Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 53 | 39 | 115 | 254 | 39 | 74 | 38 | 34 |
N.S. |
1 | 1.00 | 1.23 | 0.91 | 2.67 | 5.91 | 0.91 | 1.72 | 0.88 | 0.79 |
time (sec) |
N/A | 0.328 | 0.016 | 0.152 | 0.036 | 0.083 | 0.131 | 0.132 | 0.229 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 53 | 37 | 42 | 102 | 968 | 42 | 67 | 252 | 37 |
N.S. |
1 | 1.26 | 0.88 | 1.00 | 2.43 | 23.05 | 1.00 | 1.60 | 6.00 | 0.88 |
time (sec) |
N/A | 0.350 | 0.036 | 0.154 | 0.116 | 0.103 | 0.108 | 0.125 | 0.214 | 2.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 38 | 27 | 71 | 119 | 27 | 52 | 28 | 24 |
N.S. |
1 | 1.00 | 1.36 | 0.96 | 2.54 | 4.25 | 0.96 | 1.86 | 1.00 | 0.86 |
time (sec) |
N/A | 0.264 | 0.010 | 0.136 | 0.040 | 0.089 | 0.092 | 0.125 | 0.286 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 36 | 25 | 32 | 61 | 339 | 31 | 48 | 138 | 27 |
N.S. |
1 | 1.33 | 0.93 | 1.19 | 2.26 | 12.56 | 1.15 | 1.78 | 5.11 | 1.00 |
time (sec) |
N/A | 0.263 | 0.010 | 0.132 | 0.120 | 0.099 | 0.086 | 0.127 | 0.300 | 2.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 23 | 17 | 25 | 33 | 15 | 24 | 16 | 13 |
N.S. |
1 | 1.00 | 1.77 | 1.31 | 1.92 | 2.54 | 1.15 | 1.85 | 1.23 | 1.00 |
time (sec) |
N/A | 0.208 | 0.001 | 0.126 | 0.048 | 0.081 | 0.075 | 0.130 | 0.258 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 11 | 37 | 17 | 24 | 22 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 3.36 | 1.55 | 2.18 | 2.00 | 1.45 |
time (sec) |
N/A | 0.189 | 0.001 | 0.162 | 0.028 | 0.086 | 0.065 | 0.117 | 0.252 | 2.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 15 | 11 | 12 | 11 | 37 | 27 | 25 | 29 | 21 |
N.S. |
1 | 1.36 | 1.00 | 1.09 | 1.00 | 3.36 | 2.45 | 2.27 | 2.64 | 1.91 |
time (sec) |
N/A | 0.189 | 0.001 | 0.280 | 0.033 | 0.098 | 0.189 | 0.133 | 0.304 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 27 | 17 | 25 | 33 | 65 | 24 | 16 | 13 |
N.S. |
1 | 1.00 | 2.08 | 1.31 | 1.92 | 2.54 | 5.00 | 1.85 | 1.23 | 1.00 |
time (sec) |
N/A | 0.198 | 0.001 | 0.164 | 0.036 | 0.091 | 0.511 | 0.133 | 0.218 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 40 | 25 | 38 | 79 | 346 | 90 | 49 | 182 | 68 |
N.S. |
1 | 1.48 | 0.93 | 1.41 | 2.93 | 12.81 | 3.33 | 1.81 | 6.74 | 2.52 |
time (sec) |
N/A | 0.277 | 0.015 | 0.253 | 0.037 | 0.104 | 0.700 | 0.132 | 0.243 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 31 | 29 | 71 | 108 | 78 | 52 | 28 | 24 |
N.S. |
1 | 1.00 | 1.11 | 1.04 | 2.54 | 3.86 | 2.79 | 1.86 | 1.00 | 0.86 |
time (sec) |
N/A | 0.282 | 0.009 | 0.212 | 0.041 | 0.090 | 1.091 | 0.123 | 0.329 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 57 | 35 | 48 | 122 | 978 | 104 | 70 | 334 | 159 |
N.S. |
1 | 1.36 | 0.83 | 1.14 | 2.90 | 23.29 | 2.48 | 1.67 | 7.95 | 3.79 |
time (sec) |
N/A | 0.366 | 0.033 | 0.277 | 0.043 | 0.097 | 1.605 | 0.131 | 0.262 | 2.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 31 | 39 | 115 | 239 | 92 | 74 | 38 | 34 |
N.S. |
1 | 1.00 | 0.72 | 0.91 | 2.67 | 5.56 | 2.14 | 1.72 | 0.88 | 0.79 |
time (sec) |
N/A | 0.340 | 0.010 | 0.239 | 0.041 | 0.085 | 2.454 | 0.131 | 0.233 | 2.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 80 | 80 | 0 | 1545 | 0 | 0 | 58 | 83 |
N.S. |
