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 | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 24 | 19 | 93 | 140 | 0 | 18 | 43 | 18 |
N.S. |
1 | 1.00 | 0.96 | 0.76 | 3.72 | 5.60 | 0.00 | 0.72 | 1.72 | 0.72 |
time (sec) |
N/A | 0.233 | 0.038 | 8.989 | 0.034 | 0.076 | 0.000 | 0.121 | 0.233 | 0.079 |
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 | 34 | 39 | 34 | 67 | 73 | 670 | 0 | 45 | 135 | 137 |
N.S. |
1 | 1.15 | 1.00 | 1.97 | 2.15 | 19.71 | 0.00 | 1.32 | 3.97 | 4.03 |
time (sec) |
N/A | 0.394 | 0.110 | 0.169 | 0.115 | 0.079 | 0.000 | 0.123 | 0.268 | 2.248 |
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 | 140 | 139 | 127 | 413 | 386 | 5275 | 0 | 593 | 1798 | 301 |
N.S. |
1 | 0.99 | 0.91 | 2.95 | 2.76 | 37.68 | 0.00 | 4.24 | 12.84 | 2.15 |
time (sec) |
N/A | 0.374 | 0.425 | 0.234 | 0.145 | 0.156 | 0.000 | 0.132 | 0.237 | 2.818 |
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 | 83 | 82 | 80 | 222 | 204 | 1827 | 0 | 316 | 893 | 169 |
N.S. |
1 | 0.99 | 0.96 | 2.67 | 2.46 | 22.01 | 0.00 | 3.81 | 10.76 | 2.04 |
time (sec) |
N/A | 0.310 | 0.215 | 104.511 | 0.130 | 0.112 | 0.000 | 0.132 | 0.255 | 2.349 |
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 | 40 | 39 | 41 | 99 | 89 | 430 | 0 | 104 | 312 | 88 |
N.S. |
1 | 0.98 | 1.02 | 2.48 | 2.22 | 10.75 | 0.00 | 2.60 | 7.80 | 2.20 |
time (sec) |
N/A | 0.267 | 0.086 | 21.299 | 0.116 | 0.109 | 0.000 | 0.125 | 0.229 | 2.356 |
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 | 11 | 11 | 11 | 12 | 11 | 42 | 0 | 45 | 35 | 50 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 3.82 | 0.00 | 4.09 | 3.18 | 4.55 |
time (sec) |
N/A | 0.217 | 0.003 | 3.021 | 0.031 | 0.117 | 0.000 | 0.126 | 0.211 | 0.191 |
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 | 39 | 39 | 49 | 42 | 41 | 42 | 146 | 43 | 42 | 35 |
N.S. |
1 | 1.00 | 1.26 | 1.08 | 1.05 | 1.08 | 3.74 | 1.10 | 1.08 | 0.90 |
time (sec) |
N/A | 0.315 | 0.067 | 0.151 | 0.034 | 0.081 | 0.234 | 0.127 | 0.252 | 0.149 |
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 | 99 | 117 | 75 | 104 | 86 | 331 | 0 | 111 | 150 | 84 |
N.S. |
1 | 1.18 | 0.76 | 1.05 | 0.87 | 3.34 | 0.00 | 1.12 | 1.52 | 0.85 |
time (sec) |
N/A | 0.380 | 0.145 | 1.228 | 0.044 | 0.108 | 0.000 | 0.129 | 0.238 | 2.514 |
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 | 168 | 195 | 206 | 191 | 165 | 1281 | 0 | 227 | 355 | 143 |
N.S. |
1 | 1.16 | 1.23 | 1.14 | 0.98 | 7.62 | 0.00 | 1.35 | 2.11 | 0.85 |
time (sec) |
N/A | 0.514 | 0.246 | 11.934 | 0.038 | 0.108 | 0.000 | 0.132 | 0.302 | 2.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 165 | 166 | 323 | 0 | 6509 | 0 | 326 | 1373 | 447 |
N.S. |
1 | 1.05 | 1.06 | 2.06 | 0.00 | 41.46 | 0.00 | 2.08 | 8.75 | 2.85 |
time (sec) |
N/A | 1.531 | 0.435 | 199.657 | 0.000 | 0.256 | 0.000 | 0.134 | 0.248 | 8.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 103 | 116 | 164 | 0 | 2043 | 0 | 152 | 564 | 265 |
N.S. |
1 | 1.01 | 1.14 | 1.61 | 0.00 | 20.03 | 0.00 | 1.49 | 5.53 | 2.60 |
time (sec) |
N/A | 0.939 | 0.266 | 48.640 | 0.000 | 0.138 | 0.000 | 0.118 | 0.218 | 5.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 65 | 77 | 0 | 309 | 0 | 63 | 116 | 119 |
N.S. |
1 | 1.00 | 1.16 | 1.38 | 0.00 | 5.52 | 0.00 | 1.12 | 2.07 | 2.12 |
