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 | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 25 | 43 | 50 | 24 | 0 | 81 | 27 |
N.S. |
1 | 0.00 | 0.97 | 0.86 | 1.48 | 1.72 | 0.83 | 0.00 | 2.79 | 0.93 |
time (sec) |
N/A | 0.000 | 0.068 | 0.809 | 0.083 | 0.067 | 0.073 | 0.000 | 0.229 | 2.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 28 | 29 | 20 | 28 | 27 | 0 | 211 | 28 |
N.S. |
1 | 1.00 | 1.04 | 1.07 | 0.74 | 1.04 | 1.00 | 0.00 | 7.81 | 1.04 |
time (sec) |
N/A | 1.153 | 0.113 | 4.254 | 0.116 | 0.068 | 0.155 | 0.000 | 200.030 | 5.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 27 | 29 | 25 | 24 | 29 | 197 | 21 |
N.S. |
1 | 0.00 | 0.93 | 0.96 | 1.04 | 0.89 | 0.86 | 1.04 | 7.04 | 0.75 |
time (sec) |
N/A | 0.000 | 0.188 | 0.601 | 0.152 | 0.065 | 0.162 | 0.111 | 0.248 | 2.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 135 | 91 | 51 | 91 | 53 | 44 | 47 | 55 | 46 |
N.S. |
1 | 4.66 | 3.14 | 1.76 | 3.14 | 1.83 | 1.52 | 1.62 | 1.90 | 1.59 |
time (sec) |
N/A | 0.903 | 0.078 | 1.483 | 0.083 | 0.066 | 0.109 | 0.114 | 0.223 | 0.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 16 | 16 | 14 | 0 | 13 | 10 | 13 | 14 | 13 |
N.S. |
1 | 0.89 | 0.89 | 0.78 | 0.00 | 0.72 | 0.56 | 0.72 | 0.78 | 0.72 |
time (sec) |
N/A | 0.383 | 0.050 | 0.290 | 0.000 | 0.063 | 0.080 | 0.117 | 0.209 | 2.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 57407 | 82 | 80 | 80 | 75 | 162 | 80 | 0 |
N.S. |
1 | 0.00 | 1979.55 | 2.83 | 2.76 | 2.76 | 2.59 | 5.59 | 2.76 | 0.00 |
time (sec) |
N/A | 0.000 | 13.988 | 7.851 | 0.165 | 0.073 | 0.206 | 3.925 | 0.211 | 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 | 18 | 18 | 18 | 16 | 15 | 15 | 12 | 15 | 32 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.83 | 0.83 | 0.67 | 0.83 | 1.78 | 0.83 |
time (sec) |
N/A | 1.166 | 0.014 | 0.213 | 0.190 | 0.066 | 0.073 | 0.115 | 0.209 | 2.380 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 24 | 37 | 22 | 39 | 34 | 84 | 36 | 53 |
N.S. |
1 | 0.00 | 1.04 | 1.61 | 0.96 | 1.70 | 1.48 | 3.65 | 1.57 | 2.30 |
time (sec) |
N/A | 0.000 | 2.304 | 1.552 | 0.217 | 0.069 | 0.205 | 0.131 | 0.241 | 2.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 35 | 30 | 35 | 35 | 36 | 63 | 37 | 37 |
N.S. |
1 | 0.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.20 | 2.10 | 1.23 | 1.23 |
time (sec) |
N/A | 0.000 | 1.508 | 0.415 | 0.075 | 0.067 | 0.187 | 0.165 | 0.229 | 0.361 |
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 | 38 | 26 | 26 | 18 | 19 | 33 | 24 | 19 | 67 | 19 |
N.S. |
1 | 0.68 | 0.68 | 0.47 | 0.50 | 0.87 | 0.63 | 0.50 | 1.76 | 0.50 |
time (sec) |
N/A | 0.457 | 0.028 | 0.465 | 0.030 | 0.068 | 0.253 | 0.115 | 0.220 | 0.103 |
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 | 7 | 9 | 7 | 8 | 7 | 7 | 7 | 26 | 7 | 7 |
N.S. |
1 | 1.29 | 1.00 | 1.14 | 1.00 | 1.00 | 1.00 | 3.71 | 1.00 | 1.00 |
time (sec) |
N/A | 0.263 | 0.018 | 0.091 | 0.033 | 0.062 | 0.068 | 0.114 | 0.235 | 1.946 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 0 | 45 | 109 | 108 | 65 | 134 | 144 | 99 |
N.S. |
1 | 0.00 | 0.00 | 1.32 | 3.21 | 3.18 | 1.91 | 3.94 | 4.24 | 2.91 |
time (sec) |
N/A | 0.000 | 0.000 | 4.363 | 0.251 | 0.078 | 0.321 | 0.144 | 0.216 | 2.378 |
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 | 26 | 34 | 34 | 28 | 29 | 29 | 26 | 29 | 44 | 26 |
N.S. |
