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 | F | A | C | A | A | F(-2) | C | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 34 | 293 | 33 | 35 | 0 | 51 | 34 |
N.S. |
1 | 0.00 | 1.10 | 9.45 | 1.06 | 1.13 | 0.00 | 1.65 | 1.10 |
time (sec) |
N/A | 0.000 | 0.115 | 5.266 | 0.336 | 0.273 | 0.000 | 0.364 | 14.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 52 | 53 | 40 | 127 | 78 | 37 | 112 | 41 |
N.S. |
1 | 1.68 | 1.71 | 1.29 | 4.10 | 2.52 | 1.19 | 3.61 | 1.32 |
time (sec) |
N/A | 0.555 | 0.057 | 0.436 | 0.245 | 0.265 | 0.163 | 0.285 | 13.781 |
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 | 23 | 23 | 23 | 25 | 21 | 19 | 21 | 21 |
N.S. |
1 | 0.88 | 0.88 | 0.88 | 0.96 | 0.81 | 0.73 | 0.81 | 0.81 |
time (sec) |
N/A | 0.673 | 2.010 | 2.228 | 0.323 | 0.252 | 0.200 | 0.300 | 14.585 |
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 | 14 | 0 | 22 | 13 | 19 | 19 | 7 | 19 | 12 |
N.S. |
1 | 0.00 | 1.57 | 0.93 | 1.36 | 1.36 | 0.50 | 1.36 | 0.86 |
time (sec) |
N/A | 0.000 | 0.647 | 0.127 | 0.207 | 0.251 | 0.049 | 0.273 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 217 | 218 | 470 | 199 | 196 | 1836 | 1862 |
N.S. |
1 | 0.00 | 6.78 | 6.81 | 14.69 | 6.22 | 6.12 | 57.38 | 58.19 |
time (sec) |
N/A | 0.000 | 0.969 | 0.529 | 8.147 | 0.260 | 3.185 | 5.727 | 14.693 |
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 | 6 | 8 | 6 | 10 | 9 | 6 | 5 | 11 | 9 |
N.S. |
1 | 1.33 | 1.00 | 1.67 | 1.50 | 1.00 | 0.83 | 1.83 | 1.50 |
time (sec) |
N/A | 0.126 | 0.004 | 0.148 | 0.215 | 0.241 | 0.029 | 0.278 | 0.114 |
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 | 42 | 48 | 37 | 36 | 36 | 44 | 35 | 36 |
N.S. |
1 | 1.68 | 1.92 | 1.48 | 1.44 | 1.44 | 1.76 | 1.40 | 1.44 |
time (sec) |
N/A | 0.253 | 0.012 | 0.134 | 0.203 | 0.253 | 0.070 | 0.261 | 13.690 |
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 | 23 | 25 | 18 | 16 | 32 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.09 | 0.78 | 0.70 | 1.39 | 0.65 | 0.65 | 0.65 | 0.65 |
time (sec) |
N/A | 0.523 | 0.173 | 0.117 | 0.249 | 0.239 | 0.035 | 0.276 | 13.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 10 | 9 | 35 | 10 | 35 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 2.69 | 0.77 | 2.69 | 0.69 |
time (sec) |
N/A | 0.222 | 0.040 | 0.561 | 0.211 | 0.254 | 0.076 | 0.273 | 13.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 47 | 79 | 45 | 87 | 88 | 94 | 82 | 91 |
N.S. |
1 | 1.52 | 2.55 | 1.45 | 2.81 | 2.84 | 3.03 | 2.65 | 2.94 |
time (sec) |
N/A | 0.486 | 0.144 | 0.276 | 0.194 | 0.251 | 3.597 | 0.275 | 13.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 28 | 35 | 39 | 33 | 0 | 70 | 115 |
N.S. |
1 | 0.00 | 0.88 | 1.09 | 1.22 | 1.03 | 0.00 | 2.19 | 3.59 |
time (sec) |
N/A | 0.000 | 0.419 | 2.881 | 0.321 | 0.250 | 0.000 | 0.309 | 14.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 59 | 74 | 64 | 1021 | 47 | 49 | 47 | 48 |
N.S. |
1 | 2.27 | 2.85 | 2.46 | 39.27 | 1.81 | 1.88 | 1.81 | 1.85 |
time (sec) |
N/A | 0.505 | 0.510 | 0.427 | 0.335 | 0.243 | 0.280 | 0.279 | 18.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 105 | 25 | 22 | 85 | 33 | 17 | 35 | 16 |
N.S. |
1 | 7.00 | 1.67 | 1.47 | 5.67 | 2.20 | 1.13 | 2.33 | 1.07 |
time (sec) |
N/A | 0.799 | 0.069 | 0.240 | 0.241 | 0.264 | 0.076 | 0.278 | 13.147 |
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 | 34 | 34 | 32 | 36 | 29 | 36 | 51 |
N.S. |
1 | 0.00 | 1.21 | 1.21 | 1.14 | 1.29 | 1.04 | 1.29 | 1.82 |
time (sec) |
N/A | 0.000 | 1.453 | 0.254 | 0.329 | 0.267 | 0.090 | 0.337 | 13.539 |
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 | 24 | 24 | 26 | 25 | 24 | 24 | 23 | 28 |
N.S. |
1 | 1.09 | 1.09 | 1.18 | 1.14 | 1.09 | 1.09 | 1.05 | 1.27 |
time (sec) |
N/A | 0.194 | 0.011 | 0.104 | 0.196 | 0.253 | 0.070 | 0.264 | 12.900 |
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 | 27 | 18 | 21 | 21 | 26 | 20 | 44 | 26 |
N.S. |
1 | 1.42 | 0.95 | 1.11 | 1.11 | 1.37 | 1.05 | 2.32 | 1.37 |
time (sec) |
N/A | 0.284 | 0.393 | 0.239 | 0.201 | 0.260 | 0.069 | 0.269 | 0.246 |
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 | 23 | 0 | 37 | 40 | 21 | 19 | 44 | 43 | 19 |
N.S. |
1 | 0.00 | 1.61 | 1.74 | 0.91 | 0.83 | 1.91 | 1.87 | 0.83 |
time (sec) |
N/A | 0.000 | 0.506 | 25.062 | 0.343 | 0.265 | 1.630 | 0.541 | 14.111 |
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 | 17 | 13 | 12 | 11 | 17 | 10 | 12 | 11 |
N.S. |
1 | 0.68 | 0.52 | 0.48 | 0.44 | 0.68 | 0.40 | 0.48 | 0.44 |
time (sec) |
N/A | 0.157 | 0.002 | 0.102 | 0.184 | 0.257 | 0.031 | 0.272 | 14.206 |
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 | 25 | 0 | 29 | 29 | 36 | 32 | 36 | 68 | 70 |
N.S. |
1 | 0.00 | 1.16 | 1.16 | 1.44 | 1.28 | 1.44 | 2.72 | 2.80 |
time (sec) |
N/A | 0.000 | 5.145 | 0.519 | 0.303 | 0.261 | 0.128 | 0.329 | 15.273 |
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 | 17 | 0 | 16 | 20 | 14 | 30 | 15 | 14 | 16 |
N.S. |
1 | 0.00 | 0.94 | 1.18 | 0.82 | 1.76 | 0.88 | 0.82 | 0.94 |
time (sec) |
N/A | 0.000 | 0.887 | 0.836 | 0.292 | 0.260 | 124.108 | 0.284 | 14.789 |
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 | 30 | 20 | 19 | 20 | 20 | 19 | 19 | 23 | 19 |
N.S. |
1 | 0.67 | 0.63 | 0.67 | 0.67 | 0.63 | 0.63 | 0.77 | 0.63 |
time (sec) |
N/A | 0.229 | 0.010 | 0.075 | 0.200 | 0.273 | 0.045 | 0.277 | 0.084 |
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 | 33 | 29 | 21 | 20 | 29 | 22 | 30 | 22 |
N.S. |
1 | 1.18 | 1.04 | 0.75 | 0.71 | 1.04 | 0.79 | 1.07 | 0.79 |
time (sec) |
N/A | 0.240 | 0.058 | 0.065 | 0.215 | 0.266 | 0.121 | 0.274 | 14.273 |
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 | 19 | 41 | 35 | 32 | 34 | 30 | 31 | 34 | 34 |
N.S. |
1 | 2.16 | 1.84 | 1.68 | 1.79 | 1.58 | 1.63 | 1.79 | 1.79 |
time (sec) |
N/A | 0.259 | 0.064 | 0.146 | 0.235 | 0.270 | 0.132 | 0.273 | 13.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 34 | 50 | 73 | 35 | 53 | 0 | 0 |
N.S. |
1 | 0.00 | 1.26 | 1.85 | 2.70 | 1.30 | 1.96 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.723 | 2.954 | 0.322 | 0.263 | 0.173 | 0.000 | 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 | 25 | 17 | 15 | 16 | 15 | 24 | 12 | 16 | 15 |
N.S. |
1 | 0.68 | 0.60 | 0.64 | 0.60 | 0.96 | 0.48 | 0.64 | 0.60 |
time (sec) |