1 | 1.00 | 0.82 | 0.82 | 0.00 | 15.93 | 0.00 | 0.00 | 0.60 | 0.86 |
time (sec) |
N/A | 0.452 | 0.265 | 0.444 | 0.000 | 0.131 | 0.000 | 0.000 | 0.280 | 2.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 74 | 66 | 63 | 0 | 969 | 0 | 0 | 24 | 62 |
N.S. |
1 | 0.95 | 0.85 | 0.81 | 0.00 | 12.42 | 0.00 | 0.00 | 0.31 | 0.79 |
time (sec) |
N/A | 0.360 | 0.108 | 0.389 | 0.000 | 0.129 | 0.000 | 0.000 | 0.254 | 2.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 72 | 66 | 62 | 0 | 626 | 0 | 0 | 37 | 61 |
N.S. |
1 | 0.96 | 0.88 | 0.83 | 0.00 | 8.35 | 0.00 | 0.00 | 0.49 | 0.81 |
time (sec) |
N/A | 0.346 | 0.051 | 0.374 | 0.000 | 0.108 | 0.000 | 0.000 | 0.242 | 2.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 51 | 52 | 47 | 0 | 583 | 0 | 0 | 12 | 41 |
N.S. |
1 | 0.88 | 0.90 | 0.81 | 0.00 | 10.05 | 0.00 | 0.00 | 0.21 | 0.71 |
time (sec) |
N/A | 0.237 | 0.027 | 0.480 | 0.000 | 0.134 | 0.000 | 0.000 | 0.267 | 2.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 51 | 49 | 46 | 0 | 587 | 0 | 0 | 24 | 38 |
N.S. |
1 | 0.89 | 0.86 | 0.81 | 0.00 | 10.30 | 0.00 | 0.00 | 0.42 | 0.67 |
time (sec) |
N/A | 0.253 | 0.025 | 0.451 | 0.000 | 0.102 | 0.000 | 0.000 | 0.249 | 2.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 74 | 74 | 65 | 0 | 914 | 0 | 0 | 24 | 64 |
N.S. |
1 | 0.95 | 0.95 | 0.83 | 0.00 | 11.72 | 0.00 | 0.00 | 0.31 | 0.82 |
time (sec) |
N/A | 0.329 | 0.060 | 0.385 | 0.000 | 0.130 | 0.000 | 0.000 | 0.248 | 2.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 76 | 78 | 64 | 0 | 1425 | 0 | 0 | 24 | 63 |
N.S. |
1 | 0.96 | 0.99 | 0.81 | 0.00 | 18.04 | 0.00 | 0.00 | 0.30 | 0.80 |
time (sec) |
N/A | 0.338 | 0.075 | 0.389 | 0.000 | 0.129 | 0.000 | 0.000 | 0.227 | 2.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 101 | 90 | 83 | 0 | 2133 | 0 | 0 | 24 | 80 |
N.S. |
1 | 1.01 | 0.90 | 0.83 | 0.00 | 21.33 | 0.00 | 0.00 | 0.24 | 0.80 |
time (sec) |
N/A | 0.447 | 0.176 | 0.393 | 0.000 | 0.142 | 0.000 | 0.000 | 0.293 | 2.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 70 | 90 | 102 | 0 | 179 | 63 | 110 | 8 | 71 |
N.S. |
1 | 1.01 | 1.30 | 1.48 | 0.00 | 2.59 | 0.91 | 1.59 | 0.12 | 1.03 |
time (sec) |
N/A | 0.298 | 0.075 | 0.160 | 0.000 | 0.083 | 1.046 | 0.132 | 0.244 | 2.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.226 | 0.093 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 49 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.237 | 0.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 28 | 30 | 42 | 467 | 0 | 52 | 85 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.86 | 1.20 | 13.34 | 0.00 | 1.49 | 2.43 | 0.00 |
time (sec) |
N/A | 0.303 | 0.024 | 0.288 | 0.150 | 0.121 | 0.000 | 0.119 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 26 | 19 | 72 | 0 | 31 | 15 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.62 | 1.19 | 4.50 | 0.00 | 1.94 | 0.94 | 0.00 |
time (sec) |
N/A | 0.240 | 0.008 | 0.275 | 0.127 | 0.108 | 0.000 | 0.129 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 33 | 31 | 76 | 0 | 1 | 22 | 14 |
N.S. |
1 | 1.00 | 1.00 | 2.06 | 1.94 | 4.75 | 0.00 | 0.06 | 1.38 | 0.88 |
time (sec) |
