | 1.50 | 1.05 |
time (sec) |
N/A | 0.045 | 0.029 | 2.652 | 0.196 | 0.241 | 0.320 | 0.294 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 68 | 59 | 60 | 202 | 114 | 58 | 59 |
N.S. |
1 | 1.00 | 1.01 | 0.88 | 0.90 | 3.01 | 1.70 | 0.87 | 0.88 |
time (sec) |
N/A | 0.034 | 0.046 | 2.660 | 0.279 | 0.255 | 0.286 | 0.288 | 5.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 41 | 38 | 40 | 45 | 36 | 65 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.98 | 1.10 | 0.88 | 1.59 | 0.90 |
time (sec) |
N/A | 0.029 | 0.009 | 2.656 | 0.197 | 0.229 | 0.186 | 0.271 | 0.063 |
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 | 63 | 63 | 63 | 57 | 57 | 181 | 112 | 57 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 2.87 | 1.78 | 0.90 | 0.81 |
time (sec) |
N/A | 0.015 | 0.030 | 2.648 | 0.283 | 0.236 | 0.225 | 0.283 | 4.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 46 | 48 | 51 | 71 | 46 | 63 | 47 |
N.S. |
1 | 1.00 | 0.90 | 0.94 | 1.00 | 1.39 | 0.90 | 1.24 | 0.92 |
time (sec) |
N/A | 0.033 | 0.022 | 2.662 | 0.202 | 0.236 | 0.214 | 0.292 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 70 | 60 | 65 | 214 | 114 | 64 | 61 |
N.S. |
1 | 1.00 | 0.99 | 0.85 | 0.92 | 3.01 | 1.61 | 0.90 | 0.86 |
time (sec) |
N/A | 0.037 | 0.023 | 2.684 | 0.290 | 0.254 | 0.257 | 0.284 | 4.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 64 | 75 | 78 | 122 | 70 | 84 | 74 |
N.S. |
1 | 1.00 | 0.84 | 0.99 | 1.03 | 1.61 | 0.92 | 1.11 | 0.97 |
time (sec) |
N/A | 0.058 | 0.033 | 2.644 | 0.201 | 0.237 | 0.499 | 0.298 | 0.111 |
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 | 90 | 90 | 90 | 79 | 93 | 250 | 184 | 86 | 84 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.03 | 2.78 | 2.04 | 0.96 | 0.93 |
time (sec) |
N/A | 0.078 | 0.048 | 2.755 | 0.293 | 0.246 | 0.322 | 0.271 | 4.805 |
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 | 145 | 145 | 138 | 141 | 149 | 400 | 286 | 156 | 200 |
N.S. |
1 | 1.00 | 0.95 | 0.97 | 1.03 | 2.76 | 1.97 | 1.08 | 1.38 |
time (sec) |
N/A | 0.097 | 0.060 | 2.649 | 0.292 | 0.251 | 0.571 | 0.301 | 4.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 87 | 82 | 107 | 160 | 99 | 163 | 112 |
N.S. |
1 | 1.00 | 0.99 | 0.93 | 1.22 | 1.82 | 1.12 | 1.85 | 1.27 |
time (sec) |
N/A | 0.098 | 0.040 | 2.738 | 0.227 | 0.232 | 0.516 | 0.297 | 0.077 |
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 | 116 | 116 | 105 | 102 | 109 | 342 | 246 | 114 | 148 |
N.S. |
1 | 1.00 | 0.91 | 0.88 | 0.94 | 2.95 | 2.12 | 0.98 | 1.28 |
time (sec) |
N/A | 0.089 | 0.047 | 2.572 | 0.294 | 0.243 | 0.488 | 0.294 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 56 | 63 | 73 | 101 | 68 | 111 | 77 |
N.S. |
1 | 1.00 | 0.92 | 1.03 | 1.20 | 1.66 | 1.11 | 1.82 | 1.26 |
time (sec) |
N/A | 0.044 | 0.031 | 2.701 | 0.211 | 0.237 | 0.418 | 0.289 | 4.782 |
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 | 82 | 82 | 88 | 94 | 95 | 297 | 236 | 94 | 124 |
N.S. |
1 | 1.00 | 1.07 | 1.15 | 1.16 | 3.62 | 2.88 | 1.15 | 1.51 |
time (sec) |
N/A | 0.069 | 0.042 | 2.620 | 0.277 | 0.249 | 0.385 | 0.271 | 4.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 70 | 66 | 86 | 117 | 80 | 99 | 80 |
N.S. |
1 | 1.00 | 1.04 | 0.99 | 1.28 | 1.75 | 1.19 | 1.48 | 1.19 |
time (sec) |
N/A | 0.049 | 0.028 | 2.636 | 0.208 | 0.250 | 0.711 | 0.292 | 4.797 |
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 | 103 | 100 | 91 | 95 | 101 | 308 | 238 | 103 | 128 |
N.S. |
1 | 0.97 | 0.88 | 0.92 | 0.98 | 2.99 | 2.31 | 1.00 | 1.24 |
time (sec) |
N/A | 0.064 | 0.047 | 2.639 | 0.284 | 0.254 | 0.483 | 0.280 | 0.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 72 | 77 | 100 | 159 | 92 | 109 | 100 |
N.S. |
1 | 1.00 | 0.90 | 0.96 | 1.25 | 1.99 | 1.15 | 1.36 | 1.25 |
time (sec) |
N/A | 0.060 | 0.062 | 2.642 | 0.215 | 0.236 | 0.751 | 0.292 | 0.106 |
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 | 127 | 125 | 107 | 107 | 118 | 356 | 248 | 112 | 146 |
N.S. |
1 | 0.98 | 0.84 | 0.84 | 0.93 | 2.80 | 1.95 | 0.88 | 1.15 |
time (sec) |
N/A | 0.109 | 0.046 | 2.694 | 0.280 | 0.334 | 0.549 | 0.288 | 4.917 |
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 | 169 | 169 | 151 | 227 | 228 | 580 | 389 | 241 | 328 |
N.S. |
1 | 1.00 | 0.89 | 1.34 | 1.35 | 3.43 | 2.30 | 1.43 | 1.94 |
time (sec) |
N/A | 0.112 | 0.055 | 2.742 | 0.311 | 0.249 | 0.768 | 0.297 | 4.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 106 | 137 | 174 | 254 | 163 | 249 | 194 |
N.S. |
1 | 1.00 | 0.91 | 1.17 | 1.49 | 2.17 | 1.39 | 2.13 | 1.66 |
time (sec) |
N/A | 0.121 | 0.060 | 2.614 | 0.203 | 0.237 | 0.970 | 0.302 | 4.967 |
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 | 147 | 147 | 125 | 170 | 176 | 508 | 338 | 184 | 232 |
N.S. |
1 | 1.00 | 0.85 | 1.16 | 1.20 | 3.46 | 2.30 | 1.25 | 1.58 |
time (sec) |
N/A | 0.138 | 0.044 | 2.622 | 0.296 | 0.279 | 0.668 | 0.276 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 127 | 89 | 124 | 181 | 112 | 183 | 130 |
N.S. |
1 | 1.00 | 1.44 | 1.01 | 1.41 | 2.06 | 1.27 | 2.08 | 1.48 |
time (sec) |
N/A | 0.066 | 0.030 | 2.651 | 0.257 | 0.245 | 0.674 | 0.300 | 4.850 |
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 | 106 | 106 | 106 | 139 | 147 | 442 | 314 | 152 | 182 |
N.S. |
1 | 1.00 | 1.00 | 1.31 | 1.39 | 4.17 | 2.96 | 1.43 | 1.72 |
time (sec) |
N/A | 0.071 | 0.041 | 2.633 | 0.287 | 0.247 | 0.574 | 0.265 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 111 | 94 | 122 | 178 | 110 | 150 | 122 |
N.S. |
1 | 1.00 | 1.26 | 1.07 | 1.39 | 2.02 | 1.25 | 1.70 | 1.39 |
time (sec) |
N/A | 0.064 | 0.063 | 2.621 | 0.205 | 0.249 | 1.461 | 0.295 | 4.946 |
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 | 131 | 131 | 94 | 129 | 140 | 412 | 309 | 143 | 173 |
N.S. |
1 | 1.00 | 0.72 | 0.98 | 1.07 | 3.15 | 2.36 | 1.09 | 1.32 |
time (sec) |
N/A | 0.100 | 0.042 | 2.747 | 0.283 | 0.253 | 0.892 | 0.282 | 4.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 87 | 100 | 141 | 209 | 128 | 157 | 135 |
N.S. |
1 | 1.00 | 0.89 | 1.02 | 1.44 | 2.13 | 1.31 | 1.60 | 1.38 |
time (sec) |
N/A | 0.104 | 0.063 | 2.733 | 0.204 | 0.247 | 4.095 | 0.294 | 5.037 |
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 | 147 | 147 | 109 | 144 | 159 | 458 | 321 | 150 | 183 |
N.S. |
1 | 1.00 | 0.74 | 0.98 | 1.08 | 3.12 | 2.18 | 1.02 | 1.24 |
time (sec) |
N/A | 0.110 | 0.047 | 2.656 | 0.280 | 0.246 | 1.108 | 0.311 | 5.121 |
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 | 109 | 109 | 95 | 94 | 133 | 726 | 0 | 122 | 3558 |
N.S. |
1 | 1.00 | 0.87 | 0.86 | 1.22 | 6.66 | 0.00 | 1.12 | 32.64 |
time (sec) |
N/A | 0.064 | 0.096 | 2.829 | 0.309 | 0.292 | 0.000 | 0.290 | 6.292 |
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 | 74 | 74 | 74 | 69 | 105 | 117 | 253 | 92 | 172 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.42 | 1.58 | 3.42 | 1.24 | 2.32 |
time (sec) |
N/A | 0.050 | 0.022 | 2.671 | 0.203 | 0.245 | 1.078 | 0.292 | 5.502 |
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 | 104 | 104 | 104 | 85 | 119 | 704 | 0 | 110 | 3153 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.14 | 6.77 | 0.00 | 1.06 | 30.32 |
time (sec) |
N/A | 0.048 | 0.088 | 2.737 | 0.292 | 0.289 | 0.000 | 0.313 | 5.889 |
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 | 70 | 70 | 66 | 72 | 99 | 103 | 248 | 85 | 161 |
N.S. |
1 | 1.00 | 0.94 | 1.03 | 1.41 | 1.47 | 3.54 | 1.21 | 2.30 |
time (sec) |
N/A | 0.042 | 0.018 | 2.658 | 0.192 | 0.242 | 1.027 | 0.298 | 5.113 |
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 | 108 | 108 | 109 | 95 | 132 | 699 | 0 | 121 | 3649 |
N.S. |
1 | 1.00 | 1.01 | 0.88 | 1.22 | 6.47 | 0.00 | 1.12 | 33.79 |
time (sec) |
N/A | 0.058 | 0.084 | 2.630 | 0.284 | 0.320 | 0.000 | 0.293 | 5.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 97 | 100 | 137 | 218 | 0 | 183 | 127 |
N.S. |
1 | 1.00 | 0.98 | 1.01 | 1.38 | 2.20 | 0.00 | 1.85 | 1.28 |
time (sec) |
N/A | 0.078 | 0.068 | 2.716 | 0.208 | 0.690 | 0.000 | 0.299 | 5.755 |
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 | 144 | 144 | 123 | 108 | 178 | 1003 | 0 | 164 | 2400 |
N.S. |
1 | 1.00 | 0.85 | 0.75 | 1.24 | 6.97 | 0.00 | 1.14 | 16.67 |
time (sec) |
N/A | 0.145 | 0.113 | 2.708 | 0.285 | 0.466 | 0.000 | 0.290 | 6.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 119 | 120 | 189 | 303 | 0 | 257 | 171 |
N.S. |
1 | 1.00 | 0.94 | 0.95 | 1.50 | 2.40 | 0.00 | 2.04 | 1.36 |
time (sec) |
N/A | 0.112 | 0.101 | 2.708 | 0.203 | 1.483 | 0.000 | 0.267 | 5.974 |
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 | 189 | 189 | 142 | 128 | 236 | 1281 | 0 | 165 | 4654 |
N.S. |
1 | 1.00 | 0.75 | 0.68 | 1.25 | 6.78 | 0.00 | 0.87 | 24.62 |
time (sec) |
N/A | 0.193 | 0.181 | 2.789 | 0.287 | 0.942 | 0.000 | 0.270 | 5.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 155 | 153 | 258 | 356 | 0 | 281 | 217 |
N.S. |
1 | 1.00 | 0.97 | 0.96 | 1.61 | 2.22 | 0.00 | 1.76 | 1.36 |
time (sec) |
N/A | 0.150 | 0.127 | 2.729 | 0.200 | 3.287 | 0.000 | 0.281 | 6.015 |
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 | 250 | 250 | 179 | 161 | 303 | 1489 | 0 | 207 | 2737 |
N.S. |
1 | 1.00 | 0.72 | 0.64 | 1.21 | 5.96 | 0.00 | 0.83 | 10.95 |
time (sec) |
N/A | 0.305 | 0.187 | 2.662 | 0.297 | 1.965 | 0.000 | 0.284 | 5.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 202 | 201 | 339 | 410 | 0 | 354 | 278 |
N.S. |
1 | 1.00 | 0.96 | 0.96 | 1.61 | 1.95 | 0.00 | 1.69 | 1.32 |
time (sec) |
N/A | 0.213 | 0.179 | 2.672 | 0.224 | 5.022 | 0.000 | 0.274 | 6.020 |