Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 49 | 34 | 41 | 182 | 60 | 216 | 127 | 79 |
N.S. |
1 | 1.14 | 0.79 | 0.95 | 4.23 | 1.40 | 5.02 | 2.95 | 1.84 |
time (sec) |
N/A | 0.189 | 0.014 | 2.584 | 0.215 | 0.385 | 2.030 | 0.294 | 9.875 |
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 | 39 | 39 | 29 | 38 | 37 | 47 | 139 | 37 | 57 |
N.S. |
1 | 1.00 | 0.74 | 0.97 | 0.95 | 1.21 | 3.56 | 0.95 | 1.46 |
time (sec) |
N/A | 0.169 | 0.008 | 2.359 | 0.191 | 0.338 | 0.256 | 0.281 | 9.872 |
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 | 38 | 47 | 27 | 28 | 32 | 36 | 116 | 59 | 45 |
N.S. |
1 | 1.24 | 0.71 | 0.74 | 0.84 | 0.95 | 3.05 | 1.55 | 1.18 |
time (sec) |
N/A | 0.183 | 0.005 | 2.405 | 0.209 | 0.278 | 0.548 | 0.288 | 9.894 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 21 | 20 | 20 | 30 | 48 | 0 | 30 |
N.S. |
1 | 1.00 | 0.66 | 0.62 | 0.62 | 0.94 | 1.50 | 0.00 | 0.94 |
time (sec) |
N/A | 0.171 | 0.004 | 2.455 | 0.197 | 0.281 | 0.165 | 0.000 | 9.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 45 | 32 | 30 | 34 | 49 | 0 | 0 | 42 |
N.S. |
1 | 1.07 | 0.76 | 0.71 | 0.81 | 1.17 | 0.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.183 | 0.011 | 2.787 | 0.210 | 0.322 | 0.000 | 0.000 | 9.975 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 25 | 29 | 45 | 70 | 100 | 0 | 52 |
N.S. |
1 | 1.00 | 0.64 | 0.74 | 1.15 | 1.79 | 2.56 | 0.00 | 1.33 |
time (sec) |
N/A | 0.176 | 0.007 | 3.038 | 0.207 | 0.404 | 0.470 | 0.000 | 10.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 30 | 95 | 13 | 13 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.73 | 2.32 | 0.32 | 0.32 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.182 | 0.008 | 2.594 | 0.199 | 0.392 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 32 | 74 | 15 | 15 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 1.72 | 0.35 | 0.35 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.191 | 0.007 | 2.512 | 0.196 | 0.338 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 102 | 107 | 120 | 120 | 143 | 137 | 113 |
N.S. |
1 | 1.00 | 2.27 | 2.38 | 2.67 | 2.67 | 3.18 | 3.04 | 2.51 |
time (sec) |
N/A | 0.254 | 0.020 | 2.249 | 0.195 | 0.321 | 0.033 | 0.277 | 10.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 66 | 46 | 97 | 97 | 114 | 73 | 93 |
N.S. |
1 | 1.00 | 1.47 | 1.02 | 2.16 | 2.16 | 2.53 | 1.62 | 2.07 |
time (sec) |
N/A | 0.243 | 0.018 | 2.018 | 0.189 | 0.261 | 0.029 | 0.280 | 10.024 |
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 | 45 | 45 | 64 | 61 | 71 | 71 | 85 | 79 | 69 |
N.S. |
1 | 1.00 | 1.42 | 1.36 | 1.58 | 1.58 | 1.89 | 1.76 | 1.53 |
time (sec) |
N/A | 0.223 | 0.012 | 2.356 | 0.200 | 0.266 | 0.026 | 0.291 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 22 | 16 | 15 | 36 | 39 | 32 | 36 |
N.S. |
1 | 1.00 | 1.29 | 0.94 | 0.88 | 2.12 | 2.29 | 1.88 | 2.12 |
time (sec) |
N/A | 0.148 | 0.006 | 0.175 | 0.211 | 0.269 | 0.021 | 0.310 | 0.052 |
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 | 37 | 42 | 41 | 39 | 37 | 47 | 44 |
N.S. |
1 | 1.00 | 0.77 | 0.88 | 0.85 | 0.81 | 0.77 | 0.98 | 0.92 |
