Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 60 | 55 | 56 | 136 | 129 | 57 | 78 | 53 |
N.S. |
1 | 1.00 | 1.02 | 0.93 | 0.95 | 2.31 | 2.19 | 0.97 | 1.32 | 0.90 |
time (sec) |
N/A | 0.175 | 0.036 | 0.464 | 0.127 | 0.085 | 0.196 | 0.134 | 0.208 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 102 | 116 | 126 | 137 | 138 | 122 | 148 | 163 | 146 |
N.S. |
1 | 0.99 | 1.13 | 1.22 | 1.33 | 1.34 | 1.18 | 1.44 | 1.58 | 1.42 |
time (sec) |
N/A | 0.284 | 0.035 | 0.599 | 0.058 | 0.131 | 0.238 | 0.127 | 0.201 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 105 | 142 | 140 | 304 | 246 | 153 | 179 | 169 |
N.S. |
1 | 1.00 | 1.00 | 1.35 | 1.33 | 2.90 | 2.34 | 1.46 | 1.70 | 1.61 |
time (sec) |
N/A | 0.253 | 0.063 | 0.536 | 0.120 | 0.088 | 0.260 | 0.125 | 0.207 | 0.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 79 | 82 | 94 | 101 | 102 | 83 | 107 | 122 | 106 |
N.S. |
1 | 0.99 | 1.02 | 1.18 | 1.26 | 1.28 | 1.04 | 1.34 | 1.52 | 1.32 |
time (sec) |
N/A | 0.234 | 0.025 | 0.461 | 0.056 | 0.067 | 0.212 | 0.117 | 0.243 | 0.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 84 | 102 | 105 | 230 | 194 | 113 | 137 | 128 |
N.S. |
1 | 1.00 | 1.00 | 1.21 | 1.25 | 2.74 | 2.31 | 1.35 | 1.63 | 1.52 |
time (sec) |
N/A | 0.233 | 0.048 | 0.498 | 0.140 | 0.079 | 0.238 | 0.123 | 0.194 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 49 | 63 | 66 | 67 | 49 | 67 | 82 | 68 |
N.S. |
1 | 1.00 | 0.83 | 1.07 | 1.12 | 1.14 | 0.83 | 1.14 | 1.39 | 1.15 |
time (sec) |
N/A | 0.197 | 0.015 | 0.536 | 0.053 | 0.077 | 0.192 | 0.124 | 0.199 | 0.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 59 | 64 | 69 | 181 | 172 | 72 | 109 | 90 |
N.S. |
1 | 1.00 | 0.94 | 1.02 | 1.10 | 2.87 | 2.73 | 1.14 | 1.73 | 1.43 |
time (sec) |
N/A | 0.197 | 0.034 | 0.451 | 0.162 | 0.083 | 0.211 | 0.121 | 0.216 | 0.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 52 | 50 | 59 | 61 | 59 | 41 | 62 | 74 | 58 |
N.S. |
1 | 1.02 | 0.98 | 1.16 | 1.20 | 1.16 | 0.80 | 1.22 | 1.45 | 1.14 |
time (sec) |
N/A | 0.201 | 0.016 | 0.445 | 0.034 | 0.086 | 0.640 | 0.120 | 0.197 | 0.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 55 | 65 | 63 | 164 | 165 | 63 | 104 | 80 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 1.15 | 2.98 | 3.00 | 1.15 | 1.89 | 1.45 |
time (sec) |
N/A | 0.204 | 0.036 | 0.483 | 0.142 | 0.082 | 0.266 | 0.112 | 0.206 | 0.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 59 | 60 | 66 | 69 | 73 | 49 | 90 | 96 | 67 |
N.S. |
1 | 1.02 | 1.03 | 1.14 | 1.19 | 1.26 | 0.84 | 1.55 | 1.66 | 1.16 |
time (sec) |
N/A | 0.215 | 0.019 | 0.463 | 0.053 | 0.074 | 0.737 | 0.122 | 0.213 | 0.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 66 | 70 | 70 | 190 | 172 | 72 | 123 | 90 |
N.S. |
1 | 1.00 | 1.03 | 1.09 | 1.09 | 2.97 | 2.69 | 1.12 | 1.92 | 1.41 |
time (sec) |
N/A | 0.213 | 0.042 | 0.468 | 0.134 | 0.080 | 0.332 | 0.128 | 0.225 | 0.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 137 | 128 | 204 | 219 | 220 | 201 | 238 | 260 | 236 |
N.S. |
1 | 0.99 | 0.93 | 1.48 | 1.59 | 1.59 | 1.46 | 1.72 | 1.88 | 1.71 |
time (sec) |
N/A | 0.333 | 0.048 | 0.484 | 0.043 | 0.071 | 0.309 | 0.127 | 0.211 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 140 | 231 | 222 | 468 | 343 | 241 | 282 | 260 |
N.S. |
1 | 1.00 | 1.00 | 1.65 | 1.59 | 3.34 | 2.45 | 1.72 | 2.01 | 1.86 |
time (sec) |
N/A | 0.299 | 0.032 | 0.569 | 0.116 | 0.087 | 0.359 | 0.124 | 0.211 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 114 | 125 | 157 | 168 | 169 | 144 | 180 | 202 | 178 |
N.S. |
1 | 0.99 | 1.09 | 1.37 | 1.46 | 1.47 | 1.25 | 1.57 | 1.76 | 1.55 |
time (sec) |
N/A | 0.280 | 0.037 | 0.456 | 0.047 | 0.065 | 0.287 | 0.122 | 0.195 | 0.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 118 | 173 | 172 | 364 | 274 | 184 | 223 | 199 |
N.S. |
1 | 1.00 | 0.99 | 1.45 | 1.45 | 3.06 | 2.30 | 1.55 | 1.87 | 1.67 |
time (sec) |
N/A | 0.269 | 0.026 | 0.464 | 0.129 | 0.080 | 0.327 | 0.122 | 0.210 | 0.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 85 | 82 | 112 | 119 | 120 | 94 | 124 | 146 | 123 |
N.S. |
1 | 0.98 | 0.94 | 1.29 | 1.37 | 1.38 | 1.08 | 1.43 | 1.68 | 1.41 |
time (sec) |
N/A | 0.218 | 0.020 | 0.601 | 0.030 | 0.084 | 0.251 | 0.119 | 0.208 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 92 | 116 | 122 | 292 | 238 | 129 | 182 | 146 |
N.S. |
1 | 1.00 | 0.94 | 1.18 | 1.24 | 2.98 | 2.43 | 1.32 | 1.86 | 1.49 |
time (sec) |
N/A | 0.238 | 0.042 | 0.430 | 0.125 | 0.082 | 0.292 | 0.118 | 0.224 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 74 | 65 | 86 | 98 | 101 | 65 | 99 | 123 | 97 |
N.S. |
1 | 1.01 | 0.89 | 1.18 | 1.34 | 1.38 | 0.89 | 1.36 | 1.68 | 1.33 |
time (sec) |
N/A | 0.230 | 0.021 | 0.484 | 0.035 | 0.073 | 0.909 | 0.122 | 0.218 | 0.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 76 | 95 | 101 | 253 | 221 | 104 | 165 | 118 |
N.S. |
1 | 1.00 | 0.99 | 1.23 | 1.31 | 3.29 | 2.87 | 1.35 | 2.14 | 1.53 |
time (sec) |
N/A | 0.228 | 0.023 | 0.456 | 0.132 | 0.081 | 0.384 | 0.127 | 0.239 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 71 | 75 | 94 | 97 | 105 | 63 | 120 | 139 | 95 |
N.S. |
1 | 0.97 | 1.03 | 1.29 | 1.33 | 1.44 | 0.86 | 1.64 | 1.90 | 1.30 |
time (sec) |
N/A | 0.230 | 0.024 | 0.452 | 0.040 | 0.085 | 1.113 | 0.121 | 0.205 | 0.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 74 | 98 | 98 | 256 | 221 | 100 | 174 | 122 |
N.S. |
1 | 1.00 | 1.00 | 1.32 | 1.32 | 3.46 | 2.99 | 1.35 | 2.35 | 1.65 |
time (sec) |
N/A | 0.225 | 0.027 | 0.618 | 0.112 | 0.079 | 0.548 | 0.121 | 0.187 | 0.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 66 | 66 | 65 | 68 | 72 | 201 | 70 | 69 | 68 |
N.S. |
1 | 0.94 | 0.94 | 0.93 | 0.97 | 1.03 | 2.87 | 1.00 | 0.99 | 0.97 |
time (sec) |
N/A | 0.232 | 0.022 | 0.548 | 0.030 | 0.085 | 119.408 | 0.127 | 0.189 | 0.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 89 | 74 | 73 | 72 | 391 | 921 | 72 | 76 | 343 |
N.S. |
1 | 1.14 | 0.95 | 0.94 | 0.92 | 5.01 | 11.81 | 0.92 | 0.97 | 4.40 |
time (sec) |
N/A | 0.226 | 0.060 | 0.568 | 0.116 | 0.102 | 7.602 | 0.125 | 0.246 | 0.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 52 | 43 | 43 | 49 | 42 | 144 | 51 | 42 | 51 |
N.S. |
1 | 0.98 | 0.81 | 0.81 | 0.92 | 0.79 | 2.72 | 0.96 | 0.79 | 0.96 |
time (sec) |
N/A | 0.205 | 0.015 | 0.530 | 0.037 | 0.083 | 1.233 | 0.118 | 0.215 | 0.665 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 61 | 55 | 54 | 309 | 570 | 54 | 55 | 133 |
N.S. |
1 | 1.00 | 0.87 | 0.79 | 0.77 | 4.41 | 8.14 | 0.77 | 0.79 | 1.90 |
time (sec) |
N/A | 0.184 | 0.029 | 0.543 | 0.140 | 0.113 | 1.037 | 0.124 | 0.223 | 0.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 44 | 31 | 32 | 41 | 31 | 138 | 51 | 31 | 148 |
