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 | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 41 | 44 | 39 | 41 | 43 | 110 | 60 | 38 |
N.S. |
1 | 1.05 | 1.13 | 1.00 | 1.05 | 1.10 | 2.82 | 1.54 | 0.97 |
time (sec) |
N/A | 0.185 | 0.010 | 0.260 | 0.180 | 0.246 | 39.528 | 0.280 | 0.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 39 | 48 | 39 | 35 | 30 | 42 | 72 | 41 |
N.S. |
1 | 0.95 | 1.17 | 0.95 | 0.85 | 0.73 | 1.02 | 1.76 | 1.00 |
time (sec) |
N/A | 0.186 | 0.010 | 0.437 | 0.296 | 0.249 | 37.249 | 0.287 | 0.418 |
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 | 53 | 60 | 53 | 53 | 54 | 129 | 69 | 50 |
N.S. |
1 | 0.96 | 1.09 | 0.96 | 0.96 | 0.98 | 2.35 | 1.25 | 0.91 |
time (sec) |
N/A | 0.213 | 0.019 | 0.410 | 0.207 | 0.245 | 135.233 | 0.283 | 0.433 |
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 | 174 | 197 | 179 | 155 | 148 | 269 | 255 | 167 | 114 |
N.S. |
1 | 1.13 | 1.03 | 0.89 | 0.85 | 1.55 | 1.47 | 0.96 | 0.66 |
time (sec) |
N/A | 0.414 | 0.080 | 0.804 | 0.283 | 0.255 | 24.304 | 0.358 | 1.259 |
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 | 101 | 101 | 131 | 98 | 92 | 234 | 755 | 95 | 91 |
N.S. |
1 | 1.00 | 1.30 | 0.97 | 0.91 | 2.32 | 7.48 | 0.94 | 0.90 |
time (sec) |
N/A | 0.255 | 0.047 | 0.418 | 0.281 | 0.257 | 13.066 | 0.281 | 2.432 |
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 | 165 | 186 | 170 | 144 | 137 | 270 | 245 | 137 | 107 |
N.S. |
1 | 1.13 | 1.03 | 0.87 | 0.83 | 1.64 | 1.48 | 0.83 | 0.65 |
time (sec) |
N/A | 0.394 | 0.087 | 0.485 | 0.284 | 0.253 | 29.934 | 0.296 | 0.975 |
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 | 115 | 129 | 183 | 105 | 102 | 121 | 286 | 108 | 118 |
N.S. |
1 | 1.12 | 1.59 | 0.91 | 0.89 | 1.05 | 2.49 | 0.94 | 1.03 |
time (sec) |
N/A | 0.315 | 0.067 | 0.765 | 0.269 | 0.258 | 61.135 | 0.281 | 2.710 |
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 | 176 | 212 | 181 | 167 | 152 | 305 | 264 | 171 | 122 |
N.S. |
1 | 1.20 | 1.03 | 0.95 | 0.86 | 1.73 | 1.50 | 0.97 | 0.69 |
time (sec) |
N/A | 0.415 | 0.115 | 1.270 | 0.273 | 0.257 | 63.808 | 0.351 | 1.060 |
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 | 117 | 126 | 185 | 113 | 106 | 137 | 292 | 119 | 106 |
N.S. |
1 | 1.08 | 1.58 | 0.97 | 0.91 | 1.17 | 2.50 | 1.02 | 0.91 |
time (sec) |
N/A | 0.306 | 0.050 | 0.844 | 0.273 | 0.260 | 31.576 | 0.311 | 2.075 |
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 | 165 | 196 | 170 | 153 | 137 | 278 | 246 | 157 | 113 |
N.S. |
1 | 1.19 | 1.03 | 0.93 | 0.83 | 1.68 | 1.49 | 0.95 | 0.68 |
time (sec) |
N/A | 0.382 | 0.056 | 0.661 | 0.273 | 0.252 | 18.140 | 0.349 | 0.764 |
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 | 104 | 111 | 170 | 104 | 98 | 90 | 262 | 91 | 99 |
N.S. |
1 | 1.07 | 1.63 | 1.00 | 0.94 | 0.87 | 2.52 | 0.88 | 0.95 |
time (sec) |
N/A | 0.290 | 0.074 | 0.494 | 0.270 | 0.257 | 25.230 | 0.283 | 2.022 |
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 | 174 | 207 | 179 | 164 | 147 | 301 | 264 | 161 | 120 |
N.S. |
1 | 1.19 | 1.03 | 0.94 | 0.84 | 1.73 | 1.52 | 0.93 | 0.69 |
time (sec) |
N/A | 0.403 | 0.075 | 0.638 | 0.284 | 0.285 | 49.046 | 0.412 | 0.786 |
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 | 124 | 149 | 121 | 151 | 169 | 129 | 243 | 145 | 150 |
N.S. |
1 | 1.20 | 0.98 | 1.22 | 1.36 | 1.04 | 1.96 | 1.17 | 1.21 |
time (sec) |
N/A | 0.779 | 0.111 | 1.043 | 0.376 | 0.263 | 147.668 | 0.278 | 1.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 154 | 171 | 141 | 11449 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.92 | 74.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.774 | 0.117 | 3.690 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 85 | 110 | 126 | 91 | 194 | 100 | 112 |
N.S. |
1 | 1.00 | 0.94 | 1.22 | 1.40 | 1.01 | 2.16 | 1.11 | 1.24 |
time (sec) |
N/A | 0.451 | 0.073 | 1.474 | 0.372 | 0.265 | 50.123 | 0.282 | 0.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 113 | 107 | 140 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.03 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.481 | 0.092 | 5.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 154 | 177 | 201 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.696 | 0.182 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 100 | 107 | 125 | 11455 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.25 | 114.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.488 | 0.194 | 4.777 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 86 | 98 | 118 | 110 | 102 | 207 | 0 | 152 |
N.S. |
1 | 0.99 | 1.13 | 1.36 | 1.26 | 1.17 | 2.38 | 0.00 | 1.75 |
time (sec) |
N/A | 0.504 | 0.101 | 0.785 | 0.372 | 0.281 | 71.423 | 0.000 | 0.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 154 | 155 | 167 | 11496 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.08 | 74.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.740 | 0.458 | 5.340 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 240 | 253 | 346 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.435 | 0.591 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 147 | 166 | 170 | 935 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.16 | 6.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.883 | 0.145 | 7.574 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 154 | 224 | 275 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.61 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.704 | 0.077 | 9.008 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 232 | 267 | 421 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.007 | 0.288 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 133 | 156 | 240 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.741 | 0.447 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 146 | 153 | 196 | 11581 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.34 | 79.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.881 | 0.372 | 4.884 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 407 | 50 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 22.61 | 2.78 | 0.00 | 1.11 | 1.11 |
time (sec) |
N/A | 0.178 | 2.233 | 0.194 | 4.058 | 0.261 | 0.000 | 0.435 | 0.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 304 | 34 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 16.89 | 1.89 | 0.00 | 1.11 | 1.11 |
time (sec) |
N/A | 0.179 | 1.528 | 0.186 | 2.368 | 0.271 | 0.000 | 0.532 | 0.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.217 | 0.093 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 20 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.00 | 1.11 | 1.11 |
time (sec) |
N/A | 0.176 | 0.483 | 0.178 | 0.248 | 0.259 | 0.000 | 0.288 | 0.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 132 | 36 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 7.33 | 2.00 | 0.00 | 1.11 | 1.11 |
time (sec) |
N/A | 0.178 | 0.495 | 0.187 | 0.385 | 0.240 | 0.000 | 0.282 | 0.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 48 | 55 | 46 | 45 | 41 | 46 | 81 | 45 |
N.S. |
1 | 0.96 | 1.10 | 0.92 | 0.90 | 0.82 | 0.92 | 1.62 | 0.90 |
time (sec) |
N/A | 0.210 | 0.028 | 1.278 | 0.264 | 0.262 | 0.142 | 0.281 | 0.436 |
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 | 43 | 41 | 48 | 47 | 43 | 40 | 41 | 69 | 40 |
N.S. |
1 | 0.95 | 1.12 | 1.09 | 1.00 | 0.93 | 0.95 | 1.60 | 0.93 |
time (sec) |
N/A | 0.207 | 0.022 | 1.010 | 0.192 | 0.258 | 0.121 | 0.271 | 0.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 35 | 44 | 37 | 36 | 31 | 36 | 72 | 36 |
N.S. |
1 | 0.90 | 1.13 | 0.95 | 0.92 | 0.79 | 0.92 | 1.85 | 0.92 |
