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 | A | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 40 | 34 | 44 | 41 | 39 | 53 | 46 | 39 | 41 |
N.S. |
1 | 0.93 | 0.79 | 1.02 | 0.95 | 0.91 | 1.23 | 1.07 | 0.91 | 0.95 |
time (sec) |
N/A | 0.196 | 0.062 | 0.309 | 0.023 | 0.061 | 0.097 | 0.122 | 0.142 | 0.236 |
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 | 27 | 27 | 27 | 27 | 27 | 26 | 29 | 27 | 26 | 26 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.00 | 0.96 | 1.07 | 1.00 | 0.96 | 0.96 |
time (sec) |
N/A | 0.154 | 0.014 | 0.082 | 0.025 | 0.062 | 0.054 | 0.123 | 0.153 | 0.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 46 | 53 | 55 | 51 | 62 | 250 | 691 | 69 | 68 |
N.S. |
1 | 0.87 | 1.00 | 1.04 | 0.96 | 1.17 | 4.72 | 13.04 | 1.30 | 1.28 |
time (sec) |
N/A | 0.314 | 0.044 | 0.174 | 0.028 | 0.063 | 0.406 | 0.148 | 0.154 | 0.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 68 | 65 | 84 | 77 | 130 | 665 | 1033 | 164 | 81 |
N.S. |
1 | 0.86 | 0.82 | 1.06 | 0.97 | 1.65 | 8.42 | 13.08 | 2.08 | 1.03 |
time (sec) |
N/A | 0.324 | 0.075 | 0.247 | 0.025 | 0.062 | 1.816 | 0.165 | 0.156 | 0.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 83 | 80 | 109 | 99 | 205 | 1350 | 1359 | 289 | 106 |
N.S. |
1 | 0.85 | 0.82 | 1.11 | 1.01 | 2.09 | 13.78 | 13.87 | 2.95 | 1.08 |
time (sec) |
N/A | 0.341 | 0.079 | 0.367 | 0.031 | 0.070 | 15.018 | 0.179 | 0.155 | 0.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 80 | 73 | 0 | 0 | 0 | 0 | 0 | 104 | 0 |
N.S. |
1 | 1.11 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.261 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
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 | 28 | 28 | 28 | 28 | 28 | 28 | 29 | 28 | 27 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.04 | 1.00 | 0.96 | 0.96 |
time (sec) |
N/A | 0.155 | 0.007 | 0.062 | 0.024 | 0.062 | 0.054 | 0.122 | 0.162 | 0.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 46 | 53 | 55 | 51 | 64 | 248 | 691 | 69 | 69 |
N.S. |
1 | 0.87 | 1.00 | 1.04 | 0.96 | 1.21 | 4.68 | 13.04 | 1.30 | 1.30 |
time (sec) |
N/A | 0.295 | 0.043 | 0.137 | 0.031 | 0.063 | 0.417 | 0.141 | 0.164 | 0.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 68 | 66 | 84 | 77 | 131 | 663 | 1033 | 164 | 81 |
N.S. |
1 | 0.86 | 0.84 | 1.06 | 0.97 | 1.66 | 8.39 | 13.08 | 2.08 | 1.03 |
time (sec) |
N/A | 0.313 | 0.075 | 0.200 | 0.024 | 0.064 | 1.844 | 0.170 | 0.152 | 0.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 83 | 80 | 109 | 99 | 207 | 1348 | 1359 | 289 | 106 |
N.S. |
1 | 0.85 | 0.82 | 1.11 | 1.01 | 2.11 | 13.76 | 13.87 | 2.95 | 1.08 |
time (sec) |
N/A | 0.335 | 0.076 | 0.296 | 0.027 | 0.074 | 14.920 | 0.171 | 0.155 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 82 | 75 | 0 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 1.11 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.244 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
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 | 15 | 15 | 15 | 16 | 15 | 19 | 15 | 15 | 19 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.27 | 1.00 | 1.00 | 1.27 | 1.00 |
time (sec) |
