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 | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 119 | 79 | 79 | 74 | 150 | 0 | 73 | 62 | 0 |
N.S. |
1 | 1.20 | 0.80 | 0.80 | 0.75 | 1.52 | 0.00 | 0.74 | 0.63 | 0.00 |
time (sec) |
N/A | 0.407 | 0.079 | 0.271 | 0.169 | 0.087 | 0.000 | 0.142 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 94 | 76 | 69 | 52 | 134 | 0 | 62 | 43 | 0 |
N.S. |
1 | 1.22 | 0.99 | 0.90 | 0.68 | 1.74 | 0.00 | 0.81 | 0.56 | 0.00 |
time (sec) |
N/A | 0.307 | 0.051 | 0.266 | 0.140 | 0.085 | 0.000 | 0.141 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 83 | 99 | 128 | 0 | 184 | 0 | 97 | 32 | 0 |
N.S. |
1 | 1.06 | 1.27 | 1.64 | 0.00 | 2.36 | 0.00 | 1.24 | 0.41 | 0.00 |
time (sec) |
N/A | 0.434 | 0.061 | 0.264 | 0.000 | 0.094 | 0.000 | 0.147 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 88 | 106 | 100 | 0 | 200 | 0 | 133 | 39 | 0 |
N.S. |
1 | 1.07 | 1.29 | 1.22 | 0.00 | 2.44 | 0.00 | 1.62 | 0.48 | 0.00 |
time (sec) |
N/A | 0.425 | 0.060 | 0.295 | 0.000 | 0.083 | 0.000 | 0.143 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 87 | 79 | 78 | 0 | 138 | 0 | 201 | 52 | 0 |
N.S. |
1 | 1.12 | 1.01 | 1.00 | 0.00 | 1.77 | 0.00 | 2.58 | 0.67 | 0.00 |
time (sec) |
N/A | 0.404 | 0.078 | 0.303 | 0.000 | 0.080 | 0.000 | 0.162 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 113 | 82 | 87 | 140 | 154 | 0 | 250 | 71 | 0 |
N.S. |
1 | 1.12 | 0.81 | 0.86 | 1.39 | 1.52 | 0.00 | 2.48 | 0.70 | 0.00 |
time (sec) |
N/A | 0.435 | 0.094 | 0.318 | 0.124 | 0.086 | 0.000 | 0.140 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 149 | 95 | 95 | 0 | 170 | 0 | 324 | 90 | 0 |
N.S. |
1 | 1.15 | 0.73 | 0.73 | 0.00 | 1.31 | 0.00 | 2.49 | 0.69 | 0.00 |
time (sec) |
N/A | 0.481 | 0.112 | 0.338 | 0.000 | 0.089 | 0.000 | 0.142 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 220 | 113 | 117 | 213 | 234 | 235 | 117 | 139 | 0 |
N.S. |
1 | 1.22 | 0.63 | 0.65 | 1.18 | 1.30 | 1.31 | 0.65 | 0.77 | 0.00 |
time (sec) |
N/A | 0.519 | 0.110 | 0.297 | 0.293 | 0.120 | 3.688 | 0.144 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 187 | 105 | 109 | 189 | 216 | 287 | 107 | 120 | 0 |
N.S. |
1 | 1.22 | 0.69 | 0.71 | 1.24 | 1.41 | 1.88 | 0.70 | 0.78 | 0.00 |
time (sec) |
N/A | 0.480 | 0.094 | 0.297 | 0.252 | 0.095 | 2.772 | 0.140 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 151 | 97 | 101 | 167 | 198 | 207 | 98 | 101 | 0 |
N.S. |
1 | 1.17 | 0.75 | 0.78 | 1.29 | 1.53 | 1.60 | 0.76 | 0.78 | 0.00 |
time (sec) |
N/A | 0.409 | 0.089 | 0.276 | 0.185 | 0.094 | 3.252 | 0.162 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 119 | 117 | 90 | 146 | 180 | 255 | 85 | 82 | 0 |
N.S. |
1 | 1.19 | 1.17 | 0.90 | 1.46 | 1.80 | 2.55 | 0.85 | 0.82 | 0.00 |
time (sec) |
N/A | 0.324 | 0.096 | 0.264 | 0.151 | 0.080 | 2.722 | 0.135 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 108 | 115 | 205 | 0 | 221 | 274 | 116 | 69 | 0 |
N.S. |
1 | 1.07 | 1.14 | 2.03 | 0.00 | 2.19 | 2.71 | 1.15 | 0.68 | 0.00 |
time (sec) |
N/A | 0.461 | 0.093 | 0.268 | 0.000 | 0.127 | 3.818 | 0.155 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 120 | 124 | 148 | 0 | 237 | 340 | 165 | 79 | 0 |
N.S. |
