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 | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 136 | 112 | 127 | 117 | 441 | 0 | 126 | 158 |
N.S. |
1 | 1.01 | 0.83 | 0.94 | 0.87 | 3.27 | 0.00 | 0.93 | 1.17 |
time (sec) |
N/A | 0.473 | 0.065 | 3.450 | 0.285 | 0.319 | 0.000 | 0.285 | 6.127 |
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 | 185 | 186 | 139 | 140 | 165 | 574 | 357 | 157 | 232 |
N.S. |
1 | 1.01 | 0.75 | 0.76 | 0.89 | 3.10 | 1.93 | 0.85 | 1.25 |
time (sec) |
N/A | 0.577 | 0.070 | 3.463 | 0.290 | 0.283 | 98.075 | 0.295 | 6.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 161 | 126 | 115 | 136 | 480 | 282 | 122 | 0 |
N.S. |
1 | 1.04 | 0.81 | 0.74 | 0.88 | 3.10 | 1.82 | 0.79 | 0.00 |
time (sec) |
N/A | 0.500 | 0.049 | 3.471 | 0.286 | 0.281 | 87.259 | 0.302 | 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 | 136 | 148 | 122 | 123 | 146 | 447 | 304 | 128 | 195 |
N.S. |
1 | 1.09 | 0.90 | 0.90 | 1.07 | 3.29 | 2.24 | 0.94 | 1.43 |
time (sec) |
N/A | 0.468 | 0.062 | 3.421 | 0.289 | 0.279 | 74.789 | 0.291 | 6.034 |
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 | 119 | 127 | 99 | 97 | 111 | 357 | 178 | 97 | 0 |
N.S. |
1 | 1.07 | 0.83 | 0.82 | 0.93 | 3.00 | 1.50 | 0.82 | 0.00 |
time (sec) |
N/A | 0.355 | 0.070 | 3.493 | 0.284 | 0.285 | 7.835 | 0.281 | 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 | 116 | 127 | 104 | 98 | 122 | 346 | 184 | 106 | 163 |
N.S. |
1 | 1.09 | 0.90 | 0.84 | 1.05 | 2.98 | 1.59 | 0.91 | 1.41 |
time (sec) |
N/A | 0.266 | 0.067 | 3.433 | 0.279 | 0.281 | 3.412 | 0.293 | 5.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 144 | 117 | 130 | 133 | 488 | 0 | 128 | 0 |
N.S. |
1 | 1.11 | 0.90 | 1.00 | 1.02 | 3.75 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.382 | 0.070 | 3.450 | 0.284 | 0.317 | 0.000 | 0.297 | 0.000 |
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 | 144 | 157 | 141 | 125 | 152 | 524 | 0 | 141 | 202 |
N.S. |
1 | 1.09 | 0.98 | 0.87 | 1.06 | 3.64 | 0.00 | 0.98 | 1.40 |
time (sec) |
N/A | 0.569 | 0.062 | 3.416 | 0.299 | 0.311 | 0.000 | 0.303 | 6.257 |
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 | 174 | 188 | 147 | 169 | 172 | 696 | 0 | 162 | 229 |
N.S. |
1 | 1.08 | 0.84 | 0.97 | 0.99 | 4.00 | 0.00 | 0.93 | 1.32 |
time (sec) |
N/A | 0.646 | 0.096 | 3.595 | 0.287 | 0.338 | 0.000 | 0.307 | 6.387 |
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 | 22 | 20 | 19 | 18 | 24 | 15 | 25 | 20 |
N.S. |
1 | 1.10 | 1.00 | 0.95 | 0.90 | 1.20 | 0.75 | 1.25 | 1.00 |
time (sec) |
N/A | 0.187 | 0.006 | 3.472 | 0.199 | 0.300 | 0.035 | 0.290 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 29 | 18 | 15 | 22 | 14 | 22 | 17 | 14 |
N.S. |
1 | 1.26 | 0.78 | 0.65 | 0.96 | 0.61 | 0.96 | 0.74 | 0.61 |
time (sec) |
N/A | 0.187 | 0.017 | 3.495 | 0.199 | 0.271 | 0.110 | 0.288 | 0.105 |
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 | 25 | 33 | 25 | 21 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.32 | 1.00 | 0.84 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.177 | 0.012 | 3.491 | 0.289 | 0.280 | 0.037 | 0.285 | 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 | 30 | 30 | 30 | 25 | 24 | 24 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.73 | 0.80 | 0.80 |
time (sec) |
N/A | 0.181 | 0.006 | 3.444 | 0.293 | 0.277 | 0.041 | 0.288 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 210 | 233 | 213 | 452 | 384 | 244 | 289 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.01 | 2.15 | 1.83 | 1.16 | 1.38 |
time (sec) |
N/A | 0.405 | 0.097 | 3.470 | 0.274 | 0.274 | 0.463 | 0.281 | 5.914 |
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 | 172 | 172 | 162 | 185 | 172 | 368 | 337 | 195 | 243 |
N.S. |
1 | 1.00 | 0.94 | 1.08 | 1.00 | 2.14 | 1.96 | 1.13 | 1.41 |
time (sec) |
N/A | 0.358 | 0.076 | 3.557 | 0.277 | 0.280 | 0.446 | 0.288 | 5.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 128 | 137 | 133 | 286 | 185 | 148 | 193 |
N.S. |
1 | 1.00 | 0.94 | 1.01 | 0.98 | 2.10 | 1.36 | 1.09 | 1.42 |
time (sec) |
N/A | 0.322 | 0.065 | 3.491 | 0.285 | 0.292 | 0.405 | 0.284 | 5.576 |
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 | 98 | 94 | 94 | 236 | 160 | 103 | 96 |
N.S. |
1 | 1.00 | 0.98 | 0.94 | 0.94 | 2.36 | 1.60 | 1.03 | 0.96 |
time (sec) |
N/A | 0.264 | 0.052 | 3.501 | 0.284 | 0.296 | 0.365 | 0.301 | 5.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 83 | 79 | 80 | 211 | 150 | 84 | 76 |
N.S. |
1 | 1.00 | 0.99 | 0.94 | 0.95 | 2.51 | 1.79 | 1.00 | 0.90 |
time (sec) |
N/A | 0.285 | 0.045 | 3.468 | 0.278 | 0.284 | 0.515 | 0.301 | 5.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 83 | 79 | 79 | 216 | 151 | 80 | 80 |
N.S. |
1 | 1.00 | 1.01 | 0.96 | 0.96 | 2.63 | 1.84 | 0.98 | 0.98 |
time (sec) |
N/A | 0.283 | 0.055 | 3.493 | 0.281 | 0.287 | 0.989 | 0.274 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 103 | 94 | 97 | 246 | 167 | 103 | 94 |
N.S. |
1 | 1.00 | 0.99 | 0.90 | 0.93 | 2.37 | 1.61 | 0.99 | 0.90 |
time (sec) |
N/A | 0.296 | 0.060 | 3.425 | 0.277 | 0.274 | 2.246 | 0.278 | 5.986 |
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 | 137 | 137 | 139 | 129 | 134 | 292 | 301 | 148 | 127 |
N.S. |
1 | 1.00 | 1.01 | 0.94 | 0.98 | 2.13 | 2.20 | 1.08 | 0.93 |
time (sec) |
N/A | 0.349 | 0.078 | 3.480 | 0.291 | 0.283 | 5.860 | 0.311 | 6.017 |
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 | 175 | 175 | 174 | 163 | 175 | 374 | 354 | 197 | 161 |