N/A | 0.233 | 0.013 | 0.067 | 0.190 | 0.267 | 0.040 | 0.266 | 0.060 |
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 | 10 | 10 | 10 | 9 | 9 | 10 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.90 | 0.90 | 1.00 | 0.90 | 0.90 |
time (sec) |
N/A | 0.194 | 0.010 | 0.302 | 0.244 | 0.268 | 0.103 | 0.267 | 14.426 |
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 | 25 | 23 | 24 | 24 | 173 | 23 | 19 | 23 | 23 |
N.S. |
1 | 0.92 | 0.96 | 0.96 | 6.92 | 0.92 | 0.76 | 0.92 | 0.92 |
time (sec) |
N/A | 0.528 | 0.312 | 1.275 | 0.299 | 0.302 | 0.125 | 0.292 | 15.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 44 | 43 | 36 | 58 | 38 | 42 | 38 | 22 |
N.S. |
1 | 1.69 | 1.65 | 1.38 | 2.23 | 1.46 | 1.62 | 1.46 | 0.85 |
time (sec) |
N/A | 0.306 | 0.269 | 0.595 | 0.233 | 0.262 | 0.078 | 0.293 | 0.154 |
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 | 22 | 25 | 20 | 21 | 21 | 17 | 21 | 23 |
N.S. |
1 | 1.38 | 1.56 | 1.25 | 1.31 | 1.31 | 1.06 | 1.31 | 1.44 |
time (sec) |
N/A | 0.157 | 0.018 | 0.072 | 0.197 | 0.273 | 0.045 | 0.282 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 70 | 20 | 35 | 424 | 33 | 39 | 45 | 20 |
N.S. |
1 | 2.92 | 0.83 | 1.46 | 17.67 | 1.38 | 1.62 | 1.88 | 0.83 |
time (sec) |
N/A | 1.257 | 1.227 | 0.194 | 0.281 | 0.256 | 0.120 | 0.269 | 14.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 79 | 55 | 46 | 43 | 43 | 66 | 43 | 65 |
N.S. |
1 | 3.43 | 2.39 | 2.00 | 1.87 | 1.87 | 2.87 | 1.87 | 2.83 |
time (sec) |
N/A | 0.254 | 0.198 | 0.147 | 0.201 | 0.272 | 0.102 | 0.281 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 30 | 30 | 28 | 0 | 27 | 22 | 27 | 27 |
N.S. |
1 | 1.03 | 1.03 | 0.97 | 0.00 | 0.93 | 0.76 | 0.93 | 0.93 |
time (sec) |
N/A | 0.636 | 0.067 | 2.393 | 0.000 | 0.264 | 0.088 | 0.299 | 24.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 39 | 15 | 17 | 34 | 15 | 14 | 0 | 15 |
N.S. |
1 | 2.60 | 1.00 | 1.13 | 2.27 | 1.00 | 0.93 | 0.00 | 1.00 |
time (sec) |
N/A | 0.223 | 0.025 | 0.487 | 0.326 | 0.276 | 0.075 | 0.000 | 14.508 |
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 | 6 | 6 | 6 | 5 | 5 | 5 | 6 | 5 |
N.S. |
1 | 0.60 | 0.60 | 0.60 | 0.50 | 0.50 | 0.50 | 0.60 | 0.50 |
time (sec) |
N/A | 0.124 | 0.000 | 0.137 | 0.199 | 0.283 | 0.020 | 0.261 | 15.063 |
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 | 28 | 0 | 27 | 24 | 35 | 23 | 19 | 0 | 38 |
N.S. |
1 | 0.00 | 0.96 | 0.86 | 1.25 | 0.82 | 0.68 | 0.00 | 1.36 |
time (sec) |
N/A | 0.000 | 5.178 | 2.467 | 0.406 | 0.267 | 0.326 | 0.000 | 15.154 |
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 | 23 | 0 | 29 | 19 | 18 | 28 | 22 | 38 | 21 |
N.S. |
1 | 0.00 | 1.26 | 0.83 | 0.78 | 1.22 | 0.96 | 1.65 | 0.91 |
time (sec) |
N/A | 0.000 | 1.624 | 0.655 | 0.238 | 0.251 | 0.100 | 0.278 | 0.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 103 | 57 | 68 | 63 | 63 | 66 | 63 | 91 |
N.S. |
1 | 5.42 | 3.00 | 3.58 | 3.32 | 3.32 | 3.47 | 3.32 | 4.79 |
time (sec) |
N/A | 0.352 | 0.278 | 0.138 | 0.199 | 0.251 | 0.076 | 0.289 | 15.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 136 | 128 | 105 | 122 | 131 | 0 |
N.S. |