1 | 1.31 | 1.31 | 1.08 | 1.12 | 1.12 | 1.00 | 1.12 | 1.69 | 1.00 |
time (sec) |
N/A | 0.174 | 0.024 | 0.191 | 0.030 | 0.065 | 0.047 | 0.108 | 0.226 | 1.953 |
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 | 21 | 13 | 16 | 19 | 19 | 12 | 18 | 14 | 13 |
N.S. |
1 | 1.11 | 0.68 | 0.84 | 1.00 | 1.00 | 0.63 | 0.95 | 0.74 | 0.68 |
time (sec) |
N/A | 0.199 | 0.010 | 0.213 | 0.059 | 0.068 | 0.110 | 0.110 | 0.220 | 2.074 |
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 | 19 | 19 | 16 | 15 | 15 | 19 | 15 | 20 | 18 |
N.S. |
1 | 0.95 | 0.95 | 0.80 | 0.75 | 0.75 | 0.95 | 0.75 | 1.00 | 0.90 |
time (sec) |
N/A | 0.273 | 0.111 | 0.143 | 0.032 | 0.065 | 0.093 | 0.113 | 0.242 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | A | A | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 28 | 134 | 73 | 39 | 36 | 35 | 644 | 37 |
N.S. |
1 | 0.00 | 1.17 | 5.58 | 3.04 | 1.62 | 1.50 | 1.46 | 26.83 | 1.54 |
time (sec) |
N/A | 0.000 | 0.416 | 0.062 | 0.417 | 0.079 | 5.059 | 1.413 | 0.711 | 2.269 |
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 | 9 | 15 | 9 | 11 | 11 | 15 | 11 | 10 | 9 |
N.S. |
1 | 0.56 | 0.94 | 0.56 | 0.69 | 0.69 | 0.94 | 0.69 | 0.62 | 0.56 |
time (sec) |
N/A | 0.123 | 0.000 | 0.040 | 0.038 | 0.053 | 0.018 | 0.111 | 0.216 | 1.964 |
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 | 15 | 14 | 15 | 14 | 14 | 14 | 14 | 15 | 12 |
N.S. |
1 | 0.60 | 0.56 | 0.60 | 0.56 | 0.56 | 0.56 | 0.56 | 0.60 | 0.48 |
time (sec) |
N/A | 0.149 | 0.010 | 0.062 | 0.038 | 0.061 | 0.045 | 0.117 | 0.210 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 29 | 31 | 52 | 37 | 43 | 129 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.11 | 1.86 | 1.32 | 1.54 | 4.61 | 0.00 |
time (sec) |
N/A | 0.000 | 5.077 | 9.163 | 0.133 | 0.069 | 0.167 | 0.190 | 200.020 | 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 | 18 | 15 | 14 | 13 | 13 | 10 | 23 | 15 | 13 |
N.S. |
1 | 1.20 | 1.00 | 0.93 | 0.87 | 0.87 | 0.67 | 1.53 | 1.00 | 0.87 |
time (sec) |
N/A | 0.259 | 0.011 | 0.279 | 0.076 | 0.068 | 2.261 | 0.120 | 0.220 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 37 | 225 | 54 | 31 | 38 | 62 | 0 |
N.S. |
1 | 0.00 | 1.16 | 1.48 | 9.00 | 2.16 | 1.24 | 1.52 | 2.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.226 | 2.098 | 0.271 | 0.072 | 5.919 | 0.711 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 23 | 23 | 22 | 22 | 19 | 23 | 23 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 0.85 | 0.85 | 0.73 | 0.88 | 0.88 | 0.77 |
time (sec) |
N/A | 0.000 | 0.076 | 1.764 | 0.099 | 0.074 | 0.542 | 0.151 | 0.230 | 2.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 21 | 17 | 16 | 16 | 17 | 16 | 21 | 16 |
N.S. |
1 | 0.00 | 1.05 | 0.85 | 0.80 | 0.80 | 0.85 | 0.80 | 1.05 | 0.80 |
time (sec) |
N/A | 0.000 | 0.274 | 0.534 | 0.102 | 0.069 | 0.080 | 0.127 | 0.228 | 2.437 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 56 | 91 | 168 | 49 | 65 | 0 | 105 | 90 |
N.S. |
1 | 0.00 | 2.15 | 3.50 | 6.46 | 1.88 | 2.50 | 0.00 | 4.04 | 3.46 |
time (sec) |
N/A | 0.000 | 0.162 | 2.162 | 0.277 | 0.064 | 0.134 | 0.000 | 0.201 | 2.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 26 | 21 | 26 | 21 | 24 | 26 | 201 | 26 |
N.S. |
1 | 0.00 | 1.13 | 0.91 | 1.13 | 0.91 | 1.04 | 1.13 | 8.74 | 1.13 |
time (sec) |
N/A | 0.000 | 2.262 | 0.219 | 0.103 | 0.067 | 0.077 | 0.117 | 0.229 | 2.097 |
