Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 499 | 182 | 233 | 141 | 0 | 145 | 176 |
N.S. | 1 | 1.00 | 4.75 | 1.73 | 2.22 | 1.34 | 0.00 | 1.38 | 1.68 |
time (sec) |
N/A | 0.140 | 1.706 | 0.270 | 0.273 | 3.048 | 0.000 | 0.573 | 6.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 887 | 111 | 144 | 126 | 0 | 128 | 146 |
N.S. | 1 | 1.00 | 10.31 | 1.29 | 1.67 | 1.47 | 0.00 | 1.49 | 1.70 |
time (sec) |
N/A | 0.110 | 6.491 | 0.212 | 0.265 | 2.843 | 0.000 | 0.557 | 5.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 313 | 98 | 117 | 111 | 0 | 111 | 114 |
N.S. | 1 | 1.00 | 5.13 | 1.61 | 1.92 | 1.82 | 0.00 | 1.82 | 1.87 |
time (sec) |
N/A | 0.070 | 0.735 | 0.188 | 0.265 | 3.328 | 0.000 | 0.577 | 3.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 58 | 74 | 73 | 0 | 55 | 77 |
N.S. | 1 | 1.00 | 1.00 | 1.53 | 1.95 | 1.92 | 0.00 | 1.45 | 2.03 |
time (sec) |
N/A | 0.032 | 0.028 | 0.139 | 0.275 | 2.900 | 0.000 | 0.525 | 2.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 77 | 50 | 109 | 72 | 0 | 60 | 31 |
N.S. | 1 | 1.00 | 1.83 | 1.19 | 2.60 | 1.71 | 0.00 | 1.43 | 0.74 |
time (sec) |
N/A | 0.037 | 0.084 | 0.130 | 0.271 | 2.500 | 0.000 | 0.569 | 1.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 50 | 21 | 105 | 55 | 0 | 20 | 20 |
N.S. | 1 | 1.00 | 1.39 | 0.58 | 2.92 | 1.53 | 0.00 | 0.56 | 0.56 |
time (sec) |
N/A | 0.033 | 0.251 | 0.138 | 0.283 | 2.385 | 0.000 | 0.470 | 2.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 87 | 37 | 127 | 84 | 0 | 37 | 35 |
N.S. | 1 | 1.00 | 1.14 | 0.49 | 1.67 | 1.11 | 0.00 | 0.49 | 0.46 |
time (sec) |
N/A | 0.070 | 0.345 | 0.154 | 0.287 | 3.273 | 0.000 | 0.490 | 1.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 113 | 50 | 193 | 112 | 0 | 51 | 61 |
N.S. | 1 | 1.00 | 0.97 | 0.43 | 1.66 | 0.97 | 0.00 | 0.44 | 0.53 |
time (sec) |
N/A | 0.109 | 0.407 | 0.167 | 0.279 | 4.040 | 0.000 | 0.707 | 1.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 139 | 63 | 215 | 138 | 0 | 65 | 106 |
N.S. | 1 | 1.00 | 0.88 | 0.40 | 1.36 | 0.87 | 0.00 | 0.41 | 0.67 |
time (sec) |
N/A | 0.149 | 0.366 | 0.193 | 0.275 | 3.370 | 0.000 | 0.791 | 1.843 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 102 | 299 | 398 | 189 | 0 | 197 | 251 |
N.S. | 1 | 1.00 | 0.60 | 1.75 | 2.33 | 1.11 | 0.00 | 1.15 | 1.47 |
time (sec) |
N/A | 0.207 | 1.875 | 0.352 | 0.283 | 2.547 | 0.000 | 0.824 | 5.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 91 | 255 | 347 | 172 | 0 | 178 | 219 |
N.S. | 1 | 1.00 | 0.61 | 1.70 | 2.31 | 1.15 | 0.00 | 1.19 | 1.46 |
time (sec) |
N/A | 0.176 | 1.403 | 0.307 | 0.276 | 2.866 | 0.000 | 0.611 | 5.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 82 | 192 | 245 | 155 | 0 | 159 | 187 |
N.S. | 1 | 1.00 | 0.87 | 2.04 | 2.61 | 1.65 | 0.00 | 1.69 | 1.99 |
time (sec) |
N/A | 0.110 | 0.766 | 0.270 | 0.302 | 2.373 | 0.000 | 0.741 | 6.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 51 | 117 | 162 | 106 | 0 | 87 | 155 |
N.S. | 1 | 1.00 | 0.70 | 1.60 | 2.22 | 1.45 | 0.00 | 1.19 | 2.12 |