1 | 0.00 | 0.00 | 5.04 | 4.74 | 3.89 | 4.52 | 4.85 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.813 | 0.393 | 0.255 | 1.073 | 0.459 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 46 | 55 | 100 | 54 | 44 | 48 | 55 |
N.S. |
1 | 0.00 | 1.31 | 1.57 | 2.86 | 1.54 | 1.26 | 1.37 | 1.57 |
time (sec) |
N/A | 0.000 | 0.151 | 1.889 | 0.518 | 0.259 | 0.199 | 0.761 | 14.496 |
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 | 27 | 111 | 37 | 32 | 35 | 31 | 29 | 35 | 31 |
N.S. |
1 | 4.11 | 1.37 | 1.19 | 1.30 | 1.15 | 1.07 | 1.30 | 1.15 |
time (sec) |
N/A | 3.336 | 0.701 | 12.408 | 0.306 | 0.260 | 7.754 | 0.311 | 15.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 57 | 51 | 57 | 51 | 53 | 65 | 63 |
N.S. |
1 | 0.00 | 2.11 | 1.89 | 2.11 | 1.89 | 1.96 | 2.41 | 2.33 |
time (sec) |
N/A | 0.000 | 0.734 | 3.833 | 0.204 | 0.270 | 0.229 | 0.300 | 15.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 28 | 27 | 132 | 28 | 20 | 52 | 44 |
N.S. |
1 | 0.00 | 0.80 | 0.77 | 3.77 | 0.80 | 0.57 | 1.49 | 1.26 |
time (sec) |
N/A | 0.000 | 1.012 | 1.131 | 0.277 | 0.261 | 0.142 | 0.398 | 0.622 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 36 | 0 | 16 | 31 | 18 | 17 | 20 | 24 |
N.S. |
1 | 1.80 | 0.00 | 0.80 | 1.55 | 0.90 | 0.85 | 1.00 | 1.20 |
time (sec) |
N/A | 0.317 | 0.000 | 0.237 | 0.306 | 0.255 | 0.074 | 0.281 | 16.854 |
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 | 21 | 23 | 26 | 37 | 20 | 26 | 22 |
N.S. |
1 | 0.00 | 0.75 | 0.82 | 0.93 | 1.32 | 0.71 | 0.93 | 0.79 |
time (sec) |
N/A | 0.000 | 0.414 | 1.073 | 0.303 | 0.243 | 0.057 | 0.281 | 13.862 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 48 | 47 | 44 | 0 | 40 | 54 | 0 | 31 |
N.S. |
1 | 1.78 | 1.74 | 1.63 | 0.00 | 1.48 | 2.00 | 0.00 | 1.15 |
time (sec) |
N/A | 0.355 | 0.192 | 0.541 | 0.000 | 0.248 | 0.158 | 0.000 | 13.548 |
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 | 9 | 9 | 9 | 10 | 9 | 9 | 8 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.89 | 1.00 | 1.00 |
time (sec) |
N/A | 0.147 | 0.044 | 0.478 | 0.189 | 0.242 | 0.045 | 0.277 | 12.579 |
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 | 26 | 0 | 30 | 23 | 31 | 40 | 22 | 50 | 30 |
N.S. |
1 | 0.00 | 1.15 | 0.88 | 1.19 | 1.54 | 0.85 | 1.92 | 1.15 |
time (sec) |
N/A | 0.000 | 3.298 | 0.214 | 0.252 | 0.264 | 0.114 | 0.278 | 12.743 |
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 | 21 | 21 | 18 | 20 | 19 | 20 | 20 |
N.S. |
1 | 0.00 | 0.95 | 0.95 | 0.82 | 0.91 | 0.86 | 0.91 | 0.91 |
time (sec) |
N/A | 0.000 | 0.641 | 0.796 | 0.319 | 0.280 | 0.159 | 0.330 | 12.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 61 | 38 | 47 | 83 | 53 | 70 | 114 | 53 |
N.S. |
1 | 1.61 | 1.00 | 1.24 | 2.18 | 1.39 | 1.84 | 3.00 | 1.39 |
time (sec) |
N/A | 0.352 | 0.164 | 0.322 | 0.228 | 0.261 | 0.118 | 0.290 | 12.486 |
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 | 18 | 17 | 18 | 16 | 17 | 14 | 16 | 19 |
N.S. |
1 | 1.06 | 1.00 | 1.06 | 0.94 | 1.00 | 0.82 | 0.94 | 1.12 |
time (sec) |
N/A | 0.310 | 0.098 | 0.423 | 0.253 | 0.255 | 0.065 | 0.282 | 12.240 |
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 | 19 | 0 | 23 | 25 | 22 | 22 | 20 | 24 | 24 |
N.S. |
1 | 0.00 | 1.21 | 1.32 | 1.16 | 1.16 | 1.05 | 1.26 | 1.26 |
time (sec) |
N/A | 0.000 | 1.206 | 0.103 | 0.239 | 0.255 | 0.120 | 0.288 | 0.293 |
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 | 18 | 16 | 18 | 16 | 0 | 24 | 12 | 26 | 15 |
N.S. |
1 | 0.89 | 1.00 | 0.89 | 0.00 | 1.33 | 0.67 | 1.44 | 0.83 |
time (sec) |
N/A | 0.280 | 0.095 | 0.868 | 0.000 | 0.244 | 0.057 | 0.285 | 0.093 |
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 | 22 | 28 | 27 | 18 | 18 | 27 | 14 | 18 | 17 |
N.S. |
1 | 1.27 | 1.23 | 0.82 | 0.82 | 1.23 | 0.64 | 0.82 | 0.77 |
time (sec) |
N/A | 0.261 | 0.021 | 0.289 | 0.207 | 0.248 | 0.104 | 0.281 | 12.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | C | F | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 0 | 44 | 0 | 59 | 34 | 61 | 60 |
N.S. |
1 | 0.00 | 0.00 | 1.26 | 0.00 | 1.69 | 0.97 | 1.74 | 1.71 |
time (sec) |
N/A | 0.000 | 0.000 | 2.412 | 0.000 | 0.260 | 0.209 | 0.446 | 12.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 29 | 25 | 25 | 30 | 0 | 25 | 24 |
N.S. |
1 | 0.00 | 1.07 | 0.93 | 0.93 | 1.11 | 0.00 | 0.93 | 0.89 |
time (sec) |
N/A | 0.000 | 0.537 | 0.181 | 0.513 | 0.270 | 0.000 | 0.283 | 12.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 31 | 21 | 50 | 40 | 36 | 49 | 0 |
N.S. |
1 | 0.00 | 0.94 | 0.64 | 1.52 | 1.21 | 1.09 | 1.48 | 0.00 |
time (sec) |
N/A | 0.000 | 2.427 | 0.852 | 0.237 | 0.270 | 0.098 | 0.286 | 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 | 17 | 17 | 15 | 15 | 18 | 21 | 15 | 46 | 20 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 1.06 | 1.24 | 0.88 | 2.71 | 1.18 |
time (sec) |
N/A | 0.202 | 0.020 | 0.200 | 0.196 | 0.246 | 0.209 | 0.279 | 0.179 |
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 | 19 | 23 | 23 | 20 | 36 | 158 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 1.05 | 1.05 | 0.91 | 1.64 | 7.18 |
time (sec) |
N/A | 0.000 | 0.553 | 25.934 | 0.250 | 0.236 | 0.064 | 0.272 | 13.245 |
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 | 22 | 26 | 24 | 25 | 141 | 27 | 42 | 45 | 24 |
N.S. |
1 | 1.18 | 1.09 | 1.14 | 6.41 | 1.23 | 1.91 | 2.05 | 1.09 |
time (sec) |
N/A | 0.456 | 0.024 | 1.043 | 0.194 | 0.282 | 0.126 | 0.280 | 13.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 715 | 26 | 31 | 1175 | 29 | 26 | 30 | 30 |
N.S. |
1 | 23.83 | 0.87 | 1.03 | 39.17 | 0.97 | 0.87 | 1.00 | 1.00 |
time (sec) |
N/A | 2.365 | 0.228 | 0.998 | 0.350 | 0.258 | 0.138 | 0.314 | 14.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 49 | 59 | 54 | 62 | 53 | 68 | 56 |
N.S. |
1 | 0.00 | 1.48 | 1.79 | 1.64 | 1.88 | 1.61 | 2.06 | 1.70 |
time (sec) |
N/A | 0.000 | 0.167 | 0.728 | 0.374 | 0.266 | 0.207 | 0.631 | 12.888 |
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 | 36 | 31 | 25 | 35 | 35 | 20 | 35 | 24 |
N.S. |
1 | 1.44 | 1.24 | 1.00 | 1.40 | 1.40 | 0.80 | 1.40 | 0.96 |
time (sec) |
N/A | 0.167 | 0.042 | 0.164 | 0.190 | 0.257 | 0.024 | 0.263 | 12.617 |
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 | 17 | 44 | 16 | 18 | 17 | 15 | 15 | 17 | 17 |
N.S. |
1 | 2.59 | 0.94 | 1.06 | 1.00 | 0.88 | 0.88 | 1.00 | 1.00 |
time (sec) |
N/A | 0.274 | 0.016 | 0.460 | 0.198 | 0.257 | 0.180 | 0.278 | 0.197 |
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 | 24 | 26 | 22 | 16 | 15 | 15 | 19 | 15 | 15 |
N.S. |
1 | 1.08 | 0.92 | 0.67 | 0.62 | 0.62 | 0.79 | 0.62 | 0.62 |
time (sec) |
N/A | 0.440 | 0.110 | 1.654 | 0.224 | 0.257 | 0.064 | 0.278 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 38 | 56 | 46 | 42 | 54 | 140 | 0 |
N.S. |
1 | 0.00 | 1.36 | 2.00 | 1.64 | 1.50 | 1.93 | 5.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.659 | 3.631 | 0.350 | 0.268 | 0.136 | 0.952 | 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 | 18 | 23 | 23 | 20 | 19 | 19 | 17 | 21 | 19 |
N.S. |
1 | 1.28 | 1.28 | 1.11 | 1.06 | 1.06 | 0.94 | 1.17 | 1.06 |
time (sec) |
N/A | 0.358 | 0.019 | 0.148 | 0.186 | 0.268 | 0.320 | 0.289 | 0.248 |
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 | 36 | 0 | 34 | 38 | 35 | 35 | 29 | 36 | 0 |
N.S. |
1 | 0.00 | 0.94 | 1.06 | 0.97 | 0.97 | 0.81 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.096 | 1.766 | 0.347 | 0.272 | 0.179 | 0.310 | 0.000 |
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 | 24 | 0 | 20 | 16 | 15 | 128 | 17 | 0 | 17 |
N.S. |
1 | 0.00 | 0.83 | 0.67 | 0.62 | 5.33 | 0.71 | 0.00 | 0.71 |
time (sec) |
N/A | 0.000 | 1.253 | 0.690 | 0.605 | 0.285 | 24.071 | 0.000 | 12.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 62 | 43 | 12 | 47 | 11 | 10 | 11 | 11 |
N.S. |
1 | 5.17 | 3.58 | 1.00 | 3.92 | 0.92 | 0.83 | 0.92 | 0.92 |
time (sec) |
N/A | 0.227 | 0.133 | 0.152 | 0.216 | 0.268 | 0.040 | 0.289 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 25 | 35 | 47 | 44 | 67 | 58 | 39 | 35 |
N.S. |
1 | 1.04 | 1.46 | 1.96 | 1.83 | 2.79 | 2.42 | 1.62 | 1.46 |
time (sec) |
N/A | 0.192 | 0.015 | 0.297 | 0.189 | 0.260 | 0.114 | 0.271 | 0.193 |
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 | 23 | 27 | 27 | 24 | 40 | 28 | 20 | 27 | 24 |
N.S. |
1 | 1.17 | 1.17 | 1.04 | 1.74 | 1.22 | 0.87 | 1.17 | 1.04 |
time (sec) |
N/A | 0.376 | 0.129 | 0.164 | 0.226 | 0.260 | 0.044 | 0.295 | 12.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 24 | 26 | 89 | 49 | 49 | 43 | 104 |
N.S. |
1 | 0.96 | 0.96 | 1.04 | 3.56 | 1.96 | 1.96 | 1.72 | 4.16 |
time (sec) |
N/A | 0.433 | 0.505 | 42.910 | 0.324 | 0.244 | 0.406 | 0.610 | 13.099 |
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 | 9 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 |
N.S. |
1 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 | 0.56 | 0.78 | 0.67 |
time (sec) |
N/A | 0.133 | 0.001 | 0.074 | 0.195 | 0.234 | 0.027 | 0.282 | 0.019 |
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 | 19 | 0 | 17 | 16 | 24 | 15 | 15 | 0 | 24 |
N.S. |
1 | 0.00 | 0.89 | 0.84 | 1.26 | 0.79 | 0.79 | 0.00 | 1.26 |
time (sec) |
N/A | 0.000 | 0.311 | 0.158 | 0.390 | 0.245 | 0.119 | 0.000 | 12.458 |
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 | 15 | 15 | 16 | 15 | 15 | 14 | 15 | 15 |
N.S. |
1 | 0.88 | 0.88 | 0.94 | 0.88 | 0.88 | 0.82 | 0.88 | 0.88 |
time (sec) |
N/A | 0.534 | 0.074 | 1.048 | 0.220 | 0.256 | 0.110 | 0.277 | 12.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 21 | 17 | 23 | 22 | 19 | 0 | 0 |
N.S. |
1 | 0.00 | 1.17 | 0.94 | 1.28 | 1.22 | 1.06 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.486 | 0.154 | 0.292 | 0.245 | 0.087 | 0.000 | 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 | 13 | 13 | 13 | 21 | 12 | 20 | 14 | 12 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.62 | 0.92 | 1.54 | 1.08 | 0.92 | 1.00 |
time (sec) |
N/A | 0.398 | 0.084 | 0.332 | 0.282 | 0.278 | 0.104 | 0.267 | 12.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 53 | 46 | 50 | 67 | 48 | 48 | 50 | 47 |
N.S. |
1 | 1.47 | 1.28 | 1.39 | 1.86 | 1.33 | 1.33 | 1.39 | 1.31 |
time (sec) |
N/A | 0.333 | 0.216 | 0.394 | 0.228 | 0.263 | 0.103 | 0.277 | 0.162 |
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 | 19 | 17 | 21 | 21 | 15 | 21 | 16 |
N.S. |
1 | 0.88 | 0.76 | 0.68 | 0.84 | 0.84 | 0.60 | 0.84 | 0.64 |
time (sec) |
N/A | 0.143 | 0.003 | 0.148 | 0.182 | 0.232 | 0.021 | 0.264 | 12.268 |
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 | 9 | 9 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 0.56 | 0.56 | 0.44 | 0.38 | 0.38 | 0.31 | 0.38 | 0.38 |
time (sec) |
N/A | 0.142 | 0.001 | 0.128 | 0.195 | 0.258 | 0.033 | 0.265 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 43 | 37 | 62 | 39 | 34 | 83 | 68 |
N.S. |
1 | 0.00 | 1.54 | 1.32 | 2.21 | 1.39 | 1.21 | 2.96 | 2.43 |
time (sec) |
N/A | 0.000 | 0.370 | 20.868 | 0.372 | 0.264 | 5.810 | 0.541 | 13.708 |
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 | 28 | 31 | 29 | 29 | 29 | 29 | 90 |
N.S. |
1 | 0.00 | 1.22 | 1.35 | 1.26 | 1.26 | 1.26 | 1.26 | 3.91 |
time (sec) |
N/A | 0.000 | 0.566 | 2.800 | 0.235 | 0.250 | 0.208 | 0.292 | 13.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 59 | 59 | 48 | 59 | 47 | 48 | 47 | 67 |
N.S. |
1 | 2.46 | 2.46 | 2.00 | 2.46 | 1.96 | 2.00 | 1.96 | 2.79 |
time (sec) |
N/A | 0.432 | 0.033 | 0.115 | 0.190 | 0.268 | 0.091 | 0.271 | 13.197 |
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 | 26 | 0 | 24 | 27 | 39 | 26 | 37 | 36 | 21 |
N.S. |
1 | 0.00 | 0.92 | 1.04 | 1.50 | 1.00 | 1.42 | 1.38 | 0.81 |
time (sec) |
N/A | 0.000 | 0.192 | 9.316 | 0.326 | 0.297 | 0.143 | 0.346 | 14.422 |
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 | 17 | 31 | 31 | 30 | 54 | 30 | 32 | 33 | 15 |
N.S. |
1 | 1.82 | 1.82 | 1.76 | 3.18 | 1.76 | 1.88 | 1.94 | 0.88 |
time (sec) |
N/A | 0.329 | 0.047 | 0.926 | 0.226 | 0.240 | 0.098 | 0.279 | 14.641 |
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 | 24 | 25 | 23 | 26 | 22 | 20 | 38 | 22 |
N.S. |
1 | 0.89 | 0.93 | 0.85 | 0.96 | 0.81 | 0.74 | 1.41 | 0.81 |
time (sec) |
N/A | 0.172 | 0.048 | 0.840 | 0.197 | 0.259 | 0.053 | 0.279 | 0.115 |
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 | 32 | 32 | 31 | 27 | 36 | 31 | 31 |
N.S. |
1 | 0.00 | 1.10 | 1.10 | 1.07 | 0.93 | 1.24 | 1.07 | 1.07 |
time (sec) |
N/A | 0.000 | 0.403 | 0.388 | 0.334 | 0.276 | 0.103 | 0.285 | 14.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 67 | 47 | 65 | 78 | 61 | 61 | 69 | 59 |
N.S. |
1 | 2.91 | 2.04 | 2.83 | 3.39 | 2.65 | 2.65 | 3.00 | 2.57 |
time (sec) |
N/A | 0.385 | 0.231 | 0.132 | 0.229 | 0.247 | 0.101 | 0.283 | 13.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 5 | 16 | 13 | 10 | 47 | 14 | 39 | 12 |
N.S. |
1 | 0.31 | 1.00 | 0.81 | 0.62 | 2.94 | 0.88 | 2.44 | 0.75 |
time (sec) |
N/A | 0.357 | 0.142 | 0.352 | 0.195 | 0.263 | 0.145 | 0.301 | 14.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 48 | 22 | 20 | 19 | 19 | 20 | 19 | 0 |
N.S. |
1 | 2.18 | 1.00 | 0.91 | 0.86 | 0.86 | 0.91 | 0.86 | 0.00 |
time (sec) |
N/A | 0.261 | 0.038 | 0.152 | 0.376 | 0.266 | 2.093 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 27 | 21 | 21 | 0 | 21 | 21 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 0.78 | 0.78 | 0.00 | 0.78 | 0.78 |
time (sec) |
N/A | 0.000 | 0.063 | 111.490 | 0.443 | 0.255 | 0.000 | 0.353 | 14.211 |
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 | 40 | 40 | 39 | 30 | 30 | 27 | 31 | 31 |
N.S. |
1 | 1.43 | 1.43 | 1.39 | 1.07 | 1.07 | 0.96 | 1.11 | 1.11 |
time (sec) |
N/A | 0.185 | 0.018 | 3.328 | 0.191 | 0.254 | 0.086 | 0.277 | 13.833 |
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 | 24 | 40 | 24 | 22 | 24 | 19 | 20 | 39 | 19 |
N.S. |
1 | 1.67 | 1.00 | 0.92 | 1.00 | 0.79 | 0.83 | 1.62 | 0.79 |
time (sec) |
N/A | 0.649 | 0.091 | 0.711 | 0.323 | 0.256 | 0.108 | 0.288 | 0.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 19 | 17 | 40 | 44 | 49 | 83 | 44 |
N.S. |
1 | 0.00 | 0.76 | 0.68 | 1.60 | 1.76 | 1.96 | 3.32 | 1.76 |
time (sec) |
N/A | 0.000 | 1.121 | 0.591 | 0.234 | 0.257 | 0.102 | 0.293 | 13.819 |
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 | 9 | 9 | 10 | 9 | 9 | 7 | 9 | 9 |
N.S. |
1 | 0.75 | 0.75 | 0.83 | 0.75 | 0.75 | 0.58 | 0.75 | 0.75 |
time (sec) |
N/A | 0.131 | 0.001 | 0.059 | 0.175 | 0.232 | 0.022 | 0.265 | 0.034 |
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 | 28 | 0 | 37 | 31 | 30 | 36 | 31 | 30 | 109 |
N.S. |
1 | 0.00 | 1.32 | 1.11 | 1.07 | 1.29 | 1.11 | 1.07 | 3.89 |
time (sec) |
N/A | 0.000 | 0.150 | 0.214 | 0.221 | 0.250 | 0.150 | 0.280 | 14.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | F | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 89 | 0 | 33 | 32 | 0 | 32 |
N.S. |
1 | 0.00 | 1.00 | 3.18 | 0.00 | 1.18 | 1.14 | 0.00 | 1.14 |
time (sec) |
N/A | 0.000 | 0.037 | 4.437 | 0.000 | 0.259 | 0.156 | 0.000 | 14.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 0 | 89 | 78 | 87 | 87 | 95 | 89 |
N.S. |
1 | 0.00 | 0.00 | 3.18 | 2.79 | 3.11 | 3.11 | 3.39 | 3.18 |
time (sec) |
N/A | 0.000 | 0.000 | 3.974 | 0.424 | 0.258 | 1.566 | 0.364 | 16.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | B | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 0 | 58 | 61 | 59 | 58 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.66 | 1.74 | 1.69 | 1.66 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 256.936 | 0.337 | 0.253 | 0.332 | 0.000 | 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 | 13 | 7 | 7 | 8 | 7 | 11 | 5 | 7 | 7 |
N.S. |
1 | 0.54 | 0.54 | 0.62 | 0.54 | 0.85 | 0.38 | 0.54 | 0.54 |
time (sec) |
N/A | 0.142 | 0.001 | 0.032 | 0.187 | 0.250 | 0.027 | 0.272 | 0.025 |