time (sec) |
N/A | 0.211 | 0.016 | 2.279 | 0.194 | 0.309 | 0.124 | 0.302 | 9.830 |
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 | 38 | 38 | 41 | 25 | 40 | 43 | 36 | 170 | 36 |
N.S. |
1 | 1.00 | 1.08 | 0.66 | 1.05 | 1.13 | 0.95 | 4.47 | 0.95 |
time (sec) |
N/A | 0.191 | 0.014 | 1.992 | 0.188 | 0.276 | 0.113 | 0.280 | 9.861 |
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 | 44 | 37 | 41 | 60 | 70 | 60 | 41 | 42 |
N.S. |
1 | 1.00 | 0.84 | 0.93 | 1.36 | 1.59 | 1.36 | 0.93 | 0.95 |
time (sec) |
N/A | 0.206 | 0.018 | 2.123 | 0.200 | 0.261 | 0.209 | 0.278 | 9.961 |
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 | 38 | 38 | 71 | 71 | 75 | 37 | 71 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 1.58 | 1.58 | 1.67 | 0.82 | 1.58 |
time (sec) |
N/A | 0.205 | 0.020 | 2.184 | 0.200 | 0.350 | 0.232 | 0.283 | 9.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 38 | 38 | 85 | 85 | 90 | 60 | 85 |
N.S. |
1 | 1.00 | 1.03 | 1.03 | 2.30 | 2.30 | 2.43 | 1.62 | 2.30 |
time (sec) |
N/A | 0.169 | 0.017 | 2.176 | 0.197 | 0.331 | 0.345 | 0.286 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 43 | 38 | 99 | 99 | 105 | 37 | 99 |
N.S. |
1 | 1.00 | 0.96 | 0.84 | 2.20 | 2.20 | 2.33 | 0.82 | 2.20 |
time (sec) |
N/A | 0.212 | 0.019 | 2.454 | 0.205 | 0.346 | 0.352 | 0.279 | 10.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 43 | 38 | 113 | 113 | 121 | 37 | 113 |
N.S. |
1 | 1.00 | 0.96 | 0.84 | 2.51 | 2.51 | 2.69 | 0.82 | 2.51 |
time (sec) |
N/A | 0.205 | 0.018 | 2.578 | 0.207 | 0.371 | 0.485 | 0.299 | 10.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 39 | 38 | 127 | 127 | 136 | 37 | 127 |
N.S. |
1 | 1.00 | 0.87 | 0.84 | 2.82 | 2.82 | 3.02 | 0.82 | 2.82 |
time (sec) |
N/A | 0.210 | 0.020 | 2.175 | 0.212 | 0.597 | 0.476 | 0.262 | 10.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 168 | 227 | 237 | 237 | 291 | 286 | 224 |
N.S. |
1 | 1.00 | 2.30 | 3.11 | 3.25 | 3.25 | 3.99 | 3.92 | 3.07 |
time (sec) |
N/A | 0.357 | 0.065 | 2.536 | 0.195 | 0.270 | 0.044 | 0.285 | 10.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 179 | 190 | 201 | 201 | 248 | 240 | 190 |
N.S. |
1 | 1.00 | 2.45 | 2.60 | 2.75 | 2.75 | 3.40 | 3.29 | 2.60 |
time (sec) |
N/A | 0.320 | 0.031 | 2.510 | 0.187 | 0.269 | 0.039 | 0.278 | 10.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 97 | 46 | 161 | 161 | 194 | 124 | 152 |
N.S. |
1 | 1.00 | 1.76 | 0.84 | 2.93 | 2.93 | 3.53 | 2.25 | 2.76 |
time (sec) |
N/A | 0.205 | 0.025 | 2.546 | 0.192 | 0.276 | 0.036 | 0.276 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 111 | 116 | 127 | 127 | 156 | 148 | 120 |
N.S. |
1 | 1.00 | 1.52 | 1.59 | 1.74 | 1.74 | 2.14 | 2.03 | 1.64 |
time (sec) |
N/A | 0.290 | 0.022 | 2.745 | 0.192 | 0.283 | 0.031 | 0.279 | 9.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 37 | 16 | 15 | 73 | 80 | 52 | 67 |
N.S. |
1 | 1.00 | 2.18 | 0.94 | 0.88 | 4.29 | 4.71 | 3.06 | 3.94 |
time (sec) |
N/A | 0.156 | 0.011 | 3.055 | 0.195 | 0.263 | 0.029 | 0.267 | 9.889 |
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 | 72 | 61 | 67 | 89 | 88 | 78 | 116 | 133 |
