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 | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 156 | 70 | 88 | 106 | 96 | 206 | 106 | 114 | 45 |
N.S. |
1 | 1.84 | 0.82 | 1.04 | 1.25 | 1.13 | 2.42 | 1.25 | 1.34 | 0.53 |
time (sec) |
N/A | 0.286 | 0.083 | 0.623 | 0.108 | 0.074 | 0.927 | 0.124 | 0.164 | 0.046 |
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 | 51 | 55 | 34 | 50 | 53 | 59 | 192 | 56 | 49 | 31 |
N.S. |
1 | 1.08 | 0.67 | 0.98 | 1.04 | 1.16 | 3.76 | 1.10 | 0.96 | 0.61 |
time (sec) |
N/A | 0.158 | 0.059 | 0.612 | 0.107 | 0.074 | 0.969 | 0.197 | 0.166 | 0.164 |
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 | 51 | 55 | 34 | 50 | 53 | 59 | 238 | 56 | 49 | 32 |
N.S. |
1 | 1.08 | 0.67 | 0.98 | 1.04 | 1.16 | 4.67 | 1.10 | 0.96 | 0.63 |
time (sec) |
N/A | 0.161 | 0.057 | 0.526 | 0.110 | 0.070 | 0.820 | 0.193 | 0.166 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 197 | 93 | 107 | 142 | 139 | 0 | 148 | 115 | 49 |
N.S. |
1 | 1.86 | 0.88 | 1.01 | 1.34 | 1.31 | 0.00 | 1.40 | 1.08 | 0.46 |
time (sec) |
N/A | 0.312 | 0.101 | 0.450 | 0.125 | 0.142 | 0.000 | 0.127 | 0.165 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 203 | 97 | 113 | 148 | 143 | 0 | 156 | 121 | 51 |
N.S. |
1 | 1.85 | 0.88 | 1.03 | 1.35 | 1.30 | 0.00 | 1.42 | 1.10 | 0.46 |
time (sec) |
N/A | 0.310 | 0.094 | 0.512 | 0.120 | 0.099 | 0.000 | 0.124 | 0.167 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 60 | 47 | 57 | 61 | 139 | 0 | 193 | 56 | 45 |
N.S. |
1 | 1.05 | 0.82 | 1.00 | 1.07 | 2.44 | 0.00 | 3.39 | 0.98 | 0.79 |
time (sec) |
N/A | 0.163 | 0.038 | 0.214 | 0.114 | 0.102 | 0.000 | 0.125 | 0.167 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 62 | 49 | 61 | 65 | 143 | 0 | 201 | 118 | 47 |
N.S. |
1 | 1.05 | 0.83 | 1.03 | 1.10 | 2.42 | 0.00 | 3.41 | 2.00 | 0.80 |
time (sec) |
N/A | 0.163 | 0.038 | 0.208 | 0.156 | 0.105 | 0.000 | 0.126 | 0.167 | 0.029 |
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 | 58 | 65 | 58 | 60 | 61 | 63 | 243 | 64 | 63 | 46 |
N.S. |
1 | 1.12 | 1.00 | 1.03 | 1.05 | 1.09 | 4.19 | 1.10 | 1.09 | 0.79 |
time (sec) |
N/A | 0.166 | 0.057 | 1.332 | 0.118 | 0.086 | 1.230 | 0.155 | 0.166 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 101 | 150 | 96 | 0 | 255 | 0 | 345 | 91 | 75 |
N.S. |
1 | 1.06 | 1.58 | 1.01 | 0.00 | 2.68 | 0.00 | 3.63 | 0.96 | 0.79 |
time (sec) |
N/A | 0.230 | 0.304 | 0.481 | 0.000 | 0.078 | 0.000 | 0.132 | 0.166 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 237 | 221 | 239 | 0 | 702 | 0 | 1057 | 651 | 0 |
N.S. |
1 | 1.03 | 0.96 | 1.04 | 0.00 | 3.05 | 0.00 | 4.60 | 2.83 | 0.00 |
time (sec) |
N/A | 0.273 | 0.452 | 0.146 | 0.000 | 0.108 | 0.000 | 0.257 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 196 | 167 | 206 | 0 | 540 | 0 | 711 | 471 | 0 |
N.S. |
1 | 1.02 | 0.87 | 1.07 | 0.00 | 2.81 | 0.00 | 3.70 | 2.45 | 0.00 |
time (sec) |
N/A | 0.243 | 0.322 | 0.142 | 0.000 | 0.110 | 0.000 | 0.221 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 155 | 128 | 173 | 0 | 410 | 0 | 423 | 320 | 0 |
N.S. |
1 | 1.01 | 0.83 | 1.12 | 0.00 | 2.66 | 0.00 | 2.75 | 2.08 | 0.00 |
time (sec) |
N/A | 0.206 | 0.238 | 0.146 | 0.000 | 0.098 | 0.000 | 0.189 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 114 | 95 | 140 | 0 | 300 | 0 | 232 | 196 | 88 |
N.S. |
1 | 0.98 | 0.82 | 1.21 | 0.00 | 2.59 | 0.00 | 2.00 | 1.69 | 0.76 |
time (sec) |
N/A | 0.190 | 0.166 | 0.142 | 0.000 | 0.122 | 0.000 | 0.167 | 0.173 | 0.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 72 | 107 | 0 | 236 | 0 | 93 | 102 | 260 |
N.S. |
1 | 1.00 | 1.00 | 1.49 | 0.00 | 3.28 | 0.00 | 1.29 | 1.42 | 3.61 |
time (sec) |
N/A | 0.166 | 0.112 | 0.141 | 0.000 | 0.144 | 0.000 | 0.132 | 0.168 | 2.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 66 | 0 | 0 | 241 | 0 | 131 | 78 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 3.65 | 0.00 | 1.98 | 1.18 | 0.00 |
time (sec) |
N/A | 0.162 | 0.075 | 0.000 | 0.000 | 0.133 | 0.000 | 0.150 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 65 | 0 | 152 | 89 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 2.03 | 0.00 | 4.75 | 2.78 | 0.84 |
time (sec) |
N/A | 0.133 | 0.023 | 0.145 | 0.000 | 0.113 | 0.000 | 0.156 | 0.174 | 0.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 175 | 0 | 447 | 239 | 127 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 2.65 | 0.00 | 6.77 | 3.62 | 1.92 |
time (sec) |
N/A | 0.155 | 0.073 | 0.144 | 0.000 | 0.246 | 0.000 | 0.181 | 0.170 | 0.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 337 | 0 | 689 | 446 | 203 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 3.34 | 0.00 | 6.82 | 4.42 | 2.01 |
time (sec) |
N/A | 0.176 | 0.124 | 0.151 | 0.000 | 0.553 | 0.000 | 0.195 | 0.175 | 0.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 532 | 0 | 989 | 706 | 292 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 3.91 | 0.00 | 7.27 | 5.19 | 2.15 |
time (sec) |
N/A | 0.202 | 0.225 | 0.152 | 0.000 | 2.164 | 0.000 | 0.242 | 0.185 | 0.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 210 | 170 | 248 | 0 | 781 | 0 | 1345 | 1027 | 397 |
N.S. |
1 | 1.23 | 0.99 | 1.45 | 0.00 | 4.57 | 0.00 | 7.87 | 6.01 | 2.32 |
time (sec) |
N/A | 0.226 | 0.321 | 0.158 | 0.000 | 5.145 | 0.000 | 0.565 | 0.206 | 0.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 237 | 220 | 239 | 0 | 702 | 0 | 1673 | 651 | 0 |
N.S. |
1 | 1.04 | 0.97 | 1.05 | 0.00 | 3.09 | 0.00 | 7.37 | 2.87 | 0.00 |
time (sec) |
N/A | 0.254 | 0.394 | 0.143 | 0.000 | 0.128 | 0.000 | 0.376 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 196 | 167 | 206 | 0 | 534 | 0 | 1037 | 471 | 0 |
N.S. |
1 | 1.04 | 0.88 | 1.09 | 0.00 | 2.83 | 0.00 | 5.49 | 2.49 | 0.00 |
time (sec) |
N/A | 0.229 | 0.292 | 0.156 | 0.000 | 0.109 | 0.000 | 0.282 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 155 | 127 | 173 | 0 | 410 | 0 | 557 | 320 | 0 |
N.S. |
1 | 1.03 | 0.84 | 1.15 | 0.00 | 2.72 | 0.00 | 3.69 | 2.12 | 0.00 |
time (sec) |
N/A | 0.203 | 0.211 | 0.145 | 0.000 | 0.107 | 0.000 | 0.208 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 94 | 140 | 0 | 306 | 0 | 233 | 198 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.24 | 0.00 | 2.71 | 0.00 | 2.06 | 1.75 | 0.00 |
time (sec) |
N/A | 0.182 | 0.144 | 0.248 | 0.000 | 0.089 | 0.000 | 0.161 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 86 | 0 | 0 | 311 | 0 | 204 | 170 | 0 |
N.S. |
1 | 1.04 | 0.88 | 0.00 | 0.00 | 3.17 | 0.00 | 2.08 | 1.73 | 0.00 |