time (sec) |
N/A | 0.181 | 0.022 | 1.250 | 0.259 | 0.243 | 0.108 | 0.274 | 0.384 |
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 | 27 | 27 | 27 | 27 | 27 | 25 | 22 | 46 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.00 | 0.93 | 0.81 | 1.70 | 0.93 |
time (sec) |
N/A | 0.144 | 0.004 | 1.223 | 0.172 | 0.244 | 0.081 | 0.278 | 0.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 42 | 39 | 87 | 0 | 0 | 0 | 72 | 32 |
N.S. |
1 | 1.08 | 1.00 | 2.23 | 0.00 | 0.00 | 0.00 | 1.85 | 0.82 |
time (sec) |
N/A | 0.242 | 0.010 | 1.332 | 0.000 | 0.000 | 0.000 | 0.310 | 0.372 |
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 | 37 | 36 | 38 | 41 | 36 | 39 | 43 |
N.S. |
1 | 1.00 | 1.09 | 1.06 | 1.12 | 1.21 | 1.06 | 1.15 | 1.26 |
time (sec) |
N/A | 0.179 | 0.025 | 0.694 | 0.187 | 0.244 | 0.278 | 0.270 | 0.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 44 | 48 | 41 | 42 | 37 | 44 | 60 | 50 |
N.S. |
1 | 1.02 | 1.12 | 0.95 | 0.98 | 0.86 | 1.02 | 1.40 | 1.16 |
time (sec) |
N/A | 0.194 | 0.025 | 1.233 | 0.263 | 0.244 | 0.298 | 0.277 | 0.400 |
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 | 55 | 54 | 60 | 45 | 54 | 55 | 60 | 51 | 56 |
N.S. |
1 | 0.98 | 1.09 | 0.82 | 0.98 | 1.00 | 1.09 | 0.93 | 1.02 |
time (sec) |
N/A | 0.222 | 0.026 | 1.057 | 0.184 | 0.256 | 0.355 | 0.274 | 0.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 139 | 111 | 141 | 134 | 125 | 144 | 0 | 140 |
N.S. |
1 | 1.14 | 0.91 | 1.16 | 1.10 | 1.02 | 1.18 | 0.00 | 1.15 |
time (sec) |
N/A | 0.846 | 0.098 | 3.218 | 0.267 | 0.257 | 0.202 | 0.000 | 0.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 149 | 152 | 358 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.00 | 2.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.764 | 0.399 | 3.776 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 81 | 73 | 105 | 104 | 88 | 97 | 0 | 98 |
N.S. |
1 | 0.99 | 0.89 | 1.28 | 1.27 | 1.07 | 1.18 | 0.00 | 1.20 |
time (sec) |
N/A | 0.511 | 0.059 | 3.170 | 0.269 | 0.263 | 0.156 | 0.000 | 0.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 89 | 105 | 308 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.27 | 3.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.457 | 0.128 | 3.619 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 148 | 173 | 203 | 1106 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 1.37 | 7.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.731 | 0.166 | 0.549 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 110 | 107 | 142 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 1.11 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.497 | 0.115 | 6.113 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 85 | 99 | 103 | 120 | 109 | 117 | 137 | 143 |
N.S. |
1 | 1.01 | 1.18 | 1.23 | 1.43 | 1.30 | 1.39 | 1.63 | 1.70 |
time (sec) |
N/A | 0.434 | 0.091 | 3.085 | 0.268 | 0.253 | 0.337 | 0.294 | 2.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 214 | 301 | 253 | 480 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.41 | 1.18 | 2.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.600 | 0.726 | 14.518 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 229 | 239 | 336 | 2634 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.47 | 11.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.640 | 0.961 | 2.888 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 147 | 174 | 405 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.20 | 2.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.874 | 0.293 | 8.159 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 119 | 132 | 215 | 2028 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.81 | 17.