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 | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 127 | 154 | 75 | 0 | 140 | 0 | 132 | 0 |
N.S. |
1 | 1.07 | 1.29 | 0.63 | 0.00 | 1.18 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.447 | 1.918 | 0.244 | 0.000 | 0.277 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 93 | 117 | 65 | 0 | 115 | 0 | 102 | 0 |
N.S. |
1 | 1.04 | 1.31 | 0.73 | 0.00 | 1.29 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.350 | 1.177 | 0.233 | 0.000 | 0.254 | 0.000 | 0.330 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 89 | 53 | 0 | 76 | 0 | 67 | 0 |
N.S. |
1 | 1.00 | 1.51 | 0.90 | 0.00 | 1.29 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.257 | 0.447 | 0.184 | 0.000 | 0.279 | 0.000 | 0.342 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 65 | 43 | 0 | 50 | 0 | 36 | 33 |
N.S. |
1 | 1.00 | 2.50 | 1.65 | 0.00 | 1.92 | 0.00 | 1.38 | 1.27 |
time (sec) |
N/A | 0.179 | 0.033 | 0.155 | 0.000 | 0.274 | 0.000 | 0.326 | 0.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 73 | 75 | 0 | 167 | 0 | 111 | 49 |
N.S. |
1 | 1.00 | 1.55 | 1.60 | 0.00 | 3.55 | 0.00 | 2.36 | 1.04 |
time (sec) |
N/A | 0.201 | 0.135 | 0.228 | 0.000 | 0.279 | 0.000 | 0.326 | 0.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 108 | 125 | 0 | 252 | 0 | 133 | 0 |
N.S. |
1 | 1.00 | 1.40 | 1.62 | 0.00 | 3.27 | 0.00 | 1.73 | 0.00 |
time (sec) |
N/A | 0.274 | 0.206 | 0.228 | 0.000 | 0.270 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 196 | 199 | 0 | 320 | 0 | 153 | 0 |
N.S. |
1 | 1.05 | 1.83 | 1.86 | 0.00 | 2.99 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.364 | 0.212 | 0.259 | 0.000 | 0.291 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 223 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.258 | 1.075 | 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 | 66 | 66 | 124 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.257 | 0.265 | 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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 169 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.257 | 0.400 | 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 | 66 | 66 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.248 | 0.178 | 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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 215 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.253 | 0.654 | 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 | 69 | 69 | 130 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.249 | 0.340 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.262 | 0.118 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 80 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.267 | 0.187 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 46 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.196 | 0.145 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 49 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.208 | 0.161 | 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 | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 56 | 20 | 26 | 26 | 46 | 49 | 40 |
N.S. |
1 | 1.00 | 1.81 | 0.65 | 0.84 | 0.84 | 1.48 | 1.58 | 1.29 |
time (sec) |
N/A | 0.182 | 0.043 | 0.184 | 0.268 | 0.271 | 0.373 | 0.312 | 6.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 91 | 63 | 93 | 59 | 388 | 95 | 83 |
N.S. |
1 | 1.09 | 1.62 | 1.12 | 1.66 | 1.05 | 6.93 | 1.70 | 1.48 |
time (sec) |
N/A | 0.248 | 0.158 | 0.231 | 0.269 | 0.297 | 0.883 | 0.301 | 6.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 91 | 113 | 91 | 173 | 94 | 918 | 121 | 111 |
N.S. |
1 | 1.12 | 1.40 | 1.12 | 2.14 | 1.16 | 11.33 | 1.49 | 1.37 |
time (sec) |