time (sec) |
N/A | 0.078 | 0.155 | 0.193 | 0.274 | 3.763 | 0.000 | 0.570 | 5.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 45 | 96 | 117 | 111 | 0 | 111 | 113 |
N.S. | 1 | 1.00 | 0.74 | 1.57 | 1.92 | 1.82 | 0.00 | 1.82 | 1.85 |
time (sec) |
N/A | 0.073 | 0.119 | 0.192 | 0.263 | 2.496 | 0.000 | 0.552 | 3.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 220 | 82 | 243 | 118 | 0 | 100 | 77 |
N.S. | 1 | 1.00 | 2.97 | 1.11 | 3.28 | 1.59 | 0.00 | 1.35 | 1.04 |
time (sec) |
N/A | 0.071 | 1.885 | 0.155 | 0.279 | 2.164 | 0.000 | 0.661 | 1.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 109 | 67 | 217 | 138 | 0 | 84 | 63 |
N.S. | 1 | 1.00 | 1.22 | 0.75 | 2.44 | 1.55 | 0.00 | 0.94 | 0.71 |
time (sec) |
N/A | 0.092 | 0.088 | 0.161 | 0.277 | 2.611 | 0.000 | 0.637 | 1.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 25 | 23 | 205 | 89 | 0 | 22 | 22 |
N.S. | 1 | 1.00 | 0.66 | 0.61 | 5.39 | 2.34 | 0.00 | 0.58 | 0.58 |
time (sec) |
N/A | 0.055 | 0.125 | 0.178 | 0.284 | 2.496 | 0.000 | 0.540 | 1.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 115 | 39 | 294 | 122 | 0 | 41 | 37 |
N.S. | 1 | 1.00 | 1.44 | 0.49 | 3.68 | 1.52 | 0.00 | 0.51 | 0.46 |
time (sec) |
N/A | 0.109 | 0.450 | 0.183 | 0.310 | 1.742 | 0.000 | 0.582 | 1.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 141 | 52 | 293 | 150 | 0 | 57 | 67 |
N.S. | 1 | 1.00 | 1.17 | 0.43 | 2.42 | 1.24 | 0.00 | 0.47 | 0.55 |
time (sec) |
N/A | 0.166 | 0.435 | 0.214 | 0.307 | 3.232 | 0.000 | 0.604 | 1.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 167 | 65 | 425 | 180 | 0 | 73 | 108 |
N.S. | 1 | 1.00 | 1.02 | 0.40 | 2.61 | 1.10 | 0.00 | 0.45 | 0.66 |
time (sec) |
N/A | 0.224 | 0.660 | 0.221 | 0.311 | 2.582 | 0.000 | 0.647 | 1.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 122 | 345 | 480 | 223 | 0 | 235 | 316 |
N.S. | 1 | 1.00 | 0.54 | 1.52 | 2.11 | 0.98 | 0.00 | 1.04 | 1.39 |
time (sec) |
N/A | 0.255 | 3.262 | 0.350 | 0.282 | 2.480 | 0.000 | 0.634 | 5.579 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 111 | 322 | 442 | 206 | 0 | 216 | 284 |
N.S. | 1 | 1.00 | 0.54 | 1.56 | 2.15 | 1.00 | 0.00 | 1.05 | 1.38 |
time (sec) |
N/A | 0.224 | 2.295 | 0.389 | 0.296 | 2.563 | 0.000 | 0.664 | 5.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 102 | 302 | 398 | 189 | 0 | 197 | 252 |
N.S. | 1 | 1.00 | 0.84 | 2.50 | 3.29 | 1.56 | 0.00 | 1.63 | 2.08 |
time (sec) |
N/A | 0.128 | 1.667 | 0.364 | 0.295 | 3.046 | 0.000 | 0.605 | 5.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 60 | 180 | 264 | 123 | 0 | 103 | 220 |
N.S. | 1 | 1.00 | 0.60 | 1.80 | 2.64 | 1.23 | 0.00 | 1.03 | 2.20 |
time (sec) |
N/A | 0.099 | 0.251 | 0.243 | 0.280 | 3.063 | 0.000 | 0.606 | 5.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 81 | 192 | 245 | 155 | 0 | 159 | 188 |
N.S. | 1 | 1.00 | 0.86 | 2.04 | 2.61 | 1.65 | 0.00 | 1.69 | 2.00 |
time (sec) |
N/A | 0.113 | 0.831 | 0.271 | 0.287 | 3.071 | 0.000 | 0.601 | 6.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 70 | 111 | 144 | 126 | 0 | 128 | 146 |