N.S. |
1 | 0.98 | 0.69 | 0.71 | 0.91 | 0.69 | 3.07 | 1.13 | 0.69 | 3.29 |
time (sec) |
N/A | 0.166 | 0.012 | 0.648 | 0.057 | 0.107 | 0.474 | 0.127 | 0.197 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 61 | 55 | 54 | 292 | 712 | 54 | 55 | 135 |
N.S. |
1 | 1.00 | 0.87 | 0.79 | 0.77 | 4.17 | 10.17 | 0.77 | 0.79 | 1.93 |
time (sec) |
N/A | 0.171 | 0.031 | 0.516 | 0.128 | 0.123 | 1.406 | 0.128 | 0.239 | 0.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 63 | 54 | 55 | 61 | 54 | 0 | 73 | 54 | 58 |
N.S. |
1 | 1.02 | 0.87 | 0.89 | 0.98 | 0.87 | 0.00 | 1.18 | 0.87 | 0.94 |
time (sec) |
N/A | 0.219 | 0.019 | 0.556 | 0.052 | 0.126 | 0.000 | 0.124 | 0.199 | 0.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 92 | 76 | 76 | 75 | 384 | 1093 | 75 | 79 | 338 |
N.S. |
1 | 1.14 | 0.94 | 0.94 | 0.93 | 4.74 | 13.49 | 0.93 | 0.98 | 4.17 |
time (sec) |
N/A | 0.221 | 0.056 | 0.620 | 0.135 | 0.108 | 7.682 | 0.127 | 0.223 | 1.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 86 | 88 | 82 | 87 | 99 | 0 | 112 | 98 | 87 |
N.S. |
1 | 0.99 | 1.01 | 0.94 | 1.00 | 1.14 | 0.00 | 1.29 | 1.13 | 1.00 |
time (sec) |
N/A | 0.255 | 0.026 | 0.560 | 0.045 | 0.213 | 0.000 | 0.117 | 0.222 | 0.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 125 | 101 | 96 | 96 | 560 | 1353 | 98 | 117 | 367 |
N.S. |
1 | 1.25 | 1.01 | 0.96 | 0.96 | 5.60 | 13.53 | 0.98 | 1.17 | 3.67 |
time (sec) |
N/A | 0.294 | 0.079 | 0.629 | 0.125 | 0.114 | 29.882 | 0.126 | 0.223 | 1.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 117 | 115 | 114 | 117 | 127 | 0 | 167 | 127 | 118 |
N.S. |
1 | 0.98 | 0.97 | 0.96 | 0.98 | 1.07 | 0.00 | 1.40 | 1.07 | 0.99 |
time (sec) |
N/A | 0.296 | 0.037 | 0.559 | 0.033 | 0.675 | 0.000 | 0.123 | 0.217 | 0.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 161 | 135 | 127 | 131 | 669 | 1504 | 139 | 146 | 397 |
N.S. |
1 | 1.20 | 1.01 | 0.95 | 0.98 | 4.99 | 11.22 | 1.04 | 1.09 | 2.96 |
time (sec) |
N/A | 0.358 | 0.085 | 0.618 | 0.121 | 0.139 | 175.282 | 0.130 | 0.203 | 1.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 154 | 147 | 157 | 165 | 155 | 0 | 239 | 156 | 165 |
N.S. |
1 | 0.99 | 0.95 | 1.01 | 1.06 | 1.00 | 0.00 | 1.54 | 1.01 | 1.06 |
time (sec) |
N/A | 0.349 | 0.046 | 0.575 | 0.037 | 0.944 | 0.000 | 0.129 | 0.197 | 0.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 90 | 91 | 86 | 130 | 162 | 0 | 152 | 192 | 169 |
N.S. |
1 | 0.97 | 0.98 | 0.92 | 1.40 | 1.74 | 0.00 | 1.63 | 2.06 | 1.82 |
time (sec) |
N/A | 0.264 | 0.030 | 0.560 | 0.047 | 0.111 | 0.000 | 0.123 | 0.200 | 0.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 125 | 108 | 95 | 132 | 718 | 0 | 121 | 229 | 3572 |
N.S. |
1 | 1.16 | 1.00 | 0.88 | 1.22 | 6.65 | 0.00 | 1.12 | 2.12 | 33.07 |
time (sec) |
N/A | 0.242 | 0.083 | 0.585 | 0.159 | 0.139 | 0.000 | 0.123 | 0.207 | 1.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 71 | 74 | 68 | 105 | 117 | 253 | 91 | 129 | 173 |
N.S. |
1 | 0.96 | 1.00 | 0.92 | 1.42 | 1.58 | 3.42 | 1.23 | 1.74 | 2.34 |
time (sec) |
N/A | 0.225 | 0.023 | 0.555 | 0.040 | 0.086 | 0.909 | 0.125 | 0.195 | 0.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 117 | 90 | 85 | 119 | 705 | 0 | 110 | 217 | 3154 |
N.S. |
1 | 1.12 | 0.87 | 0.82 | 1.14 | 6.78 | 0.00 | 1.06 | 2.09 | 30.33 |
time (sec) |