N/A | 0.263 | 0.008 | 0.268 | 0.136 | 0.103 | 0.000 | 0.129 | 0.237 | 2.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | C | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 73 | 59 | 67 | 113 | 180 | 0 | 142 | 253 | 0 |
N.S. |
1 | 0.83 | 0.67 | 0.76 | 1.28 | 2.05 | 0.00 | 1.61 | 2.88 | 0.00 |
time (sec) |
N/A | 0.481 | 0.059 | 0.395 | 0.131 | 0.094 | 0.000 | 0.160 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | C | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 56 | 47 | 53 | 66 | 100 | 0 | 92 | 138 | 0 |
N.S. |
1 | 0.93 | 0.78 | 0.88 | 1.10 | 1.67 | 0.00 | 1.53 | 2.30 | 0.00 |
time (sec) |
N/A | 0.371 | 0.063 | 0.292 | 0.140 | 0.086 | 0.000 | 0.147 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | C | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 45 | 28 | 23 | 0 | 54 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.45 | 0.90 | 0.74 | 0.00 | 1.74 | 0.74 | 0.00 |
time (sec) |
N/A | 0.239 | 0.023 | 0.321 | 0.127 | 0.110 | 0.000 | 0.129 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | C | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 31 | 52 | 45 | 23 | 0 | 61 | 33 | 24 |
N.S. |
1 | 1.13 | 1.00 | 1.68 | 1.45 | 0.74 | 0.00 | 1.97 | 1.06 | 0.77 |
time (sec) |
N/A | 0.250 | 0.042 | 0.323 | 0.176 | 0.117 | 0.000 | 0.132 | 0.302 | 2.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | C | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 47 | 81 | 85 | 100 | 0 | 100 | 183 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.35 | 1.42 | 1.67 | 0.00 | 1.67 | 3.05 | 0.00 |
time (sec) |
N/A | 0.331 | 0.080 | 0.313 | 0.128 | 0.098 | 0.000 | 0.132 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | C | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 77 | 57 | 91 | 132 | 180 | 0 | 126 | 337 | 0 |
N.S. |
1 | 0.88 | 0.65 | 1.03 | 1.50 | 2.05 | 0.00 | 1.43 | 3.83 | 0.00 |
time (sec) |
N/A | 0.414 | 0.087 | 0.342 | 0.136 | 0.103 | 0.000 | 0.147 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 49 | 38 | 43 | 0 | 106 | 0 | 55 | 16 | 0 |
N.S. |
1 | 0.86 | 0.67 | 0.75 | 0.00 | 1.86 | 0.00 | 0.96 | 0.28 | 0.00 |
time (sec) |
N/A | 0.319 | 0.029 | 0.319 | 0.000 | 0.088 | 0.000 | 0.132 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 64 | 55 | 76 | 0 | 1267 | 0 | 342 | 14 | 0 |
N.S. |
1 | 0.74 | 0.64 | 0.88 | 0.00 | 14.73 | 0.00 | 3.98 | 0.16 | 0.00 |
time (sec) |
N/A | 0.395 | 0.048 | 0.351 | 0.000 | 0.122 | 0.000 | 0.205 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 51 | 40 | 62 | 0 | 365 | 0 | 115 | 19 | 0 |
N.S. |
1 | 0.81 | 0.63 | 0.98 | 0.00 | 5.79 | 0.00 | 1.83 | 0.30 | 0.00 |
time (sec) |
N/A | 0.312 | 0.026 | 0.323 | 0.000 | 0.106 | 0.000 | 0.161 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 51 | 53 | 65 | 0 | 514 | 0 | 41 | 16 | 0 |
N.S. |
1 | 0.80 | 0.83 | 1.02 | 0.00 | 8.03 | 0.00 | 0.64 | 0.25 | 0.00 |
time (sec) |
N/A | 0.327 | 0.031 | 0.345 | 0.000 | 0.108 | 0.000 | 0.143 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 39 | 39 | 46 | 82 | 2114 | 0 | 45 | 25 | 0 |
N.S. |
1 | 0.57 | 0.57 | 0.67 | 1.19 | 30.64 | 0.00 | 0.65 | 0.36 | 0.00 |
time (sec) |
N/A | 0.367 | 0.057 | 0.308 | 0.129 | 0.166 | 0.000 | 0.125 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 22 | 21 | 32 | 19 | 213 | 0 | 16 | 9 | 0 |
N.S. |