N.S. | 1 | 1.00 | 0.81 | 1.29 | 1.67 | 1.47 | 0.00 | 1.49 | 1.70 |
time (sec) |
N/A | 0.113 | 0.611 | 0.210 | 0.296 | 3.699 | 0.000 | 0.490 | 4.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 287 | 112 | 419 | 136 | 0 | 118 | 105 |
N.S. | 1 | 1.00 | 2.87 | 1.12 | 4.19 | 1.36 | 0.00 | 1.18 | 1.05 |
time (sec) |
N/A | 0.094 | 2.644 | 0.174 | 0.280 | 2.629 | 0.000 | 0.552 | 3.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 402 | 97 | 377 | 179 | 0 | 116 | 93 |
N.S. | 1 | 1.00 | 3.38 | 0.82 | 3.17 | 1.50 | 0.00 | 0.97 | 0.78 |
time (sec) |
N/A | 0.128 | 3.546 | 0.167 | 0.279 | 3.241 | 0.000 | 0.545 | 2.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 139 | 78 | 335 | 190 | 0 | 102 | 78 |
N.S. | 1 | 1.00 | 1.05 | 0.59 | 2.54 | 1.44 | 0.00 | 0.77 | 0.59 |
time (sec) |
N/A | 0.154 | 0.125 | 0.206 | 0.307 | 2.338 | 0.000 | 0.517 | 1.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 25 | 23 | 388 | 119 | 0 | 22 | 22 |
N.S. | 1 | 1.00 | 0.66 | 0.61 | 10.21 | 3.13 | 0.00 | 0.58 | 0.58 |
time (sec) |
N/A | 0.052 | 0.159 | 0.196 | 0.320 | 2.409 | 0.000 | 0.654 | 1.811 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 141 | 39 | 389 | 150 | 0 | 41 | 37 |
N.S. | 1 | 1.00 | 1.76 | 0.49 | 4.86 | 1.88 | 0.00 | 0.51 | 0.46 |
time (sec) |
N/A | 0.109 | 0.407 | 0.225 | 0.300 | 2.202 | 0.000 | 0.624 | 1.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 167 | 52 | 566 | 180 | 0 | 57 | 67 |
N.S. | 1 | 1.00 | 1.38 | 0.43 | 4.68 | 1.49 | 0.00 | 0.47 | 0.55 |
time (sec) |
N/A | 0.164 | 0.705 | 0.201 | 0.303 | 2.614 | 0.000 | 0.821 | 1.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 193 | 65 | 565 | 208 | 0 | 73 | 108 |
N.S. | 1 | 1.00 | 1.19 | 0.40 | 3.49 | 1.28 | 0.00 | 0.45 | 0.67 |
time (sec) |
N/A | 0.224 | 0.606 | 0.234 | 0.321 | 4.696 | 0.000 | 0.692 | 1.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 1036 | 140 | 641 | 165 | 0 | 132 | 112 |
N.S. | 1 | 1.00 | 8.56 | 1.16 | 5.30 | 1.36 | 0.00 | 1.09 | 0.93 |
time (sec) |
N/A | 0.120 | 6.454 | 0.187 | 0.295 | 3.270 | 0.000 | 0.556 | 1.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 287 | 110 | 418 | 151 | 0 | 116 | 96 |
N.S. | 1 | 1.00 | 2.87 | 1.10 | 4.18 | 1.51 | 0.00 | 1.16 | 0.96 |
time (sec) |
N/A | 0.097 | 2.628 | 0.175 | 0.286 | 2.716 | 0.000 | 0.562 | 1.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 220 | 80 | 242 | 129 | 0 | 97 | 77 |
N.S. | 1 | 1.00 | 2.97 | 1.08 | 3.27 | 1.74 | 0.00 | 1.31 | 1.04 |
time (sec) |
N/A | 0.073 | 1.672 | 0.139 | 0.291 | 2.820 | 0.000 | 0.562 | 1.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 77 | 48 | 109 | 76 | 0 | 58 | 31 |
N.S. | 1 | 1.00 | 1.88 | 1.17 | 2.66 | 1.85 | 0.00 | 1.41 | 0.76 |
time (sec) |
N/A | 0.039 | 0.070 | 0.149 | 0.271 | 3.176 | 0.000 | 0.642 | 1.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 19 | 19 | 19 | 0 | 18 | 18 |
N.S. | 1 | 1.00 | 1.00 | 1.19 | 1.19 | 1.19 | 0.00 | 1.12 | 1.12 |
time (sec) |
