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 | C | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 60 | 46 | 76 | 0 | 43 | 23 |
N.S. |
1 | 1.00 | 1.00 | 3.16 | 2.42 | 4.00 | 0.00 | 2.26 | 1.21 |
time (sec) |
N/A | 0.242 | 0.021 | 0.236 | 0.284 | 0.252 | 0.000 | 0.269 | 2.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 80 | 69 | 42 | 0 | 213 | 0 | 71 | 71 |
N.S. |
1 | 1.16 | 1.00 | 0.61 | 0.00 | 3.09 | 0.00 | 1.03 | 1.03 |
time (sec) |
N/A | 0.297 | 0.097 | 0.261 | 0.000 | 0.271 | 0.000 | 0.342 | 0.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 81 | 60 | 0 | 306 | 0 | 81 | 82 |
N.S. |
1 | 1.00 | 0.93 | 0.69 | 0.00 | 3.52 | 0.00 | 0.93 | 0.94 |
time (sec) |
N/A | 0.409 | 0.148 | 0.306 | 0.000 | 0.267 | 0.000 | 0.288 | 3.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 93 | 87 | 84 | 0 | 300 | 0 | 100 | 98 |
N.S. |
1 | 1.07 | 1.00 | 0.97 | 0.00 | 3.45 | 0.00 | 1.15 | 1.13 |
time (sec) |
N/A | 0.370 | 0.093 | 0.293 | 0.000 | 0.280 | 0.000 | 0.273 | 3.442 |
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 | 81 | 81 | 77 | 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 | 0.268 | 0.184 | 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 | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 14 | 10 | 9 | 16 | 42 | 0 | 16 | 16 |
N.S. |
1 | 1.40 | 1.00 | 0.90 | 1.60 | 4.20 | 0.00 | 1.60 | 1.60 |
time (sec) |
N/A | 0.201 | 0.008 | 0.199 | 0.271 | 0.257 | 0.000 | 0.256 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 17 | 49 | 118 | 0 | 36 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 2.45 | 5.90 | 0.00 | 1.80 | 2.35 |
time (sec) |
N/A | 0.203 | 0.017 | 0.200 | 0.272 | 0.263 | 0.000 | 0.269 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 30 | 28 | 72 | 60 | 128 | 0 | 54 | 52 |
N.S. |
1 | 1.07 | 1.00 | 2.57 | 2.14 | 4.57 | 0.00 | 1.93 | 1.86 |
time (sec) |
N/A | 0.266 | 0.023 | 0.244 | 0.274 | 0.257 | 0.000 | 0.263 | 2.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 76 | 42 | 0 | 293 | 0 | 75 | 141 |
N.S. |
1 | 1.00 | 0.93 | 0.51 | 0.00 | 3.57 | 0.00 | 0.91 | 1.72 |
time (sec) |
N/A | 0.369 | 0.165 | 0.256 | 0.000 | 0.254 | 0.000 | 0.280 | 4.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 42 | 38 | 102 | 0 | 164 | 0 | 68 | 56 |
N.S. |
1 | 1.11 | 1.00 | 2.68 | 0.00 | 4.32 | 0.00 | 1.79 | 1.47 |
time (sec) |
N/A | 0.291 | 0.043 | 0.243 | 0.000 | 0.270 | 0.000 | 0.274 | 2.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 42 | 39 | 42 | 35 | 0 | 38 | 35 |
N.S. |
1 | 1.00 | 2.62 | 2.44 | 2.62 | 2.19 | 0.00 | 2.38 | 2.19 |
time (sec) |
N/A | 0.189 | 0.061 | 1.183 | 0.270 | 0.252 | 0.000 | 0.258 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 27 | 17 | 26 | 45 | 52 | 0 | 41 | 27 |
N.S. |
1 | 1.29 | 0.81 | 1.24 | 2.14 | 2.48 | 0.00 | 1.95 | 1.29 |
time (sec) |
N/A | 0.207 | 0.008 | 1.229 | 0.268 | 0.253 | 0.000 | 0.260 | 2.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 110 | 40 | 0 | 215 | 0 | 115 | 251 |
N.S. |
1 | 1.00 | 1.55 | 0.56 | 0.00 | 3.03 | 0.00 | 1.62 | 3.54 |
time (sec) |
