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 | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 376 | 375 | 295 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.250 | 0.492 | 0.434 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 118 | 357 | 292 | 360 | 4537 | 847 | 400 |
N.S. | 1 | 1.00 | 0.87 | 2.62 | 2.15 | 2.65 | 33.36 | 6.23 | 2.94 |
time (sec) |
N/A | 0.067 | 0.143 | 0.542 | 0.295 | 2.440 | 1.206 | 1.073 | 1.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 177 | 200 | 178 | 181 | 230 | 210 | 182 |
N.S. | 1 | 1.00 | 1.50 | 1.69 | 1.51 | 1.53 | 1.95 | 1.78 | 1.54 |
time (sec) |
N/A | 0.116 | 0.044 | 0.570 | 0.267 | 1.869 | 0.024 | 1.419 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 135 | 152 | 138 | 141 | 177 | 164 | 146 |
N.S. | 1 | 1.00 | 1.14 | 1.29 | 1.17 | 1.19 | 1.50 | 1.39 | 1.24 |
time (sec) |
N/A | 0.091 | 0.032 | 0.527 | 0.284 | 2.924 | 0.020 | 1.378 | 1.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 91 | 104 | 98 | 101 | 121 | 117 | 102 |
N.S. | 1 | 1.00 | 0.92 | 1.05 | 0.99 | 1.02 | 1.22 | 1.18 | 1.03 |
time (sec) |
N/A | 0.068 | 0.030 | 0.524 | 0.268 | 2.747 | 0.016 | 1.410 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 55 | 56 | 58 | 61 | 66 | 69 | 57 |
N.S. | 1 | 1.00 | 0.90 | 0.92 | 0.95 | 1.00 | 1.08 | 1.13 | 0.93 |
time (sec) |
N/A | 0.043 | 0.016 | 0.121 | 0.274 | 1.990 | 0.010 | 1.289 | 1.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 29 | 28 | 27 | 27 | 29 | 29 | 28 |
N.S. | 1 | 1.00 | 0.88 | 0.85 | 0.82 | 0.82 | 0.88 | 0.88 | 0.85 |
time (sec) |
N/A | 0.016 | 0.004 | 0.081 | 0.263 | 2.591 | 0.008 | 1.253 | 1.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 88 | 111 | 108 | 102 | 95 | 117 | 113 |
N.S. | 1 | 1.00 | 1.01 | 1.28 | 1.24 | 1.17 | 1.09 | 1.34 | 1.30 |
time (sec) |
N/A | 0.068 | 0.033 | 0.542 | 0.273 | 3.104 | 0.166 | 1.308 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 93 | 104 | 113 | 162 | 121 | 167 | 116 |
N.S. | 1 | 1.00 | 0.94 | 1.05 | 1.14 | 1.64 | 1.22 | 1.69 | 1.17 |
time (sec) |
N/A | 0.078 | 0.057 | 0.596 | 0.279 | 1.541 | 0.338 | 1.379 | 1.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 96 | 109 | 121 | 178 | 138 | 113 | 123 |
N.S. | 1 | 1.00 | 0.92 | 1.05 | 1.16 | 1.71 | 1.33 | 1.09 | 1.18 |
time (sec) |
N/A | 0.070 | 0.061 | 0.532 | 0.274 | 2.664 | 0.767 | 1.406 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 112 | 116 | 135 | 158 | 158 | 119 | 134 |
N.S. | 1 | 1.00 | 1.01 | 1.05 | 1.22 | 1.42 | 1.42 | 1.07 | 1.21 |
time (sec) |
N/A | 0.066 | 0.039 | 0.568 | 0.269 | 2.164 | 1.483 | 0.919 | 1.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 101 | 118 | 135 | 130 | 168 | 177 | 134 |
N.S. | 1 | 1.00 | 0.87 | 1.02 | 1.16 | 1.12 | 1.45 | 1.53 | 1.16 |
time (sec) |
N/A | 0.065 | 0.032 | 0.577 | 0.275 | 3.105 | 2.956 | 0.720 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 104 | 118 | 151 | 142 | 185 | 115 | 154 |
N.S. | 1 | 1.00 | 0.88 | 1.00 | 1.28 | 1.20 | 1.57 | 0.97 | 1.31 |
time (sec) |
N/A | 0.063 | 0.034 | 0.525 | 0.275 | 3.008 | 7.320 | 2.010 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 282 | 309 | 1030 | 752 | 1267 | 20284 | 2827 | 1176 |