N.S. |
1 | 1.00 | 0.99 | 0.93 | 1.00 | 2.14 | 2.02 | 1.13 | 0.92 |
time (sec) |
N/A | 0.372 | 0.096 | 3.462 | 0.292 | 0.297 | 24.351 | 0.327 | 5.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 211 | 211 | 201 | 214 | 458 | 398 | 244 | 197 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.01 | 2.17 | 1.89 | 1.16 | 0.93 |
time (sec) |
N/A | 0.422 | 0.113 | 3.505 | 0.288 | 0.281 | 38.915 | 0.296 | 5.863 |
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 | 240 | 248 | 227 | 229 | 227 | 572 | 444 | 246 | 413 |
N.S. |
1 | 1.03 | 0.95 | 0.95 | 0.95 | 2.38 | 1.85 | 1.02 | 1.72 |
time (sec) |
N/A | 0.527 | 0.080 | 3.591 | 0.274 | 0.295 | 1.155 | 0.307 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 208 | 187 | 182 | 183 | 478 | 257 | 196 | 288 |
N.S. |
1 | 1.03 | 0.93 | 0.90 | 0.91 | 2.37 | 1.27 | 0.97 | 1.43 |
time (sec) |
N/A | 0.472 | 0.069 | 3.441 | 0.294 | 0.291 | 1.078 | 0.279 | 5.778 |
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 | 163 | 165 | 148 | 139 | 140 | 418 | 221 | 148 | 153 |
N.S. |
1 | 1.01 | 0.91 | 0.85 | 0.86 | 2.56 | 1.36 | 0.91 | 0.94 |
time (sec) |
N/A | 0.459 | 0.056 | 3.458 | 0.281 | 0.281 | 0.977 | 0.373 | 5.866 |
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 | 118 | 126 | 122 | 114 | 117 | 364 | 201 | 123 | 113 |
N.S. |
1 | 1.07 | 1.03 | 0.97 | 0.99 | 3.08 | 1.70 | 1.04 | 0.96 |
time (sec) |
N/A | 0.351 | 0.058 | 3.465 | 0.275 | 0.305 | 0.804 | 0.393 | 0.104 |
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 | 112 | 120 | 115 | 107 | 117 | 354 | 197 | 120 | 112 |
N.S. |
1 | 1.07 | 1.03 | 0.96 | 1.04 | 3.16 | 1.76 | 1.07 | 1.00 |
time (sec) |
N/A | 0.368 | 0.040 | 3.469 | 0.288 | 0.271 | 2.034 | 0.294 | 6.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 127 | 125 | 116 | 130 | 378 | 212 | 121 | 119 |
N.S. |
1 | 1.05 | 1.03 | 0.96 | 1.07 | 3.12 | 1.75 | 1.00 | 0.98 |
time (sec) |
N/A | 0.388 | 0.051 | 3.462 | 0.282 | 0.281 | 5.298 | 0.288 | 0.149 |
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 | 152 | 158 | 151 | 137 | 151 | 438 | 226 | 148 | 145 |
N.S. |
1 | 1.04 | 0.99 | 0.90 | 0.99 | 2.88 | 1.49 | 0.97 | 0.95 |
time (sec) |
N/A | 0.570 | 0.058 | 3.461 | 0.277 | 0.273 | 19.290 | 0.306 | 6.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 189 | 195 | 190 | 174 | 194 | 488 | 0 | 197 | 181 |
N.S. |
1 | 1.03 | 1.01 | 0.92 | 1.03 | 2.58 | 0.00 | 1.04 | 0.96 |
time (sec) |
N/A | 0.668 | 0.070 | 3.460 | 0.303 | 0.261 | 0.000 | 0.285 | 5.964 |
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 | 230 | 236 | 230 | 210 | 238 | 582 | 0 | 247 | 219 |
N.S. |
1 | 1.03 | 1.00 | 0.91 | 1.03 | 2.53 | 0.00 | 1.07 | 0.95 |