1 | 0.71 | 0.68 | 1.03 | 0.61 | 6.87 | 0.00 | 0.52 | 0.29 | 0.00 |
time (sec) |
N/A | 0.240 | 0.014 | 0.282 | 0.156 | 0.095 | 0.000 | 0.118 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 22 | 26 | 32 | 23 | 238 | 0 | 19 | 16 | 0 |
N.S. |
1 | 0.71 | 0.84 | 1.03 | 0.74 | 7.68 | 0.00 | 0.61 | 0.52 | 0.00 |
time (sec) |
N/A | 0.239 | 0.017 | 0.275 | 0.145 | 0.120 | 0.000 | 0.135 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 57 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.307 | 0.077 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 63 | 58 | 302 | 907 | 95 | 85 | 211 | 65 |
N.S. |
1 | 1.08 | 0.63 | 0.58 | 3.02 | 9.07 | 0.95 | 0.85 | 2.11 | 0.65 |
time (sec) |
N/A | 0.593 | 0.217 | 0.329 | 0.134 | 0.086 | 0.131 | 0.134 | 0.241 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 84 | 51 | 48 | 196 | 562 | 76 | 71 | 162 | 53 |
N.S. |
1 | 1.09 | 0.66 | 0.62 | 2.55 | 7.30 | 0.99 | 0.92 | 2.10 | 0.69 |
time (sec) |
N/A | 0.470 | 0.123 | 0.203 | 0.142 | 0.085 | 0.109 | 0.130 | 0.312 | 1.967 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 60 | 40 | 38 | 116 | 299 | 61 | 57 | 113 | 43 |
N.S. |
1 | 1.07 | 0.71 | 0.68 | 2.07 | 5.34 | 1.09 | 1.02 | 2.02 | 0.77 |
time (sec) |
N/A | 0.358 | 0.151 | 0.199 | 0.127 | 0.087 | 0.112 | 0.133 | 0.269 | 1.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 29 | 28 | 50 | 117 | 44 | 39 | 72 | 33 |
N.S. |
1 | 1.00 | 0.81 | 0.78 | 1.39 | 3.25 | 1.22 | 1.08 | 2.00 | 0.92 |
time (sec) |
N/A | 0.270 | 0.116 | 0.158 | 0.040 | 0.095 | 0.085 | 0.126 | 0.235 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 33 | 25 | 31 | 50 | 73 | 30 | 36 | 25 |
N.S. |
1 | 1.00 | 1.18 | 0.89 | 1.11 | 1.79 | 2.61 | 1.07 | 1.29 | 0.89 |
time (sec) |
N/A | 0.198 | 0.065 | 0.168 | 0.034 | 0.097 | 0.363 | 0.126 | 0.218 | 1.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 55 | 47 | 42 | 43 | 101 | 223 | 42 | 48 | 41 |
N.S. |
1 | 1.08 | 0.92 | 0.82 | 0.84 | 1.98 | 4.37 | 0.82 | 0.94 | 0.80 |
time (sec) |
N/A | 0.281 | 0.134 | 0.183 | 0.044 | 0.079 | 0.587 | 0.130 | 0.244 | 1.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 82 | 59 | 59 | 56 | 160 | 430 | 53 | 60 | 58 |
N.S. |
1 | 1.12 | 0.81 | 0.81 | 0.77 | 2.19 | 5.89 | 0.73 | 0.82 | 0.79 |
time (sec) |
N/A | 0.377 | 0.170 | 0.211 | 0.041 | 0.096 | 0.738 | 0.127 | 0.252 | 1.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 109 | 96 | 76 | 67 | 220 | 694 | 64 | 72 | 75 |
N.S. |
1 | 1.14 | 1.00 | 0.79 | 0.70 | 2.29 | 7.23 | 0.67 | 0.75 | 0.78 |
time (sec) |
N/A | 0.479 | 0.168 | 0.257 | 0.046 | 0.096 | 0.981 | 0.130 | 0.225 | 1.968 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 136 | 111 | 91 | 78 | 287 | 1018 | 75 | 84 | 92 |
N.S. |
1 | 1.12 | 0.92 | 0.75 | 0.64 | 2.37 | 8.41 | 0.62 | 0.69 | 0.76 |
time (sec) |
N/A | 0.616 | 0.199 | 0.302 | 0.050 | 0.108 | 1.313 | 0.133 | 0.213 | 1.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 63 | 47 | 43 | 83 | 331 | 0 | 140 | 46 | 44 |
N.S. |
1 | 1.11 | 0.82 | 0.75 | 1.46 | 5.81 | 0.00 | 2.46 | 0.81 | 0.77 |
time (sec) |
N/A | 0.474 | 0.378 | 0.231 | 0.122 | 0.098 | 0.000 | 0.134 | 0.272 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 48 | 39 | 35 | 70 | 206 | 0 | 96 | 32 | 54 |
N.S. |
1 | 1.07 | 0.87 | 0.78 | 1.56 | 4.58 | 0.00 | 2.13 | 0.71 | 1.20 |
time (sec) |
N/A | 0.358 | 0.293 | 0.204 | 0.168 | 0.110 | 0.000 | 0.128 | 0.253 | 1.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 27 | 57 | 127 | 0 | 52 | 18 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.73 | 3.85 | 0.00 | 1.58 | 0.55 | 0.79 |
time (sec) |
N/A | 0.273 | 0.213 | 0.202 | 0.116 | 0.102 | 0.000 | 0.131 | 0.240 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 17 | 43 | 99 | 0 | 27 | 7 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 2.05 | 4.71 | 0.00 | 1.29 | 0.33 | 0.76 |
time (sec) |
N/A | 0.202 | 0.152 | 0.260 | 0.110 | 0.089 | 0.000 | 0.141 | 0.241 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 26 | 27 | 57 | 141 | 0 | 50 | 26 | 26 |
N.S. |
1 | 1.00 | 0.81 | 0.84 | 1.78 | 4.41 | 0.00 | 1.56 | 0.81 | 0.81 |
time (sec) |
N/A | 0.270 | 0.175 | 0.239 | 0.122 | 0.105 | 0.000 | 0.129 | 0.236 | 2.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 28 | 35 | 69 | 244 | 0 | 95 | 66 | 32 |
N.S. |
1 | 1.00 | 0.57 | 0.71 | 1.41 | 4.98 | 0.00 | 1.94 | 1.35 | 0.65 |
time (sec) |
N/A | 0.338 | 0.214 | 0.226 | 0.124 | 0.113 | 0.000 | 0.137 | 0.209 | 2.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 28 | 43 | 79 | 338 | 0 | 139 | 125 | 40 |
N.S. |
1 | 1.08 | 0.46 | 0.70 | 1.30 | 5.54 | 0.00 | 2.28 | 2.05 | 0.66 |
time (sec) |
N/A | 0.418 | 0.238 | 0.219 | 0.118 | 0.096 | 0.000 | 0.128 | 0.223 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 142 | 114 | 182 | 310 | 2739 | 211 | 224 | 1151 | 153 |
N.S. |
1 | 1.00 | 0.80 | 1.28 | 2.18 | 19.29 | 1.49 | 1.58 | 8.11 | 1.08 |
time (sec) |
N/A | 0.835 | 0.442 | 0.334 | 0.147 | 0.105 | 0.152 | 0.135 | 0.322 | 2.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 91 | 132 | 201 | 1389 | 144 | 152 | 652 | 113 |
N.S. |
1 | 1.00 | 0.90 | 1.31 | 1.99 | 13.75 | 1.43 | 1.50 | 6.46 | 1.12 |
time (sec) |
N/A | 0.592 | 0.241 | 0.253 | 0.121 | 0.108 | 0.134 | 0.134 | 0.229 | 2.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 67 | 93 | 118 | 646 | 100 | 97 | 390 | 77 |
N.S. |
1 | 1.00 | 0.97 | 1.35 | 1.71 | 9.36 | 1.45 | 1.41 | 5.65 | 1.12 |
time (sec) |
N/A | 0.411 | 0.231 | 0.235 | 0.128 | 0.095 | 0.103 | 0.128 | 0.223 | 2.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 54 | 52 | 49 | 201 | 54 | 56 | 144 | 44 |
N.S. |
1 | 1.00 | 1.42 | 1.37 | 1.29 | 5.29 | 1.42 | 1.47 | 3.79 | 1.16 |
time (sec) |
N/A | 0.272 | 0.073 | 0.192 | 0.037 | 0.094 | 0.085 | 0.115 | 0.255 | 1.985 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 64 | 55 | 56 | 62 | 224 | 62 | 57 | 60 |
N.S. |
1 | 1.00 | 1.28 | 1.10 | 1.12 | 1.24 | 4.48 | 1.24 | 1.14 | 1.20 |
time (sec) |
N/A | 0.340 | 0.062 | 0.196 | 0.036 | 0.104 | 1.035 | 0.129 | 0.239 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 98 | 94 | 93 | 127 | 422 | 1389 | 132 | 428 | 127 |
N.S. |
1 | 1.15 | 1.11 | 1.09 | 1.49 | 4.96 | 16.34 | 1.55 | 5.04 | 1.49 |
time (sec) |
N/A | 0.497 | 0.712 | 0.227 | 0.048 | 0.094 | 9.207 | 0.129 | 0.226 | 2.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 155 | 122 | 130 | 325 | 1427 | 6412 | 205 | 1186 | 304 |
N.S. |
1 | 1.20 | 0.95 | 1.01 | 2.52 | 11.06 | 49.71 | 1.59 | 9.19 | 2.36 |
time (sec) |
N/A | 0.733 | 1.565 | 0.297 | 0.081 | 0.114 | 12.427 | 0.139 | 0.256 | 2.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 208 | 160 | 163 | 525 | 3693 | 16643 | 305 | 2312 | 452 |
N.S. |
1 | 1.23 | 0.95 | 0.96 | 3.11 | 21.85 | 98.48 | 1.80 | 13.68 | 2.67 |
time (sec) |
N/A | 1.004 | 2.218 | 0.348 | 0.084 | 0.151 | 19.447 | 0.161 | 0.240 | 3.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 53 | 28 | 28 | 49 | 42 | 30 | 42 | 34 |
N.S. |
1 | 1.00 | 1.71 | 0.90 | 0.90 | 1.58 | 1.35 | 0.97 | 1.35 | 1.10 |
time (sec) |
N/A | 0.291 | 0.023 | 0.244 | 0.038 | 0.124 | 0.264 | 0.127 | 0.219 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 53 | 28 | 29 | 48 | 42 | 25 | 37 | 33 |
N.S. |
1 | 1.00 | 1.71 | 0.90 | 0.94 | 1.55 | 1.35 | 0.81 | 1.19 | 1.06 |
time (sec) |
N/A | 0.288 | 0.023 | 0.202 | 0.039 | 0.080 | 0.244 | 0.121 | 0.219 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 90 | 74 | 63 | 0 | 2203 | 0 | 0 | 13 | 151 |
N.S. |
1 | 1.22 | 1.00 | 0.85 | 0.00 | 29.77 | 0.00 | 0.00 | 0.18 | 2.04 |
time (sec) |
N/A | 0.294 | 0.065 | 0.602 | 0.000 | 0.155 | 0.000 | 0.000 | 0.272 | 2.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 85 | 74 | 62 | 0 | 2279 | 0 | 0 | 58 | 240 |
N.S. |
1 | 1.15 | 1.00 | 0.84 | 0.00 | 30.80 | 0.00 | 0.00 | 0.78 | 3.24 |
time (sec) |
N/A | 0.261 | 0.042 | 0.454 | 0.000 | 0.136 | 0.000 | 0.000 | 0.231 | 2.383 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 62 | 42 | 35 | 36 | 92 | 0 | 42 | 47 | 34 |
N.S. |
1 | 1.03 | 0.70 | 0.58 | 0.60 | 1.53 | 0.00 | 0.70 | 0.78 | 0.57 |
time (sec) |
N/A | 0.283 | 0.083 | 3.898 | 0.041 | 0.081 | 0.000 | 0.122 | 0.212 | 2.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 35 | 34 | 24 | 27 | 56 | 134 | 25 | 32 | 23 |
N.S. |
1 | 1.40 | 1.36 | 0.96 | 1.08 | 2.24 | 5.36 | 1.00 | 1.28 | 0.92 |
time (sec) |
N/A | 0.451 | 0.078 | 1.287 | 0.040 | 0.084 | 0.330 | 0.112 | 0.241 | 2.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 40 | 24 | 23 | 22 | 51 | 0 | 30 | 33 | 22 |
N.S. |
1 | 1.05 | 0.63 | 0.61 | 0.58 | 1.34 | 0.00 | 0.79 | 0.87 | 0.58 |
time (sec) |
N/A | 0.296 | 0.013 | 0.709 | 0.029 | 0.090 | 0.000 | 0.123 | 0.225 | 2.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 25 | 19 | 12 | 11 | 23 | 48 | 11 | 34 | 11 |
N.S. |
1 | 1.47 | 1.12 | 0.71 | 0.65 | 1.35 | 2.82 | 0.65 | 2.00 | 0.65 |
time (sec) |
N/A | 0.446 | 0.012 | 0.345 | 0.036 | 0.076 | 0.205 | 0.123 | 0.235 | 2.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 24 | 49 | 17 | 21 | 38 | 0 | 18 | 29 | 21 |
N.S. |
1 | 2.00 | 4.08 | 1.42 | 1.75 | 3.17 | 0.00 | 1.50 | 2.42 | 1.75 |
time (sec) |
N/A | 0.419 | 0.103 | 0.292 | 0.052 | 0.091 | 0.000 | 0.120 | 0.269 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 11 | 24 | 29 | 77 | 0 | 29 | 67 | 23 |
N.S. |
1 | 1.00 | 0.73 | 1.60 | 1.93 | 5.13 | 0.00 | 1.93 | 4.47 | 1.53 |
time (sec) |
N/A | 0.254 | 0.009 | 0.349 | 0.051 | 0.087 | 0.000 | 0.114 | 0.321 | 2.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 30 | 59 | 33 | 48 | 209 | 0 | 34 | 97 | 48 |
N.S. |
1 | 1.67 | 3.28 | 1.83 | 2.67 | 11.61 | 0.00 | 1.89 | 5.39 | 2.67 |
time (sec) |
N/A | 0.486 | 0.201 | 0.533 | 0.048 | 0.093 | 0.000 | 0.115 | 0.241 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 20 | 19 | 75 | 84 | 0 | 18 | 36 | 18 |
N.S. |
1 | 1.00 | 1.18 | 1.12 | 4.41 | 4.94 | 0.00 | 1.06 | 2.12 | 1.06 |
time (sec) |
N/A | 0.257 | 0.172 | 1.103 | 0.047 | 0.074 | 0.000 | 0.121 | 0.235 | 2.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 46 | 69 | 48 | 74 | 640 | 0 | 49 | 180 | 117 |
N.S. |
1 | 1.35 | 2.03 | 1.41 | 2.18 | 18.82 | 0.00 | 1.44 | 5.29 | 3.44 |
time (sec) |
N/A | 0.521 | 0.320 | 2.054 | 0.054 | 0.090 | 0.000 | 0.119 | 0.225 | 2.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 27 | 25 | 149 | 185 | 0 | 24 | 57 | 24 |
N.S. |
1 | 1.00 | 0.82 | 0.76 | 4.52 | 5.61 | 0.00 | 0.73 | 1.73 | 0.73 |
time (sec) |
N/A | 0.277 | 0.227 | 4.459 | 0.034 | 0.084 | 0.000 | 0.116 | 0.211 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 58 | 124 | 60 | 98 | 1260 | 0 | 61 | 260 | 207 |
N.S. |
1 | 1.32 | 2.82 | 1.36 | 2.23 | 28.64 | 0.00 | 1.39 | 5.91 | 4.70 |
time (sec) |
N/A | 0.544 | 0.356 | 8.686 | 0.040 | 0.097 | 0.000 | 0.607 | 0.242 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 242 | 144 | 183 | 163 | 1226 | 0 | 214 | 335 | 135 |
N.S. |
1 | 1.65 | 0.98 | 1.24 | 1.11 | 8.34 | 0.00 | 1.46 | 2.28 | 0.92 |
time (sec) |
N/A | 0.694 | 0.440 | 12.167 | 0.062 | 0.107 | 0.000 | 0.128 | 0.242 | 2.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 153 | 180 | 166 | 0 | 1861 | 0 | 163 | 317 | 261 |
N.S. |
1 | 1.12 | 1.31 | 1.21 | 0.00 | 13.58 | 0.00 | 1.19 | 2.31 | 1.91 |
time (sec) |
N/A | 0.920 | 0.816 | 4.106 | 0.000 | 0.134 | 0.000 | 0.121 | 0.232 | 2.367 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 142 | 73 | 98 | 83 | 334 | 0 | 101 | 152 | 81 |
N.S. |
1 | 1.69 | 0.87 | 1.17 | 0.99 | 3.98 | 0.00 | 1.20 | 1.81 | 0.96 |
time (sec) |
N/A | 0.391 | 0.114 | 1.228 | 0.043 | 0.120 | 0.000 | 0.127 | 0.244 | 2.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 88 | 79 | 92 | 0 | 427 | 0 | 60 | 171 | 157 |
N.S. |
1 | 1.22 | 1.10 | 1.28 | 0.00 | 5.93 | 0.00 | 0.83 | 2.38 | 2.18 |
time (sec) |
N/A | 0.518 | 0.146 | 0.535 | 0.000 | 0.134 | 0.000 | 0.125 | 0.247 | 2.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 60 | 68 | 53 | 0 | 237 | 0 | 60 | 96 | 177 |
N.S. |
1 | 1.15 | 1.31 | 1.02 | 0.00 | 4.56 | 0.00 | 1.15 | 1.85 | 3.40 |
time (sec) |
N/A | 0.392 | 0.161 | 0.472 | 0.000 | 0.137 | 0.000 | 0.128 | 0.262 | 2.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 34 | 28 | 50 | 65 | 122 | 0 | 78 | 116 | 323 |
N.S. |
1 | 1.17 | 0.97 | 1.72 | 2.24 | 4.21 | 0.00 | 2.69 | 4.00 | 11.14 |
time (sec) |
N/A | 0.261 | 0.304 | 0.556 | 0.038 | 0.136 | 0.000 | 0.123 | 0.282 | 2.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 98 | 147 | 110 | 0 | 1165 | 0 | 125 | 350 | 506 |
N.S. |
1 | 1.20 | 1.79 | 1.34 | 0.00 | 14.21 | 0.00 | 1.52 | 4.27 | 6.17 |
time (sec) |
N/A | 0.547 | 0.494 | 1.209 | 0.000 | 0.125 | 0.000 | 0.120 | 0.244 | 2.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 87 | 70 | 143 | 161 | 912 | 0 | 202 | 567 | 123 |
N.S. |
1 | 1.12 | 0.90 | 1.83 | 2.06 | 11.69 | 0.00 | 2.59 | 7.27 | 1.58 |
time (sec) |
N/A | 0.331 | 2.502 | 2.564 | 0.046 | 0.099 | 0.000 | 0.125 | 0.294 | 2.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 299 | 335 | 227 | 0 | 5347 | 0 | 273 | 1133 | 753 |
N.S. |
1 | 1.37 | 1.54 | 1.04 | 0.00 | 24.53 | 0.00 | 1.25 | 5.20 | 3.45 |
time (sec) |
N/A | 0.836 | 0.983 | 6.108 | 0.000 | 0.196 | 0.000 | 0.123 | 0.233 | 4.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 139 | 119 | 277 | 308 | 2972 | 0 | 412 | 1407 | 237 |
N.S. |
1 | 1.07 | 0.92 | 2.13 | 2.37 | 22.86 | 0.00 | 3.17 | 10.82 | 1.82 |
time (sec) |
N/A | 0.393 | 5.441 | 12.853 | 0.053 | 0.139 | 0.000 | 0.130 | 0.244 | 2.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 46 | 29 | 34 | 43 | 0 | 28 | 111 | 61 |
N.S. |
1 | 1.00 | 1.39 | 0.88 | 1.03 | 1.30 | 0.00 | 0.85 | 3.36 | 1.85 |
time (sec) |
N/A | 0.346 | 0.195 | 0.888 | 0.124 | 0.101 | 0.000 | 0.114 | 0.252 | 0.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 157 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.437 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 62 | 53 | 35 | 36 | 95 | 0 | 42 | 47 | 34 |
N.S. |
1 | 1.03 | 0.88 | 0.58 | 0.60 | 1.58 | 0.00 | 0.70 | 0.78 | 0.57 |
time (sec) |
N/A | 0.291 | 0.083 | 3.799 | 0.036 | 0.097 | 0.000 | 0.122 | 0.306 | 2.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 38 | 36 | 30 | 33 | 60 | 134 | 31 | 39 | 29 |
N.S. |
1 | 1.31 | 1.24 | 1.03 | 1.14 | 2.07 | 4.62 | 1.07 | 1.34 | 1.00 |
time (sec) |
N/A | 0.286 | 0.090 | 1.314 | 0.037 | 0.082 | 0.313 | 0.123 | 0.272 | 2.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 40 | 32 | 23 | 22 | 52 | 0 | 30 | 33 | 22 |
N.S. |
1 | 1.05 | 0.84 | 0.61 | 0.58 | 1.37 | 0.00 | 0.79 | 0.87 | 0.58 |
time (sec) |
N/A | 0.272 | 0.082 | 0.700 | 0.040 | 0.076 | 0.000 | 0.123 | 0.251 | 2.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 23 | 18 | 17 | 25 | 48 | 19 | 25 | 17 |
N.S. |
1 | 1.00 | 1.21 | 0.95 | 0.89 | 1.32 | 2.53 | 1.00 | 1.32 | 0.89 |
time (sec) |
N/A | 0.259 | 0.066 | 0.350 | 0.042 | 0.088 | 0.189 | 0.126 | 0.216 | 2.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 7 | 7 | 6 | 9 | 8 | 6 | 7 | 6 |
N.S. |
1 | 1.00 | 0.70 | 0.70 | 0.60 | 0.90 | 0.80 | 0.60 | 0.70 | 0.60 |
time (sec) |
N/A | 0.222 | 0.021 | 0.722 | 0.034 | 0.077 | 0.158 | 0.115 | 0.256 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 7 | 6 | 5 | 20 | 0 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.40 | 1.20 | 1.00 | 4.00 | 0.00 | 2.60 | 2.80 | 2.60 |
time (sec) |
N/A | 0.225 | 0.006 | 1.903 | 0.038 | 0.091 | 0.000 | 0.120 | 0.294 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 12 | 21 | 22 | 48 | 0 | 18 | 29 | 18 |
N.S. |
1 | 1.00 | 2.00 | 3.50 | 3.67 | 8.00 | 0.00 | 3.00 | 4.83 | 3.00 |
time (sec) |
N/A | 0.269 | 0.102 | 4.615 | 0.127 | 0.085 | 0.000 | 0.119 | 0.245 | 2.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 10 | 10 | 37 | 53 | 0 | 10 | 18 | 16 |
N.S. |
1 | 1.00 | 0.83 | 0.83 | 3.08 | 4.42 | 0.00 | 0.83 | 1.50 | 1.33 |
time (sec) |
N/A | 0.225 | 0.029 | 1.993 | 0.029 | 0.081 | 0.000 | 0.116 | 0.234 | 2.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 41 | 49 | 288 | 0 | 31 | 85 | 61 |
N.S. |
1 | 1.00 | 1.00 | 1.71 | 2.04 | 12.00 | 0.00 | 1.29 | 3.54 | 2.54 |
time (sec) |
N/A | 0.303 | 0.104 | 54.644 | 0.116 | 0.079 | 0.000 | 0.114 | 0.241 | 0.106 |