N.S. | 1 | 1.00 | 1.10 | 3.65 | 2.67 | 4.49 | 71.93 | 10.02 | 4.17 |
time (sec) |
N/A | 0.151 | 0.421 | 0.607 | 0.293 | 2.770 | 4.413 | 0.996 | 2.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 228 | 247 | 243 | 244 | 301 | 285 | 234 |
N.S. | 1 | 1.00 | 1.00 | 1.08 | 1.07 | 1.07 | 1.32 | 1.25 | 1.03 |
time (sec) |
N/A | 0.171 | 0.060 | 0.653 | 0.277 | 3.416 | 0.027 | 1.210 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 162 | 172 | 175 | 177 | 212 | 205 | 161 |
N.S. | 1 | 1.00 | 1.00 | 1.06 | 1.08 | 1.09 | 1.31 | 1.27 | 0.99 |
time (sec) |
N/A | 0.147 | 0.041 | 0.610 | 0.268 | 2.865 | 0.021 | 0.782 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 101 | 97 | 107 | 110 | 121 | 123 | 102 |
N.S. | 1 | 1.00 | 1.01 | 0.97 | 1.07 | 1.10 | 1.21 | 1.23 | 1.02 |
time (sec) |
N/A | 0.077 | 0.022 | 0.563 | 0.271 | 1.655 | 0.016 | 1.077 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 52 | 51 | 51 | 54 | 53 | 51 |
N.S. | 1 | 1.00 | 0.89 | 0.95 | 0.93 | 0.93 | 0.98 | 0.96 | 0.93 |
time (sec) |
N/A | 0.030 | 0.009 | 0.555 | 0.264 | 1.240 | 0.012 | 1.040 | 1.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 156 | 330 | 285 | 278 | 280 | 322 | 308 |
N.S. | 1 | 1.00 | 0.97 | 2.05 | 1.77 | 1.73 | 1.74 | 2.00 | 1.91 |
time (sec) |
N/A | 0.151 | 0.104 | 0.637 | 0.271 | 2.672 | 0.346 | 0.655 | 1.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 194 | 184 | 315 | 295 | 404 | 316 | 380 | 371 |
N.S. | 1 | 1.00 | 0.95 | 1.62 | 1.52 | 2.08 | 1.63 | 1.96 | 1.91 |
time (sec) |
N/A | 0.190 | 0.055 | 0.699 | 0.273 | 2.405 | 0.741 | 1.340 | 1.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 232 | 219 | 302 | 307 | 467 | 362 | 307 | 334 |
N.S. | 1 | 1.00 | 0.94 | 1.30 | 1.32 | 2.01 | 1.56 | 1.32 | 1.44 |
time (sec) |
N/A | 0.213 | 0.115 | 0.639 | 0.276 | 2.267 | 2.106 | 1.369 | 0.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 238 | 220 | 292 | 315 | 486 | 374 | 299 | 328 |
N.S. | 1 | 1.00 | 0.92 | 1.23 | 1.32 | 2.04 | 1.57 | 1.26 | 1.38 |
time (sec) |
N/A | 0.198 | 0.124 | 0.598 | 0.281 | 2.522 | 9.270 | 1.400 | 0.141 |
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 | 240 | 240 | 275 | 298 | 320 | 456 | 0 | 474 | 338 |
N.S. |
1 | 1.00 | 1.15 | 1.24 | 1.33 | 1.90 | 0.00 | 1.98 | 1.41 |
time (sec) |
N/A | 0.181 | 0.103 | 0.686 | 0.285 | 3.718 | 0.000 | 0.886 | 1.470 |
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 | 248 | 248 | 269 | 305 | 336 | 386 | 0 | 301 | 343 |
N.S. |
1 | 1.00 | 1.08 | 1.23 | 1.35 | 1.56 | 0.00 | 1.21 | 1.38 |
time (sec) |
N/A | 0.162 | 0.092 | 0.625 | 0.284 | 2.718 | 0.000 | 0.795 | 1.465 |
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 | 253 | 253 | 257 | 307 | 334 | 322 | 0 | 318 | 337 |
N.S. |
1 | 1.00 | 1.02 | 1.21 | 1.32 | 1.27 | 0.00 | 1.26 | 1.33 |
time (sec) |
N/A | 0.154 | 0.080 | 0.579 | 0.290 | 2.623 | 0.000 | 0.741 | 0.133 |
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 | 255 | 255 | 260 | 307 | 352 | 336 | 0 | 320 | 357 |
N.S. |
1 | 1.00 | 1.02 | 1.20 | 1.38 | 1.32 | 0.00 | 1.25 | 1.40 |
time (sec) |