N.S. |
1 | 1.00 | 0.85 | 0.93 | 1.24 | 1.22 | 1.08 | 1.61 | 1.85 |
time (sec) |
N/A | 0.263 | 0.030 | 2.609 | 0.198 | 0.270 | 0.175 | 0.270 | 0.060 |
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 | 72 | 72 | 59 | 45 | 77 | 85 | 82 | 134 | 96 |
N.S. |
1 | 1.00 | 0.82 | 0.62 | 1.07 | 1.18 | 1.14 | 1.86 | 1.33 |
time (sec) |
N/A | 0.249 | 0.058 | 2.677 | 0.198 | 0.261 | 0.197 | 0.267 | 0.068 |
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 | 79 | 79 | 61 | 74 | 96 | 147 | 102 | 88 | 106 |
N.S. |
1 | 1.00 | 0.77 | 0.94 | 1.22 | 1.86 | 1.29 | 1.11 | 1.34 |
time (sec) |
N/A | 0.253 | 0.045 | 2.677 | 0.200 | 0.382 | 0.444 | 0.275 | 0.091 |
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 | 66 | 66 | 53 | 67 | 116 | 125 | 117 | 82 | 67 |
N.S. |
1 | 1.00 | 0.80 | 1.02 | 1.76 | 1.89 | 1.77 | 1.24 | 1.02 |
time (sec) |
N/A | 0.254 | 0.063 | 2.592 | 0.203 | 0.401 | 0.478 | 0.282 | 10.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 59 | 73 | 136 | 168 | 139 | 146 | 135 |
N.S. |
1 | 1.00 | 0.82 | 1.01 | 1.89 | 2.33 | 1.93 | 2.03 | 1.88 |
time (sec) |
N/A | 0.255 | 0.036 | 2.633 | 0.191 | 0.364 | 0.822 | 0.276 | 10.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 59 | 74 | 149 | 149 | 158 | 87 | 141 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 2.04 | 2.04 | 2.16 | 1.19 | 1.93 |
time (sec) |
N/A | 0.248 | 0.036 | 2.932 | 0.207 | 0.343 | 0.732 | 0.278 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 65 | 74 | 164 | 164 | 173 | 87 | 157 |
N.S. |
1 | 1.00 | 1.76 | 2.00 | 4.43 | 4.43 | 4.68 | 2.35 | 4.24 |
time (sec) |
N/A | 0.173 | 0.035 | 2.931 | 0.208 | 0.547 | 1.284 | 0.266 | 9.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 59 | 74 | 176 | 176 | 189 | 87 | 168 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 2.41 | 2.41 | 2.59 | 1.19 | 2.30 |
time (sec) |
N/A | 0.252 | 0.037 | 2.642 | 0.195 | 0.300 | 1.089 | 0.276 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 59 | 74 | 192 | 192 | 204 | 87 | 185 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 2.63 | 2.63 | 2.79 | 1.19 | 2.53 |
time (sec) |
N/A | 0.244 | 0.032 | 2.315 | 0.207 | 0.259 | 1.968 | 0.278 | 9.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 59 | 74 | 206 | 206 | 219 | 87 | 199 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 2.82 | 2.82 | 3.00 | 1.19 | 2.73 |
time (sec) |
N/A | 0.242 | 0.045 | 2.334 | 0.202 | 0.271 | 1.432 | 0.280 | 10.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 59 | 74 | 220 | 220 | 235 | 87 | 213 |
N.S. |
1 | 1.00 | 0.81 | 1.01 | 3.01 | 3.01 | 3.22 | 1.19 | 2.92 |
time (sec) |
N/A | 0.260 | 0.040 | 2.295 | 0.199 | 0.287 | 3.247 | 0.287 | 10.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 224 | 338 | 342 | 342 | 428 | 424 | 326 |
N.S. |
1 | 1.00 | 2.22 | 3.35 | 3.39 | 3.39 | 4.24 | 4.20 | 3.23 |
time (sec) |
N/A | 0.440 | 0.092 | 2.297 | 0.191 | 0.258 | 0.055 | 0.275 | 0.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 259 | 287 | 290 | 290 | 371 | 361 | 274 |
N.S. |
1 | 1.00 | 2.56 | 2.84 | 2.87 | 2.87 | 3.67 | 3.57 | 2.71 |
time (sec) |