N/A | 0.138 | 0.009 | 0.051 | 0.030 | 0.063 | 0.039 | 0.119 | 0.155 | 0.178 |
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 | 33 | 32 | 35 | 31 | 31 | 29 | 44 | 30 | 29 | 26 |
N.S. |
1 | 0.97 | 1.06 | 0.94 | 0.94 | 0.88 | 1.33 | 0.91 | 0.88 | 0.79 |
time (sec) |
N/A | 0.170 | 0.018 | 0.081 | 0.031 | 0.061 | 0.043 | 0.124 | 0.154 | 0.181 |
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 | 50 | 42 | 45 | 41 | 46 | 39 | 70 | 40 | 39 | 34 |
N.S. |
1 | 0.84 | 0.90 | 0.82 | 0.92 | 0.78 | 1.40 | 0.80 | 0.78 | 0.68 |
time (sec) |
N/A | 0.166 | 0.020 | 0.149 | 0.023 | 0.063 | 0.053 | 0.114 | 0.151 | 0.190 |
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 | 65 | 50 | 53 | 50 | 61 | 47 | 87 | 48 | 47 | 42 |
N.S. |
1 | 0.77 | 0.82 | 0.77 | 0.94 | 0.72 | 1.34 | 0.74 | 0.72 | 0.65 |
time (sec) |
N/A | 0.174 | 0.023 | 0.230 | 0.022 | 0.062 | 0.062 | 0.122 | 0.157 | 0.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 0 | 0 | 0 | 0 | 0 | 47 | 55 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 | 1.38 |
time (sec) |
N/A | 0.168 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.190 |
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 | 16 | 16 | 16 | 17 | 16 | 21 | 19 | 16 | 21 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.31 | 1.19 | 1.00 | 1.31 | 1.00 |
time (sec) |
N/A | 0.143 | 0.006 | 0.049 | 0.024 | 0.059 | 0.033 | 0.119 | 0.171 | 0.168 |
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 | 33 | 32 | 35 | 31 | 31 | 29 | 44 | 30 | 29 | 27 |
N.S. |
1 | 0.97 | 1.06 | 0.94 | 0.94 | 0.88 | 1.33 | 0.91 | 0.88 | 0.82 |
time (sec) |
N/A | 0.169 | 0.018 | 0.079 | 0.028 | 0.061 | 0.045 | 0.122 | 0.156 | 0.175 |
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 | 50 | 42 | 45 | 41 | 46 | 39 | 70 | 40 | 39 | 35 |
N.S. |
1 | 0.84 | 0.90 | 0.82 | 0.92 | 0.78 | 1.40 | 0.80 | 0.78 | 0.70 |
time (sec) |
N/A | 0.172 | 0.022 | 0.135 | 0.028 | 0.061 | 0.055 | 0.122 | 0.156 | 0.178 |
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 | 65 | 50 | 53 | 50 | 61 | 47 | 87 | 48 | 47 | 43 |
N.S. |
1 | 0.77 | 0.82 | 0.77 | 0.94 | 0.72 | 1.34 | 0.74 | 0.72 | 0.66 |
time (sec) |
N/A | 0.175 | 0.023 | 0.210 | 0.027 | 0.065 | 0.069 | 0.116 | 0.150 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 0 | 0 | 0 | 0 | 0 | 52 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 | 1.30 |
time (sec) |
N/A | 0.169 | 0.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.184 |
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 | 24 | 30 | 38 | 23 | 23 | 22 | 15 | 24 | 23 | 22 |
N.S. |
1 | 1.25 | 1.58 | 0.96 | 0.96 | 0.92 | 0.62 | 1.00 | 0.96 | 0.92 |
time (sec) |
N/A | 0.161 | 0.019 | 0.034 | 0.029 | 0.062 | 0.044 | 0.123 | 0.152 | 0.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 119 | 97 | 26 | 100 | 311 | 22 | 116 | 77 | 104 |
N.S. |
1 | 1.19 | 0.97 | 0.26 | 1.00 | 3.11 | 0.22 | 1.16 | 0.77 | 1.04 |
time (sec) |
N/A | 0.291 | 0.080 | 0.072 | 0.117 | 0.072 | 0.076 | 0.119 | 0.156 | 0.807 |
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 | 12 | 15 | 15 | 12 | 11 | 11 | 8 | 11 | 12 | 11 |
N.S. |
