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 | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 33 | 31 | 41 | 80 | 29 | 36 | 75 | 28 |
N.S. |
1 | 0.97 | 0.91 | 1.21 | 2.35 | 0.85 | 1.06 | 2.21 | 0.82 |
time (sec) |
N/A | 0.288 | 0.029 | 0.067 | 0.196 | 0.251 | 0.217 | 0.254 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 77 | 67 | 74 | 110 | 189 | 0 | 75 | 0 |
N.S. |
1 | 1.12 | 0.97 | 1.07 | 1.59 | 2.74 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.304 | 0.052 | 0.049 | 0.183 | 0.253 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 31 | 14 | 13 | 13 | 19 | 27 | 13 |
N.S. |
1 | 1.00 | 2.07 | 0.93 | 0.87 | 0.87 | 1.27 | 1.80 | 0.87 |
time (sec) |
N/A | 0.209 | 0.011 | 0.034 | 0.180 | 0.245 | 0.087 | 0.276 | 1.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 45 | 40 | 87 | 49 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.75 | 1.64 | 0.92 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.224 | 0.025 | 0.028 | 0.204 | 0.235 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 33 | 24 | 39 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.32 | 0.96 | 1.56 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.290 | 0.012 | 0.047 | 0.254 | 0.240 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 70 | 70 | 70 | 55 | 183 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.06 | 1.06 | 0.83 | 2.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.295 | 0.053 | 0.050 | 0.178 | 0.252 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 48 | 38 | 58 | 40 | 71 | 0 | 108 | 0 |
N.S. |
1 | 1.14 | 0.90 | 1.38 | 0.95 | 1.69 | 0.00 | 2.57 | 0.00 |
time (sec) |
N/A | 0.439 | 0.032 | 0.058 | 0.239 | 0.252 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 55 | 40 | 46 | 59 | 60 | 78 | 142 | 42 |
N.S. |
1 | 1.08 | 0.78 | 0.90 | 1.16 | 1.18 | 1.53 | 2.78 | 0.82 |
time (sec) |
N/A | 0.258 | 0.076 | 0.148 | 0.197 | 0.248 | 0.287 | 0.265 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 101 | 90 | 95 | 427 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.91 | 0.96 | 4.31 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.282 | 0.157 | 0.104 | 0.259 | 0.256 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 27 | 24 | 38 | 28 | 60 | 54 | 22 |
N.S. |
1 | 1.13 | 0.87 | 0.77 | 1.23 | 0.90 | 1.94 | 1.74 | 0.71 |
time (sec) |
N/A | 0.228 | 0.020 | 0.071 | 0.190 | 0.245 | 0.114 | 0.254 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 86 | 51 | 56 | 73 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 1.10 | 0.65 | 0.72 | 0.94 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.225 | 0.053 | 0.065 | 0.267 | 0.246 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 33 | 34 | 31 | 49 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.92 | 0.84 | 1.32 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.237 | 0.016 | 0.104 | 0.233 | 0.240 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 92 | 94 | 86 | 61 | 394 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.07 | 0.98 | 0.69 | 4.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.424 | 0.181 | 0.101 | 0.258 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 46 | 66 | 36 | 90 | 0 | 126 | 0 |
N.S. |
1 | 1.00 | 0.81 | 1.16 | 0.63 | 1.58 | 0.00 | 2.21 | 0.00 |
time (sec) |
N/A | 0.313 | 0.069 | 0.110 | 0.243 | 0.245 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 83 | 55 | 93 | 100 | 96 | 92 | 192 | 70 |
N.S. |
1 | 1.05 | 0.70 | 1.18 | 1.27 | 1.22 | 1.16 | 2.43 | 0.89 |
time (sec) |
N/A | 0.405 | 0.126 | 0.223 | 0.196 | 0.252 | 0.418 | 0.265 | 1.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 184 | 157 | 162 | 903 | 0 | 166 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.98 | 1.01 | 5.64 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.357 | 0.241 | 0.186 | 0.274 | 0.264 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 29 | 33 | 28 | 62 | 38 | 44 | 56 | 26 |
N.S. |
1 | 0.88 | 1.00 | 0.85 | 1.88 | 1.15 | 1.33 | 1.70 | 0.79 |
time (sec) |
N/A | 0.249 | 0.009 | 0.088 | 0.175 | 0.255 | 0.233 | 0.257 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 136 | 86 | 91 | 113 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 1.09 | 0.69 | 0.73 | 0.90 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.278 | 0.097 | 0.104 | 0.276 | 0.264 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 69 | 50 | 83 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.25 | 0.91 | 1.51 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.281 | 0.025 | 0.170 | 0.263 | 0.247 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 144 | 204 | 149 | 102 | 891 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.50 | 1.10 | 0.75 | 6.55 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.355 | 0.251 | 0.178 | 0.263 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 92 | 121 | 58 | 168 | 0 | 224 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.33 | 0.64 | 1.85 | 0.00 | 2.46 | 0.00 |
time (sec) |
N/A | 0.413 | 0.063 | 0.181 | 0.267 | 0.247 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 41 | 67 | 52 | 126 | 128 | 94 | 108 | 52 |
N.S. |
1 | 0.61 | 1.00 | 0.78 | 1.88 | 1.91 | 1.40 | 1.61 | 0.78 |
time (sec) |
N/A | 0.257 | 0.022 | 0.793 | 0.180 | 0.243 | 0.750 | 0.266 | 1.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 5 | 15 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.62 | 1.88 | 0.75 |
time (sec) |
N/A | 0.205 | 0.003 | 0.053 | 0.179 | 0.238 | 0.108 | 0.261 | 1.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 8 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 1.00 | 1.88 | 1.88 |
time (sec) |
N/A | 0.201 | 0.005 | 0.086 | 0.197 | 0.236 | 2.502 | 0.252 | 1.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 41 | 33 | 56 | 37 | 58 | 0 | 173 | 0 |
N.S. |
1 | 1.24 | 1.00 | 1.70 | 1.12 | 1.76 | 0.00 | 5.24 | 0.00 |
time (sec) |
N/A | 0.436 | 0.021 | 0.110 | 0.223 | 0.243 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 27 | 24 | 39 | 17 | 43 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 1.14 | 1.86 | 0.81 | 2.05 | 0.00 |
time (sec) |
N/A | 0.287 | 0.008 | 0.075 | 0.218 | 0.240 | 0.462 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 13 | 15 | 15 | 29 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.15 | 1.15 | 2.23 | 1.00 |
time (sec) |
N/A | 0.219 | 0.005 | 0.052 | 0.179 | 0.236 | 0.259 | 0.296 | 1.548 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 43 | 47 | 33 | 29 | 93 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.48 | 1.62 | 1.14 | 1.00 | 3.21 | 1.00 |
time (sec) |
N/A | 0.280 | 0.020 | 0.088 | 0.252 | 0.244 | 0.394 | 0.274 | 1.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 58 | 39 | 65 | 48 | 43 | 46 | 216 | 66 |
N.S. |
1 | 1.26 | 0.85 | 1.41 | 1.04 | 0.93 | 1.00 | 4.70 | 1.43 |
time (sec) |
N/A | 0.366 | 0.035 | 0.117 | 0.226 | 0.242 | 0.503 | 0.313 | 1.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 71 | 71 | 70 | 72 | 225 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.06 | 1.04 | 1.07 | 3.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.351 | 0.060 | 0.079 | 0.215 | 0.261 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 33 | 24 | 39 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.32 | 0.96 | 1.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.286 | 0.014 | 0.073 | 0.229 | 0.246 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 49 | 44 | 63 | 53 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.77 | 1.11 | 0.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.296 | 0.026 | 0.078 | 0.240 | 0.245 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 17 | 22 | 33 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.13 | 1.47 | 2.20 | 0.87 |
time (sec) |
N/A | 0.222 | 0.005 | 0.060 | 0.182 | 0.237 | 0.534 | 0.262 | 1.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 83 | 74 | 82 | 63 | 250 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.99 | 1.09 | 0.84 | 3.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.355 | 0.051 | 0.112 | 0.242 | 0.249 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 62 | 74 | 61 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.10 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 0.040 | 0.111 | 0.095 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 33 | 30 | 54 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.32 | 1.20 | 2.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.277 | 0.020 | 0.130 | 0.247 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 81 | 0 | 68 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.267 | 0.075 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 36 | 40 | 37 | 69 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.93 | 0.86 | 1.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.243 | 0.022 | 0.495 | 0.254 | 0.256 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 138 | 0 | 125 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 0.067 | 0.000 | 0.149 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 52 | 67 | 62 | 114 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.00 | 0.93 | 1.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.277 | 0.039 | 0.891 | 0.273 | 0.260 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.185 | 4.106 | 0.042 | 0.401 | 0.255 | 8.296 | 1.354 | 1.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 20 | 20 | 22 | 20 | 22 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.191 | 6.143 | 0.035 | 0.413 | 0.268 | 25.338 | 7.712 | 1.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 90 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.370 | 0.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 24 | 24 | 20 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.287 | 4.414 | 0.053 | 0.420 | 0.256 | 7.942 | 1.322 | 1.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 148 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.443 | 0.374 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 24 | 24 | 26 | 24 | 26 | 26 | 22 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.92 | 1.08 | 1.08 |
time (sec) |
N/A | 0.291 | 6.373 | 0.051 | 0.421 | 0.277 | 24.084 | 7.296 | 1.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 84 | 110 | 85 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.24 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.283 | 0.104 | 0.295 | 0.115 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 116 | 0 | 101 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.360 | 0.190 | 0.000 | 0.112 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 182 | 0 | 173 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.427 | 0.144 | 0.000 | 0.164 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 50 | 46 | 63 | 34 | 140 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.02 | 1.40 | 0.76 | 3.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.459 | 0.044 | 0.281 | 0.245 | 0.261 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 54 | 75 | 47 | 182 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 1.12 | 0.70 | 2.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.329 | 0.094 | 1.352 | 0.240 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 97 | 126 | 70 | 320 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.12 | 0.62 | 2.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.438 | 0.107 | 7.612 | 0.286 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 70 | 57 | 54 | 69 | 98 | 0 | 52 | 0 |
N.S. |
1 | 0.99 | 0.80 | 0.76 | 0.97 | 1.38 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.297 | 0.033 | 0.244 | 0.258 | 0.245 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 99 | 62 | 136 | 818 | 321 | 0 | 137 | 0 |
N.S. |
1 | 0.88 | 0.55 | 1.20 | 7.24 | 2.84 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.325 | 0.091 | 0.081 | 0.443 | 0.261 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 49 | 39 | 66 | 650 | 261 | 0 | 99 | 0 |
N.S. |
1 | 0.91 | 0.72 | 1.22 | 12.04 | 4.83 | 0.00 | 1.83 | 0.00 |
time (sec) |
N/A | 0.288 | 0.025 | 0.050 | 0.405 | 0.259 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 35 | 25 | 36 | 478 | 59 | 0 | 39 | 0 |
N.S. |
1 | 0.95 | 0.68 | 0.97 | 12.92 | 1.59 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.250 | 0.006 | 0.029 | 0.387 | 0.262 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 23 | 20 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.92 | 1.67 | 1.17 | 1.17 |
time (sec) |
N/A | 0.254 | 1.091 | 0.020 | 0.846 | 0.246 | 3.020 | 0.273 | 1.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 23 | 22 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.92 | 1.83 | 1.17 | 1.17 |
time (sec) |
N/A | 0.256 | 3.360 | 0.020 | 0.610 | 0.251 | 3.036 | 0.271 | 1.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 346 | 313 | 209 | 831 | 486 | 104 | 269 | 915 | 0 |
N.S. |
1 | 0.90 | 0.60 | 2.40 | 1.40 | 0.30 | 0.78 | 2.64 | 0.00 |
time (sec) |
N/A | 0.652 | 0.323 | 0.183 | 0.211 | 0.259 | 0.331 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 153 | 72 | 301 | 291 | 68 | 151 | 300 | 0 |
N.S. |
1 | 0.92 | 0.43 | 1.80 | 1.74 | 0.41 | 0.90 | 1.80 | 0.00 |
time (sec) |
N/A | 0.458 | 0.153 | 0.125 | 0.203 | 0.278 | 0.254 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 52 | 50 | 63 | 110 | 44 | 65 | 65 | 43 |
N.S. |
1 | 0.96 | 0.93 | 1.17 | 2.04 | 0.81 | 1.20 | 1.20 | 0.80 |
time (sec) |
N/A | 0.347 | 0.046 | 0.011 | 0.188 | 0.265 | 0.239 | 0.259 | 1.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 124 | 143 | 127 | 0 | 0 | 217 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 1.02 | 0.00 | 0.00 | 1.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.581 | 0.288 | 0.000 | 0.000 | 0.267 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 182 | 194 | 204 | 0 | 0 | 317 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.12 | 0.00 | 0.00 | 1.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.662 | 1.027 | 0.000 | 0.000 | 0.261 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 537 | 486 | 353 | 1815 | 642 | 181 | 0 | 2163 | 0 |
N.S. |
1 | 0.91 | 0.66 | 3.38 | 1.20 | 0.34 | 0.00 | 4.03 | 0.00 |
time (sec) |
N/A | 0.880 | 0.489 | 0.207 | 0.208 | 0.259 | 0.000 | 0.364 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 238 | 118 | 659 | 369 | 109 | 0 | 707 | 0 |
N.S. |
1 | 0.91 | 0.45 | 2.52 | 1.41 | 0.42 | 0.00 | 2.71 | 0.00 |
time (sec) |
N/A | 0.538 | 0.254 | 0.186 | 0.193 | 0.264 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 92 | 65 | 133 | 136 | 58 | 94 | 128 | 75 |
N.S. |
1 | 1.08 | 0.76 | 1.56 | 1.60 | 0.68 | 1.11 | 1.51 | 0.88 |
time (sec) |
N/A | 0.445 | 0.062 | 0.009 | 0.201 | 0.270 | 0.296 | 0.263 | 1.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 232 | 253 | 231 | 0 | 0 | 503 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.00 | 0.00 | 0.00 | 2.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.801 | 0.053 | 0.000 | 0.000 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 329 | 334 | 211 | 0 | 0 | 706 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.64 | 0.00 | 0.00 | 2.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.973 | 0.364 | 0.000 | 0.000 | 0.292 | 0.000 | 0.000 | 0.000 |