N/A | 0.397 | 0.045 | 2.783 | 0.191 | 0.254 | 0.054 | 0.280 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 132 | 46 | 243 | 243 | 299 | 171 | 229 |
N.S. |
1 | 1.00 | 2.40 | 0.84 | 4.42 | 4.42 | 5.44 | 3.11 | 4.16 |
time (sec) |
N/A | 0.215 | 0.038 | 2.529 | 0.189 | 0.364 | 0.044 | 0.283 | 9.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 179 | 185 | 198 | 198 | 246 | 235 | 188 |
N.S. |
1 | 1.00 | 1.77 | 1.83 | 1.96 | 1.96 | 2.44 | 2.33 | 1.86 |
time (sec) |
N/A | 0.336 | 0.034 | 2.531 | 0.197 | 0.393 | 0.041 | 0.283 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 52 | 16 | 15 | 129 | 144 | 73 | 119 |
N.S. |
1 | 1.00 | 3.06 | 0.94 | 0.88 | 7.59 | 8.47 | 4.29 | 7.00 |
time (sec) |
N/A | 0.149 | 0.020 | 2.507 | 0.183 | 0.399 | 0.037 | 0.282 | 10.107 |
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 | 100 | 100 | 111 | 169 | 163 | 162 | 156 | 213 | 304 |
N.S. |
1 | 1.00 | 1.11 | 1.69 | 1.63 | 1.62 | 1.56 | 2.13 | 3.04 |
time (sec) |
N/A | 0.311 | 0.051 | 2.520 | 0.202 | 0.381 | 0.297 | 0.273 | 0.076 |
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 | 94 | 94 | 101 | 75 | 138 | 138 | 160 | 221 | 293 |
N.S. |
1 | 1.00 | 1.07 | 0.80 | 1.47 | 1.47 | 1.70 | 2.35 | 3.12 |
time (sec) |
N/A | 0.283 | 0.089 | 2.647 | 0.195 | 0.588 | 0.349 | 0.288 | 9.953 |
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 | 100 | 100 | 90 | 114 | 147 | 252 | 156 | 148 | 223 |
N.S. |
1 | 1.00 | 0.90 | 1.14 | 1.47 | 2.52 | 1.56 | 1.48 | 2.23 |
time (sec) |
N/A | 0.294 | 0.104 | 3.108 | 0.188 | 0.273 | 0.718 | 0.276 | 10.015 |
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 | 103 | 103 | 81 | 116 | 175 | 198 | 192 | 164 | 194 |
N.S. |
1 | 1.00 | 0.79 | 1.13 | 1.70 | 1.92 | 1.86 | 1.59 | 1.88 |
time (sec) |
N/A | 0.285 | 0.067 | 2.587 | 0.199 | 0.275 | 0.786 | 0.292 | 0.098 |
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 | 107 | 107 | 80 | 121 | 194 | 291 | 209 | 262 | 202 |
N.S. |
1 | 1.00 | 0.75 | 1.13 | 1.81 | 2.72 | 1.95 | 2.45 | 1.89 |
time (sec) |
N/A | 0.293 | 0.047 | 2.589 | 0.229 | 0.286 | 1.719 | 0.290 | 9.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 72 | 114 | 218 | 227 | 223 | 160 | 129 |
N.S. |
1 | 1.00 | 0.77 | 1.21 | 2.32 | 2.41 | 2.37 | 1.70 | 1.37 |
time (sec) |
N/A | 0.276 | 0.067 | 2.643 | 0.211 | 0.292 | 1.572 | 0.282 | 9.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 78 | 120 | 238 | 292 | 245 | 163 | 229 |
N.S. |
1 | 1.00 | 0.78 | 1.20 | 2.38 | 2.92 | 2.45 | 1.63 | 2.29 |
time (sec) |
N/A | 0.278 | 0.048 | 2.350 | 0.207 | 0.265 | 4.522 | 0.277 | 9.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 79 | 121 | 248 | 248 | 267 | 165 | 233 |
N.S. |
1 | 1.00 | 0.78 | 1.20 | 2.46 | 2.46 | 2.64 | 1.63 | 2.31 |
time (sec) |
N/A | 0.281 | 0.054 | 2.870 | 0.214 | 0.258 | 2.523 | 0.281 | 9.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 96 | 121 | 266 | 266 | 282 | 165 | 254 |
N.S. |
1 | 1.00 | 2.59 | 3.27 | 7.19 | 7.19 | 7.62 | 4.46 | 6.86 |
time (sec) |
N/A | 0.167 | 0.054 | 3.066 | 0.229 | 0.349 | 22.720 | 0.272 | 9.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 79 | 121 | 280 | 280 | 298 | 165 | 268 |
N.S. |
1 | 1.00 | 0.78 | 1.20 | 2.77 | 2.77 | 2.95 | 1.63 | 2.65 |
time (sec) |
N/A | 0.276 | 0.064 | 2.394 | 0.210 | 0.388 | 5.012 | 0.279 | 9.767 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 79 | 121 | 294 | 294 | 313 | 165 | 282 |
N.S. |
1 | 1.00 | 0.78 | 1.20 | 2.91 | 2.91 | 3.10 | 1.63 | 2.79 |
time (sec) |
N/A | 0.280 | 0.060 | 2.398 | 0.229 | 0.368 | 120.148 | 0.289 | 9.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 79 | 121 | 306 | 306 | 328 | 165 | 292 |
N.S. |
1 | 1.00 | 0.78 | 1.20 | 3.03 | 3.03 | 3.25 | 1.63 | 2.89 |
time (sec) |
N/A | 0.300 | 0.068 | 2.524 | 0.225 | 0.328 | 10.400 | 0.275 | 0.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 115 | 188 | 246 | 0 | 536 | 502 | 313 | 761 |
N.S. |
1 | 0.94 | 1.54 | 2.02 | 0.00 | 4.39 | 4.11 | 2.57 | 6.24 |
time (sec) |
N/A | 0.333 | 0.118 | 2.494 | 0.000 | 0.419 | 0.671 | 0.296 | 9.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 79 | 110 | 167 | 181 | 181 | 185 | 219 | 418 |
N.S. |
1 | 0.92 | 1.28 | 1.94 | 2.10 | 2.10 | 2.15 | 2.55 | 4.86 |
time (sec) |
N/A | 0.264 | 0.063 | 2.861 | 0.207 | 0.309 | 0.576 | 0.286 | 9.593 |
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 | 97 | 93 | 120 | 154 | 0 | 356 | 337 | 197 | 296 |
N.S. |
1 | 0.96 | 1.24 | 1.59 | 0.00 | 3.67 | 3.47 | 2.03 | 3.05 |
time (sec) |
N/A | 0.279 | 0.074 | 2.798 | 0.000 | 0.299 | 0.494 | 0.278 | 9.382 |
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 | 61 | 57 | 54 | 89 | 99 | 99 | 99 | 118 | 139 |
N.S. |
1 | 0.93 | 0.89 | 1.46 | 1.62 | 1.62 | 1.62 | 1.93 | 2.28 |
time (sec) |
N/A | 0.215 | 0.024 | 2.427 | 0.217 | 0.268 | 0.440 | 0.274 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 71 | 72 | 90 | 0 | 208 | 204 | 115 | 133 |
N.S. |
1 | 0.99 | 1.00 | 1.25 | 0.00 | 2.89 | 2.83 | 1.60 | 1.85 |
time (sec) |
N/A | 0.233 | 0.045 | 2.437 | 0.000 | 0.274 | 0.346 | 0.287 | 0.077 |
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 | 36 | 36 | 33 | 39 | 43 | 43 | 44 | 50 | 47 |
N.S. |
1 | 1.00 | 0.92 | 1.08 | 1.19 | 1.19 | 1.22 | 1.39 | 1.31 |
time (sec) |
N/A | 0.183 | 0.014 | 2.462 | 0.201 | 0.313 | 0.288 | 0.285 | 9.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 47 | 52 | 0 | 132 | 99 | 57 | 81 |
N.S. |
1 | 1.00 | 0.96 | 1.06 | 0.00 | 2.69 | 2.02 | 1.16 | 1.65 |
time (sec) |
N/A | 0.193 | 0.029 | 2.634 | 0.000 | 0.284 | 0.222 | 0.308 | 0.068 |
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 | 13 | 13 | 12 | 14 | 13 | 13 | 12 | 21 | 13 |
N.S. |
1 | 1.00 | 0.92 | 1.08 | 1.00 | 1.00 | 0.92 | 1.62 | 1.00 |
time (sec) |
N/A | 0.144 | 0.003 | 3.037 | 0.192 | 0.274 | 0.121 | 0.399 | 0.037 |
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 | 34 | 41 | 48 | 35 | 42 | 57 | 47 |
N.S. |
1 | 1.00 | 0.71 | 0.85 | 1.00 | 0.73 | 0.88 | 1.19 | 0.98 |
time (sec) |
N/A | 0.197 | 0.024 | 2.726 | 0.200 | 0.339 | 0.438 | 0.373 | 9.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 63 | 62 | 0 | 256 | 240 | 117 | 115 |
N.S. |
1 | 1.00 | 1.03 | 1.02 | 0.00 | 4.20 | 3.93 | 1.92 | 1.89 |
time (sec) |
N/A | 0.210 | 0.056 | 2.566 | 0.000 | 0.391 | 0.504 | 0.372 | 9.476 |
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 | 70 | 79 | 65 | 73 | 129 | 156 | 119 | 111 | 151 |
N.S. |
1 | 1.13 | 0.93 | 1.04 | 1.84 | 2.23 | 1.70 | 1.59 | 2.16 |
time (sec) |
N/A | 0.237 | 0.042 | 2.519 | 0.205 | 0.341 | 0.962 | 0.366 | 0.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 95 | 83 | 84 | 0 | 627 | 442 | 128 | 219 |
N.S. |
1 | 1.10 | 0.97 | 0.98 | 0.00 | 7.29 | 5.14 | 1.49 | 2.55 |
time (sec) |
N/A | 0.251 | 0.054 | 2.656 | 0.000 | 0.353 | 1.039 | 0.323 | 9.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 119 | 155 | 240 | 0 | 753 | 476 | 308 | 508 |
N.S. |
1 | 0.94 | 1.23 | 1.90 | 0.00 | 5.98 | 3.78 | 2.44 | 4.03 |
time (sec) |
N/A | 0.312 | 0.082 | 2.991 | 0.000 | 0.798 | 1.427 | 0.321 | 0.122 |
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 | 89 | 83 | 103 | 138 | 155 | 283 | 160 | 181 | 234 |
N.S. |
1 | 0.93 | 1.16 | 1.55 | 1.74 | 3.18 | 1.80 | 2.03 | 2.63 |
time (sec) |
N/A | 0.262 | 0.085 | 2.982 | 0.213 | 0.287 | 1.575 | 0.321 | 9.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 97 | 108 | 151 | 0 | 504 | 313 | 197 | 230 |
N.S. |
1 | 0.97 | 1.08 | 1.51 | 0.00 | 5.04 | 3.13 | 1.97 | 2.30 |
time (sec) |
N/A | 0.277 | 0.065 | 2.604 | 0.000 | 0.306 | 1.074 | 0.328 | 0.085 |
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 | 65 | 61 | 64 | 78 | 86 | 165 | 90 | 100 | 97 |
N.S. |
1 | 0.94 | 0.98 | 1.20 | 1.32 | 2.54 | 1.38 | 1.54 | 1.49 |
time (sec) |
N/A | 0.216 | 0.033 | 2.573 | 0.205 | 0.279 | 0.993 | 0.345 | 9.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 75 | 77 | 84 | 0 | 297 | 173 | 112 | 143 |
N.S. |
1 | 0.99 | 1.01 | 1.11 | 0.00 | 3.91 | 2.28 | 1.47 | 1.88 |
time (sec) |
N/A | 0.232 | 0.050 | 2.603 | 0.000 | 0.313 | 0.629 | 0.350 | 0.107 |
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 | 43 | 43 | 42 | 43 | 43 | 64 | 42 | 101 | 47 |
N.S. |
1 | 1.00 | 0.98 | 1.00 | 1.00 | 1.49 | 0.98 | 2.35 | 1.09 |
time (sec) |
N/A | 0.187 | 0.022 | 2.567 | 0.190 | 0.282 | 0.557 | 0.328 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 65 | 62 | 0 | 309 | 211 | 66 | 88 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 0.00 | 4.98 | 3.40 | 1.06 | 1.42 |
time (sec) |
N/A | 0.193 | 0.039 | 2.962 | 0.000 | 0.282 | 0.476 | 0.302 | 9.440 |
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 | 15 | 15 | 14 | 16 | 15 | 15 | 12 | 22 | 15 |
N.S. |
1 | 1.00 | 0.93 | 1.07 | 1.00 | 1.00 | 0.80 | 1.47 | 1.00 |
time (sec) |
N/A | 0.148 | 0.005 | 2.806 | 0.199 | 0.303 | 0.271 | 0.309 | 9.524 |
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 | 78 | 86 | 59 | 78 | 121 | 141 | 102 | 108 | 125 |
N.S. |
1 | 1.10 | 0.76 | 1.00 | 1.55 | 1.81 | 1.31 | 1.38 | 1.60 |
time (sec) |
N/A | 0.235 | 0.055 | 2.608 | 0.199 | 0.373 | 0.942 | 0.290 | 9.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 107 | 84 | 98 | 0 | 644 | 459 | 220 | 232 |
N.S. |
1 | 1.09 | 0.86 | 1.00 | 0.00 | 6.57 | 4.68 | 2.24 | 2.37 |
time (sec) |
