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 | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 69 | 15 | 12 | 16 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 4.93 | 1.07 | 0.86 | 1.14 | 1.07 | 1.00 |
time (sec) |
N/A | 0.271 | 0.018 | 0.121 | 0.095 | 0.100 | 0.057 | 0.149 | 0.185 | 23.623 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 104 | 15 | 12 | 18 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 7.43 | 1.07 | 0.86 | 1.29 | 1.07 | 1.00 |
time (sec) |
N/A | 0.256 | 0.018 | 0.056 | 0.037 | 0.074 | 0.085 | 0.143 | 0.170 | 23.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | C | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 52 | 13 | 13 | 60 | 13 | 10 | 701 | 13 | 12 |
N.S. |
1 | 4.33 | 1.08 | 1.08 | 5.00 | 1.08 | 0.83 | 58.42 | 1.08 | 1.00 |
time (sec) |
N/A | 0.319 | 0.016 | 0.043 | 0.037 | 0.070 | 0.079 | 0.161 | 0.184 | 23.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 44 | 17 | 10 | 0 | 17 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 3.14 | 1.21 | 0.71 | 0.00 | 1.21 | 1.00 |
time (sec) |
N/A | 0.259 | 0.021 | 0.079 | 0.095 | 0.069 | 0.078 | 0.000 | 0.162 | 24.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 74 | 19 | 12 | 0 | 19 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 5.29 | 1.36 | 0.86 | 0.00 | 1.36 | 1.00 |
time (sec) |
N/A | 0.257 | 0.021 | 0.072 | 0.095 | 0.083 | 0.080 | 0.000 | 0.184 | 24.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 69 | 19 | 12 | 0 | 19 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 4.93 | 1.36 | 0.86 | 0.00 | 1.36 | 1.00 |
time (sec) |
N/A | 0.260 | 0.021 | 0.093 | 0.102 | 0.072 | 0.085 | 0.000 | 0.179 | 23.802 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 94 | 18 | 14 | 16 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 6.71 | 1.29 | 1.00 | 1.14 | 1.07 | 1.07 |
time (sec) |
N/A | 0.268 | 0.026 | 0.460 | 0.126 | 0.082 | 0.229 | 0.153 | 0.182 | 22.983 |
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 | 35 | 44 | 35 | 34 | 94 | 34 | 61 | 49 | 34 | 34 |
N.S. |
1 | 1.26 | 1.00 | 0.97 | 2.69 | 0.97 | 1.74 | 1.40 | 0.97 | 0.97 |
time (sec) |
N/A | 0.309 | 0.024 | 0.057 | 0.105 | 0.081 | 0.060 | 0.144 | 0.187 | 22.833 |
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 | 35 | 42 | 35 | 34 | 129 | 34 | 61 | 37 | 34 | 34 |
N.S. |
1 | 1.20 | 1.00 | 0.97 | 3.69 | 0.97 | 1.74 | 1.06 | 0.97 | 0.97 |
time (sec) |
N/A | 0.295 | 0.022 | 0.048 | 0.040 | 0.080 | 0.079 | 0.146 | 0.170 | 23.923 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 53 | 30 | 30 | 82 | 30 | 49 | 787 | 30 | 30 |
N.S. |
1 | 1.83 | 1.03 | 1.03 | 2.83 | 1.03 | 1.69 | 27.14 | 1.03 | 1.03 |
time (sec) |
N/A | 0.322 | 0.021 | 0.034 | 0.038 | 0.097 | 0.080 | 0.137 | 0.205 | 23.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 42 | 33 | 35 | 69 | 36 | 49 | 0 | 36 | 34 |
N.S. |
1 | 1.27 | 1.00 | 1.06 | 2.09 | 1.09 | 1.48 | 0.00 | 1.09 | 1.03 |
time (sec) |
N/A | 0.296 | 0.026 | 0.058 | 0.099 | 0.072 | 0.093 | 0.000 | 0.175 | 23.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 44 | 35 | 39 | 99 | 40 | 58 | 0 | 40 | 36 |
N.S. |
1 | 1.26 | 1.00 | 1.11 | 2.83 | 1.14 | 1.66 | 0.00 | 1.14 | 1.03 |
time (sec) |
N/A | 0.303 | 0.028 | 0.072 | 0.094 | 0.074 | 0.113 | 0.000 | 0.171 | 23.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 44 | 35 | 39 | 94 | 40 | 60 | 0 | 40 | 36 |
N.S. |
1 | 1.26 | 1.00 | 1.11 | 2.69 | 1.14 | 1.71 | 0.00 | 1.14 | 1.03 |
time (sec) |
N/A | 0.302 | 0.029 | 0.092 | 0.094 | 0.071 | 0.107 | 0.000 | 0.203 | 22.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 50 | 35 | 36 | 121 | 39 | 104 | 51 | 36 | 0 |
N.S. |
1 | 1.43 | 1.00 | 1.03 | 3.46 | 1.11 | 2.97 | 1.46 | 1.03 | 0.00 |
time (sec) |
N/A | 0.361 | 0.068 | 8.490 | 0.120 | 0.078 | 4.176 | 0.198 | 0.166 | 0.000 |
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 | 141 | 226 | 100 | 150 | 183 | 143 | 202 | 5426 | 150 | 150 |
N.S. |
1 | 1.60 | 0.71 | 1.06 | 1.30 | 1.01 | 1.43 | 38.48 | 1.06 | 1.06 |
time (sec) |
N/A | 0.725 | 0.173 | 0.065 | 0.034 | 0.076 | 0.089 | 0.192 | 0.178 | 22.609 |
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 | 74 | 92 | 53 | 61 | 81 | 60 | 85 | 1690 | 61 | 62 |
N.S. |
1 | 1.24 | 0.72 | 0.82 | 1.09 | 0.81 | 1.15 | 22.84 | 0.82 | 0.84 |
time (sec) |
N/A | 0.420 | 0.107 | 0.030 | 0.033 | 0.068 | 0.086 | 0.161 | 0.174 | 22.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 91 | 130 | 0 | 155 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.12 | 0.00 | 1.34 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.486 | 0.264 | 0.098 | 0.000 | 0.086 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 306 | 176 | 0 | 0 | 276 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.01 | 0.58 | 0.00 | 0.00 | 0.91 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.169 | 0.668 | 0.000 | 0.000 | 0.114 | 0.000 | 0.000 | 0.183 | 0.000 |
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 | 203 | 306 | 144 | 203 | 243 | 193 | 262 | 9878 | 203 | 203 |
N.S. |
1 | 1.51 | 0.71 | 1.00 | 1.20 | 0.95 | 1.29 | 48.66 | 1.00 | 1.00 |
time (sec) |
N/A | 0.947 | 0.186 | 0.082 | 0.039 | 0.070 | 0.104 | 0.237 | 0.186 | 22.975 |
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 | 99 | 117 | 67 | 77 | 101 | 76 | 104 | 2601 | 77 | 77 |
N.S. |
1 | 1.18 | 0.68 | 0.78 | 1.02 | 0.77 | 1.05 | 26.27 | 0.78 | 0.78 |
time (sec) |
N/A | 0.483 | 0.115 | 0.033 | 0.033 | 0.068 | 0.068 | 0.162 | 0.186 | 22.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 211 | 46 | 120 | 0 | 268 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.22 | 0.57 | 0.00 | 1.27 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.885 | 5.098 | 0.086 | 0.000 | 0.084 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 617 | 618 | 121 | 0 | 0 | 460 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.20 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.239 | 0.214 | 0.000 | 0.000 | 0.085 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 389 | 120 | 284 | 360 | 241 | 384 | 9704 | 284 | 284 |
N.S. |
1 | 2.20 | 0.68 | 1.60 | 2.03 | 1.36 | 2.17 | 54.82 | 1.60 | 1.60 |
time (sec) |
N/A | 1.097 | 0.275 | 0.116 | 0.043 | 0.077 | 0.115 | 0.237 | 0.190 | 23.144 |
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 | 80 | 135 | 56 | 80 | 117 | 74 | 116 | 2068 | 80 | 80 |
N.S. |
1 | 1.69 | 0.70 | 1.00 | 1.46 | 0.92 | 1.45 | 25.85 | 1.00 | 1.00 |
time (sec) |
N/A | 0.518 | 0.156 | 0.036 | 0.035 | 0.071 | 0.073 | 0.164 | 0.171 | 23.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 128 | 223 | 0 | 305 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.51 | 0.00 | 2.06 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.726 | 0.970 | 0.139 | 0.000 | 0.080 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 393 | 249 | 624 | 0 | 632 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.29 | 0.82 | 2.05 | 0.00 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.548 | 1.767 | 0.118 | 0.000 | 0.092 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 120 | 127 | 0 | 106 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.96 | 0.00 | 0.80 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.677 | 0.359 | 0.079 | 0.000 | 0.078 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 83 | 100 | 0 | 72 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.00 | 0.00 | 0.72 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.503 | 0.198 | 0.038 | 0.000 | 0.073 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 94 | 102 | 0 | 98 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.86 | 0.00 | 0.83 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.486 | 0.142 | 0.033 | 0.000 | 0.070 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 93 | 112 | 0 | 80 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.01 | 0.00 | 0.72 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.666 | 0.304 | 0.046 | 0.000 | 0.083 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 121 | 142 | 0 | 128 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.98 | 0.00 | 0.88 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.720 | 0.567 | 0.056 | 0.000 | 0.080 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 232 | 268 | 755 | 0 | 330 | 0 | 0 | 119 | 0 |
N.S. |
1 | 1.00 | 1.16 | 3.25 | 0.00 | 1.42 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.101 | 0.905 | 0.226 | 0.000 | 0.081 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 217 | 561 | 0 | 267 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 1.17 | 3.02 | 0.00 | 1.44 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.893 | 1.865 | 0.073 | 0.000 | 0.082 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 153 | 350 | 0 | 224 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.97 | 2.22 | 0.00 | 1.42 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.685 | 0.610 | 0.059 | 0.000 | 0.080 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 127 | 169 | 0 | 192 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.22 | 0.00 | 1.39 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.619 | 0.536 | 0.048 | 0.000 | 0.080 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 163 | 363 | 0 | 241 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.96 | 2.15 | 0.00 | 1.43 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.897 | 0.665 | 0.065 | 0.000 | 0.094 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 212 | 320 | 561 | 0 | 313 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.51 | 2.65 | 0.00 | 1.48 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.056 | 0.738 | 0.082 | 0.000 | 0.084 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 171 | 100 | 260 | 309 | 227 | 350 | 8802 | 260 | 260 |
N.S. |
1 | 1.21 | 0.71 | 1.84 | 2.19 | 1.61 | 2.48 | 62.43 | 1.84 | 1.84 |
time (sec) |
N/A | 0.770 | 0.176 | 0.077 | 0.043 | 0.073 | 0.116 | 0.218 | 0.184 | 23.736 |
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 | 110 | 130 | 78 | 165 | 206 | 147 | 231 | 4706 | 165 | 165 |
N.S. |
1 | 1.18 | 0.71 | 1.50 | 1.87 | 1.34 | 2.10 | 42.78 | 1.50 | 1.50 |
time (sec) |
N/A | 0.584 | 0.139 | 0.058 | 0.039 | 0.072 | 0.090 | 0.199 | 0.167 | 22.994 |
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 | 79 | 89 | 56 | 91 | 123 | 84 | 133 | 2214 | 91 | 91 |
N.S. |
1 | 1.13 | 0.71 | 1.15 | 1.56 | 1.06 | 1.68 | 28.03 | 1.15 | 1.15 |
time (sec) |
N/A | 0.444 | 0.125 | 0.040 | 0.040 | 0.070 | 0.070 | 0.167 | 0.184 | 22.808 |
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 | 48 | 48 | 34 | 38 | 60 | 38 | 60 | 898 | 38 | 38 |
N.S. |
1 | 1.00 | 0.71 | 0.79 | 1.25 | 0.79 | 1.25 | 18.71 | 0.79 | 0.79 |
time (sec) |
N/A | 0.324 | 0.091 | 0.028 | 0.034 | 0.074 | 0.057 | 0.132 | 0.163 | 22.774 |
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 | 21 | 21 | 20 | 21 | 20 | 21 | 21 | 21 |
N.S. |
1 | 1.00 | 1.05 | 1.05 | 1.00 | 1.05 | 1.00 | 1.05 | 1.05 | 1.05 |
time (sec) |
N/A | 0.243 | 0.027 | 0.016 | 0.026 | 0.070 | 0.035 | 0.132 | 0.173 | 22.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 56 | 0 | 39 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.81 | 0.00 | 1.26 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.294 | 0.098 | 0.052 | 0.000 | 0.069 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 55 | 99 | 0 | 77 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 0.96 | 1.74 | 0.00 | 1.35 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.369 | 0.177 | 0.063 | 0.000 | 0.068 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 92 | 88 | 155 | 0 | 134 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.97 | 0.93 | 1.63 | 0.00 | 1.41 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.472 | 0.179 | 0.083 | 0.000 | 0.071 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 127 | 99 | 199 | 0 | 209 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.99 | 0.77 | 1.55 | 0.00 | 1.63 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.590 | 0.190 | 0.115 | 0.000 | 0.068 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 162 | 121 | 243 | 0 | 300 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.01 | 0.75 | 1.51 | 0.00 | 1.86 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.704 | 0.213 | 0.157 | 0.000 | 0.072 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 171 | 100 | 260 | 309 | 227 | 350 | 8802 | 260 | 260 |
N.S. |
1 | 1.21 | 0.71 | 1.84 | 2.19 | 1.61 | 2.48 | 62.43 | 1.84 | 1.84 |
time (sec) |
N/A | 0.787 | 0.035 | 0.073 | 0.043 | 0.072 | 0.105 | 0.222 | 0.177 | 22.891 |
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 | 110 | 130 | 78 | 165 | 206 | 147 | 231 | 4706 | 165 | 165 |
N.S. |
1 | 1.18 | 0.71 | 1.50 | 1.87 | 1.34 | 2.10 | 42.78 | 1.50 | 1.50 |
time (sec) |
N/A | 0.602 | 0.027 | 0.050 | 0.042 | 0.072 | 0.089 | 0.189 | 0.180 | 22.774 |
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 | 79 | 89 | 56 | 91 | 123 | 84 | 133 | 2214 | 91 | 91 |
N.S. |
1 | 1.13 | 0.71 | 1.15 | 1.56 | 1.06 | 1.68 | 28.03 | 1.15 | 1.15 |
time (sec) |
N/A | 0.468 | 0.025 | 0.037 | 0.040 | 0.074 | 0.066 | 0.170 | 0.197 | 22.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 55 | 99 | 0 | 77 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 0.96 | 1.74 | 0.00 | 1.35 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.393 | 0.016 | 0.080 | 0.000 | 0.076 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 92 | 88 | 155 | 0 | 134 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.97 | 0.93 | 1.63 | 0.00 | 1.41 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.503 | 0.033 | 0.103 | 0.000 | 0.072 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 127 | 99 | 199 | 0 | 209 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.99 | 0.77 | 1.55 | 0.00 | 1.63 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.635 | 0.069 | 0.151 | 0.000 | 0.076 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 162 | 121 | 243 | 0 | 300 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.01 | 0.75 | 1.51 | 0.00 | 1.86 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.768 | 0.024 | 0.221 | 0.000 | 0.089 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | C | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 41 | 10 | 11 | 45 | 10 | 8 | 569 | 10 | 10 |
N.S. |
1 | 4.10 | 1.00 | 1.10 | 4.50 | 1.00 | 0.80 | 56.90 | 1.00 | 1.00 |
time (sec) |
N/A | 0.321 | 0.011 | 0.042 | 0.032 | 0.076 | 0.049 | 0.132 | 0.199 | 22.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 42 | 17 | 18 | 45 | 17 | 32 | 609 | 17 | 17 |
N.S. |
1 | 2.47 | 1.00 | 1.06 | 2.65 | 1.00 | 1.88 | 35.82 | 1.00 | 1.00 |
time (sec) |
N/A | 0.336 | 0.015 | 0.030 | 0.032 | 0.091 | 0.052 | 0.125 | 0.170 | 22.842 |