N/A | 0.146 | 0.080 | 0.665 | 0.294 | 2.742 | 0.000 | 0.732 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 484 | 484 | 525 | 2224 | 1511 | 2986 | 59148 | 6663 | 2500 |
N.S. | 1 | 1.00 | 1.08 | 4.60 | 3.12 | 6.17 | 122.21 | 13.77 | 5.17 |
time (sec) |
N/A | 0.267 | 0.947 | 0.688 | 0.321 | 4.096 | 13.332 | 0.773 | 2.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 412 | 412 | 412 | 444 | 437 | 431 | 564 | 524 | 445 |
N.S. | 1 | 1.00 | 1.00 | 1.08 | 1.06 | 1.05 | 1.37 | 1.27 | 1.08 |
time (sec) |
N/A | 0.340 | 0.110 | 0.614 | 0.282 | 2.768 | 0.043 | 0.936 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 305 | 305 | 342 | 336 | 339 | 430 | 408 | 340 |
N.S. | 1 | 1.00 | 1.00 | 1.12 | 1.10 | 1.11 | 1.41 | 1.34 | 1.11 |
time (sec) |
N/A | 0.314 | 0.085 | 0.658 | 0.268 | 3.248 | 0.033 | 1.282 | 1.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 225 | 225 | 240 | 249 | 247 | 303 | 292 | 235 |
N.S. | 1 | 1.00 | 1.00 | 1.07 | 1.11 | 1.10 | 1.35 | 1.30 | 1.04 |
time (sec) |
N/A | 0.200 | 0.054 | 0.577 | 0.273 | 2.902 | 0.026 | 1.522 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 141 | 138 | 155 | 155 | 177 | 177 | 147 |
N.S. | 1 | 1.00 | 1.01 | 0.99 | 1.12 | 1.12 | 1.27 | 1.27 | 1.06 |
time (sec) |
N/A | 0.110 | 0.033 | 0.585 | 0.265 | 3.133 | 0.020 | 0.860 | 1.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 75 | 76 | 73 | 73 | 80 | 77 | 69 |
N.S. | 1 | 1.00 | 1.00 | 1.01 | 0.97 | 0.97 | 1.07 | 1.03 | 0.92 |
time (sec) |
N/A | 0.052 | 0.009 | 0.500 | 0.268 | 2.473 | 0.015 | 0.791 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 248 | 657 | 538 | 523 | 578 | 629 | 560 |
N.S. | 1 | 1.00 | 0.96 | 2.56 | 2.09 | 2.04 | 2.25 | 2.45 | 2.18 |
time (sec) |
N/A | 0.290 | 0.075 | 0.657 | 0.279 | 2.361 | 0.561 | 0.853 | 1.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 274 | 637 | 550 | 697 | 619 | 673 | 997 |
N.S. | 1 | 1.00 | 0.95 | 2.22 | 1.92 | 2.43 | 2.16 | 2.34 | 3.47 |
time (sec) |
N/A | 0.371 | 0.086 | 0.699 | 0.284 | 2.649 | 1.212 | 1.101 | 1.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 359 | 342 | 613 | 559 | 795 | 660 | 599 | 828 |
N.S. | 1 | 1.00 | 0.95 | 1.71 | 1.56 | 2.21 | 1.84 | 1.67 | 2.31 |
time (sec) |
N/A | 0.379 | 0.105 | 0.643 | 0.302 | 2.261 | 3.556 | 1.588 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 422 | 422 | 400 | 596 | 570 | 883 | 700 | 581 | 676 |
N.S. | 1 | 1.00 | 0.95 | 1.41 | 1.35 | 2.09 | 1.66 | 1.38 | 1.60 |
time (sec) |
N/A | 0.420 | 0.119 | 0.610 | 0.290 | 2.319 | 69.170 | 1.372 | 0.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 207 | 187 | 339 | 309 | 320 | 396 | 330 | 322 |
N.S. | 1 | 1.00 | 0.90 | 1.64 | 1.49 | 1.55 | 1.91 | 1.59 | 1.56 |
time (sec) |
N/A | 0.173 | 0.096 | 0.699 | 0.269 | 3.512 | 6.197 | 1.604 | 1.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 118 | 208 | 201 | 209 | 264 | 207 | 208 |
N.S. | 1 | 1.00 | 0.92 | 1.62 | 1.57 | 1.63 | 2.06 | 1.62 | 1.62 |
time (sec) |
N/A | 0.103 | 0.058 | 0.647 | 0.274 | 3.456 | 2.562 | 1.083 | 1.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 74 | 111 | 115 | 122 | 163 | 117 | 122 |
N.S. | 1 | 1.00 | 0.96 | 1.44 | 1.49 | 1.58 | 2.12 | 1.52 | 1.58 |
time (sec) |