1 | 1.25 | 1.25 | 1.00 | 0.92 | 0.92 | 0.67 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.174 | 0.013 | 0.036 | 0.031 | 0.060 | 0.029 | 0.134 | 0.149 | 0.026 |
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 | 47 | 54 | 45 | 38 | 37 | 39 | 22 | 37 | 132 | 39 |
N.S. |
1 | 1.15 | 0.96 | 0.81 | 0.79 | 0.83 | 0.47 | 0.79 | 2.81 | 0.83 |
time (sec) |
N/A | 0.233 | 0.044 | 0.059 | 0.116 | 0.063 | 0.060 | 0.120 | 0.153 | 0.194 |
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 | 39 | 39 | 37 | 29 | 28 | 28 | 48 | 29 | 33 | 28 |
N.S. |
1 | 1.00 | 0.95 | 0.74 | 0.72 | 0.72 | 1.23 | 0.74 | 0.85 | 0.72 |
time (sec) |
N/A | 0.239 | 0.049 | 0.072 | 0.105 | 0.070 | 0.089 | 0.118 | 0.153 | 0.051 |
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 | 30 | 30 | 30 | 33 | 32 | 37 | 94 | 32 | 37 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.07 | 1.23 | 3.13 | 1.07 | 1.23 | 0.97 |
time (sec) |
N/A | 0.181 | 0.046 | 0.108 | 0.031 | 0.069 | 0.397 | 0.123 | 0.157 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 55 | 54 | 57 | 56 | 56 | 61 | 57 | 13 | 33 |
N.S. |
1 | 1.02 | 1.00 | 1.06 | 1.04 | 1.04 | 1.13 | 1.06 | 0.24 | 0.61 |
time (sec) |
N/A | 0.178 | 0.030 | 0.076 | 0.107 | 0.064 | 0.529 | 0.123 | 0.155 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 59 | 0 | 0 | 0 | 0 | 0 | 58 | 75 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 1.27 |
time (sec) |
N/A | 0.184 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 22 | 15 | 7 | 18 | 37 | 18 | 27 | 14 |
N.S. |
1 | 1.00 | 1.22 | 0.83 | 0.39 | 1.00 | 2.06 | 1.00 | 1.50 | 0.78 |
time (sec) |
N/A | 0.182 | 0.028 | 0.049 | 0.030 | 0.063 | 0.247 | 0.129 | 0.150 | 0.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 24 | 17 | 20 | 20 | 37 | 20 | 31 | 16 |
N.S. |
1 | 1.00 | 1.20 | 0.85 | 1.00 | 1.00 | 1.85 | 1.00 | 1.55 | 0.80 |
time (sec) |
N/A | 0.171 | 0.029 | 0.075 | 0.030 | 0.062 | 0.246 | 0.122 | 0.149 | 0.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 0 | 39 | 46 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.98 | 1.15 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.240 | 0.113 | 0.000 | 0.105 | 0.064 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 57 | 54 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.54 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.222 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 75 | 44 | 37 | 49 | 30 | 49 | 65 | 19 | 30 |
N.S. |
1 | 1.03 | 0.60 | 0.51 | 0.67 | 0.41 | 0.67 | 0.89 | 0.26 | 0.41 |
time (sec) |
N/A | 0.204 | 0.039 | 0.036 | 0.025 | 0.059 | 0.838 | 0.136 | 0.150 | 0.189 |
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 | 44 | 50 | 23 | 21 | 19 | 19 | 20 | 19 | 24 | 21 |
N.S. |
1 | 1.14 | 0.52 | 0.48 | 0.43 | 0.43 | 0.45 | 0.43 | 0.55 | 0.48 |
time (sec) |
N/A | 0.226 | 0.014 | 0.042 | 0.038 | 0.057 | 0.030 | 0.123 | 0.157 | 0.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 41 | 26 | 27 | 7 | 23 | 32 | 27 | 30 | 22 |
N.S. |
1 | 1.05 | 0.67 | 0.69 | 0.18 | 0.59 | 0.82 | 0.69 | 0.77 | 0.56 |
time (sec) |
N/A | 0.204 | 0.023 | 0.076 | 0.054 | 0.057 | 0.670 | 0.125 | 0.154 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 53 | 29 | 28 | 27 | 27 | 37 | 826 | 27 | 27 |