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 | 14 | 11 | 11 | 12 | 11 | 11 | 10 | 11 | 11 | 11 |
N.S. |
1 | 0.79 | 0.79 | 0.86 | 0.79 | 0.79 | 0.71 | 0.79 | 0.79 | 0.79 |
time (sec) |
N/A | 0.306 | 0.023 | 0.131 | 0.105 | 0.065 | 0.063 | 0.112 | 0.209 | 2.088 |
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 | 15 | 15 | 16 | 14 | 15 | 14 | 14 | 15 | 15 |
N.S. |
1 | 0.75 | 0.75 | 0.80 | 0.70 | 0.75 | 0.70 | 0.70 | 0.75 | 0.75 |
time (sec) |
N/A | 0.146 | 0.000 | 0.049 | 0.039 | 0.060 | 0.018 | 0.109 | 0.224 | 0.002 |
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 | 28 | 39 | 29 | 52 | 28 | 31 | 28 | 40 | 25 |
N.S. |
1 | 1.17 | 1.62 | 1.21 | 2.17 | 1.17 | 1.29 | 1.17 | 1.67 | 1.04 |
time (sec) |
N/A | 0.379 | 0.020 | 0.957 | 0.109 | 0.068 | 0.271 | 0.111 | 0.216 | 2.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 27 | 29 | 31 | 31 | 29 | 33 | 46 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.04 | 1.11 | 1.11 | 1.04 | 1.18 | 1.64 | 0.00 |
time (sec) |
N/A | 0.000 | 1.743 | 0.328 | 0.114 | 0.062 | 0.151 | 0.130 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 51 | 50 | 63 | 49 | 42 | 0 | 48 | 50 |
N.S. |
1 | 0.00 | 1.42 | 1.39 | 1.75 | 1.36 | 1.17 | 0.00 | 1.33 | 1.39 |
time (sec) |
N/A | 0.000 | 0.170 | 1.599 | 0.104 | 0.068 | 0.359 | 0.000 | 0.194 | 2.813 |
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 | 10 | 14 | 17 | 12 | 18 | 18 | 14 | 18 | 11 | 16 |
N.S. |
1 | 1.40 | 1.70 | 1.20 | 1.80 | 1.80 | 1.40 | 1.80 | 1.10 | 1.60 |
time (sec) |
N/A | 0.150 | 0.000 | 0.095 | 0.050 | 0.054 | 0.022 | 0.109 | 0.258 | 1.937 |
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 | 23 | 24 | 31 | 30 | 26 | 32 | 31 | 34 | 32 | 32 |
N.S. |
1 | 1.04 | 1.35 | 1.30 | 1.13 | 1.39 | 1.35 | 1.48 | 1.39 | 1.39 |
time (sec) |
N/A | 0.461 | 0.013 | 0.145 | 0.047 | 0.065 | 1.912 | 0.119 | 0.212 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 28 | 26 | 0 | 25 | 34 | 25 | 26 | 38 |
N.S. |
1 | 0.00 | 1.12 | 1.04 | 0.00 | 1.00 | 1.36 | 1.00 | 1.04 | 1.52 |
time (sec) |
N/A | 0.000 | 0.591 | 2.134 | 0.000 | 0.065 | 0.105 | 0.120 | 0.206 | 2.222 |
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 | 18 | 17 | 15 | 16 | 15 | 22 | 10 | 16 | 24 | 15 |
N.S. |
1 | 0.94 | 0.83 | 0.89 | 0.83 | 1.22 | 0.56 | 0.89 | 1.33 | 0.83 |
time (sec) |
N/A | 0.221 | 0.007 | 0.060 | 0.042 | 0.059 | 0.044 | 0.115 | 0.214 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 25 | 27 | 129 | 28 | 22 | 37 | 29 | 37 |
N.S. |
1 | 0.00 | 0.78 | 0.84 | 4.03 | 0.88 | 0.69 | 1.16 | 0.91 | 1.16 |
time (sec) |
N/A | 0.000 | 0.043 | 2.092 | 0.240 | 0.067 | 0.100 | 0.145 | 0.216 | 2.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 48 | 60 | 54 | 55 | 48 | 62 | 0 | 0 |
N.S. |
1 | 0.00 | 1.55 | 1.94 | 1.74 | 1.77 | 1.55 | 2.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.058 | 1.747 | 0.498 | 0.068 | 0.411 | 0.314 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F(-1) | B | B | B | F(-1) | B | F(-1) |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 0 | 266 | 136 | 128 | 0 | 152 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 9.85 | 5.04 | 4.74 | 0.00 | 5.63 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 19.209 | 0.072 | 0.697 | 0.000 | 0.919 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 25 | 20 | 24 | 19 | 26 | 24 | 21 | 19 |