N/A | 0.215 | 0.081 | 0.690 | 0.136 | 0.148 | 0.000 | 0.126 | 0.209 | 1.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 66 | 66 | 73 | 99 | 103 | 248 | 85 | 138 | 160 |
N.S. |
1 | 0.94 | 0.94 | 1.04 | 1.41 | 1.47 | 3.54 | 1.21 | 1.97 | 2.29 |
time (sec) |
N/A | 0.222 | 0.019 | 0.572 | 0.050 | 0.095 | 0.862 | 0.115 | 0.190 | 0.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 127 | 95 | 93 | 133 | 711 | 0 | 122 | 229 | 3637 |
N.S. |
1 | 1.17 | 0.87 | 0.85 | 1.22 | 6.52 | 0.00 | 1.12 | 2.10 | 33.37 |
time (sec) |
N/A | 0.239 | 0.104 | 0.517 | 0.135 | 0.185 | 0.000 | 0.124 | 0.194 | 1.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 99 | 98 | 99 | 138 | 219 | 0 | 185 | 266 | 127 |
N.S. |
1 | 0.99 | 0.98 | 0.99 | 1.38 | 2.19 | 0.00 | 1.85 | 2.66 | 1.27 |
time (sec) |
N/A | 0.274 | 0.059 | 0.573 | 0.069 | 0.557 | 0.000 | 0.125 | 0.191 | 1.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 161 | 123 | 109 | 178 | 1005 | 0 | 164 | 302 | 432 |
N.S. |
1 | 1.12 | 0.85 | 0.76 | 1.24 | 6.98 | 0.00 | 1.14 | 2.10 | 3.00 |
time (sec) |
N/A | 0.328 | 0.109 | 0.601 | 0.129 | 0.322 | 0.000 | 0.128 | 0.209 | 1.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 122 | 119 | 120 | 188 | 302 | 0 | 257 | 344 | 171 |
N.S. |
1 | 0.97 | 0.94 | 0.95 | 1.49 | 2.40 | 0.00 | 2.04 | 2.73 | 1.36 |
time (sec) |
N/A | 0.311 | 0.078 | 0.566 | 0.062 | 1.248 | 0.000 | 0.108 | 0.231 | 1.380 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 202 | 142 | 127 | 236 | 1281 | 0 | 165 | 368 | 469 |
N.S. |
1 | 1.07 | 0.75 | 0.67 | 1.25 | 6.78 | 0.00 | 0.87 | 1.95 | 2.48 |
time (sec) |
N/A | 0.403 | 0.259 | 0.597 | 0.171 | 0.772 | 0.000 | 0.130 | 0.221 | 1.366 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 112 | 115 | 124 | 236 | 290 | 418 | 232 | 315 | 370 |
N.S. |
1 | 0.97 | 0.99 | 1.07 | 2.03 | 2.50 | 3.60 | 2.00 | 2.72 | 3.19 |
time (sec) |
N/A | 0.281 | 0.043 | 0.559 | 0.060 | 0.086 | 1.621 | 0.119 | 0.210 | 0.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 186 | 133 | 154 | 264 | 1573 | 0 | 204 | 552 | 5754 |
N.S. |
1 | 1.18 | 0.85 | 0.98 | 1.68 | 10.02 | 0.00 | 1.30 | 3.52 | 36.65 |
time (sec) |
N/A | 0.315 | 0.208 | 0.701 | 0.129 | 0.316 | 0.000 | 0.128 | 0.214 | 2.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 97 | 97 | 105 | 217 | 256 | 411 | 174 | 306 | 343 |
N.S. |
1 | 0.97 | 0.97 | 1.05 | 2.17 | 2.56 | 4.11 | 1.74 | 3.06 | 3.43 |
time (sec) |
N/A | 0.259 | 0.034 | 0.546 | 0.038 | 0.085 | 1.422 | 0.122 | 0.212 | 0.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 187 | 147 | 151 | 266 | 1587 | 0 | 206 | 550 | 5898 |
N.S. |
1 | 1.21 | 0.95 | 0.97 | 1.72 | 10.24 | 0.00 | 1.33 | 3.55 | 38.05 |
time (sec) |
N/A | 0.303 | 0.166 | 0.915 | 0.141 | 0.308 | 0.000 | 0.139 | 0.207 | 2.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 94 | 93 | 111 | 211 | 254 | 391 | 174 | 313 | 340 |
N.S. |
1 | 0.96 | 0.95 | 1.13 | 2.15 | 2.59 | 3.99 | 1.78 | 3.19 | 3.47 |
time (sec) |
N/A | 0.254 | 0.028 | 0.561 | 0.046 | 0.082 | 1.354 | 0.120 | 0.194 | 0.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 198 | 151 | 158 | 277 | 1585 | 0 | 217 | 571 | 6033 |
N.S. |
1 | 1.24 | 0.94 | 0.99 | 1.73 | 9.91 | 0.00 | 1.36 | 3.57 | 37.71 |
time (sec) |
N/A | 0.335 | 0.195 | 0.513 | 0.145 | 0.604 | 0.000 | 0.125 | 0.231 | 2.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 148 | 126 | 165 | 278 | 520 | 0 | 315 | 646 | 246 |
N.S. |
1 | 0.99 | 0.85 | 1.11 | 1.87 | 3.49 | 0.00 | 2.11 | 4.34 | 1.65 |
time (sec) |
N/A | 0.336 | 0.170 | 0.582 | 0.051 | 2.143 | 0.000 | 0.125 | 0.225 | 1.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 240 | 172 | 170 | 352 | 1991 | 0 | 236 | 673 | 738 |
N.S. |
1 | 1.14 | 0.82 | 0.81 | 1.67 | 9.44 | 0.00 | 1.12 | 3.19 | 3.50 |
time (sec) |
N/A | 0.429 | 0.249 | 0.647 | 0.177 | 1.110 | 0.000 | 0.122 | 0.194 | 1.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 174 | 171 | 187 | 364 | 640 | 0 | 357 | 776 | 314 |
N.S. |
1 | 0.98 | 0.96 | 1.05 | 2.04 | 3.60 | 0.00 | 2.01 | 4.36 | 1.76 |
time (sec) |
N/A | 0.388 | 0.281 | 0.590 | 0.062 | 4.681 | 0.000 | 0.123 | 0.192 | 1.957 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 301 | 196 | 190 | 440 | 2397 | 0 | 256 | 775 | 785 |
N.S. |
1 | 1.11 | 0.73 | 0.70 | 1.63 | 8.88 | 0.00 | 0.95 | 2.87 | 2.91 |
time (sec) |
N/A | 0.566 | 0.283 | 0.763 | 0.164 | 2.965 | 0.000 | 0.131 | 0.241 | 1.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 25 | 21 | 18 | 17 | 17 | 15 | 17 | 17 | 17 |
N.S. |
1 | 1.19 | 1.00 | 0.86 | 0.81 | 0.81 | 0.71 | 0.81 | 0.81 | 0.81 |
time (sec) |
N/A | 0.153 | 0.004 | 0.392 | 0.044 | 0.069 | 0.039 | 0.115 | 0.218 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 88 | 89 | 76 | 84 | 240 | 129 | 88 | 151 | 104 |
N.S. |
1 | 1.01 | 1.02 | 0.87 | 0.97 | 2.76 | 1.48 | 1.01 | 1.74 | 1.20 |
time (sec) |
N/A | 0.263 | 0.051 | 0.434 | 0.136 | 0.089 | 0.328 | 0.124 | 0.207 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 55 | 50 | 59 | 59 | 78 | 56 | 90 | 98 | 63 |
N.S. |
1 | 0.92 | 0.83 | 0.98 | 0.98 | 1.30 | 0.93 | 1.50 | 1.63 | 1.05 |
time (sec) |
N/A | 0.214 | 0.026 | 0.411 | 0.039 | 0.069 | 0.288 | 0.120 | 0.204 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 70 | 68 | 59 | 60 | 202 | 114 | 58 | 134 | 59 |
N.S. |
1 | 1.04 | 1.01 | 0.88 | 0.90 | 3.01 | 1.70 | 0.87 | 2.00 | 0.88 |
time (sec) |
N/A | 0.198 | 0.049 | 0.425 | 0.124 | 0.094 | 0.268 | 0.124 | 0.209 | 0.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 40 | 41 | 38 | 40 | 45 | 36 | 65 | 62 | 37 |
N.S. |
1 | 0.98 | 1.00 | 0.93 | 0.98 | 1.10 | 0.88 | 1.59 | 1.51 | 0.90 |
time (sec) |
N/A | 0.187 | 0.009 | 0.406 | 0.042 | 0.070 | 0.171 | 0.121 | 0.191 | 0.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 63 | 57 | 57 | 181 | 112 | 57 | 121 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 2.87 | 1.78 | 0.90 | 1.92 | 0.81 |
time (sec) |
N/A | 0.174 | 0.030 | 0.500 | 0.115 | 0.082 | 0.197 | 0.122 | 0.199 | 0.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 52 | 46 | 48 | 51 | 71 | 46 | 63 | 70 | 47 |
N.S. |
1 | 1.02 | 0.90 | 0.94 | 1.00 | 1.39 | 0.90 | 1.24 | 1.37 | 0.92 |
time (sec) |
N/A | 0.207 | 0.021 | 0.439 | 0.039 | 0.066 | 0.195 | 0.122 | 0.214 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 74 | 70 | 60 | 65 | 214 | 114 | 64 | 139 | 61 |
N.S. |
1 | 1.04 | 0.99 | 0.85 | 0.92 | 3.01 | 1.61 | 0.90 | 1.96 | 0.86 |
time (sec) |
N/A | 0.217 | 0.025 | 0.444 | 0.115 | 0.084 | 0.242 | 0.119 | 0.202 | 0.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 75 | 64 | 75 | 78 | 122 | 70 | 84 | 149 | 74 |
N.S. |
1 | 0.99 | 0.84 | 0.99 | 1.03 | 1.61 | 0.92 | 1.11 | 1.96 | 0.97 |
time (sec) |
N/A | 0.238 | 0.036 | 0.421 | 0.037 | 0.092 | 0.455 | 0.113 | 0.198 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 100 | 90 | 79 | 93 | 250 | 184 | 86 | 161 | 84 |
N.S. |
1 | 1.11 | 1.00 | 0.88 | 1.03 | 2.78 | 2.04 | 0.96 | 1.79 | 0.93 |
time (sec) |
N/A | 0.305 | 0.048 | 0.427 | 0.117 | 0.084 | 0.285 | 0.112 | 0.201 | 0.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 116 | 138 | 141 | 149 | 400 | 286 | 156 | 270 | 200 |
N.S. |
1 | 0.92 | 1.10 | 1.12 | 1.18 | 3.17 | 2.27 | 1.24 | 2.14 | 1.59 |
time (sec) |
N/A | 0.273 | 0.061 | 0.473 | 0.120 | 0.081 | 0.485 | 0.122 | 0.204 | 0.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 87 | 87 | 82 | 107 | 160 | 99 | 163 | 188 | 112 |
N.S. |
1 | 0.99 | 0.99 | 0.93 | 1.22 | 1.82 | 1.12 | 1.85 | 2.14 | 1.27 |
time (sec) |
N/A | 0.259 | 0.040 | 0.494 | 0.052 | 0.073 | 0.459 | 0.125 | 0.223 | 0.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 103 | 105 | 102 | 109 | 342 | 246 | 114 | 241 | 148 |
N.S. |
1 | 1.04 | 1.06 | 1.03 | 1.10 | 3.45 | 2.48 | 1.15 | 2.43 | 1.49 |
time (sec) |
N/A | 0.243 | 0.049 | 0.464 | 0.118 | 0.080 | 0.420 | 0.125 | 0.214 | 0.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 56 | 63 | 73 | 101 | 68 | 111 | 133 | 77 |
N.S. |
1 | 1.00 | 0.92 | 1.03 | 1.20 | 1.66 | 1.11 | 1.82 | 2.18 | 1.26 |
time (sec) |
N/A | 0.218 | 0.032 | 0.441 | 0.035 | 0.067 | 0.370 | 0.126 | 0.222 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 88 | 94 | 95 | 297 | 236 | 94 | 215 | 124 |
N.S. |
1 | 1.00 | 1.07 | 1.15 | 1.16 | 3.62 | 2.88 | 1.15 | 2.62 | 1.51 |
time (sec) |
N/A | 0.249 | 0.041 | 0.427 | 0.127 | 0.122 | 0.356 | 0.124 | 0.199 | 0.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 68 | 70 | 66 | 86 | 117 | 80 | 99 | 146 | 80 |
N.S. |
1 | 1.01 | 1.04 | 0.99 | 1.28 | 1.75 | 1.19 | 1.48 | 2.18 | 1.19 |
time (sec) |
N/A | 0.234 | 0.028 | 0.454 | 0.036 | 0.073 | 0.632 | 0.122 | 0.202 | 0.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 106 | 91 | 95 | 101 | 308 | 238 | 103 | 225 | 128 |
N.S. |
1 | 1.25 | 1.07 | 1.12 | 1.19 | 3.62 | 2.80 | 1.21 | 2.65 | 1.51 |
time (sec) |
N/A | 0.234 | 0.048 | 0.469 | 0.133 | 0.086 | 0.423 | 0.125 | 0.190 | 0.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 83 | 72 | 77 | 100 | 159 | 92 | 109 | 176 | 100 |
N.S. |
1 | 1.04 | 0.90 | 0.96 | 1.25 | 1.99 | 1.15 | 1.36 | 2.20 | 1.25 |
time (sec) |
N/A | 0.249 | 0.061 | 0.467 | 0.030 | 0.075 | 0.685 | 0.121 | 0.208 | 0.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 131 | 107 | 107 | 118 | 356 | 248 | 112 | 256 | 146 |
N.S. |
1 | 1.28 | 1.05 | 1.05 | 1.16 | 3.49 | 2.43 | 1.10 | 2.51 | 1.43 |
time (sec) |
N/A | 0.317 | 0.047 | 0.487 | 0.123 | 0.081 | 0.498 | 0.124 | 0.206 | 0.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 172 | 151 | 227 | 228 | 580 | 389 | 241 | 406 | 328 |
N.S. |
1 | 1.15 | 1.01 | 1.51 | 1.52 | 3.87 | 2.59 | 1.61 | 2.71 | 2.19 |
time (sec) |
N/A | 0.339 | 0.054 | 0.478 | 0.114 | 0.105 | 0.675 | 0.125 | 0.223 | 0.590 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 113 | 106 | 137 | 174 | 254 | 163 | 249 | 294 | 194 |
N.S. |
1 | 0.97 | 0.91 | 1.17 | 1.49 | 2.17 | 1.39 | 2.13 | 2.51 | 1.66 |
time (sec) |
N/A | 0.315 | 0.059 | 0.549 | 0.043 | 0.070 | 0.680 | 0.129 | 0.185 | 0.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 166 | 125 | 170 | 176 | 508 | 338 | 184 | 363 | 232 |