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 | 14 | 13 | 13 | 14 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.93 | 0.87 | 0.93 | 0.87 |
time (sec) |
N/A | 0.239 | 0.023 | 0.021 | 0.030 | 0.066 | 0.037 | 0.118 | 0.177 | 23.070 |
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 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.242 | 0.001 | 0.017 | 0.030 | 0.076 | 0.036 | 0.139 | 0.178 | 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 | 19 | 19 | 19 | 12 | 13 | 13 | 10 | 13 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.63 | 0.68 | 0.68 | 0.53 | 0.68 | 0.58 | 0.58 |
time (sec) |
N/A | 0.247 | 0.025 | 0.051 | 0.032 | 0.074 | 0.035 | 0.117 | 0.168 | 0.096 |
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 | 131 | 158 | 36 | 99 | 24 | 89 | 0 | 94 | 117 | 82 |
N.S. |
1 | 1.21 | 0.27 | 0.76 | 0.18 | 0.68 | 0.00 | 0.72 | 0.89 | 0.63 |
time (sec) |
N/A | 0.773 | 0.114 | 0.034 | 0.074 | 0.084 | 0.000 | 0.117 | 0.186 | 23.417 |
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 | 108 | 126 | 36 | 87 | 24 | 77 | 0 | 82 | 93 | 72 |
N.S. |
1 | 1.17 | 0.33 | 0.81 | 0.22 | 0.71 | 0.00 | 0.76 | 0.86 | 0.67 |
time (sec) |
N/A | 0.631 | 0.112 | 0.026 | 0.071 | 0.101 | 0.000 | 0.116 | 0.183 | 17.450 |
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 | 85 | 94 | 36 | 75 | 24 | 65 | 0 | 70 | 69 | 75 |
N.S. |
1 | 1.11 | 0.42 | 0.88 | 0.28 | 0.76 | 0.00 | 0.82 | 0.81 | 0.88 |
time (sec) |
N/A | 0.500 | 0.147 | 0.022 | 0.075 | 0.076 | 0.000 | 0.117 | 0.174 | 24.068 |
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 | 62 | 62 | 30 | 66 | 24 | 51 | 0 | 58 | 50 | 55 |
N.S. |
1 | 1.00 | 0.48 | 1.06 | 0.39 | 0.82 | 0.00 | 0.94 | 0.81 | 0.89 |
time (sec) |
N/A | 0.394 | 0.097 | 0.022 | 0.075 | 0.087 | 0.000 | 0.121 | 0.183 | 23.131 |
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 | 38 | 38 | 30 | 27 | 29 | 34 | 0 | 28 | 27 | 32 |
N.S. |
1 | 1.00 | 0.79 | 0.71 | 0.76 | 0.89 | 0.00 | 0.74 | 0.71 | 0.84 |
time (sec) |
N/A | 0.302 | 0.102 | 0.022 | 0.075 | 0.073 | 0.000 | 0.121 | 0.162 | 22.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 38 | 64 | 24 | 44 | 0 | 0 | 19 | 42 |
N.S. |
1 | 1.00 | 0.70 | 1.19 | 0.44 | 0.81 | 0.00 | 0.00 | 0.35 | 0.78 |
time (sec) |
N/A | 0.372 | 0.185 | 0.020 | 0.074 | 0.079 | 0.000 | 0.000 | 0.185 | 22.855 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 78 | 49 | 72 | 24 | 58 | 0 | 0 | 19 | 61 |
N.S. |
1 | 1.01 | 0.64 | 0.94 | 0.31 | 0.75 | 0.00 | 0.00 | 0.25 | 0.79 |
time (sec) |
N/A | 0.461 | 0.164 | 0.023 | 0.077 | 0.076 | 0.000 | 0.000 | 0.180 | 22.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 102 | 61 | 84 | 24 | 74 | 0 | 0 | 19 | 80 |
N.S. |
1 | 1.02 | 0.61 | 0.84 | 0.24 | 0.74 | 0.00 | 0.00 | 0.19 | 0.80 |
time (sec) |
N/A | 0.546 | 0.187 | 0.023 | 0.081 | 0.078 | 0.000 | 0.000 | 0.188 | 22.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 126 | 73 | 96 | 24 | 86 | 0 | 0 | 19 | 99 |
N.S. |
1 | 1.02 | 0.59 | 0.78 | 0.20 | 0.70 | 0.00 | 0.00 | 0.15 | 0.80 |
time (sec) |
N/A | 0.631 | 0.205 | 0.023 | 0.071 | 0.075 | 0.000 | 0.000 | 0.190 | 22.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 240 | 72 | 0 | 0 | 230 | 0 | 1023 | 94 | 0 |
N.S. |
1 | 1.15 | 0.35 | 0.00 | 0.00 | 1.11 | 0.00 | 4.92 | 0.45 | 0.00 |
time (sec) |
N/A | 1.010 | 0.243 | 0.000 | 0.000 | 0.080 | 0.000 | 0.198 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 195 | 72 | 0 | 0 | 167 | 0 | 643 | 68 | 0 |
N.S. |
1 | 1.13 | 0.42 | 0.00 | 0.00 | 0.97 | 0.00 | 3.72 | 0.39 | 0.00 |
time (sec) |
N/A | 0.804 | 0.200 | 0.000 | 0.000 | 0.082 | 0.000 | 0.177 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 150 | 63 | 0 | 0 | 121 | 0 | 372 | 42 | 0 |
N.S. |
1 | 1.09 | 0.46 | 0.00 | 0.00 | 0.88 | 0.00 | 2.70 | 0.30 | 0.00 |
time (sec) |
N/A | 0.633 | 0.240 | 0.000 | 0.000 | 0.080 | 0.000 | 0.147 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 63 | 0 | 0 | 90 | 0 | 189 | 21 | 0 |
N.S. |
1 | 1.00 | 0.60 | 0.00 | 0.00 | 0.86 | 0.00 | 1.80 | 0.20 | 0.00 |
time (sec) |
N/A | 0.478 | 0.194 | 0.000 | 0.000 | 0.112 | 0.000 | 0.133 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 63 | 0 | 0 | 64 | 0 | 56 | 23 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.89 | 0.00 | 0.78 | 0.32 | 0.00 |
time (sec) |
N/A | 0.363 | 0.155 | 0.000 | 0.000 | 0.074 | 0.000 | 0.119 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 75 | 0 | 0 | 90 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.93 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.470 | 0.272 | 0.000 | 0.000 | 0.074 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 134 | 92 | 0 | 0 | 140 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.03 | 0.71 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.587 | 0.453 | 0.000 | 0.000 | 0.106 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 171 | 118 | 0 | 0 | 230 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.04 | 0.72 | 0.00 | 0.00 | 1.39 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.722 | 0.402 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 208 | 144 | 0 | 0 | 321 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.04 | 0.72 | 0.00 | 0.00 | 1.60 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.861 | 0.532 | 0.000 | 0.000 | 0.078 | 0.000 | 0.000 | 0.173 | 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 | 151 | 187 | 24 | 78 | 79 | 82 | 138 | 80 | 95 | 89 |
N.S. |
1 | 1.24 | 0.16 | 0.52 | 0.52 | 0.54 | 0.91 | 0.53 | 0.63 | 0.59 |
time (sec) |
N/A | 0.901 | 0.617 | 0.105 | 0.028 | 0.084 | 124.397 | 0.111 | 0.176 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 63 | 0 | 0 | 117 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 1.65 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.345 | 0.284 | 0.000 | 0.000 | 0.081 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 78 | 0 | 0 | 133 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 1.36 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.487 | 0.318 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 0.190 | 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 | 71 | 71 | 71 | 0 | 0 | 0 | 0 | 0 | 124 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.75 | 0.00 |
time (sec) |
N/A | 0.382 | 0.061 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 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 | 71 | 71 | 71 | 0 | 0 | 0 | 0 | 0 | 102 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.367 | 0.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 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 | 71 | 71 | 71 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.365 | 0.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 67 | 0 | 0 | 65 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.97 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.313 | 0.066 | 0.000 | 0.000 | 0.069 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 69 | 0 | 0 | 67 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.97 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.320 | 0.054 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 0.180 | 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 | 73 | 73 | 73 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.365 | 0.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 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 | 73 | 73 | 73 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.371 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 67 | 0 | 0 | 65 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.97 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.307 | 0.001 | 0.000 | 0.000 | 0.074 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 72 | 0 | 0 | 68 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.94 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.368 | 0.050 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.170 | 0.000 |
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 | 48 | 48 | 34 | 38 | 60 | 38 | 60 | 898 | 38 | 38 |
N.S. |
1 | 1.00 | 0.71 | 0.79 | 1.25 | 0.79 | 1.25 | 18.71 | 0.79 | 0.79 |
time (sec) |
N/A | 0.320 | 0.019 | 0.000 | 0.048 | 0.079 | 0.057 | 0.135 | 0.174 | 0.002 |
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 | 80 | 135 | 56 | 80 | 117 | 74 | 116 | 2068 | 80 | 80 |
N.S. |
1 | 1.69 | 0.70 | 1.00 | 1.46 | 0.92 | 1.45 | 25.85 | 1.00 | 1.00 |
time (sec) |
N/A | 0.498 | 0.039 | 0.000 | 0.057 | 0.068 | 0.070 | 0.147 | 0.183 | 0.002 |
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 | 118 | 229 | 84 | 138 | 194 | 122 | 190 | 4188 | 138 | 138 |
N.S. |
1 | 1.94 | 0.71 | 1.17 | 1.64 | 1.03 | 1.61 | 35.49 | 1.17 | 1.17 |
time (sec) |
N/A | 0.686 | 0.260 | 0.046 | 0.052 | 0.071 | 0.088 | 0.183 | 0.161 | 22.575 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 348 | 117 | 212 | 291 | 182 | 284 | 7630 | 212 | 212 |
N.S. |
1 | 2.15 | 0.72 | 1.31 | 1.80 | 1.12 | 1.75 | 47.10 | 1.31 | 1.31 |
time (sec) |
N/A | 0.964 | 0.704 | 0.053 | 0.081 | 0.073 | 0.110 | 0.223 | 0.180 | 22.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 61 | 334 | 123 | 126 | 99 | 0 | 448 | 0 |
N.S. |
1 | 1.00 | 0.53 | 2.88 | 1.06 | 1.09 | 0.85 | 0.00 | 3.86 | 0.00 |
time (sec) |
N/A | 0.600 | 0.131 | 0.588 | 0.158 | 0.074 | 9.028 | 0.000 | 0.172 | 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 | 227 | 397 | 121 | 178 | 196 | 121 | 236 | 202 | 182 | 175 |
N.S. |
1 | 1.75 | 0.53 | 0.78 | 0.86 | 0.53 | 1.04 | 0.89 | 0.80 | 0.77 |
time (sec) |
N/A | 1.323 | 0.402 | 0.079 | 0.056 | 0.070 | 0.106 | 0.118 | 0.174 | 22.452 |
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 | 318 | 130 | 143 | 164 | 102 | 196 | 163 | 143 | 126 |
N.S. |
1 | 1.70 | 0.70 | 0.76 | 0.88 | 0.55 | 1.05 | 0.87 | 0.76 | 0.67 |
time (sec) |
N/A | 1.103 | 0.339 | 0.054 | 0.052 | 0.069 | 0.094 | 0.112 | 0.174 | 22.563 |
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 | 137 | 184 | 96 | 102 | 132 | 78 | 148 | 123 | 104 | 117 |
N.S. |
1 | 1.34 | 0.70 | 0.74 | 0.96 | 0.57 | 1.08 | 0.90 | 0.76 | 0.85 |
time (sec) |
N/A | 0.754 | 0.269 | 0.049 | 0.046 | 0.068 | 0.080 | 0.112 | 0.167 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 41 | 68 | 103 | 57 | 104 | 87 | 69 | 66 |
N.S. |
1 | 1.08 | 0.51 | 0.85 | 1.29 | 0.71 | 1.30 | 1.09 | 0.86 | 0.82 |
time (sec) |
N/A | 0.517 | 0.255 | 0.037 | 0.044 | 0.114 | 0.077 | 0.124 | 0.180 | 22.535 |
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 | 102 | 102 | 52 | 96 | 69 | 50 | 70 | 95 | 51 | 69 |
N.S. |
1 | 1.00 | 0.51 | 0.94 | 0.68 | 0.49 | 0.69 | 0.93 | 0.50 | 0.68 |
time (sec) |
N/A | 0.570 | 0.267 | 0.046 | 0.094 | 0.078 | 3.218 | 0.118 | 0.167 | 22.872 |
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 | 94 | 94 | 54 | 88 | 61 | 56 | 99 | 92 | 70 | 72 |
N.S. |
1 | 1.00 | 0.57 | 0.94 | 0.65 | 0.60 | 1.05 | 0.98 | 0.74 | 0.77 |
time (sec) |
N/A | 0.568 | 0.287 | 0.055 | 0.093 | 0.070 | 1.372 | 0.135 | 0.163 | 22.661 |