N/A | 0.058 | 0.036 | 0.701 | 0.286 | 3.601 | 1.592 | 1.164 | 0.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 46 | 55 | 60 | 59 | 88 | 59 | 58 |
N.S. | 1 | 1.00 | 1.02 | 1.22 | 1.33 | 1.31 | 1.96 | 1.31 | 1.29 |
time (sec) |
N/A | 0.031 | 0.017 | 0.550 | 0.268 | 2.959 | 0.802 | 0.864 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 30 | 29 | 28 | 41 | 31 | 28 |
N.S. | 1 | 1.00 | 1.00 | 1.03 | 1.00 | 0.97 | 1.41 | 1.07 | 0.97 |
time (sec) |
N/A | 0.015 | 0.009 | 0.584 | 0.268 | 2.353 | 0.237 | 0.757 | 1.400 |
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 | 68 | 68 | 63 | 69 | 72 | 69 | 0 | 85 | 67 |
N.S. |
1 | 1.00 | 0.93 | 1.01 | 1.06 | 1.01 | 0.00 | 1.25 | 0.99 |
time (sec) |
N/A | 0.050 | 0.033 | 0.650 | 0.265 | 7.308 | 0.000 | 0.705 | 1.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 106 | 111 | 153 | 265 | 0 | 323 | 141 |
N.S. |
1 | 1.00 | 0.96 | 1.01 | 1.39 | 2.41 | 0.00 | 2.94 | 1.28 |
time (sec) |
N/A | 0.094 | 0.098 | 0.644 | 0.270 | 27.505 | 0.000 | 0.718 | 1.809 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 169 | 171 | 307 | 637 | 0 | 308 | 284 |
N.S. |
1 | 1.00 | 0.99 | 1.00 | 1.80 | 3.73 | 0.00 | 1.80 | 1.66 |
time (sec) |
N/A | 0.152 | 0.147 | 0.703 | 0.290 | 68.853 | 0.000 | 0.912 | 1.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 245 | 241 | 245 | 536 | 1132 | 0 | 475 | 471 |
N.S. |
1 | 1.00 | 0.98 | 1.00 | 2.19 | 4.62 | 0.00 | 1.94 | 1.92 |
time (sec) |
N/A | 0.205 | 0.245 | 0.679 | 0.315 | 242.884 | 0.000 | 0.908 | 2.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 155 | 303 | 309 | 513 | 644 | 315 | 331 |
N.S. | 1 | 1.00 | 0.99 | 1.94 | 1.98 | 3.29 | 4.13 | 2.02 | 2.12 |
time (sec) |
N/A | 0.151 | 0.064 | 0.713 | 0.288 | 3.731 | 20.590 | 1.043 | 1.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 128 | 220 | 226 | 365 | 502 | 229 | 212 |
N.S. | 1 | 1.00 | 1.00 | 1.72 | 1.77 | 2.85 | 3.92 | 1.79 | 1.66 |
time (sec) |
N/A | 0.107 | 0.052 | 0.627 | 0.286 | 2.849 | 5.098 | 0.894 | 1.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 101 | 156 | 168 | 262 | 367 | 167 | 154 |
N.S. | 1 | 1.00 | 0.94 | 1.44 | 1.56 | 2.43 | 3.40 | 1.55 | 1.43 |
time (sec) |
N/A | 0.081 | 0.081 | 0.612 | 0.272 | 3.044 | 2.203 | 1.074 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 80 | 97 | 108 | 187 | 233 | 112 | 117 |
N.S. | 1 | 1.00 | 0.93 | 1.13 | 1.26 | 2.17 | 2.71 | 1.30 | 1.36 |
time (sec) |
N/A | 0.058 | 0.076 | 0.612 | 0.266 | 2.881 | 0.687 | 0.952 | 1.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 56 | 64 | 67 | 107 | 128 | 71 | 58 |
N.S. | 1 | 1.00 | 0.90 | 1.03 | 1.08 | 1.73 | 2.06 | 1.15 | 0.94 |
time (sec) |
N/A | 0.036 | 0.034 | 0.605 | 0.267 | 3.729 | 0.252 | 1.167 | 1.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 146 | 147 | 231 | 457 | 0 | 268 | 201 |
N.S. |
1 | 1.00 | 0.99 | 1.00 | 1.57 | 3.11 | 0.00 | 1.82 | 1.37 |
time (sec) |
N/A | 0.137 | 0.119 | 0.669 | 0.283 | 84.335 | 0.000 | 0.885 | 2.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 201 | 201 | 203 | 468 | 1044 | 0 | 670 | 410 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 2.33 | 5.19 | 0.00 | 3.33 | 2.04 |
time (sec) |