1 | 1.07 | 1.11 | 1.32 | 0.00 | 2.12 | 3.04 | 1.47 | 0.71 | 0.00 |
time (sec) |
N/A | 0.452 | 0.115 | 0.297 | 0.000 | 0.104 | 4.680 | 0.146 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 122 | 129 | 130 | 0 | 255 | 366 | 274 | 92 | 0 |
N.S. |
1 | 1.01 | 1.07 | 1.07 | 0.00 | 2.11 | 3.02 | 2.26 | 0.76 | 0.00 |
time (sec) |
N/A | 0.469 | 0.185 | 0.307 | 0.000 | 0.090 | 5.101 | 0.147 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 122 | 127 | 129 | 0 | 254 | 359 | 259 | 112 | 0 |
N.S. |
1 | 1.06 | 1.10 | 1.12 | 0.00 | 2.21 | 3.12 | 2.25 | 0.97 | 0.00 |
time (sec) |
N/A | 0.463 | 0.124 | 0.312 | 0.000 | 0.088 | 7.664 | 0.150 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 116 | 96 | 97 | 0 | 181 | 447 | 371 | 91 | 0 |
N.S. |
1 | 1.09 | 0.91 | 0.92 | 0.00 | 1.71 | 4.22 | 3.50 | 0.86 | 0.00 |
time (sec) |
N/A | 0.402 | 0.109 | 0.317 | 0.000 | 0.086 | 5.149 | 0.155 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 147 | 104 | 105 | 221 | 199 | 484 | 414 | 110 | 0 |
N.S. |
1 | 1.11 | 0.79 | 0.80 | 1.67 | 1.51 | 3.67 | 3.14 | 0.83 | 0.00 |
time (sec) |
N/A | 0.443 | 0.125 | 0.430 | 0.127 | 0.087 | 10.182 | 0.139 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 178 | 109 | 113 | 0 | 217 | 636 | 443 | 129 | 0 |
N.S. |
1 | 1.13 | 0.69 | 0.72 | 0.00 | 1.38 | 4.05 | 2.82 | 0.82 | 0.00 |
time (sec) |
N/A | 0.488 | 0.219 | 0.375 | 0.000 | 0.089 | 9.307 | 0.142 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 206 | 120 | 121 | 287 | 235 | 660 | 529 | 148 | 0 |
N.S. |
1 | 1.13 | 0.66 | 0.66 | 1.57 | 1.28 | 3.61 | 2.89 | 0.81 | 0.00 |
time (sec) |
N/A | 0.523 | 0.158 | 0.395 | 0.130 | 0.098 | 16.092 | 0.138 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 249 | 131 | 133 | 239 | 307 | 391 | 155 | 179 | 0 |
N.S. |
1 | 1.19 | 0.62 | 0.63 | 1.14 | 1.46 | 1.86 | 0.74 | 0.85 | 0.00 |
time (sec) |
N/A | 0.560 | 0.172 | 0.342 | 0.356 | 0.096 | 5.007 | 0.152 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 213 | 123 | 125 | 215 | 285 | 372 | 143 | 160 | 0 |
N.S. |
1 | 1.18 | 0.68 | 0.69 | 1.19 | 1.58 | 2.07 | 0.79 | 0.89 | 0.00 |
time (sec) |
N/A | 0.513 | 0.153 | 0.305 | 0.290 | 0.107 | 4.804 | 0.144 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 177 | 115 | 117 | 193 | 263 | 350 | 131 | 141 | 0 |
N.S. |
1 | 1.13 | 0.73 | 0.75 | 1.23 | 1.68 | 2.23 | 0.83 | 0.90 | 0.00 |
time (sec) |
N/A | 0.426 | 0.142 | 0.979 | 0.237 | 0.098 | 5.367 | 0.150 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 145 | 135 | 106 | 172 | 241 | 325 | 116 | 122 | 0 |
N.S. |
1 | 1.18 | 1.10 | 0.86 | 1.40 | 1.96 | 2.64 | 0.94 | 0.99 | 0.00 |
time (sec) |
N/A | 0.351 | 0.150 | 0.273 | 0.172 | 0.091 | 4.198 | 0.145 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 147 | 136 | 282 | 0 | 283 | 435 | 150 | 110 | 0 |
N.S. |
1 | 1.08 | 1.00 | 2.07 | 0.00 | 2.08 | 3.20 | 1.10 | 0.81 | 0.00 |
time (sec) |
N/A | 0.503 | 0.130 | 0.289 | 0.000 | 0.105 | 9.536 | 0.151 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 151 | 143 | 214 | 0 | 302 | 434 | 195 | 120 | 0 |
N.S. |
1 | 1.07 | 1.01 | 1.52 | 0.00 | 2.14 | 3.08 | 1.38 | 0.85 | 0.00 |
time (sec) |
