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 | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 30 | 28 | 27 | 25 | 25 | 24 | 25 | 22 |
N.S. |
1 | 1.43 | 1.33 | 1.29 | 1.19 | 1.19 | 1.14 | 1.19 | 1.05 |
time (sec) |
N/A | 0.184 | 0.090 | 0.024 | 0.182 | 0.240 | 0.046 | 0.281 | 7.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 10 | 8 | 9 | 8 | 8 | 5 | 9 | 8 |
N.S. |
1 | 0.71 | 0.57 | 0.64 | 0.57 | 0.57 | 0.36 | 0.64 | 0.57 |
time (sec) |
N/A | 0.138 | 0.003 | 0.058 | 0.186 | 0.243 | 0.027 | 0.282 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 20 | 29 | 17 | 136 | 26 | 0 | 20 |
N.S. |
1 | 0.00 | 0.67 | 0.97 | 0.57 | 4.53 | 0.87 | 0.00 | 0.67 |
time (sec) |
N/A | 0.000 | 4.855 | 4.331 | 0.403 | 0.254 | 0.236 | 0.000 | 8.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 15 | 14 | 14 | 13 | 13 | 14 | 13 | 14 |
N.S. |
1 | 0.68 | 0.64 | 0.64 | 0.59 | 0.59 | 0.64 | 0.59 | 0.64 |
time (sec) |
N/A | 0.147 | 0.032 | 0.024 | 0.174 | 0.247 | 0.036 | 0.285 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 30 | 27 | 40 | 40 | 44 | 40 | 26 |
N.S. |
1 | 0.00 | 1.30 | 1.17 | 1.74 | 1.74 | 1.91 | 1.74 | 1.13 |
time (sec) |
N/A | 0.000 | 0.294 | 0.461 | 0.234 | 0.258 | 0.092 | 0.301 | 7.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 22 | 26 | 26 | 31 | 31 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.18 | 1.18 | 1.41 | 1.41 | 0.95 |
time (sec) |
N/A | 0.000 | 0.693 | 1.535 | 0.227 | 0.253 | 0.128 | 0.303 | 7.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 79 | 28 | 26 | 25 | 25 | 0 | 25 | 25 |
N.S. |
1 | 3.43 | 1.22 | 1.13 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.381 | 0.061 | 0.345 | 0.211 | 0.260 | 0.000 | 0.391 | 7.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 17 | 17 | 15 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 0.89 | 0.89 | 0.79 | 0.74 | 0.74 | 0.74 | 0.74 | 0.74 |
time (sec) |
N/A | 0.167 | 0.029 | 0.526 | 0.214 | 0.251 | 0.159 | 0.277 | 7.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 22 | 22 | 21 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 0.88 | 0.88 | 0.84 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.544 | 0.050 | 0.144 | 0.296 | 0.247 | 0.096 | 0.304 | 7.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 18 | 18 | 18 | 37 | 24 | 20 | 37 | 17 |
N.S. |
1 | 0.69 | 0.69 | 0.69 | 1.42 | 0.92 | 0.77 | 1.42 | 0.65 |
time (sec) |
N/A | 0.332 | 0.075 | 0.050 | 0.170 | 0.253 | 0.075 | 0.288 | 7.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 45 | 37 | 46 | 43 | 45 | 42 | 48 | 46 |
N.S. |
1 | 1.55 | 1.28 | 1.59 | 1.48 | 1.55 | 1.45 | 1.66 | 1.59 |
time (sec) |
N/A | 0.506 | 0.037 | 0.777 | 0.308 | 0.253 | 0.093 | 0.363 | 7.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 16 | 10 | 16 | 9 | 15 | 12 | 9 | 10 |
N.S. |
1 | 1.60 | 1.00 | 1.60 | 0.90 | 1.50 | 1.20 | 0.90 | 1.00 |
time (sec) |
N/A | 0.258 | 0.032 | 0.028 | 0.229 | 0.231 | 0.050 | 0.277 | 7.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 36 | 30 | 34 | 32 | 0 | 33 |
N.S. |