N.S. |
1 | 0.00 | 0.81 | 0.65 | 0.77 | 0.61 | 0.84 | 0.77 | 0.68 | 0.61 |
time (sec) |
N/A | 0.000 | 0.225 | 4.363 | 0.229 | 0.066 | 0.690 | 0.144 | 0.203 | 2.393 |
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 | 26 | 41 | 26 | 26 | 35 | 25 | 20 | 25 | 26 | 25 |
N.S. |
1 | 1.58 | 1.00 | 1.00 | 1.35 | 0.96 | 0.77 | 0.96 | 1.00 | 0.96 |
time (sec) |
N/A | 0.210 | 0.013 | 0.432 | 0.047 | 0.064 | 0.062 | 0.115 | 0.268 | 0.049 |
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 | 9 | 9 | 7 | 6 | 10 | 8 | 10 | 8 | 6 |
N.S. |
1 | 0.60 | 0.60 | 0.47 | 0.40 | 0.67 | 0.53 | 0.67 | 0.53 | 0.40 |
time (sec) |
N/A | 0.145 | 0.003 | 0.059 | 0.034 | 0.066 | 0.042 | 0.114 | 0.221 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 25 | 34 | 21 | 67 | 25 | 20 | 28 | 30 | 20 |
N.S. |
1 | 0.81 | 1.10 | 0.68 | 2.16 | 0.81 | 0.65 | 0.90 | 0.97 | 0.65 |
time (sec) |
N/A | 0.211 | 0.039 | 0.286 | 0.079 | 0.063 | 0.069 | 0.112 | 0.213 | 0.092 |
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 | 29 | 28 | 28 | 26 | 22 | 25 | 26 | 23 | 30 | 25 |
N.S. |
1 | 0.97 | 0.97 | 0.90 | 0.76 | 0.86 | 0.90 | 0.79 | 1.03 | 0.86 |
time (sec) |
N/A | 0.194 | 0.007 | 0.100 | 0.060 | 0.056 | 0.055 | 0.113 | 0.195 | 2.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 16 | 14 | 13 | 33 | 12 | 12 | 15 | 21 | 15 |
N.S. |
1 | 1.14 | 1.00 | 0.93 | 2.36 | 0.86 | 0.86 | 1.07 | 1.50 | 1.07 |
time (sec) |
N/A | 0.181 | 0.035 | 0.252 | 0.104 | 0.058 | 0.065 | 0.112 | 0.212 | 0.071 |
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 | 18 | 18 | 18 | 18 | 20 | 20 | 22 | 34 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.11 | 1.11 | 1.22 | 1.89 | 1.00 | 1.06 |
time (sec) |
N/A | 0.193 | 0.007 | 0.220 | 0.033 | 0.059 | 0.128 | 0.111 | 0.205 | 2.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 20 | 20 | 20 | 19 | 15 | 29 | 23 | 19 |
N.S. |
1 | 0.00 | 0.71 | 0.71 | 0.71 | 0.68 | 0.54 | 1.04 | 0.82 | 0.68 |
time (sec) |
N/A | 0.000 | 0.147 | 0.355 | 0.131 | 0.059 | 0.077 | 0.109 | 0.208 | 2.082 |
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 | 23 | 25 | 26 | 20 | 19 | 19 | 17 | 19 | 21 | 19 |
N.S. |
1 | 1.09 | 1.13 | 0.87 | 0.83 | 0.83 | 0.74 | 0.83 | 0.91 | 0.83 |
time (sec) |
N/A | 0.172 | 0.007 | 0.178 | 0.046 | 0.069 | 0.070 | 0.109 | 0.243 | 2.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 19 | 0 | 18 | 15 | 18 | 19 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.00 | 0.90 | 0.75 | 0.90 | 0.95 | 0.85 |
time (sec) |
N/A | 0.000 | 0.271 | 0.521 | 0.000 | 0.074 | 3.464 | 0.117 | 0.224 | 2.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 34 | 25 | 23 | 55 | 24 | 29 | 30 | 24 | 29 |
N.S. |
1 | 1.36 | 1.00 | 0.92 | 2.20 | 0.96 | 1.16 | 1.20 | 0.96 | 1.16 |
time (sec) |
N/A | 0.275 | 0.051 | 0.132 | 0.200 | 0.064 | 0.078 | 0.110 | 0.191 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 23 | 25 | 22 | 0 | 25 | 22 | 25 |
N.S. |
1 | 0.00 | 0.92 | 0.96 | 1.04 | 0.92 | 0.00 | 1.04 | 0.92 | 1.04 |
time (sec) |
N/A | 0.000 | 0.051 | 19.197 | 0.209 | 0.068 | 0.000 | 0.151 | 0.228 | 2.781 |
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 | 12 | 12 | 12 | 9 | 8 | 17 | 8 | 8 | 10 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.67 | 1.42 | 0.67 | 0.67 | 0.83 | 0.67 |
time (sec) |
N/A | 0.178 | 0.008 | 0.135 | 0.029 | 0.068 | 0.067 | 0.104 | 0.232 | 2.024 |