N/A | 0.216 | 0.221 | 0.692 | 0.290 | 242.447 | 0.000 | 0.993 | 2.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 279 | 285 | 809 | 0 | 0 | 745 | 726 |
N.S. |
1 | 1.00 | 0.99 | 1.01 | 2.86 | 0.00 | 0.00 | 2.63 | 2.57 |
time (sec) |
N/A | 0.313 | 0.353 | 0.734 | 0.336 | 0.000 | 0.000 | 0.732 | 2.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 254 | 493 | 520 | 921 | 0 | 511 | 498 |
N.S. |
1 | 1.00 | 0.99 | 1.92 | 2.02 | 3.58 | 0.00 | 1.99 | 1.94 |
time (sec) |
N/A | 0.268 | 0.094 | 0.715 | 0.283 | 3.343 | 0.000 | 1.230 | 1.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 235 | 228 | 404 | 438 | 764 | 0 | 428 | 403 |
N.S. |
1 | 1.00 | 0.97 | 1.72 | 1.86 | 3.25 | 0.00 | 1.82 | 1.71 |
time (sec) |
N/A | 0.217 | 0.117 | 0.628 | 0.291 | 3.871 | 0.000 | 0.864 | 1.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 185 | 177 | 320 | 356 | 656 | 653 | 391 | 345 |
N.S. | 1 | 1.00 | 0.96 | 1.73 | 1.92 | 3.55 | 3.53 | 2.11 | 1.86 |
time (sec) |
N/A | 0.165 | 0.090 | 0.612 | 0.292 | 2.950 | 140.179 | 0.732 | 1.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 190 | 259 | 302 | 583 | 660 | 324 | 319 |
N.S. | 1 | 1.00 | 0.96 | 1.31 | 1.53 | 2.94 | 3.33 | 1.64 | 1.61 |
time (sec) |
N/A | 0.162 | 0.195 | 0.622 | 0.278 | 3.564 | 5.451 | 0.838 | 0.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 162 | 179 | 218 | 415 | 449 | 225 | 223 |
N.S. | 1 | 1.00 | 0.96 | 1.07 | 1.30 | 2.47 | 2.67 | 1.34 | 1.33 |
time (sec) |
N/A | 0.139 | 0.107 | 0.619 | 0.282 | 3.085 | 1.476 | 0.744 | 1.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 106 | 107 | 131 | 225 | 219 | 124 | 136 |
N.S. | 1 | 1.00 | 0.97 | 0.98 | 1.20 | 2.06 | 2.01 | 1.14 | 1.25 |
time (sec) |
N/A | 0.072 | 0.057 | 0.552 | 0.269 | 3.374 | 0.379 | 0.878 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 276 | 287 | 619 | 0 | 0 | 649 | 512 |
N.S. |
1 | 1.00 | 0.99 | 1.03 | 2.22 | 0.00 | 0.00 | 2.33 | 1.84 |
time (sec) |
N/A | 0.326 | 0.777 | 0.737 | 0.300 | 0.000 | 0.000 | 0.644 | 2.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 331 | 328 | 339 | 1051 | 0 | 0 | 1292 | 879 |
N.S. |
1 | 1.00 | 0.99 | 1.02 | 3.18 | 0.00 | 0.00 | 3.90 | 2.66 |
time (sec) |
N/A | 0.451 | 0.389 | 0.757 | 0.362 | 0.000 | 0.000 | 0.843 | 3.260 |
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 | 404 | 404 | 423 | 573 | 745 | 988 | 0 | 521 | 827 |
N.S. | 1 | 1.00 | 1.05 | 1.42 | 1.84 | 2.45 | 0.00 | 1.29 | 2.05 |
time (sec) |
N/A | 0.355 | 1.114 | 0.700 | 0.288 | 4.056 | 0.000 | 0.993 | 3.839 |
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 | 267 | 267 | 294 | 399 | 510 | 666 | 0 | 349 | 537 |
N.S. | 1 | 1.00 | 1.10 | 1.49 | 1.91 | 2.49 | 0.00 | 1.31 | 2.01 |
time (sec) |
N/A | 0.178 | 0.704 | 0.612 | 0.276 | 3.696 | 0.000 | 0.914 | 3.030 |
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 | 154 | 154 | 178 | 251 | 304 | 402 | 0 | 205 | 299 |
N.S. | 1 | 1.00 | 1.16 | 1.63 | 1.97 | 2.61 | 0.00 | 1.33 | 1.94 |
time (sec) |
N/A | 0.089 | 0.302 | 0.545 | 0.276 | 3.429 | 0.000 | 0.923 | 2.441 |
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 | 97 | 97 | 109 | 139 | 154 | 204 | 0 | 102 | 127 |
N.S. | 1 | 1.00 | 1.12 | 1.43 | 1.59 | 2.10 | 0.00 | 1.05 | 1.31 |