1 | 0.00 | 0.90 | 1.20 | 1.00 | 1.13 | 1.07 | 0.00 | 1.10 |
time (sec) |
N/A | 0.000 | 5.162 | 0.830 | 0.347 | 0.252 | 0.383 | 0.000 | 7.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 29 | 23 | 27 | 31 | 31 | 27 | 28 |
N.S. |
1 | 0.00 | 1.38 | 1.10 | 1.29 | 1.48 | 1.48 | 1.29 | 1.33 |
time (sec) |
N/A | 0.000 | 0.826 | 0.242 | 0.282 | 0.262 | 0.160 | 0.404 | 7.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 24 | 36 | 36 | 20 | 49 | 0 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 1.44 | 1.44 | 0.80 | 1.96 | 0.00 |
time (sec) |
N/A | 0.000 | 0.381 | 0.188 | 0.306 | 0.242 | 0.084 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 90 | 29 | 29 | 24 | 26 | 26 | 26 | 24 |
N.S. |
1 | 3.21 | 1.04 | 1.04 | 0.86 | 0.93 | 0.93 | 0.93 | 0.86 |
time (sec) |
N/A | 1.016 | 0.258 | 0.251 | 0.302 | 0.251 | 0.107 | 0.302 | 7.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 43 | 53 | 36 | 37 | 38 | 42 | 40 | 97 |
N.S. |
1 | 2.05 | 2.52 | 1.71 | 1.76 | 1.81 | 2.00 | 1.90 | 4.62 |
time (sec) |
N/A | 0.276 | 0.042 | 0.075 | 0.180 | 0.277 | 0.905 | 0.283 | 7.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 37 | 47 | 44 | 46 | 44 | 50 | 46 |
N.S. |
1 | 0.00 | 1.28 | 1.62 | 1.52 | 1.59 | 1.52 | 1.72 | 1.59 |
time (sec) |
N/A | 0.000 | 0.111 | 0.324 | 0.223 | 0.259 | 0.144 | 0.418 | 43.920 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 30 | 30 | 28 | 32 | 24 | 42 | 46 |
N.S. |
1 | 0.00 | 0.97 | 0.97 | 0.90 | 1.03 | 0.77 | 1.35 | 1.48 |
time (sec) |
N/A | 0.000 | 0.159 | 0.446 | 0.483 | 0.256 | 0.257 | 0.419 | 7.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 13 | 13 | 13 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 0.93 | 0.93 | 0.93 | 0.86 | 0.86 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.174 | 0.031 | 0.044 | 0.175 | 0.250 | 0.045 | 0.281 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 17 | 19 | 17 | 17 | 15 | 21 | 0 |
N.S. |
1 | 0.00 | 0.65 | 0.73 | 0.65 | 0.65 | 0.58 | 0.81 | 0.00 |
time (sec) |
N/A | 0.000 | 0.179 | 1.075 | 0.314 | 0.249 | 0.064 | 0.295 | 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 | 27 | 137 | 26 | 27 | 25 | 29 | 29 | 36 | 29 |
N.S. |
1 | 5.07 | 0.96 | 1.00 | 0.93 | 1.07 | 1.07 | 1.33 | 1.07 |
time (sec) |
N/A | 2.620 | 5.065 | 0.235 | 0.305 | 0.256 | 0.124 | 0.292 | 8.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 80 | 52 | 46 | 73 | 42 | 53 | 48 | 48 |
N.S. |
1 | 3.64 | 2.36 | 2.09 | 3.32 | 1.91 | 2.41 | 2.18 | 2.18 |
time (sec) |
N/A | 0.294 | 0.013 | 0.046 | 0.202 | 0.254 | 0.097 | 0.285 | 8.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 23 | 22 | 22 | 24 | 40 | 26 |
N.S. |
1 | 0.00 | 0.93 | 0.85 | 0.81 | 0.81 | 0.89 | 1.48 | 0.96 |
time (sec) |
N/A | 0.000 | 0.998 | 0.079 | 0.221 | 0.245 | 0.085 | 0.300 | 8.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 90 | 25 | 65 | 106 | 71 | 82 | 373 | 64 |
N.S. |
1 | 3.91 | 1.09 | 2.83 | 4.61 | 3.09 | 3.57 | 16.22 | 2.78 |
time (sec) |
N/A | 1.482 | 0.258 | 0.138 | 0.262 | 0.261 | 0.136 | 0.304 | 0.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 31 | 102 | 18 | 17 | 17 | 15 | 17 | 17 |
N.S. |
1 | 1.29 | 4.25 | 0.75 | 0.71 | 0.71 | 0.62 | 0.71 | 0.71 |
time (sec) |
N/A | 0.214 | 0.152 | 0.045 | 0.173 | 0.253 | 0.065 | 0.300 | 7.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 17 | 10 | 10 | 15 | 9 | 8 | 9 | 7 |
N.S. |
1 | 1.42 | 0.83 | 0.83 | 1.25 | 0.75 | 0.67 | 0.75 | 0.58 |
time (sec) |
N/A | 0.152 | 0.007 | 0.018 | 0.174 | 0.254 | 0.035 | 0.292 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 100 | 49 | 0 | 35 | 24 | 43 | 41 |
N.S. |
1 | 0.00 | 3.33 | 1.63 | 0.00 | 1.17 | 0.80 | 1.43 | 1.37 |
time (sec) |
N/A | 0.000 | 0.311 | 0.260 | 0.000 | 0.267 | 0.137 | 0.284 | 8.493 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 27 | 29 | 0 | 63 | 26 | 23 | 21 |
N.S. |
1 | 0.00 | 0.82 | 0.88 | 0.00 | 1.91 | 0.79 | 0.70 | 0.64 |
time (sec) |
N/A | 0.000 | 0.921 | 0.121 | 0.000 | 0.271 | 4.799 | 0.285 | 8.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 19 | 18 | 20 | 23 | 19 | 17 | 19 | 19 |
N.S. |
1 | 0.58 | 0.55 | 0.61 | 0.70 | 0.58 | 0.52 | 0.58 | 0.58 |
time (sec) |
N/A | 0.317 | 0.022 | 0.060 | 0.290 | 0.248 | 0.057 | 0.295 | 7.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 26 | 22 | 21 | 29 | 22 | 21 | 29 |
N.S. |
1 | 0.00 | 1.13 | 0.96 | 0.91 | 1.26 | 0.96 | 0.91 | 1.26 |
time (sec) |
N/A | 0.000 | 0.323 | 0.132 | 0.234 | 0.290 | 0.118 | 0.279 | 7.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 9 | 12 | 8 | 7 | 12 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 1.00 | 0.67 | 0.58 | 1.00 | 0.67 |
time (sec) |
N/A | 0.149 | 0.004 | 0.017 | 0.177 | 0.250 | 0.039 | 0.276 | 7.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | A | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 51 | 64 | 39 | 73 | 61 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.04 | 2.56 | 1.56 | 2.92 | 2.44 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.200 | 0.304 | 0.262 | 0.280 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 71 | 99 | 97 | 97 | 97 | 0 | 98 |
N.S. |
1 | 0.00 | 3.55 | 4.95 | 4.85 | 4.85 | 4.85 | 0.00 | 4.90 |
time (sec) |
N/A | 0.000 | 0.177 | 14.178 | 0.326 | 0.260 | 0.741 | 0.000 | 8.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 41 | 20 | 30 | 40 | 19 | 46 | 33 | 21 |
N.S. |
1 | 1.64 | 0.80 | 1.20 | 1.60 | 0.76 | 1.84 | 1.32 | 0.84 |
time (sec) |
N/A | 0.990 | 0.162 | 0.307 | 0.287 | 0.246 | 0.345 | 0.334 | 7.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 96 | 47 | 41 | 37 | 48 | 68 | 48 | 46 |
N.S. |
1 | 3.31 | 1.62 | 1.41 | 1.28 | 1.66 | 2.34 | 1.66 | 1.59 |
time (sec) |
N/A | 0.398 | 3.229 | 0.147 | 0.228 | 0.264 | 0.603 | 0.290 | 0.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 60 | 22 | 27 | 17 | 26 | 26 | 0 | 18 |
N.S. |
1 | 2.73 | 1.00 | 1.23 | 0.77 | 1.18 | 1.18 | 0.00 | 0.82 |
time (sec) |
N/A | 0.235 | 0.070 | 0.271 | 0.302 | 0.243 | 0.117 | 0.000 | 7.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 29 | 22 | 23 | 22 | 22 | 20 | 36 | 18 |
N.S. |
1 | 1.45 | 1.10 | 1.15 | 1.10 | 1.10 | 1.00 | 1.80 | 0.90 |
time (sec) |
N/A | 0.232 | 0.287 | 0.037 | 0.171 | 0.235 | 0.051 | 0.307 | 7.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 53 | 53 | 13 | 32 | 12 | 10 | 12 | 13 |
N.S. |
1 | 4.82 | 4.82 | 1.18 | 2.91 | 1.09 | 0.91 | 1.09 | 1.18 |
time (sec) |
N/A | 0.410 | 0.025 | 0.077 | 0.256 | 0.242 | 0.062 | 0.285 | 7.542 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 20 | 26 | 25 | 18 | 46 | 25 | 18 |
N.S. |
1 | 0.00 | 0.87 | 1.13 | 1.09 | 0.78 | 2.00 | 1.09 | 0.78 |
time (sec) |
N/A | 0.000 | 0.519 | 0.257 | 0.292 | 0.253 | 0.315 | 0.291 | 8.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 13 | 13 | 11 | 10 | 10 | 8 | 10 | 9 |
N.S. |
1 | 1.30 | 1.30 | 1.10 | 1.00 | 1.00 | 0.80 | 1.00 | 0.90 |
time (sec) |
N/A | 0.361 | 0.027 | 0.035 | 0.217 | 0.265 | 0.047 | 0.277 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 30 | 27 | 30 | 30 | 26 | 26 | 34 |
N.S. |
1 | 0.00 | 1.07 | 0.96 | 1.07 | 1.07 | 0.93 | 0.93 | 1.21 |
time (sec) |
N/A | 0.000 | 0.335 | 0.187 | 0.209 | 0.268 | 0.098 | 0.281 | 8.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 20 | 20 | 18 | 17 | 17 | 19 | 17 | 18 |
N.S. |
1 | 0.91 | 0.91 | 0.82 | 0.77 | 0.77 | 0.86 | 0.77 | 0.82 |
time (sec) |
N/A | 0.354 | 0.020 | 0.144 | 0.181 | 0.252 | 0.091 | 0.292 | 8.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 31 | 33 | 30 | 26 | 32 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.11 | 1.18 | 1.07 | 0.93 | 1.14 | 1.04 |
time (sec) |
N/A | 0.000 | 0.131 | 0.942 | 0.559 | 0.249 | 0.162 | 0.588 | 8.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 86 | 157 | 105 | 105 | 135 | 122 | 0 | 195 |
N.S. |
1 | 3.58 | 6.54 | 4.38 | 4.38 | 5.62 | 5.08 | 0.00 | 8.12 |
time (sec) |
N/A | 0.523 | 0.127 | 0.112 | 0.194 | 0.251 | 0.576 | 0.000 | 8.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 41 | 30 | 36 | 42 | 32 | 37 | 35 | 36 |
N.S. |
1 | 1.58 | 1.15 | 1.38 | 1.62 | 1.23 | 1.42 | 1.35 | 1.38 |
time (sec) |
N/A | 0.237 | 1.268 | 0.054 | 0.211 | 0.251 | 0.062 | 0.269 | 7.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 12 | 12 | 12 | 11 | 11 | 10 | 11 | 13 |
N.S. |
1 | 0.67 | 0.67 | 0.67 | 0.61 | 0.61 | 0.56 | 0.61 | 0.72 |
time (sec) |
N/A | 0.155 | 0.020 | 0.053 | 0.191 | 0.255 | 0.040 | 0.297 | 8.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 15 | 12 | 14 | 11 | 13 | 14 | 11 | 11 |
N.S. |
1 | 0.94 | 0.75 | 0.88 | 0.69 | 0.81 | 0.88 | 0.69 | 0.69 |
time (sec) |
N/A | 0.131 | 0.000 | 0.010 | 0.189 | 0.228 | 0.018 | 0.276 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 35 | 36 | 40 | 38 | 38 | 48 | 40 | 42 |
N.S. |
1 | 1.46 | 1.50 | 1.67 | 1.58 | 1.58 | 2.00 | 1.67 | 1.75 |
time (sec) |
N/A | 0.327 | 0.046 | 0.176 | 0.193 | 0.254 | 1.889 | 0.280 | 7.971 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 119 | 24 | 24 | 222 | 40 | 22 | 159 | 23 |
N.S. |
1 | 4.58 | 0.92 | 0.92 | 8.54 | 1.54 | 0.85 | 6.12 | 0.88 |
time (sec) |
N/A | 0.763 | 0.977 | 0.174 | 0.276 | 0.261 | 0.061 | 0.280 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 35 | 35 | 52 | 859 | 51 | 46 | 51 | 51 |
N.S. |
1 | 1.09 | 1.09 | 1.62 | 26.84 | 1.59 | 1.44 | 1.59 | 1.59 |
time (sec) |
N/A | 4.498 | 0.074 | 0.049 | 1.650 | 0.265 | 0.971 | 0.330 | 8.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 14 | 12 | 10 | 9 | 9 | 10 | 9 | 11 |
N.S. |
1 | 0.52 | 0.44 | 0.37 | 0.33 | 0.33 | 0.37 | 0.33 | 0.41 |
time (sec) |
N/A | 0.133 | 0.001 | 0.014 | 0.199 | 0.246 | 0.022 | 0.298 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 24 | 23 | 22 | 22 | 22 | 21 |
N.S. |
1 | 0.00 | 0.96 | 1.04 | 1.00 | 0.96 | 0.96 | 0.96 | 0.91 |
time (sec) |
N/A | 0.000 | 0.247 | 0.345 | 0.323 | 0.244 | 0.074 | 0.302 | 8.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 38 | 33 | 32 | 103 | 32 | 0 | 35 |
N.S. |
1 | 0.00 | 1.23 | 1.06 | 1.03 | 3.32 | 1.03 | 0.00 | 1.13 |
time (sec) |
N/A | 0.000 | 1.481 | 0.102 | 0.217 | 0.247 | 0.105 | 0.000 | 7.946 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 26 | 25 | 25 | 34 | 20 | 19 | 24 | 22 |
N.S. |
1 | 1.13 | 1.09 | 1.09 | 1.48 | 0.87 | 0.83 | 1.04 | 0.96 |
time (sec) |
N/A | 0.385 | 0.053 | 0.092 | 0.256 | 0.260 | 0.070 | 0.302 | 7.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | F(-2) | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 314 | 81 | 70 | 0 | 76 | 78 | 0 | 81 |
N.S. |
1 | 8.72 | 2.25 | 1.94 | 0.00 | 2.11 | 2.17 | 0.00 | 2.25 |
time (sec) |
N/A | 12.409 | 0.384 | 97.556 | 0.000 | 0.258 | 1.970 | 0.000 | 8.304 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 25 | 36 | 34 | 34 | 162 | 24 |
N.S. |
1 | 0.00 | 0.96 | 0.93 | 1.33 | 1.26 | 1.26 | 6.00 | 0.89 |
time (sec) |
N/A | 0.000 | 0.434 | 1.331 | 0.222 | 0.253 | 0.065 | 0.290 | 7.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 14 | 12 | 12 | 11 | 11 | 12 | 11 | 11 |
N.S. |
1 | 0.67 | 0.57 | 0.57 | 0.52 | 0.52 | 0.57 | 0.52 | 0.52 |
time (sec) |
N/A | 0.144 | 0.003 | 0.020 | 0.178 | 0.255 | 0.032 | 0.280 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 23 | 19 | 18 | 57 | 18 | 22 | 18 | 19 |
N.S. |
1 | 1.10 | 0.90 | 0.86 | 2.71 | 0.86 | 1.05 | 0.86 | 0.90 |
time (sec) |
N/A | 0.196 | 0.196 | 0.076 | 0.326 | 0.247 | 0.054 | 0.284 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 37 | 29 | 50 | 47 | 26 | 57 | 27 |
N.S. |
1 | 0.00 | 1.23 | 0.97 | 1.67 | 1.57 | 0.87 | 1.90 | 0.90 |
time (sec) |
N/A | 0.000 | 0.334 | 1.901 | 0.242 | 0.258 | 0.162 | 0.305 | 8.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 23 | 19 | 21 | 21 | 22 | 29 | 22 | 16 |
N.S. |
1 | 1.35 | 1.12 | 1.24 | 1.24 | 1.29 | 1.71 | 1.29 | 0.94 |
time (sec) |
N/A | 0.367 | 0.090 | 0.830 | 0.221 | 0.271 | 0.135 | 0.286 | 7.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 25 | 16 | 17 | 24 | 24 | 24 | 24 | 16 |
N.S. |
1 | 1.14 | 0.73 | 0.77 | 1.09 | 1.09 | 1.09 | 1.09 | 0.73 |
time (sec) |
N/A | 0.188 | 0.004 | 0.035 | 0.208 | 0.247 | 0.045 | 0.277 | 7.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 26 | 25 | 22 | 22 | 21 | 19 | 26 | 19 |
N.S. |
1 | 0.93 | 0.89 | 0.79 | 0.79 | 0.75 | 0.68 | 0.93 | 0.68 |
time (sec) |
N/A | 0.266 | 0.011 | 0.027 | 0.273 | 0.229 | 0.058 | 0.273 | 7.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 11 | 11 | 11 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 0.50 | 0.50 | 0.50 | 0.45 | 0.45 | 0.45 | 0.45 | 0.45 |
time (sec) |
N/A | 0.155 | 0.008 | 0.017 | 0.193 | 0.242 | 0.049 | 0.269 | 7.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 27 | 25 | 24 | 25 | 26 | 27 | 25 |
N.S. |
1 | 1.04 | 1.04 | 0.96 | 0.92 | 0.96 | 1.00 | 1.04 | 0.96 |
time (sec) |
N/A | 0.193 | 0.028 | 0.040 | 0.184 | 0.250 | 0.077 | 0.270 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 193 | 53 | 216 | 319 | 199 | 202 | 783 | 152 |
N.S. |
1 | 6.43 | 1.77 | 7.20 | 10.63 | 6.63 | 6.73 | 26.10 | 5.07 |
time (sec) |
N/A | 0.617 | 0.573 | 0.352 | 0.229 | 0.258 | 0.145 | 0.333 | 8.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 45 | 40 | 42 | 39 | 39 | 0 | 37 |
N.S. |
1 | 0.00 | 1.41 | 1.25 | 1.31 | 1.22 | 1.22 | 0.00 | 1.16 |
time (sec) |
N/A | 0.000 | 0.355 | 0.166 | 0.250 | 0.250 | 0.129 | 0.000 | 7.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 18 | 17 | 17 | 19 | 17 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.89 | 1.00 | 0.89 | 0.84 |
time (sec) |
N/A | 0.137 | 0.002 | 0.019 | 0.171 | 0.289 | 0.023 | 0.279 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 15 | 14 | 14 | 15 | 12 | 16 | 9 |
N.S. |
1 | 1.00 | 1.15 | 1.08 | 1.08 | 1.15 | 0.92 | 1.23 | 0.69 |
time (sec) |
N/A | 0.145 | 0.003 | 0.020 | 0.178 | 0.263 | 0.044 | 0.280 | 8.640 |
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 | 54 | 49 | 50 | 55 | 59 | 54 | 52 | 56 |
N.S. |
1 | 1.74 | 1.58 | 1.61 | 1.77 | 1.90 | 1.74 | 1.68 | 1.81 |
time (sec) |
N/A | 0.382 | 0.039 | 0.059 | 0.184 | 0.245 | 0.612 | 0.278 | 0.176 |
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 | 24 | 41 | 21 | 31 | 22 | 29 | 0 | 24 | 0 |
N.S. |
1 | 1.71 | 0.88 | 1.29 | 0.92 | 1.21 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.239 | 0.050 | 0.485 | 0.247 | 0.292 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 17 | 15 | 14 | 19 | 17 | 12 | 13 | 13 |
N.S. |
1 | 0.89 | 0.79 | 0.74 | 1.00 | 0.89 | 0.63 | 0.68 | 0.68 |
time (sec) |
N/A | 0.275 | 0.086 | 0.023 | 0.263 | 0.248 | 0.043 | 0.264 | 8.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 26 | 42 | 40 | 41 | 42 | 0 |
N.S. |
1 | 0.00 | 1.16 | 1.04 | 1.68 | 1.60 | 1.64 | 1.68 | 0.00 |
time (sec) |
N/A | 0.000 | 1.411 | 0.232 | 0.315 | 0.254 | 0.074 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | C | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 29 | 265 | 38 | 310 | 127 | 34 | 34 | 36 | 0 |
N.S. |
1 | 9.14 | 1.31 | 10.69 | 4.38 | 1.17 | 1.17 | 1.24 | 0.00 |
time (sec) |
N/A | 1.229 | 0.078 | 0.323 | 0.305 | 0.271 | 0.177 | 0.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 43 | 26 | 71 | 51 | 49 | 51 | 56 |
N.S. |
1 | 0.00 | 1.59 | 0.96 | 2.63 | 1.89 | 1.81 | 1.89 | 2.07 |
time (sec) |
N/A | 0.000 | 5.958 | 0.076 | 0.284 | 0.261 | 0.110 | 0.338 | 8.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 25 | 24 | 37 | 24 | 46 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.09 | 1.04 | 1.61 | 1.04 | 2.00 | 1.04 |
time (sec) |
N/A | 0.000 | 1.137 | 0.320 | 0.250 | 0.256 | 0.099 | 0.270 | 7.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 46 | 88 | 34 | 81 | 92 | 107 | 326 |
N.S. |
1 | 0.00 | 1.35 | 2.59 | 1.00 | 2.38 | 2.71 | 3.15 | 9.59 |
time (sec) |
N/A | 0.000 | 0.142 | 1.659 | 0.357 | 0.263 | 0.214 | 4.247 | 8.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 52 | 79 | 79 | 80 | 80 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.73 | 2.63 | 2.63 | 2.67 | 2.67 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 3.408 | 0.556 | 0.280 | 0.177 | 0.571 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 24 | 24 | 25 | 40 | 24 | 17 | 24 | 24 |
N.S. |
1 | 0.92 | 0.92 | 0.96 | 1.54 | 0.92 | 0.65 | 0.92 | 0.92 |
time (sec) |
N/A | 0.333 | 0.063 | 0.129 | 0.312 | 0.259 | 0.065 | 0.271 | 8.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 16 | 16 | 17 | 25 | 14 | 15 | 14 | 14 |
N.S. |
1 | 1.23 | 1.23 | 1.31 | 1.92 | 1.08 | 1.15 | 1.08 | 1.08 |
time (sec) |
N/A | 0.313 | 0.087 | 0.039 | 0.216 | 0.265 | 0.036 | 0.272 | 8.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 20 | 20 | 17 | 25 | 16 | 24 | 16 | 16 |
N.S. |
1 | 0.95 | 0.95 | 0.81 | 1.19 | 0.76 | 1.14 | 0.76 | 0.76 |
time (sec) |
N/A | 0.378 | 0.304 | 0.092 | 0.211 | 0.257 | 0.107 | 0.271 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 49 | 39 | 29 | 0 | 41 | 26 | 41 | 41 |
N.S. |
1 | 1.44 | 1.15 | 0.85 | 0.00 | 1.21 | 0.76 | 1.21 | 1.21 |
time (sec) |
N/A | 0.593 | 0.153 | 0.117 | 0.000 | 0.251 | 0.113 | 0.269 | 0.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 99 | 95 | 23 | 61 | 38 | 32 | 194 | 61 |
N.S. |
1 | 4.71 | 4.52 | 1.10 | 2.90 | 1.81 | 1.52 | 9.24 | 2.90 |
time (sec) |
N/A | 1.014 | 0.439 | 10.441 | 0.314 | 0.299 | 0.074 | 0.462 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 19 | 17 | 18 | 25 | 17 | 14 | 17 | 0 |
N.S. |
1 | 1.06 | 0.94 | 1.00 | 1.39 | 0.94 | 0.78 | 0.94 | 0.00 |
time (sec) |
N/A | 0.667 | 0.146 | 0.796 | 0.327 | 0.271 | 0.108 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 28 | 44 | 45 | 42 | 20 | 44 | 43 |
N.S. |
1 | 0.00 | 0.93 | 1.47 | 1.50 | 1.40 | 0.67 | 1.47 | 1.43 |
time (sec) |
N/A | 0.000 | 0.157 | 0.716 | 0.416 | 0.254 | 0.829 | 0.330 | 8.494 |
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 | 28 | 40 | 38 | 30 | 218 | 35 | 34 | 42 | 39 |
N.S. |
1 | 1.43 | 1.36 | 1.07 | 7.79 | 1.25 | 1.21 | 1.50 | 1.39 |
time (sec) |
N/A | 3.034 | 0.377 | 1.018 | 0.431 | 0.259 | 0.360 | 0.541 | 8.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 20 | 26 | 22 | 19 | 29 | 15 | 19 | 61 |
N.S. |
1 | 0.87 | 1.13 | 0.96 | 0.83 | 1.26 | 0.65 | 0.83 | 2.65 |
time (sec) |
N/A | 0.233 | 0.027 | 0.112 | 0.198 | 0.255 | 0.114 | 0.278 | 7.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 0 | 47 | 53 | 53 | 48 | 48 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.27 | 1.43 | 1.43 | 1.30 | 1.30 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 4.987 | 0.251 | 0.267 | 0.395 | 0.449 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 21 | 22 | 21 | 28 | 21 | 19 | 21 | 0 |
N.S. |
1 | 0.88 | 0.92 | 0.88 | 1.17 | 0.88 | 0.79 | 0.88 | 0.00 |
time (sec) |
N/A | 0.388 | 0.185 | 0.134 | 0.301 | 0.244 | 0.334 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 20 | 20 | 16 | 15 | 27 | 17 | 19 | 15 |
N.S. |
1 | 0.77 | 0.77 | 0.62 | 0.58 | 1.04 | 0.65 | 0.73 | 0.58 |
time (sec) |
N/A | 0.278 | 0.239 | 0.104 | 0.171 | 0.252 | 0.137 | 0.297 | 0.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 18 | 31 | 28 | 28 | 32 | 28 | 30 |
N.S. |
1 | 0.90 | 0.90 | 1.55 | 1.40 | 1.40 | 1.60 | 1.40 | 1.50 |
time (sec) |
N/A | 0.773 | 0.201 | 0.540 | 0.437 | 0.284 | 0.236 | 1.345 | 8.315 |
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 | 37 | 65 | 58 | 48 | 88 | 45 | 48 | 376 | 59 |
N.S. |
1 | 1.76 | 1.57 | 1.30 | 2.38 | 1.22 | 1.30 | 10.16 | 1.59 |
time (sec) |
N/A | 0.438 | 3.152 | 0.098 | 0.330 | 0.252 | 0.081 | 0.328 | 7.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | F(-1) | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 28 | 24 | 20 | 0 | 19 | 0 | 23 |
N.S. |
1 | 0.00 | 1.22 | 1.04 | 0.87 | 0.00 | 0.83 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 1.524 | 0.816 | 0.380 | 0.000 | 0.133 | 0.000 | 8.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 17 | 21 | 16 | 14 | 20 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.85 | 1.05 | 0.80 | 0.70 | 1.00 | 0.85 |
time (sec) |
N/A | 0.000 | 0.250 | 1.007 | 0.313 | 0.277 | 0.071 | 0.322 | 8.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 59 | 58 | 432 | 134 | 133 | 0 | 1107 |
N.S. |
1 | 0.00 | 2.36 | 2.32 | 17.28 | 5.36 | 5.32 | 0.00 | 44.28 |
time (sec) |
N/A | 0.000 | 0.509 | 0.326 | 195.694 | 0.276 | 1.770 | 0.000 | 9.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 29 | 42 | 29 | 35 | 19 | 32 | 30 | 27 |
N.S. |
1 | 1.45 | 2.10 | 1.45 | 1.75 | 0.95 | 1.60 | 1.50 | 1.35 |
time (sec) |
N/A | 0.571 | 0.104 | 0.218 | 0.295 | 0.254 | 0.242 | 0.324 | 8.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 20 | 20 | 21 | 21 | 28 | 19 | 21 | 23 |
N.S. |
1 | 1.05 | 1.05 | 1.11 | 1.11 | 1.47 | 1.00 | 1.11 | 1.21 |
time (sec) |
N/A | 0.499 | 0.127 | 0.094 | 0.289 | 0.277 | 0.064 | 0.297 | 8.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 21 | 0 | 20 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.95 | 0.00 | 0.95 | 0.95 |
time (sec) |
N/A | 0.640 | 0.364 | 0.099 | 0.000 | 0.251 | 0.000 | 0.705 | 9.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 35 | 86 | 32 | 31 | 0 | 38 |
N.S. |
1 | 0.00 | 1.00 | 1.25 | 3.07 | 1.14 | 1.11 | 0.00 | 1.36 |
time (sec) |
N/A | 0.000 | 2.756 | 0.679 | 0.385 | 0.257 | 0.820 | 0.000 | 13.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 30 | 27 | 41 | 18 | 41 | 25 | 35 |
N.S. |
1 | 0.00 | 1.43 | 1.29 | 1.95 | 0.86 | 1.95 | 1.19 | 1.67 |
time (sec) |
N/A | 0.000 | 0.159 | 0.711 | 0.290 | 0.247 | 0.158 | 0.301 | 9.540 |