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 | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 91 | 35 | 30 | 325 | 115 | 0 | 35 | 74 | 110 |
N.S. |
1 | 1.12 | 0.43 | 0.37 | 4.01 | 1.42 | 0.00 | 0.43 | 0.91 | 1.36 |
time (sec) |
N/A | 0.159 | 0.045 | 0.327 | 0.216 | 0.233 | 0.000 | 0.330 | 0.004 | 0.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 116 | 40 | 35 | 386 | 130 | 0 | 42 | 84 | 124 |
N.S. |
1 | 1.15 | 0.40 | 0.35 | 3.82 | 1.29 | 0.00 | 0.42 | 0.83 | 1.23 |
time (sec) |
N/A | 0.173 | 0.056 | 0.178 | 0.210 | 0.228 | 0.000 | 0.331 | 0.003 | 0.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 141 | 45 | 40 | 452 | 145 | 0 | 48 | 94 | 140 |
N.S. |
1 | 1.17 | 0.37 | 0.33 | 3.74 | 1.20 | 0.00 | 0.40 | 0.78 | 1.16 |
time (sec) |
N/A | 0.185 | 0.063 | 0.333 | 0.206 | 0.226 | 0.000 | 0.346 | 0.004 | 0.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 59 | 55 | 98 | 42 | 55 | 0 | 42 | 53 | 0 |
N.S. |
1 | 0.92 | 0.86 | 1.53 | 0.66 | 0.86 | 0.00 | 0.66 | 0.83 | 0.00 |
time (sec) |
N/A | 0.164 | 0.105 | 0.200 | 0.297 | 0.231 | 0.000 | 0.318 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 59 | 55 | 60 | 42 | 48 | 76 | 34 | 41 | 55 |
N.S. |
1 | 0.95 | 0.89 | 0.97 | 0.68 | 0.77 | 1.23 | 0.55 | 0.66 | 0.89 |
time (sec) |
N/A | 0.175 | 0.157 | 0.359 | 0.307 | 0.234 | 4.051 | 0.291 | 0.002 | 0.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 89 | 53 | 82 | 56 | 52 | 197 | 101 | 70 | 0 |
N.S. |
1 | 1.02 | 0.61 | 0.94 | 0.64 | 0.60 | 2.26 | 1.16 | 0.80 | 0.00 |
time (sec) |
N/A | 0.166 | 0.119 | 0.169 | 0.283 | 0.239 | 20.724 | 0.319 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 64 | 46 | 71 | 42 | 47 | 173 | 69 | 55 | 0 |
N.S. |
1 | 0.96 | 0.69 | 1.06 | 0.63 | 0.70 | 2.58 | 1.03 | 0.82 | 0.00 |
time (sec) |
N/A | 0.150 | 0.093 | 0.325 | 0.298 | 0.224 | 5.296 | 0.314 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 39 | 39 | 57 | 28 | 40 | 138 | 44 | 40 | 0 |
N.S. |
1 | 0.83 | 0.83 | 1.21 | 0.60 | 0.85 | 2.94 | 0.94 | 0.85 | 0.00 |
time (sec) |
N/A | 0.142 | 0.073 | 0.169 | 0.295 | 0.224 | 2.823 | 0.288 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 14 | 32 | 41 | 12 | 36 | 99 | 27 | 26 | 12 |
N.S. |
1 | 0.70 | 1.60 | 2.05 | 0.60 | 1.80 | 4.95 | 1.35 | 1.30 | 0.60 |
time (sec) |
N/A | 0.127 | 0.003 | 0.323 | 0.280 | 0.222 | 1.306 | 0.289 | 0.001 | 0.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 20 | 27 | 2 | 22 | 39 | 13 | 14 | 22 |
N.S. |
1 | 1.00 | 10.00 | 13.50 | 1.00 | 11.00 | 19.50 | 6.50 | 7.00 | 11.00 |
time (sec) |
N/A | 0.112 | 0.001 | 0.165 | 0.276 | 0.224 | 1.284 | 0.304 | 0.000 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 16 | 23 | 31 | 19 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.94 | 1.35 | 1.82 | 1.12 | 0.76 | 0.76 |
time (sec) |
N/A | 0.122 | 0.015 | 0.169 | 0.301 | 0.228 | 0.570 | 0.295 | 0.000 | 0.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 25 | 18 | 38 | 39 | 128 | 22 | 22 | 43 |
N.S. |
1 | 1.00 | 0.61 | 0.44 | 0.93 | 0.95 | 3.12 | 0.54 | 0.54 | 1.05 |
time (sec) |
N/A | 0.133 | 0.022 | 0.326 | 0.290 | 0.224 | 1.163 | 0.309 | 0.002 | 0.424 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 30 | 25 | 64 | 56 | 303 | 29 | 34 | 55 |