N.S. |
1 | 1.20 | 0.66 | 0.64 | 0.61 | 0.61 | 0.84 | 18.77 | 0.61 | 0.61 |
time (sec) |
N/A | 0.206 | 0.015 | 0.054 | 0.024 | 0.060 | 0.044 | 0.134 | 0.156 | 0.027 |
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 | 12 | 12 | 12 | 10 | 18 | 9 | 8 | 18 | 10 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.50 | 0.75 | 0.67 | 1.50 | 0.83 | 0.75 |
time (sec) |
N/A | 0.186 | 0.020 | 0.050 | 0.031 | 0.060 | 0.029 | 0.122 | 0.155 | 0.171 |
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 | 32 | 36 | 31 | 25 | 25 | 33 | 22 | 40 | 46 | 26 |
N.S. |
1 | 1.12 | 0.97 | 0.78 | 0.78 | 1.03 | 0.69 | 1.25 | 1.44 | 0.81 |
time (sec) |
N/A | 0.229 | 0.075 | 0.062 | 0.105 | 0.066 | 0.042 | 0.126 | 0.157 | 0.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 20 | 21 | 12 | 0 | 0 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.40 | 0.80 | 0.00 | 0.00 | 0.80 | 0.80 |
time (sec) |
N/A | 0.185 | 0.176 | 0.106 | 0.071 | 0.065 | 0.000 | 0.000 | 0.155 | 0.255 |
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 | 27 | 27 | 22 | 20 | 19 | 21 | 26 | 19 | 22 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.70 | 0.78 | 0.96 | 0.70 | 0.81 | 0.70 |
time (sec) |
N/A | 0.162 | 0.030 | 0.221 | 0.025 | 0.066 | 0.155 | 0.119 | 0.151 | 0.015 |
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 | 35 | 51 | 26 | 18 | 39 | 21 | 29 | 39 | 20 | 19 |
N.S. |
1 | 1.46 | 0.74 | 0.51 | 1.11 | 0.60 | 0.83 | 1.11 | 0.57 | 0.54 |
time (sec) |
N/A | 0.347 | 0.074 | 0.427 | 0.030 | 0.064 | 0.221 | 0.121 | 0.158 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 70 | 37 | 32 | 31 | 0 | 70 | 39 | 32 | 33 |
N.S. |
1 | 1.23 | 0.65 | 0.56 | 0.54 | 0.00 | 1.23 | 0.68 | 0.56 | 0.58 |
time (sec) |
N/A | 0.217 | 0.077 | 0.395 | 0.106 | 0.000 | 0.412 | 0.123 | 0.150 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 39 | 37 | 45 | 37 | 265 | 43 | 37 | 37 |
N.S. |
1 | 1.00 | 0.72 | 0.69 | 0.83 | 0.69 | 4.91 | 0.80 | 0.69 | 0.69 |
time (sec) |
N/A | 0.211 | 0.026 | 0.479 | 0.033 | 0.069 | 0.364 | 0.119 | 0.145 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 81 | 64 | 66 | 73 | 65 | 638 | 63 | 61 | 47 |
N.S. |
1 | 0.99 | 0.78 | 0.80 | 0.89 | 0.79 | 7.78 | 0.77 | 0.74 | 0.57 |
time (sec) |
N/A | 0.253 | 0.126 | 0.657 | 0.034 | 0.072 | 0.852 | 0.128 | 0.162 | 0.032 |
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 | 79 | 99 | 36 | 28 | 27 | 42 | 76 | 33 | 42 | 39 |
N.S. |
1 | 1.25 | 0.46 | 0.35 | 0.34 | 0.53 | 0.96 | 0.42 | 0.53 | 0.49 |
time (sec) |
N/A | 0.264 | 0.056 | 0.642 | 0.033 | 0.071 | 0.376 | 0.120 | 0.157 | 0.033 |
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 | 36 | 36 | 21 | 19 | 27 | 40 | 70 | 24 | 35 | 18 |
N.S. |
1 | 1.00 | 0.58 | 0.53 | 0.75 | 1.11 | 1.94 | 0.67 | 0.97 | 0.50 |
time (sec) |
N/A | 0.197 | 0.034 | 0.532 | 0.031 | 0.066 | 0.431 | 0.119 | 0.158 | 0.219 |
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 | 36 | 36 | 21 | 19 | 27 | 50 | 99 | 24 | 47 | 18 |
N.S. |
1 | 1.00 | 0.58 | 0.53 | 0.75 | 1.39 | 2.75 | 0.67 | 1.31 | 0.50 |
time (sec) |
