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 | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 76 | 46 | 45 | 135 | 135 | 143 | 44 | 134 | 136 |
N.S. |
1 | 1.06 | 0.64 | 0.62 | 1.88 | 1.88 | 1.99 | 0.61 | 1.86 | 1.89 |
time (sec) |
N/A | 0.202 | 0.009 | 0.306 | 0.043 | 0.062 | 0.667 | 0.121 | 0.212 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 57 | 35 | 34 | 124 | 124 | 131 | 33 | 123 | 125 |
N.S. |
1 | 1.08 | 0.66 | 0.64 | 2.34 | 2.34 | 2.47 | 0.62 | 2.32 | 2.36 |
time (sec) |
N/A | 0.186 | 0.010 | 0.296 | 0.035 | 0.061 | 0.615 | 0.119 | 0.226 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 38 | 24 | 23 | 113 | 113 | 119 | 22 | 112 | 114 |
N.S. |
1 | 1.12 | 0.71 | 0.68 | 3.32 | 3.32 | 3.50 | 0.65 | 3.29 | 3.35 |
time (sec) |
N/A | 0.166 | 0.007 | 0.302 | 0.043 | 0.062 | 0.645 | 0.125 | 0.243 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 14 | 103 | 110 | 14 | 102 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 6.44 | 6.88 | 0.88 | 6.38 | 0.88 |
time (sec) |
N/A | 0.130 | 0.002 | 0.310 | 0.030 | 0.061 | 0.659 | 0.122 | 0.204 | 0.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 167 | 120 | 123 | 214 | 398 | 223 | 136 | 485 | 210 |
N.S. |
1 | 1.01 | 0.72 | 0.74 | 1.29 | 2.40 | 1.34 | 0.82 | 2.92 | 1.27 |
time (sec) |
N/A | 0.296 | 0.053 | 0.310 | 0.045 | 0.071 | 0.916 | 0.120 | 0.239 | 0.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 184 | 136 | 142 | 231 | 427 | 245 | 159 | 511 | 229 |
N.S. |
1 | 1.00 | 0.74 | 0.77 | 1.26 | 2.32 | 1.33 | 0.86 | 2.78 | 1.24 |
time (sec) |
N/A | 0.339 | 0.075 | 0.342 | 0.069 | 0.075 | 1.369 | 0.119 | 0.230 | 0.627 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 217 | 151 | 155 | 246 | 442 | 260 | 174 | 526 | 243 |
N.S. |
1 | 1.00 | 0.70 | 0.71 | 1.13 | 2.04 | 1.20 | 0.80 | 2.42 | 1.12 |
time (sec) |
N/A | 0.382 | 0.058 | 0.344 | 0.057 | 0.076 | 1.010 | 0.125 | 0.200 | 1.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 224 | 162 | 165 | 257 | 453 | 270 | 187 | 537 | 255 |
N.S. |
1 | 0.99 | 0.72 | 0.73 | 1.14 | 2.00 | 1.19 | 0.83 | 2.38 | 1.13 |
time (sec) |
N/A | 0.405 | 0.070 | 0.350 | 0.058 | 0.075 | 0.971 | 0.127 | 0.205 | 1.128 |
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 | 238 | 298 | 166 | 151 | 248 | 718 | 314 | 162 | 488 | 241 |
N.S. |
1 | 1.25 | 0.70 | 0.63 | 1.04 | 3.02 | 1.32 | 0.68 | 2.05 | 1.01 |
time (sec) |
N/A | 0.390 | 0.053 | 0.349 | 0.139 | 0.081 | 1.087 | 0.121 | 0.244 | 0.465 |
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 | 225 | 285 | 155 | 140 | 236 | 692 | 299 | 150 | 475 | 231 |
N.S. |
1 | 1.27 | 0.69 | 0.62 | 1.05 | 3.08 | 1.33 | 0.67 | 2.11 | 1.03 |
time (sec) |
N/A | 0.380 | 0.050 | 0.326 | 0.122 | 0.077 | 1.065 | 0.124 | 0.219 | 0.492 |
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 | 211 | 274 | 144 | 128 | 222 | 664 | 274 | 131 | 461 | 218 |
N.S. |
1 | 1.30 | 0.68 | 0.61 | 1.05 | 3.15 | 1.30 | 0.62 | 2.18 | 1.03 |
time (sec) |
N/A | 0.324 | 0.052 | 0.336 | 0.127 | 0.077 | 0.937 | 0.120 | 0.185 | 0.436 |
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 | 197 | 261 | 134 | 124 | 213 | 650 | 277 | 122 | 456 | 210 |
N.S. |
1 | 1.32 | 0.68 | 0.63 | 1.08 | 3.30 | 1.41 | 0.62 | 2.31 | 1.07 |
time (sec) |
N/A | 0.296 | 0.050 | 0.385 | 0.131 | 0.077 | 0.810 | 0.124 | 0.216 | 0.481 |