N.S. |
1 | 1.08 | 0.49 | 0.41 | 1.05 | 0.92 | 4.97 | 0.48 | 0.56 | 0.90 |
time (sec) |
N/A | 0.151 | 0.025 | 0.175 | 0.285 | 0.239 | 4.835 | 0.296 | 0.001 | 0.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 91 | 35 | 30 | 95 | 71 | 542 | 35 | 44 | 67 |
N.S. |
1 | 1.12 | 0.43 | 0.37 | 1.17 | 0.88 | 6.69 | 0.43 | 0.54 | 0.83 |
time (sec) |
N/A | 0.159 | 0.030 | 0.329 | 0.297 | 0.223 | 19.316 | 0.316 | 0.003 | 0.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 116 | 40 | 35 | 131 | 86 | 850 | 42 | 54 | 80 |
N.S. |
1 | 1.15 | 0.40 | 0.35 | 1.30 | 0.85 | 8.42 | 0.42 | 0.53 | 0.79 |
time (sec) |
N/A | 0.173 | 0.034 | 0.174 | 0.297 | 0.226 | 55.843 | 0.291 | 0.002 | 0.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 56 | 84 | 70 | 65 | 206 | 81 | 66 | 0 |
N.S. |
1 | 1.00 | 0.66 | 0.99 | 0.82 | 0.76 | 2.42 | 0.95 | 0.78 | 0.00 |
time (sec) |
N/A | 0.165 | 0.087 | 0.329 | 0.290 | 0.230 | 15.435 | 0.320 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 60 | 49 | 77 | 56 | 58 | 167 | 73 | 54 | 0 |
N.S. |
1 | 0.92 | 0.75 | 1.18 | 0.86 | 0.89 | 2.57 | 1.12 | 0.83 | 0.00 |
time (sec) |
N/A | 0.155 | 0.063 | 0.172 | 0.294 | 0.219 | 6.230 | 0.304 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 35 | 42 | 71 | 41 | 53 | 131 | 70 | 43 | 0 |
N.S. |
1 | 0.85 | 1.02 | 1.73 | 1.00 | 1.29 | 3.20 | 1.71 | 1.05 | 0.00 |
time (sec) |
N/A | 0.142 | 0.050 | 0.326 | 0.299 | 0.224 | 3.344 | 0.303 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 39 | 67 | 21 | 50 | 102 | 55 | 34 | 0 |
N.S. |
1 | 1.00 | 1.70 | 2.91 | 0.91 | 2.17 | 4.43 | 2.39 | 1.48 | 0.00 |
time (sec) |
N/A | 0.134 | 0.031 | 0.171 | 0.300 | 0.226 | 1.046 | 0.295 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 16 | 23 | 31 | 43 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.89 | 1.28 | 1.72 | 2.39 | 0.78 | 0.78 |
time (sec) |
N/A | 0.123 | 0.008 | 0.340 | 0.296 | 0.217 | 0.740 | 0.298 | 0.001 | 0.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 13 | 13 | 15 | 11 | 22 | 63 | 62 | 16 | 14 |
N.S. |
1 | 0.72 | 0.72 | 0.83 | 0.61 | 1.22 | 3.50 | 3.44 | 0.89 | 0.78 |
time (sec) |
N/A | 0.123 | 0.024 | 0.174 | 0.200 | 0.223 | 0.859 | 0.287 | 0.001 | 0.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 37 | 30 | 25 | 40 | 54 | 160 | 67 | 31 | 42 |
N.S. |
1 | 0.88 | 0.71 | 0.60 | 0.95 | 1.29 | 3.81 | 1.60 | 0.74 | 1.00 |
time (sec) |
N/A | 0.139 | 0.025 | 0.330 | 0.205 | 0.223 | 3.188 | 0.313 | 0.002 | 0.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 33 | 28 | 79 | 59 | 284 | 73 | 39 | 55 |
N.S. |
1 | 1.00 | 0.53 | 0.45 | 1.27 | 0.95 | 4.58 | 1.18 | 0.63 | 0.89 |
time (sec) |
N/A | 0.151 | 0.028 | 0.177 | 0.219 | 0.219 | 10.308 | 0.316 | 0.002 | 0.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 87 | 40 | 35 | 134 | 86 | 425 | 79 | 51 | 68 |
N.S. |
1 | 1.06 | 0.49 | 0.43 | 1.63 | 1.05 | 5.18 | 0.96 | 0.62 | 0.83 |
time (sec) |
N/A | 0.163 | 0.033 | 0.337 | 0.210 | 0.225 | 38.903 | 0.336 | 0.003 | 0.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 112 | 45 | 40 | 201 | 91 | 593 | 85 | 61 | 80 |
N.S. |
1 | 1.10 | 0.44 | 0.39 | 1.97 | 0.89 | 5.81 | 0.83 | 0.60 | 0.78 |
time (sec) |
N/A | 0.172 | 0.039 | 0.179 | 0.216 | 0.236 | 113.359 | 0.309 | 0.003 | 0.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 108 | 61 | 89 | 125 | 85 | 248 | 127 | 101 | 0 |
N.S. |
1 | 1.05 | 0.59 | 0.86 | 1.21 | 0.83 | 2.41 | 1.23 | 0.98 | 0.00 |
time (sec) |
N/A | 0.178 | 0.084 | 0.338 | 0.304 | 0.232 | 57.288 | 0.351 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 85 | 56 | 84 | 111 | 81 | 212 | 119 | 90 | 0 |
N.S. |
1 | 0.98 | 0.64 | 0.97 | 1.28 | 0.93 | 2.44 | 1.37 | 1.03 | 0.00 |
time (sec) |
N/A | 0.164 | 0.069 | 0.185 | 0.293 | 0.231 | 16.831 | 0.346 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 60 | 51 | 79 | 98 | 75 | 162 | 115 | 79 | 0 |
N.S. |
1 | 0.95 | 0.81 | 1.25 | 1.56 | 1.19 | 2.57 | 1.83 | 1.25 | 0.00 |
time (sec) |
N/A | 0.152 | 0.072 | 0.337 | 0.284 | 0.225 | 7.043 | 0.324 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 46 | 73 | 66 | 71 | 128 | 102 | 68 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.78 | 1.61 | 1.73 | 3.12 | 2.49 | 1.66 | 0.00 |
time (sec) |
N/A | 0.137 | 0.051 | 0.176 | 0.287 | 0.227 | 2.914 | 0.320 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 38 | 37 | 66 | 89 | 22 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 1.90 | 1.85 | 3.30 | 4.45 | 1.10 | 1.60 |
time (sec) |
N/A | 0.123 | 0.012 | 0.331 | 0.197 | 0.228 | 1.072 | 0.311 | 0.001 | 0.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 25 | 18 | 38 | 38 | 66 | 89 | 24 | 33 |
N.S. |
1 | 1.00 | 0.61 | 0.44 | 0.93 | 0.93 | 1.61 | 2.17 | 0.59 | 0.80 |
time (sec) |
N/A | 0.136 | 0.020 | 0.172 | 0.290 | 0.222 | 1.696 | 0.311 | 0.002 | 0.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 61 | 30 | 25 | 38 | 49 | 167 | 108 | 31 | 48 |
N.S. |
1 | 1.05 | 0.52 | 0.43 | 0.66 | 0.84 | 2.88 | 1.86 | 0.53 | 0.83 |
time (sec) |
N/A | 0.144 | 0.028 | 0.336 | 0.189 | 0.221 | 5.132 | 0.301 | 0.002 | 0.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 33 | 24 | 23 | 25 | 35 | 280 | 113 | 31 | 41 |
N.S. |
1 | 0.77 | 0.56 | 0.53 | 0.58 | 0.81 | 6.51 | 2.63 | 0.72 | 0.95 |
time (sec) |
N/A | 0.132 | 0.034 | 0.176 | 0.200 | 0.218 | 7.263 | 0.319 | 0.003 | 0.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 58 | 40 | 35 | 52 | 84 | 425 | 119 | 51 | 75 |
N.S. |
1 | 0.92 | 0.63 | 0.56 | 0.83 | 1.33 | 6.75 | 1.89 | 0.81 | 1.19 |
time (sec) |
N/A | 0.151 | 0.032 | 0.340 | 0.201 | 0.227 | 24.523 | 0.307 | 0.003 | 0.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 45 | 40 | 91 | 101 | 593 | 125 | 56 | 86 |
N.S. |
1 | 1.00 | 0.54 | 0.48 | 1.10 | 1.22 | 7.14 | 1.51 | 0.67 | 1.04 |
time (sec) |
N/A | 0.163 | 0.036 | 0.183 | 0.201 | 0.228 | 61.340 | 0.303 | 0.003 | 0.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 108 | 50 | 45 | 146 | 114 | 0 | 131 | 71 | 99 |
N.S. |
1 | 1.05 | 0.49 | 0.44 | 1.42 | 1.11 | 0.00 | 1.27 | 0.69 | 0.96 |
time (sec) |
N/A | 0.178 | 0.044 | 0.344 | 0.190 | 0.218 | 0.000 | 0.298 | 0.004 | 0.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 129 | 114 | 105 | 72 | 201 | 0 | 679 | 70 | 0 |
N.S. |
1 | 1.02 | 0.90 | 0.83 | 0.57 | 1.60 | 0.00 | 5.39 | 0.56 | 0.00 |
time (sec) |
N/A | 0.197 | 0.313 | 0.212 | 0.282 | 0.235 | 0.000 | 0.548 | 0.005 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 98 | 104 | 100 | 50 | 155 | 0 | 403 | 51 | 0 |
N.S. |
1 | 1.02 | 1.08 | 1.04 | 0.52 | 1.61 | 0.00 | 4.20 | 0.53 | 0.00 |
time (sec) |
N/A | 0.181 | 0.152 | 0.503 | 0.291 | 0.231 | 0.000 | 0.452 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 69 | 85 | 28 | 127 | 0 | 173 | 33 | 59 |
N.S. |
1 | 1.00 | 1.03 | 1.27 | 0.42 | 1.90 | 0.00 | 2.58 | 0.49 | 0.88 |
time (sec) |
N/A | 0.160 | 0.079 | 0.182 | 0.292 | 0.233 | 0.000 | 0.379 | 0.001 | 0.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 47 | 57 | 8 | 101 | 85 | 49 | 24 | 44 |
N.S. |
1 | 1.00 | 1.09 | 1.33 | 0.19 | 2.35 | 1.98 | 1.14 | 0.56 | 1.02 |
time (sec) |
N/A | 0.147 | 0.047 | 0.346 | 0.299 | 0.240 | 24.434 | 0.344 | 0.001 | 0.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 21 | 39 | 82 | 116 | 26 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 1.44 | 3.04 | 4.30 | 0.96 | 0.85 |
time (sec) |
N/A | 0.132 | 0.068 | 0.175 | 0.202 | 0.222 | 2.753 | 0.291 | 0.002 | 0.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 42 | 32 | 45 | 57 | 82 | 237 | 41 | 62 |
N.S. |
1 | 1.00 | 0.69 | 0.52 | 0.74 | 0.93 | 1.34 | 3.89 | 0.67 | 1.02 |
time (sec) |
N/A | 0.155 | 0.099 | 0.336 | 0.203 | 0.225 | 10.455 | 0.324 | 0.004 | 0.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 102 | 49 | 37 | 67 | 74 | 85 | 333 | 51 | 50 |
N.S. |
1 | 1.12 | 0.54 | 0.41 | 0.74 | 0.81 | 0.93 | 3.66 | 0.56 | 0.55 |
time (sec) |
N/A | 0.173 | 0.202 | 0.175 | 0.207 | 0.230 | 50.312 | 0.361 | 0.005 | 0.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 143 | 54 | 42 | 89 | 89 | 0 | 437 | 61 | 66 |
N.S. |
1 | 1.18 | 0.45 | 0.35 | 0.74 | 0.74 | 0.00 | 3.61 | 0.50 | 0.55 |
time (sec) |
N/A | 0.192 | 0.431 | 0.337 | 0.204 | 0.225 | 0.000 | 0.478 | 0.007 | 0.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 103 | 136 | 89 | 232 | 0 | 622 | 98 | 0 |
N.S. |
1 | 1.04 | 0.76 | 1.01 | 0.66 | 1.72 | 0.00 | 4.61 | 0.73 | 0.00 |
time (sec) |
N/A | 0.203 | 0.217 | 0.235 | 0.293 | 0.240 | 0.000 | 0.482 | 0.005 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 105 | 92 | 125 | 63 | 193 | 0 | 354 | 72 | 0 |
N.S. |
1 | 1.03 | 0.90 | 1.23 | 0.62 | 1.89 | 0.00 | 3.47 | 0.71 | 0.00 |
time (sec) |
N/A | 0.186 | 0.132 | 0.203 | 0.297 | 0.249 | 0.000 | 0.410 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 69 | 67 | 107 | 39 | 159 | 0 | 148 | 46 | 72 |
N.S. |
1 | 1.01 | 0.99 | 1.57 | 0.57 | 2.34 | 0.00 | 2.18 | 0.68 | 1.06 |
time (sec) |
N/A | 0.163 | 0.083 | 0.364 | 0.287 | 0.236 | 0.000 | 0.337 | 0.001 | 0.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 39 | 48 | 71 | 14 | 108 | 90 | 42 | 27 | 53 |
N.S. |
1 | 1.03 | 1.26 | 1.87 | 0.37 | 2.84 | 2.37 | 1.11 | 0.71 | 1.39 |
time (sec) |
N/A | 0.148 | 0.040 | 0.202 | 0.291 | 0.233 | 25.645 | 0.313 | 0.000 | 0.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 29 | 30 | 25 | 45 | 94 | 103 | 27 | 26 |
N.S. |
1 | 1.00 | 0.97 | 1.00 | 0.83 | 1.50 | 3.13 | 3.43 | 0.90 | 0.87 |
time (sec) |
N/A | 0.138 | 0.042 | 0.370 | 0.196 | 0.228 | 4.532 | 0.306 | 0.002 | 0.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 46 | 45 | 53 | 72 | 94 | 199 | 56 | 80 |
N.S. |
1 | 1.00 | 0.69 | 0.67 | 0.79 | 1.07 | 1.40 | 2.97 | 0.84 | 1.19 |
time (sec) |
N/A | 0.158 | 0.070 | 0.208 | 0.216 | 0.245 | 12.544 | 0.335 | 0.005 | 0.830 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 111 | 57 | 56 | 79 | 98 | 97 | 296 | 77 | 111 |
N.S. |
1 | 1.11 | 0.57 | 0.56 | 0.79 | 0.98 | 0.97 | 2.96 | 0.77 | 1.11 |
time (sec) |
N/A | 0.178 | 0.131 | 0.369 | 0.199 | 0.256 | 57.999 | 0.370 | 0.006 | 0.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 155 | 68 | 67 | 105 | 122 | 0 | 393 | 100 | 170 |
N.S. |
1 | 1.17 | 0.51 | 0.50 | 0.79 | 0.92 | 0.00 | 2.95 | 0.75 | 1.28 |
time (sec) |
N/A | 0.207 | 0.236 | 0.210 | 0.200 | 0.274 | 0.000 | 0.455 | 0.008 | 0.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 84 | 59 | 107 | 46 | 65 | 0 | 227 | 72 | 0 |
N.S. |
1 | 0.84 | 0.59 | 1.07 | 0.46 | 0.65 | 0.00 | 2.27 | 0.72 | 0.00 |
time (sec) |
N/A | 0.163 | 0.336 | 0.532 | 0.278 | 0.233 | 0.000 | 0.329 | 0.004 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 62 | 54 | 102 | 34 | 60 | 0 | 125 | 55 | 0 |
N.S. |
1 | 0.84 | 0.73 | 1.38 | 0.46 | 0.81 | 0.00 | 1.69 | 0.74 | 0.00 |
time (sec) |
N/A | 0.151 | 0.222 | 0.189 | 0.269 | 0.225 | 0.000 | 0.318 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 36 | 42 | 70 | 22 | 52 | 187 | 55 | 36 | 44 |
N.S. |
1 | 0.84 | 0.98 | 1.63 | 0.51 | 1.21 | 4.35 | 1.28 | 0.84 | 1.02 |
time (sec) |
N/A | 0.139 | 0.135 | 0.357 | 0.274 | 0.221 | 4.781 | 0.299 | 0.002 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 27 | 37 | 9 | 28 | 41 | 21 | 16 | 40 |
N.S. |
1 | 1.00 | 2.08 | 2.85 | 0.69 | 2.15 | 3.15 | 1.62 | 1.23 | 3.08 |
time (sec) |
N/A | 0.123 | 0.044 | 0.186 | 0.269 | 0.236 | 1.370 | 0.301 | 0.001 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 21 | 16 | 28 | 12 | 26 | 156 | 79 | 21 | 24 |
N.S. |
1 | 0.75 | 0.57 | 1.00 | 0.43 | 0.93 | 5.57 | 2.82 | 0.75 | 0.86 |
time (sec) |
N/A | 0.125 | 0.101 | 0.349 | 0.199 | 0.219 | 52.678 | 0.297 | 0.001 | 0.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 43 | 28 | 35 | 25 | 39 | 0 | 145 | 37 | 49 |
N.S. |
1 | 0.75 | 0.49 | 0.61 | 0.44 | 0.68 | 0.00 | 2.54 | 0.65 | 0.86 |
time (sec) |
N/A | 0.141 | 0.112 | 0.185 | 0.188 | 0.222 | 0.000 | 0.306 | 0.003 | 0.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 69 | 33 | 40 | 37 | 49 | 0 | 208 | 47 | 66 |
N.S. |
1 | 0.81 | 0.39 | 0.47 | 0.44 | 0.58 | 0.00 | 2.45 | 0.55 | 0.78 |
time (sec) |
N/A | 0.154 | 0.135 | 0.351 | 0.206 | 0.234 | 0.000 | 0.337 | 0.004 | 0.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 103 | 79 | 86 | 67 | 62 | 199 | 101 | 65 | 0 |
N.S. |
1 | 1.13 | 0.87 | 0.95 | 0.74 | 0.68 | 2.19 | 1.11 | 0.71 | 0.00 |
time (sec) |
N/A | 0.196 | 0.084 | 0.230 | 0.270 | 0.225 | 15.428 | 0.309 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 53 | 53 | 61 | 38 | 52 | 124 | 42 | 35 | 41 |
N.S. |
1 | 1.04 | 1.04 | 1.20 | 0.75 | 1.02 | 2.43 | 0.82 | 0.69 | 0.80 |
time (sec) |
N/A | 0.161 | 0.064 | 0.362 | 0.278 | 0.224 | 2.571 | 0.293 | 0.002 | 0.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 44 | 31 | 6 | 32 | 26 | 8 | 9 | 31 |
N.S. |
1 | 1.00 | 5.50 | 3.88 | 0.75 | 4.00 | 3.25 | 1.00 | 1.12 | 3.88 |
time (sec) |
N/A | 0.135 | 0.024 | 0.192 | 0.268 | 0.223 | 1.971 | 0.308 | 0.000 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 21 | 20 | 30 | 29 | 100 | 53 | 21 | 32 |
N.S. |
1 | 1.00 | 0.57 | 0.54 | 0.81 | 0.78 | 2.70 | 1.43 | 0.57 | 0.86 |
time (sec) |
N/A | 0.138 | 0.023 | 0.363 | 0.205 | 0.220 | 1.774 | 0.301 | 0.002 | 0.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 85 | 31 | 30 | 59 | 49 | 282 | 97 | 41 | 69 |
N.S. |
1 | 1.08 | 0.39 | 0.38 | 0.75 | 0.62 | 3.57 | 1.23 | 0.52 | 0.87 |
time (sec) |
N/A | 0.161 | 0.034 | 0.197 | 0.213 | 0.226 | 5.821 | 0.286 | 0.002 | 0.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 16 | 16 | 16 | 12 | 22 | 71 | 62 | 17 | 22 |
N.S. |
1 | 0.76 | 0.76 | 0.76 | 0.57 | 1.05 | 3.38 | 2.95 | 0.81 | 1.05 |
time (sec) |
N/A | 0.129 | 0.026 | 0.353 | 0.214 | 0.220 | 1.245 | 0.289 | 0.001 | 0.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 19 | 19 | 19 | 15 | 29 | 73 | 77 | 20 | 26 |
N.S. |
1 | 0.79 | 0.79 | 0.79 | 0.62 | 1.21 | 3.04 | 3.21 | 0.83 | 1.08 |
time (sec) |
N/A | 0.131 | 0.041 | 0.203 | 0.201 | 0.222 | 4.546 | 0.287 | 0.002 | 0.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 21 | 21 | 19 | 12 | 22 | 92 | 71 | 19 | 22 |
N.S. |
1 | 0.81 | 0.81 | 0.73 | 0.46 | 0.85 | 3.54 | 2.73 | 0.73 | 0.85 |
time (sec) |
N/A | 0.131 | 0.059 | 0.357 | 0.194 | 0.227 | 10.344 | 0.293 | 0.001 | 0.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 24 | 19 | 24 | 15 | 29 | 83 | 79 | 22 | 26 |
N.S. |
1 | 0.83 | 0.66 | 0.83 | 0.52 | 1.00 | 2.86 | 2.72 | 0.76 | 0.90 |
time (sec) |
N/A | 0.131 | 0.098 | 0.199 | 0.207 | 0.231 | 13.190 | 0.300 | 0.002 | 0.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 76 | 39 | 108 | 88 | 37 | 35 | 56 |
N.S. |
1 | 1.00 | 1.00 | 1.95 | 1.00 | 2.77 | 2.26 | 0.95 | 0.90 | 1.44 |
time (sec) |
N/A | 0.148 | 0.069 | 0.393 | 0.187 | 0.231 | 20.856 | 0.305 | 0.001 | 0.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 190 | 103 | 0 | 0 | 244 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.79 | 0.43 | 0.00 | 0.00 | 1.01 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.307 | 0.991 | 0.000 | 0.000 | 0.232 | 0.000 | 0.000 | 0.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 131 | 70 | 104 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 0.91 | 0.49 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.197 | 0.028 | 0.233 | 0.000 | 0.000 | 0.000 | 0.000 | 0.048 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 92 | 70 | 94 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.87 | 0.66 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.173 | 0.019 | 0.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 57 | 70 | 0 | 0 | 0 | 102 | 0 | 23 | 0 |
N.S. |
1 | 0.80 | 0.99 | 0.00 | 0.00 | 0.00 | 1.44 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.157 | 0.018 | 0.000 | 0.000 | 0.000 | 2.395 | 0.000 | 0.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 68 | 94 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.87 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.166 | 0.020 | 0.201 | 0.000 | 0.000 | 0.000 | 0.000 | 0.045 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 70 | 105 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.160 | 0.021 | 0.382 | 0.000 | 0.000 | 0.000 | 0.000 | 0.101 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 123 | 70 | 113 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.07 | 0.61 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.181 | 0.021 | 0.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.100 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 164 | 70 | 114 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.11 | 0.47 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.201 | 0.023 | 0.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.127 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 236 | 70 | 477 | 0 | 194 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.92 | 0.27 | 1.86 | 0.00 | 0.76 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.316 | 0.351 | 1.144 | 0.000 | 0.230 | 0.000 | 0.000 | 0.010 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 207 | 68 | 0 | 0 | 221 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.89 | 0.29 | 0.00 | 0.00 | 0.95 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.296 | 1.126 | 0.000 | 0.000 | 0.241 | 0.000 | 0.000 | 0.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 31 | 0 | 31 | 0 | 0 | 45 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 0.94 | 0.00 | 0.00 | 1.36 | 1.15 |
time (sec) |
N/A | 0.133 | 4.981 | 0.183 | 0.000 | 0.222 | 0.000 | 0.000 | 0.035 | 0.614 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 45 | 37 | 0 | 44 | 0 | 0 | 65 | 46 |
N.S. |
1 | 1.00 | 0.67 | 0.55 | 0.00 | 0.66 | 0.00 | 0.00 | 0.97 | 0.69 |
time (sec) |
N/A | 0.154 | 6.176 | 0.533 | 0.000 | 0.229 | 0.000 | 0.000 | 0.043 | 0.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 52 | 43 | 0 | 57 | 0 | 0 | 84 | 51 |
N.S. |
1 | 1.08 | 0.52 | 0.43 | 0.00 | 0.57 | 0.00 | 0.00 | 0.84 | 0.51 |
time (sec) |
N/A | 0.177 | 6.851 | 0.191 | 0.000 | 0.225 | 0.000 | 0.000 | 0.046 | 0.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 149 | 57 | 48 | 0 | 68 | 0 | 0 | 104 | 57 |
N.S. |
1 | 1.12 | 0.43 | 0.36 | 0.00 | 0.51 | 0.00 | 0.00 | 0.78 | 0.43 |
time (sec) |
N/A | 0.189 | 10.097 | 0.367 | 0.000 | 0.220 | 0.000 | 0.000 | 0.056 | 0.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 236 | 70 | 465 | 0 | 198 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.92 | 0.27 | 1.82 | 0.00 | 0.77 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.322 | 0.388 | 1.115 | 0.000 | 0.243 | 0.000 | 0.000 | 0.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 207 | 70 | 0 | 0 | 221 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.89 | 0.30 | 0.00 | 0.00 | 0.95 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.312 | 0.885 | 0.000 | 0.000 | 0.237 | 0.000 | 0.000 | 0.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 31 | 0 | 31 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.133 | 2.341 | 0.182 | 0.000 | 0.219 | 0.000 | 0.000 | 0.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 45 | 37 | 0 | 44 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.55 | 0.00 | 0.66 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.158 | 5.806 | 0.357 | 0.000 | 0.221 | 0.000 | 0.000 | 0.047 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 52 | 43 | 0 | 57 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.08 | 0.52 | 0.43 | 0.00 | 0.57 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.164 | 7.974 | 0.192 | 0.000 | 0.222 | 0.000 | 0.000 | 0.046 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 115 | 70 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.03 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.176 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 70 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.163 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.013 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 68 | 0 | 0 | 0 | 100 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.58 | 0.00 | 0.00 | 0.00 | 2.33 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.147 | 0.017 | 0.000 | 0.000 | 0.000 | 2.853 | 0.000 | 0.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 70 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.165 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 123 | 70 | 0 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.07 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.182 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.054 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 274 | 70 | 466 | 0 | 235 | 0 | 0 | 67 | 0 |
N.S. |
1 | 0.94 | 0.24 | 1.60 | 0.00 | 0.81 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.355 | 0.982 | 1.081 | 0.000 | 0.241 | 0.000 | 0.000 | 0.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 241 | 70 | 459 | 0 | 298 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.91 | 0.26 | 1.73 | 0.00 | 1.12 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.338 | 0.973 | 0.974 | 0.000 | 0.244 | 0.000 | 0.000 | 0.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 31 | 0 | 31 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 0.94 | 0.00 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.133 | 1.707 | 0.144 | 0.000 | 0.232 | 0.000 | 0.000 | 0.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 38 | 33 | 0 | 36 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.58 | 0.51 | 0.00 | 0.55 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.152 | 2.272 | 0.372 | 0.000 | 0.229 | 0.000 | 0.000 | 0.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 106 | 50 | 43 | 0 | 56 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.06 | 0.50 | 0.43 | 0.00 | 0.56 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.166 | 5.927 | 0.198 | 0.000 | 0.228 | 0.000 | 0.000 | 0.052 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 151 | 70 | 0 | 0 | 0 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.09 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.205 | 0.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.062 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 114 | 70 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.01 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.177 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.034 | 0.000 |