time (sec) |
N/A | 0.178 | 0.161 | 0.000 | 0.000 | 0.125 | 0.000 | 0.192 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 97 | 81 | 0 | 0 | 325 | 0 | 455 | 150 | 0 |
N.S. |
1 | 1.05 | 0.88 | 0.00 | 0.00 | 3.53 | 0.00 | 4.95 | 1.63 | 0.00 |
time (sec) |
N/A | 0.173 | 0.118 | 0.000 | 0.000 | 0.221 | 0.000 | 0.223 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 104 | 0 | 374 | 161 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 3.25 | 0.00 | 11.69 | 5.03 | 0.84 |
time (sec) |
N/A | 0.133 | 0.025 | 0.148 | 0.000 | 0.245 | 0.000 | 0.235 | 0.172 | 0.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 235 | 0 | 1024 | 345 | 178 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 3.56 | 0.00 | 15.52 | 5.23 | 2.70 |
time (sec) |
N/A | 0.153 | 0.090 | 0.145 | 0.000 | 0.735 | 0.000 | 0.270 | 0.172 | 0.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 426 | 0 | 1394 | 592 | 268 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 4.22 | 0.00 | 13.80 | 5.86 | 2.65 |
time (sec) |
N/A | 0.181 | 0.166 | 0.160 | 0.000 | 2.348 | 0.000 | 0.320 | 0.190 | 0.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 649 | 0 | 1823 | 892 | 376 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 4.77 | 0.00 | 13.40 | 6.56 | 2.76 |
time (sec) |
N/A | 0.207 | 0.295 | 0.157 | 0.000 | 5.371 | 0.000 | 0.391 | 0.206 | 0.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 278 | 283 | 272 | 0 | 882 | 0 | 3002 | 860 | 0 |
N.S. |
1 | 1.06 | 1.08 | 1.04 | 0.00 | 3.37 | 0.00 | 11.46 | 3.28 | 0.00 |
time (sec) |
N/A | 0.286 | 0.486 | 0.153 | 0.000 | 0.144 | 0.000 | 0.513 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 237 | 220 | 239 | 0 | 702 | 0 | 1877 | 651 | 0 |
N.S. |
1 | 1.06 | 0.98 | 1.07 | 0.00 | 3.13 | 0.00 | 8.38 | 2.91 | 0.00 |
time (sec) |
N/A | 0.254 | 0.347 | 0.144 | 0.000 | 0.134 | 0.000 | 0.380 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 196 | 168 | 206 | 0 | 540 | 0 | 1045 | 471 | 0 |
N.S. |
1 | 1.05 | 0.90 | 1.11 | 0.00 | 2.90 | 0.00 | 5.62 | 2.53 | 0.00 |
time (sec) |
N/A | 0.236 | 0.265 | 0.148 | 0.000 | 0.122 | 0.000 | 0.272 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 154 | 124 | 173 | 0 | 412 | 0 | 427 | 320 | 0 |
N.S. |
1 | 1.04 | 0.84 | 1.17 | 0.00 | 2.78 | 0.00 | 2.89 | 2.16 | 0.00 |
time (sec) |
N/A | 0.212 | 0.192 | 0.143 | 0.000 | 0.096 | 0.000 | 0.191 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 143 | 124 | 0 | 0 | 439 | 0 | 287 | 304 | 0 |
N.S. |
1 | 1.04 | 0.90 | 0.00 | 0.00 | 3.18 | 0.00 | 2.08 | 2.20 | 0.00 |
time (sec) |
N/A | 0.209 | 0.245 | 0.000 | 0.000 | 0.152 | 0.000 | 0.244 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 136 | 119 | 0 | 0 | 475 | 0 | 650 | 379 | 0 |
N.S. |
1 | 1.06 | 0.93 | 0.00 | 0.00 | 3.71 | 0.00 | 5.08 | 2.96 | 0.00 |
time (sec) |
N/A | 0.200 | 0.186 | 0.000 | 0.000 | 0.193 | 0.000 | 0.290 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 128 | 111 | 0 | 0 | 463 | 0 | 1025 | 332 | 0 |
N.S. |
1 | 1.07 | 0.92 | 0.00 | 0.00 | 3.86 | 0.00 | 8.54 | 2.77 | 0.00 |
time (sec) |
N/A | 0.193 | 0.140 | 0.000 | 0.000 | 0.353 | 0.000 | 0.342 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 138 | 0 | 706 | 229 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 4.31 | 0.00 | 22.06 | 7.16 | 0.84 |
time (sec) |
N/A | 0.131 | 0.029 | 0.145 | 0.000 | 0.620 | 0.000 | 0.351 | 0.183 | 0.579 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 295 | 0 | 1826 | 451 | 229 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 4.47 | 0.00 | 27.67 | 6.83 | 3.47 |
time (sec) |
N/A | 0.149 | 0.117 | 0.254 | 0.000 | 2.440 | 0.000 | 0.447 | 0.187 | 0.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 513 | 0 | 2316 | 738 | 333 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 5.08 | 0.00 | 22.93 | 7.31 | 3.30 |
time (sec) |
N/A | 0.174 | 0.205 | 0.150 | 0.000 | 5.826 | 0.000 | 0.553 | 0.217 | 0.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 765 | 0 | 2868 | 1078 | 459 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 5.62 | 0.00 | 21.09 | 7.93 | 3.38 |
time (sec) |
N/A | 0.208 | 0.412 | 0.155 | 0.000 | 11.542 | 0.000 | 0.688 | 0.259 | 0.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 196 | 164 | 206 | 0 | 542 | 0 | 268 | 471 | 0 |
N.S. |
1 | 1.07 | 0.90 | 1.13 | 0.00 | 2.96 | 0.00 | 1.46 | 2.57 | 0.00 |
time (sec) |
N/A | 0.232 | 0.359 | 0.141 | 0.000 | 0.107 | 0.000 | 0.153 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 155 | 125 | 173 | 0 | 412 | 0 | 198 | 320 | 0 |
N.S. |
1 | 1.05 | 0.84 | 1.17 | 0.00 | 2.78 | 0.00 | 1.34 | 2.16 | 0.00 |
time (sec) |
N/A | 0.208 | 0.277 | 0.142 | 0.000 | 0.105 | 0.000 | 0.148 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 114 | 94 | 140 | 0 | 306 | 0 | 139 | 198 | 0 |
N.S. |
1 | 1.01 | 0.83 | 1.24 | 0.00 | 2.71 | 0.00 | 1.23 | 1.75 | 0.00 |
time (sec) |
N/A | 0.186 | 0.172 | 0.140 | 0.000 | 0.095 | 0.000 | 0.138 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 72 | 107 | 0 | 235 | 0 | 97 | 102 | 261 |
N.S. |
1 | 1.00 | 0.99 | 1.47 | 0.00 | 3.22 | 0.00 | 1.33 | 1.40 | 3.58 |
time (sec) |
N/A | 0.166 | 0.120 | 0.141 | 0.000 | 0.107 | 0.000 | 0.146 | 0.165 | 2.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 76 | 0 | 178 | 0 | 50 | 44 | 45 |
N.S. |
1 | 1.00 | 1.00 | 1.81 | 0.00 | 4.24 | 0.00 | 1.19 | 1.05 | 1.07 |
time (sec) |
N/A | 0.146 | 0.048 | 0.141 | 0.000 | 0.085 | 0.000 | 0.139 | 0.165 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 27 | 0 | 42 | 0 | 66 | 43 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 1.40 | 0.00 | 2.20 | 1.43 | 0.87 |
time (sec) |
N/A | 0.134 | 0.022 | 0.147 | 0.000 | 0.078 | 0.000 | 0.134 | 0.168 | 0.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 45 | 54 | 0 | 118 | 0 | 121 | 131 | 71 |
N.S. |
1 | 1.00 | 0.68 | 0.82 | 0.00 | 1.79 | 0.00 | 1.83 | 1.98 | 1.08 |
time (sec) |
N/A | 0.151 | 0.063 | 0.145 | 0.000 | 0.114 | 0.000 | 0.138 | 0.173 | 0.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 75 | 95 | 0 | 251 | 0 | 227 | 302 | 133 |
N.S. |
1 | 1.13 | 0.74 | 0.94 | 0.00 | 2.49 | 0.00 | 2.25 | 2.99 | 1.32 |
time (sec) |
N/A | 0.172 | 0.105 | 0.147 | 0.000 | 0.220 | 0.000 | 0.144 | 0.171 | 0.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 116 | 135 | 0 | 419 | 0 | 386 | 522 | 209 |
N.S. |
1 | 1.19 | 0.85 | 0.99 | 0.00 | 3.08 | 0.00 | 2.84 | 3.84 | 1.54 |
time (sec) |
N/A | 0.208 | 0.168 | 0.151 | 0.000 | 0.515 | 0.000 | 0.172 | 0.173 | 0.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 210 | 168 | 175 | 0 | 638 | 0 | 596 | 803 | 303 |
N.S. |
1 | 1.23 | 0.98 | 1.02 | 0.00 | 3.73 | 0.00 | 3.49 | 4.70 | 1.77 |
time (sec) |
N/A | 0.222 | 0.255 | 0.160 | 0.000 | 2.364 | 0.000 | 0.188 | 0.186 | 0.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 185 | 166 | 0 | 0 | 603 | 0 | 279 | 724 | 0 |
N.S. |
1 | 1.06 | 0.95 | 0.00 | 0.00 | 3.47 | 0.00 | 1.60 | 4.16 | 0.00 |
time (sec) |
N/A | 0.222 | 0.328 | 0.000 | 0.000 | 0.249 | 0.000 | 0.194 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 144 | 124 | 0 | 0 | 441 | 0 | 201 | 485 | 0 |
N.S. |
1 | 1.04 | 0.90 | 0.00 | 0.00 | 3.20 | 0.00 | 1.46 | 3.51 | 0.00 |
time (sec) |
N/A | 0.197 | 0.224 | 0.000 | 0.000 | 0.194 | 0.000 | 0.165 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 86 | 0 | 0 | 311 | 0 | 137 | 275 | 0 |
N.S. |
1 | 1.05 | 0.88 | 0.00 | 0.00 | 3.17 | 0.00 | 1.40 | 2.81 | 0.00 |
time (sec) |
N/A | 0.174 | 0.169 | 0.000 | 0.000 | 0.143 | 0.000 | 0.166 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 66 | 0 | 0 | 241 | 0 | 96 | 120 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 3.65 | 0.00 | 1.45 | 1.82 | 0.00 |
time (sec) |
N/A | 0.154 | 0.078 | 0.000 | 0.000 | 0.112 | 0.000 | 0.151 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 27 | 0 | 42 | 0 | 47 | 60 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 1.40 | 0.00 | 1.57 | 2.00 | 0.87 |
time (sec) |
N/A | 0.128 | 0.021 | 0.151 | 0.000 | 0.094 | 0.000 | 0.128 | 0.164 | 0.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 42 | 52 | 0 | 125 | 0 | 142 | 121 | 71 |
N.S. |
1 | 1.00 | 0.68 | 0.84 | 0.00 | 2.02 | 0.00 | 2.29 | 1.95 | 1.15 |
time (sec) |
N/A | 0.144 | 0.063 | 0.150 | 0.000 | 0.115 | 0.000 | 0.149 | 0.169 | 0.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 110 | 75 | 105 | 0 | 273 | 0 | 368 | 298 | 141 |
N.S. |
1 | 1.12 | 0.77 | 1.07 | 0.00 | 2.79 | 0.00 | 3.76 | 3.04 | 1.44 |
time (sec) |
N/A | 0.163 | 0.095 | 0.159 | 0.000 | 0.215 | 0.000 | 0.202 | 0.172 | 0.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 158 | 114 | 145 | 0 | 455 | 0 | 830 | 579 | 227 |
N.S. |
1 | 1.18 | 0.85 | 1.08 | 0.00 | 3.40 | 0.00 | 6.19 | 4.32 | 1.69 |
time (sec) |
N/A | 0.205 | 0.144 | 0.170 | 0.000 | 0.420 | 0.000 | 0.309 | 0.196 | 0.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 206 | 166 | 185 | 0 | 689 | 0 | 1518 | 886 | 337 |
N.S. |
1 | 1.21 | 0.98 | 1.09 | 0.00 | 4.05 | 0.00 | 8.93 | 5.21 | 1.98 |
time (sec) |
N/A | 0.221 | 0.220 | 0.163 | 0.000 | 1.396 | 0.000 | 0.511 | 0.233 | 0.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 254 | 229 | 225 | 0 | 955 | 0 | 2438 | 1278 | 454 |
N.S. |
1 | 1.23 | 1.11 | 1.09 | 0.00 | 4.64 | 0.00 | 11.83 | 6.20 | 2.20 |
time (sec) |
N/A | 0.252 | 0.341 | 0.171 | 0.000 | 3.654 | 0.000 | 0.891 | 0.342 | 1.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 217 | 218 | 0 | 0 | 879 | 0 | 500 | 1159 | 0 |
N.S. |
1 | 1.06 | 1.07 | 0.00 | 0.00 | 4.31 | 0.00 | 2.45 | 5.68 | 0.00 |
time (sec) |
N/A | 0.240 | 0.376 | 0.000 | 0.000 | 0.619 | 0.000 | 0.234 | 17.106 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 178 | 166 | 0 | 0 | 657 | 0 | 380 | 817 | 0 |
N.S. |
1 | 1.05 | 0.98 | 0.00 | 0.00 | 3.86 | 0.00 | 2.24 | 4.81 | 0.00 |
time (sec) |
N/A | 0.217 | 0.274 | 0.000 | 0.000 | 0.350 | 0.000 | 0.219 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 137 | 121 | 0 | 0 | 475 | 0 | 276 | 504 | 0 |
N.S. |
1 | 1.07 | 0.95 | 0.00 | 0.00 | 3.71 | 0.00 | 2.16 | 3.94 | 0.00 |
time (sec) |
N/A | 0.189 | 0.203 | 0.000 | 0.000 | 0.242 | 0.000 | 0.197 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 97 | 81 | 0 | 0 | 325 | 0 | 181 | 207 | 0 |
N.S. |
1 | 1.05 | 0.88 | 0.00 | 0.00 | 3.53 | 0.00 | 1.97 | 2.25 | 0.00 |
time (sec) |
N/A | 0.171 | 0.112 | 0.000 | 0.000 | 0.255 | 0.000 | 0.183 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 65 | 0 | 51 | 125 | 130 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 2.03 | 0.00 | 1.59 | 3.91 | 4.06 |
time (sec) |
N/A | 0.135 | 0.021 | 0.154 | 0.000 | 0.131 | 0.000 | 0.160 | 0.171 | 0.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 53 | 0 | 118 | 0 | 126 | 186 | 127 |
N.S. |
1 | 1.00 | 0.70 | 0.80 | 0.00 | 1.79 | 0.00 | 1.91 | 2.82 | 1.92 |
time (sec) |
N/A | 0.150 | 0.050 | 0.156 | 0.000 | 0.187 | 0.000 | 0.141 | 0.167 | 0.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 110 | 78 | 95 | 0 | 273 | 0 | 373 | 288 | 132 |
N.S. |
1 | 1.12 | 0.80 | 0.97 | 0.00 | 2.79 | 0.00 | 3.81 | 2.94 | 1.35 |
time (sec) |
N/A | 0.176 | 0.096 | 0.165 | 0.000 | 0.311 | 0.000 | 0.160 | 0.188 | 0.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 156 | 118 | 135 | 0 | 447 | 0 | 670 | 579 | 224 |
N.S. |
1 | 1.16 | 0.87 | 1.00 | 0.00 | 3.31 | 0.00 | 4.96 | 4.29 | 1.66 |
time (sec) |
N/A | 0.202 | 0.136 | 0.156 | 0.000 | 0.462 | 0.000 | 0.252 | 0.180 | 0.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 204 | 170 | 175 | 0 | 715 | 0 | 1203 | 918 | 346 |
N.S. |
1 | 1.17 | 0.97 | 1.00 | 0.00 | 4.09 | 0.00 | 6.87 | 5.25 | 1.98 |
time (sec) |
N/A | 0.240 | 0.201 | 0.158 | 0.000 | 1.945 | 0.000 | 0.454 | 0.236 | 0.875 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 252 | 233 | 215 | 0 | 999 | 0 | 1964 | 1344 | 478 |
N.S. |
1 | 1.18 | 1.09 | 1.01 | 0.00 | 4.69 | 0.00 | 9.22 | 6.31 | 2.24 |
time (sec) |
N/A | 0.253 | 0.304 | 0.160 | 0.000 | 4.459 | 0.000 | 0.868 | 0.336 | 1.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 26 | 86 | 48 | 31 | 0 | 24 | 24 | 50 |
N.S. |
1 | 1.00 | 1.37 | 4.53 | 2.53 | 1.63 | 0.00 | 1.26 | 1.26 | 2.63 |
time (sec) |
N/A | 0.135 | 0.035 | 0.171 | 0.027 | 0.083 | 0.000 | 0.128 | 0.162 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 25 | 66 | 33 | 27 | 0 | 23 | 23 | 47 |
N.S. |
1 | 1.00 | 1.32 | 3.47 | 1.74 | 1.42 | 0.00 | 1.21 | 1.21 | 2.47 |
time (sec) |
N/A | 0.136 | 0.031 | 0.121 | 0.046 | 0.074 | 0.000 | 0.132 | 0.163 | 0.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 25 | 66 | 33 | 27 | 0 | 23 | 23 | 43 |
N.S. |
1 | 1.00 | 1.32 | 3.47 | 1.74 | 1.42 | 0.00 | 1.21 | 1.21 | 2.26 |
time (sec) |
N/A | 0.136 | 0.030 | 0.114 | 0.035 | 0.070 | 0.000 | 0.130 | 0.165 | 0.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 44 | 23 | 32 | 25 | 15 | 21 | 21 | 33 |
N.S. |
1 | 1.00 | 2.59 | 1.35 | 1.88 | 1.47 | 0.88 | 1.24 | 1.24 | 1.94 |
time (sec) |
N/A | 0.134 | 0.048 | 0.098 | 0.032 | 0.086 | 0.576 | 0.131 | 0.162 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 25 | 64 | 33 | 27 | 0 | 23 | 23 | 44 |
N.S. |
1 | 1.00 | 1.32 | 3.37 | 1.74 | 1.42 | 0.00 | 1.21 | 1.21 | 2.32 |
time (sec) |
N/A | 0.136 | 0.031 | 0.109 | 0.044 | 0.085 | 0.000 | 0.126 | 0.166 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 25 | 57 | 26 | 26 | 75 | 23 | 23 | 50 |
N.S. |
1 | 1.00 | 2.27 | 5.18 | 2.36 | 2.36 | 6.82 | 2.09 | 2.09 | 4.55 |
time (sec) |
N/A | 0.125 | 0.030 | 0.112 | 0.025 | 0.090 | 12.283 | 0.126 | 0.164 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 25 | 66 | 33 | 27 | 0 | 23 | 23 | 46 |
N.S. |
1 | 1.00 | 1.32 | 3.47 | 1.74 | 1.42 | 0.00 | 1.21 | 1.21 | 2.42 |
time (sec) |
N/A | 0.133 | 0.029 | 0.112 | 0.030 | 0.089 | 0.000 | 0.127 | 0.163 | 0.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 25 | 66 | 33 | 28 | 0 | 23 | 19 | 47 |
N.S. |
1 | 1.00 | 1.67 | 4.40 | 2.20 | 1.87 | 0.00 | 1.53 | 1.27 | 3.13 |
time (sec) |
N/A | 0.129 | 0.029 | 0.220 | 0.029 | 0.069 | 0.000 | 0.122 | 0.161 | 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 | 10 | 10 | 10 | 11 | 10 | 10 | 7 | 11 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.70 | 1.10 | 1.00 | 1.00 |
time (sec) |
N/A | 0.122 | 0.000 | 0.078 | 0.044 | 0.077 | 0.027 | 0.121 | 0.165 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 25 | 66 | 33 | 28 | 0 | 23 | 19 | 43 |
N.S. |
1 | 1.00 | 1.67 | 4.40 | 2.20 | 1.87 | 0.00 | 1.53 | 1.27 | 2.87 |
time (sec) |
N/A | 0.129 | 0.028 | 0.115 | 0.030 | 0.068 | 0.000 | 0.122 | 0.161 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 42 | 26 | 32 | 25 | 20 | 21 | 23 | 37 |
N.S. |
1 | 1.00 | 2.21 | 1.37 | 1.68 | 1.32 | 1.05 | 1.11 | 1.21 | 1.95 |
time (sec) |
N/A | 0.133 | 0.006 | 0.101 | 0.028 | 0.073 | 0.609 | 0.124 | 0.165 | 0.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 25 | 65 | 30 | 28 | 0 | 23 | 24 | 44 |
N.S. |
1 | 1.00 | 1.19 | 3.10 | 1.43 | 1.33 | 0.00 | 1.10 | 1.14 | 2.10 |
time (sec) |
N/A | 0.135 | 0.029 | 0.222 | 0.031 | 0.066 | 0.000 | 0.118 | 0.167 | 0.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 25 | 57 | 26 | 26 | 75 | 23 | 23 | 50 |
N.S. |
1 | 1.00 | 2.27 | 5.18 | 2.36 | 2.36 | 6.82 | 2.09 | 2.09 | 4.55 |
time (sec) |
N/A | 0.122 | 0.001 | 0.100 | 0.034 | 0.065 | 12.249 | 0.124 | 0.165 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 25 | 66 | 33 | 28 | 0 | 23 | 24 | 50 |
N.S. |
1 | 1.00 | 1.19 | 3.14 | 1.57 | 1.33 | 0.00 | 1.10 | 1.14 | 2.38 |
time (sec) |
N/A | 0.137 | 0.029 | 0.121 | 0.051 | 0.142 | 0.000 | 0.122 | 0.164 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 30 | 65 | 21 | 44 | 0 | 18 | 18 | 44 |
N.S. |
1 | 1.00 | 1.43 | 3.10 | 1.00 | 2.10 | 0.00 | 0.86 | 0.86 | 2.10 |
time (sec) |
N/A | 0.149 | 0.037 | 0.121 | 0.126 | 0.092 | 0.000 | 0.123 | 0.163 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 27 | 56 | 9 | 31 | 76 | 15 | 15 | 44 |
N.S. |
1 | 1.00 | 2.45 | 5.09 | 0.82 | 2.82 | 6.91 | 1.36 | 1.36 | 4.00 |
time (sec) |
N/A | 0.127 | 0.033 | 0.116 | 0.110 | 0.081 | 12.456 | 0.126 | 0.166 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 23 | 30 | 66 | 19 | 43 | 0 | 18 | 18 | 40 |
N.S. |
1 | 1.10 | 1.43 | 3.14 | 0.90 | 2.05 | 0.00 | 0.86 | 0.86 | 1.90 |
time (sec) |
N/A | 0.145 | 0.036 | 0.122 | 0.132 | 0.085 | 0.000 | 0.121 | 0.165 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 23 | 57 | 27 | 18 | 20 | 24 | 18 | 24 | 34 |
N.S. |
1 | 2.30 | 5.70 | 2.70 | 1.80 | 2.00 | 2.40 | 1.80 | 2.40 | 3.40 |
time (sec) |
N/A | 0.149 | 0.013 | 0.107 | 0.160 | 0.092 | 0.593 | 0.132 | 0.161 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 20 | 59 | 66 | 21 | 44 | 0 | 13 | 20 | 41 |
N.S. |
1 | 1.82 | 5.36 | 6.00 | 1.91 | 4.00 | 0.00 | 1.18 | 1.82 | 3.73 |
time (sec) |
N/A | 0.152 | 0.015 | 0.131 | 0.112 | 0.078 | 0.000 | 0.125 | 0.163 | 0.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 28 | 26 | 16 | 18 | 87 | 17 | 14 | 47 |
N.S. |
1 | 1.00 | 0.97 | 0.90 | 0.55 | 0.62 | 3.00 | 0.59 | 0.48 | 1.62 |
time (sec) |
N/A | 0.142 | 0.006 | 0.115 | 0.035 | 0.070 | 0.937 | 0.113 | 0.162 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 33 | 66 | 21 | 44 | 0 | 23 | 14 | 47 |
N.S. |
1 | 1.00 | 1.27 | 2.54 | 0.81 | 1.69 | 0.00 | 0.88 | 0.54 | 1.81 |
time (sec) |
N/A | 0.144 | 0.029 | 0.130 | 0.107 | 0.104 | 0.000 | 0.128 | 0.166 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 60 | 70 | 33 | 30 | 0 | 25 | 21 | 49 |
N.S. |
1 | 1.00 | 3.75 | 4.38 | 2.06 | 1.88 | 0.00 | 1.56 | 1.31 | 3.06 |
time (sec) |
N/A | 0.139 | 0.048 | 0.134 | 0.031 | 0.078 | 0.000 | 0.123 | 0.171 | 0.180 |
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 | 12 | 11 | 11 | 8 | 12 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.67 | 1.00 | 0.92 | 0.92 |
time (sec) |
N/A | 0.128 | 0.000 | 0.089 | 0.031 | 0.074 | 0.021 | 0.125 | 0.163 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 60 | 70 | 33 | 30 | 0 | 25 | 21 | 45 |
N.S. |
1 | 1.00 | 3.75 | 4.38 | 2.06 | 1.88 | 0.00 | 1.56 | 1.31 | 2.81 |
time (sec) |
N/A | 0.135 | 0.047 | 0.260 | 0.025 | 0.089 | 0.000 | 0.124 | 0.164 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 52 | 27 | 32 | 27 | 51 | 23 | 25 | 39 |
N.S. |
1 | 1.00 | 2.60 | 1.35 | 1.60 | 1.35 | 2.55 | 1.15 | 1.25 | 1.95 |
time (sec) |
N/A | 0.138 | 0.059 | 0.112 | 0.031 | 0.089 | 0.621 | 0.129 | 0.162 | 0.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 60 | 70 | 33 | 30 | 0 | 25 | 19 | 46 |
N.S. |
1 | 1.00 | 2.73 | 3.18 | 1.50 | 1.36 | 0.00 | 1.14 | 0.86 | 2.09 |
time (sec) |
N/A | 0.138 | 0.048 | 0.121 | 0.031 | 0.078 | 0.000 | 0.133 | 0.162 | 0.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 60 | 61 | 26 | 28 | 78 | 25 | 25 | 52 |
N.S. |
1 | 1.00 | 5.00 | 5.08 | 2.17 | 2.33 | 6.50 | 2.08 | 2.08 | 4.33 |
time (sec) |
N/A | 0.123 | 0.046 | 0.114 | 0.031 | 0.069 | 12.689 | 0.125 | 0.161 | 0.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 60 | 69 | 30 | 30 | 0 | 25 | 26 | 52 |
N.S. |
1 | 1.00 | 2.73 | 3.14 | 1.36 | 1.36 | 0.00 | 1.14 | 1.18 | 2.36 |
time (sec) |
N/A | 0.135 | 0.046 | 0.134 | 0.031 | 0.074 | 0.000 | 0.127 | 0.165 | 0.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 51 | 100 | 0 | 175 | 0 | 67 | 27 | 66 |
N.S. |
1 | 1.00 | 1.19 | 2.33 | 0.00 | 4.07 | 0.00 | 1.56 | 0.63 | 1.53 |
time (sec) |
N/A | 0.150 | 0.049 | 0.252 | 0.000 | 0.085 | 0.000 | 0.157 | 0.164 | 0.288 |