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 | 23 | 18 | 20 | 30 | 30 | 17 | 22 | 31 | 31 |
N.S. |
1 | 1.21 | 0.95 | 1.05 | 1.58 | 1.58 | 0.89 | 1.16 | 1.63 | 1.63 |
time (sec) |
N/A | 0.631 | 0.089 | 0.484 | 0.256 | 0.067 | 0.059 | 0.111 | 0.226 | 2.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 42 | 36 | 34 | 34 | 48 | 48 | 34 | 0 |
N.S. |
1 | 0.00 | 1.45 | 1.24 | 1.17 | 1.17 | 1.66 | 1.66 | 1.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.809 | 1.411 | 0.218 | 0.069 | 0.256 | 0.120 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-1) | A | B | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 39 | 41 | 0 | 46 | 46 | 0 | 158 | 51 |
N.S. |
1 | 0.00 | 1.39 | 1.46 | 0.00 | 1.64 | 1.64 | 0.00 | 5.64 | 1.82 |
time (sec) |
N/A | 0.000 | 0.282 | 25.847 | 0.000 | 0.072 | 0.786 | 0.000 | 200.036 | 2.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 23 | 21 | 22 | 23 | 29 | 37 | 22 | 20 |
N.S. |
1 | 0.00 | 0.68 | 0.62 | 0.65 | 0.68 | 0.85 | 1.09 | 0.65 | 0.59 |
time (sec) |
N/A | 0.000 | 0.098 | 0.316 | 0.094 | 0.063 | 8.024 | 0.117 | 0.211 | 2.116 |
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 | 20 | 20 | 20 | 19 | 227 | 18 | 17 | 18 | 20 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 11.35 | 0.90 | 0.85 | 0.90 | 1.00 | 0.90 |
time (sec) |
N/A | 0.392 | 0.023 | 1.588 | 0.212 | 0.069 | 0.070 | 0.145 | 0.193 | 2.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 147 | 21 | 52 | 0 | 52 | 56 | 62 | 64 | 48 |
N.S. |
1 | 4.74 | 0.68 | 1.68 | 0.00 | 1.68 | 1.81 | 2.00 | 2.06 | 1.55 |
time (sec) |
N/A | 0.613 | 0.210 | 1.460 | 0.000 | 0.070 | 92.825 | 0.231 | 0.199 | 2.787 |
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 | 33 | 58 | 38 | 50 | 45 | 45 | 51 | 45 | 46 | 40 |
N.S. |
1 | 1.76 | 1.15 | 1.52 | 1.36 | 1.36 | 1.55 | 1.36 | 1.39 | 1.21 |
time (sec) |
N/A | 0.262 | 0.099 | 0.436 | 0.042 | 0.064 | 0.086 | 0.128 | 0.195 | 2.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 17 | 17 | 16 | 16 | 15 | 16 | 17 | 17 |
N.S. |
1 | 0.00 | 0.74 | 0.74 | 0.70 | 0.70 | 0.65 | 0.70 | 0.74 | 0.74 |
time (sec) |
N/A | 0.000 | 0.698 | 0.122 | 0.069 | 0.068 | 0.080 | 0.117 | 0.214 | 0.136 |
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 | 16 | 19 | 19 | 20 | 24 | 27 | 24 | 23 | 19 | 702 |
N.S. |
1 | 1.19 | 1.19 | 1.25 | 1.50 | 1.69 | 1.50 | 1.44 | 1.19 | 43.88 |
time (sec) |
N/A | 0.186 | 0.005 | 0.145 | 0.034 | 0.056 | 0.161 | 0.109 | 0.196 | 2.361 |
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 | 20 | 20 | 31 | 17 | 23 | 15 | 17 | 44 | 17 | 16 |
N.S. |
1 | 1.00 | 1.55 | 0.85 | 1.15 | 0.75 | 0.85 | 2.20 | 0.85 | 0.80 |
time (sec) |
N/A | 0.195 | 0.041 | 0.117 | 0.119 | 0.063 | 0.088 | 0.118 | 0.194 | 2.802 |
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 | 23 | 11 | 9 | 8 | 7 | 7 | 5 | 7 | 8 | 8 |
N.S. |
1 | 0.48 | 0.39 | 0.35 | 0.30 | 0.30 | 0.22 | 0.30 | 0.35 | 0.35 |
time (sec) |
N/A | 0.127 | 0.000 | 0.031 | 0.026 | 0.050 | 0.017 | 0.115 | 0.182 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 78 | 20 | 13 | 46 | 12 | 15 | 16 | 10 | 10 |
N.S. |
1 | 5.57 | 1.43 | 0.93 | 3.29 | 0.86 | 1.07 | 1.14 | 0.71 | 0.71 |
time (sec) |
N/A | 0.298 | 0.013 | 0.355 | 0.123 | 0.063 | 0.053 | 0.115 | 0.188 | 2.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 27 | 890 | 28 | 27 | 27 | 27 | 27 | 27 | 27 |
N.S. |
1 | 1.29 | 42.38 | 1.33 | 1.29 | 1.29 | 1.29 | 1.29 | 1.29 | 1.29 |
time (sec) |
N/A | 0.971 | 0.188 | 2.556 | 0.098 | 0.067 | 0.170 | 0.146 | 0.198 | 2.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 217 | 85 | 84 | 69 | 42 | 68 | 107 | 0 |
N.S. |
1 | 0.00 | 7.23 | 2.83 | 2.80 | 2.30 | 1.40 | 2.27 | 3.57 | 0.00 |
time (sec) |
N/A | 0.000 | 0.043 | 0.889 | 0.130 | 0.073 | 0.445 | 0.121 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 46 | 34 | 66 | 39 | 0 | 53 | 38 | 38 |
N.S. |
1 | 0.00 | 2.00 | 1.48 | 2.87 | 1.70 | 0.00 | 2.30 | 1.65 | 1.65 |
time (sec) |
N/A | 0.000 | 0.517 | 0.650 | 0.175 | 0.072 | 0.000 | 0.118 | 0.206 | 2.446 |
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 | 11 | 11 | 9 | 9 | 9 | 8 | 9 | 8 | 8 |
N.S. |
1 | 0.69 | 0.69 | 0.56 | 0.56 | 0.56 | 0.50 | 0.56 | 0.50 | 0.50 |
time (sec) |
N/A | 0.133 | 0.000 | 0.033 | 0.031 | 0.055 | 0.015 | 0.115 | 0.216 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 28 | 81 | 103 | 39 | 212 | 109 | 49 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 3.12 | 3.96 | 1.50 | 8.15 | 4.19 | 1.88 |
time (sec) |
N/A | 0.000 | 0.130 | 23.307 | 0.099 | 0.072 | 0.140 | 0.169 | 0.199 | 2.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 27 | 26 | 52 | 58 | 36 | 378 | 67 | 60 |
N.S. |
1 | 0.00 | 1.04 | 1.00 | 2.00 | 2.23 | 1.38 | 14.54 | 2.58 | 2.31 |
time (sec) |
N/A | 0.000 | 4.803 | 3.522 | 0.189 | 0.071 | 0.165 | 0.209 | 0.188 | 2.421 |
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 | 17 | 17 | 18 | 17 | 21 | 14 | 17 | 21 | 16 |
N.S. |
1 | 0.85 | 0.85 | 0.90 | 0.85 | 1.05 | 0.70 | 0.85 | 1.05 | 0.80 |
time (sec) |
N/A | 0.182 | 0.003 | 0.167 | 0.032 | 0.064 | 0.055 | 0.118 | 0.181 | 2.084 |
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 | 22 | 22 | 21 | 19 | 21 | 27 | 32 | 20 | 20 |
N.S. |
1 | 0.92 | 0.92 | 0.88 | 0.79 | 0.88 | 1.12 | 1.33 | 0.83 | 0.83 |
time (sec) |
N/A | 0.555 | 0.127 | 2.547 | 0.062 | 0.071 | 0.136 | 0.153 | 0.214 | 2.295 |
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 | 26 | 39 | 28 | 35 | 35 | 31 | 36 | 38 | 40 | 35 |
N.S. |
1 | 1.50 | 1.08 | 1.35 | 1.35 | 1.19 | 1.38 | 1.46 | 1.54 | 1.35 |
time (sec) |
N/A | 0.202 | 0.008 | 0.105 | 0.026 | 0.059 | 0.268 | 0.115 | 0.201 | 2.050 |
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 | 10 | 10 | 8 | 7 | 7 | 8 | 7 | 8 | 7 |
N.S. |
1 | 0.83 | 0.83 | 0.67 | 0.58 | 0.58 | 0.67 | 0.58 | 0.67 | 0.58 |
time (sec) |
N/A | 0.133 | 0.000 | 0.052 | 0.031 | 0.056 | 0.019 | 0.105 | 0.206 | 0.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 22 | 20 | 21 | 26 | 24 | 17 | 20 | 22 | 20 |
N.S. |
1 | 0.92 | 0.83 | 0.88 | 1.08 | 1.00 | 0.71 | 0.83 | 0.92 | 0.83 |
time (sec) |
N/A | 0.393 | 0.036 | 0.172 | 0.086 | 0.065 | 0.045 | 0.119 | 0.195 | 2.159 |
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 | 14 | 21 | 12 | 17 | 20 | 16 | 17 | 16 | 14 | 13 |
N.S. |
1 | 1.50 | 0.86 | 1.21 | 1.43 | 1.14 | 1.21 | 1.14 | 1.00 | 0.93 |
time (sec) |
N/A | 0.162 | 0.012 | 0.111 | 0.038 | 0.059 | 0.048 | 0.109 | 0.190 | 2.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | F(-2) | B | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 42 | 10690 | 81 | 45 | 0 | 86 | 49 | 45 |
N.S. |
1 | 0.00 | 1.45 | 368.62 | 2.79 | 1.55 | 0.00 | 2.97 | 1.69 | 1.55 |
time (sec) |
N/A | 0.000 | 0.155 | 51.036 | 0.118 | 0.075 | 0.000 | 2.301 | 0.437 | 2.948 |
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 | 22 | 34 | 27 | 32 | 40 | 32 | 27 | 40 | 29 | 31 |
N.S. |
1 | 1.55 | 1.23 | 1.45 | 1.82 | 1.45 | 1.23 | 1.82 | 1.32 | 1.41 |
time (sec) |
N/A | 0.266 | 0.061 | 0.502 | 0.034 | 0.067 | 0.097 | 0.109 | 0.199 | 2.149 |
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 | 9 | 9 | 9 | 7 | 6 | 6 | 5 | 6 | 7 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 0.78 | 0.67 |
time (sec) |
N/A | 0.159 | 0.012 | 0.079 | 0.024 | 0.068 | 0.040 | 0.111 | 0.197 | 0.040 |
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 | 20 | 22 | 20 | 55 | 141 | 54 | 65 | 141 | 54 | 20 |
N.S. |
1 | 1.10 | 1.00 | 2.75 | 7.05 | 2.70 | 3.25 | 7.05 | 2.70 | 1.00 |
time (sec) |
N/A | 0.156 | 0.004 | 0.144 | 0.035 | 0.061 | 0.041 | 0.110 | 0.247 | 2.139 |
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 | 22 | 18 | 17 | 18 | 29 | 14 | 18 | 26 | 16 |
N.S. |
1 | 0.88 | 0.72 | 0.68 | 0.72 | 1.16 | 0.56 | 0.72 | 1.04 | 0.64 |
time (sec) |
N/A | 0.245 | 0.007 | 0.067 | 0.026 | 0.055 | 0.046 | 0.109 | 0.229 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | C | C | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 56 | 22 | 31 | 91 | 57 | 53 | 92 | 20 | 29 |
N.S. |
1 | 2.55 | 1.00 | 1.41 | 4.14 | 2.59 | 2.41 | 4.18 | 0.91 | 1.32 |
time (sec) |
N/A | 0.345 | 0.040 | 2.106 | 0.028 | 0.064 | 0.132 | 0.116 | 0.217 | 2.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 23 | 23 | 22 | 20 | 21 | 22 | 0 | 62 | 23 |
N.S. |
1 | 0.92 | 0.92 | 0.88 | 0.80 | 0.84 | 0.88 | 0.00 | 2.48 | 0.92 |
time (sec) |
N/A | 0.763 | 0.521 | 5.104 | 0.137 | 0.069 | 2.357 | 0.000 | 200.023 | 2.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 43 | 26 | 31 | 28 | 28 | 34 | 28 | 39 | 36 |
N.S. |
1 | 2.26 | 1.37 | 1.63 | 1.47 | 1.47 | 1.79 | 1.47 | 2.05 | 1.89 |
time (sec) |
N/A | 0.222 | 0.128 | 0.286 | 0.030 | 0.064 | 0.058 | 0.113 | 0.219 | 2.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 85 | 32 | 63 | 99 | 62 | 83 | 81 | 71 | 39 |
N.S. |
1 | 2.43 | 0.91 | 1.80 | 2.83 | 1.77 | 2.37 | 2.31 | 2.03 | 1.11 |
time (sec) |
N/A | 0.280 | 0.030 | 0.390 | 0.113 | 0.070 | 0.370 | 0.114 | 0.208 | 2.136 |
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 | 29 | 25 | 12 | 13 | 37 | 12 | 8 | 23 | 26 | 10 |
N.S. |
1 | 0.86 | 0.41 | 0.45 | 1.28 | 0.41 | 0.28 | 0.79 | 0.90 | 0.34 |
time (sec) |
N/A | 0.242 | 0.012 | 0.208 | 0.038 | 0.063 | 0.045 | 0.114 | 0.204 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 22 | 22 | 22 | 22 | 26 | 22 | 20 | 21 |
N.S. |
1 | 0.00 | 1.05 | 1.05 | 1.05 | 1.05 | 1.24 | 1.05 | 0.95 | 1.00 |
time (sec) |
N/A | 0.000 | 0.267 | 1.770 | 0.088 | 0.071 | 0.136 | 0.136 | 0.202 | 2.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 69 | 36 | 39 | 80 | 31 | 37 | 38 | 128 | 37 |
N.S. |
1 | 2.30 | 1.20 | 1.30 | 2.67 | 1.03 | 1.23 | 1.27 | 4.27 | 1.23 |
time (sec) |
N/A | 0.358 | 0.085 | 0.351 | 0.044 | 0.066 | 0.165 | 0.125 | 0.327 | 0.464 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 20 | 17 | 18 | 25 | 17 | 14 | 17 | 17 | 16 |
N.S. |
1 | 1.05 | 0.89 | 0.95 | 1.32 | 0.89 | 0.74 | 0.89 | 0.89 | 0.84 |
time (sec) |
N/A | 0.197 | 0.063 | 0.177 | 0.061 | 0.067 | 0.058 | 0.114 | 0.212 | 2.109 |
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 | 28 | 27 | 20 | 19 | 19 | 19 | 19 | 41 | 22 |
N.S. |
1 | 1.12 | 1.08 | 0.80 | 0.76 | 0.76 | 0.76 | 0.76 | 1.64 | 0.88 |
time (sec) |
N/A | 0.258 | 0.334 | 0.273 | 0.097 | 0.063 | 0.105 | 0.126 | 0.221 | 0.126 |
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 | 22 | 20 | 19 | 27 | 22 | 27 | 28 | 18 |
N.S. |
1 | 1.00 | 0.79 | 0.71 | 0.68 | 0.96 | 0.79 | 0.96 | 1.00 | 0.64 |
time (sec) |
N/A | 0.199 | 0.005 | 0.316 | 0.036 | 0.073 | 0.064 | 0.110 | 0.206 | 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 | 14 | 9 | 9 | 10 | 9 | 9 | 8 | 9 | 9 | 9 |
N.S. |
1 | 0.64 | 0.64 | 0.71 | 0.64 | 0.64 | 0.57 | 0.64 | 0.64 | 0.64 |
time (sec) |
N/A | 0.198 | 0.017 | 0.114 | 0.031 | 0.060 | 0.056 | 0.112 | 0.216 | 0.231 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 48 | 50 | 21 | 28 | 28 | 63 | 29 | 28 | 17 |
N.S. |
1 | 1.78 | 1.85 | 0.78 | 1.04 | 1.04 | 2.33 | 1.07 | 1.04 | 0.63 |
time (sec) |
N/A | 0.181 | 0.008 | 0.352 | 0.033 | 0.064 | 0.106 | 0.128 | 0.206 | 2.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 22 | 35 | 37 | 17 | 53 | 41 | 45 |
N.S. |
1 | 0.00 | 0.96 | 0.85 | 1.35 | 1.42 | 0.65 | 2.04 | 1.58 | 1.73 |
time (sec) |
N/A | 0.000 | 0.060 | 0.434 | 0.082 | 0.064 | 0.131 | 0.117 | 0.212 | 2.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 35 | 35 | 32 | 0 | 37 | 34 | 33 |
N.S. |
1 | 0.00 | 1.09 | 1.09 | 1.09 | 1.00 | 0.00 | 1.16 | 1.06 | 1.03 |
time (sec) |
N/A | 0.000 | 0.484 | 20.383 | 0.144 | 0.067 | 0.000 | 0.149 | 0.199 | 2.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 46 | 40 | 46 | 44 | 39 | 42 | 42 | 0 |
N.S. |
1 | 0.00 | 1.92 | 1.67 | 1.92 | 1.83 | 1.62 | 1.75 | 1.75 | 0.00 |
time (sec) |
N/A | 0.000 | 0.033 | 1.254 | 0.153 | 0.069 | 0.246 | 0.114 | 0.216 | 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 | 26 | 47 | 21 | 23 | 31 | 20 | 19 | 20 | 21 | 17 |
N.S. |
1 | 1.81 | 0.81 | 0.88 | 1.19 | 0.77 | 0.73 | 0.77 | 0.81 | 0.65 |
time (sec) |
N/A | 0.214 | 0.076 | 0.127 | 0.047 | 0.063 | 0.055 | 0.108 | 0.216 | 2.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 50 | 56 | 52 | 64 | 73 | 64 | 53 | 25 |
N.S. |
1 | 0.00 | 2.00 | 2.24 | 2.08 | 2.56 | 2.92 | 2.56 | 2.12 | 1.00 |
time (sec) |
N/A | 0.000 | 5.026 | 28.819 | 0.154 | 0.068 | 0.082 | 0.131 | 0.213 | 2.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 26 | 26 | 53 | 0 | 57 | 0 | 0 | 99 | 0 |
N.S. |
1 | 0.84 | 0.84 | 1.71 | 0.00 | 1.84 | 0.00 | 0.00 | 3.19 | 0.00 |
time (sec) |
N/A | 1.022 | 0.246 | 2.004 | 0.000 | 0.073 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 52 | 51 | 39 | 49 | 165 | 51 | 202 | 52 | 52 |
N.S. |
1 | 2.36 | 2.32 | 1.77 | 2.23 | 7.50 | 2.32 | 9.18 | 2.36 | 2.36 |
time (sec) |
N/A | 0.741 | 0.355 | 15.959 | 0.107 | 0.077 | 0.424 | 0.922 | 0.920 | 2.383 |
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 | 61 | 34 | 44 | 47 | 34 | 39 | 54 | 86 | 46 |
N.S. |
1 | 1.85 | 1.03 | 1.33 | 1.42 | 1.03 | 1.18 | 1.64 | 2.61 | 1.39 |
time (sec) |
N/A | 2.733 | 0.064 | 2.863 | 0.156 | 0.074 | 0.223 | 0.130 | 0.209 | 2.594 |
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 | 10 | 12 | 10 | 9 | 8 | 8 | 8 | 9 | 8 | 8 |
N.S. |
1 | 1.20 | 1.00 | 0.90 | 0.80 | 0.80 | 0.80 | 0.90 | 0.80 | 0.80 |
time (sec) |
N/A | 0.144 | 0.001 | 0.041 | 0.025 | 0.057 | 0.031 | 0.112 | 0.194 | 0.017 |