time (sec) |
N/A | 0.529 | 0.143 | 8.367 | 0.000 | 0.110 | 0.000 | 0.123 | 0.261 | 4.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 46 | 39 | 0 | 148 | 0 | 35 | 48 | 35 |
N.S. |
1 | 1.00 | 1.24 | 1.05 | 0.00 | 4.00 | 0.00 | 0.95 | 1.30 | 0.95 |
time (sec) |
N/A | 0.248 | 0.017 | 0.783 | 0.000 | 0.093 | 0.000 | 0.125 | 0.274 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 64 | 80 | 93 | 0 | 435 | 0 | 61 | 127 | 157 |
N.S. |
1 | 0.88 | 1.10 | 1.27 | 0.00 | 5.96 | 0.00 | 0.84 | 1.74 | 2.15 |
time (sec) |
N/A | 0.532 | 0.214 | 0.591 | 0.000 | 0.098 | 0.000 | 0.121 | 0.231 | 2.271 |
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 | 132 | 125 | 258 | 172 | 0 | 1871 | 0 | 162 | 322 | 221 |
N.S. |
1 | 0.95 | 1.95 | 1.30 | 0.00 | 14.17 | 0.00 | 1.23 | 2.44 | 1.67 |
time (sec) |
N/A | 0.958 | 0.360 | 4.119 | 0.000 | 0.126 | 0.000 | 0.121 | 0.258 | 3.127 |
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 | 43 | 70 | 52 | 40 | 55 | 571 | 104 | 47 | 62 | 35 |
N.S. |
1 | 1.63 | 1.21 | 0.93 | 1.28 | 13.28 | 2.42 | 1.09 | 1.44 | 0.81 |
time (sec) |
N/A | 0.577 | 0.124 | 0.213 | 0.111 | 0.092 | 0.209 | 0.120 | 0.223 | 0.100 |
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 | 37 | 49 | 45 | 30 | 43 | 354 | 85 | 39 | 51 | 29 |
N.S. |
1 | 1.32 | 1.22 | 0.81 | 1.16 | 9.57 | 2.30 | 1.05 | 1.38 | 0.78 |
time (sec) |
N/A | 0.501 | 0.083 | 0.189 | 0.109 | 0.103 | 0.207 | 0.120 | 0.247 | 0.083 |
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 | 31 | 44 | 41 | 28 | 29 | 186 | 75 | 35 | 40 | 21 |
N.S. |
1 | 1.42 | 1.32 | 0.90 | 0.94 | 6.00 | 2.42 | 1.13 | 1.29 | 0.68 |
time (sec) |
N/A | 0.384 | 0.109 | 0.168 | 0.130 | 0.088 | 0.203 | 0.120 | 0.226 | 2.025 |
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 | 19 | 24 | 34 | 18 | 17 | 73 | 61 | 17 | 31 | 21 |
N.S. |
1 | 1.26 | 1.79 | 0.95 | 0.89 | 3.84 | 3.21 | 0.89 | 1.63 | 1.11 |
time (sec) |
N/A | 0.232 | 0.062 | 0.186 | 0.119 | 0.089 | 0.170 | 0.131 | 0.255 | 0.070 |
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 | 16 | 24 | 14 | 11 | 10 | 26 | 27 | 10 | 19 | 10 |
N.S. |
1 | 1.50 | 0.88 | 0.69 | 0.62 | 1.62 | 1.69 | 0.62 | 1.19 | 0.62 |
time (sec) |
N/A | 0.210 | 0.070 | 0.155 | 0.028 | 0.076 | 0.162 | 0.117 | 0.254 | 0.063 |
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 | 16 | 16 | 18 | 11 | 10 | 26 | 27 | 10 | 19 | 10 |
N.S. |
1 | 1.00 | 1.12 | 0.69 | 0.62 | 1.62 | 1.69 | 0.62 | 1.19 | 0.62 |
time (sec) |
N/A | 0.184 | 0.025 | 0.137 | 0.029 | 0.096 | 0.165 | 0.123 | 0.202 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 32 | 34 | 18 | 24 | 73 | 0 | 18 | 45 | 17 |
N.S. |
1 | 1.68 | 1.79 | 0.95 | 1.26 | 3.84 | 0.00 | 0.95 | 2.37 | 0.89 |
time (sec) |
N/A | 0.299 | 0.093 | 0.398 | 0.029 | 0.107 | 0.000 | 0.118 | 0.234 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 39 | 47 | 30 | 38 | 196 | 0 | 36 | 95 | 29 |
N.S. |
1 | 1.34 | 1.62 | 1.03 | 1.31 | 6.76 | 0.00 | 1.24 | 3.28 | 1.00 |
time (sec) |
N/A | 0.412 | 0.197 | 0.458 | 0.044 | 0.091 | 0.000 | 0.117 | 0.237 | 2.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 60 | 54 | 30 | 54 | 357 | 0 | 40 | 141 | 35 |
N.S. |
1 | 1.62 | 1.46 | 0.81 | 1.46 | 9.65 | 0.00 | 1.08 | 3.81 | 0.95 |