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 | 198 | 259 | 138 | 124 | 219 | 654 | 289 | 128 | 456 | 207 |
N.S. |
1 | 1.31 | 0.70 | 0.63 | 1.11 | 3.30 | 1.46 | 0.65 | 2.30 | 1.05 |
time (sec) |
N/A | 0.293 | 0.046 | 0.368 | 0.121 | 0.077 | 0.757 | 0.129 | 0.222 | 0.230 |
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 | 199 | 257 | 138 | 122 | 221 | 654 | 291 | 128 | 456 | 205 |
N.S. |
1 | 1.29 | 0.69 | 0.61 | 1.11 | 3.29 | 1.46 | 0.64 | 2.29 | 1.03 |
time (sec) |
N/A | 0.290 | 0.040 | 0.362 | 0.122 | 0.076 | 0.734 | 0.125 | 0.203 | 0.257 |
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 | 200 | 255 | 138 | 122 | 221 | 654 | 291 | 128 | 456 | 205 |
N.S. |
1 | 1.28 | 0.69 | 0.61 | 1.10 | 3.27 | 1.46 | 0.64 | 2.28 | 1.02 |
time (sec) |
N/A | 0.290 | 0.045 | 0.378 | 0.121 | 0.077 | 0.692 | 0.129 | 0.191 | 0.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 253 | 138 | 122 | 221 | 654 | 291 | 128 | 456 | 205 |
N.S. |
1 | 1.26 | 0.69 | 0.61 | 1.10 | 3.25 | 1.45 | 0.64 | 2.27 | 1.02 |
time (sec) |
N/A | 0.287 | 0.044 | 0.386 | 0.125 | 0.080 | 0.616 | 0.123 | 0.224 | 0.253 |
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 | 202 | 251 | 138 | 122 | 221 | 654 | 291 | 128 | 456 | 204 |
N.S. |
1 | 1.24 | 0.68 | 0.60 | 1.09 | 3.24 | 1.44 | 0.63 | 2.26 | 1.01 |
time (sec) |
N/A | 0.286 | 0.037 | 0.397 | 0.128 | 0.080 | 0.628 | 0.125 | 0.190 | 0.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 249 | 138 | 122 | 221 | 654 | 291 | 128 | 456 | 204 |
N.S. |
1 | 1.23 | 0.68 | 0.60 | 1.09 | 3.22 | 1.43 | 0.63 | 2.25 | 1.00 |
time (sec) |
N/A | 0.282 | 0.038 | 0.374 | 0.164 | 0.081 | 0.550 | 0.125 | 0.196 | 0.245 |
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 | 204 | 247 | 138 | 122 | 221 | 654 | 291 | 128 | 456 | 204 |
N.S. |
1 | 1.21 | 0.68 | 0.60 | 1.08 | 3.21 | 1.43 | 0.63 | 2.24 | 1.00 |
time (sec) |
N/A | 0.274 | 0.040 | 0.369 | 0.129 | 0.078 | 0.533 | 0.123 | 0.203 | 0.251 |
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 | 205 | 245 | 138 | 124 | 219 | 654 | 286 | 128 | 456 | 206 |
N.S. |
1 | 1.20 | 0.67 | 0.60 | 1.07 | 3.19 | 1.40 | 0.62 | 2.22 | 1.00 |
time (sec) |
N/A | 0.272 | 0.036 | 0.362 | 0.157 | 0.074 | 0.534 | 0.124 | 0.209 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 245 | 131 | 150 | 212 | 650 | 272 | 122 | 456 | 209 |
N.S. |
1 | 1.35 | 0.72 | 0.83 | 1.17 | 3.59 | 1.50 | 0.67 | 2.52 | 1.15 |
time (sec) |
N/A | 0.274 | 0.057 | 0.356 | 0.120 | 0.076 | 0.562 | 0.127 | 0.231 | 0.165 |
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 | 198 | 277 | 147 | 131 | 225 | 664 | 282 | 134 | 464 | 220 |
N.S. |
1 | 1.40 | 0.74 | 0.66 | 1.14 | 3.35 | 1.42 | 0.68 | 2.34 | 1.11 |
time (sec) |
N/A | 0.309 | 0.058 | 0.380 | 0.131 | 0.082 | 0.706 | 0.121 | 0.198 | 0.636 |
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 | 294 | 157 | 141 | 240 | 700 | 304 | 148 | 480 | 234 |
N.S. |
1 | 1.30 | 0.69 | 0.62 | 1.06 | 3.08 | 1.34 | 0.65 | 2.11 | 1.03 |
time (sec) |
N/A | 0.330 | 0.052 | 0.391 | 0.130 | 0.088 | 0.756 | 0.119 | 0.234 | 0.657 |
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 | 240 | 311 | 169 | 153 | 251 | 726 | 316 | 159 | 493 | 246 |
N.S. |
1 | 1.30 | 0.70 | 0.64 | 1.05 | 3.02 | 1.32 | 0.66 | 2.05 | 1.02 |
time (sec) |
N/A | 0.354 | 0.054 | 0.386 | 0.131 | 0.089 | 0.776 | 0.121 | 0.248 | 1.281 |
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 | 19 | 15 | 14 | 17 | 13 | 12 | 18 | 13 | 14 |
N.S. |
1 | 1.27 | 1.00 | 0.93 | 1.13 | 0.87 | 0.80 | 1.20 | 0.87 | 0.93 |
time (sec) |
N/A | 0.133 | 0.004 | 0.337 | 0.031 | 0.060 | 0.077 | 0.123 | 0.177 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 20 | 18 | 16 | 17 | 15 | 12 | 18 | 25 | 16 |
N.S. |
1 | 1.11 | 1.00 | 0.89 | 0.94 | 0.83 | 0.67 | 1.00 | 1.39 | 0.89 |
time (sec) |
N/A | 0.136 | 0.004 | 0.290 | 0.026 | 0.059 | 0.085 | 0.122 | 0.192 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 26 | 23 | 24 | 28 | 22 | 32 | 28 | 22 |
N.S. |
1 | 1.04 | 1.00 | 0.88 | 0.92 | 1.08 | 0.85 | 1.23 | 1.08 | 0.85 |
time (sec) |
N/A | 0.159 | 0.005 | 0.307 | 0.028 | 0.061 | 0.123 | 0.119 | 0.228 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 27 | 23 | 24 | 28 | 22 | 32 | 41 | 22 |
N.S. |
1 | 0.96 | 1.00 | 0.85 | 0.89 | 1.04 | 0.81 | 1.19 | 1.52 | 0.81 |
time (sec) |
N/A | 0.164 | 0.003 | 0.311 | 0.050 | 0.062 | 0.139 | 0.122 | 0.211 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 25 | 25 | 28 | 40 | 22 | 36 | 54 | 24 |
N.S. |
1 | 1.00 | 0.89 | 0.89 | 1.00 | 1.43 | 0.79 | 1.29 | 1.93 | 0.86 |
time (sec) |
N/A | 0.157 | 0.008 | 0.312 | 0.034 | 0.061 | 0.115 | 0.119 | 0.203 | 0.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 26 | 25 | 28 | 40 | 22 | 36 | 74 | 26 |
N.S. |
1 | 1.00 | 0.87 | 0.83 | 0.93 | 1.33 | 0.73 | 1.20 | 2.47 | 0.87 |
time (sec) |
N/A | 0.166 | 0.008 | 0.320 | 0.038 | 0.063 | 0.113 | 0.121 | 0.244 | 0.039 |
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 | 10 | 9 | 8 | 8 | 7 | 9 | 13 | 8 |
N.S. |
1 | 1.00 | 0.83 | 0.75 | 0.67 | 0.67 | 0.58 | 0.75 | 1.08 | 0.67 |
time (sec) |
N/A | 0.127 | 0.001 | 0.290 | 0.038 | 0.061 | 0.028 | 0.125 | 0.207 | 0.048 |
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 | 16 | 15 | 21 | 12 | 15 | 22 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 1.11 | 0.63 | 0.79 | 1.16 | 0.89 |
time (sec) |
N/A | 0.134 | 0.006 | 0.362 | 0.110 | 0.061 | 0.037 | 0.115 | 0.200 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 17 | 16 | 16 | 17 | 16 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.73 | 0.73 | 0.77 | 0.73 | 0.77 | 0.77 |
time (sec) |
N/A | 0.143 | 0.001 | 0.318 | 0.025 | 0.057 | 0.015 | 0.122 | 0.203 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 11 | 10 | 9 | 24 | 22 | 9 | 24 | 9 |
N.S. |
1 | 1.00 | 0.85 | 0.77 | 0.69 | 1.85 | 1.69 | 0.69 | 1.85 | 0.69 |
time (sec) |
N/A | 0.129 | 0.002 | 0.293 | 0.032 | 0.060 | 0.047 | 0.121 | 0.256 | 0.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 81 | 11 | 13 | 57 | 24 | 22 | 57 | 24 | 9 |
N.S. |
1 | 6.23 | 0.85 | 1.00 | 4.38 | 1.85 | 1.69 | 4.38 | 1.85 | 0.69 |
time (sec) |
N/A | 0.184 | 0.001 | 0.830 | 0.031 | 0.060 | 0.156 | 0.121 | 0.214 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 24 | 25 | 23 | 22 | 26 | 41 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.89 | 0.82 | 0.79 | 0.93 | 1.46 | 0.82 |
time (sec) |
N/A | 0.158 | 0.005 | 0.280 | 0.034 | 0.059 | 0.085 | 0.125 | 0.184 | 0.054 |
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 | 31 | 31 | 31 | 27 | 42 | 80 | 49 | 29 | 44 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 1.35 | 2.58 | 1.58 | 0.94 | 1.42 | 0.74 |
time (sec) |
N/A | 0.140 | 0.006 | 0.295 | 0.105 | 0.069 | 0.078 | 0.118 | 0.210 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 15 | 15 | 12 | 16 | 33 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 0.94 | 0.75 | 1.00 | 2.06 | 0.94 |
time (sec) |
N/A | 0.128 | 0.003 | 0.271 | 0.024 | 0.060 | 0.062 | 0.127 | 0.205 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 16 | 31 | 68 | 46 | 18 | 38 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 1.29 | 2.83 | 1.92 | 0.75 | 1.58 | 0.67 |
time (sec) |
N/A | 0.134 | 0.002 | 0.266 | 0.105 | 0.068 | 0.077 | 0.119 | 0.203 | 0.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 23 | 22 | 25 | 20 | 15 | 26 | 37 | 21 |
N.S. |
1 | 1.17 | 1.00 | 0.96 | 1.09 | 0.87 | 0.65 | 1.13 | 1.61 | 0.91 |
time (sec) |
N/A | 0.138 | 0.005 | 0.279 | 0.026 | 0.064 | 0.124 | 0.120 | 0.196 | 0.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 29 | 44 | 82 | 58 | 31 | 48 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.33 | 2.48 | 1.76 | 0.94 | 1.45 | 0.76 |
time (sec) |
N/A | 0.138 | 0.008 | 0.326 | 0.104 | 0.067 | 0.099 | 0.120 | 0.214 | 0.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 37 | 35 | 32 | 35 | 33 | 31 | 43 | 55 | 31 |
N.S. |
1 | 1.06 | 1.00 | 0.91 | 1.00 | 0.94 | 0.89 | 1.23 | 1.57 | 0.89 |
time (sec) |
N/A | 0.162 | 0.007 | 0.286 | 0.025 | 0.063 | 0.140 | 0.116 | 0.220 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 29 | 32 | 35 | 42 | 29 | 53 | 83 | 32 |
N.S. |
1 | 0.94 | 0.83 | 0.91 | 1.00 | 1.20 | 0.83 | 1.51 | 2.37 | 0.91 |
time (sec) |
N/A | 0.162 | 0.009 | 0.280 | 0.026 | 0.063 | 0.117 | 0.117 | 0.213 | 0.162 |
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 | 46 | 46 | 47 | 37 | 52 | 127 | 71 | 39 | 102 | 34 |
N.S. |
1 | 1.00 | 1.02 | 0.80 | 1.13 | 2.76 | 1.54 | 0.85 | 2.22 | 0.74 |
time (sec) |
N/A | 0.145 | 0.019 | 0.295 | 0.106 | 0.067 | 0.113 | 0.123 | 0.226 | 0.115 |
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 | 17 | 17 | 17 | 16 | 16 | 16 | 15 | 16 | 18 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 0.94 | 0.88 | 0.94 | 1.06 | 0.88 |
time (sec) |
N/A | 0.127 | 0.002 | 0.275 | 0.037 | 0.058 | 0.092 | 0.124 | 0.251 | 0.022 |
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 | 46 | 46 | 47 | 37 | 52 | 126 | 71 | 39 | 102 | 34 |
N.S. |
1 | 1.00 | 1.02 | 0.80 | 1.13 | 2.74 | 1.54 | 0.85 | 2.22 | 0.74 |
time (sec) |
N/A | 0.144 | 0.003 | 0.274 | 0.106 | 0.067 | 0.119 | 0.127 | 0.218 | 0.155 |
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 | 40 | 41 | 35 | 37 | 41 | 53 | 34 | 51 | 96 | 36 |
N.S. |
1 | 1.02 | 0.88 | 0.92 | 1.02 | 1.32 | 0.85 | 1.28 | 2.40 | 0.90 |
time (sec) |
N/A | 0.166 | 0.011 | 0.283 | 0.033 | 0.065 | 0.220 | 0.122 | 0.204 | 0.069 |
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 | 55 | 61 | 56 | 45 | 65 | 140 | 83 | 50 | 113 | 45 |
N.S. |
1 | 1.11 | 1.02 | 0.82 | 1.18 | 2.55 | 1.51 | 0.91 | 2.05 | 0.82 |
time (sec) |
N/A | 0.161 | 0.024 | 0.309 | 0.107 | 0.069 | 0.158 | 0.114 | 0.225 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 53 | 44 | 53 | 57 | 80 | 49 | 56 | 127 | 55 |
N.S. |
1 | 1.02 | 0.85 | 1.02 | 1.10 | 1.54 | 0.94 | 1.08 | 2.44 | 1.06 |
time (sec) |
N/A | 0.182 | 0.022 | 0.306 | 0.026 | 0.064 | 0.201 | 0.114 | 0.236 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 25 | 24 | 38 | 38 | 36 | 26 | 28 | 37 |
N.S. |
1 | 1.00 | 1.25 | 1.20 | 1.90 | 1.90 | 1.80 | 1.30 | 1.40 | 1.85 |
time (sec) |
N/A | 0.136 | 0.007 | 0.286 | 0.047 | 0.058 | 0.125 | 0.126 | 0.224 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 72 | 56 | 50 | 76 | 188 | 105 | 53 | 176 | 54 |
N.S. |
1 | 1.07 | 0.84 | 0.75 | 1.13 | 2.81 | 1.57 | 0.79 | 2.63 | 0.81 |
time (sec) |
N/A | 0.166 | 0.020 | 0.296 | 0.107 | 0.070 | 0.162 | 0.124 | 0.193 | 0.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 16 | 26 | 26 | 16 | 25 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 1.53 | 1.53 | 0.94 | 1.47 | 1.53 |
time (sec) |
N/A | 0.129 | 0.002 | 0.283 | 0.026 | 0.055 | 0.124 | 0.125 | 0.219 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 72 | 56 | 59 | 73 | 188 | 99 | 49 | 178 | 55 |
N.S. |
1 | 1.12 | 0.88 | 0.92 | 1.14 | 2.94 | 1.55 | 0.77 | 2.78 | 0.86 |
time (sec) |
N/A | 0.162 | 0.003 | 0.276 | 0.109 | 0.069 | 0.165 | 0.122 | 0.222 | 0.185 |
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 | 57 | 58 | 45 | 48 | 62 | 92 | 56 | 63 | 174 | 57 |
N.S. |
1 | 1.02 | 0.79 | 0.84 | 1.09 | 1.61 | 0.98 | 1.11 | 3.05 | 1.00 |
time (sec) |
N/A | 0.186 | 0.022 | 0.290 | 0.038 | 0.062 | 0.217 | 0.127 | 0.190 | 0.162 |
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 | 74 | 89 | 69 | 54 | 86 | 202 | 107 | 61 | 187 | 66 |
N.S. |
1 | 1.20 | 0.93 | 0.73 | 1.16 | 2.73 | 1.45 | 0.82 | 2.53 | 0.89 |
time (sec) |
N/A | 0.176 | 0.029 | 0.339 | 0.104 | 0.072 | 0.247 | 0.125 | 0.225 | 0.111 |
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 | 69 | 72 | 60 | 65 | 79 | 121 | 78 | 84 | 204 | 76 |
N.S. |
1 | 1.04 | 0.87 | 0.94 | 1.14 | 1.75 | 1.13 | 1.22 | 2.96 | 1.10 |
time (sec) |
N/A | 0.201 | 0.034 | 0.300 | 0.039 | 0.063 | 0.252 | 0.119 | 0.232 | 0.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 40 | 25 | 24 | 60 | 60 | 60 | 39 | 57 | 59 |
N.S. |
1 | 1.11 | 0.69 | 0.67 | 1.67 | 1.67 | 1.67 | 1.08 | 1.58 | 1.64 |
time (sec) |
N/A | 0.168 | 0.008 | 0.290 | 0.031 | 0.060 | 0.224 | 0.120 | 0.233 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 124 | 81 | 70 | 124 | 324 | 160 | 77 | 328 | 96 |
N.S. |
1 | 1.14 | 0.74 | 0.64 | 1.14 | 2.97 | 1.47 | 0.71 | 3.01 | 0.88 |
time (sec) |
N/A | 0.198 | 0.033 | 0.326 | 0.113 | 0.072 | 0.289 | 0.123 | 0.196 | 0.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 16 | 48 | 49 | 16 | 47 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 2.82 | 2.88 | 0.94 | 2.76 | 2.82 |
time (sec) |
N/A | 0.134 | 0.002 | 0.293 | 0.027 | 0.060 | 0.217 | 0.125 | 0.227 | 0.131 |
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 | 100 | 124 | 79 | 92 | 117 | 320 | 146 | 71 | 328 | 99 |
N.S. |
1 | 1.24 | 0.79 | 0.92 | 1.17 | 3.20 | 1.46 | 0.71 | 3.28 | 0.99 |
time (sec) |
N/A | 0.189 | 0.027 | 0.327 | 0.105 | 0.068 | 0.276 | 0.123 | 0.211 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 92 | 67 | 70 | 106 | 180 | 104 | 85 | 332 | 101 |
N.S. |
1 | 1.01 | 0.74 | 0.77 | 1.16 | 1.98 | 1.14 | 0.93 | 3.65 | 1.11 |
time (sec) |
N/A | 0.212 | 0.021 | 0.302 | 0.051 | 0.067 | 0.350 | 0.124 | 0.224 | 0.170 |
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 | 112 | 145 | 92 | 76 | 130 | 334 | 155 | 83 | 337 | 110 |
N.S. |
1 | 1.29 | 0.82 | 0.68 | 1.16 | 2.98 | 1.38 | 0.74 | 3.01 | 0.98 |
time (sec) |
N/A | 0.220 | 0.033 | 0.345 | 0.111 | 0.072 | 0.415 | 0.124 | 0.194 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 108 | 83 | 87 | 123 | 209 | 126 | 106 | 364 | 120 |
N.S. |
1 | 1.02 | 0.78 | 0.82 | 1.16 | 1.97 | 1.19 | 1.00 | 3.43 | 1.13 |
time (sec) |
N/A | 0.238 | 0.040 | 0.308 | 0.045 | 0.064 | 0.438 | 0.127 | 0.225 | 0.303 |
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 | 21 | 21 | 21 | 14 | 13 | 18 | 19 | 13 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.62 | 0.86 | 0.90 | 0.62 | 0.81 | 0.71 |
time (sec) |
N/A | 0.141 | 0.011 | 0.243 | 0.031 | 0.062 | 0.401 | 0.123 | 0.217 | 0.135 |
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 | 21 | 21 | 19 | 14 | 13 | 18 | 19 | 13 | 17 | 15 |
N.S. |
1 | 1.00 | 0.90 | 0.67 | 0.62 | 0.86 | 0.90 | 0.62 | 0.81 | 0.71 |
time (sec) |
N/A | 0.142 | 0.010 | 0.236 | 0.051 | 0.062 | 0.261 | 0.123 | 0.206 | 0.031 |
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 | 21 | 21 | 21 | 14 | 13 | 18 | 19 | 13 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.62 | 0.86 | 0.90 | 0.62 | 0.81 | 0.71 |
time (sec) |
N/A | 0.143 | 0.010 | 0.256 | 0.031 | 0.061 | 0.157 | 0.122 | 0.199 | 0.029 |
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 | 21 | 21 | 21 | 14 | 13 | 16 | 19 | 13 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.62 | 0.76 | 0.90 | 0.62 | 0.71 | 0.71 |
time (sec) |
N/A | 0.143 | 0.010 | 0.109 | 0.044 | 0.060 | 0.369 | 0.123 | 0.255 | 0.035 |
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 | 20 | 14 | 13 | 14 | 17 | 13 | 13 | 14 |
N.S. |
1 | 1.00 | 1.05 | 0.74 | 0.68 | 0.74 | 0.89 | 0.68 | 0.68 | 0.74 |
time (sec) |
N/A | 0.143 | 0.010 | 0.114 | 0.046 | 0.063 | 0.078 | 0.123 | 0.220 | 0.033 |
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 | 14 | 13 | 14 | 17 | 13 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.68 | 0.74 | 0.89 | 0.68 | 0.79 | 0.79 |
time (sec) |
N/A | 0.142 | 0.012 | 0.105 | 0.025 | 0.066 | 0.162 | 0.121 | 0.198 | 0.031 |
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 | 17 | 14 | 13 | 15 | 17 | 13 | 19 | 15 |
N.S. |
1 | 1.00 | 0.89 | 0.74 | 0.68 | 0.79 | 0.89 | 0.68 | 1.00 | 0.79 |
time (sec) |
N/A | 0.140 | 0.012 | 0.107 | 0.025 | 0.061 | 0.262 | 0.123 | 0.239 | 0.035 |
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 | 17 | 14 | 13 | 13 | 19 | 13 | 19 | 15 |
N.S. |
1 | 1.00 | 0.89 | 0.74 | 0.68 | 0.68 | 1.00 | 0.68 | 1.00 | 0.79 |
time (sec) |
N/A | 0.141 | 0.014 | 0.125 | 0.032 | 0.064 | 0.287 | 0.118 | 0.198 | 0.029 |
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 | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 25 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.69 |
time (sec) |
N/A | 0.147 | 0.014 | 0.320 | 0.027 | 0.059 | 0.630 | 0.120 | 0.188 | 0.165 |
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 | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 26 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.72 |
time (sec) |
N/A | 0.149 | 0.013 | 0.306 | 0.044 | 0.060 | 0.392 | 0.117 | 0.207 | 0.041 |
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 | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 26 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.72 |
time (sec) |
N/A | 0.151 | 0.014 | 0.289 | 0.032 | 0.060 | 0.293 | 0.125 | 0.267 | 0.135 |
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 | 36 | 36 | 30 | 25 | 24 | 27 | 34 | 24 | 26 | 26 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.75 | 0.94 | 0.67 | 0.72 | 0.72 |
time (sec) |
N/A | 0.147 | 0.013 | 0.280 | 0.027 | 0.061 | 0.411 | 0.120 | 0.204 | 0.151 |
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 | 34 | 34 | 30 | 25 | 24 | 26 | 32 | 24 | 25 | 26 |
N.S. |
1 | 1.00 | 0.88 | 0.74 | 0.71 | 0.76 | 0.94 | 0.71 | 0.74 | 0.76 |
time (sec) |
N/A | 0.147 | 0.013 | 0.429 | 0.025 | 0.061 | 0.149 | 0.117 | 0.190 | 0.040 |
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 | 34 | 34 | 30 | 25 | 24 | 26 | 32 | 24 | 27 | 26 |
N.S. |
1 | 1.00 | 0.88 | 0.74 | 0.71 | 0.76 | 0.94 | 0.71 | 0.79 | 0.76 |
time (sec) |
N/A | 0.145 | 0.016 | 0.277 | 0.038 | 0.062 | 0.257 | 0.122 | 0.196 | 0.040 |
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 | 34 | 34 | 30 | 25 | 24 | 26 | 32 | 24 | 30 | 26 |
N.S. |
1 | 1.00 | 0.88 | 0.74 | 0.71 | 0.76 | 0.94 | 0.71 | 0.88 | 0.76 |
time (sec) |
N/A | 0.144 | 0.016 | 0.263 | 0.026 | 0.064 | 0.256 | 0.119 | 0.225 | 0.038 |
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 | 34 | 34 | 30 | 25 | 25 | 26 | 32 | 25 | 30 | 26 |
N.S. |
1 | 1.00 | 0.88 | 0.74 | 0.74 | 0.76 | 0.94 | 0.74 | 0.88 | 0.76 |
time (sec) |
N/A | 0.143 | 0.018 | 0.270 | 0.032 | 0.063 | 0.327 | 0.125 | 0.217 | 0.035 |
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 | 51 | 51 | 41 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.153 | 0.016 | 0.325 | 0.035 | 0.063 | 0.931 | 0.122 | 0.211 | 0.062 |
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 | 51 | 51 | 41 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.150 | 0.016 | 0.332 | 0.036 | 0.063 | 0.636 | 0.122 | 0.250 | 0.046 |
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 | 51 | 51 | 41 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.153 | 0.017 | 0.294 | 0.025 | 0.062 | 0.451 | 0.120 | 0.229 | 0.046 |
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 | 51 | 51 | 41 | 36 | 35 | 38 | 49 | 35 | 37 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.75 | 0.96 | 0.69 | 0.73 | 0.69 |
time (sec) |
N/A | 0.154 | 0.015 | 0.292 | 0.046 | 0.061 | 0.552 | 0.122 | 0.191 | 0.046 |
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 | 49 | 49 | 41 | 36 | 35 | 37 | 48 | 35 | 36 | 35 |
N.S. |
1 | 1.00 | 0.84 | 0.73 | 0.71 | 0.76 | 0.98 | 0.71 | 0.73 | 0.71 |
time (sec) |
N/A | 0.153 | 0.015 | 0.263 | 0.026 | 0.064 | 0.236 | 0.119 | 0.192 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 41 | 36 | 35 | 37 | 46 | 35 | 38 | 35 |
N.S. |
1 | 1.00 | 0.87 | 0.77 | 0.74 | 0.79 | 0.98 | 0.74 | 0.81 | 0.74 |
time (sec) |
N/A | 0.157 | 0.019 | 0.267 | 0.030 | 0.063 | 0.348 | 0.118 | 0.276 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 41 | 36 | 35 | 37 | 48 | 35 | 41 | 35 |
N.S. |
1 | 1.00 | 0.84 | 0.73 | 0.71 | 0.76 | 0.98 | 0.71 | 0.84 | 0.71 |
time (sec) |
N/A | 0.154 | 0.019 | 0.267 | 0.030 | 0.063 | 0.376 | 0.119 | 0.187 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 41 | 36 | 36 | 37 | 46 | 36 | 41 | 37 |
N.S. |
1 | 1.00 | 0.87 | 0.77 | 0.77 | 0.79 | 0.98 | 0.77 | 0.87 | 0.79 |
time (sec) |
N/A | 0.156 | 0.020 | 0.275 | 0.032 | 0.066 | 0.468 | 0.122 | 0.199 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 248 | 128 | 125 | 194 | 167 | 136 | 196 | 157 | 67 |
N.S. |
1 | 1.56 | 0.81 | 0.79 | 1.22 | 1.05 | 0.86 | 1.23 | 0.99 | 0.42 |
time (sec) |
N/A | 0.420 | 0.146 | 0.325 | 0.112 | 0.074 | 17.173 | 0.124 | 0.204 | 0.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 231 | 119 | 116 | 186 | 158 | 124 | 178 | 147 | 54 |
N.S. |
1 | 1.56 | 0.80 | 0.78 | 1.26 | 1.07 | 0.84 | 1.20 | 0.99 | 0.36 |
time (sec) |
N/A | 0.385 | 0.116 | 0.322 | 0.108 | 0.073 | 5.339 | 0.130 | 0.237 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 229 | 118 | 115 | 185 | 117 | 110 | 178 | 145 | 55 |
N.S. |
1 | 1.56 | 0.80 | 0.78 | 1.26 | 0.80 | 0.75 | 1.21 | 0.99 | 0.37 |
time (sec) |
N/A | 0.381 | 0.115 | 0.312 | 0.108 | 0.074 | 2.053 | 0.128 | 0.214 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 214 | 91 | 106 | 172 | 132 | 104 | 182 | 112 | 38 |
N.S. |
1 | 1.56 | 0.66 | 0.77 | 1.26 | 0.96 | 0.76 | 1.33 | 0.82 | 0.28 |
time (sec) |
N/A | 0.364 | 0.097 | 0.280 | 0.127 | 0.077 | 1.101 | 0.132 | 0.225 | 0.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 214 | 92 | 106 | 172 | 120 | 104 | 182 | 112 | 37 |
N.S. |
1 | 1.57 | 0.68 | 0.78 | 1.26 | 0.88 | 0.76 | 1.34 | 0.82 | 0.27 |
time (sec) |
N/A | 0.356 | 0.098 | 0.290 | 0.107 | 0.073 | 1.846 | 0.123 | 0.241 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 229 | 117 | 115 | 186 | 140 | 114 | 190 | 155 | 54 |
N.S. |
1 | 1.57 | 0.80 | 0.79 | 1.27 | 0.96 | 0.78 | 1.30 | 1.06 | 0.37 |
time (sec) |
N/A | 0.373 | 0.133 | 0.312 | 0.108 | 0.073 | 3.913 | 0.127 | 0.206 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 231 | 119 | 116 | 187 | 165 | 128 | 178 | 163 | 53 |
N.S. |
1 | 1.55 | 0.80 | 0.78 | 1.26 | 1.11 | 0.86 | 1.19 | 1.09 | 0.36 |
time (sec) |
N/A | 0.379 | 0.136 | 0.303 | 0.110 | 0.074 | 9.168 | 0.121 | 0.203 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 248 | 127 | 124 | 198 | 191 | 139 | 200 | 180 | 66 |
N.S. |
1 | 1.55 | 0.79 | 0.78 | 1.24 | 1.19 | 0.87 | 1.25 | 1.12 | 0.41 |
time (sec) |
N/A | 0.399 | 0.154 | 0.310 | 0.109 | 0.074 | 30.962 | 0.123 | 0.192 | 0.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 258 | 138 | 136 | 206 | 209 | 338 | 196 | 313 | 80 |
N.S. |
1 | 1.46 | 0.78 | 0.77 | 1.16 | 1.18 | 1.91 | 1.11 | 1.77 | 0.45 |
time (sec) |
N/A | 0.408 | 0.258 | 0.349 | 0.111 | 0.080 | 81.878 | 0.130 | 0.250 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 241 | 128 | 124 | 195 | 200 | 393 | 199 | 307 | 64 |
N.S. |
1 | 1.46 | 0.78 | 0.75 | 1.18 | 1.21 | 2.38 | 1.21 | 1.86 | 0.39 |
time (sec) |
N/A | 0.380 | 0.231 | 0.321 | 0.109 | 0.072 | 52.327 | 0.128 | 0.241 | 0.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 241 | 127 | 127 | 195 | 191 | 323 | 199 | 304 | 64 |
N.S. |
1 | 1.46 | 0.77 | 0.77 | 1.18 | 1.16 | 1.96 | 1.21 | 1.84 | 0.39 |
time (sec) |
N/A | 0.388 | 0.223 | 0.287 | 0.111 | 0.078 | 29.299 | 0.127 | 0.188 | 0.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 241 | 128 | 127 | 194 | 204 | 400 | 199 | 305 | 64 |
N.S. |
1 | 1.46 | 0.78 | 0.77 | 1.18 | 1.24 | 2.42 | 1.21 | 1.85 | 0.39 |
time (sec) |
N/A | 0.383 | 0.216 | 0.287 | 0.115 | 0.076 | 17.495 | 0.130 | 0.257 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 241 | 128 | 124 | 194 | 193 | 316 | 199 | 306 | 64 |
N.S. |
1 | 1.46 | 0.78 | 0.75 | 1.18 | 1.17 | 1.92 | 1.21 | 1.85 | 0.39 |
time (sec) |
N/A | 0.390 | 0.211 | 0.239 | 0.111 | 0.073 | 24.666 | 0.126 | 0.222 | 0.188 |