time (sec) |
N/A | 0.025 | 0.061 | 0.542 | 0.279 | 2.477 | 0.000 | 0.706 | 1.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | F | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 223 | 353 | 0 | 800 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.12 | 1.76 | 0.00 | 4.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.185 | 0.571 | 0.747 | 0.000 | 5.585 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | B | F | F(-1) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 185 | 202 | 882 | 0 | 1487 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.09 | 4.77 | 0.00 | 8.04 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.124 | 0.758 | 0.665 | 0.000 | 4.832 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 235 | 690 | 1584 | 0 | 2200 | 0 | 819 | -1 |
N.S. |
1 | 1.00 | 2.94 | 6.74 | 0.00 | 9.36 | 0.00 | 3.49 | -0.00 |
time (sec) |
N/A | 0.211 | 12.462 | 0.606 | 0.000 | 6.534 | 0.000 | 2.815 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 199 | 2080 | 0 | 1217 | 0 | 1555 | -1 |
N.S. |
1 | 1.00 | 1.00 | 10.40 | 0.00 | 6.08 | 0.00 | 7.78 | -0.00 |
time (sec) |
N/A | 0.124 | 10.285 | 0.609 | 0.000 | 4.160 | 0.000 | 3.710 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 310 | 279 | 3278 | 0 | 2198 | 0 | 1720 | -1 |
N.S. |
1 | 1.00 | 0.90 | 10.57 | 0.00 | 7.09 | 0.00 | 5.55 | -0.00 |
time (sec) |
N/A | 0.279 | 10.562 | 0.687 | 0.000 | 3.100 | 0.000 | 4.401 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 449 | 387 | 5575 | 0 | 3437 | 0 | 4102 | -1 |
N.S. |
1 | 1.00 | 0.86 | 12.42 | 0.00 | 7.65 | 0.00 | 9.14 | -0.00 |
time (sec) |
N/A | 0.515 | 11.810 | 0.611 | 0.000 | 3.773 | 0.000 | 2.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 345 | 407 | 523 | 726 | 969 | 0 | 518 | -1 |
N.S. | 1 | 1.00 | 1.18 | 1.52 | 2.10 | 2.81 | 0.00 | 1.50 | -0.00 |
time (sec) |
N/A | 0.219 | 1.160 | 0.605 | 0.285 | 4.667 | 0.000 | 1.782 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 209 | 246 | 344 | 447 | 595 | 0 | 317 | -1 |
N.S. | 1 | 1.00 | 1.18 | 1.65 | 2.14 | 2.85 | 0.00 | 1.52 | -0.00 |
time (sec) |
N/A | 0.119 | 0.589 | 0.545 | 0.291 | 4.156 | 0.000 | 1.596 | 0.000 |
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 | 134 | 134 | 147 | 201 | 236 | 297 | 0 | 162 | 208 |
N.S. | 1 | 1.00 | 1.10 | 1.50 | 1.76 | 2.22 | 0.00 | 1.21 | 1.55 |
time (sec) |
N/A | 0.037 | 0.081 | 0.595 | 0.282 | 3.606 | 0.000 | 2.534 | 1.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | F | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 392 | 392 | 400 | 649 | 0 | 1631 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.02 | 1.66 | 0.00 | 4.16 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.384 | 1.133 | 0.651 | 0.000 | 90.365 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | A | F | F(-1) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 323 | 368 | 1524 | 0 | 1979 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.14 | 4.72 | 0.00 | 6.13 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.284 | 1.589 | 0.681 | 0.000 | 14.085 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 314 | 1073 | 2603 | 0 | 3276 | 0 | 936 | -1 |