time (sec) |
N/A | 0.534 | 0.206 | 0.503 | 0.034 | 0.103 | 0.000 | 0.129 | 0.256 | 2.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 67 | 53 | 44 | 64 | 582 | 0 | 48 | 191 | 69 |
N.S. |
1 | 1.56 | 1.23 | 1.02 | 1.49 | 13.53 | 0.00 | 1.12 | 4.44 | 1.60 |
time (sec) |
N/A | 0.607 | 0.223 | 0.536 | 0.037 | 0.098 | 0.000 | 0.123 | 0.237 | 2.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 56 | 39 | 35 | 0 | 206 | 58 | 96 | 23 | 34 |
N.S. |
1 | 1.24 | 0.87 | 0.78 | 0.00 | 4.58 | 1.29 | 2.13 | 0.51 | 0.76 |
time (sec) |
N/A | 0.352 | 0.493 | 0.237 | 0.000 | 0.087 | 3.556 | 0.135 | 0.235 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 41 | 32 | 26 | 0 | 128 | 48 | 53 | 10 | 25 |
N.S. |
1 | 1.28 | 1.00 | 0.81 | 0.00 | 4.00 | 1.50 | 1.66 | 0.31 | 0.78 |
time (sec) |
N/A | 0.264 | 0.293 | 0.241 | 0.000 | 0.086 | 0.751 | 0.130 | 0.211 | 2.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 41 | 30 | 25 | 0 | 141 | 46 | 52 | 16 | 24 |
N.S. |
1 | 1.37 | 1.00 | 0.83 | 0.00 | 4.70 | 1.53 | 1.73 | 0.53 | 0.80 |
time (sec) |
N/A | 0.275 | 0.348 | 0.250 | 0.000 | 0.092 | 1.146 | 0.130 | 0.268 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | F | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 57 | 36 | 35 | 0 | 240 | 60 | 73 | 22 | 32 |
N.S. |
1 | 1.16 | 0.73 | 0.71 | 0.00 | 4.90 | 1.22 | 1.49 | 0.45 | 0.65 |
time (sec) |
N/A | 0.339 | 0.389 | 0.224 | 0.000 | 0.091 | 4.726 | 0.120 | 0.275 | 2.127 |
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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 45 | 35 | 0 | 329 | 58 | 140 | 25 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.00 | 7.31 | 1.29 | 3.11 | 0.56 | 0.76 |
time (sec) |
N/A | 0.352 | 0.611 | 0.233 | 0.000 | 0.097 | 4.874 | 0.136 | 0.266 | 0.146 |
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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 26 | 0 | 194 | 49 | 96 | 12 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 5.71 | 1.44 | 2.82 | 0.35 | 0.74 |
time (sec) |
N/A | 0.264 | 0.372 | 0.245 | 0.000 | 0.092 | 0.976 | 0.144 | 0.243 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 34 | 35 | 0 | 161 | 58 | 54 | 18 | 36 |
N.S. |
1 | 1.00 | 0.81 | 0.83 | 0.00 | 3.83 | 1.38 | 1.29 | 0.43 | 0.86 |
time (sec) |
N/A | 0.344 | 0.478 | 0.269 | 0.000 | 0.116 | 1.375 | 0.136 | 0.320 | 0.123 |
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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 48 | 35 | 0 | 244 | 60 | 95 | 24 | 31 |
N.S. |
1 | 1.00 | 0.98 | 0.71 | 0.00 | 4.98 | 1.22 | 1.94 | 0.49 | 0.63 |
time (sec) |
N/A | 0.386 | 0.781 | 0.233 | 0.000 | 0.108 | 5.069 | 0.130 | 0.281 | 2.022 |
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 | 94 | 131 | 92 | 96 | 150 | 1296 | 546 | 142 | 139 | 85 |
N.S. |
1 | 1.39 | 0.98 | 1.02 | 1.60 | 13.79 | 5.81 | 1.51 | 1.48 | 0.90 |
time (sec) |
N/A | 1.073 | 0.465 | 0.228 | 0.116 | 0.163 | 0.472 | 0.121 | 0.285 | 0.222 |
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 | 76 | 99 | 77 | 76 | 100 | 644 | 442 | 98 | 115 | 68 |
N.S. |
1 | 1.30 | 1.01 | 1.00 | 1.32 | 8.47 | 5.82 | 1.29 | 1.51 | 0.89 |
time (sec) |
N/A | 0.793 | 0.316 | 0.208 | 0.137 | 0.125 | 0.402 | 0.126 | 0.261 | 0.167 |