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.660 | 0.277 | 102.875 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 230 | 263 | 422 | 2225 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 1.83 | 9.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.033 | 0.274 | 26.327 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 151 | 222 | 275 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.63 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.713 | 0.126 | 9.309 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 162 | 178 | 321 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.21 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.914 | 0.319 | 14.681 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 52 | 34 | 30 | 31 | 27 | 39 | 31 | 31 |
N.S. |
1 | 1.02 | 0.67 | 0.59 | 0.61 | 0.53 | 0.76 | 0.61 | 0.61 |
time (sec) |
N/A | 0.180 | 0.017 | 0.162 | 0.302 | 0.247 | 1.131 | 0.281 | 0.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 43 | 28 | 25 | 26 | 20 | 32 | 26 | 26 |
N.S. |
1 | 1.02 | 0.67 | 0.60 | 0.62 | 0.48 | 0.76 | 0.62 | 0.62 |
time (sec) |
N/A | 0.169 | 0.014 | 0.039 | 0.280 | 0.240 | 0.632 | 0.275 | 0.377 |
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 | 22 | 29 | 18 | 17 | 16 | 14 | 19 | 16 | 16 |
N.S. |
1 | 1.32 | 0.82 | 0.77 | 0.73 | 0.64 | 0.86 | 0.73 | 0.73 |
time (sec) |
N/A | 0.155 | 0.021 | 0.031 | 0.279 | 0.253 | 0.396 | 0.266 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 37 | 31 | 24 | 35 | 0 | 0 | 0 | 24 |
N.S. |
1 | 1.19 | 1.00 | 0.77 | 1.13 | 0.00 | 0.00 | 0.00 | 0.77 |
time (sec) |
N/A | 0.222 | 0.007 | 1.046 | 0.279 | 0.000 | 0.000 | 0.000 | 0.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 32 | 30 | 19 | 21 | 17 | 94 | 21 | 21 |
N.S. |
1 | 1.19 | 1.11 | 0.70 | 0.78 | 0.63 | 3.48 | 0.78 | 0.78 |
time (sec) |
N/A | 0.168 | 0.012 | 0.037 | 0.279 | 0.248 | 0.557 | 0.279 | 0.366 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 43 | 34 | 27 | 26 | 26 | 160 | 26 | 24 |
N.S. |
1 | 1.02 | 0.81 | 0.64 | 0.62 | 0.62 | 3.81 | 0.62 | 0.57 |
time (sec) |
N/A | 0.172 | 0.014 | 0.045 | 0.270 | 0.250 | 1.346 | 0.271 | 0.375 |
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 | 35 | 30 | 25 | 24 | 24 | 85 | 24 | 24 |
N.S. |
1 | 0.97 | 0.83 | 0.69 | 0.67 | 0.67 | 2.36 | 0.67 | 0.67 |
time (sec) |
N/A | 0.178 | 0.019 | 0.036 | 0.195 | 0.274 | 1.010 | 0.270 | 0.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 25 | 20 | 19 | 19 | 24 | 19 | 0 |
N.S. |
1 | 0.97 | 0.86 | 0.69 | 0.66 | 0.66 | 0.83 | 0.66 | 0.00 |
time (sec) |
N/A | 0.177 | 0.013 | 0.036 | 0.193 | 0.255 | 0.606 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 17 | 16 | 16 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.80 | 0.80 | 0.85 | 0.80 | 0.80 |
time (sec) |
N/A | 0.158 | 0.009 | 0.055 | 0.198 | 0.240 | 0.136 | 0.266 | 0.364 |
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 | 22 | 22 | 22 | 19 | 18 | 26 | 20 | 18 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.18 | 0.91 | 0.82 | 1.00 |
time (sec) |
N/A | 0.159 | 0.015 | 0.196 | 0.202 | 0.255 | 0.404 | 0.271 | 0.383 |
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 | 37 | 34 | 31 | 26 | 25 | 33 | 143 | 28 | 27 |
N.S. |
1 | 0.92 | 0.84 | 0.70 | 0.68 | 0.89 | 3.86 | 0.76 | 0.73 |
time (sec) |
N/A | 0.178 | 0.023 | 0.310 | 0.190 | 0.259 | 1.355 | 0.271 | 0.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 37 | 33 | 57 | 50 | 0 | 0 | 0 | 25 |
N.S. |
1 | 1.12 | 1.00 | 1.73 | 1.52 | 0.00 | 0.00 | 0.00 | 0.76 |
time (sec) |
N/A | 0.226 | 0.010 | 0.882 | 0.290 | 0.000 | 0.000 | 0.000 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 37 | 32 | 75 | 0 | 63 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.82 | 1.92 | 0.00 | 1.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.235 | 0.016 | 1.899 | 0.000 | 0.267 | 0.000 | 0.000 | 0.000 |