N/A | 0.499 | 0.211 | 0.318 | 0.000 | 0.095 | 6.501 | 0.141 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 153 | 151 | 208 | 0 | 317 | 408 | 302 | 131 | 0 |
N.S. |
1 | 1.01 | 1.00 | 1.38 | 0.00 | 2.10 | 2.70 | 2.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.507 | 0.242 | 0.326 | 0.000 | 0.105 | 4.874 | 0.165 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 155 | 149 | 172 | 0 | 318 | 468 | 292 | 132 | 0 |
N.S. |
1 | 1.03 | 0.99 | 1.15 | 0.00 | 2.12 | 3.12 | 1.95 | 0.88 | 0.00 |
time (sec) |
N/A | 0.507 | 0.234 | 0.358 | 0.000 | 0.099 | 8.183 | 0.147 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 159 | 151 | 159 | 0 | 317 | 575 | 440 | 132 | 0 |
N.S. |
1 | 1.03 | 0.97 | 1.03 | 0.00 | 2.05 | 3.71 | 2.84 | 0.85 | 0.00 |
time (sec) |
N/A | 0.511 | 0.236 | 0.373 | 0.000 | 0.092 | 6.893 | 0.160 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 171 | 151 | 122 | 194 | 286 | 648 | 141 | 160 | 0 |
N.S. |
1 | 1.17 | 1.03 | 0.84 | 1.33 | 1.96 | 4.44 | 0.97 | 1.10 | 0.00 |
time (sec) |
N/A | 0.367 | 0.143 | 0.278 | 0.212 | 0.094 | 5.430 | 0.148 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 166 | 97 | 124 | 113 | 200 | 0 | 0 | 154 | 0 |
N.S. |
1 | 1.27 | 0.74 | 0.95 | 0.86 | 1.53 | 0.00 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.595 | 0.141 | 0.303 | 0.186 | 0.106 | 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 | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 125 | 94 | 116 | 89 | 184 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.13 | 0.85 | 1.05 | 0.80 | 1.66 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.475 | 0.072 | 0.292 | 0.162 | 0.089 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 97 | 78 | 103 | 67 | 166 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.15 | 0.93 | 1.23 | 0.80 | 1.98 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.341 | 0.085 | 0.279 | 0.136 | 0.113 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 65 | 82 | 80 | 45 | 152 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.08 | 1.37 | 1.33 | 0.75 | 2.53 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.277 | 0.035 | 0.316 | 0.129 | 0.089 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 57 | 66 | 80 | 0 | 135 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.10 | 1.27 | 1.54 | 0.00 | 2.60 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.368 | 0.090 | 0.266 | 0.000 | 0.110 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 87 | 78 | 99 | 0 | 167 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.13 | 1.01 | 1.29 | 0.00 | 2.17 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.399 | 0.110 | 0.299 | 0.000 | 0.099 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 120 | 94 | 121 | 0 | 198 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.10 | 0.86 | 1.11 | 0.00 | 1.82 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.535 | 0.133 | 0.308 | 0.000 | 0.089 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 154 | 101 | 132 | 0 | 214 | 0 | 0 | 132 | 0 |
N.S. |
1 | 1.14 | 0.75 | 0.98 | 0.00 | 1.59 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.691 | 0.143 | 0.323 | 0.000 | 0.102 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 137 | 90 | 164 | 260 | 229 | 0 | 0 | 183 | 0 |
N.S. |
1 | 1.17 | 0.77 | 1.40 | 2.22 | 1.96 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.544 | 0.130 | 0.308 | 0.197 | 0.094 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 108 | 82 | 189 | 230 | 215 | 0 | 0 | 114 | 0 |
N.S. |
1 | 1.16 | 0.88 | 2.03 | 2.47 | 2.31 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.423 | 0.093 | 0.312 | 0.189 | 0.090 | 0.000 | 0.000 | 0.163 | 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 | 60 | 65 | 38 | 32 | 218 | 50 | 0 | 117 | 54 | 34 |
N.S. |
1 | 1.08 | 0.63 | 0.53 | 3.63 | 0.83 | 0.00 | 1.95 | 0.90 | 0.57 |
time (sec) |
N/A | 0.330 | 0.028 | 0.327 | 0.150 | 0.089 | 0.000 | 0.160 | 0.163 | 25.243 |
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 | 51 | 56 | 63 | 31 | 196 | 47 | 0 | 148 | 54 | 33 |
N.S. |
1 | 1.10 | 1.24 | 0.61 | 3.84 | 0.92 | 0.00 | 2.90 | 1.06 | 0.65 |
time (sec) |
N/A | 0.275 | 0.027 | 0.300 | 0.060 | 0.086 | 0.000 | 0.176 | 0.167 | 25.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 92 | 75 | 152 | 0 | 192 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.12 | 0.91 | 1.85 | 0.00 | 2.34 | 0.00 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.413 | 0.104 | 0.382 | 0.000 | 0.101 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 124 | 89 | 159 | 0 | 228 | 0 | 100 | 197 | 0 |
N.S. |
1 | 0.98 | 0.71 | 1.26 | 0.00 | 1.81 | 0.00 | 0.79 | 1.56 | 0.00 |
time (sec) |
N/A | 0.555 | 0.110 | 0.305 | 0.000 | 0.112 | 0.000 | 0.157 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 159 | 105 | 172 | 0 | 256 | 0 | 204 | 38 | 0 |
N.S. |
1 | 0.98 | 0.65 | 1.06 | 0.00 | 1.58 | 0.00 | 1.26 | 0.23 | 0.00 |
time (sec) |
N/A | 0.706 | 0.107 | 0.316 | 0.000 | 0.116 | 0.000 | 0.148 | 200.020 | 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 | 74 | 87 | 53 | 47 | 218 | 75 | 0 | 0 | 107 | 56 |
N.S. |
1 | 1.18 | 0.72 | 0.64 | 2.95 | 1.01 | 0.00 | 0.00 | 1.45 | 0.76 |
time (sec) |
N/A | 0.280 | 0.032 | 0.271 | 0.081 | 0.112 | 0.000 | 0.000 | 0.160 | 25.511 |
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 | 97 | 118 | 96 | 64 | 242 | 124 | 0 | 0 | 150 | 133 |
N.S. |
1 | 1.22 | 0.99 | 0.66 | 2.49 | 1.28 | 0.00 | 0.00 | 1.55 | 1.37 |
time (sec) |
N/A | 0.306 | 0.046 | 0.273 | 0.110 | 0.202 | 0.000 | 0.000 | 0.160 | 25.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 103 | 88 | 475 | 304 | 540 | 3009 | 0 | 474 | 531 |
N.S. |
1 | 0.86 | 0.73 | 3.96 | 2.53 | 4.50 | 25.08 | 0.00 | 3.95 | 4.42 |
time (sec) |
N/A | 0.354 | 0.051 | 0.348 | 0.081 | 0.096 | 0.825 | 0.000 | 0.151 | 25.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 59 | 69 | 78 | 114 | 179 | 706 | 0 | 142 | 173 |
N.S. |
1 | 0.88 | 1.03 | 1.16 | 1.70 | 2.67 | 10.54 | 0.00 | 2.12 | 2.58 |
time (sec) |
N/A | 0.312 | 0.103 | 0.270 | 0.070 | 0.076 | 0.509 | 0.000 | 0.150 | 25.883 |
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 | 42 | 41 | 34 | 50 | 62 | 82 | 299 | 0 | 72 | 92 |
N.S. |
1 | 0.98 | 0.81 | 1.19 | 1.48 | 1.95 | 7.12 | 0.00 | 1.71 | 2.19 |
time (sec) |
N/A | 0.276 | 0.026 | 0.267 | 0.067 | 0.096 | 0.361 | 0.000 | 0.153 | 25.241 |
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 | 25 | 25 | 25 | 0 | 0 | 0 | 0 | 0 | 220 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.80 | 0.00 |
time (sec) |
N/A | 0.276 | 0.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 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 | 140 | 107 | 92 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.76 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.404 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 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 | 187 | 149 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.16 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.546 | 0.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 182 | 180 | 0 | 0 | 0 | 221 | 0 | 95 | 0 |
N.S. |
1 | 1.03 | 1.02 | 0.00 | 0.00 | 0.00 | 1.26 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.490 | 0.142 | 0.000 | 0.000 | 0.000 | 12.602 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 180 | 158 | 0 | 0 | 0 | 168 | 0 | 67 | 0 |
N.S. |
1 | 1.05 | 0.92 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.493 | 0.085 | 0.000 | 0.000 | 0.000 | 5.827 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 130 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.483 | 0.199 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 179 | 66 | 0 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.08 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.486 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 191 | 173 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.07 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.488 | 0.169 | 0.000 | 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 | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 68 | 0 | 0 | 0 | 649 | 0 | 197 | 0 |
N.S. |
1 | 1.00 | 1.24 | 0.00 | 0.00 | 0.00 | 11.80 | 0.00 | 3.58 | 0.00 |
time (sec) |
N/A | 0.284 | 0.014 | 0.000 | 0.000 | 0.000 | 9.043 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 187 | 70 | 98 | 169 | 89 | 156 | 78 | 118 | 140 |
N.S. |
1 | 1.26 | 0.47 | 0.66 | 1.14 | 0.60 | 1.05 | 0.53 | 0.80 | 0.95 |
time (sec) |
N/A | 0.549 | 0.064 | 0.471 | 0.115 | 0.081 | 6.086 | 0.150 | 0.149 | 28.573 |
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 | 125 | 155 | 62 | 90 | 148 | 80 | 146 | 69 | 99 | 119 |
N.S. |
1 | 1.24 | 0.50 | 0.72 | 1.18 | 0.64 | 1.17 | 0.55 | 0.79 | 0.95 |
time (sec) |
N/A | 0.501 | 0.051 | 0.502 | 0.114 | 0.078 | 5.909 | 0.154 | 0.153 | 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 | 98 | 119 | 54 | 82 | 126 | 71 | 124 | 58 | 80 | 98 |
N.S. |
1 | 1.21 | 0.55 | 0.84 | 1.29 | 0.72 | 1.27 | 0.59 | 0.82 | 1.00 |
time (sec) |
N/A | 0.408 | 0.044 | 0.411 | 0.120 | 0.081 | 5.224 | 0.135 | 0.172 | 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 | 78 | 94 | 57 | 71 | 106 | 62 | 112 | 46 | 61 | 74 |
N.S. |
1 | 1.21 | 0.73 | 0.91 | 1.36 | 0.79 | 1.44 | 0.59 | 0.78 | 0.95 |
time (sec) |
N/A | 0.289 | 0.047 | 0.420 | 0.114 | 0.076 | 5.062 | 0.130 | 0.148 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 78 | 49 | 222 | 111 | 69 | 178 | 76 | 49 | 70 |
N.S. |
1 | 1.18 | 0.74 | 3.36 | 1.68 | 1.05 | 2.70 | 1.15 | 0.74 | 1.06 |
time (sec) |
N/A | 0.427 | 0.032 | 0.394 | 0.111 | 0.090 | 5.921 | 0.165 | 0.152 | 27.968 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 64 | 52 | 89 | 111 | 80 | 148 | 131 | 79 | 79 |
N.S. |
1 | 0.97 | 0.79 | 1.35 | 1.68 | 1.21 | 2.24 | 1.98 | 1.20 | 1.20 |
time (sec) |
N/A | 0.408 | 0.054 | 0.438 | 0.112 | 0.086 | 6.452 | 0.136 | 0.151 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 77 | 60 | 91 | 116 | 85 | 219 | 179 | 63 | 83 |
N.S. |
1 | 1.01 | 0.79 | 1.20 | 1.53 | 1.12 | 2.88 | 2.36 | 0.83 | 1.09 |
time (sec) |
N/A | 0.454 | 0.069 | 0.427 | 0.110 | 0.085 | 5.079 | 0.144 | 0.150 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 96 | 60 | 69 | 128 | 66 | 265 | 218 | 70 | 82 |
N.S. |
1 | 1.02 | 0.64 | 0.73 | 1.36 | 0.70 | 2.82 | 2.32 | 0.74 | 0.87 |
time (sec) |
N/A | 0.430 | 0.042 | 0.457 | 0.033 | 0.094 | 11.824 | 0.141 | 0.157 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 119 | 97 | 77 | 149 | 75 | 410 | 280 | 89 | 103 |
N.S. |
1 | 1.03 | 0.84 | 0.67 | 1.30 | 0.65 | 3.57 | 2.43 | 0.77 | 0.90 |
time (sec) |
N/A | 0.457 | 0.107 | 0.451 | 0.040 | 0.080 | 6.912 | 0.142 | 0.154 | 27.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 150 | 110 | 85 | 170 | 84 | 517 | 332 | 108 | 124 |
N.S. |
1 | 1.04 | 0.76 | 0.59 | 1.18 | 0.58 | 3.59 | 2.31 | 0.75 | 0.86 |
time (sec) |
N/A | 0.501 | 0.113 | 0.508 | 0.033 | 0.078 | 21.636 | 0.139 | 0.153 | 0.045 |
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 | 108 | 120 | 75 | 91 | 164 | 93 | 178 | 78 | 101 | 128 |
N.S. |
1 | 1.11 | 0.69 | 0.84 | 1.52 | 0.86 | 1.65 | 0.72 | 0.94 | 1.19 |
time (sec) |
N/A | 0.308 | 0.109 | 0.547 | 0.112 | 0.093 | 7.980 | 0.141 | 0.154 | 0.036 |
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 | 130 | 144 | 91 | 107 | 210 | 114 | 228 | 102 | 139 | 174 |
N.S. |
1 | 1.11 | 0.70 | 0.82 | 1.62 | 0.88 | 1.75 | 0.78 | 1.07 | 1.34 |
time (sec) |
N/A | 0.328 | 0.132 | 0.695 | 0.110 | 0.084 | 8.110 | 0.152 | 0.152 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 168 | 107 | 123 | 256 | 137 | 257 | 125 | 177 | 220 |
N.S. |
1 | 1.11 | 0.70 | 0.81 | 1.68 | 0.90 | 1.69 | 0.82 | 1.16 | 1.45 |
time (sec) |
N/A | 0.338 | 0.155 | 1.164 | 0.121 | 0.085 | 11.995 | 0.159 | 0.150 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 90 | 78 | 147 | 364 | 103 | 0 | 0 | 181 | 133 |
N.S. |
1 | 0.97 | 0.84 | 1.58 | 3.91 | 1.11 | 0.00 | 0.00 | 1.95 | 1.43 |
time (sec) |
N/A | 0.352 | 0.039 | 0.487 | 0.216 | 0.078 | 0.000 | 0.000 | 0.157 | 27.834 |
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 | 70 | 72 | 70 | 187 | 241 | 96 | 0 | 112 | 112 | 108 |
N.S. |
1 | 1.03 | 1.00 | 2.67 | 3.44 | 1.37 | 0.00 | 1.60 | 1.60 | 1.54 |
time (sec) |
N/A | 0.310 | 0.030 | 0.402 | 0.175 | 0.099 | 0.000 | 0.153 | 0.152 | 28.388 |
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 | 18 | 18 | 29 | 28 | 329 | 54 | 0 | 66 | 71 | 32 |
N.S. |
1 | 1.00 | 1.61 | 1.56 | 18.28 | 3.00 | 0.00 | 3.67 | 3.94 | 1.78 |
time (sec) |
N/A | 0.224 | 0.010 | 0.396 | 0.150 | 0.080 | 0.000 | 0.140 | 0.152 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 97 | 43 | 42 | 0 | 91 | 0 | 145 | 96 | 127 |
N.S. |
1 | 1.17 | 0.52 | 0.51 | 0.00 | 1.10 | 0.00 | 1.75 | 1.16 | 1.53 |
time (sec) |
N/A | 0.303 | 0.017 | 0.431 | 0.000 | 0.080 | 0.000 | 0.153 | 0.148 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 121 | 61 | 63 | 0 | 144 | 0 | 0 | 140 | 125 |
N.S. |
1 | 1.15 | 0.58 | 0.60 | 0.00 | 1.37 | 0.00 | 0.00 | 1.33 | 1.19 |
time (sec) |
N/A | 0.316 | 0.020 | 0.539 | 0.000 | 0.084 | 0.000 | 0.000 | 0.148 | 27.967 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 145 | 75 | 74 | 0 | 198 | 0 | 0 | 210 | 156 |
N.S. |
1 | 1.14 | 0.59 | 0.58 | 0.00 | 1.56 | 0.00 | 0.00 | 1.65 | 1.23 |
time (sec) |
N/A | 0.335 | 0.026 | 0.799 | 0.000 | 0.116 | 0.000 | 0.000 | 0.147 | 27.939 |
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 | 226 | 82 | 79 | 77 | 0 | 399 | 0 | 61 | 52 | 0 |
N.S. |
1 | 0.36 | 0.35 | 0.34 | 0.00 | 1.77 | 0.00 | 0.27 | 0.23 | 0.00 |
time (sec) |
N/A | 0.507 | 0.025 | 0.324 | 0.000 | 0.113 | 0.000 | 0.114 | 0.152 | 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 | 185 | 70 | 70 | 68 | 0 | 381 | 0 | 52 | 44 | 0 |
N.S. |
1 | 0.38 | 0.38 | 0.37 | 0.00 | 2.06 | 0.00 | 0.28 | 0.24 | 0.00 |
time (sec) |
N/A | 0.490 | 0.019 | 0.319 | 0.000 | 0.114 | 0.000 | 0.117 | 0.144 | 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 | 150 | 64 | 64 | 61 | 0 | 367 | 0 | 45 | 36 | 0 |
N.S. |
1 | 0.43 | 0.43 | 0.41 | 0.00 | 2.45 | 0.00 | 0.30 | 0.24 | 0.00 |
time (sec) |
N/A | 0.422 | 0.018 | 0.332 | 0.000 | 0.112 | 0.000 | 0.137 | 0.142 | 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 | 111 | 54 | 54 | 52 | 0 | 345 | 0 | 36 | 28 | 0 |
N.S. |
1 | 0.49 | 0.49 | 0.47 | 0.00 | 3.11 | 0.00 | 0.32 | 0.25 | 0.00 |
time (sec) |
N/A | 0.358 | 0.016 | 0.315 | 0.000 | 0.101 | 0.000 | 0.112 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 46 | 46 | 43 | 0 | 0 | 0 | 23 | 18 | 0 |
N.S. |
1 | 0.44 | 0.44 | 0.41 | 0.00 | 0.00 | 0.00 | 0.22 | 0.17 | 0.00 |
time (sec) |
N/A | 0.455 | 0.016 | 0.320 | 0.000 | 0.000 | 0.000 | 0.112 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 51 | 51 | 49 | 0 | 0 | 0 | 25 | 24 | 0 |
N.S. |
1 | 0.47 | 0.47 | 0.45 | 0.00 | 0.00 | 0.00 | 0.23 | 0.22 | 0.00 |
time (sec) |
N/A | 0.463 | 0.016 | 0.314 | 0.000 | 0.000 | 0.000 | 0.112 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 63 | 63 | 62 | 160 | 450 | 0 | 36 | 37 | 0 |
N.S. |
1 | 0.42 | 0.42 | 0.42 | 1.07 | 3.02 | 0.00 | 0.24 | 0.25 | 0.00 |
time (sec) |
N/A | 0.465 | 0.026 | 0.324 | 0.058 | 0.118 | 0.000 | 0.122 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 73 | 73 | 70 | 216 | 478 | 0 | 44 | 45 | 0 |
N.S. |
1 | 0.39 | 0.39 | 0.37 | 1.15 | 2.54 | 0.00 | 0.23 | 0.24 | 0.00 |
time (sec) |
N/A | 0.471 | 0.031 | 0.332 | 0.061 | 0.153 | 0.000 | 0.114 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 79 | 79 | 78 | 306 | 504 | 0 | 52 | 53 | 0 |
N.S. |
1 | 0.35 | 0.35 | 0.35 | 1.37 | 2.26 | 0.00 | 0.23 | 0.24 | 0.00 |
time (sec) |
N/A | 0.480 | 0.029 | 0.329 | 0.066 | 0.118 | 0.000 | 0.127 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 58 | 47 | 0 | 67 | 0 | 0 | 27 | 54 |
N.S. |
1 | 1.00 | 1.32 | 1.07 | 0.00 | 1.52 | 0.00 | 0.00 | 0.61 | 1.23 |
time (sec) |
N/A | 0.337 | 0.019 | 0.319 | 0.000 | 0.084 | 0.000 | 0.000 | 0.146 | 27.385 |
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 | 93 | 62 | 52 | 71 | 237 | 98 | 0 | 0 | 46 | 85 |