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 | 64 | 81 | 65 | 67 | 71 | 264 | 330 | 75 | 92 | 59 |
N.S. |
1 | 1.27 | 1.02 | 1.05 | 1.11 | 4.12 | 5.16 | 1.17 | 1.44 | 0.92 |
time (sec) |
N/A | 0.565 | 0.235 | 0.205 | 0.121 | 0.107 | 0.324 | 0.124 | 0.319 | 2.202 |
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 | 63 | 61 | 59 | 52 | 56 | 76 | 243 | 58 | 73 | 46 |
N.S. |
1 | 0.97 | 0.94 | 0.83 | 0.89 | 1.21 | 3.86 | 0.92 | 1.16 | 0.73 |
time (sec) |
N/A | 0.512 | 0.137 | 0.167 | 0.124 | 0.121 | 0.276 | 0.119 | 0.272 | 0.118 |
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 | 39 | 48 | 50 | 40 | 40 | 43 | 141 | 43 | 43 | 36 |
N.S. |
1 | 1.23 | 1.28 | 1.03 | 1.03 | 1.10 | 3.62 | 1.10 | 1.10 | 0.92 |
time (sec) |
N/A | 0.342 | 0.137 | 0.147 | 0.033 | 0.088 | 0.221 | 0.132 | 0.266 | 2.091 |
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 | 39 | 39 | 49 | 42 | 41 | 42 | 146 | 43 | 42 | 35 |
N.S. |
1 | 1.00 | 1.26 | 1.08 | 1.05 | 1.08 | 3.74 | 1.10 | 1.08 | 0.90 |
time (sec) |
N/A | 0.296 | 0.006 | 0.121 | 0.033 | 0.106 | 0.218 | 0.129 | 0.341 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 63 | 65 | 56 | 65 | 73 | 0 | 58 | 93 | 58 |
N.S. |
1 | 1.24 | 1.27 | 1.10 | 1.27 | 1.43 | 0.00 | 1.14 | 1.82 | 1.14 |
time (sec) |
N/A | 0.413 | 0.116 | 0.424 | 0.043 | 0.103 | 0.000 | 0.123 | 0.276 | 2.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 77 | 66 | 71 | 86 | 271 | 0 | 75 | 252 | 73 |
N.S. |
1 | 1.28 | 1.10 | 1.18 | 1.43 | 4.52 | 0.00 | 1.25 | 4.20 | 1.22 |
time (sec) |
N/A | 0.558 | 0.225 | 0.442 | 0.046 | 0.103 | 0.000 | 0.125 | 3.049 | 2.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 109 | 76 | 92 | 121 | 641 | 0 | 97 | 15 | 111 |
N.S. |
1 | 1.43 | 1.00 | 1.21 | 1.59 | 8.43 | 0.00 | 1.28 | 0.20 | 1.46 |
time (sec) |
N/A | 0.775 | 0.231 | 0.536 | 0.042 | 0.115 | 0.000 | 0.121 | 200.039 | 2.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 131 | 92 | 114 | 173 | 1299 | 0 | 142 | 15 | 163 |
N.S. |
1 | 1.35 | 0.95 | 1.18 | 1.78 | 13.39 | 0.00 | 1.46 | 0.15 | 1.68 |
time (sec) |
N/A | 1.072 | 0.357 | 0.575 | 0.049 | 0.117 | 0.000 | 0.120 | 200.032 | 2.663 |
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 | 55 | 58 | 49 | 73 | 68 | 182 | 0 | 174 | 2513 | 69 |
N.S. |
1 | 1.05 | 0.89 | 1.33 | 1.24 | 3.31 | 0.00 | 3.16 | 45.69 | 1.25 |
time (sec) |
N/A | 0.407 | 0.114 | 8.961 | 0.221 | 0.103 | 0.000 | 0.128 | 0.271 | 2.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 245 | 250 | 953 | 0 | 1516 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.06 | 1.08 | 4.13 | 0.00 | 6.56 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.030 | 1.305 | 6.418 | 0.000 | 0.204 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 353 | 268 | 1186 | 0 | 2110 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.01 | 0.76 | 3.38 | 0.00 | 6.01 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.525 | 0.705 | 6.407 | 0.000 | 0.175 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 56 | 50 | 33 | 31 | 0 | 37 | 87 | 33 |
N.S. |
1 | 1.00 | 1.75 | 1.56 | 1.03 | 0.97 | 0.00 | 1.16 | 2.72 | 1.03 |
time (sec) |
N/A | 0.236 | 0.174 | 0.586 | 0.118 | 0.095 | 0.000 | 0.118 | 0.255 | 2.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 64 | 24 | 23 | 28 | 0 | 23 | 62 | 21 |
N.S. |
1 | 0.93 | 2.21 | 0.83 | 0.79 | 0.97 | 0.00 | 0.79 | 2.14 | 0.72 |
time (sec) |
N/A | 0.260 | 0.015 | 0.367 | 0.042 | 0.075 | 0.000 | 0.115 | 0.248 | 2.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 35 | 41 | 19 | 22 | 0 | 19 | 75 | 25 |
N.S. |
1 | 1.00 | 1.52 | 1.78 | 0.83 | 0.96 | 0.00 | 0.83 | 3.26 | 1.09 |
time (sec) |
N/A | 0.209 | 0.127 | 0.464 | 0.115 | 0.089 | 0.000 | 0.118 | 0.238 | 2.023 |
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 | 12 | 12 | 12 | 11 | 10 | 18 | 15 | 20 | 48 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 1.50 | 1.25 | 1.67 | 4.00 | 1.25 |
time (sec) |
N/A | 0.222 | 0.019 | 0.240 | 0.031 | 0.089 | 0.109 | 0.121 | 0.264 | 2.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 40 | 44 | 19 | 21 | 0 | 16 | 79 | 24 |
N.S. |
1 | 1.00 | 2.00 | 2.20 | 0.95 | 1.05 | 0.00 | 0.80 | 3.95 | 1.20 |
time (sec) |
N/A | 0.231 | 0.112 | 0.296 | 0.126 | 0.107 | 0.000 | 0.124 | 0.251 | 2.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 80 | 32 | 21 | 38 | 0 | 44 | 78 | 29 |
N.S. |
1 | 1.00 | 2.11 | 0.84 | 0.55 | 1.00 | 0.00 | 1.16 | 2.05 | 0.76 |
time (sec) |
N/A | 0.257 | 0.019 | 0.315 | 0.046 | 0.087 | 0.000 | 0.119 | 0.273 | 2.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 174 | 64 | 37 | 128 | 111 | 0 | 123 | 151 | 47 |
N.S. |
1 | 1.60 | 0.59 | 0.34 | 1.17 | 1.02 | 0.00 | 1.13 | 1.39 | 0.43 |
time (sec) |
N/A | 0.472 | 0.156 | 0.451 | 0.132 | 0.129 | 0.000 | 0.119 | 0.229 | 2.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 158 | 58 | 33 | 124 | 99 | 0 | 119 | 144 | 44 |
N.S. |
1 | 1.52 | 0.56 | 0.32 | 1.19 | 0.95 | 0.00 | 1.14 | 1.38 | 0.42 |
time (sec) |
N/A | 0.460 | 0.124 | 0.233 | 0.117 | 0.089 | 0.000 | 0.122 | 0.282 | 2.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 175 | 59 | 42 | 125 | 107 | 0 | 121 | 141 | 45 |
N.S. |
1 | 1.65 | 0.56 | 0.40 | 1.18 | 1.01 | 0.00 | 1.14 | 1.33 | 0.42 |
time (sec) |
N/A | 0.497 | 0.125 | 0.279 | 0.140 | 0.122 | 0.000 | 0.122 | 0.255 | 2.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 169 | 61 | 45 | 133 | 116 | 0 | 123 | 150 | 48 |
N.S. |
1 | 1.55 | 0.56 | 0.41 | 1.22 | 1.06 | 0.00 | 1.13 | 1.38 | 0.44 |
time (sec) |
N/A | 0.429 | 0.125 | 0.309 | 0.136 | 0.104 | 0.000 | 0.112 | 0.276 | 2.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 70 | 53 | 77 | 54 | 61 | 0 | 59 | 186 | 54 |
N.S. |
1 | 1.25 | 0.95 | 1.38 | 0.96 | 1.09 | 0.00 | 1.05 | 3.32 | 0.96 |
time (sec) |
N/A | 0.314 | 0.329 | 0.515 | 0.120 | 0.076 | 0.000 | 0.126 | 0.253 | 2.138 |
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 | 47 | 47 | 86 | 42 | 40 | 58 | 0 | 39 | 144 | 39 |
N.S. |
1 | 1.00 | 1.83 | 0.89 | 0.85 | 1.23 | 0.00 | 0.83 | 3.06 | 0.83 |
time (sec) |
N/A | 0.263 | 0.071 | 0.319 | 0.043 | 0.094 | 0.000 | 0.127 | 0.253 | 2.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 52 | 41 | 57 | 35 | 50 | 0 | 35 | 174 | 41 |
N.S. |
1 | 1.30 | 1.02 | 1.42 | 0.88 | 1.25 | 0.00 | 0.88 | 4.35 | 1.02 |
time (sec) |
N/A | 0.261 | 0.258 | 0.319 | 0.127 | 0.091 | 0.000 | 0.121 | 0.303 | 2.191 |
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 | 14 | 14 | 24 | 13 | 21 | 28 | 12 | 19 | 12 | 28 |
N.S. |
1 | 1.00 | 1.71 | 0.93 | 1.50 | 2.00 | 0.86 | 1.36 | 0.86 | 2.00 |
time (sec) |
N/A | 0.223 | 0.030 | 0.170 | 0.036 | 0.105 | 0.123 | 0.123 | 0.303 | 2.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 59 | 40 | 66 | 37 | 51 | 0 | 39 | 178 | 47 |
N.S. |
1 | 1.34 | 0.91 | 1.50 | 0.84 | 1.16 | 0.00 | 0.89 | 4.05 | 1.07 |
time (sec) |
N/A | 0.280 | 0.271 | 0.299 | 0.120 | 0.096 | 0.000 | 0.128 | 0.295 | 2.157 |
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 | 55 | 60 | 96 | 54 | 35 | 78 | 0 | 54 | 172 | 50 |
N.S. |
1 | 1.09 | 1.75 | 0.98 | 0.64 | 1.42 | 0.00 | 0.98 | 3.13 | 0.91 |
time (sec) |
N/A | 0.277 | 0.081 | 0.330 | 0.052 | 0.083 | 0.000 | 0.134 | 0.292 | 2.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 77 | 57 | 79 | 48 | 62 | 0 | 50 | 192 | 55 |
N.S. |
1 | 1.40 | 1.04 | 1.44 | 0.87 | 1.13 | 0.00 | 0.91 | 3.49 | 1.00 |
time (sec) |
N/A | 0.291 | 0.272 | 0.465 | 0.131 | 0.100 | 0.000 | 0.119 | 0.250 | 2.120 |
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 | 64 | 72 | 117 | 63 | 45 | 87 | 0 | 82 | 182 | 59 |
N.S. |
1 | 1.12 | 1.83 | 0.98 | 0.70 | 1.36 | 0.00 | 1.28 | 2.84 | 0.92 |
time (sec) |
N/A | 0.284 | 0.104 | 0.633 | 0.042 | 0.093 | 0.000 | 0.121 | 0.239 | 2.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 214 | 191 | 71 | 165 | 176 | 0 | 159 | 323 | 76 |
N.S. |
1 | 1.47 | 1.31 | 0.49 | 1.13 | 1.21 | 0.00 | 1.09 | 2.21 | 0.52 |
time (sec) |
N/A | 0.511 | 0.501 | 0.464 | 0.124 | 0.097 | 0.000 | 0.119 | 0.291 | 2.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 209 | 174 | 53 | 144 | 169 | 0 | 139 | 317 | 67 |
N.S. |
1 | 1.56 | 1.30 | 0.40 | 1.07 | 1.26 | 0.00 | 1.04 | 2.37 | 0.50 |
time (sec) |
N/A | 0.510 | 0.498 | 0.312 | 0.129 | 0.097 | 0.000 | 0.130 | 0.251 | 2.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 165 | 146 | 47 | 138 | 163 | 0 | 133 | 309 | 61 |
N.S. |
1 | 1.31 | 1.16 | 0.37 | 1.10 | 1.29 | 0.00 | 1.06 | 2.45 | 0.48 |
time (sec) |
N/A | 0.360 | 0.388 | 0.247 | 0.154 | 0.086 | 0.000 | 0.126 | 0.266 | 2.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 213 | 181 | 64 | 146 | 161 | 0 | 143 | 306 | 68 |
N.S. |
1 | 1.54 | 1.31 | 0.46 | 1.06 | 1.17 | 0.00 | 1.04 | 2.22 | 0.49 |
time (sec) |
N/A | 0.503 | 0.540 | 0.290 | 0.128 | 0.091 | 0.000 | 0.122 | 0.281 | 2.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 208 | 189 | 68 | 152 | 184 | 0 | 142 | 316 | 70 |
N.S. |
1 | 1.51 | 1.37 | 0.49 | 1.10 | 1.33 | 0.00 | 1.03 | 2.29 | 0.51 |
time (sec) |
N/A | 0.496 | 0.495 | 0.320 | 0.135 | 0.107 | 0.000 | 0.125 | 0.306 | 2.226 |
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 | 60 | 60 | 47 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.240 | 0.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.257 | 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 | 79 | 97 | 79 | 0 | 0 | 0 | 0 | 0 | 565 | 0 |
N.S. |
1 | 1.23 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.15 | 0.00 |
time (sec) |
N/A | 0.318 | 0.152 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.293 | 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 | 125 | 197 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.58 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.477 | 0.180 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 259 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 3.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.276 | 0.434 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.259 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 126 | 0 | 0 | 0 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.312 | 0.486 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 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 | 51 | 51 | 76 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.243 | 0.554 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.322 | 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 | 106 | 109 | 121 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.03 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.298 | 0.622 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 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 | 158 | 173 | 141 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.09 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.355 | 0.687 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 205 | 228 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 0.94 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.355 | 0.886 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 171 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 2.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.248 | 0.390 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 171 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 2.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.270 | 0.439 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 171 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 2.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.244 | 0.436 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.637 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 95 | 127 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.61 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.395 | 5.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 99 | 136 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.57 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.337 | 4.929 | 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 | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 91 | 122 | 0 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.65 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.338 | 4.977 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 88 | 126 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.66 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.318 | 5.648 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 24 | 25 | 24 | 76 | 36 | 88 | 41 | 34 |
N.S. |
1 | 1.00 | 0.96 | 1.00 | 0.96 | 3.04 | 1.44 | 3.52 | 1.64 | 1.36 |
time (sec) |
N/A | 0.232 | 0.036 | 0.427 | 0.037 | 0.098 | 1.390 | 0.198 | 0.238 | 2.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 93 | 126 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.58 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.337 | 2.056 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 92 | 120 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.64 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.337 | 2.061 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 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 | 133 | 183 | 159 | 0 | 0 | 0 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.38 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.508 | 5.424 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 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 | 137 | 187 | 169 | 0 | 0 | 0 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.36 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.485 | 5.174 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 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 | 131 | 181 | 155 | 0 | 0 | 0 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.38 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.494 | 5.011 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.325 | 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 | 127 | 177 | 163 | 0 | 0 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.39 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.474 | 5.891 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.000 |
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 | 33 | 51 | 33 | 36 | 72 | 70 | 52 | 36 | 34 |
N.S. |
1 | 1.18 | 1.82 | 1.18 | 1.29 | 2.57 | 2.50 | 1.86 | 1.29 | 1.21 |
time (sec) |
N/A | 0.245 | 0.073 | 0.364 | 0.132 | 0.083 | 2.411 | 0.209 | 0.234 | 2.434 |
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 | 135 | 182 | 162 | 0 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.35 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.497 | 2.186 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.292 | 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 | 136 | 183 | 159 | 0 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.35 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.493 | 2.264 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 49 | 38 | 47 | 304 | 566 | 68 | 137 | 211 | 94 |
N.S. |
1 | 1.14 | 0.88 | 1.09 | 7.07 | 13.16 | 1.58 | 3.19 | 4.91 | 2.19 |
time (sec) |
N/A | 0.308 | 0.109 | 0.540 | 0.101 | 0.102 | 0.770 | 0.200 | 0.250 | 2.237 |
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 | 45 | 47 | 62 | 42 | 494 | 194 | 65 | 78 | 46 | 162 |
N.S. |
1 | 1.04 | 1.38 | 0.93 | 10.98 | 4.31 | 1.44 | 1.73 | 1.02 | 3.60 |
time (sec) |
N/A | 0.333 | 0.065 | 0.826 | 0.129 | 0.087 | 1.668 | 0.185 | 0.271 | 2.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 71 | 55 | 62 | 829 | 1568 | 87 | 171 | 385 | 227 |
N.S. |
1 | 1.08 | 0.83 | 0.94 | 12.56 | 23.76 | 1.32 | 2.59 | 5.83 | 3.44 |
time (sec) |
N/A | 0.421 | 0.119 | 1.536 | 0.166 | 0.112 | 3.888 | 0.220 | 0.280 | 2.224 |
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 | 88 | 124 | 160 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.41 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.432 | 8.852 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 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 | 169 | 213 | 317 | 0 | 0 | 0 | 0 | 0 | 158 | 0 |
N.S. |
1 | 1.26 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.633 | 11.968 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.260 | 0.000 |