N/A | 0.252 | 0.038 | 1.228 | 0.000 | 0.261 | 0.000 | 0.342 | 2.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 80 | 57 | 101 | 0 | 182 | 0 | 118 | 100 |
N.S. |
1 | 1.29 | 0.92 | 1.63 | 0.00 | 2.94 | 0.00 | 1.90 | 1.61 |
time (sec) |
N/A | 0.311 | 0.057 | 1.320 | 0.000 | 0.246 | 0.000 | 0.291 | 2.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 269 | 78 | 0 | 250 | 0 | 154 | 288 |
N.S. |
1 | 1.00 | 3.16 | 0.92 | 0.00 | 2.94 | 0.00 | 1.81 | 3.39 |
time (sec) |
N/A | 0.304 | 0.071 | 1.254 | 0.000 | 0.264 | 0.000 | 0.283 | 2.440 |
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 | 7 | 7 | 7 | 6 | 7 | 6 | 0 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.00 | 0.86 | 0.00 | 0.43 | 0.43 |
time (sec) |
N/A | 0.213 | 0.001 | 0.233 | 0.269 | 0.249 | 0.000 | 0.269 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 40 | 39 | 31 | 0 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 2.67 | 2.60 | 2.07 | 0.00 | 1.27 | 1.27 |
time (sec) |
N/A | 0.205 | 0.021 | 0.251 | 0.273 | 0.253 | 0.000 | 0.299 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 62 | 50 | 76 | 0 | 44 | 42 |
N.S. |
1 | 1.00 | 1.00 | 2.38 | 1.92 | 2.92 | 0.00 | 1.69 | 1.62 |
time (sec) |
N/A | 0.208 | 0.017 | 0.272 | 0.269 | 0.257 | 0.000 | 0.280 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 87 | 84 | 41 | 0 | 243 | 0 | 68 | 282 |
N.S. |
1 | 1.16 | 1.12 | 0.55 | 0.00 | 3.24 | 0.00 | 0.91 | 3.76 |
time (sec) |
N/A | 0.278 | 0.091 | 0.295 | 0.000 | 0.258 | 0.000 | 0.283 | 4.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 38 | 30 | 92 | 0 | 107 | 0 | 58 | 41 |
N.S. |
1 | 1.06 | 0.83 | 2.56 | 0.00 | 2.97 | 0.00 | 1.61 | 1.14 |
time (sec) |
N/A | 0.241 | 0.018 | 0.271 | 0.000 | 0.250 | 0.000 | 0.265 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 23 | 15 | 12 | 27 | 19 | 20 | 25 | 6 |
N.S. |
1 | 2.88 | 1.88 | 1.50 | 3.38 | 2.38 | 2.50 | 3.12 | 0.75 |
time (sec) |
N/A | 0.181 | 0.003 | 0.321 | 0.198 | 0.254 | 0.130 | 0.249 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 25 | 17 | 14 | 27 | 33 | 20 | 26 | 11 |
N.S. |
1 | 1.47 | 1.00 | 0.82 | 1.59 | 1.94 | 1.18 | 1.53 | 0.65 |
time (sec) |
N/A | 0.179 | 0.006 | 0.428 | 0.180 | 0.243 | 0.140 | 0.258 | 2.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 25 | 17 | 14 | 27 | 36 | 20 | 27 | 14 |
N.S. |
1 | 1.47 | 1.00 | 0.82 | 1.59 | 2.12 | 1.18 | 1.59 | 0.82 |
time (sec) |
N/A | 0.181 | 0.004 | 0.405 | 0.180 | 0.237 | 0.130 | 0.266 | 2.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 25 | 28 | 0 | 42 | 42 | 59 | 26 |
N.S. |
1 | 1.00 | 0.71 | 0.80 | 0.00 | 1.20 | 1.20 | 1.69 | 0.74 |
time (sec) |
N/A | 0.212 | 0.025 | 0.338 | 0.000 | 0.247 | 0.248 | 0.259 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 27 | 17 | 20 | 25 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.80 | 1.13 | 1.33 | 1.67 | 0.60 |
time (sec) |
N/A | 0.178 | 0.005 | 0.326 | 0.185 | 0.248 | 0.125 | 0.265 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 27 | 20 | 20 | 27 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.59 | 1.18 | 1.18 | 1.59 | 1.18 |