N/A | 0.200 | 0.042 | 0.675 | 0.032 | 0.067 | 0.423 | 0.119 | 0.162 | 0.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 85 | 97 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.47 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.239 | 0.180 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 90 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.172 | 0.143 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 81 | 66 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.59 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.237 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.204 | 0.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 84 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.199 | 0.115 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 61 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.203 | 0.578 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 61 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.206 | 0.602 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 12 | 9 | 22 | 12 | 0 | 10 | 11 | 8 |
N.S. |
1 | 1.00 | 0.80 | 0.60 | 1.47 | 0.80 | 0.00 | 0.67 | 0.73 | 0.53 |
time (sec) |
N/A | 0.166 | 0.102 | 0.238 | 0.092 | 0.064 | 0.000 | 0.129 | 0.159 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 46 | 100 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.12 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.373 | 0.596 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 8 | 22 | 11 | 0 | 7 | 8 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 1.83 | 0.92 | 0.00 | 0.58 | 0.67 | 0.58 |
time (sec) |
N/A | 0.161 | 0.093 | 0.201 | 0.090 | 0.065 | 0.000 | 0.130 | 0.174 | 0.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 45 | 87 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.07 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.361 | 0.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 49 | 72 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.07 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.385 | 0.668 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 13 | 19 | 22 | 24 | 0 | 20 | 19 | 24 |
N.S. |
1 | 1.00 | 0.93 | 1.36 | 1.57 | 1.71 | 0.00 | 1.43 | 1.36 | 1.71 |
time (sec) |
N/A | 0.160 | 0.045 | 0.313 | 0.091 | 0.065 | 0.000 | 0.127 | 0.148 | 0.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 48 | 73 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.12 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.391 | 0.175 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 22 | 24 | 0 | 21 | 18 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.69 | 1.85 | 0.00 | 1.62 | 1.38 | 1.54 |
time (sec) |
N/A | 0.158 | 0.040 | 0.286 | 0.094 | 0.064 | 0.000 | 0.126 | 0.152 | 0.246 |
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 | 30 | 30 | 18 | 16 | 17 | 17 | 27 | 15 | 18 | 17 |
N.S. |
1 | 1.00 | 0.60 | 0.53 | 0.57 | 0.57 | 0.90 | 0.50 | 0.60 | 0.57 |
time (sec) |
N/A | 0.198 | 0.020 | 0.247 | 0.026 | 0.067 | 0.135 | 0.125 | 0.157 | 0.203 |
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 | 50 | 50 | 25 | 22 | 26 | 26 | 48 | 25 | 32 | 21 |
N.S. |
1 | 1.00 | 0.50 | 0.44 | 0.52 | 0.52 | 0.96 | 0.50 | 0.64 | 0.42 |
time (sec) |
N/A | 0.284 | 0.028 | 0.260 | 0.028 | 0.068 | 0.236 | 0.118 | 0.152 | 0.207 |
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 | 75 | 80 | 38 | 31 | 33 | 37 | 80 | 33 | 42 | 39 |
N.S. |
1 | 1.07 | 0.51 | 0.41 | 0.44 | 0.49 | 1.07 | 0.44 | 0.56 | 0.52 |
time (sec) |
N/A | 0.321 | 0.026 | 0.299 | 0.034 | 0.067 | 0.330 | 0.141 | 0.149 | 0.211 |
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 | 187 | 258 | 72 | 59 | 77 | 72 | 202 | 73 | 90 | 83 |
N.S. |
1 | 1.38 | 0.39 | 0.32 | 0.41 | 0.39 | 1.08 | 0.39 | 0.48 | 0.44 |
time (sec) |
N/A | 0.648 | 0.101 | 0.885 | 0.044 | 0.069 | 0.756 | 0.125 | 0.152 | 0.182 |
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 | 92 | 40 | 40 | 41 | 41 | 85 | 39 | 52 | 51 |
N.S. |
1 | 1.06 | 0.46 | 0.46 | 0.47 | 0.47 | 0.98 | 0.45 | 0.60 | 0.59 |
time (sec) |
N/A | 0.344 | 0.056 | 0.447 | 0.037 | 0.067 | 0.234 | 0.113 | 0.145 | 0.199 |
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 | 185 | 185 | 76 | 78 | 77 | 72 | 202 | 73 | 90 | 83 |
N.S. |
1 | 1.00 | 0.41 | 0.42 | 0.42 | 0.39 | 1.09 | 0.39 | 0.49 | 0.45 |
time (sec) |
N/A | 0.495 | 0.144 | 1.433 | 0.039 | 0.067 | 0.748 | 0.119 | 0.150 | 0.304 |
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 | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 11 | 2 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 | 1.00 | 5.50 | 1.00 | 1.00 |
time (sec) |
N/A | 0.144 | 0.002 | 0.049 | 0.028 | 0.058 | 0.063 | 0.118 | 0.152 | 0.009 |
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 | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 11 | 2 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 | 1.00 | 5.50 | 1.00 | 1.00 |
time (sec) |
N/A | 0.143 | 0.002 | 0.043 | 0.031 | 0.054 | 0.058 | 0.122 | 0.151 | 0.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 3 | 18 | 7 | 11 | 12 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 6.00 | 2.33 | 3.67 | 4.00 | 1.00 |
time (sec) |
N/A | 0.147 | 0.004 | 0.052 | 0.029 | 0.060 | 0.043 | 0.127 | 0.150 | 0.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 3 | 18 | 12 | 12 | 16 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 6.00 | 4.00 | 4.00 | 5.33 | 1.00 |
time (sec) |
N/A | 0.153 | 0.003 | 0.079 | 0.042 | 0.062 | 0.120 | 0.126 | 0.153 | 0.015 |
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 | 3 | 3 | 5 | 4 | 3 | 8 | 7 | 5 | 6 | 5 |
N.S. |
1 | 1.00 | 1.67 | 1.33 | 1.00 | 2.67 | 2.33 | 1.67 | 2.00 | 1.67 |
time (sec) |
N/A | 0.150 | 0.002 | 0.198 | 0.024 | 0.059 | 0.159 | 0.118 | 0.144 | 0.012 |
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 | 5 | 5 | 5 | 6 | 5 | 17 | 5 | 14 | 15 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 3.40 | 1.00 | 2.80 | 3.00 | 1.00 |
time (sec) |
N/A | 0.154 | 0.002 | 0.041 | 0.027 | 0.053 | 0.112 | 0.124 | 0.152 | 0.007 |
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 | 14 | 14 | 14 | 11 | 16 | 10 | 24 | 24 | 24 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 1.14 | 0.71 | 1.71 | 1.71 | 1.71 | 0.71 |
time (sec) |
N/A | 0.162 | 0.006 | 0.125 | 0.032 | 0.058 | 0.062 | 0.126 | 0.153 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 23 | 18 | 35 | 42 | 29 | 37 | 46 | 15 |
