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 | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 82 | 79 | 78 | 114 | 189 | 83 | 114 | 190 | 106 |
N.S. |
1 | 0.87 | 0.84 | 0.83 | 1.21 | 2.01 | 0.88 | 1.21 | 2.02 | 1.13 |
time (sec) |
N/A | 0.305 | 0.224 | 162.023 | 0.040 | 0.076 | 4.343 | 0.174 | 0.161 | 0.667 |
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 | 75 | 68 | 63 | 67 | 92 | 153 | 68 | 92 | 153 | 149 |
N.S. |
1 | 0.91 | 0.84 | 0.89 | 1.23 | 2.04 | 0.91 | 1.23 | 2.04 | 1.99 |
time (sec) |
N/A | 0.294 | 0.073 | 58.354 | 0.036 | 0.076 | 2.655 | 0.147 | 0.183 | 0.344 |
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 | 62 | 58 | 55 | 56 | 70 | 117 | 60 | 70 | 116 | 112 |
N.S. |
1 | 0.94 | 0.89 | 0.90 | 1.13 | 1.89 | 0.97 | 1.13 | 1.87 | 1.81 |
time (sec) |
N/A | 0.297 | 0.075 | 14.390 | 0.033 | 0.065 | 1.715 | 0.140 | 0.163 | 0.322 |
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 | 46 | 46 | 43 | 45 | 48 | 81 | 48 | 48 | 79 | 48 |
N.S. |
1 | 1.00 | 0.93 | 0.98 | 1.04 | 1.76 | 1.04 | 1.04 | 1.72 | 1.04 |
time (sec) |
N/A | 0.291 | 0.031 | 3.215 | 0.042 | 0.079 | 1.204 | 0.141 | 0.154 | 0.318 |
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 | 27 | 30 | 30 | 28 | 21 | 45 | 37 | 26 | 42 | 23 |
N.S. |
1 | 1.11 | 1.11 | 1.04 | 0.78 | 1.67 | 1.37 | 0.96 | 1.56 | 0.85 |
time (sec) |
N/A | 0.270 | 0.020 | 0.612 | 0.028 | 0.068 | 0.784 | 0.128 | 0.154 | 0.296 |
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 | 19 | 19 | 19 | 23 | 17 | 18 | 24 | 18 | 24 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.21 | 0.89 | 0.95 | 1.26 | 0.95 | 1.26 | 0.89 |
time (sec) |
N/A | 0.164 | 0.006 | 0.089 | 0.037 | 0.114 | 0.097 | 0.128 | 0.186 | 0.354 |
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 | 45 | 46 | 48 | 22 | 38 | 23 | 39 | 46 | 33 | 22 |
N.S. |
1 | 1.02 | 1.07 | 0.49 | 0.84 | 0.51 | 0.87 | 1.02 | 0.73 | 0.49 |
time (sec) |
N/A | 0.265 | 0.068 | 0.593 | 0.115 | 0.072 | 0.095 | 0.136 | 0.154 | 0.347 |
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 | 72 | 46 | 53 | 61 | 56 | 136 | 77 | 63 | 64 |
N.S. |
1 | 1.07 | 0.69 | 0.79 | 0.91 | 0.84 | 2.03 | 1.15 | 0.94 | 0.96 |
time (sec) |
N/A | 0.335 | 0.064 | 2.937 | 0.114 | 0.072 | 0.184 | 0.129 | 0.154 | 0.429 |
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 | 89 | 98 | 56 | 63 | 82 | 80 | 211 | 97 | 90 | 108 |
N.S. |
1 | 1.10 | 0.63 | 0.71 | 0.92 | 0.90 | 2.37 | 1.09 | 1.01 | 1.21 |
time (sec) |
N/A | 0.420 | 0.076 | 12.924 | 0.117 | 0.076 | 0.219 | 0.128 | 0.153 | 0.685 |
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 | 111 | 124 | 68 | 73 | 103 | 104 | 279 | 117 | 117 | 152 |
N.S. |
1 | 1.12 | 0.61 | 0.66 | 0.93 | 0.94 | 2.51 | 1.05 | 1.05 | 1.37 |
time (sec) |
N/A | 0.505 | 0.140 | 44.458 | 0.152 | 0.084 | 0.320 | 0.130 | 0.153 | 1.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 107 | 98 | 74 | 106 | 372 | 0 | 181 | 364 | 247 |
N.S. |
1 | 1.09 | 1.00 | 0.76 | 1.08 | 3.80 | 0.00 | 1.85 | 3.71 | 2.52 |
time (sec) |
N/A | 0.534 | 0.018 | 32.582 | 0.040 | 0.089 | 0.000 | 0.173 | 0.172 | 4.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 81 | 76 | 64 | 86 | 276 | 0 | 139 | 265 | 178 |
N.S. |
1 | 1.07 | 1.00 | 0.84 | 1.13 | 3.63 | 0.00 | 1.83 | 3.49 | 2.34 |
time (sec) |