N/A | 0.268 | 0.135 | 2.801 | 0.000 | 0.362 | 1.086 | 0.282 | 9.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 125 | 79 | 100 | 296 | 409 | 304 | 203 | 278 |
N.S. |
1 | 1.14 | 0.72 | 0.91 | 2.69 | 3.72 | 2.76 | 1.85 | 2.53 |
time (sec) |
N/A | 0.295 | 0.090 | 2.664 | 0.207 | 0.393 | 1.867 | 0.284 | 9.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 147 | 192 | 351 | 0 | 1185 | 660 | 460 | 695 |
N.S. |
1 | 0.92 | 1.20 | 2.19 | 0.00 | 7.41 | 4.12 | 2.88 | 4.34 |
time (sec) |
N/A | 0.358 | 0.106 | 2.631 | 0.000 | 0.362 | 6.018 | 0.307 | 9.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 111 | 131 | 228 | 278 | 490 | 320 | 299 | 385 |
N.S. |
1 | 0.90 | 1.07 | 1.85 | 2.26 | 3.98 | 2.60 | 2.43 | 3.13 |
time (sec) |
N/A | 0.309 | 0.060 | 3.130 | 0.204 | 0.294 | 22.246 | 0.325 | 0.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 125 | 142 | 236 | 0 | 868 | 469 | 315 | 368 |
N.S. |
1 | 0.93 | 1.06 | 1.76 | 0.00 | 6.48 | 3.50 | 2.35 | 2.75 |
time (sec) |
N/A | 0.319 | 0.080 | 2.670 | 0.000 | 0.278 | 2.955 | 0.318 | 9.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 89 | 92 | 144 | 189 | 346 | 219 | 191 | 214 |
N.S. |
1 | 0.92 | 0.95 | 1.48 | 1.95 | 3.57 | 2.26 | 1.97 | 2.21 |
time (sec) |
N/A | 0.260 | 0.035 | 2.643 | 0.205 | 0.283 | 5.651 | 0.312 | 0.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 103 | 113 | 151 | 0 | 571 | 299 | 196 | 254 |
N.S. |
1 | 0.95 | 1.05 | 1.40 | 0.00 | 5.29 | 2.77 | 1.81 | 2.35 |
time (sec) |
N/A | 0.290 | 0.066 | 2.590 | 0.000 | 0.287 | 2.013 | 0.307 | 9.395 |
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 | 71 | 65 | 89 | 124 | 182 | 141 | 110 | 136 |
N.S. |
1 | 0.97 | 0.89 | 1.22 | 1.70 | 2.49 | 1.93 | 1.51 | 1.86 |
time (sec) |
N/A | 0.232 | 0.044 | 2.521 | 0.191 | 0.272 | 2.125 | 0.283 | 9.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 90 | 89 | 96 | 0 | 625 | 304 | 114 | 166 |
N.S. |
1 | 0.98 | 0.97 | 1.04 | 0.00 | 6.79 | 3.30 | 1.24 | 1.80 |
time (sec) |
N/A | 0.240 | 0.068 | 2.732 | 0.000 | 0.315 | 1.154 | 0.292 | 0.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 38 | 39 | 71 | 71 | 80 | 50 | 74 |
N.S. |
1 | 1.00 | 1.03 | 1.05 | 1.92 | 1.92 | 2.16 | 1.35 | 2.00 |
time (sec) |
N/A | 0.173 | 0.028 | 2.788 | 0.196 | 0.280 | 0.946 | 0.281 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 97 | 98 | 148 | 0 | 713 | 430 | 134 | 233 |
N.S. |
1 | 0.97 | 0.98 | 1.48 | 0.00 | 7.13 | 4.30 | 1.34 | 2.33 |
time (sec) |
N/A | 0.255 | 0.093 | 2.338 | 0.000 | 0.300 | 0.907 | 0.288 | 9.659 |
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 | 17 | 17 | 16 | 16 | 15 | 40 | 44 | 22 | 44 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 2.35 | 2.59 | 1.29 | 2.59 |
time (sec) |
N/A | 0.146 | 0.008 | 2.251 | 0.186 | 0.368 | 0.576 | 0.273 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 126 | 87 | 128 | 266 | 386 | 246 | 188 | 239 |
N.S. |
1 | 1.12 | 0.78 | 1.14 | 2.38 | 3.45 | 2.20 | 1.68 | 2.13 |
time (sec) |
N/A | 0.297 | 0.094 | 2.394 | 0.214 | 0.397 | 1.824 | 0.272 | 9.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 155 | 119 | 139 | 0 | 1170 | 804 | 302 | 494 |
N.S. |
1 | 1.11 | 0.85 | 0.99 | 0.00 | 8.36 | 5.74 | 2.16 | 3.53 |
time (sec) |
N/A | 0.312 | 0.135 | 2.373 | 0.000 | 0.447 | 2.127 | 0.272 | 9.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 173 | 111 | 152 | 553 | 809 | 600 | 302 | 522 |
N.S. |
1 | 1.12 | 0.72 | 0.99 | 3.59 | 5.25 | 3.90 | 1.96 | 3.39 |
time (sec) |
N/A | 0.342 | 0.155 | 2.345 | 0.242 | 0.634 | 3.036 | 0.286 | 10.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 189 | 140 | 165 | 0 | 2077 | 1238 | 311 | 827 |
N.S. |
1 | 1.12 | 0.83 | 0.98 | 0.00 | 12.36 | 7.37 | 1.85 | 4.92 |
time (sec) |
N/A | 0.372 | 0.307 | 2.786 | 0.000 | 0.348 | 3.347 | 0.285 | 10.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 159 | 151 | 193 | 0 | 473 | 1149 | 257 | 1144 |
N.S. |
1 | 0.96 | 0.92 | 1.17 | 0.00 | 2.87 | 6.96 | 1.56 | 6.93 |
time (sec) |
N/A | 0.316 | 2.066 | 2.790 | 0.000 | 0.308 | 0.859 | 0.297 | 11.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 80 | 41 | 0 | 91 | 216 | 58 | 89 |
N.S. |
1 | 1.00 | 1.36 | 0.69 | 0.00 | 1.54 | 3.66 | 0.98 | 1.51 |
time (sec) |
N/A | 0.196 | 1.132 | 2.594 | 0.000 | 0.290 | 0.118 | 0.272 | 9.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 120 | 101 | 114 | 0 | 309 | 379 | 153 | 335 |
N.S. |
1 | 0.98 | 0.82 | 0.93 | 0.00 | 2.51 | 3.08 | 1.24 | 2.72 |
time (sec) |
N/A | 0.269 | 1.086 | 2.713 | 0.000 | 0.304 | 0.691 | 0.303 | 10.208 |
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 | 19 | 19 | 18 | 16 | 15 | 28 | 65 | 15 | 15 |
N.S. |
1 | 1.00 | 0.95 | 0.84 | 0.79 | 1.47 | 3.42 | 0.79 | 0.79 |
time (sec) |
N/A | 0.146 | 0.027 | 2.487 | 0.187 | 0.293 | 0.081 | 0.277 | 9.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 96 | 78 | 0 | 182 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 1.16 | 0.94 | 0.00 | 2.19 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.236 | 0.537 | 3.090 | 0.000 | 0.313 | 0.000 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 292 | 182 | 0 | 189 | 0 | 215 | 0 |
N.S. |
1 | 1.00 | 3.89 | 2.43 | 0.00 | 2.52 | 0.00 | 2.87 | 0.00 |
time (sec) |
N/A | 0.206 | 1.208 | 2.945 | 0.000 | 0.369 | 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 | 91 | 91 | 103 | 89 | 0 | 378 | 0 | 246 | 0 |
N.S. |
1 | 1.00 | 1.13 | 0.98 | 0.00 | 4.15 | 0.00 | 2.70 | 0.00 |
time (sec) |
N/A | 0.225 | 10.227 | 2.482 | 0.000 | 0.507 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 38 | 38 | 0 | 98 | 0 | 199 | 111 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.00 | 2.51 | 0.00 | 5.10 | 2.85 |
time (sec) |
N/A | 0.169 | 10.036 | 2.945 | 0.000 | 0.636 | 0.000 | 0.329 | 9.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 132 | 62 | 135 | 0 | 728 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.47 | 1.02 | 0.00 | 5.47 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 10.061 | 2.439 | 0.000 | 1.032 | 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 | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 62 | 70 | 0 | 274 | 0 | 417 | 589 |
N.S. |
1 | 1.00 | 0.78 | 0.89 | 0.00 | 3.47 | 0.00 | 5.28 | 7.46 |
time (sec) |
N/A | 0.204 | 10.045 | 3.190 | 0.000 | 2.028 | 0.000 | 0.430 | 10.159 |