N.S. |
1 | 1.00 | 1.21 | 0.95 | 1.84 | 2.21 | 1.53 | 1.95 | 2.42 | 0.79 |
time (sec) |
N/A | 0.172 | 0.012 | 0.589 | 0.024 | 0.057 | 0.171 | 0.118 | 0.144 | 0.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 13 | 38 | 68 | 10 | 26 | 12 | 12 |
N.S. |
1 | 1.00 | 1.14 | 0.93 | 2.71 | 4.86 | 0.71 | 1.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.201 | 0.005 | 0.053 | 0.030 | 0.060 | 0.068 | 0.120 | 0.146 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 24 | 47 | 11 | 45 | 211 | 0 | 45 | 97 | 16 |
N.S. |
1 | 1.50 | 2.94 | 0.69 | 2.81 | 13.19 | 0.00 | 2.81 | 6.06 | 1.00 |
time (sec) |
N/A | 0.203 | 0.015 | 0.194 | 0.035 | 0.059 | 0.000 | 0.120 | 0.141 | 0.164 |
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 | 26 | 31 | 26 | 21 | 61 | 461 | 422 | 60 | 110 | 22 |
N.S. |
1 | 1.19 | 1.00 | 0.81 | 2.35 | 17.73 | 16.23 | 2.31 | 4.23 | 0.85 |
time (sec) |
N/A | 0.264 | 0.004 | 0.747 | 0.104 | 0.062 | 0.820 | 0.126 | 0.141 | 0.037 |
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 | 18 | 24 | 18 | 17 | 35 | 257 | 0 | 43 | 53 | 35 |
N.S. |
1 | 1.33 | 1.00 | 0.94 | 1.94 | 14.28 | 0.00 | 2.39 | 2.94 | 1.94 |
time (sec) |
N/A | 0.188 | 0.006 | 9.319 | 0.120 | 0.067 | 0.000 | 0.126 | 0.152 | 0.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 27 | 20 | 0 | 359 | 41 | 0 | 20 | 120 |
N.S. |
1 | 1.00 | 0.87 | 0.65 | 0.00 | 11.58 | 1.32 | 0.00 | 0.65 | 3.87 |
time (sec) |
N/A | 0.195 | 0.055 | 0.158 | 0.000 | 0.068 | 19.510 | 0.000 | 0.149 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 42 | 41 | 36 | 0 | 175 | 126 | 32 | 44 | 43 |
N.S. |
1 | 1.02 | 1.00 | 0.88 | 0.00 | 4.27 | 3.07 | 0.78 | 1.07 | 1.05 |
time (sec) |
N/A | 0.207 | 0.029 | 0.104 | 0.000 | 0.064 | 1.675 | 0.116 | 0.153 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 16 | 15 | 49 | 58 | 14 | 14 | 32 | 14 |
N.S. |
1 | 1.00 | 0.64 | 0.60 | 1.96 | 2.32 | 0.56 | 0.56 | 1.28 | 0.56 |
time (sec) |
N/A | 0.212 | 0.009 | 0.079 | 0.029 | 0.053 | 0.140 | 0.119 | 0.146 | 0.167 |
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 | 39 | 39 | 49 | 42 | 41 | 42 | 146 | 43 | 42 | 35 |
N.S. |
1 | 1.00 | 1.26 | 1.08 | 1.05 | 1.08 | 3.74 | 1.10 | 1.08 | 0.90 |
time (sec) |
N/A | 0.280 | 0.087 | 0.076 | 0.031 | 0.066 | 0.201 | 0.117 | 0.144 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 33 | 31 | 98 | 76 | 288 | 1129 | 84 | 97 | 109 |
N.S. |
1 | 1.06 | 1.00 | 3.16 | 2.45 | 9.29 | 36.42 | 2.71 | 3.13 | 3.52 |
time (sec) |
N/A | 0.204 | 0.462 | 0.349 | 0.121 | 0.068 | 14.358 | 0.122 | 0.159 | 0.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 37 | 35 | 74 | 0 | 388 | 874 | 50 | 103 | 106 |
N.S. |
1 | 1.06 | 1.00 | 2.11 | 0.00 | 11.09 | 24.97 | 1.43 | 2.94 | 3.03 |
time (sec) |
N/A | 0.206 | 0.077 | 0.257 | 0.000 | 0.078 | 13.652 | 0.125 | 0.151 | 0.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 24 | 46 | 69 | 113 | 908 | 48 | 140 | 63 |
N.S. |
1 | 1.00 | 0.96 | 1.84 | 2.76 | 4.52 | 36.32 | 1.92 | 5.60 | 2.52 |
time (sec) |
N/A | 0.179 | 0.273 | 0.549 | 0.105 | 0.063 | 2.294 | 0.130 | 0.151 | 0.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 37 | 44 | 70 | 74 | 102 | 22 | 39 | 22 |
N.S. |
1 | 1.00 | 1.12 | 1.33 | 2.12 | 2.24 | 3.09 | 0.67 | 1.18 | 0.67 |
time (sec) |
N/A | 0.319 | 5.033 | 0.487 | 0.116 | 0.067 | 0.449 | 0.138 | 0.150 | 0.220 |
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 | 30 | 30 | 30 | 23 | 42 | 44 | 112 | 48 | 89 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 1.40 | 1.47 | 3.73 | 1.60 | 2.97 | 1.33 |
time (sec) |
N/A | 0.208 | 0.055 | 3.025 | 0.035 | 0.059 | 0.696 | 0.122 | 0.153 | 0.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 23 | 42 | 111 | 139 | 48 | 89 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 1.40 | 3.70 | 4.63 | 1.60 | 2.97 | 1.33 |
time (sec) |
N/A | 0.223 | 0.040 | 3.034 | 0.031 | 0.059 | 0.712 | 0.125 | 0.154 | 0.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 67 | 160 | 167 | 0 | 303 | 0 | 90 | 65 | 0 |
N.S. |
1 | 0.97 | 2.32 | 2.42 | 0.00 | 4.39 | 0.00 | 1.30 | 0.94 | 0.00 |
time (sec) |
N/A | 0.830 | 20.320 | 1.704 | 0.000 | 0.079 | 0.000 | 0.162 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 26 | 30 | 125 | 474 | 0 | 38 | 36 | 57 |
N.S. |
1 | 1.00 | 0.70 | 0.81 | 3.38 | 12.81 | 0.00 | 1.03 | 0.97 | 1.54 |
time (sec) |
N/A | 0.210 | 0.069 | 0.210 | 0.058 | 0.071 | 0.000 | 0.145 | 0.159 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 21 | 30 | 177 | 161 | 0 | 0 | 34 | 47 |
N.S. |
1 | 1.00 | 0.72 | 1.03 | 6.10 | 5.55 | 0.00 | 0.00 | 1.17 | 1.62 |
time (sec) |
N/A | 0.285 | 0.038 | 0.296 | 0.152 | 0.069 | 0.000 | 0.000 | 0.144 | 0.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 63 | 0 | 542 | 0 | 58 | 16 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.20 | 0.00 | 36.13 | 0.00 | 3.87 | 1.07 | 0.00 |
time (sec) |
N/A | 0.190 | 0.010 | 0.257 | 0.000 | 0.071 | 0.000 | 0.132 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 24 | 49 | 93 | 17 | 51 | 58 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 3.06 | 5.81 | 1.06 | 3.19 | 3.62 | 1.31 |
time (sec) |
N/A | 0.225 | 0.015 | 0.083 | 0.172 | 0.067 | 0.057 | 0.123 | 0.148 | 0.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 27 | 53 | 95 | 22 | 53 | 77 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.69 | 3.31 | 5.94 | 1.38 | 3.31 | 4.81 | 1.69 |
time (sec) |
N/A | 0.225 | 0.015 | 0.125 | 0.074 | 0.063 | 0.229 | 0.131 | 0.142 | 0.171 |
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 | 20 | 20 | 23 | 14 | 13 | 20 | 26 | 15 | 13 | 16 |
N.S. |
1 | 1.00 | 1.15 | 0.70 | 0.65 | 1.00 | 1.30 | 0.75 | 0.65 | 0.80 |
time (sec) |
N/A | 0.276 | 0.043 | 0.573 | 0.057 | 0.061 | 0.175 | 0.124 | 0.152 | 0.036 |
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 | 15 | 15 | 20 | 16 | 35 | 20 | 12 | 14 | 15 | 17 |
N.S. |
1 | 1.00 | 1.33 | 1.07 | 2.33 | 1.33 | 0.80 | 0.93 | 1.00 | 1.13 |
time (sec) |
N/A | 0.290 | 0.062 | 0.202 | 0.034 | 0.060 | 0.137 | 0.119 | 0.153 | 0.167 |
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 | 20 | 20 | 20 | 24 | 22 | 75 | 0 | 24 | 32 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.10 | 3.75 | 0.00 | 1.20 | 1.60 | 1.20 |
time (sec) |
N/A | 0.163 | 0.010 | 0.539 | 0.034 | 0.058 | 0.000 | 0.121 | 0.156 | 0.181 |