N.S. |
1 | 0.67 | 0.56 | 0.76 | 2.55 | 1.05 | 0.00 | 0.00 | 0.49 | 0.91 |
time (sec) |
N/A | 0.376 | 0.031 | 0.323 | 0.072 | 0.075 | 0.000 | 0.000 | 0.148 | 28.772 |
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 | 139 | 76 | 60 | 87 | 323 | 120 | 0 | 0 | 62 | 107 |
N.S. |
1 | 0.55 | 0.43 | 0.63 | 2.32 | 0.86 | 0.00 | 0.00 | 0.45 | 0.77 |
time (sec) |
N/A | 0.406 | 0.032 | 0.331 | 0.076 | 0.072 | 0.000 | 0.000 | 0.141 | 28.958 |
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 | 185 | 90 | 68 | 87 | 409 | 120 | 0 | 0 | 62 | 106 |
N.S. |
1 | 0.49 | 0.37 | 0.47 | 2.21 | 0.65 | 0.00 | 0.00 | 0.34 | 0.57 |
time (sec) |
N/A | 0.428 | 0.032 | 0.327 | 0.081 | 0.078 | 0.000 | 0.000 | 0.146 | 27.977 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 55 | 51 | 60 | 0 | 382 | 0 | 30 | 38 | 0 |
N.S. |
1 | 0.66 | 0.61 | 0.72 | 0.00 | 4.60 | 0.00 | 0.36 | 0.46 | 0.00 |
time (sec) |
N/A | 0.375 | 0.028 | 0.327 | 0.000 | 0.118 | 0.000 | 0.114 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 46 | 42 | 0 | 72 | 0 | 0 | 25 | 74 |
N.S. |
1 | 1.00 | 0.98 | 0.89 | 0.00 | 1.53 | 0.00 | 0.00 | 0.53 | 1.57 |
time (sec) |
N/A | 0.344 | 0.014 | 0.313 | 0.000 | 0.080 | 0.000 | 0.000 | 0.141 | 28.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 90 | 73 | 148 | 0 | 459 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.49 | 0.39 | 0.80 | 0.00 | 2.48 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.433 | 0.033 | 0.329 | 0.000 | 0.131 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 119 | 101 | 227 | 0 | 565 | 0 | 0 | 223 | 0 |
N.S. |
1 | 0.43 | 0.36 | 0.82 | 0.00 | 2.03 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.441 | 0.043 | 0.322 | 0.000 | 0.128 | 0.000 | 0.000 | 0.146 | 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 | 136 | 79 | 74 | 0 | 0 | 0 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.58 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.479 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.140 | 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 | 251 | 233 | 186 | 0 | 0 | 0 | 0 | 0 | 162 | 0 |
N.S. |
1 | 0.93 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.797 | 0.149 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.733 | 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 | 224 | 186 | 173 | 0 | 0 | 0 | 0 | 0 | 158 | 0 |
N.S. |
1 | 0.83 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.623 | 0.203 | 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 | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 185 | 172 | 0 | 0 | 0 | 0 | 0 | 158 | 0 |
N.S. |
1 | 0.83 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.646 | 0.198 | 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 | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 128 | 134 | 0 | 0 | 0 | 0 | 0 | 156 | 0 |
N.S. |
1 | 0.93 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.463 | 0.344 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 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 | 85 | 85 | 83 | 0 | 0 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.80 | 0.00 |
time (sec) |
N/A | 0.340 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |