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 | B | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 147 | 48 | 102 | 76 | 0 | 48 | 128 |
N.S. |
1 | 1.00 | 3.97 | 1.30 | 2.76 | 2.05 | 0.00 | 1.30 | 3.46 |
time (sec) |
N/A | 0.164 | 0.776 | 2.158 | 0.197 | 0.251 | 0.000 | 0.265 | 9.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 73 | 187 | 37 | 47 | 65 | 0 | 37 | 47 |
N.S. |
1 | 0.68 | 1.75 | 0.35 | 0.44 | 0.61 | 0.00 | 0.35 | 0.44 |
time (sec) |
N/A | 0.219 | 0.669 | 2.148 | 0.198 | 0.239 | 0.000 | 0.283 | 9.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 212 | 26 | 39 | 54 | 0 | 26 | 36 |
N.S. |
1 | 1.00 | 3.37 | 0.41 | 0.62 | 0.86 | 0.00 | 0.41 | 0.57 |
time (sec) |
N/A | 0.183 | 0.670 | 2.137 | 0.213 | 0.246 | 0.000 | 0.294 | 9.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 23 | 20 | 14 | 46 | 0 | 20 | 30 |
N.S. |
1 | 1.00 | 0.68 | 0.59 | 0.41 | 1.35 | 0.00 | 0.59 | 0.88 |
time (sec) |
N/A | 0.154 | 0.012 | 2.128 | 0.188 | 0.250 | 0.000 | 0.282 | 9.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 97 | 84 | 104 | 118 | 168 | 0 | 89 | 0 |
N.S. |
1 | 0.50 | 0.43 | 0.54 | 0.61 | 0.87 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.246 | 1.044 | 2.403 | 0.198 | 0.252 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 235 | 113 | 103 | 123 | 148 | 197 | 0 | 106 | 0 |
N.S. |
1 | 0.48 | 0.44 | 0.52 | 0.63 | 0.84 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.270 | 1.057 | 2.545 | 0.202 | 0.257 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 278 | 131 | 121 | 137 | 178 | 218 | 0 | 121 | 0 |
N.S. |
1 | 0.47 | 0.44 | 0.49 | 0.64 | 0.78 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.290 | 1.053 | 2.162 | 0.214 | 0.254 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 44 | 27 | 47 | 44 | 31 | 54 | 75 | 0 |
N.S. |
1 | 1.05 | 0.64 | 1.12 | 1.05 | 0.74 | 1.29 | 1.79 | 0.00 |
time (sec) |
N/A | 0.169 | 0.246 | 2.065 | 0.274 | 0.238 | 0.468 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 44 | 37 | 37 | 44 | 21 | 41 | 53 | 24 |
N.S. |
1 | 1.05 | 0.88 | 0.88 | 1.05 | 0.50 | 0.98 | 1.26 | 0.57 |
time (sec) |
N/A | 0.170 | 0.138 | 2.076 | 0.277 | 0.245 | 0.356 | 0.269 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 30 | 21 | 44 | 11 | 24 | 31 | 23 |
N.S. |
1 | 1.00 | 0.71 | 0.50 | 1.05 | 0.26 | 0.57 | 0.74 | 0.55 |
time (sec) |
N/A | 0.171 | 0.098 | 2.000 | 0.276 | 0.243 | 0.318 | 0.265 | 0.029 |
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 | 48 | 48 | 33 | 13 | 21 | 12 | 39 | 29 | 32 |
N.S. |
1 | 1.00 | 0.69 | 0.27 | 0.44 | 0.25 | 0.81 | 0.60 | 0.67 |
time (sec) |
N/A | 0.171 | 0.096 | 2.130 | 0.274 | 0.249 | 0.311 | 0.373 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 25 | 13 | 24 | 19 | 0 | 22 | 26 |
N.S. |
1 | 1.00 | 0.57 | 0.30 | 0.55 | 0.43 | 0.00 | 0.50 | 0.59 |
time (sec) |
N/A | 0.165 | 0.167 | 2.062 | 0.275 | 0.246 | 0.000 | 0.346 | 9.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 27 | 22 | 24 | 29 | 0 | 22 | 26 |
N.S. |
1 | 1.00 | 0.61 | 0.50 | 0.55 | 0.66 | 0.00 | 0.50 | 0.59 |
time (sec) |
N/A | 0.163 | 0.243 | 1.949 | 0.289 | 0.246 | 0.000 | 0.341 | 9.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 27 | 22 | 24 | 39 | 0 | 22 | 26 |
N.S. |
1 | 1.00 | 0.61 | 0.50 | 0.55 | 0.89 | 0.00 | 0.50 | 0.59 |
time (sec) |
N/A | 0.162 | 0.335 | 2.052 | 0.272 | 0.247 | 0.000 | 0.261 | 9.548 |
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 | 48 | 48 | 33 | 29 | 21 | 12 | 39 | 25 | 32 |
N.S. |
1 | 1.00 | 0.69 | 0.60 | 0.44 | 0.25 | 0.81 | 0.52 | 0.67 |
time (sec) |
N/A | 0.165 | 0.102 | 2.226 | 0.284 | 0.248 | 0.486 | 0.278 | 9.723 |
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 | 48 | 48 | 33 | 29 | 21 | 12 | 39 | 25 | 32 |
N.S. |
1 | 1.00 | 0.69 | 0.60 | 0.44 | 0.25 | 0.81 | 0.52 | 0.67 |
time (sec) |
N/A | 0.177 | 0.111 | 2.248 | 0.279 | 0.250 | 0.489 | 0.265 | 10.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 35 | 16 | 21 | 10 | 41 | 29 | 36 |
N.S. |
1 | 1.00 | 0.73 | 0.33 | 0.44 | 0.21 | 0.85 | 0.60 | 0.75 |
time (sec) |
N/A | 0.170 | 1.013 | 2.087 | 0.282 | 0.256 | 0.499 | 0.281 | 10.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 35 | 16 | 21 | 10 | 44 | 29 | 36 |
N.S. |
1 | 1.00 | 0.73 | 0.33 | 0.44 | 0.21 | 0.92 | 0.60 | 0.75 |
time (sec) |
N/A | 0.169 | 1.011 | 2.075 | 0.283 | 0.253 | 0.486 | 0.269 | 10.019 |
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 | 12 | 12 | 15 | 9 | 10 | 10 | 8 | 13 | 8 |
N.S. |
1 | 1.00 | 1.25 | 0.75 | 0.83 | 0.83 | 0.67 | 1.08 | 0.67 |
time (sec) |
N/A | 0.139 | 0.005 | 1.976 | 0.185 | 0.260 | 0.034 | 0.267 | 0.061 |
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 | 10 | 10 | 9 | 9 | 10 | 10 | 8 | 11 | 8 |
N.S. |
1 | 1.00 | 0.90 | 0.90 | 1.00 | 1.00 | 0.80 | 1.10 | 0.80 |
time (sec) |
N/A | 0.140 | 0.007 | 1.974 | 0.233 | 0.257 | 0.056 | 0.262 | 0.059 |
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 | 62 | 62 | 99 | 97 | 99 | 99 | 107 | 100 | 91 |
N.S. |
1 | 1.00 | 1.60 | 1.56 | 1.60 | 1.60 | 1.73 | 1.61 | 1.47 |
time (sec) |
N/A | 0.227 | 0.018 | 1.984 | 0.197 | 0.248 | 0.035 | 0.263 | 0.053 |
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 | 62 | 62 | 67 | 74 | 73 | 73 | 80 | 76 | 68 |
N.S. |
1 | 1.00 | 1.08 | 1.19 | 1.18 | 1.18 | 1.29 | 1.23 | 1.10 |
time (sec) |
N/A | 0.226 | 0.019 | 1.924 | 0.215 | 0.253 | 0.030 | 0.269 | 9.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 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 | 0.202 | 0.015 | 1.845 | 0.209 | 0.258 | 0.023 | 0.262 | 0.051 |
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 | 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 | 0.181 | 0.006 | 0.096 | 0.209 | 0.240 | 0.017 | 0.266 | 0.040 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.148 | 0.000 | 0.021 | 0.206 | 0.252 | 0.016 | 0.265 | 0.020 |
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 | 45 | 45 | 41 | 43 | 45 | 47 | 37 | 45 | 46 |
N.S. |
1 | 1.00 | 0.91 | 0.96 | 1.00 | 1.04 | 0.82 | 1.00 | 1.02 |
time (sec) |
N/A | 0.203 | 0.017 | 1.825 | 0.195 | 0.268 | 0.107 | 0.261 | 0.064 |
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 | 48 | 48 | 41 | 46 | 53 | 72 | 44 | 96 | 54 |
N.S. |
1 | 1.00 | 0.85 | 0.96 | 1.10 | 1.50 | 0.92 | 2.00 | 1.12 |
time (sec) |
N/A | 0.206 | 0.031 | 1.966 | 0.188 | 0.250 | 0.164 | 0.259 | 9.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 52 | 50 | 65 | 81 | 63 | 54 | 63 |
N.S. |
1 | 1.00 | 0.95 | 0.91 | 1.18 | 1.47 | 1.15 | 0.98 | 1.15 |
time (sec) |
N/A | 0.215 | 0.022 | 1.943 | 0.201 | 0.256 | 0.189 | 0.261 | 9.937 |
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 | 60 | 60 | 44 | 46 | 71 | 71 | 75 | 45 | 68 |
N.S. |
1 | 1.00 | 0.73 | 0.77 | 1.18 | 1.18 | 1.25 | 0.75 | 1.13 |
time (sec) |
N/A | 0.213 | 0.020 | 1.813 | 0.218 | 0.252 | 0.239 | 0.275 | 0.047 |
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 | 62 | 62 | 43 | 45 | 80 | 80 | 85 | 76 | 78 |
N.S. |
1 | 1.00 | 0.69 | 0.73 | 1.29 | 1.29 | 1.37 | 1.23 | 1.26 |
time (sec) |
N/A | 0.209 | 0.020 | 1.841 | 0.196 | 0.256 | 0.309 | 0.270 | 9.957 |
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 | 137 | 137 | 159 | 162 | 161 | 161 | 178 | 175 | 149 |
N.S. |
1 | 1.00 | 1.16 | 1.18 | 1.18 | 1.18 | 1.30 | 1.28 | 1.09 |
time (sec) |
N/A | 0.338 | 0.027 | 1.860 | 0.192 | 0.293 | 0.036 | 0.276 | 0.073 |
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 | 127 | 127 | 127 | 125 | 127 | 127 | 138 | 134 | 118 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 1.00 | 1.00 | 1.09 | 1.06 | 0.93 |
time (sec) |
N/A | 0.294 | 0.021 | 1.865 | 0.208 | 0.262 | 0.034 | 0.258 | 9.656 |
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 | 87 | 87 | 87 | 89 | 85 | 85 | 94 | 94 | 78 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 0.98 | 0.98 | 1.08 | 1.08 | 0.90 |
time (sec) |
N/A | 0.259 | 0.015 | 1.955 | 0.204 | 0.263 | 0.027 | 0.264 | 9.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 50 | 52 | 51 | 51 | 54 | 53 | 51 |
N.S. |
1 | 1.00 | 0.91 | 0.95 | 0.93 | 0.93 | 0.98 | 0.96 | 0.93 |
time (sec) |
N/A | 0.208 | 0.012 | 2.076 | 0.221 | 0.258 | 0.023 | 0.269 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 25 | 24 | 24 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.169 | 0.003 | 1.868 | 0.206 | 0.270 | 0.018 | 0.264 | 0.033 |
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 | 93 | 93 | 106 | 122 | 131 | 133 | 116 | 139 | 141 |
N.S. |
1 | 1.00 | 1.14 | 1.31 | 1.41 | 1.43 | 1.25 | 1.49 | 1.52 |
time (sec) |
N/A | 0.267 | 0.043 | 1.906 | 0.193 | 0.263 | 0.184 | 0.265 | 9.551 |
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 | 107 | 107 | 114 | 131 | 138 | 203 | 126 | 189 | 158 |
N.S. |
1 | 1.00 | 1.07 | 1.22 | 1.29 | 1.90 | 1.18 | 1.77 | 1.48 |
time (sec) |
N/A | 0.290 | 0.104 | 2.024 | 0.199 | 0.280 | 0.299 | 0.265 | 9.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 116 | 128 | 147 | 238 | 155 | 139 | 151 |
N.S. |
1 | 1.00 | 0.97 | 1.08 | 1.24 | 2.00 | 1.30 | 1.17 | 1.27 |
time (sec) |
N/A | 0.306 | 0.078 | 1.928 | 0.212 | 0.268 | 0.488 | 0.281 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 134 | 130 | 159 | 245 | 163 | 135 | 158 |
N.S. |
1 | 1.00 | 1.12 | 1.08 | 1.32 | 2.04 | 1.36 | 1.12 | 1.32 |
time (sec) |
N/A | 0.298 | 0.060 | 2.048 | 0.197 | 0.265 | 0.765 | 0.268 | 9.594 |
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 | 131 | 131 | 126 | 130 | 177 | 225 | 180 | 216 | 167 |
N.S. |
1 | 1.00 | 0.96 | 0.99 | 1.35 | 1.72 | 1.37 | 1.65 | 1.27 |
time (sec) |
N/A | 0.298 | 0.048 | 2.050 | 0.204 | 0.261 | 1.185 | 0.263 | 9.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 116 | 127 | 181 | 181 | 196 | 139 | 169 |
N.S. |
1 | 1.00 | 0.88 | 0.96 | 1.37 | 1.37 | 1.48 | 1.05 | 1.28 |
time (sec) |
N/A | 0.297 | 0.052 | 2.026 | 0.201 | 0.279 | 4.038 | 0.267 | 0.084 |
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 | 137 | 137 | 116 | 126 | 191 | 191 | 207 | 139 | 181 |
N.S. |
1 | 1.00 | 0.85 | 0.92 | 1.39 | 1.39 | 1.51 | 1.01 | 1.32 |
time (sec) |
N/A | 0.299 | 0.043 | 2.003 | 0.224 | 0.262 | 21.430 | 0.263 | 0.091 |
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 | 137 | 137 | 117 | 131 | 207 | 207 | 221 | 140 | 197 |
N.S. |
1 | 1.00 | 0.85 | 0.96 | 1.51 | 1.51 | 1.61 | 1.02 | 1.44 |
time (sec) |
N/A | 0.299 | 0.050 | 2.188 | 0.208 | 0.260 | 103.252 | 0.254 | 9.569 |
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 | 225 | 225 | 225 | 227 | 229 | 229 | 257 | 250 | 213 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.02 | 1.02 | 1.14 | 1.11 | 0.95 |
time (sec) |
N/A | 0.444 | 0.041 | 2.263 | 0.191 | 0.267 | 0.037 | 0.267 | 0.086 |
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 | 162 | 162 | 169 | 177 | 171 | 171 | 199 | 193 | 156 |
N.S. |
1 | 1.00 | 1.04 | 1.09 | 1.06 | 1.06 | 1.23 | 1.19 | 0.96 |
time (sec) |
N/A | 0.362 | 0.030 | 1.978 | 0.187 | 0.260 | 0.032 | 0.268 | 9.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 127 | 125 | 127 | 127 | 138 | 134 | 118 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 1.00 | 1.00 | 1.09 | 1.06 | 0.93 |
time (sec) |
N/A | 0.304 | 0.025 | 2.051 | 0.197 | 0.256 | 0.030 | 0.260 | 0.051 |
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 | 75 | 75 | 75 | 75 | 73 | 73 | 80 | 77 | 69 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.97 | 0.97 | 1.07 | 1.03 | 0.92 |
time (sec) |
N/A | 0.239 | 0.012 | 1.972 | 0.191 | 0.249 | 0.025 | 0.264 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 36 | 35 | 35 | 37 | 35 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.81 | 0.86 | 0.81 | 0.81 |
time (sec) |
N/A | 0.187 | 0.003 | 1.996 | 0.204 | 0.249 | 0.020 | 0.264 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 144 | 247 | 264 | 266 | 243 | 285 | 294 |
N.S. |
1 | 1.00 | 0.95 | 1.64 | 1.75 | 1.76 | 1.61 | 1.89 | 1.95 |
time (sec) |
N/A | 0.362 | 0.086 | 2.053 | 0.203 | 0.253 | 0.254 | 0.259 | 9.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 160 | 260 | 273 | 370 | 257 | 346 | 435 |
N.S. |
1 | 1.00 | 0.96 | 1.57 | 1.64 | 2.23 | 1.55 | 2.08 | 2.62 |
time (sec) |
N/A | 0.401 | 0.064 | 2.011 | 0.200 | 0.260 | 0.464 | 0.262 | 9.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 207 | 260 | 280 | 428 | 284 | 279 | 352 |
N.S. |
1 | 1.00 | 1.04 | 1.30 | 1.40 | 2.14 | 1.42 | 1.40 | 1.76 |
time (sec) |
N/A | 0.433 | 0.128 | 2.027 | 0.204 | 0.274 | 0.825 | 0.263 | 9.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 210 | 256 | 294 | 480 | 301 | 276 | 307 |
N.S. |
1 | 1.00 | 0.99 | 1.20 | 1.38 | 2.25 | 1.41 | 1.30 | 1.44 |
time (sec) |
N/A | 0.439 | 0.109 | 2.109 | 0.227 | 0.260 | 1.668 | 0.262 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 210 | 253 | 303 | 481 | 316 | 389 | 302 |
N.S. |
1 | 1.00 | 0.99 | 1.19 | 1.42 | 2.26 | 1.48 | 1.83 | 1.42 |
time (sec) |
N/A | 0.444 | 0.116 | 2.354 | 0.232 | 0.258 | 11.673 | 0.266 | 0.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 218 | 218 | 242 | 255 | 311 | 462 | 326 | 265 | 312 |
N.S. |
1 | 1.00 | 1.11 | 1.17 | 1.43 | 2.12 | 1.50 | 1.22 | 1.43 |
time (sec) |
N/A | 0.441 | 0.105 | 1.958 | 0.199 | 0.258 | 145.838 | 0.259 | 9.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 231 | 252 | 331 | 407 | 0 | 274 | 268 |
N.S. |
1 | 1.00 | 1.01 | 1.11 | 1.45 | 1.79 | 0.00 | 1.20 | 1.18 |
time (sec) |
N/A | 0.428 | 0.082 | 2.028 | 0.198 | 0.254 | 0.000 | 0.277 | 9.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 230 | 230 | 221 | 250 | 334 | 334 | 0 | 284 | 315 |
N.S. |
1 | 1.00 | 0.96 | 1.09 | 1.45 | 1.45 | 0.00 | 1.23 | 1.37 |
time (sec) |
N/A | 0.426 | 0.078 | 2.017 | 0.206 | 0.260 | 0.000 | 0.260 | 9.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 231 | 221 | 249 | 344 | 344 | 0 | 284 | 325 |
N.S. |
1 | 1.00 | 0.96 | 1.08 | 1.49 | 1.49 | 0.00 | 1.23 | 1.41 |
time (sec) |
N/A | 0.423 | 0.085 | 2.046 | 0.209 | 0.266 | 0.000 | 0.261 | 9.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 234 | 234 | 222 | 255 | 361 | 361 | 0 | 285 | 343 |
N.S. |
1 | 1.00 | 0.95 | 1.09 | 1.54 | 1.54 | 0.00 | 1.22 | 1.47 |
time (sec) |
N/A | 0.415 | 0.078 | 2.031 | 0.206 | 0.261 | 0.000 | 0.273 | 9.664 |
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 | 99 | 104 | 90 | 134 | 142 | 151 | 165 | 144 | 106 |
N.S. |
1 | 1.05 | 0.91 | 1.35 | 1.43 | 1.53 | 1.67 | 1.45 | 1.07 |
time (sec) |
N/A | 0.291 | 0.048 | 1.919 | 0.197 | 0.266 | 0.964 | 0.262 | 9.610 |
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 | 64 | 69 | 59 | 85 | 91 | 97 | 112 | 91 | 65 |
N.S. |
1 | 1.08 | 0.92 | 1.33 | 1.42 | 1.52 | 1.75 | 1.42 | 1.02 |
time (sec) |
N/A | 0.240 | 0.031 | 1.883 | 0.196 | 0.271 | 0.697 | 0.259 | 0.132 |
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 | 42 | 47 | 42 | 54 | 53 | 53 | 73 | 55 | 49 |
N.S. |
1 | 1.12 | 1.00 | 1.29 | 1.26 | 1.26 | 1.74 | 1.31 | 1.17 |
time (sec) |
N/A | 0.213 | 0.022 | 1.888 | 0.210 | 0.256 | 0.450 | 0.263 | 9.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 35 | 29 | 30 | 30 | 29 | 41 | 32 | 28 |
N.S. |
1 | 1.17 | 0.97 | 1.00 | 1.00 | 0.97 | 1.37 | 1.07 | 0.93 |
time (sec) |
N/A | 0.191 | 0.012 | 2.107 | 0.189 | 0.255 | 0.228 | 0.256 | 0.096 |
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 | 18 | 18 | 18 | 16 | 18 | 16 | 10 | 20 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.00 | 0.89 | 0.56 | 1.11 | 0.83 |
time (sec) |
N/A | 0.169 | 0.005 | 2.044 | 0.204 | 0.263 | 0.069 | 0.257 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 60 | 48 | 49 | 53 | 50 | 0 | 66 | 93 |
N.S. |
1 | 1.13 | 0.91 | 0.92 | 1.00 | 0.94 | 0.00 | 1.25 | 1.75 |
time (sec) |
N/A | 0.238 | 0.026 | 1.908 | 0.190 | 0.324 | 0.000 | 0.265 | 9.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 96 | 83 | 87 | 128 | 207 | 0 | 286 | 116 |
N.S. |
1 | 1.10 | 0.95 | 1.00 | 1.47 | 2.38 | 0.00 | 3.29 | 1.33 |
time (sec) |
N/A | 0.295 | 0.100 | 1.927 | 0.189 | 0.686 | 0.000 | 0.275 | 9.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 148 | 116 | 131 | 266 | 506 | 0 | 234 | 235 |
N.S. |
1 | 1.10 | 0.87 | 0.98 | 1.99 | 3.78 | 0.00 | 1.75 | 1.75 |
time (sec) |
N/A | 0.380 | 0.248 | 2.094 | 0.220 | 4.247 | 0.000 | 0.281 | 10.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 128 | 116 | 200 | 216 | 349 | 381 | 216 | 218 |
N.S. |
1 | 1.08 | 0.98 | 1.69 | 1.83 | 2.96 | 3.23 | 1.83 | 1.85 |
time (sec) |
N/A | 0.352 | 0.058 | 1.913 | 0.205 | 0.275 | 2.151 | 0.286 | 9.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 104 | 95 | 154 | 163 | 257 | 306 | 163 | 166 |
N.S. |
1 | 1.11 | 1.01 | 1.64 | 1.73 | 2.73 | 3.26 | 1.73 | 1.77 |
time (sec) |
N/A | 0.315 | 0.098 | 1.904 | 0.199 | 0.273 | 1.406 | 0.278 | 9.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 97 | 79 | 121 | 132 | 198 | 250 | 129 | 118 |
N.S. |
1 | 1.11 | 0.91 | 1.39 | 1.52 | 2.28 | 2.87 | 1.48 | 1.36 |
time (sec) |
N/A | 0.291 | 0.080 | 1.902 | 0.189 | 0.271 | 0.763 | 0.285 | 9.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 86 | 67 | 85 | 93 | 149 | 173 | 99 | 101 |
N.S. |
1 | 1.18 | 0.92 | 1.16 | 1.27 | 2.04 | 2.37 | 1.36 | 1.38 |
time (sec) |
N/A | 0.270 | 0.077 | 1.888 | 0.189 | 0.253 | 0.394 | 0.267 | 0.100 |
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 | 65 | 81 | 56 | 63 | 69 | 111 | 128 | 74 | 57 |
N.S. |
1 | 1.25 | 0.86 | 0.97 | 1.06 | 1.71 | 1.97 | 1.14 | 0.88 |
time (sec) |
N/A | 0.257 | 0.043 | 2.222 | 0.196 | 0.268 | 0.266 | 0.273 | 9.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 35 | 43 | 45 | 63 | 37 | 45 | 41 |
N.S. |
1 | 0.98 | 0.81 | 1.00 | 1.05 | 1.47 | 0.86 | 1.05 | 0.95 |
time (sec) |
N/A | 0.194 | 0.044 | 2.183 | 0.194 | 0.265 | 0.126 | 0.261 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 117 | 111 | 111 | 177 | 288 | 0 | 200 | 143 |
N.S. |
1 | 1.06 | 1.01 | 1.01 | 1.61 | 2.62 | 0.00 | 1.82 | 1.30 |
time (sec) |
N/A | 0.338 | 0.098 | 1.895 | 0.197 | 2.378 | 0.000 | 0.267 | 9.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 156 | 145 | 146 | 373 | 653 | 0 | 557 | 304 |
N.S. |
1 | 1.08 | 1.01 | 1.01 | 2.59 | 4.53 | 0.00 | 3.87 | 2.11 |
time (sec) |
N/A | 0.414 | 0.181 | 1.953 | 0.232 | 7.890 | 0.000 | 0.277 | 10.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 203 | 216 | 202 | 371 | 408 | 694 | 0 | 397 | 399 |
N.S. |
1 | 1.06 | 1.00 | 1.83 | 2.01 | 3.42 | 0.00 | 1.96 | 1.97 |
time (sec) |
N/A | 0.515 | 0.120 | 1.947 | 0.206 | 0.308 | 0.000 | 0.268 | 9.839 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 192 | 179 | 312 | 341 | 579 | 597 | 325 | 333 |
N.S. |
1 | 1.07 | 1.00 | 1.74 | 1.91 | 3.23 | 3.34 | 1.82 | 1.86 |
time (sec) |
N/A | 0.468 | 0.091 | 1.931 | 0.195 | 0.280 | 147.213 | 0.276 | 9.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 184 | 165 | 262 | 296 | 493 | 524 | 280 | 268 |
N.S. |
1 | 1.08 | 0.96 | 1.53 | 1.73 | 2.88 | 3.06 | 1.64 | 1.57 |
time (sec) |
N/A | 0.435 | 0.101 | 2.011 | 0.201 | 0.274 | 12.126 | 0.263 | 9.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 152 | 130 | 212 | 250 | 426 | 389 | 256 | 238 |
N.S. |
1 | 1.12 | 0.96 | 1.56 | 1.84 | 3.13 | 2.86 | 1.88 | 1.75 |
time (sec) |
N/A | 0.392 | 0.083 | 2.037 | 0.194 | 0.266 | 1.683 | 0.267 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 156 | 138 | 181 | 217 | 385 | 371 | 219 | 211 |
N.S. |
1 | 1.14 | 1.01 | 1.32 | 1.58 | 2.81 | 2.71 | 1.60 | 1.54 |
time (sec) |
N/A | 0.396 | 0.154 | 1.907 | 0.198 | 0.277 | 0.937 | 0.273 | 9.615 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 166 | 144 | 158 | 180 | 327 | 345 | 181 | 149 |
N.S. |
1 | 1.15 | 1.00 | 1.10 | 1.25 | 2.27 | 2.40 | 1.26 | 1.03 |
time (sec) |
N/A | 0.389 | 0.094 | 2.073 | 0.199 | 0.274 | 0.563 | 0.270 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 128 | 102 | 106 | 136 | 234 | 219 | 127 | 132 |
N.S. |
1 | 1.16 | 0.93 | 0.96 | 1.24 | 2.13 | 1.99 | 1.15 | 1.20 |
time (sec) |
N/A | 0.333 | 0.086 | 2.079 | 0.201 | 0.270 | 0.393 | 0.260 | 9.590 |
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 | 72 | 76 | 68 | 72 | 86 | 130 | 78 | 73 | 79 |
N.S. |
1 | 1.06 | 0.94 | 1.00 | 1.19 | 1.81 | 1.08 | 1.01 | 1.10 |
time (sec) |
N/A | 0.232 | 0.054 | 1.971 | 0.192 | 0.260 | 0.187 | 0.259 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 193 | 200 | 192 | 193 | 439 | 716 | 0 | 422 | 331 |
N.S. |
1 | 1.04 | 0.99 | 1.00 | 2.27 | 3.71 | 0.00 | 2.19 | 1.72 |
time (sec) |
N/A | 0.482 | 0.185 | 1.952 | 0.217 | 18.684 | 0.000 | 0.273 | 10.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 230 | 243 | 230 | 226 | 752 | 1305 | 0 | 867 | 603 |
N.S. |
1 | 1.06 | 1.00 | 0.98 | 3.27 | 5.67 | 0.00 | 3.77 | 2.62 |
time (sec) |
N/A | 0.608 | 0.266 | 1.927 | 0.235 | 40.403 | 0.000 | 0.289 | 10.421 |
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 | 210 | 194 | 281 | 188 | 439 | 497 | 434 | 255 | 361 |
N.S. |
1 | 0.92 | 1.34 | 0.90 | 2.09 | 2.37 | 2.07 | 1.21 | 1.72 |
time (sec) |
N/A | 0.390 | 1.783 | 1.990 | 0.208 | 0.318 | 0.468 | 0.284 | 10.239 |
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 | 162 | 155 | 173 | 132 | 283 | 337 | 284 | 171 | 231 |
N.S. |
1 | 0.96 | 1.07 | 0.81 | 1.75 | 2.08 | 1.75 | 1.06 | 1.43 |
time (sec) |
N/A | 0.313 | 1.109 | 2.049 | 0.190 | 0.265 | 0.441 | 0.285 | 9.992 |
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 | 99 | 98 | 122 | 85 | 154 | 205 | 167 | 102 | 127 |
N.S. |
1 | 0.99 | 1.23 | 0.86 | 1.56 | 2.07 | 1.69 | 1.03 | 1.28 |
time (sec) |
N/A | 0.223 | 0.647 | 1.888 | 0.193 | 0.281 | 0.432 | 0.282 | 9.469 |
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 | 60 | 60 | 83 | 56 | 63 | 121 | 102 | 59 | 55 |
N.S. |
1 | 1.00 | 1.38 | 0.93 | 1.05 | 2.02 | 1.70 | 0.98 | 0.92 |
time (sec) |
N/A | 0.186 | 0.069 | 1.833 | 0.240 | 0.290 | 0.229 | 0.268 | 9.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 138 | 402 | 99 | 0 | 488 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 3.12 | 0.77 | 0.00 | 3.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.334 | 3.289 | 2.544 | 0.000 | 0.334 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 146 | 159 | 120 | 0 | 846 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.14 | 0.86 | 0.00 | 6.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.313 | 0.704 | 2.371 | 0.000 | 0.315 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 122 | 94 | 0 | 479 | 0 | 407 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.74 | 0.00 | 3.77 | 0.00 | 3.20 | 0.00 |
time (sec) |
N/A | 0.257 | 10.229 | 2.133 | 0.000 | 0.287 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 183 | 192 | 191 | 167 | 0 | 969 | 0 | 831 | 0 |
N.S. |
1 | 1.05 | 1.04 | 0.91 | 0.00 | 5.30 | 0.00 | 4.54 | 0.00 |
time (sec) |
N/A | 0.320 | 10.314 | 2.153 | 0.000 | 0.573 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 258 | 271 | 243 | 243 | 0 | 1611 | 0 | 1219 | 0 |
N.S. |
1 | 1.05 | 0.94 | 0.94 | 0.00 | 6.24 | 0.00 | 4.72 | 0.00 |
time (sec) |
N/A | 0.445 | 10.799 | 2.087 | 0.000 | 0.521 | 0.000 | 0.567 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 337 | 359 | 308 | 357 | 0 | 2449 | 0 | 2144 | 0 |
N.S. |
1 | 1.07 | 0.91 | 1.06 | 0.00 | 7.27 | 0.00 | 6.36 | 0.00 |
time (sec) |
N/A | 0.601 | 11.115 | 2.170 | 0.000 | 0.467 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 271 | 231 | 370 | 266 | 624 | 706 | 864 | 372 | 0 |
N.S. |
1 | 0.85 | 1.37 | 0.98 | 2.30 | 2.61 | 3.19 | 1.37 | 0.00 |
time (sec) |
N/A | 0.427 | 2.488 | 2.085 | 0.202 | 0.312 | 0.523 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 214 | 192 | 280 | 188 | 416 | 490 | 570 | 261 | 0 |
N.S. |
1 | 0.90 | 1.31 | 0.88 | 1.94 | 2.29 | 2.66 | 1.22 | 0.00 |
time (sec) |
N/A | 0.352 | 1.816 | 2.017 | 0.201 | 0.287 | 0.492 | 0.286 | 0.000 |
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 | 137 | 135 | 167 | 116 | 236 | 302 | 326 | 163 | 208 |
N.S. |
1 | 0.99 | 1.22 | 0.85 | 1.72 | 2.20 | 2.38 | 1.19 | 1.52 |
time (sec) |
N/A | 0.254 | 1.138 | 1.869 | 0.195 | 0.297 | 0.478 | 0.296 | 9.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 97 | 107 | 73 | 102 | 170 | 257 | 81 | 87 |
N.S. |
1 | 1.09 | 1.20 | 0.82 | 1.15 | 1.91 | 2.89 | 0.91 | 0.98 |
time (sec) |
N/A | 0.210 | 0.069 | 1.829 | 0.208 | 0.269 | 0.378 | 0.292 | 0.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 216 | 235 | 500 | 184 | 0 | 901 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 2.31 | 0.85 | 0.00 | 4.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.487 | 3.737 | 2.193 | 0.000 | 0.513 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 210 | 205 | 185 | 0 | 1015 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.04 | 0.93 | 0.00 | 5.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.449 | 10.722 | 2.488 | 0.000 | 0.333 | 0.000 | 0.000 | 0.000 |