time (sec) |
N/A | 0.178 | 0.004 | 0.434 | 0.186 | 0.263 | 0.130 | 0.259 | 2.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 27 | 34 | 20 | 27 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.59 | 2.00 | 1.18 | 1.59 | 0.88 |
time (sec) |
N/A | 0.176 | 0.004 | 0.411 | 0.189 | 0.238 | 0.129 | 0.274 | 2.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 25 | 28 | 0 | 42 | 56 | 59 | 26 |
N.S. |
1 | 1.00 | 0.71 | 0.80 | 0.00 | 1.20 | 1.60 | 1.69 | 0.74 |
time (sec) |
N/A | 0.202 | 0.020 | 0.312 | 0.000 | 0.251 | 0.255 | 0.256 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 27 | 51 | 16 | 52 | 73 | 0 | 45 | 48 |
N.S. |
1 | 1.42 | 2.68 | 0.84 | 2.74 | 3.84 | 0.00 | 2.37 | 2.53 |
time (sec) |
N/A | 0.203 | 0.042 | 0.194 | 0.283 | 0.252 | 0.000 | 0.263 | 2.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 55 | 17 | 153 | 82 | 0 | 45 | 53 |
N.S. |
1 | 1.00 | 2.75 | 0.85 | 7.65 | 4.10 | 0.00 | 2.25 | 2.65 |
time (sec) |
N/A | 0.198 | 0.053 | 0.196 | 0.287 | 0.255 | 0.000 | 0.259 | 2.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 80 | 113 | 42 | 0 | 213 | 0 | 119 | 133 |
N.S. |
1 | 1.16 | 1.64 | 0.61 | 0.00 | 3.09 | 0.00 | 1.72 | 1.93 |
time (sec) |
N/A | 0.282 | 0.033 | 0.304 | 0.000 | 0.260 | 0.000 | 0.351 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 249 | 42 | 0 | 293 | 0 | 127 | 141 |
N.S. |
1 | 1.00 | 3.04 | 0.51 | 0.00 | 3.57 | 0.00 | 1.55 | 1.72 |
time (sec) |
N/A | 0.317 | 0.033 | 0.272 | 0.000 | 0.262 | 0.000 | 0.303 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 93 | 281 | 79 | 0 | 258 | 0 | 157 | 170 |
N.S. |
1 | 1.07 | 3.23 | 0.91 | 0.00 | 2.97 | 0.00 | 1.80 | 1.95 |
time (sec) |
N/A | 0.356 | 0.068 | 0.303 | 0.000 | 0.259 | 0.000 | 0.287 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 14 | 25 | 16 | 29 | 52 | 0 | 26 | 29 |
N.S. |
1 | 1.40 | 2.50 | 1.60 | 2.90 | 5.20 | 0.00 | 2.60 | 2.90 |
time (sec) |
N/A | 0.194 | 0.021 | 0.313 | 0.191 | 0.249 | 0.000 | 0.254 | 2.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 55 | 47 | 50 | 57 | 104 | 0 | 55 | 57 |
N.S. |
1 | 1.22 | 1.04 | 1.11 | 1.27 | 2.31 | 0.00 | 1.22 | 1.27 |
time (sec) |
N/A | 0.295 | 0.027 | 0.257 | 0.276 | 0.251 | 0.000 | 0.263 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 30 | 73 | 63 | 70 | 101 | 0 | 67 | 71 |
N.S. |
1 | 1.07 | 2.61 | 2.25 | 2.50 | 3.61 | 0.00 | 2.39 | 2.54 |
time (sec) |
N/A | 0.264 | 0.051 | 0.248 | 0.275 | 0.266 | 0.000 | 0.255 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 133 | 190 | 0 | 272 | 0 | 157 | 143 |
N.S. |
1 | 1.00 | 1.21 | 1.73 | 0.00 | 2.47 | 0.00 | 1.43 | 1.30 |
time (sec) |
N/A | 0.411 | 0.105 | 0.276 | 0.000 | 0.264 | 0.000 | 0.296 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 42 | 95 | 87 | 0 | 157 | 0 | 89 | 101 |
N.S. |
1 | 1.11 | 2.50 | 2.29 | 0.00 | 4.13 | 0.00 | 2.34 | 2.66 |
time (sec) |
N/A | 0.298 | 0.056 | 0.285 | 0.000 | 0.261 | 0.000 | 0.254 | 0.089 |
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 | 76 | 76 | 75 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.264 | 0.321 | 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 | C | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 44 | 43 | 68 | 0 | 39 | 32 |
N.S. |
1 | 1.00 | 1.00 | 2.93 | 2.87 | 4.53 | 0.00 | 2.60 | 2.13 |
time (sec) |
N/A | 0.191 | 0.006 | 1.274 | 0.278 | 0.252 | 0.000 | 0.272 | 2.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 40 | 114 | 31 | 0 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 2.67 | 7.60 | 2.07 | 0.00 | 1.27 | 1.27 |
time (sec) |
N/A | 0.197 | 0.020 | 1.375 | 0.277 | 0.248 | 0.000 | 0.259 | 2.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 67 | 40 | 0 | 215 | 0 | 135 | 126 |
N.S. |
1 | 1.00 | 0.94 | 0.56 | 0.00 | 3.03 | 0.00 | 1.90 | 1.77 |
time (sec) |
N/A | 0.239 | 0.072 | 1.448 | 0.000 | 0.259 | 0.000 | 0.359 | 1.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 89 | 84 | 41 | 0 | 243 | 0 | 68 | 297 |
N.S. |
1 | 1.19 | 1.12 | 0.55 | 0.00 | 3.24 | 0.00 | 0.91 | 3.96 |
time (sec) |
N/A | 0.293 | 0.088 | 1.189 | 0.000 | 0.253 | 0.000 | 0.282 | 4.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 81 | 83 | 0 | 282 | 0 | 177 | 206 |
N.S. |
1 | 1.00 | 0.95 | 0.98 | 0.00 | 3.32 | 0.00 | 2.08 | 2.42 |
time (sec) |
N/A | 0.267 | 0.055 | 1.282 | 0.000 | 0.266 | 0.000 | 0.266 | 4.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 21 | 8 | 19 | 19 | 0 | 16 | 19 |
N.S. |
1 | 1.00 | 3.00 | 1.14 | 2.71 | 2.71 | 0.00 | 2.29 | 2.71 |
time (sec) |
N/A | 0.210 | 0.010 | 0.255 | 0.204 | 0.264 | 0.000 | 0.256 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 27 | 21 | 24 | 47 | 52 | 0 | 40 | 29 |
N.S. |
1 | 1.29 | 1.00 | 1.14 | 2.24 | 2.48 | 0.00 | 1.90 | 1.38 |
time (sec) |
N/A | 0.197 | 0.008 | 0.271 | 0.267 | 0.252 | 0.000 | 0.281 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 67 | 53 | 60 | 54 | 0 | 57 | 61 |
N.S. |
1 | 1.00 | 2.58 | 2.04 | 2.31 | 2.08 | 0.00 | 2.19 | 2.35 |
time (sec) |
N/A | 0.213 | 0.061 | 0.271 | 0.275 | 0.250 | 0.000 | 0.276 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 80 | 57 | 101 | 0 | 180 | 0 | 108 | 104 |
N.S. |
1 | 1.29 | 0.92 | 1.63 | 0.00 | 2.90 | 0.00 | 1.74 | 1.68 |
time (sec) |
N/A | 0.309 | 0.068 | 0.290 | 0.000 | 0.259 | 0.000 | 0.280 | 2.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 37 | 91 | 77 | 0 | 101 | 0 | 79 | 91 |
N.S. |
1 | 1.03 | 2.53 | 2.14 | 0.00 | 2.81 | 0.00 | 2.19 | 2.53 |
time (sec) |
N/A | 0.267 | 0.058 | 0.280 | 0.000 | 0.255 | 0.000 | 0.264 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 70 | 82 | 66 | 0 | 59 | 88 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 0.94 | 0.00 | 0.84 | 1.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.336 | 0.094 | 0.000 | 0.089 | 0.076 | 0.000 | 0.000 | 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 | 94 | 104 | 50 | 74 | 86 | 74 | 119 | 73 | 64 |
N.S. |
1 | 1.11 | 0.53 | 0.79 | 0.91 | 0.79 | 1.27 | 0.78 | 0.68 |
time (sec) |
N/A | 0.386 | 0.067 | 0.883 | 0.190 | 0.256 | 0.306 | 0.260 | 2.206 |
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 | 64 | 66 | 39 | 58 | 64 | 62 | 75 | 57 | 46 |
N.S. |
1 | 1.03 | 0.61 | 0.91 | 1.00 | 0.97 | 1.17 | 0.89 | 0.72 |
time (sec) |
N/A | 0.283 | 0.045 | 0.652 | 0.195 | 0.257 | 0.233 | 0.273 | 2.162 |
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 | 44 | 49 | 28 | 42 | 46 | 42 | 56 | 41 | 28 |
N.S. |
1 | 1.11 | 0.64 | 0.95 | 1.05 | 0.95 | 1.27 | 0.93 | 0.64 |
time (sec) |
N/A | 0.241 | 0.041 | 0.499 | 0.204 | 0.256 | 0.201 | 0.258 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 37 | 14 | 13 | 22 | 19 | 29 | 13 |
N.S. |
1 | 1.00 | 2.47 | 0.93 | 0.87 | 1.47 | 1.27 | 1.93 | 0.87 |
time (sec) |
N/A | 0.184 | 0.004 | 0.288 | 0.184 | 0.252 | 0.088 | 0.272 | 2.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 33 | 25 | 26 | 23 | 37 | 0 | 23 | 0 |
N.S. |
1 | 1.22 | 0.93 | 0.96 | 0.85 | 1.37 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.362 | 0.014 | 0.882 | 0.245 | 0.250 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 49 | 42 | 55 | 27 | 65 | 0 | 52 | 0 |
N.S. |
1 | 1.26 | 1.08 | 1.41 | 0.69 | 1.67 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.433 | 0.051 | 1.133 | 0.254 | 0.257 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 77 | 61 | 89 | 30 | 104 | 0 | 86 | 0 |
N.S. |
1 | 1.28 | 1.02 | 1.48 | 0.50 | 1.73 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.534 | 0.101 | 1.205 | 0.250 | 0.246 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 97 | 77 | 121 | 31 | 115 | 0 | 120 | 0 |
N.S. |
1 | 1.14 | 0.91 | 1.42 | 0.36 | 1.35 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.628 | 0.093 | 1.542 | 0.253 | 0.248 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 114 | 0 | 113 | 162 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.84 | 1.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.400 | 0.180 | 0.000 | 0.119 | 0.082 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 152 | 86 | 141 | 160 | 135 | 146 | 140 | 108 |
N.S. |
1 | 1.30 | 0.74 | 1.21 | 1.37 | 1.15 | 1.25 | 1.20 | 0.92 |
time (sec) |
N/A | 0.679 | 0.279 | 2.872 | 0.210 | 0.257 | 0.410 | 0.271 | 2.229 |
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 | 83 | 91 | 65 | 109 | 122 | 105 | 105 | 108 | 69 |
N.S. |
1 | 1.10 | 0.78 | 1.31 | 1.47 | 1.27 | 1.27 | 1.30 | 0.83 |
time (sec) |
N/A | 0.446 | 0.152 | 2.421 | 0.213 | 0.271 | 0.308 | 0.274 | 2.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 51 | 46 | 56 | 84 | 74 | 61 | 76 | 41 |
N.S. |
1 | 1.13 | 1.02 | 1.24 | 1.87 | 1.64 | 1.36 | 1.69 | 0.91 |
time (sec) |
N/A | 0.259 | 0.085 | 1.899 | 0.207 | 0.258 | 0.254 | 0.280 | 0.099 |
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 | 15 | 15 | 15 | 14 | 13 | 38 | 20 | 54 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 2.53 | 1.33 | 3.60 | 0.87 |
time (sec) |
N/A | 0.188 | 0.003 | 0.757 | 0.189 | 0.244 | 0.100 | 0.278 | 2.147 |
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 | 47 | 47 | 39 | 47 | 42 | 67 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.00 | 0.89 | 1.43 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.309 | 0.015 | 1.376 | 0.262 | 0.266 | 0.000 | 0.271 | 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 | 80 | 80 | 70 | 95 | 50 | 124 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.19 | 0.62 | 1.55 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.365 | 0.125 | 1.773 | 0.272 | 0.254 | 0.000 | 0.268 | 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 | 119 | 119 | 105 | 159 | 58 | 196 | 0 | 156 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.34 | 0.49 | 1.65 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.429 | 0.187 | 2.607 | 0.276 | 0.263 | 0.000 | 0.273 | 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 | 154 | 154 | 138 | 226 | 58 | 223 | 0 | 223 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.47 | 0.38 | 1.45 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.487 | 0.217 | 3.464 | 0.273 | 0.250 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 110 | 0 | 117 | 172 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.84 | 1.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.449 | 0.135 | 0.000 | 0.115 | 0.089 | 0.000 | 0.000 | 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 | 155 | 207 | 91 | 146 | 171 | 191 | 226 | 145 | 125 |
N.S. |
1 | 1.34 | 0.59 | 0.94 | 1.10 | 1.23 | 1.46 | 0.94 | 0.81 |
time (sec) |
N/A | 0.771 | 0.420 | 7.582 | 0.200 | 0.264 | 0.688 | 0.291 | 2.348 |
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 | 101 | 111 | 70 | 114 | 127 | 154 | 150 | 113 | 89 |
N.S. |
1 | 1.10 | 0.69 | 1.13 | 1.26 | 1.52 | 1.49 | 1.12 | 0.88 |
time (sec) |
N/A | 0.392 | 0.162 | 5.505 | 0.214 | 0.248 | 0.442 | 0.273 | 2.240 |
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 | 75 | 50 | 69 | 91 | 108 | 110 | 81 | 57 |
N.S. |
1 | 1.15 | 0.77 | 1.06 | 1.40 | 1.66 | 1.69 | 1.25 | 0.88 |
time (sec) |
N/A | 0.328 | 0.091 | 3.924 | 0.206 | 0.261 | 0.302 | 0.268 | 0.120 |
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 | 15 | 15 | 15 | 14 | 13 | 54 | 20 | 57 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 3.60 | 1.33 | 3.80 | 0.87 |
time (sec) |
N/A | 0.186 | 0.002 | 2.097 | 0.183 | 0.253 | 0.146 | 0.271 | 2.128 |
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 | 53 | 53 | 47 | 50 | 45 | 73 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.94 | 0.85 | 1.38 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.315 | 0.040 | 2.880 | 0.286 | 0.251 | 0.000 | 0.260 | 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 | 89 | 89 | 80 | 105 | 53 | 139 | 0 | 100 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.18 | 0.60 | 1.56 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.388 | 0.126 | 4.392 | 0.294 | 0.244 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 112 | 173 | 60 | 227 | 0 | 168 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.38 | 0.48 | 1.82 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.457 | 0.371 | 6.585 | 0.327 | 0.246 | 0.000 | 0.263 | 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 | 169 | 169 | 150 | 241 | 59 | 261 | 0 | 236 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.43 | 0.35 | 1.54 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.507 | 0.334 | 9.278 | 0.288 | 0.247 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 13 | 13 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.62 | 1.62 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 0.221 | 0.004 | 0.361 | 0.233 | 0.245 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 26 | 16 | 15 | 15 | 24 | 0 | 30 | 0 |
N.S. |
1 | 1.62 | 1.00 | 0.94 | 0.94 | 1.50 | 0.00 | 1.88 | 0.00 |
time (sec) |
N/A | 0.284 | 0.005 | 0.406 | 0.252 | 0.242 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 40 | 27 | 24 | 13 | 43 | 0 | 48 | 0 |
N.S. |
1 | 1.48 | 1.00 | 0.89 | 0.48 | 1.59 | 0.00 | 1.78 | 0.00 |
time (sec) |
N/A | 0.355 | 0.006 | 0.451 | 0.241 | 0.254 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 114 | 0 | 113 | 162 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.84 | 1.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.397 | 0.216 | 0.000 | 0.125 | 0.085 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 150 | 84 | 141 | 160 | 135 | 146 | 140 | 119 |
N.S. |
1 | 1.28 | 0.72 | 1.21 | 1.37 | 1.15 | 1.25 | 1.20 | 1.02 |
time (sec) |
N/A | 0.683 | 0.275 | 3.878 | 0.251 | 0.270 | 0.411 | 0.253 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 102 | 66 | 109 | 122 | 104 | 105 | 108 | 82 |
N.S. |
1 | 1.23 | 0.80 | 1.31 | 1.47 | 1.25 | 1.27 | 1.30 | 0.99 |
time (sec) |
N/A | 0.436 | 0.304 | 2.984 | 0.215 | 0.251 | 0.330 | 0.306 | 2.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 43 | 38 | 56 | 84 | 76 | 61 | 76 | 44 |
N.S. |
1 | 0.96 | 0.84 | 1.24 | 1.87 | 1.69 | 1.36 | 1.69 | 0.98 |
time (sec) |
N/A | 0.258 | 0.094 | 2.505 | 0.216 | 0.281 | 0.217 | 0.254 | 2.153 |
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 | 15 | 15 | 15 | 14 | 13 | 32 | 20 | 54 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 2.13 | 1.33 | 3.60 | 0.87 |
time (sec) |
N/A | 0.182 | 0.003 | 1.153 | 0.201 | 0.257 | 0.099 | 0.258 | 2.091 |
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 | 47 | 47 | 41 | 47 | 42 | 67 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.87 | 1.00 | 0.89 | 1.43 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.288 | 0.015 | 1.663 | 0.287 | 0.266 | 0.000 | 0.265 | 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 | 80 | 80 | 68 | 96 | 50 | 126 | 0 | 91 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.20 | 0.62 | 1.58 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.343 | 0.141 | 1.881 | 0.309 | 0.242 | 0.000 | 0.268 | 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 | 119 | 119 | 107 | 159 | 58 | 195 | 0 | 156 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.34 | 0.49 | 1.64 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.407 | 0.153 | 2.733 | 0.272 | 0.251 | 0.000 | 0.262 | 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 | 154 | 154 | 138 | 229 | 58 | 224 | 0 | 222 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.49 | 0.38 | 1.45 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.472 | 0.174 | 3.822 | 0.289 | 0.248 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 106 | 0 | 71 | 122 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.84 | 1.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.324 | 0.121 | 0.000 | 0.091 | 0.088 | 0.000 | 0.000 | 0.000 |
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 | 79 | 79 | 58 | 79 | 91 | 140 | 250 | 78 | 70 |
N.S. |
1 | 1.00 | 0.73 | 1.00 | 1.15 | 1.77 | 3.16 | 0.99 | 0.89 |
time (sec) |
N/A | 0.305 | 0.110 | 11.058 | 0.214 | 0.247 | 0.553 | 0.274 | 2.284 |
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 | 60 | 60 | 48 | 63 | 69 | 110 | 204 | 62 | 52 |
N.S. |
1 | 1.00 | 0.80 | 1.05 | 1.15 | 1.83 | 3.40 | 1.03 | 0.87 |
time (sec) |
N/A | 0.282 | 0.099 | 7.806 | 0.250 | 0.263 | 0.440 | 0.249 | 2.207 |
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 | 41 | 41 | 41 | 47 | 51 | 88 | 131 | 46 | 36 |
N.S. |
1 | 1.00 | 1.00 | 1.15 | 1.24 | 2.15 | 3.20 | 1.12 | 0.88 |
time (sec) |
N/A | 0.228 | 0.154 | 4.937 | 0.229 | 0.270 | 0.311 | 0.268 | 0.108 |
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 | 46 | 51 | 23 | 33 | 39 | 40 | 92 | 32 | 18 |
N.S. |
1 | 1.11 | 0.50 | 0.72 | 0.85 | 0.87 | 2.00 | 0.70 | 0.39 |
time (sec) |
N/A | 0.260 | 0.011 | 3.158 | 0.211 | 0.255 | 0.157 | 0.256 | 0.071 |
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 | 33 | 33 | 32 | 30 | 27 | 41 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.91 | 0.82 | 1.24 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.255 | 0.262 | 3.394 | 0.252 | 0.255 | 0.000 | 0.271 | 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 | 52 | 52 | 45 | 54 | 32 | 88 | 0 | 55 | 0 |
N.S. |
1 | 1.00 | 0.87 | 1.04 | 0.62 | 1.69 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.280 | 0.058 | 4.190 | 0.265 | 0.250 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 65 | 92 | 36 | 140 | 0 | 89 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.37 | 0.54 | 2.09 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.318 | 0.069 | 5.999 | 0.253 | 0.266 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 79 | 122 | 36 | 172 | 0 | 123 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.33 | 0.39 | 1.87 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.360 | 0.130 | 8.790 | 0.271 | 0.263 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 209 | 209 | 175 | 0 | 171 | 248 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.82 | 1.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.526 | 0.261 | 0.000 | 0.154 | 0.102 | 0.000 | 0.000 | 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 | 202 | 202 | 125 | 213 | 245 | 274 | 253 | 212 | 167 |
N.S. |
1 | 1.00 | 0.62 | 1.05 | 1.21 | 1.36 | 1.25 | 1.05 | 0.83 |
time (sec) |
N/A | 0.481 | 0.780 | 24.677 | 0.238 | 0.253 | 0.753 | 0.263 | 0.548 |
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 | 148 | 148 | 105 | 165 | 187 | 209 | 182 | 164 | 123 |
N.S. |
1 | 1.00 | 0.71 | 1.11 | 1.26 | 1.41 | 1.23 | 1.11 | 0.83 |
time (sec) |
N/A | 0.401 | 0.188 | 18.546 | 0.267 | 0.249 | 0.554 | 0.267 | 2.570 |