N/A | 0.064 | 0.030 | 0.123 | 0.270 | 3.248 | 0.000 | 0.546 | 1.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 81 | 48 | 83 | 54 | 0 | 56 | 50 |
N.S. | 1 | 1.00 | 1.37 | 0.81 | 1.41 | 0.92 | 0.00 | 0.95 | 0.85 |
time (sec) |
N/A | 0.106 | 0.500 | 0.142 | 0.281 | 1.797 | 0.000 | 0.810 | 1.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 107 | 61 | 105 | 80 | 0 | 69 | 63 |
N.S. | 1 | 1.00 | 1.37 | 0.78 | 1.35 | 1.03 | 0.00 | 0.88 | 0.81 |
time (sec) |
N/A | 0.136 | 0.845 | 0.165 | 0.270 | 3.277 | 0.000 | 0.723 | 1.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 145 | 74 | 127 | 110 | 0 | 82 | 83 |
N.S. | 1 | 1.00 | 1.21 | 0.62 | 1.06 | 0.92 | 0.00 | 0.68 | 0.69 |
time (sec) |
N/A | 0.172 | 0.918 | 0.164 | 0.295 | 3.026 | 0.000 | 0.578 | 2.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 164 | 380 | 155 | 829 | 226 | 0 | 156 | 170 |
N.S. | 1 | 1.00 | 2.32 | 0.95 | 5.05 | 1.38 | 0.00 | 0.95 | 1.04 |
time (sec) |
N/A | 0.183 | 1.204 | 0.228 | 0.293 | 3.983 | 0.000 | 0.666 | 1.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 349 | 125 | 575 | 212 | 0 | 140 | 136 |
N.S. | 1 | 1.00 | 2.33 | 0.83 | 3.83 | 1.41 | 0.00 | 0.93 | 0.91 |
time (sec) |
N/A | 0.152 | 2.004 | 0.198 | 0.292 | 3.481 | 0.000 | 0.687 | 1.681 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 485 | 95 | 369 | 192 | 0 | 121 | 104 |
N.S. | 1 | 1.00 | 4.08 | 0.80 | 3.10 | 1.61 | 0.00 | 1.02 | 0.87 |
time (sec) |
N/A | 0.134 | 4.378 | 0.175 | 0.281 | 3.364 | 0.000 | 0.610 | 1.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 109 | 65 | 212 | 148 | 0 | 89 | 46 |
N.S. | 1 | 1.00 | 1.24 | 0.74 | 2.41 | 1.68 | 0.00 | 1.01 | 0.52 |
time (sec) |
N/A | 0.093 | 0.093 | 0.171 | 0.283 | 2.713 | 0.000 | 0.560 | 1.612 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 23 | 21 | 102 | 57 | 0 | 20 | 20 |
N.S. | 1 | 1.00 | 0.64 | 0.58 | 2.83 | 1.58 | 0.00 | 0.56 | 0.56 |
time (sec) |
N/A | 0.035 | 0.090 | 0.155 | 0.275 | 3.412 | 0.000 | 0.598 | 1.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 83 | 48 | 82 | 53 | 0 | 69 | 61 |
N.S. | 1 | 1.00 | 1.41 | 0.81 | 1.39 | 0.90 | 0.00 | 1.17 | 1.03 |
time (sec) |
N/A | 0.103 | 0.594 | 0.145 | 0.279 | 2.824 | 0.000 | 0.534 | 1.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 33 | 66 | 33 | 53 | 0 | 31 | 28 |
N.S. | 1 | 1.00 | 0.87 | 1.74 | 0.87 | 1.39 | 0.00 | 0.82 | 0.74 |
time (sec) |
N/A | 0.074 | 0.052 | 0.207 | 0.281 | 2.394 | 0.000 | 0.540 | 1.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 147 | 76 | 131 | 117 | 0 | 96 | 76 |
N.S. | 1 | 1.00 | 1.84 | 0.95 | 1.64 | 1.46 | 0.00 | 1.20 | 0.95 |
time (sec) |
N/A | 0.110 | 0.987 | 0.170 | 0.297 | 2.846 | 0.000 | 0.498 | 2.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 179 | 87 | 152 | 129 | 0 | 109 | 89 |
N.S. | 1 | 1.00 | 1.83 | 0.89 | 1.55 | 1.32 | 0.00 | 1.11 | 0.91 |
time (sec) |
N/A | 0.146 | 0.935 | 0.193 | 0.308 | 2.052 | 0.000 | 0.513 | 2.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 211 | 102 | 175 | 175 | 0 | 122 | 102 |
N.S. | 1 | 1.00 | 1.50 | 0.72 | 1.24 | 1.24 | 0.00 | 0.87 | 0.72 |
time (sec) |
N/A | 0.185 | 1.253 | 0.191 | 0.291 | 2.114 | 0.000 | 0.566 | 4.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 215 | 406 | 168 | 1015 | 283 | 0 | 176 | 193 |
N.S. | 1 | 1.00 | 1.89 | 0.78 | 4.72 | 1.32 | 0.00 | 0.82 | 0.90 |
time (sec) |
N/A | 0.247 | 2.124 | 0.212 | 0.309 | 2.336 | 0.000 | 0.647 | 1.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 193 | 380 | 136 | 738 | 269 | 0 | 159 | 159 |
N.S. | 1 | 1.00 | 1.97 | 0.70 | 3.82 | 1.39 | 0.00 | 0.82 | 0.82 |
time (sec) |
N/A | 0.215 | 1.307 | 0.223 | 0.301 | 2.227 | 0.000 | 0.659 | 1.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 164 | 826 | 108 | 510 | 249 | 0 | 141 | 126 |
N.S. | 1 | 1.00 | 5.04 | 0.66 | 3.11 | 1.52 | 0.00 | 0.86 | 0.77 |
time (sec) |
N/A | 0.188 | 6.335 | 0.200 | 0.289 | 2.389 | 0.000 | 0.605 | 1.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 139 | 76 | 330 | 206 | 0 | 109 | 61 |
N.S. | 1 | 1.00 | 1.06 | 0.58 | 2.52 | 1.57 | 0.00 | 0.83 | 0.47 |
time (sec) |
N/A | 0.151 | 0.124 | 0.195 | 0.283 | 3.267 | 0.000 | 0.585 | 1.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 25 | 23 | 201 | 88 | 0 | 22 | 22 |
N.S. | 1 | 1.00 | 0.66 | 0.61 | 5.29 | 2.32 | 0.00 | 0.58 | 0.58 |
time (sec) |
N/A | 0.051 | 0.108 | 0.167 | 0.284 | 2.391 | 0.000 | 0.647 | 1.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 87 | 37 | 125 | 85 | 0 | 37 | 35 |
N.S. | 1 | 1.00 | 1.14 | 0.49 | 1.64 | 1.12 | 0.00 | 0.49 | 0.46 |
time (sec) |
N/A | 0.070 | 0.347 | 0.180 | 0.291 | 2.570 | 0.000 | 0.566 | 1.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 109 | 61 | 103 | 82 | 0 | 87 | 74 |
N.S. | 1 | 1.00 | 1.40 | 0.78 | 1.32 | 1.05 | 0.00 | 1.12 | 0.95 |
time (sec) |
N/A | 0.140 | 0.798 | 0.147 | 0.276 | 2.688 | 0.000 | 0.528 | 1.624 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 147 | 76 | 130 | 117 | 0 | 103 | 111 |
N.S. | 1 | 1.00 | 1.84 | 0.95 | 1.62 | 1.46 | 0.00 | 1.29 | 1.39 |
time (sec) |
N/A | 0.109 | 0.795 | 0.166 | 0.290 | 4.183 | 0.000 | 0.640 | 1.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 50 | 95 | 44 | 81 | 0 | 41 | 38 |
N.S. | 1 | 1.00 | 0.85 | 1.61 | 0.75 | 1.37 | 0.00 | 0.69 | 0.64 |
time (sec) |
N/A | 0.083 | 0.069 | 0.220 | 0.316 | 4.666 | 0.000 | 0.577 | 1.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 211 | 102 | 173 | 175 | 0 | 128 | 129 |
N.S. | 1 | 1.00 | 2.13 | 1.03 | 1.75 | 1.77 | 0.00 | 1.29 | 1.30 |
time (sec) |
N/A | 0.113 | 1.256 | 0.191 | 0.284 | 3.690 | 0.000 | 0.664 | 2.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 257 | 115 | 197 | 204 | 0 | 142 | 109 |
N.S. | 1 | 1.00 | 2.14 | 0.96 | 1.64 | 1.70 | 0.00 | 1.18 | 0.91 |
time (sec) |
N/A | 0.161 | 1.503 | 0.192 | 0.321 | 3.671 | 0.000 | 0.736 | 2.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 289 | 128 | 218 | 233 | 0 | 155 | 120 |
N.S. | 1 | 1.00 | 1.78 | 0.79 | 1.35 | 1.44 | 0.00 | 0.96 | 0.74 |
time (sec) |
N/A | 0.194 | 2.112 | 0.191 | 0.278 | 4.143 | 0.000 | 0.683 | 3.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 86 | 83 | 0 | 128 | 0 | 107 | 483 |
N.S. |
1 | 1.00 | 0.53 | 0.51 | 0.00 | 0.79 | 0.00 | 0.66 | 2.96 |
time (sec) |
N/A | 0.195 | 0.852 | 2.042 | 0.000 | 3.437 | 0.000 | 1.029 | 9.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 76 | 73 | 0 | 113 | 0 | 83 | 384 |
N.S. | 1 | 1.00 | 0.62 | 0.60 | 0.00 | 0.93 | 0.00 | 0.68 | 3.15 |
time (sec) |
N/A | 0.142 | 0.470 | 2.322 | 0.000 | 3.766 | 0.000 | 1.078 | 6.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 64 | 63 | 0 | 89 | 0 | 56 | 120 |
N.S. | 1 | 1.00 | 0.79 | 0.78 | 0.00 | 1.10 | 0.00 | 0.69 | 1.48 |
time (sec) |
N/A | 0.094 | 0.264 | 2.413 | 0.000 | 2.887 | 0.000 | 0.878 | 5.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 51 | 53 | 0 | 71 | 0 | 31 | 87 |
N.S. | 1 | 1.00 | 1.31 | 1.36 | 0.00 | 1.82 | 0.00 | 0.79 | 2.23 |
time (sec) |
N/A | 0.043 | 0.181 | 2.308 | 0.000 | 3.310 | 0.000 | 0.802 | 2.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 132 | 85 | 0 | 294 | 0 | 61 | -1 |
N.S. | 1 | 1.00 | 1.71 | 1.10 | 0.00 | 3.82 | 0.00 | 0.79 | -0.01 |
time (sec) |
N/A | 0.078 | 0.636 | 2.181 | 0.000 | 3.536 | 0.000 | 1.134 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | B | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 246 | 164 | 0 | 370 | 0 | 72 | -1 |
N.S. | 1 | 1.00 | 3.24 | 2.16 | 0.00 | 4.87 | 0.00 | 0.95 | -0.01 |
time (sec) |
N/A | 0.080 | 1.122 | 2.254 | 0.000 | 3.567 | 0.000 | 1.107 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 309 | 308 | 0 | 439 | 0 | 104 | -1 |
N.S. | 1 | 1.00 | 2.73 | 2.73 | 0.00 | 3.88 | 0.00 | 0.92 | -0.01 |
time (sec) |
N/A | 0.112 | 1.131 | 1.964 | 0.000 | 4.371 | 0.000 | 1.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-1) | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 88 | 85 | 0 | 157 | 0 | 109 | 606 |
N.S. |
1 | 1.00 | 0.51 | 0.50 | 0.00 | 0.92 | 0.00 | 0.64 | 3.54 |
time (sec) |
N/A | 0.310 | 1.662 | 2.467 | 0.000 | 4.051 | 0.000 | 1.129 | 14.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 78 | 75 | 0 | 140 | 0 | 85 | 503 |
N.S. | 1 | 1.00 | 0.61 | 0.59 | 0.00 | 1.09 | 0.00 | 0.66 | 3.93 |
time (sec) |
N/A | 0.229 | 1.265 | 2.193 | 0.000 | 4.129 | 0.000 | 1.006 | 7.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 66 | 65 | 0 | 113 | 0 | 58 | 384 |
N.S. | 1 | 1.00 | 0.78 | 0.76 | 0.00 | 1.33 | 0.00 | 0.68 | 4.52 |
time (sec) |
N/A | 0.145 | 0.780 | 2.319 | 0.000 | 3.877 | 0.000 | 1.027 | 6.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 55 | 55 | 0 | 91 | 0 | 33 | 93 |
N.S. | 1 | 1.00 | 1.34 | 1.34 | 0.00 | 2.22 | 0.00 | 0.80 | 2.27 |
time (sec) |
N/A | 0.067 | 0.460 | 2.197 | 0.000 | 2.429 | 0.000 | 0.955 | 5.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 123 | 173 | 145 | 0 | 371 | 0 | 82 | -1 |
N.S. | 1 | 1.05 | 1.48 | 1.24 | 0.00 | 3.17 | 0.00 | 0.70 | -0.01 |
time (sec) |
N/A | 0.159 | 0.920 | 2.238 | 0.000 | 3.205 | 0.000 | 1.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 124 | 184 | 144 | 0 | 400 | 0 | 109 | -1 |
N.S. | 1 | 1.10 | 1.63 | 1.27 | 0.00 | 3.54 | 0.00 | 0.96 | -0.01 |
time (sec) |
N/A | 0.161 | 1.453 | 2.401 | 0.000 | 2.865 | 0.000 | 2.569 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 130 | 359 | 230 | 0 | 463 | 0 | 106 | -1 |
N.S. | 1 | 1.11 | 3.07 | 1.97 | 0.00 | 3.96 | 0.00 | 0.91 | -0.01 |
time (sec) |
N/A | 0.159 | 2.486 | 2.427 | 0.000 | 3.238 | 0.000 | 1.391 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F(-1) | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 164 | 398 | 402 | 0 | 557 | 0 | 139 | -1 |
N.S. |
1 | 1.00 | 2.43 | 2.45 | 0.00 | 3.40 | 0.00 | 0.85 | -0.01 |
time (sec) |
N/A | 0.196 | 5.745 | 2.481 | 0.000 | 3.640 | 0.000 | 1.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-1) | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 88 | 85 | 0 | 174 | 0 | 109 | 710 |
N.S. |
1 | 1.00 | 0.51 | 0.50 | 0.00 | 1.02 | 0.00 | 0.64 | 4.15 |
time (sec) |
N/A | 0.303 | 2.554 | 2.397 | 0.000 | 2.683 | 0.000 | 1.261 | 14.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-1) | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 78 | 75 | 0 | 157 | 0 | 85 | 607 |
N.S. |
1 | 1.00 | 0.61 | 0.59 | 0.00 | 1.23 | 0.00 | 0.66 | 4.74 |
time (sec) |
N/A | 0.219 | 1.563 | 2.458 | 0.000 | 2.342 | 0.000 | 1.182 | 13.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 66 | 65 | 0 | 128 | 0 | 58 | 471 |
N.S. | 1 | 1.00 | 0.78 | 0.76 | 0.00 | 1.51 | 0.00 | 0.68 | 5.54 |
time (sec) |
N/A | 0.141 | 1.044 | 2.299 | 0.000 | 3.230 | 0.000 | 0.983 | 9.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 55 | 55 | 0 | 105 | 0 | 33 | 375 |
N.S. | 1 | 1.00 | 1.34 | 1.34 | 0.00 | 2.56 | 0.00 | 0.80 | 9.15 |
time (sec) |
N/A | 0.065 | 0.738 | 2.308 | 0.000 | 2.993 | 0.000 | 1.004 | 5.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 164 | 185 | 206 | 0 | 407 | 0 | 111 | -1 |
N.S. | 1 | 1.00 | 1.13 | 1.26 | 0.00 | 2.48 | 0.00 | 0.68 | -0.01 |
time (sec) |
N/A | 0.228 | 1.548 | 2.326 | 0.000 | 4.108 | 0.000 | 2.097 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 324 | 157 | 0 | 466 | 0 | 124 | -1 |
N.S. | 1 | 1.00 | 1.93 | 0.93 | 0.00 | 2.77 | 0.00 | 0.74 | -0.01 |
time (sec) |
N/A | 0.232 | 2.940 | 2.369 | 0.000 | 3.673 | 0.000 | 1.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F(-1) | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 263 | 206 | 0 | 475 | 0 | 133 | -1 |
N.S. |
1 | 1.00 | 1.51 | 1.18 | 0.00 | 2.73 | 0.00 | 0.76 | -0.01 |
time (sec) |
N/A | 0.244 | 4.590 | 2.520 | 0.000 | 3.433 | 0.000 | 1.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 142 | 86 | 83 | 175 | 95 | 0 | 108 | 164 |
N.S. |
1 | 1.00 | 0.61 | 0.58 | 1.23 | 0.67 | 0.00 | 0.76 | 1.15 |
time (sec) |
N/A | 0.160 | 0.771 | 2.323 | 0.506 | 2.735 | 0.000 | 0.960 | 6.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 74 | 73 | 147 | 83 | 0 | 84 | 125 |
N.S. | 1 | 1.00 | 0.69 | 0.68 | 1.36 | 0.77 | 0.00 | 0.78 | 1.16 |
time (sec) |
N/A | 0.132 | 0.430 | 2.046 | 0.533 | 2.672 | 0.000 | 0.891 | 4.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 54 | 63 | 118 | 54 | 0 | 60 | 77 |
N.S. | 1 | 1.00 | 0.75 | 0.88 | 1.64 | 0.75 | 0.00 | 0.83 | 1.07 |
time (sec) |
N/A | 0.105 | 0.245 | 2.462 | 0.518 | 3.719 | 0.000 | 0.813 | 2.367 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 29 | 43 | 90 | 49 | 0 | 59 | 40 |
N.S. | 1 | 1.00 | 0.74 | 1.10 | 2.31 | 1.26 | 0.00 | 1.51 | 1.03 |
time (sec) |
N/A | 0.072 | 0.142 | 2.549 | 0.525 | 3.388 | 0.000 | 0.772 | 1.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 155 | 107 | 0 | 291 | 0 | 64 | -1 |
N.S. | 1 | 1.00 | 1.74 | 1.20 | 0.00 | 3.27 | 0.00 | 0.72 | -0.01 |
time (sec) |
N/A | 0.113 | 0.501 | 2.290 | 0.000 | 3.776 | 0.000 | 0.585 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 183 | 266 | 0 | 357 | 0 | 97 | -1 |
N.S. | 1 | 1.00 | 1.50 | 2.18 | 0.00 | 2.93 | 0.00 | 0.80 | -0.01 |
time (sec) |
N/A | 0.148 | 1.407 | 2.231 | 0.000 | 4.091 | 0.000 | 0.627 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 306 | 471 | 0 | 435 | 0 | 128 | -1 |
N.S. | 1 | 1.00 | 1.96 | 3.02 | 0.00 | 2.79 | 0.00 | 0.82 | -0.01 |
time (sec) |
N/A | 0.180 | 3.009 | 2.264 | 0.000 | 3.205 | 0.000 | 0.680 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 84 | 85 | 202 | 111 | 0 | 121 | 188 |
N.S. |
1 | 1.00 | 0.54 | 0.55 | 1.30 | 0.72 | 0.00 | 0.78 | 1.21 |
time (sec) |
N/A | 0.223 | 0.932 | 2.213 | 0.506 | 2.812 | 0.000 | 1.039 | 6.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 68 | 75 | 175 | 88 | 0 | 99 | 136 |
N.S. |
1 | 1.00 | 0.55 | 0.61 | 1.42 | 0.72 | 0.00 | 0.80 | 1.11 |
time (sec) |
N/A | 0.193 | 0.416 | 2.210 | 0.508 | 2.741 | 0.000 | 0.935 | 5.542 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 60 | 53 | 118 | 78 | 0 | 60 | 134 |
N.S. | 1 | 1.00 | 0.67 | 0.60 | 1.33 | 0.88 | 0.00 | 0.67 | 1.51 |
time (sec) |
N/A | 0.153 | 0.259 | 2.461 | 0.509 | 4.022 | 0.000 | 0.805 | 5.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 55 | 53 | 117 | 65 | 0 | 62 | 94 |
N.S. | 1 | 1.00 | 1.34 | 1.29 | 2.85 | 1.59 | 0.00 | 1.51 | 2.29 |
time (sec) |
N/A | 0.070 | 0.155 | 2.493 | 0.529 | 3.114 | 0.000 | 0.763 | 5.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 259 | 131 | 0 | 359 | 0 | 93 | -1 |
N.S. | 1 | 1.00 | 1.88 | 0.95 | 0.00 | 2.60 | 0.00 | 0.67 | -0.01 |
time (sec) |
N/A | 0.196 | 2.159 | 2.295 | 0.000 | 3.377 | 0.000 | 0.702 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 365 | 320 | 0 | 399 | 0 | 129 | -1 |
N.S. | 1 | 1.00 | 2.16 | 1.89 | 0.00 | 2.36 | 0.00 | 0.76 | -0.01 |
time (sec) |
N/A | 0.243 | 1.392 | 2.460 | 0.000 | 4.569 | 0.000 | 0.677 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 203 | 434 | 551 | 0 | 527 | 0 | 160 | -1 |
N.S. | 1 | 1.00 | 2.14 | 2.71 | 0.00 | 2.60 | 0.00 | 0.79 | -0.00 |
time (sec) |
N/A | 0.271 | 2.412 | 2.420 | 0.000 | 3.958 | 0.000 | 0.692 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 78 | 85 | 230 | 117 | 0 | 126 | 492 |
N.S. |
1 | 1.00 | 0.46 | 0.50 | 1.36 | 0.69 | 0.00 | 0.75 | 2.91 |
time (sec) |
N/A | 0.276 | 0.623 | 2.656 | 0.525 | 1.976 | 0.000 | 1.106 | 10.238 |