N.S. |
1 | 1.00 | 3.42 | 8.29 | 0.00 | 10.43 | 0.00 | 2.98 | -0.00 |
time (sec) |
N/A | 0.280 | 14.981 | 0.678 | 0.000 | 5.599 | 0.000 | 2.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 426 | 426 | 1199 | 4344 | 0 | 4911 | 0 | 1788 | -1 |
N.S. |
1 | 1.00 | 2.81 | 10.20 | 0.00 | 11.53 | 0.00 | 4.20 | -0.00 |
time (sec) |
N/A | 0.349 | 15.845 | 0.764 | 0.000 | 17.654 | 0.000 | 1.718 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | F(-2) | B | F | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 421 | 1984 | 7164 | 0 | 5679 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 4.71 | 17.02 | 0.00 | 13.49 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.357 | 16.155 | 0.662 | 0.000 | 61.041 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | B | F(-1) | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 269 | 268 | 9004 | 0 | 2370 | 0 | 4214 | -1 |
N.S. |
1 | 1.00 | 1.00 | 33.47 | 0.00 | 8.81 | 0.00 | 15.67 | -0.00 |
time (sec) |
N/A | 0.169 | 10.694 | 0.613 | 0.000 | 3.911 | 0.000 | 2.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 402 | 352 | 13664 | 0 | 3757 | 0 | 5748 | -1 |
N.S. |
1 | 1.00 | 0.88 | 33.99 | 0.00 | 9.35 | 0.00 | 14.30 | -0.00 |
time (sec) |
N/A | 0.379 | 11.059 | 0.701 | 0.000 | 4.169 | 0.000 | 2.798 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | B | F(-1) | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 565 | 565 | 505 | 22885 | 0 | 5424 | 0 | 7914 | -1 |
N.S. |
1 | 1.00 | 0.89 | 40.50 | 0.00 | 9.60 | 0.00 | 14.01 | -0.00 |
time (sec) |
N/A | 0.652 | 12.222 | 0.661 | 0.000 | 4.188 | 0.000 | 2.611 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 423 | 423 | 518 | 647 | 942 | 1274 | 0 | 681 | -1 |
N.S. | 1 | 1.00 | 1.22 | 1.53 | 2.23 | 3.01 | 0.00 | 1.61 | -0.00 |
time (sec) |
N/A | 0.264 | 1.916 | 0.620 | 0.306 | 2.873 | 0.000 | 1.973 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 264 | 316 | 437 | 590 | 792 | 0 | 425 | -1 |
N.S. | 1 | 1.00 | 1.20 | 1.66 | 2.23 | 3.00 | 0.00 | 1.61 | -0.00 |
time (sec) |
N/A | 0.148 | 0.901 | 0.615 | 0.279 | 3.681 | 0.000 | 2.674 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 185 | 263 | 318 | 392 | 0 | 221 | -1 |
N.S. | 1 | 1.00 | 1.08 | 1.54 | 1.86 | 2.29 | 0.00 | 1.29 | -0.01 |
time (sec) |
N/A | 0.048 | 0.106 | 0.523 | 0.279 | 4.445 | 0.000 | 2.138 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | F(-1) | F | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 703 | 703 | 663 | 1057 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.94 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.729 | 2.602 | 0.647 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | A | F | F(-1) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 574 | 574 | 631 | 2390 | 0 | 3623 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.10 | 4.16 | 0.00 | 6.31 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.594 | 3.582 | 0.780 | 0.000 | 154.548 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 508 | 508 | 2047 | 3958 | 0 | 4007 | 0 | 1425 | -1 |
N.S. |
1 | 1.00 | 4.03 | 7.79 | 0.00 | 7.89 | 0.00 | 2.81 | -0.00 |
time (sec) |
