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 | 74 | 74 | 74 | 107 | 114 | 115 | 83 | 116 | 118 |
N.S. |
1 | 1.00 | 1.00 | 1.45 | 1.54 | 1.55 | 1.12 | 1.57 | 1.59 |
time (sec) |
N/A | 0.226 | 0.018 | 2.563 | 0.197 | 0.362 | 0.170 | 0.264 | 9.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 43 | 56 | 60 | 62 | 44 | 60 | 62 |
N.S. |
1 | 1.00 | 0.86 | 1.12 | 1.20 | 1.24 | 0.88 | 1.20 | 1.24 |
time (sec) |
N/A | 0.203 | 0.011 | 2.836 | 0.185 | 0.415 | 0.128 | 0.262 | 9.968 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 25 | 26 | 26 | 25 | 20 | 27 | 25 |
N.S. |
1 | 1.00 | 0.96 | 1.00 | 1.00 | 0.96 | 0.77 | 1.04 | 0.96 |
time (sec) |
N/A | 0.185 | 0.005 | 2.384 | 0.204 | 0.380 | 0.080 | 0.283 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 11 | 10 | 10 | 7 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.70 | 1.10 | 1.00 |
time (sec) |
N/A | 0.145 | 0.001 | 2.282 | 0.206 | 0.661 | 0.027 | 0.283 | 0.024 |
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 | 36 | 51 | 26 | 28 | 36 | 26 | 128 | 46 | 40 |
N.S. |
1 | 1.42 | 0.72 | 0.78 | 1.00 | 0.72 | 3.56 | 1.28 | 1.11 |
time (sec) |
N/A | 0.215 | 0.009 | 2.363 | 0.189 | 0.358 | 0.167 | 0.277 | 0.087 |
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 | 57 | 57 | 53 | 57 | 92 | 93 | 233 | 94 | 76 |
N.S. |
1 | 1.00 | 0.93 | 1.00 | 1.61 | 1.63 | 4.09 | 1.65 | 1.33 |
time (sec) |
N/A | 0.223 | 0.018 | 2.734 | 0.196 | 0.292 | 0.371 | 0.279 | 10.046 |
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 | 82 | 82 | 67 | 81 | 202 | 242 | 381 | 145 | 182 |
N.S. |
1 | 1.00 | 0.82 | 0.99 | 2.46 | 2.95 | 4.65 | 1.77 | 2.22 |
time (sec) |
N/A | 0.248 | 0.038 | 2.805 | 0.191 | 0.294 | 0.576 | 0.277 | 10.080 |
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 | 107 | 107 | 107 | 103 | 361 | 425 | 570 | 243 | 312 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 3.37 | 3.97 | 5.33 | 2.27 | 2.92 |
time (sec) |
N/A | 0.284 | 0.028 | 2.502 | 0.215 | 0.278 | 0.835 | 0.272 | 10.007 |
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 | 130 | 130 | 130 | 125 | 558 | 657 | 802 | 338 | 505 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 4.29 | 5.05 | 6.17 | 2.60 | 3.88 |
time (sec) |
N/A | 0.307 | 0.031 | 2.570 | 0.220 | 0.298 | 1.541 | 0.280 | 10.192 |
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 | 104 | 104 | 165 | 175 | 183 | 267 | 155 | 188 | 203 |
N.S. |
1 | 1.00 | 1.59 | 1.68 | 1.76 | 2.57 | 1.49 | 1.81 | 1.95 |
time (sec) |
N/A | 0.301 | 0.038 | 2.581 | 0.196 | 0.272 | 0.427 | 0.282 | 0.074 |
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 | 75 | 75 | 114 | 108 | 117 | 172 | 102 | 118 | 123 |
N.S. |
1 | 1.00 | 1.52 | 1.44 | 1.56 | 2.29 | 1.36 | 1.57 | 1.64 |
time (sec) |
N/A | 0.256 | 0.023 | 3.259 | 0.198 | 0.282 | 0.295 | 0.265 | 9.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 47 | 63 | 67 | 92 | 60 | 65 | 71 |
N.S. |
1 | 1.00 | 0.92 | 1.24 | 1.31 | 1.80 | 1.18 | 1.27 | 1.39 |
time (sec) |
N/A | 0.226 | 0.023 | 2.643 | 0.213 | 0.267 | 0.194 | 0.278 | 9.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 33 | 34 | 37 | 27 | 32 | 32 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.10 | 1.19 | 0.87 | 1.03 | 1.03 |