N/A | 0.353 | 0.274 | 0.302 | 0.270 | 0.280 | 1.920 | 0.320 | 6.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 121 | 133 | 117 | 253 | 130 | 1693 | 147 | 187 |
N.S. |
1 | 1.14 | 1.25 | 1.10 | 2.39 | 1.23 | 15.97 | 1.39 | 1.76 |
time (sec) |
N/A | 0.491 | 0.382 | 0.398 | 0.276 | 0.295 | 4.351 | 0.310 | 6.238 |
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 | 33 | 33 | 56 | 20 | 26 | 26 | 46 | 50 | 40 |
N.S. |
1 | 1.00 | 1.70 | 0.61 | 0.79 | 0.79 | 1.39 | 1.52 | 1.21 |
time (sec) |
N/A | 0.173 | 0.034 | 0.185 | 0.270 | 0.271 | 0.387 | 0.311 | 6.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 63 | 91 | 63 | 93 | 59 | 384 | 96 | 83 |
N.S. |
1 | 1.09 | 1.57 | 1.09 | 1.60 | 1.02 | 6.62 | 1.66 | 1.43 |
time (sec) |
N/A | 0.252 | 0.178 | 0.233 | 0.263 | 0.283 | 0.912 | 0.305 | 6.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 93 | 113 | 91 | 173 | 94 | 915 | 122 | 111 |
N.S. |
1 | 1.12 | 1.36 | 1.10 | 2.08 | 1.13 | 11.02 | 1.47 | 1.34 |
time (sec) |
N/A | 0.362 | 0.451 | 0.296 | 0.276 | 0.266 | 1.976 | 0.313 | 6.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 123 | 133 | 117 | 253 | 130 | 1690 | 148 | 187 |
N.S. |
1 | 1.14 | 1.23 | 1.08 | 2.34 | 1.20 | 15.65 | 1.37 | 1.73 |
time (sec) |
N/A | 0.478 | 0.397 | 0.405 | 0.273 | 0.278 | 4.393 | 0.317 | 6.638 |
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 | 33 | 33 | 56 | 20 | 26 | 26 | 48 | 50 | 40 |
N.S. |
1 | 1.00 | 1.70 | 0.61 | 0.79 | 0.79 | 1.45 | 1.52 | 1.21 |
time (sec) |
N/A | 0.178 | 0.026 | 0.127 | 0.263 | 0.278 | 0.390 | 0.305 | 5.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 63 | 91 | 63 | 93 | 59 | 384 | 96 | 83 |
N.S. |
1 | 1.09 | 1.57 | 1.09 | 1.60 | 1.02 | 6.62 | 1.66 | 1.43 |
time (sec) |
N/A | 0.253 | 0.055 | 0.219 | 0.274 | 0.267 | 0.906 | 0.305 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 93 | 113 | 91 | 173 | 94 | 915 | 122 | 112 |
N.S. |
1 | 1.12 | 1.36 | 1.10 | 2.08 | 1.13 | 11.02 | 1.47 | 1.35 |
time (sec) |
N/A | 0.351 | 0.243 | 0.292 | 0.272 | 0.262 | 1.950 | 0.294 | 6.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 123 | 133 | 117 | 253 | 130 | 1690 | 148 | 187 |
N.S. |
1 | 1.14 | 1.23 | 1.08 | 2.34 | 1.20 | 15.65 | 1.37 | 1.73 |
time (sec) |
N/A | 0.486 | 0.011 | 0.362 | 0.267 | 0.288 | 4.320 | 0.320 | 0.003 |
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 | 31 | 31 | 56 | 20 | 26 | 26 | 49 | 49 | 40 |
N.S. |
1 | 1.00 | 1.81 | 0.65 | 0.84 | 0.84 | 1.58 | 1.58 | 1.29 |
time (sec) |
N/A | 0.177 | 0.030 | 0.126 | 0.270 | 0.269 | 0.388 | 0.311 | 5.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 91 | 63 | 93 | 59 | 389 | 95 | 83 |
N.S. |
1 | 1.09 | 1.62 | 1.12 | 1.66 | 1.05 | 6.95 | 1.70 | 1.48 |
time (sec) |
N/A | 0.247 | 0.071 | 0.228 | 0.274 | 0.272 | 0.884 | 0.300 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 91 | 114 | 91 | 173 | 94 | 921 | 121 | 112 |
N.S. |
1 | 1.12 | 1.41 | 1.12 | 2.14 | 1.16 | 11.37 | 1.49 | 1.38 |
time (sec) |
N/A | 0.355 | 0.425 | 0.291 | 0.265 | 0.295 | 1.933 | 0.284 | 6.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 121 | 133 | 117 | 253 | 130 | 1695 | 147 | 187 |
N.S. |
1 | 1.14 | 1.25 | 1.10 | 2.39 | 1.23 | 15.99 | 1.39 | 1.76 |
time (sec) |
N/A | 0.485 | 0.254 | 0.325 | 0.278 | 0.271 | 4.403 | 0.293 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 42 | 63 | 36 | 49 | 46 | 42 | 36 | 19 |
N.S. |
1 | 0.67 | 1.00 | 0.57 | 0.78 | 0.73 | 0.67 | 0.57 | 0.30 |
time (sec) |
N/A | 0.207 | 0.031 | 0.148 | 0.182 | 0.274 | 0.330 | 0.305 | 6.033 |
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 | 88 | 70 | 126 | 68 | 115 | 88 | 466 | 81 | 64 |
N.S. |
1 | 0.80 | 1.43 | 0.77 | 1.31 | 1.00 | 5.30 | 0.92 | 0.73 |
time (sec) |
N/A | 0.282 | 0.171 | 0.254 | 0.184 | 0.279 | 0.716 | 0.318 | 5.720 |
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 | 113 | 100 | 180 | 100 | 195 | 133 | 1227 | 107 | 115 |
N.S. |
1 | 0.88 | 1.59 | 0.88 | 1.73 | 1.18 | 10.86 | 0.95 | 1.02 |
time (sec) |
N/A | 0.394 | 0.356 | 0.277 | 0.183 | 0.263 | 1.390 | 0.326 | 7.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 130 | 235 | 132 | 275 | 181 | 2356 | 133 | 168 |
N.S. |
1 | 0.94 | 1.70 | 0.96 | 1.99 | 1.31 | 17.07 | 0.96 | 1.22 |
time (sec) |
N/A | 0.534 | 0.640 | 0.346 | 0.193 | 0.308 | 3.129 | 0.323 | 8.675 |
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 | 65 | 44 | 65 | 36 | 49 | 46 | 42 | 36 | 19 |
N.S. |
1 | 0.68 | 1.00 | 0.55 | 0.75 | 0.71 | 0.65 | 0.55 | 0.29 |
time (sec) |
N/A | 0.204 | 0.033 | 0.148 | 0.191 | 0.258 | 0.339 | 0.311 | 5.726 |
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 | 72 | 130 | 68 | 115 | 88 | 462 | 81 | 64 |
N.S. |
1 | 0.80 | 1.44 | 0.76 | 1.28 | 0.98 | 5.13 | 0.90 | 0.71 |
time (sec) |
N/A | 0.283 | 0.214 | 0.256 | 0.188 | 0.281 | 0.746 | 0.301 | 6.107 |
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 | 102 | 184 | 100 | 195 | 133 | 1224 | 107 | 116 |
N.S. |
1 | 0.89 | 1.60 | 0.87 | 1.70 | 1.16 | 10.64 | 0.93 | 1.01 |
time (sec) |
N/A | 0.405 | 0.522 | 0.273 | 0.193 | 0.280 | 1.432 | 0.308 | 7.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 132 | 241 | 132 | 275 | 181 | 2353 | 133 | 168 |
N.S. |
1 | 0.94 | 1.72 | 0.94 | 1.96 | 1.29 | 16.81 | 0.95 | 1.20 |
time (sec) |
N/A | 0.531 | 0.713 | 0.343 | 0.193 | 0.297 | 3.153 | 0.325 | 9.100 |
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 | 65 | 44 | 65 | 36 | 49 | 46 | 42 | 36 | 19 |
N.S. |
1 | 0.68 | 1.00 | 0.55 | 0.75 | 0.71 | 0.65 | 0.55 | 0.29 |
time (sec) |
N/A | 0.209 | 0.027 | 0.116 | 0.189 | 0.281 | 0.348 | 0.301 | 5.757 |
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 | 72 | 130 | 68 | 115 | 88 | 462 | 81 | 64 |
N.S. |
1 | 0.80 | 1.44 | 0.76 | 1.28 | 0.98 | 5.13 | 0.90 | 0.71 |
time (sec) |
N/A | 0.305 | 0.084 | 0.148 | 0.177 | 0.301 | 0.724 | 0.310 | 0.003 |
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 | 102 | 183 | 100 | 195 | 133 | 1224 | 107 | 115 |
N.S. |
1 | 0.89 | 1.59 | 0.87 | 1.70 | 1.16 | 10.64 | 0.93 | 1.00 |
time (sec) |
N/A | 0.388 | 0.374 | 0.266 | 0.193 | 0.270 | 1.412 | 0.320 | 7.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 132 | 241 | 132 | 275 | 181 | 2353 | 133 | 168 |
N.S. |
1 | 0.94 | 1.72 | 0.94 | 1.96 | 1.29 | 16.81 | 0.95 | 1.20 |
time (sec) |
N/A | 0.515 | 0.009 | 0.227 | 0.206 | 0.287 | 3.118 | 0.324 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 42 | 63 | 36 | 49 | 46 | 44 | 36 | 19 |
N.S. |
1 | 0.67 | 1.00 | 0.57 | 0.78 | 0.73 | 0.70 | 0.57 | 0.30 |
time (sec) |
N/A | 0.199 | 0.028 | 0.121 | 0.213 | 0.269 | 0.330 | 0.303 | 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 | 88 | 70 | 126 | 68 | 115 | 88 | 468 | 81 | 64 |
N.S. |
1 | 0.80 | 1.43 | 0.77 | 1.31 | 1.00 | 5.32 | 0.92 | 0.73 |
time (sec) |
N/A | 0.280 | 0.007 | 0.194 | 0.186 | 0.290 | 0.723 | 0.303 | 0.003 |
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 | 113 | 100 | 179 | 100 | 195 | 133 | 1229 | 107 | 116 |
N.S. |
1 | 0.88 | 1.58 | 0.88 | 1.73 | 1.18 | 10.88 | 0.95 | 1.03 |
time (sec) |
N/A | 0.393 | 0.462 | 0.267 | 0.195 | 0.267 | 1.417 | 0.309 | 7.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 130 | 235 | 132 | 275 | 181 | 2358 | 133 | 168 |
N.S. |
1 | 0.94 | 1.70 | 0.96 | 1.99 | 1.31 | 17.09 | 0.96 | 1.22 |
time (sec) |