N.S. |
1 | 1.33 | 1.00 | 1.36 | 1.41 | 4.06 | 2.70 | 1.47 | 2.90 | 1.86 |
time (sec) |
N/A | 0.323 | 0.044 | 0.489 | 0.147 | 0.083 | 0.605 | 0.124 | 0.197 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 85 | 127 | 89 | 124 | 181 | 112 | 183 | 225 | 130 |
N.S. |
1 | 0.97 | 1.44 | 1.01 | 1.41 | 2.06 | 1.27 | 2.08 | 2.56 | 1.48 |
time (sec) |
N/A | 0.247 | 0.029 | 0.490 | 0.030 | 0.073 | 0.572 | 0.117 | 0.189 | 0.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 106 | 139 | 147 | 442 | 314 | 152 | 325 | 182 |
N.S. |
1 | 1.00 | 1.00 | 1.31 | 1.39 | 4.17 | 2.96 | 1.43 | 3.07 | 1.72 |
time (sec) |
N/A | 0.269 | 0.043 | 0.538 | 0.127 | 0.082 | 0.526 | 0.126 | 0.220 | 0.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 86 | 111 | 94 | 122 | 178 | 110 | 150 | 219 | 122 |
N.S. |
1 | 0.98 | 1.26 | 1.07 | 1.39 | 2.02 | 1.25 | 1.70 | 2.49 | 1.39 |
time (sec) |
N/A | 0.259 | 0.066 | 0.450 | 0.033 | 0.081 | 1.193 | 0.125 | 0.213 | 0.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 130 | 94 | 129 | 140 | 412 | 309 | 143 | 322 | 173 |
N.S. |
1 | 1.38 | 1.00 | 1.37 | 1.49 | 4.38 | 3.29 | 1.52 | 3.43 | 1.84 |
time (sec) |
N/A | 0.328 | 0.042 | 0.477 | 0.138 | 0.089 | 0.782 | 0.128 | 0.203 | 0.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 97 | 87 | 100 | 141 | 209 | 128 | 157 | 262 | 135 |
N.S. |
1 | 0.99 | 0.89 | 1.02 | 1.44 | 2.13 | 1.31 | 1.60 | 2.67 | 1.38 |
time (sec) |
N/A | 0.277 | 0.062 | 0.461 | 0.039 | 0.086 | 1.626 | 0.121 | 0.201 | 0.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 146 | 109 | 144 | 159 | 458 | 321 | 150 | 345 | 183 |
N.S. |
1 | 1.35 | 1.01 | 1.33 | 1.47 | 4.24 | 2.97 | 1.39 | 3.19 | 1.69 |
time (sec) |
N/A | 0.337 | 0.044 | 0.469 | 0.115 | 0.087 | 0.922 | 0.126 | 0.187 | 0.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 126 | 95 | 94 | 133 | 726 | 0 | 122 | 229 | 3558 |
N.S. |
1 | 1.16 | 0.87 | 0.86 | 1.22 | 6.66 | 0.00 | 1.12 | 2.10 | 32.64 |
time (sec) |
N/A | 0.251 | 0.098 | 0.591 | 0.113 | 0.133 | 0.000 | 0.124 | 0.206 | 1.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 70 | 74 | 69 | 105 | 117 | 253 | 92 | 129 | 172 |
N.S. |
1 | 0.95 | 1.00 | 0.93 | 1.42 | 1.58 | 3.42 | 1.24 | 1.74 | 2.32 |
time (sec) |
N/A | 0.231 | 0.022 | 0.565 | 0.037 | 0.103 | 0.935 | 0.123 | 0.203 | 0.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 116 | 104 | 85 | 119 | 704 | 0 | 110 | 217 | 3153 |
N.S. |
1 | 1.12 | 1.00 | 0.82 | 1.14 | 6.77 | 0.00 | 1.06 | 2.09 | 30.32 |
time (sec) |
N/A | 0.222 | 0.092 | 0.572 | 0.124 | 0.123 | 0.000 | 0.119 | 0.236 | 1.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 67 | 66 | 72 | 99 | 103 | 248 | 85 | 138 | 161 |
N.S. |
1 | 0.96 | 0.94 | 1.03 | 1.41 | 1.47 | 3.54 | 1.21 | 1.97 | 2.30 |
time (sec) |
N/A | 0.218 | 0.019 | 0.545 | 0.049 | 0.080 | 0.893 | 0.122 | 0.202 | 0.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 125 | 109 | 95 | 132 | 699 | 0 | 121 | 229 | 3649 |
N.S. |
1 | 1.16 | 1.01 | 0.88 | 1.22 | 6.47 | 0.00 | 1.12 | 2.12 | 33.79 |
time (sec) |
N/A | 0.248 | 0.085 | 0.505 | 0.119 | 0.174 | 0.000 | 0.128 | 0.224 | 1.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 98 | 97 | 100 | 137 | 218 | 0 | 183 | 266 | 127 |
N.S. |
1 | 0.99 | 0.98 | 1.01 | 1.38 | 2.20 | 0.00 | 1.85 | 2.69 | 1.28 |
time (sec) |
N/A | 0.279 | 0.067 | 0.554 | 0.039 | 0.549 | 0.000 | 0.121 | 0.202 | 1.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 160 | 123 | 108 | 178 | 1003 | 0 | 164 | 302 | 2400 |
N.S. |
1 | 1.11 | 0.85 | 0.75 | 1.24 | 6.97 | 0.00 | 1.14 | 2.10 | 16.67 |
time (sec) |
N/A | 0.335 | 0.117 | 0.605 | 0.116 | 0.291 | 0.000 | 0.121 | 0.196 | 1.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 122 | 119 | 120 | 189 | 303 | 0 | 257 | 344 | 171 |
N.S. |
1 | 0.97 | 0.94 | 0.95 | 1.50 | 2.40 | 0.00 | 2.04 | 2.73 | 1.36 |
time (sec) |
N/A | 0.319 | 0.101 | 0.685 | 0.047 | 1.466 | 0.000 | 0.128 | 0.219 | 1.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 201 | 142 | 128 | 236 | 1281 | 0 | 165 | 368 | 4654 |
N.S. |
1 | 1.06 | 0.75 | 0.68 | 1.25 | 6.78 | 0.00 | 0.87 | 1.95 | 24.62 |
time (sec) |
N/A | 0.416 | 0.184 | 0.746 | 0.122 | 0.954 | 0.000 | 0.117 | 0.234 | 1.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 156 | 155 | 153 | 258 | 356 | 0 | 281 | 405 | 217 |
N.S. |
1 | 0.98 | 0.97 | 0.96 | 1.61 | 2.22 | 0.00 | 1.76 | 2.53 | 1.36 |
time (sec) |
N/A | 0.369 | 0.127 | 0.560 | 0.038 | 3.040 | 0.000 | 0.122 | 0.204 | 1.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 260 | 179 | 161 | 303 | 1489 | 0 | 207 | 426 | 2737 |
N.S. |
1 | 1.04 | 0.72 | 0.64 | 1.21 | 5.96 | 0.00 | 0.83 | 1.70 | 10.95 |
time (sec) |
N/A | 0.540 | 0.199 | 0.621 | 0.118 | 1.815 | 0.000 | 0.132 | 0.206 | 1.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 206 | 202 | 201 | 339 | 410 | 0 | 354 | 463 | 278 |
N.S. |
1 | 0.98 | 0.96 | 0.96 | 1.61 | 1.95 | 0.00 | 1.69 | 2.20 | 1.32 |
time (sec) |
N/A | 0.450 | 0.190 | 0.586 | 0.039 | 4.889 | 0.000 | 0.116 | 0.230 | 1.787 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 183 | 136 | 117 | 249 | 1407 | 0 | 198 | 565 | 5395 |
N.S. |
1 | 1.13 | 0.84 | 0.72 | 1.54 | 8.69 | 0.00 | 1.22 | 3.49 | 33.30 |
time (sec) |
N/A | 0.326 | 0.148 | 0.637 | 0.121 | 0.189 | 0.000 | 0.124 | 0.188 | 2.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 100 | 86 | 113 | 228 | 296 | 507 | 178 | 417 | 522 |
N.S. |
1 | 0.93 | 0.80 | 1.06 | 2.13 | 2.77 | 4.74 | 1.66 | 3.90 | 4.88 |
time (sec) |
N/A | 0.280 | 0.042 | 0.557 | 0.040 | 0.088 | 2.002 | 0.119 | 0.195 | 0.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 169 | 135 | 117 | 249 | 1387 | 0 | 196 | 565 | 5236 |
N.S. |
1 | 1.15 | 0.92 | 0.80 | 1.69 | 9.44 | 0.00 | 1.33 | 3.84 | 35.62 |
time (sec) |
N/A | 0.290 | 0.156 | 0.618 | 0.122 | 0.261 | 0.000 | 0.119 | 0.200 | 2.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 93 | 77 | 106 | 215 | 253 | 410 | 163 | 515 | 378 |
N.S. |
1 | 1.01 | 0.84 | 1.15 | 2.34 | 2.75 | 4.46 | 1.77 | 5.60 | 4.11 |
time (sec) |
N/A | 0.254 | 0.040 | 0.566 | 0.038 | 0.084 | 1.339 | 0.131 | 0.242 | 0.804 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 190 | 136 | 133 | 294 | 1681 | 0 | 232 | 613 | 6183 |
N.S. |
1 | 1.14 | 0.81 | 0.80 | 1.76 | 10.07 | 0.00 | 1.39 | 3.67 | 37.02 |
time (sec) |
N/A | 0.344 | 0.201 | 0.512 | 0.159 | 0.565 | 0.000 | 0.121 | 0.211 | 2.622 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 137 | 133 | 136 | 295 | 540 | 0 | 321 | 678 | 193 |
N.S. |
1 | 0.97 | 0.94 | 0.96 | 2.09 | 3.83 | 0.00 | 2.28 | 4.81 | 1.37 |
time (sec) |
N/A | 0.337 | 0.140 | 0.602 | 0.043 | 2.093 | 0.000 | 0.130 | 0.203 | 1.971 |