time (sec) |
N/A | 0.761 | 0.079 | 3.489 | 0.286 | 0.270 | 0.000 | 0.314 | 5.613 |
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 | 287 | 298 | 272 | 268 | 281 | 762 | 503 | 294 | 506 |
N.S. |
1 | 1.04 | 0.95 | 0.93 | 0.98 | 2.66 | 1.75 | 1.02 | 1.76 |
time (sec) |
N/A | 0.859 | 0.110 | 3.619 | 0.281 | 0.267 | 19.388 | 0.310 | 5.587 |
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 | 247 | 258 | 232 | 219 | 237 | 668 | 316 | 244 | 348 |
N.S. |
1 | 1.04 | 0.94 | 0.89 | 0.96 | 2.70 | 1.28 | 0.99 | 1.41 |
time (sec) |
N/A | 0.782 | 0.090 | 3.516 | 0.295 | 0.289 | 17.925 | 0.278 | 0.116 |
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 | 207 | 216 | 176 | 177 | 193 | 614 | 280 | 195 | 206 |
N.S. |
1 | 1.04 | 0.85 | 0.86 | 0.93 | 2.97 | 1.35 | 0.94 | 1.00 |
time (sec) |
N/A | 0.643 | 0.105 | 3.503 | 0.298 | 0.273 | 15.945 | 0.286 | 5.616 |
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 | 167 | 178 | 156 | 151 | 169 | 555 | 260 | 169 | 163 |
N.S. |
1 | 1.07 | 0.93 | 0.90 | 1.01 | 3.32 | 1.56 | 1.01 | 0.98 |
time (sec) |
N/A | 0.524 | 0.100 | 3.489 | 0.285 | 0.259 | 5.710 | 0.294 | 5.512 |
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 | 147 | 164 | 141 | 139 | 154 | 504 | 243 | 146 | 148 |
N.S. |
1 | 1.12 | 0.96 | 0.95 | 1.05 | 3.43 | 1.65 | 0.99 | 1.01 |
time (sec) |
N/A | 0.367 | 0.076 | 3.499 | 0.282 | 0.286 | 3.400 | 0.278 | 5.543 |
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 | 153 | 170 | 155 | 140 | 161 | 517 | 250 | 150 | 149 |
N.S. |
1 | 1.11 | 1.01 | 0.92 | 1.05 | 3.38 | 1.63 | 0.98 | 0.97 |
time (sec) |
N/A | 0.423 | 0.084 | 3.516 | 0.288 | 0.283 | 11.076 | 0.285 | 0.170 |
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 | 168 | 186 | 169 | 152 | 181 | 570 | 0 | 167 | 166 |
N.S. |
1 | 1.11 | 1.01 | 0.90 | 1.08 | 3.39 | 0.00 | 0.99 | 0.99 |
time (sec) |
N/A | 0.511 | 0.098 | 3.513 | 0.275 | 0.277 | 0.000 | 0.316 | 5.715 |
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 | 196 | 210 | 196 | 176 | 202 | 628 | 0 | 194 | 192 |
N.S. |
1 | 1.07 | 1.00 | 0.90 | 1.03 | 3.20 | 0.00 | 0.99 | 0.98 |
time (sec) |
N/A | 0.836 | 0.078 | 3.516 | 0.280 | 0.274 | 0.000 | 0.279 | 5.595 |
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 | 234 | 248 | 234 | 212 | 247 | 678 | 0 | 245 | 230 |
N.S. |
1 | 1.06 | 1.00 | 0.91 | 1.06 | 2.90 | 0.00 | 1.05 | 0.98 |
time (sec) |
N/A | 1.056 | 0.090 | 3.639 | 0.289 | 0.270 | 0.000 | 0.299 | 5.612 |
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 | 277 | 291 | 276 | 248 | 291 | 772 | 0 | 295 | 268 |
N.S. |
1 | 1.05 | 1.00 | 0.90 | 1.05 | 2.79 | 0.00 | 1.06 | 0.97 |
time (sec) |
N/A | 1.196 | 0.108 | 3.499 | 0.297 | 0.263 | 0.000 | 0.298 | 5.645 |
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 | 214 | 219 | 158 | 142 | 347 | 177 | 442 | 259 | 186 |
N.S. |
1 | 1.02 | 0.74 | 0.66 | 1.62 | 0.83 | 2.07 | 1.21 | 0.87 |
time (sec) |
N/A | 0.503 | 0.126 | 3.515 | 0.204 | 0.295 | 0.461 | 0.290 | 5.823 |
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 | 167 | 171 | 122 | 111 | 263 | 134 | 340 | 193 | 146 |
N.S. |
1 | 1.02 | 0.73 | 0.66 | 1.57 | 0.80 | 2.04 | 1.16 | 0.87 |
time (sec) |
N/A | 0.444 | 0.092 | 3.487 | 0.197 | 0.262 | 0.378 | 0.312 | 5.778 |
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 | 121 | 126 | 89 | 82 | 180 | 94 | 238 | 127 | 103 |
N.S. |
1 | 1.04 | 0.74 | 0.68 | 1.49 | 0.78 | 1.97 | 1.05 | 0.85 |
time (sec) |
N/A | 0.348 | 0.071 | 3.470 | 0.275 | 0.254 | 0.294 | 0.269 | 5.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 108 | 86 | 82 | 122 | 205 | 134 | 125 | 99 |
N.S. |
1 | 1.05 | 0.83 | 0.80 | 1.18 | 1.99 | 1.30 | 1.21 | 0.96 |
time (sec) |
N/A | 0.362 | 0.113 | 3.516 | 0.469 | 0.286 | 4.479 | 0.285 | 6.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 101 | 92 | 88 | 104 | 210 | 138 | 113 | 99 |
N.S. |
1 | 1.01 | 0.92 | 0.88 | 1.04 | 2.10 | 1.38 | 1.13 | 0.99 |
time (sec) |
N/A | 0.440 | 0.182 | 3.537 | 0.206 | 0.309 | 12.825 | 0.295 | 6.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 145 | 102 | 95 | 128 | 221 | 194 | 140 | 133 |
N.S. |
1 | 1.27 | 0.89 | 0.83 | 1.12 | 1.94 | 1.70 | 1.23 | 1.17 |
time (sec) |
N/A | 0.437 | 0.210 | 3.561 | 0.203 | 0.315 | 33.693 | 0.288 | 6.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 182 | 126 | 116 | 193 | 261 | 303 | 228 | 199 |
N.S. |
1 | 1.25 | 0.86 | 0.79 | 1.32 | 1.79 | 2.08 | 1.56 | 1.36 |
time (sec) |
N/A | 0.463 | 0.243 | 3.572 | 0.196 | 0.294 | 40.705 | 0.288 | 7.622 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 218 | 159 | 148 | 275 | 341 | 444 | 356 | 277 |
N.S. |
1 | 1.12 | 0.82 | 0.76 | 1.41 | 1.75 | 2.28 | 1.83 | 1.42 |
time (sec) |
N/A | 0.497 | 0.367 | 3.568 | 0.192 | 0.354 | 103.418 | 0.293 | 7.854 |
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 | 245 | 221 | 218 | 169 | 339 | 414 | 243 | 218 | 0 |
N.S. |
1 | 0.90 | 0.89 | 0.69 | 1.38 | 1.69 | 0.99 | 0.89 | 0.00 |
time (sec) |
N/A | 0.443 | 0.977 | 3.699 | 0.201 | 0.360 | 0.613 | 0.316 | 0.000 |
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 | 194 | 191 | 159 | 137 | 255 | 329 | 199 | 170 | 0 |
N.S. |
1 | 0.98 | 0.82 | 0.71 | 1.31 | 1.70 | 1.03 | 0.88 | 0.00 |
time (sec) |
N/A | 0.406 | 0.630 | 3.649 | 0.197 | 0.313 | 0.571 | 0.310 | 0.000 |
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 | 145 | 161 | 129 | 108 | 174 | 250 | 155 | 125 | 0 |
N.S. |
1 | 1.11 | 0.89 | 0.74 | 1.20 | 1.72 | 1.07 | 0.86 | 0.00 |
time (sec) |
N/A | 0.333 | 0.335 | 3.685 | 0.200 | 0.297 | 0.407 | 0.307 | 0.000 |
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 | 117 | 132 | 105 | 93 | 118 | 216 | 246 | 113 | 0 |
N.S. |
1 | 1.13 | 0.90 | 0.79 | 1.01 | 1.85 | 2.10 | 0.97 | 0.00 |
time (sec) |
N/A | 0.340 | 0.193 | 3.608 | 0.214 | 0.269 | 0.918 | 0.317 | 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 | 110 | 120 | 95 | 83 | 102 | 210 | 196 | 171 | 143 |
N.S. |
1 | 1.09 | 0.86 | 0.75 | 0.93 | 1.91 | 1.78 | 1.55 | 1.30 |
time (sec) |
N/A | 0.336 | 0.194 | 3.605 | 0.196 | 0.284 | 1.088 | 0.363 | 7.205 |
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 | 118 | 136 | 98 | 90 | 128 | 221 | 427 | 319 | 105 |
N.S. |
1 | 1.15 | 0.83 | 0.76 | 1.08 | 1.87 | 3.62 | 2.70 | 0.89 |
time (sec) |
N/A | 0.342 | 0.228 | 3.555 | 0.199 | 0.279 | 1.490 | 0.331 | 6.653 |
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 | 140 | 156 | 103 | 92 | 193 | 100 | 891 | 548 | 124 |
N.S. |
1 | 1.11 | 0.74 | 0.66 | 1.38 | 0.71 | 6.36 | 3.91 | 0.89 |
time (sec) |
N/A | 0.438 | 0.205 | 3.583 | 0.197 | 0.313 | 2.123 | 0.324 | 6.072 |
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 | 189 | 186 | 134 | 123 | 275 | 141 | 1642 | 660 | 171 |
N.S. |
1 | 0.98 | 0.71 | 0.65 | 1.46 | 0.75 | 8.69 | 3.49 | 0.90 |
time (sec) |
N/A | 0.464 | 0.295 | 3.677 | 0.192 | 0.396 | 2.922 | 0.336 | 6.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 381 | 310 | 259 | 236 | 1221 | 987 | 0 | 342 | 0 |
N.S. |
1 | 0.81 | 0.68 | 0.62 | 3.20 | 2.59 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.650 | 1.262 | 3.750 | 0.224 | 0.529 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 279 | 245 | 215 | 196 | 986 | 816 | 0 | 265 | 0 |
N.S. |
1 | 0.88 | 0.77 | 0.70 | 3.53 | 2.92 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.548 | 1.008 | 3.672 | 0.229 | 0.434 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 230 | 178 | 164 | 753 | 653 | 6467 | 203 | 0 |
N.S. |
1 | 1.10 | 0.85 | 0.78 | 3.59 | 3.11 | 30.80 | 0.97 | 0.00 |
time (sec) |
N/A | 0.613 | 1.005 | 3.646 | 0.233 | 0.400 | 94.777 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 220 | 147 | 139 | 533 | 491 | 3803 | 160 | 0 |
N.S. |
1 | 1.23 | 0.82 | 0.78 | 2.98 | 2.74 | 21.25 | 0.89 | 0.00 |
time (sec) |
N/A | 0.562 | 0.592 | 3.585 | 0.247 | 0.385 | 66.249 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 183 | 98 | 89 | 335 | 141 | 2088 | 131 | 0 |
N.S. |
1 | 1.37 | 0.73 | 0.66 | 2.50 | 1.05 | 15.58 | 0.98 | 0.00 |
time (sec) |
N/A | 0.522 | 0.421 | 3.575 | 0.202 | 0.339 | 47.665 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 187 | 133 | 123 | 313 | 182 | 2392 | 211 | 0 |
N.S. |
1 | 1.01 | 0.72 | 0.66 | 1.69 | 0.98 | 12.93 | 1.14 | 0.00 |
time (sec) |
N/A | 0.458 | 0.652 | 3.548 | 0.202 | 0.322 | 77.574 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 242 | 218 | 165 | 156 | 337 | 225 | 2861 | 349 | 0 |
N.S. |
1 | 0.90 | 0.68 | 0.64 | 1.39 | 0.93 | 11.82 | 1.44 | 0.00 |
time (sec) |
N/A | 0.515 | 0.512 | 3.553 | 0.222 | 0.394 | 120.749 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 281 | 233 | 202 | 185 | 398 | 270 | 0 | 592 | 405 |
N.S. |
1 | 0.83 | 0.72 | 0.66 | 1.42 | 0.96 | 0.00 | 2.11 | 1.44 |
time (sec) |
N/A | 0.514 | 0.565 | 3.641 | 0.212 | 0.523 | 0.000 | 0.304 | 7.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 334 | 261 | 234 | 218 | 489 | 311 | 0 | 938 | 421 |
N.S. |
1 | 0.78 | 0.70 | 0.65 | 1.46 | 0.93 | 0.00 | 2.81 | 1.26 |
time (sec) |
N/A | 0.554 | 0.631 | 3.579 | 0.207 | 0.700 | 0.000 | 0.322 | 7.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 392 | 289 | 270 | 249 | 579 | 354 | 0 | 1162 | 0 |
N.S. |
1 | 0.74 | 0.69 | 0.64 | 1.48 | 0.90 | 0.00 | 2.96 | 0.00 |
time (sec) |
N/A | 0.567 | 0.720 | 3.653 | 0.210 | 0.973 | 0.000 | 0.310 | 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 | 214 | 219 | 158 | 142 | 347 | 177 | 442 | 259 | 186 |
N.S. |
1 | 1.02 | 0.74 | 0.66 | 1.62 | 0.83 | 2.07 | 1.21 | 0.87 |
time (sec) |
N/A | 0.527 | 0.029 | 3.685 | 0.200 | 0.293 | 0.458 | 0.291 | 6.072 |
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 | 167 | 171 | 122 | 111 | 263 | 134 | 340 | 193 | 146 |
N.S. |
1 | 1.02 | 0.73 | 0.66 | 1.57 | 0.80 | 2.04 | 1.16 | 0.87 |
time (sec) |
N/A | 0.451 | 0.020 | 3.508 | 0.215 | 0.289 | 0.365 | 0.294 | 5.886 |
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 | 121 | 126 | 89 | 82 | 180 | 94 | 238 | 127 | 103 |
N.S. |
1 | 1.04 | 0.74 | 0.68 | 1.49 | 0.78 | 1.97 | 1.05 | 0.85 |
time (sec) |
N/A | 0.374 | 0.016 | 3.550 | 0.211 | 0.294 | 0.291 | 0.282 | 5.992 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 285 | 205 | 193 | 826 | 705 | 6987 | 224 | 0 |
N.S. |
1 | 1.09 | 0.79 | 0.74 | 3.16 | 2.70 | 26.77 | 0.86 | 0.00 |
time (sec) |
N/A | 1.097 | 1.183 | 3.640 | 0.228 | 0.430 | 108.770 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 214 | 269 | 176 | 167 | 597 | 567 | 5071 | 204 | 0 |
N.S. |
1 | 1.26 | 0.82 | 0.78 | 2.79 | 2.65 | 23.70 | 0.95 | 0.00 |
time (sec) |
N/A | 0.806 | 0.640 | 3.594 | 0.245 | 0.429 | 74.123 | 0.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 193 | 246 | 138 | 131 | 421 | 187 | 2490 | 220 | 0 |
N.S. |
1 | 1.27 | 0.72 | 0.68 | 2.18 | 0.97 | 12.90 | 1.14 | 0.00 |
time (sec) |
N/A | 0.641 | 0.498 | 3.607 | 0.207 | 0.342 | 98.387 | 0.310 | 0.000 |