time (sec) |
N/A | 0.191 | 0.007 | 2.439 | 0.195 | 0.264 | 0.105 | 0.268 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 13 | 13 | 13 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.08 | 1.08 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.151 | 0.002 | 2.479 | 0.190 | 0.260 | 0.071 | 0.273 | 9.804 |
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 | 56 | 56 | 53 | 58 | 90 | 92 | 233 | 93 | 77 |
N.S. |
1 | 1.00 | 0.95 | 1.04 | 1.61 | 1.64 | 4.16 | 1.66 | 1.38 |
time (sec) |
N/A | 0.219 | 0.016 | 2.388 | 0.203 | 0.277 | 0.378 | 0.303 | 0.114 |
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 | 86 | 106 | 66 | 82 | 208 | 241 | 406 | 166 | 182 |
N.S. |
1 | 1.23 | 0.77 | 0.95 | 2.42 | 2.80 | 4.72 | 1.93 | 2.12 |
time (sec) |
N/A | 0.290 | 0.040 | 2.824 | 0.197 | 0.312 | 0.585 | 0.281 | 9.947 |
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 | 109 | 109 | 98 | 109 | 386 | 494 | 634 | 253 | 330 |
N.S. |
1 | 1.00 | 0.90 | 1.00 | 3.54 | 4.53 | 5.82 | 2.32 | 3.03 |
time (sec) |
N/A | 0.289 | 0.043 | 2.737 | 0.207 | 0.274 | 0.928 | 0.274 | 0.242 |
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 | 133 | 133 | 230 | 254 | 271 | 416 | 258 | 264 | 291 |
N.S. |
1 | 1.00 | 1.73 | 1.91 | 2.04 | 3.13 | 1.94 | 1.98 | 2.19 |
time (sec) |
N/A | 0.350 | 0.048 | 2.469 | 0.203 | 0.273 | 2.737 | 0.275 | 9.843 |
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 | 103 | 103 | 167 | 172 | 191 | 291 | 185 | 183 | 196 |
N.S. |
1 | 1.00 | 1.62 | 1.67 | 1.85 | 2.83 | 1.80 | 1.78 | 1.90 |
time (sec) |
N/A | 0.290 | 0.032 | 2.494 | 0.193 | 0.296 | 0.866 | 0.276 | 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 | 78 | 78 | 114 | 114 | 125 | 188 | 128 | 112 | 130 |
N.S. |
1 | 1.00 | 1.46 | 1.46 | 1.60 | 2.41 | 1.64 | 1.44 | 1.67 |
time (sec) |
N/A | 0.254 | 0.026 | 2.712 | 0.204 | 0.256 | 0.499 | 0.274 | 9.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 48 | 66 | 80 | 100 | 80 | 69 | 77 |
N.S. |
1 | 1.00 | 0.81 | 1.12 | 1.36 | 1.69 | 1.36 | 1.17 | 1.31 |
time (sec) |
N/A | 0.222 | 0.016 | 2.683 | 0.197 | 0.275 | 0.274 | 0.270 | 9.914 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 26 | 25 | 38 | 38 | 39 | 24 | 39 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 1.36 | 1.36 | 1.39 | 0.86 | 1.39 |
time (sec) |
N/A | 0.166 | 0.007 | 2.387 | 0.190 | 0.252 | 0.157 | 0.267 | 0.034 |
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 | 14 | 14 | 14 | 13 | 24 | 24 | 26 | 12 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.71 | 1.71 | 1.86 | 0.86 | 1.86 |
time (sec) |
N/A | 0.150 | 0.002 | 2.376 | 0.189 | 0.245 | 0.105 | 0.266 | 0.031 |
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 | 82 | 82 | 67 | 81 | 202 | 242 | 381 | 165 | 183 |
N.S. |
1 | 1.00 | 0.82 | 0.99 | 2.46 | 2.95 | 4.65 | 2.01 | 2.23 |
time (sec) |
N/A | 0.244 | 0.029 | 2.579 | 0.204 | 0.302 | 0.570 | 0.270 | 0.150 |
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 | 110 | 110 | 97 | 108 | 386 | 495 | 632 | 254 | 329 |
N.S. |
1 | 1.00 | 0.88 | 0.98 | 3.51 | 4.50 | 5.75 | 2.31 | 2.99 |
time (sec) |
N/A | 0.286 | 0.060 | 2.715 | 0.206 | 0.264 | 0.917 | 0.282 | 9.996 |
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 | 143 | 160 | 128 | 140 | 594 | 760 | 881 | 345 | 542 |
N.S. |
1 | 1.12 | 0.90 | 0.98 | 4.15 | 5.31 | 6.16 | 2.41 | 3.79 |
time (sec) |
N/A | 0.371 | 0.070 | 2.426 | 0.209 | 0.309 | 1.350 | 0.277 | 10.052 |
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 | 170 | 170 | 154 | 165 | 889 | 1151 | 1217 | 458 | 797 |
N.S. |
1 | 1.00 | 0.91 | 0.97 | 5.23 | 6.77 | 7.16 | 2.69 | 4.69 |
time (sec) |
N/A | 0.385 | 0.130 | 2.495 | 0.250 | 0.281 | 2.711 | 0.286 | 10.109 |
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 | 39 | 39 | 117 | 123 | 121 | 121 | 136 | 127 | 122 |
N.S. |
1 | 1.00 | 3.00 | 3.15 | 3.10 | 3.10 | 3.49 | 3.26 | 3.13 |
time (sec) |
N/A | 0.206 | 0.020 | 2.106 | 0.189 | 0.253 | 0.031 | 0.273 | 0.061 |
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 | 39 | 39 | 95 | 100 | 102 | 102 | 107 | 103 | 99 |
N.S. |
1 | 1.00 | 2.44 | 2.56 | 2.62 | 2.62 | 2.74 | 2.64 | 2.54 |
time (sec) |
N/A | 0.197 | 0.012 | 2.471 | 0.189 | 0.305 | 0.030 | 0.273 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 73 | 76 | 75 | 75 | 80 | 78 | 75 |
N.S. |
1 | 1.00 | 1.87 | 1.95 | 1.92 | 1.92 | 2.05 | 2.00 | 1.92 |
time (sec) |
N/A | 0.190 | 0.013 | 2.182 | 0.194 | 0.270 | 0.027 | 0.282 | 9.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 51 | 54 | 54 | 54 | 56 | 55 | 53 |
N.S. |
1 | 1.00 | 1.31 | 1.38 | 1.38 | 1.38 | 1.44 | 1.41 | 1.36 |
time (sec) |
N/A | 0.202 | 0.008 | 0.210 | 0.192 | 0.310 | 0.024 | 0.278 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 38 | 31 | 30 | 30 | 32 | 30 | 31 |
N.S. |
1 | 1.00 | 1.12 | 0.91 | 0.88 | 0.88 | 0.94 | 0.88 | 0.91 |
time (sec) |
N/A | 0.171 | 0.000 | 0.036 | 0.199 | 0.262 | 0.017 | 0.263 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 20 | 14 | 13 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.43 | 1.00 | 0.93 | 0.86 | 0.86 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.161 | 0.001 | 2.657 | 0.195 | 0.254 | 0.023 | 0.269 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 30 | 31 | 31 | 30 | 26 | 119 | 30 |
N.S. |
1 | 1.00 | 1.15 | 1.19 | 1.19 | 1.15 | 1.00 | 4.58 | 1.15 |
time (sec) |
N/A | 0.189 | 0.007 | 2.380 | 0.193 | 0.321 | 0.081 | 0.278 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 36 | 38 | 39 | 44 | 32 | 37 | 37 |
N.S. |
1 | 1.00 | 1.09 | 1.15 | 1.18 | 1.33 | 0.97 | 1.12 | 1.12 |
time (sec) |
N/A | 0.196 | 0.010 | 2.218 | 0.192 | 0.353 | 0.104 | 0.268 | 9.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 29 | 30 | 43 | 43 | 44 | 29 | 30 |
N.S. |
1 | 1.00 | 0.83 | 0.86 | 1.23 | 1.23 | 1.26 | 0.83 | 0.86 |
time (sec) |
N/A | 0.167 | 0.009 | 2.289 | 0.184 | 0.440 | 0.147 | 0.269 | 10.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 30 | 31 | 55 | 55 | 58 | 41 | 57 |
N.S. |
1 | 1.00 | 0.77 | 0.79 | 1.41 | 1.41 | 1.49 | 1.05 | 1.46 |
time (sec) |
N/A | 0.192 | 0.009 | 2.273 | 0.205 | 0.354 | 0.189 | 0.293 | 0.044 |
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 | 39 | 39 | 30 | 31 | 66 | 66 | 70 | 30 | 68 |
N.S. |
1 | 1.00 | 0.77 | 0.79 | 1.69 | 1.69 | 1.79 | 0.77 | 1.74 |
time (sec) |
N/A | 0.195 | 0.009 | 2.362 | 0.188 | 0.358 | 0.246 | 0.273 | 10.137 |
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 | 77 | 77 | 160 | 173 | 172 | 172 | 185 | 186 | 168 |
N.S. |
1 | 1.00 | 2.08 | 2.25 | 2.23 | 2.23 | 2.40 | 2.42 | 2.18 |
time (sec) |
N/A | 0.306 | 0.022 | 2.399 | 0.193 | 0.588 | 0.035 | 0.268 | 10.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 120 | 137 | 140 | 140 | 150 | 146 | 135 |
N.S. |
1 | 1.00 | 1.56 | 1.78 | 1.82 | 1.82 | 1.95 | 1.90 | 1.75 |
time (sec) |
N/A | 0.267 | 0.022 | 2.302 | 0.186 | 0.322 | 0.035 | 0.272 | 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 | 77 | 97 | 87 | 93 | 93 | 97 | 104 | 105 | 99 |
N.S. |
1 | 1.26 | 1.13 | 1.21 | 1.21 | 1.26 | 1.35 | 1.36 | 1.29 |
time (sec) |
N/A | 0.287 | 0.017 | 2.377 | 0.194 | 0.256 | 0.028 | 0.288 | 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 | 54 | 54 | 54 | 64 | 64 | 64 | 66 | 65 | 63 |
N.S. |
1 | 1.00 | 1.00 | 1.19 | 1.19 | 1.19 | 1.22 | 1.20 | 1.17 |
time (sec) |
N/A | 0.228 | 0.009 | 2.661 | 0.184 | 0.264 | 0.045 | 0.310 | 10.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 28 | 28 | 29 | 97 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.40 | 1.40 | 1.45 | 4.85 | 1.40 |
time (sec) |
N/A | 0.161 | 0.002 | 2.689 | 0.190 | 0.256 | 0.039 | 0.268 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 52 | 66 | 72 | 72 | 53 | 72 | 69 |
N.S. |
1 | 1.00 | 0.84 | 1.06 | 1.16 | 1.16 | 0.85 | 1.16 | 1.11 |
time (sec) |
N/A | 0.217 | 0.015 | 2.366 | 0.202 | 0.271 | 0.134 | 0.269 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 59 | 75 | 79 | 108 | 71 | 77 | 83 |
N.S. |
1 | 1.00 | 0.94 | 1.19 | 1.25 | 1.71 | 1.13 | 1.22 | 1.32 |
time (sec) |
N/A | 0.234 | 0.028 | 2.541 | 0.200 | 0.312 | 0.204 | 0.278 | 10.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 59 | 78 | 90 | 112 | 90 | 120 | 89 |
N.S. |
1 | 1.00 | 0.83 | 1.10 | 1.27 | 1.58 | 1.27 | 1.69 | 1.25 |
time (sec) |
N/A | 0.244 | 0.022 | 2.874 | 0.190 | 0.263 | 0.280 | 0.271 | 10.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 59 | 70 | 94 | 94 | 99 | 69 | 65 |
N.S. |
1 | 1.00 | 1.69 | 2.00 | 2.69 | 2.69 | 2.83 | 1.97 | 1.86 |
time (sec) |
N/A | 0.169 | 0.020 | 2.370 | 0.200 | 0.325 | 0.436 | 0.269 | 10.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 61 | 72 | 108 | 108 | 114 | 71 | 85 |
N.S. |
1 | 1.00 | 0.79 | 0.94 | 1.40 | 1.40 | 1.48 | 0.92 | 1.10 |
time (sec) |
N/A | 0.234 | 0.016 | 2.419 | 0.199 | 0.263 | 1.032 | 0.268 | 9.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 61 | 72 | 119 | 119 | 126 | 71 | 119 |
N.S. |
1 | 1.00 | 0.79 | 0.94 | 1.55 | 1.55 | 1.64 | 0.92 | 1.55 |
time (sec) |
N/A | 0.238 | 0.020 | 2.968 | 0.201 | 0.284 | 3.593 | 0.281 | 0.073 |
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 | 61 | 72 | 130 | 130 | 138 | 71 | 130 |
N.S. |
1 | 1.00 | 0.79 | 0.94 | 1.69 | 1.69 | 1.79 | 0.92 | 1.69 |
time (sec) |
N/A | 0.236 | 0.016 | 2.448 | 0.259 | 0.265 | 13.383 | 0.272 | 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 | 111 | 111 | 255 | 299 | 303 | 303 | 335 | 329 | 295 |
N.S. |
1 | 1.00 | 2.30 | 2.69 | 2.73 | 2.73 | 3.02 | 2.96 | 2.66 |
time (sec) |
N/A | 0.400 | 0.046 | 2.406 | 0.225 | 0.251 | 0.049 | 0.269 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 211 | 248 | 251 | 251 | 270 | 271 | 242 |
N.S. |
1 | 1.00 | 1.90 | 2.23 | 2.26 | 2.26 | 2.43 | 2.44 | 2.18 |
time (sec) |
N/A | 0.341 | 0.041 | 2.615 | 0.202 | 0.264 | 0.046 | 0.291 | 10.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 131 | 167 | 198 | 183 | 193 | 218 | 214 | 186 |
N.S. |
1 | 1.18 | 1.50 | 1.78 | 1.65 | 1.74 | 1.96 | 1.93 | 1.68 |
time (sec) |
N/A | 0.371 | 0.033 | 2.634 | 0.207 | 0.262 | 0.037 | 0.292 | 10.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 123 | 147 | 150 | 150 | 160 | 156 | 145 |
N.S. |
1 | 1.00 | 1.35 | 1.62 | 1.65 | 1.65 | 1.76 | 1.71 | 1.59 |
time (sec) |
N/A | 0.294 | 0.024 | 2.427 | 0.222 | 0.261 | 0.063 | 0.272 | 9.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 79 | 99 | 95 | 95 | 100 | 174 | 91 |
N.S. |
1 | 1.00 | 1.46 | 1.83 | 1.76 | 1.76 | 1.85 | 3.22 | 1.69 |
time (sec) |
N/A | 0.213 | 0.018 | 2.401 | 0.195 | 0.265 | 0.060 | 0.262 | 9.947 |
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 | 20 | 20 | 20 | 19 | 45 | 45 | 49 | 45 | 45 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 2.25 | 2.25 | 2.45 | 2.25 | 2.25 |
time (sec) |
N/A | 0.158 | 0.002 | 2.340 | 0.199 | 0.264 | 0.058 | 0.294 | 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 | 89 | 89 | 85 | 124 | 131 | 130 | 95 | 133 | 128 |
N.S. |
1 | 1.00 | 0.96 | 1.39 | 1.47 | 1.46 | 1.07 | 1.49 | 1.44 |
time (sec) |
N/A | 0.248 | 0.027 | 2.835 | 0.205 | 0.271 | 0.201 | 0.264 | 0.062 |
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 | 94 | 94 | 129 | 125 | 136 | 193 | 117 | 182 | 141 |
N.S. |
1 | 1.00 | 1.37 | 1.33 | 1.45 | 2.05 | 1.24 | 1.94 | 1.50 |
time (sec) |
N/A | 0.277 | 0.029 | 2.497 | 0.200 | 0.269 | 0.332 | 0.282 | 0.078 |
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 | 97 | 97 | 129 | 133 | 142 | 209 | 144 | 129 | 149 |
N.S. |
1 | 1.00 | 1.33 | 1.37 | 1.46 | 2.15 | 1.48 | 1.33 | 1.54 |
time (sec) |
N/A | 0.277 | 0.031 | 2.353 | 0.203 | 0.273 | 0.749 | 0.284 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 92 | 133 | 158 | 194 | 163 | 136 | 157 |
N.S. |
1 | 1.00 | 0.88 | 1.27 | 1.50 | 1.85 | 1.55 | 1.30 | 1.50 |
time (sec) |
N/A | 0.276 | 0.033 | 2.371 | 0.203 | 0.260 | 7.185 | 0.261 | 10.046 |
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 | 35 | 35 | 100 | 123 | 158 | 158 | 170 | 126 | 102 |
N.S. |
1 | 1.00 | 2.86 | 3.51 | 4.51 | 4.51 | 4.86 | 3.60 | 2.91 |
time (sec) |
N/A | 0.170 | 0.023 | 2.602 | 0.215 | 0.294 | 47.476 | 0.277 | 9.888 |
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 | 73 | 108 | 103 | 129 | 175 | 175 | 187 | 129 | 135 |
N.S. |
1 | 1.48 | 1.41 | 1.77 | 2.40 | 2.40 | 2.56 | 1.77 | 1.85 |
time (sec) |
N/A | 0.276 | 0.026 | 2.758 | 0.221 | 0.260 | 112.463 | 0.270 | 9.800 |
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 | 111 | 111 | 103 | 129 | 186 | 186 | 0 | 129 | 184 |
N.S. |
1 | 1.00 | 0.93 | 1.16 | 1.68 | 1.68 | 0.00 | 1.16 | 1.66 |
time (sec) |
N/A | 0.270 | 0.022 | 2.441 | 0.213 | 0.315 | 0.000 | 0.262 | 9.905 |
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 | 111 | 111 | 103 | 129 | 197 | 197 | 0 | 129 | 195 |
N.S. |
1 | 1.00 | 0.93 | 1.16 | 1.77 | 1.77 | 0.00 | 1.16 | 1.76 |
time (sec) |
N/A | 0.278 | 0.023 | 2.354 | 0.228 | 0.268 | 0.000 | 0.282 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 131 | 134 | 201 | 205 | 207 | 153 | 210 | 217 |
N.S. |
1 | 1.00 | 1.02 | 1.53 | 1.56 | 1.58 | 1.17 | 1.60 | 1.66 |
time (sec) |
N/A | 0.288 | 0.036 | 2.810 | 0.230 | 0.308 | 0.256 | 0.280 | 9.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 91 | 132 | 135 | 137 | 99 | 136 | 138 |
N.S. |
1 | 1.00 | 0.91 | 1.32 | 1.35 | 1.37 | 0.99 | 1.36 | 1.38 |
time (sec) |
N/A | 0.254 | 0.024 | 2.700 | 0.216 | 0.304 | 0.189 | 0.280 | 9.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 58 | 74 | 77 | 79 | 58 | 76 | 77 |
N.S. |
1 | 1.00 | 0.84 | 1.07 | 1.12 | 1.14 | 0.84 | 1.10 | 1.12 |
time (sec) |
N/A | 0.223 | 0.015 | 2.365 | 0.227 | 0.269 | 0.138 | 0.273 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 35 | 39 | 38 | 35 | 32 | 39 | 39 |
N.S. |
1 | 1.00 | 0.92 | 1.03 | 1.00 | 0.92 | 0.84 | 1.03 | 1.03 |
time (sec) |
N/A | 0.203 | 0.007 | 2.393 | 0.223 | 0.266 | 0.088 | 0.279 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 17 | 16 | 16 | 12 | 17 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.75 | 1.06 | 1.00 |
time (sec) |
N/A | 0.152 | 0.001 | 2.655 | 0.230 | 0.257 | 0.026 | 0.285 | 9.673 |
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 | 47 | 69 | 33 | 34 | 47 | 33 | 172 | 57 | 51 |
N.S. |
1 | 1.47 | 0.70 | 0.72 | 1.00 | 0.70 | 3.66 | 1.21 | 1.09 |
time (sec) |
N/A | 0.236 | 0.011 | 2.512 | 0.190 | 0.317 | 0.174 | 0.278 | 0.087 |
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 | 73 | 73 | 66 | 75 | 107 | 109 | 301 | 111 | 95 |
N.S. |
1 | 1.00 | 0.90 | 1.03 | 1.47 | 1.49 | 4.12 | 1.52 | 1.30 |
time (sec) |
N/A | 0.246 | 0.019 | 2.431 | 0.196 | 0.359 | 0.382 | 0.269 | 0.136 |
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 | 108 | 108 | 102 | 107 | 228 | 266 | 471 | 158 | 220 |
N.S. |
1 | 1.00 | 0.94 | 0.99 | 2.11 | 2.46 | 4.36 | 1.46 | 2.04 |
time (sec) |
N/A | 0.284 | 0.031 | 2.588 | 0.207 | 0.367 | 0.616 | 0.286 | 9.761 |
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 | 139 | 139 | 135 | 137 | 393 | 454 | 672 | 275 | 359 |
N.S. |
1 | 1.00 | 0.97 | 0.99 | 2.83 | 3.27 | 4.83 | 1.98 | 2.58 |
time (sec) |
N/A | 0.318 | 0.043 | 2.838 | 0.207 | 0.378 | 0.917 | 0.271 | 9.855 |
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 | 219 | 219 | 339 | 402 | 398 | 545 | 345 | 418 | 625 |
N.S. |
1 | 1.00 | 1.55 | 1.84 | 1.82 | 2.49 | 1.58 | 1.91 | 2.85 |
time (sec) |
N/A | 0.505 | 0.074 | 2.347 | 0.205 | 0.389 | 3.749 | 0.277 | 0.108 |
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 | 184 | 184 | 263 | 298 | 300 | 417 | 264 | 312 | 387 |
N.S. |
1 | 1.00 | 1.43 | 1.62 | 1.63 | 2.27 | 1.43 | 1.70 | 2.10 |
time (sec) |
N/A | 0.428 | 0.052 | 2.350 | 0.207 | 0.578 | 1.144 | 0.280 | 9.654 |
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 | 145 | 145 | 196 | 208 | 214 | 305 | 185 | 222 | 242 |
N.S. |
1 | 1.00 | 1.35 | 1.43 | 1.48 | 2.10 | 1.28 | 1.53 | 1.67 |
time (sec) |
N/A | 0.362 | 0.047 | 2.397 | 0.216 | 0.291 | 0.513 | 0.271 | 9.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 142 | 137 | 143 | 205 | 131 | 146 | 152 |
N.S. |
1 | 1.00 | 1.35 | 1.30 | 1.36 | 1.95 | 1.25 | 1.39 | 1.45 |
time (sec) |
N/A | 0.288 | 0.032 | 2.735 | 0.198 | 0.313 | 0.328 | 0.274 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 65 | 86 | 89 | 117 | 85 | 86 | 96 |
N.S. |
1 | 1.00 | 0.88 | 1.16 | 1.20 | 1.58 | 1.15 | 1.16 | 1.30 |
time (sec) |
N/A | 0.249 | 0.029 | 2.409 | 0.206 | 0.284 | 0.215 | 0.289 | 9.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 47 | 49 | 52 | 56 | 46 | 49 | 47 |
N.S. |
1 | 1.00 | 0.98 | 1.02 | 1.08 | 1.17 | 0.96 | 1.02 | 0.98 |
time (sec) |
N/A | 0.212 | 0.010 | 2.408 | 0.194 | 0.296 | 0.112 | 0.272 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 18 | 18 | 17 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.159 | 0.002 | 2.763 | 0.199 | 0.255 | 0.077 | 0.275 | 9.704 |
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 | 75 | 75 | 74 | 75 | 113 | 116 | 287 | 112 | 96 |
N.S. |
1 | 1.00 | 0.99 | 1.00 | 1.51 | 1.55 | 3.83 | 1.49 | 1.28 |
time (sec) |
N/A | 0.236 | 0.019 | 2.658 | 0.203 | 0.296 | 0.404 | 0.274 | 9.684 |
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 | 114 | 143 | 86 | 107 | 236 | 277 | 486 | 195 | 223 |
N.S. |
1 | 1.25 | 0.75 | 0.94 | 2.07 | 2.43 | 4.26 | 1.71 | 1.96 |
time (sec) |
N/A | 0.333 | 0.059 | 2.354 | 0.215 | 0.305 | 0.657 | 0.299 | 9.908 |
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 | 146 | 146 | 130 | 144 | 423 | 544 | 734 | 289 | 381 |
N.S. |
1 | 1.00 | 0.89 | 0.99 | 2.90 | 3.73 | 5.03 | 1.98 | 2.61 |
time (sec) |
N/A | 0.333 | 0.060 | 2.667 | 0.218 | 0.282 | 1.062 | 0.282 | 9.807 |
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 | 176 | 176 | 160 | 174 | 641 | 807 | 996 | 480 | 595 |
N.S. |
1 | 1.00 | 0.91 | 0.99 | 3.64 | 4.59 | 5.66 | 2.73 | 3.38 |
time (sec) |
N/A | 0.390 | 0.084 | 2.842 | 0.223 | 0.288 | 2.052 | 0.300 | 10.027 |
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 | 221 | 221 | 337 | 399 | 408 | 606 | 386 | 403 | 516 |
N.S. |
1 | 1.00 | 1.52 | 1.81 | 1.85 | 2.74 | 1.75 | 1.82 | 2.33 |
time (sec) |
N/A | 0.503 | 0.078 | 2.887 | 0.214 | 0.332 | 112.750 | 0.285 | 0.133 |
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 | 185 | 185 | 262 | 297 | 310 | 469 | 303 | 301 | 341 |
N.S. |
1 | 1.00 | 1.42 | 1.61 | 1.68 | 2.54 | 1.64 | 1.63 | 1.84 |
time (sec) |
N/A | 0.400 | 0.058 | 2.468 | 0.195 | 0.265 | 47.698 | 0.268 | 9.871 |
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 | 142 | 142 | 191 | 211 | 224 | 338 | 226 | 214 | 232 |
N.S. |
1 | 1.00 | 1.35 | 1.49 | 1.58 | 2.38 | 1.59 | 1.51 | 1.63 |
time (sec) |
N/A | 0.352 | 0.044 | 2.488 | 0.199 | 0.290 | 7.285 | 0.272 | 0.112 |
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 | 111 | 111 | 139 | 147 | 156 | 227 | 163 | 136 | 163 |
N.S. |
1 | 1.00 | 1.25 | 1.32 | 1.41 | 2.05 | 1.47 | 1.23 | 1.47 |
time (sec) |
N/A | 0.299 | 0.033 | 2.872 | 0.191 | 0.310 | 0.772 | 0.269 | 9.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 65 | 90 | 105 | 126 | 109 | 89 | 106 |
N.S. |
1 | 1.00 | 0.76 | 1.06 | 1.24 | 1.48 | 1.28 | 1.05 | 1.25 |
time (sec) |
N/A | 0.258 | 0.022 | 2.598 | 0.186 | 0.326 | 0.303 | 0.276 | 0.095 |
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 | 35 | 35 | 35 | 36 | 56 | 56 | 60 | 35 | 43 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.60 | 1.60 | 1.71 | 1.00 | 1.23 |
time (sec) |
N/A | 0.170 | 0.011 | 2.399 | 0.188 | 0.287 | 0.176 | 0.272 | 0.047 |
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 | 20 | 20 | 20 | 19 | 35 | 35 | 39 | 18 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.75 | 1.75 | 1.95 | 0.90 | 1.85 |
time (sec) |
N/A | 0.158 | 0.002 | 2.637 | 0.180 | 0.267 | 0.121 | 0.293 | 0.031 |
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 | 107 | 107 | 83 | 106 | 238 | 280 | 457 | 190 | 225 |
N.S. |
1 | 1.00 | 0.78 | 0.99 | 2.22 | 2.62 | 4.27 | 1.78 | 2.10 |
time (sec) |
N/A | 0.287 | 0.051 | 2.786 | 0.193 | 0.313 | 0.654 | 0.281 | 10.030 |
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 | 142 | 142 | 127 | 142 | 429 | 555 | 736 | 286 | 392 |
N.S. |
1 | 1.00 | 0.89 | 1.00 | 3.02 | 3.91 | 5.18 | 2.01 | 2.76 |
time (sec) |
N/A | 0.334 | 0.063 | 2.421 | 0.201 | 0.295 | 1.139 | 0.280 | 9.994 |
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 | 191 | 214 | 168 | 186 | 642 | 828 | 1001 | 386 | 616 |
N.S. |
1 | 1.12 | 0.88 | 0.97 | 3.36 | 4.34 | 5.24 | 2.02 | 3.23 |
time (sec) |
N/A | 0.459 | 0.092 | 2.437 | 0.195 | 0.361 | 2.347 | 0.268 | 10.207 |
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 | 223 | 223 | 201 | 218 | 947 | 1222 | 1357 | 503 | 878 |
N.S. |
1 | 1.00 | 0.90 | 0.98 | 4.25 | 5.48 | 6.09 | 2.26 | 3.94 |
time (sec) |
N/A | 0.462 | 0.119 | 2.698 | 0.225 | 0.306 | 9.934 | 0.266 | 10.351 |
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 | 217 | 217 | 335 | 399 | 424 | 644 | 0 | 398 | 452 |
N.S. |
1 | 1.00 | 1.54 | 1.84 | 1.95 | 2.97 | 0.00 | 1.83 | 2.08 |
time (sec) |
N/A | 0.504 | 0.082 | 2.872 | 0.203 | 0.341 | 0.000 | 0.271 | 0.161 |
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 | 179 | 179 | 259 | 300 | 326 | 488 | 0 | 299 | 331 |
N.S. |
1 | 1.00 | 1.45 | 1.68 | 1.82 | 2.73 | 0.00 | 1.67 | 1.85 |
time (sec) |
N/A | 0.407 | 0.058 | 2.435 | 0.196 | 0.289 | 0.000 | 0.281 | 0.144 |
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 | 146 | 146 | 194 | 216 | 243 | 347 | 257 | 206 | 246 |
N.S. |
1 | 1.00 | 1.33 | 1.48 | 1.66 | 2.38 | 1.76 | 1.41 | 1.68 |
time (sec) |
N/A | 0.350 | 0.046 | 2.475 | 0.209 | 0.340 | 132.674 | 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 | 122 | 99 | 145 | 179 | 217 | 189 | 142 | 178 |
N.S. |
1 | 1.00 | 0.81 | 1.19 | 1.47 | 1.78 | 1.55 | 1.16 | 1.46 |
time (sec) |
N/A | 0.305 | 0.035 | 2.903 | 0.193 | 0.280 | 10.566 | 0.271 | 9.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 65 | 76 | 113 | 113 | 121 | 75 | 81 |
N.S. |
1 | 1.00 | 1.86 | 2.17 | 3.23 | 3.23 | 3.46 | 2.14 | 2.31 |
time (sec) |
N/A | 0.169 | 0.022 | 2.424 | 0.189 | 0.266 | 0.715 | 0.287 | 0.066 |