N/A | 0.508 | 0.518 | 0.230 | 0.202 | 0.300 | 3.127 | 0.304 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 256 | 267 | 220 | 1040 | 0 | 491 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.86 | 4.06 | 0.00 | 1.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.332 | 0.759 | 1.193 | 0.000 | 0.127 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 207 | 213 | 185 | 890 | 0 | 447 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.89 | 4.30 | 0.00 | 2.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.985 | 0.720 | 0.802 | 0.000 | 0.125 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 168 | 142 | 656 | 0 | 404 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.85 | 3.93 | 0.00 | 2.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.733 | 0.621 | 0.585 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 61 | 239 | 0 | 363 | 0 | 0 | 55 |
N.S. |
1 | 1.00 | 0.98 | 3.85 | 0.00 | 5.85 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.271 | 2.374 | 0.911 | 0.000 | 0.098 | 0.000 | 0.000 | 5.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 61 | 126 | 0 | 148 | 0 | 0 | 55 |
N.S. |
1 | 1.00 | 0.98 | 2.03 | 0.00 | 2.39 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.274 | 0.084 | 0.281 | 0.000 | 0.093 | 0.000 | 0.000 | 6.288 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 87 | 443 | 0 | 486 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.78 | 3.99 | 0.00 | 4.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.402 | 0.240 | 0.373 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 241 | 166 | 497 | 0 | 731 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.72 | 2.15 | 0.00 | 3.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.045 | 0.709 | 0.617 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 292 | 318 | 198 | 584 | 0 | 1051 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.68 | 2.00 | 0.00 | 3.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.411 | 0.966 | 0.872 | 0.000 | 0.161 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 244 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.254 | 1.180 | 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 | 106 | 106 | 118 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.240 | 0.201 | 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 | 106 | 106 | 118 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.241 | 0.202 | 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 | 106 | 106 | 118 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.244 | 0.177 | 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 | 106 | 106 | 116 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.244 | 0.174 | 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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 262 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.237 | 1.354 | 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 | 104 | 104 | 120 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.241 | 0.218 | 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 | 72 | 72 | 83 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 0.115 | 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 | 69 | 69 | 84 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.221 | 0.120 | 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 | 64 | 64 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.220 | 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 | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 96 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.214 | 0.097 | 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 | 67 | 67 | 83 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 0.106 | 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 | 64 | 64 | 84 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.213 | 0.117 | 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 | 95 | 95 | 95 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.232 | 0.089 | 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 | 110 | 110 | 100 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.244 | 0.102 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |