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 | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 233 | 128 | 128 | 0 | 249 | 0 | 0 | 252 | 0 |
N.S. |
1 | 1.10 | 0.61 | 0.61 | 0.00 | 1.18 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 1.252 | 0.142 | 1.714 | 0.000 | 0.088 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 91 | 98 | 60 | 99 | 71 | 158 | 239 | 139 | 83 |
N.S. |
1 | 1.18 | 1.27 | 0.78 | 1.29 | 0.92 | 2.05 | 3.10 | 1.81 | 1.08 |
time (sec) |
N/A | 0.284 | 0.102 | 0.440 | 0.025 | 0.082 | 0.778 | 0.128 | 0.182 | 4.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 105 | 61 | 78 | 179 | 95 | 0 | 0 | 90 | 150 |
N.S. |
1 | 1.05 | 0.61 | 0.78 | 1.79 | 0.95 | 0.00 | 0.00 | 0.90 | 1.50 |
time (sec) |
N/A | 0.350 | 0.108 | 0.480 | 0.033 | 0.072 | 0.000 | 0.000 | 0.165 | 3.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 82 | 88 | 60 | 82 | 71 | 158 | 239 | 151 | 105 |
N.S. |
1 | 1.09 | 1.17 | 0.80 | 1.09 | 0.95 | 2.11 | 3.19 | 2.01 | 1.40 |
time (sec) |
N/A | 0.257 | 0.084 | 0.405 | 0.030 | 0.077 | 0.799 | 0.120 | 0.163 | 3.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 65 | 90 | 182 | 97 | 0 | 0 | 90 | 154 |
N.S. |
1 | 1.05 | 0.69 | 0.96 | 1.94 | 1.03 | 0.00 | 0.00 | 0.96 | 1.64 |
time (sec) |
N/A | 0.330 | 0.086 | 0.445 | 0.035 | 0.067 | 0.000 | 0.000 | 0.159 | 4.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 195 | 81 | 234 | 268 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.51 | 0.63 | 1.81 | 2.08 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.139 | 0.206 | 0.484 | 0.039 | 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 | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 205 | 94 | 198 | 204 | 161 | 549 | 0 | 213 | 183 |
N.S. |
1 | 1.67 | 0.76 | 1.61 | 1.66 | 1.31 | 4.46 | 0.00 | 1.73 | 1.49 |
time (sec) |
N/A | 1.309 | 0.171 | 0.544 | 0.039 | 0.074 | 1.613 | 0.000 | 0.168 | 4.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 144 | 71 | 90 | 226 | 99 | 0 | 250 | 90 | 372 |
N.S. |
1 | 1.13 | 0.56 | 0.71 | 1.78 | 0.78 | 0.00 | 1.97 | 0.71 | 2.93 |
time (sec) |
N/A | 0.682 | 0.126 | 0.707 | 0.036 | 0.084 | 0.000 | 0.125 | 0.178 | 4.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 316 | 121 | 120 | 388 | 136 | 0 | 0 | 205 | 350 |
N.S. |
1 | 1.94 | 0.74 | 0.74 | 2.38 | 0.83 | 0.00 | 0.00 | 1.26 | 2.15 |
time (sec) |
N/A | 1.039 | 0.146 | 50.193 | 0.041 | 0.075 | 0.000 | 0.000 | 0.173 | 4.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 132 | 71 | 90 | 206 | 99 | 0 | 251 | 90 | 319 |
N.S. |
1 | 1.06 | 0.57 | 0.72 | 1.65 | 0.79 | 0.00 | 2.01 | 0.72 | 2.55 |
time (sec) |
N/A | 0.460 | 0.098 | 0.526 | 0.033 | 0.080 | 0.000 | 0.123 | 0.171 | 4.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 206 | 127 | 120 | 392 | 137 | 0 | 0 | 205 | 358 |
N.S. |
1 | 1.36 | 0.84 | 0.79 | 2.60 | 0.91 | 0.00 | 0.00 | 1.36 | 2.37 |
time (sec) |
N/A | 0.615 | 0.120 | 76.608 | 0.041 | 0.083 | 0.000 | 0.000 | 0.169 | 4.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 303 | 129 | 1305 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.55 | 0.66 | 6.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 2.378 | 0.457 | 261.635 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 385 | 127 | 3116 | 534 | 0 | 0 | 0 | 357 | 0 |
N.S. |
1 | 1.84 | 0.61 | 14.91 | 2.56 | 0.00 | 0.00 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 3.010 | 0.459 | 174.773 | 0.064 | 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 | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 264 | 135 | 120 | 437 | 140 | 0 | 341 | 205 | 414 |
N.S. |
1 | 1.38 | 0.70 | 0.62 | 2.28 | 0.73 | 0.00 | 1.78 | 1.07 | 2.16 |
time (sec) |
N/A | 0.857 | 0.145 | 342.845 | 0.043 | 0.077 | 0.000 | 0.126 | 0.168 | 6.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 420 | 107 | 142 | 657 | 161 | 0 | 0 | 150 | 831 |
N.S. |
1 | 1.95 | 0.50 | 0.66 | 3.06 | 0.75 | 0.00 | 0.00 | 0.70 | 3.87 |
time (sec) |
N/A | 1.840 | 0.146 | 349.190 | 0.051 | 0.076 | 0.000 | 0.000 | 0.166 | 6.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 239 | 148 | 848 | 422 | 140 | 0 | 342 | 205 | 414 |
N.S. |
1 | 1.27 | 0.79 | 4.51 | 2.24 | 0.74 | 0.00 | 1.82 | 1.09 | 2.20 |
time (sec) |
N/A | 0.733 | 0.115 | 1.484 | 0.063 | 0.071 | 0.000 | 0.128 | 0.160 | 5.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 283 | 111 | 150 | 663 | 166 | 0 | 0 | 150 | 736 |
N.S. |
1 | 1.39 | 0.55 | 0.74 | 3.27 | 0.82 | 0.00 | 0.00 | 0.74 | 3.63 |
time (sec) |
N/A | 1.140 | 0.301 | 12.401 | 0.083 | 0.076 | 0.000 | 0.000 | 0.161 | 5.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 484 | 189 | 1446 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.75 | 0.68 | 5.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 3.762 | 0.399 | 15.924 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 522 | 218 | 351 | 0 | 0 | 0 | 0 | 307 | 0 |
N.S. |
1 | 1.86 | 0.78 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 5.285 | 0.528 | 7.113 | 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(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 151 | 152 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.90 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.453 | 0.415 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 25 | 40 | 49 | 24 | 52 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.14 | 1.82 | 2.23 | 1.09 | 2.36 | 1.14 |
time (sec) |
N/A | 0.248 | 7.119 | 1.241 | 0.125 | 0.075 | 1.551 | 0.600 | 0.166 | 3.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 25 | 40 | 49 | 24 | 52 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.14 | 1.82 | 2.23 | 1.09 | 2.36 | 1.14 |
time (sec) |
N/A | 0.245 | 5.523 | 1.955 | 0.120 | 0.078 | 1.532 | 0.544 | 0.169 | 3.834 |
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 | 41 | 36 | 31 | 31 | 0 | 118 | 0 | 0 | 113 | 0 |
N.S. |
1 | 0.88 | 0.76 | 0.76 | 0.00 | 2.88 | 0.00 | 0.00 | 2.76 | 0.00 |
time (sec) |
N/A | 0.352 | 0.163 | 0.888 | 0.000 | 0.086 | 0.000 | 0.000 | 0.169 | 0.000 |
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 | 29 | 27 | 24 | 24 | 0 | 102 | 0 | 0 | 52 | 0 |
N.S. |
1 | 0.93 | 0.83 | 0.83 | 0.00 | 3.52 | 0.00 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.333 | 0.136 | 0.976 | 0.000 | 0.075 | 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 | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 22 | 24 | 0 | 88 | 0 | 0 | 52 | 0 |
N.S. |
1 | 0.93 | 0.81 | 0.89 | 0.00 | 3.26 | 0.00 | 0.00 | 1.93 | 0.00 |
time (sec) |
N/A | 0.332 | 0.134 | 0.950 | 0.000 | 0.074 | 0.000 | 0.000 | 0.173 | 0.000 |
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 | 29 | 27 | 24 | 24 | 0 | 102 | 0 | 0 | 50 | 0 |
N.S. |
1 | 0.93 | 0.83 | 0.83 | 0.00 | 3.52 | 0.00 | 0.00 | 1.72 | 0.00 |
time (sec) |
N/A | 0.314 | 0.129 | 0.661 | 0.000 | 0.085 | 0.000 | 0.000 | 0.163 | 0.000 |
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 | 41 | 36 | 33 | 31 | 0 | 118 | 0 | 0 | 48 | 0 |
N.S. |
1 | 0.88 | 0.80 | 0.76 | 0.00 | 2.88 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.314 | 0.090 | 0.793 | 0.000 | 0.087 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 25 | 39 | 49 | 24 | 49 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.14 | 1.77 | 2.23 | 1.09 | 2.23 | 1.14 |
time (sec) |
N/A | 0.239 | 0.924 | 1.947 | 0.115 | 0.078 | 2.113 | 0.446 | 0.167 | 3.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 151 | 40 | 56 | 24 | 60 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 6.86 | 1.82 | 2.55 | 1.09 | 2.73 | 1.14 |
time (sec) |
N/A | 3.229 | 7.504 | 0.129 | 0.137 | 0.081 | 2.194 | 0.165 | 0.192 | 3.954 |
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 | 53 | 55 | 49 | 62 | 0 | 232 | 0 | 0 | 395 | 0 |
N.S. |
1 | 1.04 | 0.92 | 1.17 | 0.00 | 4.38 | 0.00 | 0.00 | 7.45 | 0.00 |
time (sec) |
N/A | 0.491 | 0.187 | 1.512 | 0.000 | 0.082 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 172 | 80 | 54 | 0 | 231 | 0 | 0 | 60 | 0 |
N.S. |
1 | 3.13 | 1.45 | 0.98 | 0.00 | 4.20 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 1.793 | 0.140 | 1.526 | 0.000 | 0.087 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 97 | 56 | 38 | 0 | 164 | 0 | 0 | 392 | 0 |
N.S. |
1 | 2.37 | 1.37 | 0.93 | 0.00 | 4.00 | 0.00 | 0.00 | 9.56 | 0.00 |
time (sec) |
N/A | 0.808 | 0.204 | 1.418 | 0.000 | 0.082 | 0.000 | 0.000 | 0.167 | 0.000 |
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 | 53 | 87 | 75 | 54 | 0 | 225 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.64 | 1.42 | 1.02 | 0.00 | 4.25 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.948 | 0.126 | 1.314 | 0.000 | 0.082 | 0.000 | 0.000 | 0.167 | 0.000 |
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 | 49 | 52 | 43 | 60 | 0 | 222 | 0 | 0 | 208 | 0 |
N.S. |
1 | 1.06 | 0.88 | 1.22 | 0.00 | 4.53 | 0.00 | 0.00 | 4.24 | 0.00 |
time (sec) |
N/A | 0.434 | 0.133 | 1.523 | 0.000 | 0.083 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 153 | 39 | 56 | 24 | 57 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 6.95 | 1.77 | 2.55 | 1.09 | 2.59 | 1.14 |
time (sec) |
N/A | 2.462 | 3.235 | 1.812 | 0.142 | 0.078 | 2.818 | 0.162 | 0.176 | 3.894 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 206 | 60 | 90 | 0 | 256 | 0 | 0 | 441 | 0 |
N.S. |
1 | 2.06 | 0.60 | 0.90 | 0.00 | 2.56 | 0.00 | 0.00 | 4.41 | 0.00 |
time (sec) |
N/A | 2.112 | 0.207 | 1.367 | 0.000 | 0.089 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 270 | 66 | 82 | 0 | 267 | 0 | 0 | 479 | 0 |
N.S. |
1 | 2.52 | 0.62 | 0.77 | 0.00 | 2.50 | 0.00 | 0.00 | 4.48 | 0.00 |
time (sec) |
N/A | 2.377 | 0.219 | 1.300 | 0.000 | 0.095 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 229 | 56 | 51 | 0 | 193 | 0 | 0 | 453 | 0 |
N.S. |
1 | 2.66 | 0.65 | 0.59 | 0.00 | 2.24 | 0.00 | 0.00 | 5.27 | 0.00 |
time (sec) |
N/A | 2.307 | 0.175 | 1.378 | 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 | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 188 | 96 | 82 | 0 | 256 | 0 | 0 | 622 | 0 |
N.S. |
1 | 1.88 | 0.96 | 0.82 | 0.00 | 2.56 | 0.00 | 0.00 | 6.22 | 0.00 |
time (sec) |
N/A | 1.584 | 0.185 | 1.287 | 0.000 | 0.080 | 0.000 | 0.000 | 0.181 | 0.000 |
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 | 69 | 116 | 86 | 88 | 0 | 241 | 0 | 0 | 239 | 0 |
N.S. |
1 | 1.68 | 1.25 | 1.28 | 0.00 | 3.49 | 0.00 | 0.00 | 3.46 | 0.00 |
time (sec) |
N/A | 1.103 | 0.312 | 0.645 | 0.000 | 0.082 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 255 | 39 | 56 | 24 | 57 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 11.59 | 1.77 | 2.55 | 1.09 | 2.59 | 1.14 |
time (sec) |
N/A | 2.996 | 3.845 | 1.003 | 0.159 | 0.083 | 2.963 | 0.195 | 0.177 | 3.661 |
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 | 125 | 219 | 108 | 122 | 0 | 272 | 0 | 0 | 444 | 0 |
N.S. |
1 | 1.75 | 0.86 | 0.98 | 0.00 | 2.18 | 0.00 | 0.00 | 3.55 | 0.00 |
time (sec) |
N/A | 1.627 | 0.204 | 0.848 | 0.000 | 0.085 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 409 | 132 | 152 | 0 | 303 | 0 | 0 | 468 | 0 |
N.S. |
1 | 2.41 | 0.78 | 0.89 | 0.00 | 1.78 | 0.00 | 0.00 | 2.75 | 0.00 |
time (sec) |
N/A | 3.771 | 0.149 | 2.029 | 0.000 | 0.079 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 621 | 166 | 182 | 0 | 341 | 0 | 0 | 468 | 0 |
N.S. |
1 | 2.42 | 0.65 | 0.71 | 0.00 | 1.33 | 0.00 | 0.00 | 1.82 | 0.00 |
time (sec) |
N/A | 4.799 | 0.381 | 1.829 | 0.000 | 0.092 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 144 | 81 | 124 | 240 | 131 | 0 | 0 | 132 | 206 |
N.S. |
1 | 1.07 | 0.60 | 0.93 | 1.79 | 0.98 | 0.00 | 0.00 | 0.99 | 1.54 |
time (sec) |
N/A | 0.453 | 0.176 | 0.694 | 0.047 | 0.085 | 0.000 | 0.000 | 0.166 | 4.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 334 | 157 | 168 | 516 | 179 | 0 | 0 | 295 | 493 |
N.S. |
1 | 1.56 | 0.73 | 0.79 | 2.41 | 0.84 | 0.00 | 0.00 | 1.38 | 2.30 |
time (sec) |
N/A | 0.940 | 0.223 | 14.471 | 0.043 | 0.080 | 0.000 | 0.000 | 0.162 | 5.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 484 | 143 | 212 | 871 | 216 | 0 | 0 | 220 | 1041 |
N.S. |
1 | 1.66 | 0.49 | 0.73 | 2.99 | 0.74 | 0.00 | 0.00 | 0.76 | 3.58 |
time (sec) |
N/A | 2.281 | 0.091 | 7.473 | 0.062 | 0.093 | 0.000 | 0.000 | 0.164 | 5.800 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 226 | 257 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 0.90 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.556 | 0.483 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 23 | 47 | 22 | 23 | 60 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 2.14 | 1.00 | 1.05 | 2.73 | 1.05 |