N/A | 0.437 | 0.016 | 6.928 | 0.039 | 0.086 | 0.000 | 0.162 | 0.167 | 4.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 55 | 54 | 51 | 61 | 180 | 0 | 97 | 166 | 107 |
N.S. |
1 | 1.02 | 1.00 | 0.94 | 1.13 | 3.33 | 0.00 | 1.80 | 3.07 | 1.98 |
time (sec) |
N/A | 0.344 | 0.012 | 1.628 | 0.051 | 0.109 | 0.000 | 0.156 | 0.184 | 2.321 |
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 | 27 | 27 | 27 | 34 | 32 | 82 | 41 | 52 | 63 | 39 |
N.S. |
1 | 1.00 | 1.00 | 1.26 | 1.19 | 3.04 | 1.52 | 1.93 | 2.33 | 1.44 |
time (sec) |
N/A | 0.247 | 0.008 | 0.309 | 0.040 | 0.080 | 2.450 | 0.145 | 0.159 | 0.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 51 | 17 | 22 | 15 | 26 | 84 | 22 | 20 |
N.S. |
1 | 1.00 | 1.96 | 0.65 | 0.85 | 0.58 | 1.00 | 3.23 | 0.85 | 0.77 |
time (sec) |
N/A | 0.250 | 0.047 | 0.372 | 0.041 | 0.068 | 0.079 | 0.142 | 0.179 | 0.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 37 | 36 | 42 | 105 | 196 | 51 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.78 | 0.91 | 2.28 | 4.26 | 1.11 | 1.17 |
time (sec) |
N/A | 0.282 | 0.010 | 1.417 | 0.046 | 0.132 | 0.176 | 0.160 | 0.151 | 0.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 58 | 62 | 47 | 49 | 66 | 184 | 220 | 81 | 70 |
N.S. |
1 | 0.94 | 1.00 | 0.76 | 0.79 | 1.06 | 2.97 | 3.55 | 1.31 | 1.13 |
time (sec) |
N/A | 0.283 | 0.014 | 6.537 | 0.035 | 0.079 | 0.266 | 0.193 | 0.156 | 2.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 66 | 76 | 57 | 58 | 90 | 253 | 244 | 108 | 93 |
N.S. |
1 | 0.87 | 1.00 | 0.75 | 0.76 | 1.18 | 3.33 | 3.21 | 1.42 | 1.22 |
time (sec) |
N/A | 0.291 | 0.031 | 27.092 | 0.043 | 0.080 | 0.345 | 0.204 | 0.163 | 3.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 94 | 79 | 80 | 108 | 189 | 0 | 108 | 172 | 151 |
N.S. |
1 | 0.86 | 0.72 | 0.73 | 0.99 | 1.73 | 0.00 | 0.99 | 1.58 | 1.39 |
time (sec) |
N/A | 0.297 | 0.501 | 107.834 | 0.036 | 0.087 | 0.000 | 0.165 | 0.160 | 0.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 72 | 63 | 69 | 95 | 151 | 0 | 95 | 135 | 132 |
N.S. |
1 | 0.88 | 0.77 | 0.84 | 1.16 | 1.84 | 0.00 | 1.16 | 1.65 | 1.61 |
time (sec) |
N/A | 0.270 | 0.329 | 33.528 | 0.028 | 0.088 | 0.000 | 0.166 | 0.164 | 0.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 34 | 58 | 56 | 113 | 0 | 56 | 98 | 56 |
N.S. |
1 | 0.91 | 0.62 | 1.05 | 1.02 | 2.05 | 0.00 | 1.02 | 1.78 | 1.02 |
time (sec) |
N/A | 0.254 | 0.157 | 7.170 | 0.034 | 0.081 | 0.000 | 0.152 | 0.156 | 0.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 50 | 47 | 21 | 75 | 0 | 42 | 61 | 35 |
N.S. |
1 | 1.00 | 1.85 | 1.74 | 0.78 | 2.78 | 0.00 | 1.56 | 2.26 | 1.30 |
time (sec) |
N/A | 0.227 | 0.086 | 1.713 | 0.036 | 0.103 | 0.000 | 0.149 | 0.157 | 0.313 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 34 | 40 | 41 | 56 | 53 | 32 | 33 | 29 |
N.S. |
1 | 1.00 | 0.89 | 1.05 | 1.08 | 1.47 | 1.39 | 0.84 | 0.87 | 0.76 |
time (sec) |
N/A | 0.255 | 0.120 | 0.116 | 0.118 | 0.075 | 0.141 | 0.135 | 0.150 | 0.329 |
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 | 25 | 25 | 31 | 19 | 32 | 17 | 36 | 17 | 28 | 18 |
N.S. |
1 | 1.00 | 1.24 | 0.76 | 1.28 | 0.68 | 1.44 | 0.68 | 1.12 | 0.72 |
time (sec) |
N/A | 0.228 | 0.111 | 1.385 | 0.108 | 0.072 | 0.108 | 0.150 | 0.184 | 0.323 |
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 | 71 | 52 | 44 | 67 | 41 | 87 | 57 | 64 | 50 |
N.S. |
1 | 1.06 | 0.78 | 0.66 | 1.00 | 0.61 | 1.30 | 0.85 | 0.96 | 0.75 |
time (sec) |
N/A | 0.283 | 0.195 | 5.940 | 0.118 | 0.077 | 0.162 | 0.186 | 0.149 | 0.373 |
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 | 125 | 115 | 99 | 79 | 92 | 78 | 185 | 89 | 92 | 88 |
N.S. |
1 | 0.92 | 0.79 | 0.63 | 0.74 | 0.62 | 1.48 | 0.71 | 0.74 | 0.70 |
time (sec) |
N/A | 0.310 | 0.256 | 24.302 | 0.116 | 0.108 | 0.245 | 0.177 | 0.159 | 0.487 |
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 | 179 | 159 | 142 | 114 | 115 | 106 | 270 | 109 | 119 | 144 |
N.S. |
1 | 0.89 | 0.79 | 0.64 | 0.64 | 0.59 | 1.51 | 0.61 | 0.66 | 0.80 |
time (sec) |
N/A | 0.347 | 0.323 | 75.840 | 0.116 | 0.087 | 0.303 | 0.184 | 0.153 | 1.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 121 | 108 | 133 | 181 | 364 | 0 | 237 | 274 | 290 |
N.S. |
1 | 1.03 | 0.92 | 1.13 | 1.53 | 3.08 | 0.00 | 2.01 | 2.32 | 2.46 |
time (sec) |
N/A | 0.631 | 0.218 | 15.062 | 0.038 | 0.084 | 0.000 | 0.201 | 0.159 | 4.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 95 | 84 | 111 | 130 | 256 | 0 | 173 | 199 | 198 |
N.S. |
1 | 1.01 | 0.89 | 1.18 | 1.38 | 2.72 | 0.00 | 1.84 | 2.12 | 2.11 |
time (sec) |
N/A | 0.511 | 0.113 | 3.524 | 0.044 | 0.094 | 0.000 | 0.200 | 0.186 | 3.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 65 | 70 | 86 | 83 | 148 | 0 | 107 | 122 | 104 |
N.S. |
1 | 0.96 | 1.03 | 1.26 | 1.22 | 2.18 | 0.00 | 1.57 | 1.79 | 1.53 |
time (sec) |
N/A | 0.369 | 0.116 | 0.741 | 0.035 | 0.087 | 0.000 | 0.162 | 0.163 | 0.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 180 | 56 | 61 | 52 | 68 | 56 | 54 | 41 |
N.S. |
1 | 1.00 | 3.91 | 1.22 | 1.33 | 1.13 | 1.48 | 1.22 | 1.17 | 0.89 |
time (sec) |
N/A | 0.294 | 0.471 | 0.664 | 0.042 | 0.082 | 0.171 | 0.188 | 0.163 | 0.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 52 | 38 | 52 | 34 | 75 | 531 | 56 | 78 |
N.S. |
1 | 1.00 | 1.02 | 0.75 | 1.02 | 0.67 | 1.47 | 10.41 | 1.10 | 1.53 |
time (sec) |
N/A | 0.285 | 0.072 | 2.892 | 0.062 | 0.074 | 0.158 | 0.238 | 0.161 | 0.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 66 | 68 | 67 | 79 | 62 | 153 | 613 | 83 | 71 |
N.S. |
1 | 0.96 | 0.99 | 0.97 | 1.14 | 0.90 | 2.22 | 8.88 | 1.20 | 1.03 |
time (sec) |
N/A | 0.311 | 0.121 | 12.795 | 0.036 | 0.070 | 0.234 | 0.297 | 0.182 | 1.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 78 | 85 | 102 | 98 | 90 | 238 | 641 | 110 | 256 |
N.S. |
1 | 0.90 | 0.98 | 1.17 | 1.13 | 1.03 | 2.74 | 7.37 | 1.26 | 2.94 |
time (sec) |
N/A | 0.318 | 0.122 | 44.045 | 0.040 | 0.080 | 0.337 | 0.325 | 0.165 | 0.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 86 | 104 | 131 | 119 | 118 | 314 | 669 | 137 | 330 |
N.S. |
1 | 0.82 | 0.99 | 1.25 | 1.13 | 1.12 | 2.99 | 6.37 | 1.30 | 3.14 |
time (sec) |
N/A | 0.323 | 0.282 | 124.663 | 0.036 | 0.096 | 0.425 | 0.367 | 0.155 | 2.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 94 | 79 | 91 | 108 | 215 | 0 | 108 | 192 | 151 |
N.S. |
1 | 0.86 | 0.72 | 0.83 | 0.99 | 1.97 | 0.00 | 0.99 | 1.76 | 1.39 |
time (sec) |
N/A | 0.279 | 0.607 | 169.061 | 0.051 | 0.088 | 0.000 | 0.196 | 0.166 | 0.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 72 | 63 | 80 | 108 | 177 | 0 | 108 | 155 | 151 |
N.S. |
1 | 0.88 | 0.77 | 0.98 | 1.32 | 2.16 | 0.00 | 1.32 | 1.89 | 1.84 |
time (sec) |
N/A | 0.264 | 0.345 | 59.881 | 0.034 | 0.074 | 0.000 | 0.203 | 0.162 | 0.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 34 | 69 | 82 | 139 | 0 | 82 | 118 | 114 |
N.S. |
1 | 0.91 | 0.62 | 1.25 | 1.49 | 2.53 | 0.00 | 1.49 | 2.15 | 2.07 |
time (sec) |
N/A | 0.247 | 0.283 | 15.386 | 0.039 | 0.069 | 0.000 | 0.186 | 0.164 | 0.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 50 | 58 | 21 | 101 | 0 | 56 | 81 | 56 |
N.S. |
1 | 1.00 | 1.85 | 2.15 | 0.78 | 3.74 | 0.00 | 2.07 | 3.00 | 2.07 |
time (sec) |
N/A | 0.219 | 0.128 | 3.667 | 0.036 | 0.086 | 0.000 | 0.168 | 0.170 | 0.341 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 67 | 46 | 51 | 76 | 97 | 94 | 50 | 46 | 41 |
N.S. |
1 | 1.06 | 0.73 | 0.81 | 1.21 | 1.54 | 1.49 | 0.79 | 0.73 | 0.65 |
time (sec) |
N/A | 0.337 | 0.135 | 0.124 | 0.117 | 0.079 | 0.181 | 0.152 | 0.154 | 0.346 |
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 | 48 | 43 | 40 | 50 | 62 | 36 | 61 | 36 | 85 | 39 |
N.S. |
1 | 0.90 | 0.83 | 1.04 | 1.29 | 0.75 | 1.27 | 0.75 | 1.77 | 0.81 |
time (sec) |
N/A | 0.249 | 0.095 | 2.723 | 0.119 | 0.096 | 0.199 | 0.184 | 0.149 | 0.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 24 | 38 | 57 | 34 | 80 | 18 | 59 | 36 |
N.S. |
1 | 1.00 | 0.89 | 1.41 | 2.11 | 1.26 | 2.96 | 0.67 | 2.19 | 1.33 |
time (sec) |
N/A | 0.225 | 0.074 | 12.587 | 0.107 | 0.087 | 0.179 | 0.216 | 0.177 | 0.399 |
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 | 98 | 93 | 65 | 62 | 105 | 55 | 131 | 69 | 92 | 77 |
N.S. |
1 | 0.95 | 0.66 | 0.63 | 1.07 | 0.56 | 1.34 | 0.70 | 0.94 | 0.79 |
time (sec) |
N/A | 0.288 | 0.229 | 43.668 | 0.116 | 0.085 | 0.229 | 0.224 | 0.191 | 0.444 |
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 | 160 | 137 | 137 | 97 | 128 | 92 | 226 | 99 | 119 | 125 |
N.S. |
1 | 0.86 | 0.86 | 0.61 | 0.80 | 0.58 | 1.41 | 0.62 | 0.74 | 0.78 |
time (sec) |
N/A | 0.318 | 0.291 | 128.325 | 0.120 | 0.092 | 0.352 | 0.266 | 0.162 | 0.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 134 | 102 | 122 | 155 | 310 | 0 | 189 | 278 | 228 |
N.S. |
1 | 1.06 | 0.80 | 0.96 | 1.22 | 2.44 | 0.00 | 1.49 | 2.19 | 1.80 |
time (sec) |
N/A | 0.665 | 1.664 | 7.762 | 0.038 | 0.091 | 0.000 | 0.250 | 0.162 | 4.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 102 | 93 | 100 | 109 | 202 | 0 | 125 | 179 | 136 |
N.S. |
1 | 1.03 | 0.94 | 1.01 | 1.10 | 2.04 | 0.00 | 1.26 | 1.81 | 1.37 |
time (sec) |
N/A | 0.495 | 1.329 | 1.663 | 0.041 | 0.091 | 0.000 | 0.232 | 0.162 | 2.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 62 | 123 | 93 | 82 | 107 | 107 | 234 | 93 | 102 |
N.S. |
1 | 1.02 | 2.02 | 1.52 | 1.34 | 1.75 | 1.75 | 3.84 | 1.52 | 1.67 |
time (sec) |
N/A | 0.386 | 1.440 | 1.421 | 0.040 | 0.085 | 0.219 | 0.310 | 0.164 | 0.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 31 | 19 | 75 | 17 | 36 | 901 | 54 | 66 |
N.S. |
1 | 1.00 | 0.97 | 0.59 | 2.34 | 0.53 | 1.12 | 28.16 | 1.69 | 2.06 |
time (sec) |
N/A | 0.222 | 0.165 | 6.287 | 0.048 | 0.082 | 0.143 | 0.380 | 0.201 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 87 | 145 | 56 | 105 | 48 | 116 | 929 | 83 | 130 |
N.S. |
1 | 0.99 | 1.65 | 0.64 | 1.19 | 0.55 | 1.32 | 10.56 | 0.94 | 1.48 |
time (sec) |
N/A | 0.429 | 0.664 | 24.548 | 0.038 | 0.077 | 0.254 | 0.454 | 0.202 | 0.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 99 | 180 | 85 | 123 | 76 | 190 | 465 | 110 | 134 |
N.S. |
1 | 0.93 | 1.70 | 0.80 | 1.16 | 0.72 | 1.79 | 4.39 | 1.04 | 1.26 |
time (sec) |
N/A | 0.418 | 0.576 | 77.052 | 0.037 | 0.085 | 0.330 | 0.529 | 0.209 | 1.630 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 107 | 226 | 120 | 145 | 104 | 275 | 1039 | 137 | 330 |
N.S. |
1 | 0.86 | 1.82 | 0.97 | 1.17 | 0.84 | 2.22 | 8.38 | 1.10 | 2.66 |
time (sec) |
N/A | 0.432 | 0.852 | 198.495 | 0.067 | 0.079 | 0.409 | 0.612 | 0.165 | 1.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 173 | 171 | 133 | 246 | 364 | 0 | 237 | 291 | 290 |
N.S. |
1 | 1.06 | 1.05 | 0.82 | 1.51 | 2.23 | 0.00 | 1.45 | 1.79 | 1.78 |
time (sec) |
N/A | 0.833 | 1.843 | 15.612 | 0.047 | 0.084 | 0.000 | 0.322 | 0.157 | 4.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 139 | 237 | 111 | 180 | 256 | 0 | 173 | 216 | 198 |
N.S. |
1 | 1.05 | 1.78 | 0.83 | 1.35 | 1.92 | 0.00 | 1.30 | 1.62 | 1.49 |
time (sec) |
N/A | 0.647 | 1.358 | 3.456 | 0.056 | 0.091 | 0.000 | 0.299 | 0.155 | 3.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 100 | 906 | 107 | 137 | 162 | 153 | 372 | 151 | 159 |
N.S. |
1 | 1.03 | 9.34 | 1.10 | 1.41 | 1.67 | 1.58 | 3.84 | 1.56 | 1.64 |
time (sec) |
N/A | 0.503 | 6.710 | 2.958 | 0.040 | 0.092 | 0.269 | 0.401 | 0.174 | 2.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 85 | 246 | 79 | 121 | 68 | 109 | 1299 | 76 | 88 |
N.S. |
1 | 1.09 | 3.15 | 1.01 | 1.55 | 0.87 | 1.40 | 16.65 | 0.97 | 1.13 |
time (sec) |
N/A | 0.417 | 0.864 | 12.561 | 0.037 | 0.093 | 0.266 | 0.588 | 0.186 | 0.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 145 | 38 | 118 | 34 | 80 | 915 | 83 | 130 |
N.S. |
1 | 1.00 | 2.20 | 0.58 | 1.79 | 0.52 | 1.21 | 13.86 | 1.26 | 1.97 |
time (sec) |
N/A | 0.343 | 0.497 | 43.372 | 0.039 | 0.094 | 0.226 | 0.752 | 0.216 | 0.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 107 | 181 | 74 | 149 | 62 | 156 | 1327 | 110 | 186 |
N.S. |
1 | 1.05 | 1.77 | 0.73 | 1.46 | 0.61 | 1.53 | 13.01 | 1.08 | 1.82 |
time (sec) |
N/A | 0.445 | 0.568 | 123.247 | 0.039 | 0.117 | 0.291 | 0.609 | 0.167 | 1.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 119 | 216 | 103 | 181 | 90 | 228 | 1409 | 137 | 145 |
N.S. |
1 | 0.99 | 1.80 | 0.86 | 1.51 | 0.75 | 1.90 | 11.74 | 1.14 | 1.21 |
time (sec) |
N/A | 0.466 | 0.808 | 306.935 | 0.241 | 0.089 | 0.399 | 0.462 | 0.219 | 1.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 94 | 81 | 377 | 160 | 267 | 0 | 160 | 229 | 146 |
N.S. |
1 | 0.86 | 0.74 | 3.46 | 1.47 | 2.45 | 0.00 | 1.47 | 2.10 | 1.34 |
time (sec) |
N/A | 0.284 | 0.785 | 0.414 | 0.044 | 0.083 | 0.000 | 0.275 | 0.163 | 0.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 72 | 63 | 102 | 108 | 229 | 0 | 108 | 192 | 151 |
N.S. |
1 | 0.88 | 0.77 | 1.24 | 1.32 | 2.79 | 0.00 | 1.32 | 2.34 | 1.84 |
time (sec) |
N/A | 0.269 | 0.488 | 166.158 | 0.042 | 0.079 | 0.000 | 0.257 | 0.158 | 0.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 36 | 91 | 108 | 191 | 0 | 108 | 155 | 151 |
N.S. |
1 | 0.91 | 0.65 | 1.65 | 1.96 | 3.47 | 0.00 | 1.96 | 2.82 | 2.75 |
time (sec) |
N/A | 0.248 | 0.348 | 59.603 | 0.039 | 0.083 | 0.000 | 0.268 | 0.164 | 0.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 72 | 80 | 21 | 153 | 0 | 82 | 118 | 114 |
N.S. |
1 | 1.00 | 2.67 | 2.96 | 0.78 | 5.67 | 0.00 | 3.04 | 4.37 | 4.22 |
time (sec) |
N/A | 0.222 | 0.320 | 15.513 | 0.037 | 0.070 | 0.000 | 0.244 | 0.164 | 0.392 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 125 | 71 | 72 | 165 | 177 | 178 | 86 | 67 | 73 |
N.S. |
1 | 1.07 | 0.61 | 0.62 | 1.41 | 1.51 | 1.52 | 0.74 | 0.57 | 0.62 |
time (sec) |
N/A | 0.554 | 0.161 | 0.153 | 0.148 | 0.100 | 0.275 | 0.192 | 0.191 | 0.400 |
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 | 83 | 78 | 62 | 85 | 86 | 125 | 131 | 68 | 221 | 70 |
N.S. |
1 | 0.94 | 0.75 | 1.02 | 1.04 | 1.51 | 1.58 | 0.82 | 2.66 | 0.84 |
time (sec) |
N/A | 0.267 | 0.533 | 12.457 | 0.108 | 0.118 | 0.294 | 0.295 | 0.217 | 0.403 |
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 | 65 | 49 | 68 | 88 | 51 | 102 | 50 | 96 | 64 |
N.S. |
1 | 0.92 | 0.69 | 0.96 | 1.24 | 0.72 | 1.44 | 0.70 | 1.35 | 0.90 |
time (sec) |
N/A | 0.267 | 0.246 | 42.712 | 0.131 | 0.078 | 0.275 | 0.356 | 0.194 | 0.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 36 | 38 | 93 | 34 | 80 | 30 | 86 | 53 |
N.S. |
1 | 0.91 | 0.65 | 0.69 | 1.69 | 0.62 | 1.45 | 0.55 | 1.56 | 0.96 |
time (sec) |
N/A | 0.256 | 0.107 | 122.739 | 0.113 | 0.108 | 0.266 | 0.242 | 0.181 | 0.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 24 | 74 | 103 | 62 | 162 | 18 | 113 | 63 |
N.S. |
1 | 1.00 | 0.89 | 2.74 | 3.81 | 2.30 | 6.00 | 0.67 | 4.19 | 2.33 |
time (sec) |
N/A | 0.225 | 0.161 | 298.986 | 0.120 | 0.085 | 0.358 | 0.245 | 0.168 | 0.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 137 | 123 | 331 | 164 | 83 | 209 | 89 | 146 | 122 |
N.S. |
1 | 0.88 | 0.79 | 2.12 | 1.05 | 0.53 | 1.34 | 0.57 | 0.94 | 0.78 |
time (sec) |
N/A | 0.335 | 0.296 | 0.646 | 0.136 | 0.122 | 0.369 | 0.262 | 0.162 | 0.778 |
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 | 214 | 181 | 159 | 361 | 187 | 120 | 301 | 119 | 173 | 171 |
N.S. |
1 | 0.85 | 0.74 | 1.69 | 0.87 | 0.56 | 1.41 | 0.56 | 0.81 | 0.80 |
time (sec) |
N/A | 0.357 | 0.590 | 0.604 | 0.110 | 0.108 | 0.483 | 0.286 | 0.164 | 2.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 176 | 115 | 122 | 215 | 310 | 0 | 189 | 289 | 228 |
N.S. |
1 | 1.05 | 0.69 | 0.73 | 1.29 | 1.86 | 0.00 | 1.13 | 1.73 | 1.37 |
time (sec) |
N/A | 0.803 | 2.005 | 7.194 | 0.040 | 0.102 | 0.000 | 0.371 | 0.164 | 4.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 137 | 151 | 118 | 173 | 216 | 197 | 510 | 206 | 222 |
N.S. |
1 | 1.05 | 1.16 | 0.91 | 1.33 | 1.66 | 1.52 | 3.92 | 1.58 | 1.71 |
time (sec) |
N/A | 0.665 | 1.643 | 6.112 | 0.057 | 0.095 | 0.305 | 0.500 | 0.197 | 4.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 130 | 111 | 154 | 122 | 148 | 1683 | 121 | 162 |
N.S. |
1 | 1.05 | 1.33 | 1.13 | 1.57 | 1.24 | 1.51 | 17.17 | 1.23 | 1.65 |
time (sec) |
N/A | 0.535 | 1.816 | 23.620 | 0.040 | 0.092 | 0.326 | 0.779 | 0.219 | 2.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 31 | 19 | 152 | 17 | 36 | 1669 | 81 | 104 |
N.S. |
1 | 1.00 | 0.97 | 0.59 | 4.75 | 0.53 | 1.12 | 52.16 | 2.53 | 3.25 |
time (sec) |
N/A | 0.222 | 0.380 | 74.598 | 0.042 | 0.090 | 0.211 | 0.710 | 0.181 | 0.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 104 | 122 | 56 | 187 | 48 | 121 | 1697 | 110 | 186 |
N.S. |
1 | 1.03 | 1.21 | 0.55 | 1.85 | 0.48 | 1.20 | 16.80 | 1.09 | 1.84 |
time (sec) |
N/A | 0.485 | 0.556 | 194.967 | 0.047 | 0.104 | 0.345 | 0.569 | 0.190 | 1.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 140 | 146 | 287 | 217 | 76 | 192 | 1725 | 137 | 79 |
N.S. |
1 | 0.99 | 1.04 | 2.04 | 1.54 | 0.54 | 1.36 | 12.23 | 0.97 | 0.56 |
time (sec) |
N/A | 0.588 | 0.672 | 1.477 | 0.050 | 0.129 | 0.402 | 0.642 | 0.176 | 0.995 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 148 | 170 | 317 | 246 | 104 | 265 | 1807 | 164 | 139 |
N.S. |
1 | 0.93 | 1.07 | 1.99 | 1.55 | 0.65 | 1.67 | 11.36 | 1.03 | 0.87 |
time (sec) |
N/A | 0.595 | 0.958 | 0.690 | 0.042 | 0.101 | 0.560 | 0.669 | 0.175 | 1.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 94 | 56 | 611 | 186 | 345 | 0 | 186 | 283 | 153 |
N.S. |
1 | 0.86 | 0.51 | 5.61 | 1.71 | 3.17 | 0.00 | 1.71 | 2.60 | 1.40 |
time (sec) |
N/A | 0.302 | 1.731 | 1.241 | 0.054 | 0.092 | 0.000 | 0.336 | 0.170 | 1.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 72 | 44 | 475 | 173 | 307 | 0 | 173 | 246 | 190 |
N.S. |
1 | 0.88 | 0.54 | 5.79 | 2.11 | 3.74 | 0.00 | 2.11 | 3.00 | 2.32 |
time (sec) |
N/A | 0.274 | 0.931 | 1.233 | 0.033 | 0.087 | 0.000 | 0.320 | 0.189 | 2.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 34 | 124 | 134 | 269 | 0 | 134 | 209 | 107 |
N.S. |
1 | 0.91 | 0.62 | 2.25 | 2.44 | 4.89 | 0.00 | 2.44 | 3.80 | 1.95 |
time (sec) |
N/A | 0.257 | 0.650 | 267.171 | 0.036 | 0.101 | 0.000 | 0.295 | 0.197 | 1.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 102 | 113 | 21 | 231 | 0 | 120 | 172 | 83 |
N.S. |
1 | 1.00 | 3.78 | 4.19 | 0.78 | 8.56 | 0.00 | 4.44 | 6.37 | 3.07 |
time (sec) |
N/A | 0.220 | 0.588 | 103.982 | 0.037 | 0.086 | 0.000 | 0.294 | 0.167 | 0.927 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 212 | 100 | 103 | 121 | 297 | 301 | 134 | 98 | 113 |
N.S. |
1 | 1.06 | 0.50 | 0.52 | 0.60 | 1.48 | 1.50 | 0.67 | 0.49 | 0.56 |
time (sec) |
N/A | 0.985 | 0.462 | 0.353 | 0.125 | 0.080 | 0.396 | 0.273 | 0.218 | 0.424 |
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 | 133 | 121 | 96 | 118 | 124 | 245 | 257 | 119 | 460 | 102 |
N.S. |
1 | 0.91 | 0.72 | 0.89 | 0.93 | 1.84 | 1.93 | 0.89 | 3.46 | 0.77 |
time (sec) |
N/A | 0.301 | 0.814 | 75.777 | 0.119 | 0.089 | 0.391 | 0.234 | 0.170 | 0.415 |
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 | 124 | 113 | 86 | 114 | 135 | 179 | 216 | 101 | 309 | 111 |
N.S. |
1 | 0.91 | 0.69 | 0.92 | 1.09 | 1.44 | 1.74 | 0.81 | 2.49 | 0.90 |
time (sec) |
N/A | 0.298 | 1.381 | 193.975 | 0.113 | 0.091 | 0.387 | 0.240 | 0.165 | 0.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 101 | 77 | 319 | 146 | 113 | 172 | 76 | 190 | 103 |
N.S. |
1 | 0.89 | 0.68 | 2.80 | 1.28 | 0.99 | 1.51 | 0.67 | 1.67 | 0.90 |
time (sec) |
N/A | 0.292 | 0.821 | 0.779 | 0.111 | 0.094 | 0.417 | 0.271 | 0.163 | 0.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 31 | 451 | 136 | 17 | 36 | 39 | 110 | 66 |
N.S. |
1 | 0.98 | 0.72 | 10.49 | 3.16 | 0.40 | 0.84 | 0.91 | 2.56 | 1.53 |
time (sec) |
N/A | 0.234 | 1.555 | 0.769 | 0.113 | 0.084 | 0.344 | 0.293 | 0.157 | 0.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 70 | 44 | 588 | 152 | 48 | 121 | 45 | 140 | 82 |
N.S. |
1 | 0.88 | 0.55 | 7.35 | 1.90 | 0.60 | 1.51 | 0.56 | 1.75 | 1.02 |
time (sec) |
N/A | 0.266 | 0.221 | 1.280 | 0.134 | 0.109 | 0.449 | 0.294 | 0.197 | 0.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 34 | 639 | 162 | 76 | 197 | 32 | 167 | 82 |
N.S. |
1 | 0.91 | 0.62 | 11.62 | 2.95 | 1.38 | 3.58 | 0.58 | 3.04 | 1.49 |
time (sec) |
N/A | 0.248 | 0.388 | 0.860 | 0.115 | 0.117 | 0.565 | 0.331 | 0.160 | 0.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 116 | 689 | 171 | 104 | 279 | 18 | 194 | 105 |
N.S. |
1 | 1.00 | 4.30 | 25.52 | 6.33 | 3.85 | 10.33 | 0.67 | 7.19 | 3.89 |
time (sec) |
N/A | 0.228 | 2.871 | 0.871 | 0.116 | 0.116 | 0.658 | 0.330 | 0.166 | 0.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 203 | 152 | 739 | 246 | 125 | 323 | 119 | 227 | 195 |
N.S. |
1 | 0.87 | 0.65 | 3.17 | 1.06 | 0.54 | 1.39 | 0.51 | 0.97 | 0.84 |
time (sec) |
N/A | 0.355 | 0.903 | 0.844 | 0.133 | 0.137 | 0.697 | 0.337 | 0.168 | 2.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 247 | 186 | 789 | 269 | 162 | 413 | 149 | 254 | 231 |
N.S. |
1 | 0.86 | 0.65 | 2.75 | 0.94 | 0.56 | 1.44 | 0.52 | 0.89 | 0.80 |
time (sec) |
N/A | 0.407 | 1.074 | 1.474 | 0.137 | 0.167 | 0.836 | 0.356 | 0.159 | 2.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 248 | 205 | 151 | 396 | 378 | 320 | 924 | 335 | 399 |
N.S. |
1 | 1.06 | 0.87 | 0.64 | 1.69 | 1.61 | 1.36 | 3.93 | 1.43 | 1.70 |
time (sec) |
N/A | 1.216 | 2.617 | 80.802 | 0.048 | 0.105 | 0.478 | 0.957 | 0.199 | 5.538 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 215 | 1540 | 147 | 352 | 284 | 277 | 2835 | 270 | 343 |
N.S. |
1 | 1.05 | 7.51 | 0.72 | 1.72 | 1.39 | 1.35 | 13.83 | 1.32 | 1.67 |
time (sec) |
N/A | 1.024 | 8.147 | 226.998 | 0.058 | 0.098 | 0.464 | 0.882 | 0.162 | 4.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | A | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 182 | 1162 | 322 | 326 | 190 | 235 | 2849 | 205 | 281 |
N.S. |
1 | 1.05 | 6.72 | 1.86 | 1.88 | 1.10 | 1.36 | 16.47 | 1.18 | 1.62 |
time (sec) |
N/A | 0.861 | 7.938 | 2.782 | 0.045 | 0.122 | 0.475 | 0.967 | 0.158 | 4.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 163 | 305 | 385 | 309 | 96 | 187 | 2863 | 130 | 207 |
N.S. |
1 | 1.07 | 2.01 | 2.53 | 2.03 | 0.63 | 1.23 | 18.84 | 0.86 | 1.36 |
time (sec) |
N/A | 0.740 | 2.990 | 1.417 | 0.051 | 0.110 | 0.506 | 1.063 | 0.159 | 3.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 146 | 447 | 302 | 34 | 80 | 2451 | 137 | 37 |
N.S. |
1 | 1.00 | 2.21 | 6.77 | 4.58 | 0.52 | 1.21 | 37.14 | 2.08 | 0.56 |
time (sec) |
N/A | 0.339 | 0.716 | 1.388 | 0.040 | 0.110 | 0.464 | 1.160 | 0.159 | 0.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 142 | 151 | 567 | 355 | 62 | 162 | 2863 | 164 | 65 |
N.S. |
1 | 1.04 | 1.11 | 4.17 | 2.61 | 0.46 | 1.19 | 21.05 | 1.21 | 0.48 |
time (sec) |
N/A | 0.611 | 0.875 | 1.660 | 0.050 | 0.098 | 0.553 | 1.247 | 0.190 | 0.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 218 | 168 | 617 | 405 | 90 | 240 | 2891 | 191 | 93 |
N.S. |
1 | 1.03 | 0.80 | 2.92 | 1.92 | 0.43 | 1.14 | 13.70 | 0.91 | 0.44 |
time (sec) |
N/A | 0.960 | 1.655 | 2.910 | 0.044 | 0.108 | 0.658 | 1.338 | 0.159 | 1.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 209 | 173 | 667 | 453 | 118 | 313 | 2919 | 218 | 222 |
N.S. |
1 | 0.99 | 0.82 | 3.15 | 2.14 | 0.56 | 1.48 | 13.77 | 1.03 | 1.05 |
time (sec) |
N/A | 0.789 | 1.965 | 1.679 | 0.056 | 0.135 | 0.732 | 1.409 | 0.163 | 2.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 92 | 56 | 58 | 87 | 146 | 0 | 87 | 27 | 92 |
N.S. |
1 | 0.86 | 0.52 | 0.54 | 0.81 | 1.36 | 0.00 | 0.81 | 0.25 | 0.86 |
time (sec) |
N/A | 0.278 | 0.253 | 0.494 | 0.034 | 0.087 | 0.000 | 0.168 | 0.152 | 0.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 70 | 46 | 47 | 67 | 109 | 0 | 67 | 27 | 114 |
N.S. |
1 | 0.88 | 0.58 | 0.59 | 0.84 | 1.36 | 0.00 | 0.84 | 0.34 | 1.42 |
time (sec) |
N/A | 0.268 | 0.141 | 0.460 | 0.035 | 0.086 | 0.000 | 0.163 | 0.162 | 0.407 |