N/A | 0.483 | 16.133 | 0.680 | 0.000 | 27.974 | 0.000 | 4.880 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 495 | 2233 | 6565 | 0 | 5824 | 0 | 1907 | -1 |
N.S. |
1 | 1.00 | 4.51 | 13.26 | 0.00 | 11.77 | 0.00 | 3.85 | -0.00 |
time (sec) |
N/A | 0.435 | 16.190 | 0.698 | 0.000 | 16.857 | 0.000 | 4.647 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | F(-2) | B | F | F(-1) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 633 | 633 | 2680 | 10740 | 0 | 7967 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 4.23 | 16.97 | 0.00 | 12.59 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.602 | 16.201 | 0.797 | 0.000 | 38.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 305 | 286 | 417 | 463 | 593 | 0 | 311 | -1 |
N.S. | 1 | 1.00 | 0.94 | 1.37 | 1.52 | 1.94 | 0.00 | 1.02 | -0.00 |
time (sec) |
N/A | 0.272 | 0.501 | 0.614 | 0.278 | 3.818 | 0.000 | 3.492 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 192 | 275 | 297 | 377 | 0 | 196 | -1 |
N.S. | 1 | 1.00 | 1.02 | 1.46 | 1.57 | 1.99 | 0.00 | 1.04 | -0.01 |
time (sec) |
N/A | 0.120 | 0.287 | 0.614 | 0.287 | 4.546 | 0.000 | 2.132 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 123 | 159 | 164 | 217 | 0 | 110 | -1 |
N.S. | 1 | 1.00 | 1.24 | 1.61 | 1.66 | 2.19 | 0.00 | 1.11 | -0.01 |
time (sec) |
N/A | 0.050 | 0.148 | 0.598 | 0.278 | 4.462 | 0.000 | 2.450 | 0.000 |
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 | 55 | 55 | 77 | 79 | 75 | 115 | 0 | 60 | 77 |
N.S. | 1 | 1.00 | 1.40 | 1.44 | 1.36 | 2.09 | 0.00 | 1.09 | 1.40 |
time (sec) |
N/A | 0.016 | 0.022 | 0.538 | 0.286 | 3.420 | 0.000 | 2.138 | 2.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | F | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 158 | 173 | 0 | 552 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.40 | 1.53 | 0.00 | 4.88 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.054 | 0.292 | 0.673 | 0.000 | 3.641 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | A | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 149 | 370 | 0 | 406 | 0 | 509 | -1 |
N.S. |
1 | 1.00 | 1.16 | 2.89 | 0.00 | 3.17 | 0.00 | 3.98 | -0.01 |
time (sec) |
N/A | 0.057 | 0.548 | 0.685 | 0.000 | 4.732 | 0.000 | 2.100 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 216 | 217 | 711 | 0 | 951 | 0 | 769 | -1 |
N.S. |
1 | 1.00 | 1.00 | 3.29 | 0.00 | 4.40 | 0.00 | 3.56 | -0.00 |
time (sec) |
N/A | 0.178 | 10.274 | 0.619 | 0.000 | 3.507 | 0.000 | 1.689 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 331 | 345 | 1297 | 0 | 1774 | 0 | 1667 | -1 |
N.S. |
1 | 1.00 | 1.04 | 3.92 | 0.00 | 5.36 | 0.00 | 5.04 | -0.00 |
time (sec) |
N/A | 0.341 | 11.146 | 0.630 | 0.000 | 3.287 | 0.000 | 1.763 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 238 | 230 | 473 | 358 | 685 | 0 | 251 | -1 |
N.S. | 1 | 1.00 | 0.97 | 1.99 | 1.50 | 2.88 | 0.00 | 1.05 | -0.00 |
time (sec) |
N/A | 0.143 | 0.755 | 0.725 | 0.277 | 4.795 | 0.000 | 1.422 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 150 | 309 | 225 | 439 | 0 | 155 | -1 |
N.S. | 1 | 1.00 | 0.99 | 2.05 | 1.49 | 2.91 | 0.00 | 1.03 | -0.01 |
time (sec) |
N/A | 0.104 | 0.361 | 0.635 | 0.284 | 3.849 | 0.000 | 1.561 | 0.000 |