time (sec) |
N/A | 0.228 | 7.554 | 0.344 | 0.118 | 0.081 | 1.508 | 0.552 | 0.176 | 4.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 23 | 47 | 22 | 23 | 60 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 2.14 | 1.00 | 1.05 | 2.73 | 1.05 |
time (sec) |
N/A | 0.242 | 16.259 | 1.172 | 0.132 | 0.082 | 1.484 | 0.586 | 0.175 | 4.397 |
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 | 55 | 47 | 40 | 40 | 0 | 220 | 0 | 0 | 200 | 0 |
N.S. |
1 | 0.85 | 0.73 | 0.73 | 0.00 | 4.00 | 0.00 | 0.00 | 3.64 | 0.00 |
time (sec) |
N/A | 0.367 | 0.116 | 0.914 | 0.000 | 0.089 | 0.000 | 0.000 | 0.182 | 0.000 |
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 | 43 | 38 | 33 | 33 | 0 | 200 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.88 | 0.77 | 0.77 | 0.00 | 4.65 | 0.00 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.357 | 0.124 | 0.885 | 0.000 | 0.092 | 0.000 | 0.000 | 0.169 | 0.000 |
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 | 55 | 47 | 40 | 40 | 0 | 216 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.85 | 0.73 | 0.73 | 0.00 | 3.93 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.367 | 0.099 | 0.879 | 0.000 | 0.084 | 0.000 | 0.000 | 0.170 | 0.000 |
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 | 29 | 27 | 24 | 24 | 0 | 136 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.93 | 0.83 | 0.83 | 0.00 | 4.69 | 0.00 | 0.00 | 2.07 | 0.00 |
time (sec) |
N/A | 0.346 | 0.107 | 0.742 | 0.000 | 0.082 | 0.000 | 0.000 | 0.168 | 0.000 |
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 | 55 | 47 | 55 | 40 | 0 | 216 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.85 | 1.00 | 0.73 | 0.00 | 3.93 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.364 | 0.207 | 0.871 | 0.000 | 0.086 | 0.000 | 0.000 | 0.166 | 0.000 |
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 | 43 | 38 | 43 | 33 | 0 | 200 | 0 | 0 | 58 | 0 |
N.S. |
1 | 0.88 | 1.00 | 0.77 | 0.00 | 4.65 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.332 | 0.212 | 0.725 | 0.000 | 0.080 | 0.000 | 0.000 | 0.166 | 0.000 |
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 | 55 | 47 | 40 | 40 | 0 | 216 | 0 | 0 | 56 | 0 |
N.S. |
1 | 0.85 | 0.73 | 0.73 | 0.00 | 3.93 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.342 | 0.187 | 0.910 | 0.000 | 0.086 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 23 | 44 | 22 | 23 | 58 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 2.00 | 1.00 | 1.05 | 2.64 | 1.05 |
time (sec) |
N/A | 0.232 | 1.011 | 0.229 | 0.130 | 0.080 | 2.190 | 0.423 | 0.164 | 3.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 23 | 46 | 24 | 23 | 60 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 2.09 | 1.09 | 1.05 | 2.73 | 1.05 |
time (sec) |
N/A | 0.240 | 2.222 | 0.416 | 0.116 | 0.085 | 2.099 | 0.457 | 0.165 | 3.572 |
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 | 67 | 120 | 56 | 78 | 0 | 418 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.79 | 0.84 | 1.16 | 0.00 | 6.24 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.960 | 0.137 | 1.565 | 0.000 | 0.099 | 0.000 | 0.000 | 0.168 | 0.000 |
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 | 66 | 63 | 56 | 86 | 0 | 413 | 0 | 0 | 316 | 0 |
N.S. |
1 | 0.95 | 0.85 | 1.30 | 0.00 | 6.26 | 0.00 | 0.00 | 4.79 | 0.00 |
time (sec) |
N/A | 0.442 | 0.252 | 1.710 | 0.000 | 0.085 | 0.000 | 0.000 | 0.163 | 0.000 |
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 | 114 | 227 | 73 | 121 | 0 | 447 | 0 | 0 | 954 | 0 |
N.S. |
1 | 1.99 | 0.64 | 1.06 | 0.00 | 3.92 | 0.00 | 0.00 | 8.37 | 0.00 |
time (sec) |
N/A | 1.364 | 0.236 | 1.726 | 0.000 | 0.083 | 0.000 | 0.000 | 0.169 | 0.000 |
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 | 89 | 149 | 83 | 131 | 0 | 435 | 0 | 0 | 365 | 0 |
N.S. |
1 | 1.67 | 0.93 | 1.47 | 0.00 | 4.89 | 0.00 | 0.00 | 4.10 | 0.00 |
time (sec) |
N/A | 1.138 | 0.132 | 0.853 | 0.000 | 0.088 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 218 | 79 | 118 | 163 | 91 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.57 | 0.57 | 0.85 | 1.17 | 0.65 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.717 | 0.068 | 1.759 | 0.113 | 0.098 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 234 | 160 | 173 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.19 | 0.81 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.652 | 0.364 | 0.773 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 109 | 60 | 97 | 88 | 72 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.25 | 0.69 | 1.11 | 1.01 | 0.83 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.423 | 0.050 | 0.754 | 0.112 | 0.106 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 150 | 125 | 152 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.03 | 0.86 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.385 | 0.197 | 0.740 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 29 | 79 | 30 | 58 | 0 | 47 | 21 | 0 |
N.S. |
1 | 1.00 | 0.91 | 2.47 | 0.94 | 1.81 | 0.00 | 1.47 | 0.66 | 0.00 |
time (sec) |
N/A | 0.228 | 0.025 | 0.635 | 0.105 | 0.097 | 0.000 | 0.137 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 76 | 113 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.80 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.238 | 0.081 | 0.707 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 57 | 99 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.76 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.270 | 0.099 | 0.791 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 48 | 70 | 51 | 58 | 0 | 111 | 23 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.67 | 1.21 | 1.38 | 0.00 | 2.64 | 0.55 | 0.00 |
time (sec) |
N/A | 0.277 | 0.039 | 0.913 | 0.117 | 0.104 | 0.000 | 0.146 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 130 | 126 | 139 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.95 | 0.92 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.426 | 0.522 | 0.911 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 321 | 160 | 173 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.57 | 0.78 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.098 | 0.322 | 0.503 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 158 | 188 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.98 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.098 | 0.571 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 126 | 104 | 149 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.05 | 0.87 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.372 | 0.190 | 0.477 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 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 | 103 | 90 | 119 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.87 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.472 | 0.103 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 80 | 100 | 158 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.18 | 1.47 | 2.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.506 | 0.103 | 0.461 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 104 | 89 | 129 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.99 | 0.85 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.434 | 0.394 | 0.477 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 157 | 188 | 229 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.03 | 1.24 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.124 | 0.883 | 0.508 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 317 | 215 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.45 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.691 | 0.713 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 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 | 305 | 303 | 570 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.99 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.609 | 3.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 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 | 128 | 117 | 157 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.91 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.628 | 0.165 | 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 | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 138 | 451 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.90 | 2.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.598 | 0.302 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 122 | 146 | 215 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.20 | 1.43 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.645 | 0.135 | 0.537 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 107 | 131 | 188 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.09 | 1.34 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.710 | 0.307 | 0.550 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 264 | 301 | 384 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.99 | 1.13 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.629 | 6.348 | 0.567 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 41 | 24 | 22 | 46 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.86 | 1.09 | 1.00 | 2.09 | 1.00 |
time (sec) |
N/A | 0.251 | 2.345 | 2.191 | 0.222 | 0.085 | 46.297 | 0.201 | 0.195 | 3.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 85 | 76 | 123 | 96 | 94 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.15 | 1.03 | 1.66 | 1.30 | 1.27 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.421 | 0.046 | 1.129 | 0.113 | 0.094 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 143 | 121 | 190 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.04 | 0.88 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.400 | 0.241 | 1.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 27 | 38 | 39 | 51 | 0 | 61 | 44 | 0 |
N.S. |
1 | 1.00 | 0.63 | 0.88 | 0.91 | 1.19 | 0.00 | 1.42 | 1.02 | 0.00 |
time (sec) |
N/A | 0.243 | 0.031 | 0.645 | 0.027 | 0.092 | 0.000 | 0.143 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 27 | 38 | 36 | 47 | 0 | 59 | 43 | 0 |
N.S. |
1 | 1.00 | 0.68 | 0.95 | 0.90 | 1.18 | 0.00 | 1.48 | 1.08 | 0.00 |
time (sec) |
N/A | 0.211 | 0.024 | 0.737 | 0.034 | 0.095 | 0.000 | 0.156 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 122 | 97 | 157 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.09 | 0.87 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.569 | 0.180 | 1.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 86 | 89 | 182 | 84 | 107 | 0 | 155 | 46 | 0 |
N.S. |
1 | 1.05 | 1.09 | 2.22 | 1.02 | 1.30 | 0.00 | 1.89 | 0.56 | 0.00 |
time (sec) |
N/A | 0.553 | 0.087 | 1.283 | 0.032 | 0.098 | 0.000 | 0.156 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 256 | 182 | 347 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.43 | 1.02 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.237 | 1.133 | 1.406 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 43 | 26 | 24 | 48 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.79 | 1.08 | 1.00 | 2.00 | 1.00 |
time (sec) |
N/A | 0.277 | 0.476 | 0.819 | 0.296 | 0.090 | 43.210 | 0.156 | 0.202 | 3.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 206 | 165 | 219 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.11 | 0.89 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.796 | 0.305 | 0.505 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 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 | 171 | 159 | 193 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 0.93 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.967 | 0.278 | 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 | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 70 | 34 | 45 | 62 | 69 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.03 | 0.50 | 0.66 | 0.91 | 1.01 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.358 | 0.044 | 0.431 | 0.032 | 0.099 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 38 | 49 | 57 | 69 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.60 | 0.78 | 0.90 | 1.10 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.241 | 0.033 | 0.437 | 0.034 | 0.100 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 155 | 159 | 232 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.22 | 1.25 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.177 | 0.216 | 0.509 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |