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 | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 19 | 18 | 28 | 36 | 44 | 31 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.73 | 1.64 | 2.55 | 3.27 | 4.00 | 2.82 | 1.00 |
time (sec) |
N/A | 0.159 | 0.003 | 0.143 | 0.027 | 0.074 | 0.809 | 0.141 | 0.172 | 0.111 |
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 | 10 | 10 | 10 | 11 | 10 | 18 | 0 | 10 | 18 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.80 | 0.00 | 1.00 | 1.80 | 1.00 |
time (sec) |
N/A | 0.170 | 0.004 | 0.237 | 0.029 | 0.065 | 0.000 | 0.113 | 0.163 | 10.098 |
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 | 34 | 34 | 34 | 36 | 46 | 61 | 0 | 48 | 95 | 36 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.35 | 1.79 | 0.00 | 1.41 | 2.79 | 1.06 |
time (sec) |
N/A | 0.229 | 0.009 | 0.346 | 0.026 | 0.079 | 0.000 | 0.155 | 0.171 | 0.071 |
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 | 26 | 26 | 23 | 24 | 22 | 31 | 0 | 22 | 43 | 21 |
N.S. |
1 | 1.00 | 0.88 | 0.92 | 0.85 | 1.19 | 0.00 | 0.85 | 1.65 | 0.81 |
time (sec) |
N/A | 0.187 | 0.034 | 0.312 | 0.025 | 0.079 | 0.000 | 0.124 | 0.171 | 9.972 |
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 | 55 | 49 | 71 | 74 | 0 | 63 | 162 | 58 |
N.S. |
1 | 1.09 | 1.00 | 0.89 | 1.29 | 1.35 | 0.00 | 1.15 | 2.95 | 1.05 |
time (sec) |
N/A | 0.311 | 0.011 | 0.473 | 0.031 | 0.081 | 0.000 | 0.135 | 0.174 | 9.589 |
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 | 41 | 38 | 35 | 34 | 34 | 41 | 0 | 34 | 63 | 31 |
N.S. |
1 | 0.93 | 0.85 | 0.83 | 0.83 | 1.00 | 0.00 | 0.83 | 1.54 | 0.76 |
time (sec) |
N/A | 0.195 | 0.085 | 0.385 | 0.026 | 0.066 | 0.000 | 0.135 | 0.152 | 10.056 |
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 | 76 | 86 | 76 | 59 | 91 | 84 | 0 | 73 | 226 | 79 |
N.S. |
1 | 1.13 | 1.00 | 0.78 | 1.20 | 1.11 | 0.00 | 0.96 | 2.97 | 1.04 |
time (sec) |
N/A | 0.421 | 0.009 | 0.650 | 0.033 | 0.080 | 0.000 | 0.113 | 0.154 | 10.369 |
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 | 53 | 48 | 43 | 44 | 44 | 51 | 0 | 44 | 83 | 39 |
N.S. |
1 | 0.91 | 0.81 | 0.83 | 0.83 | 0.96 | 0.00 | 0.83 | 1.57 | 0.74 |
time (sec) |
N/A | 0.204 | 0.132 | 0.480 | 0.033 | 0.066 | 0.000 | 0.139 | 0.156 | 10.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 86 | 59 | 358 | 0 | 110 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.01 | 0.69 | 4.21 | 0.00 | 1.29 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.414 | 0.130 | 1.486 | 0.000 | 0.099 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 46 | 213 | 0 | 88 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.74 | 3.44 | 0.00 | 1.42 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.316 | 0.057 | 0.868 | 0.000 | 0.081 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 45 | 182 | 0 | 73 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.78 | 3.14 | 0.00 | 1.26 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.316 | 0.040 | 0.458 | 0.000 | 0.078 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 133 | 0 | 51 | 0 | 0 | 9 | 33 |
N.S. |
1 | 1.00 | 1.00 | 3.69 | 0.00 | 1.42 | 0.00 | 0.00 | 0.25 | 0.92 |
time (sec) |
N/A | 0.230 | 0.026 | 0.366 | 0.000 | 0.082 | 0.000 | 0.000 | 0.172 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 133 | 0 | 57 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.69 | 0.00 | 1.58 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.237 | 0.033 | 0.992 | 0.000 | 0.077 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 49 | 179 | 0 | 68 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.79 | 2.89 | 0.00 | 1.10 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.315 | 0.047 | 1.435 | 0.000 | 0.085 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 55 | 202 | 0 | 74 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.89 | 3.26 | 0.00 | 1.19 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.312 | 0.060 | 2.691 | 0.000 | 0.085 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 90 | 61 | 199 | 0 | 87 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.06 | 0.72 | 2.34 | 0.00 | 1.02 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.404 | 0.073 | 4.207 | 0.000 | 0.090 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 100 | 62 | 207 | 0 | 125 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.02 | 0.63 | 2.11 | 0.00 | 1.28 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.457 | 0.140 | 3.290 | 0.000 | 0.089 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 51 | 90 | 0 | 101 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.73 | 1.29 | 0.00 | 1.44 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.329 | 0.059 | 2.468 | 0.000 | 0.086 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 48 | 182 | 0 | 84 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.73 | 2.76 | 0.00 | 1.27 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.337 | 0.040 | 1.811 | 0.000 | 0.082 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 77 | 0 | 57 | 0 | 0 | 12 | 35 |
N.S. |
1 | 1.00 | 1.00 | 2.03 | 0.00 | 1.50 | 0.00 | 0.00 | 0.32 | 0.92 |
time (sec) |
N/A | 0.241 | 0.026 | 1.260 | 0.000 | 0.090 | 0.000 | 0.000 | 0.192 | 0.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 175 | 0 | 66 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.61 | 0.00 | 1.74 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.239 | 0.032 | 1.181 | 0.000 | 0.078 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 59 | 90 | 0 | 87 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.25 | 0.00 | 1.21 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.339 | 0.057 | 1.487 | 0.000 | 0.087 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 60 | 191 | 0 | 95 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.83 | 2.65 | 0.00 | 1.32 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.339 | 0.061 | 2.451 | 0.000 | 0.109 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 66 | 104 | 0 | 100 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.08 | 0.66 | 1.04 | 0.00 | 1.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.443 | 0.081 | 3.066 | 0.000 | 0.091 | 0.000 | 0.000 | 0.198 | 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 | 55 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.247 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 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 | 55 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.250 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 53 | 53 | 53 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.245 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 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 | 53 | 53 | 53 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.244 | 0.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 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 | 53 | 53 | 55 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.249 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 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 | 53 | 53 | 55 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.242 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 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 | 54 | 54 | 57 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.258 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.288 | 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 | 54 | 54 | 57 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.263 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 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 | 56 | 56 | 55 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.257 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 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 | 56 | 56 | 55 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.262 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 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 | 56 | 56 | 57 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.258 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 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 | 56 | 56 | 57 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.267 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 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 | 70 | 70 | 61 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.279 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 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 | 73 | 73 | 61 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.295 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 66 | 39 | 51 | 42 | 49 | 0 | 59 | 136 | 0 |
N.S. |
1 | 1.32 | 0.78 | 1.02 | 0.84 | 0.98 | 0.00 | 1.18 | 2.72 | 0.00 |
time (sec) |
N/A | 0.204 | 0.040 | 2.869 | 0.105 | 0.082 | 0.000 | 0.132 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 45 | 33 | 43 | 30 | 43 | 0 | 53 | 98 | 0 |
N.S. |
1 | 1.25 | 0.92 | 1.19 | 0.83 | 1.19 | 0.00 | 1.47 | 2.72 | 0.00 |
time (sec) |
N/A | 0.197 | 0.025 | 2.707 | 0.103 | 0.084 | 0.000 | 0.135 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 24 | 23 | 33 | 18 | 34 | 0 | 44 | 57 | 0 |
N.S. |
1 | 1.09 | 1.05 | 1.50 | 0.82 | 1.55 | 0.00 | 2.00 | 2.59 | 0.00 |
time (sec) |
N/A | 0.183 | 0.013 | 0.316 | 0.105 | 0.080 | 0.000 | 0.115 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 14 | 19 | 3 | 17 | 0 | 35 | 17 | 0 |
N.S. |
1 | 1.00 | 4.67 | 6.33 | 1.00 | 5.67 | 0.00 | 11.67 | 5.67 | 0.00 |
time (sec) |
N/A | 0.173 | 0.005 | 0.267 | 0.102 | 0.078 | 0.000 | 0.108 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 13 | 11 | 7 | 11 | 4 | 10 | 6 | 2 | 12 |
N.S. |
1 | 1.18 | 1.00 | 0.64 | 1.00 | 0.36 | 0.91 | 0.55 | 0.18 | 1.09 |
time (sec) |
N/A | 0.184 | 0.018 | 0.257 | 0.025 | 0.073 | 0.222 | 0.151 | 0.154 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 33 | 28 | 19 | 25 | 10 | 27 | 16 | 12 | 0 |
N.S. |
1 | 1.14 | 0.97 | 0.66 | 0.86 | 0.34 | 0.93 | 0.55 | 0.41 | 0.00 |
time (sec) |
N/A | 0.187 | 0.014 | 0.291 | 0.033 | 0.075 | 0.354 | 0.117 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 54 | 28 | 22 | 37 | 18 | 44 | 25 | 18 | 0 |
N.S. |
1 | 1.26 | 0.65 | 0.51 | 0.86 | 0.42 | 1.02 | 0.58 | 0.42 | 0.00 |
time (sec) |
N/A | 0.194 | 0.018 | 0.336 | 0.028 | 0.078 | 1.370 | 0.116 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 75 | 34 | 28 | 49 | 24 | 60 | 34 | 24 | 0 |
N.S. |
1 | 1.32 | 0.60 | 0.49 | 0.86 | 0.42 | 1.05 | 0.60 | 0.42 | 0.00 |
time (sec) |
N/A | 0.197 | 0.024 | 0.366 | 0.030 | 0.078 | 10.920 | 0.117 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 99 | 44 | 60 | 2175 | 65 | 0 | 79 | 141 | 0 |
N.S. |
1 | 1.18 | 0.52 | 0.71 | 25.89 | 0.77 | 0.00 | 0.94 | 1.68 | 0.00 |
time (sec) |
N/A | 0.237 | 0.061 | 3.008 | 2.039 | 0.089 | 0.000 | 0.157 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 75 | 37 | 52 | 1111 | 56 | 0 | 55 | 103 | 0 |
N.S. |
1 | 1.15 | 0.57 | 0.80 | 17.09 | 0.86 | 0.00 | 0.85 | 1.58 | 0.00 |
time (sec) |
N/A | 0.223 | 0.036 | 2.830 | 0.292 | 0.086 | 0.000 | 0.138 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 51 | 24 | 42 | 324 | 39 | 0 | 42 | 60 | 0 |
N.S. |
1 | 1.11 | 0.52 | 0.91 | 7.04 | 0.85 | 0.00 | 0.91 | 1.30 | 0.00 |
time (sec) |
N/A | 0.205 | 0.025 | 0.318 | 0.149 | 0.090 | 0.000 | 0.139 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 16 | 21 | 38 | 55 | 0 | 31 | 20 | 0 |
N.S. |
1 | 1.08 | 0.64 | 0.84 | 1.52 | 2.20 | 0.00 | 1.24 | 0.80 | 0.00 |
time (sec) |
N/A | 0.192 | 0.005 | 0.268 | 0.155 | 0.088 | 0.000 | 0.147 | 0.166 | 0.000 |
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 | 13 | 15 | 13 | 12 | 6 | 16 | 12 | 11 | 8 | 15 |
N.S. |
1 | 1.15 | 1.00 | 0.92 | 0.46 | 1.23 | 0.92 | 0.85 | 0.62 | 1.15 |
time (sec) |
N/A | 0.192 | 0.016 | 0.259 | 0.141 | 0.072 | 0.278 | 0.142 | 0.169 | 11.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 45 | 25 | 24 | 14 | 24 | 31 | 19 | 17 | 0 |
N.S. |
1 | 1.25 | 0.69 | 0.67 | 0.39 | 0.67 | 0.86 | 0.53 | 0.47 | 0.00 |
time (sec) |
N/A | 0.203 | 0.018 | 0.288 | 0.143 | 0.109 | 0.403 | 0.118 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 74 | 33 | 29 | 22 | 32 | 49 | 27 | 23 | 0 |
N.S. |
1 | 1.35 | 0.60 | 0.53 | 0.40 | 0.58 | 0.89 | 0.49 | 0.42 | 0.00 |
time (sec) |
N/A | 0.219 | 0.017 | 0.310 | 0.145 | 0.080 | 1.401 | 0.138 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 103 | 39 | 35 | 28 | 38 | 66 | 33 | 29 | 0 |
N.S. |
1 | 1.39 | 0.53 | 0.47 | 0.38 | 0.51 | 0.89 | 0.45 | 0.39 | 0.00 |
time (sec) |
N/A | 0.229 | 0.021 | 0.341 | 0.151 | 0.088 | 11.362 | 0.132 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 103 | 59 | 164 | 0 | 102 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.88 | 0.50 | 1.40 | 0.00 | 0.87 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.609 | 0.084 | 18.677 | 0.000 | 0.091 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 71 | 43 | 68 | 0 | 74 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.09 | 0.66 | 1.05 | 0.00 | 1.14 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.424 | 0.038 | 3.232 | 0.000 | 0.085 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 49 | 32 | 114 | 0 | 57 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.17 | 0.76 | 2.71 | 0.00 | 1.36 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.352 | 0.023 | 1.269 | 0.000 | 0.083 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 53 | 31 | 57 | 0 | 58 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.20 | 0.70 | 1.30 | 0.00 | 1.32 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.349 | 0.040 | 1.154 | 0.000 | 0.079 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 43 | 140 | 0 | 73 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.59 | 1.92 | 0.00 | 1.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.434 | 0.079 | 4.363 | 0.000 | 0.085 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 107 | 59 | 84 | 0 | 79 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.91 | 0.50 | 0.72 | 0.00 | 0.68 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.611 | 0.078 | 10.907 | 0.000 | 0.098 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 68 | 54 | 58 | 61 | 76 | 0 | 67 | 89 | 589 |
N.S. |
1 | 0.42 | 0.33 | 0.36 | 0.37 | 0.47 | 0.00 | 0.41 | 0.55 | 3.61 |
time (sec) |
N/A | 0.268 | 0.155 | 29.658 | 0.107 | 0.089 | 0.000 | 0.138 | 0.162 | 15.774 |
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 | 117 | 56 | 42 | 46 | 43 | 58 | 0 | 34 | 65 | 119 |
N.S. |
1 | 0.48 | 0.36 | 0.39 | 0.37 | 0.50 | 0.00 | 0.29 | 0.56 | 1.02 |
time (sec) |
N/A | 0.258 | 0.088 | 29.541 | 0.109 | 0.078 | 0.000 | 0.113 | 0.164 | 12.993 |
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 | 61 | 38 | 33 | 31 | 25 | 34 | 0 | 22 | 39 | 36 |
N.S. |
1 | 0.62 | 0.54 | 0.51 | 0.41 | 0.56 | 0.00 | 0.36 | 0.64 | 0.59 |
time (sec) |
N/A | 0.254 | 0.027 | 0.304 | 0.107 | 0.076 | 0.000 | 0.151 | 0.256 | 0.572 |
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 | 15 | 15 | 15 | 14 | 6 | 13 | 0 | 6 | 9 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.40 | 0.87 | 0.00 | 0.40 | 0.60 | 0.40 |
time (sec) |
N/A | 0.236 | 0.006 | 0.260 | 0.108 | 0.072 | 0.000 | 0.132 | 0.164 | 10.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 29 | 23 | 20 | 25 | 27 | 0 | 31 | 14 | 0 |
N.S. |
1 | 0.81 | 0.64 | 0.56 | 0.69 | 0.75 | 0.00 | 0.86 | 0.39 | 0.00 |
time (sec) |
N/A | 0.226 | 0.030 | 0.277 | 0.111 | 0.091 | 0.000 | 0.115 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 62 | 38 | 39 | 58 | 43 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.72 | 0.44 | 0.45 | 0.67 | 0.50 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.347 | 0.046 | 0.383 | 0.110 | 0.100 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 92 | 55 | 51 | 88 | 55 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.70 | 0.42 | 0.39 | 0.67 | 0.42 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.490 | 0.082 | 0.657 | 0.108 | 0.086 | 0.000 | 0.000 | 0.172 | 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 | 81 | 81 | 69 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.381 | 0.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 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 | 83 | 83 | 71 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.359 | 0.056 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 108 | 69 | 103 | 0 | 114 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.11 | 0.71 | 1.06 | 0.00 | 1.18 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.492 | 0.268 | 3.821 | 0.000 | 0.090 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 104 | 69 | 204 | 0 | 120 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.09 | 0.73 | 2.15 | 0.00 | 1.26 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.480 | 0.196 | 2.875 | 0.000 | 0.113 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 74 | 51 | 87 | 0 | 98 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.07 | 0.74 | 1.26 | 0.00 | 1.42 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.360 | 0.114 | 2.129 | 0.000 | 0.088 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 70 | 47 | 181 | 0 | 83 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.11 | 0.75 | 2.87 | 0.00 | 1.32 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.361 | 0.048 | 1.801 | 0.000 | 0.077 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 77 | 0 | 57 | 0 | 0 | 12 | 35 |
N.S. |
1 | 1.00 | 1.00 | 2.03 | 0.00 | 1.50 | 0.00 | 0.00 | 0.32 | 0.92 |
time (sec) |
N/A | 0.236 | 0.027 | 1.316 | 0.000 | 0.080 | 0.000 | 0.000 | 0.169 | 10.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 187 | 0 | 63 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.79 | 0.00 | 1.62 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.296 | 0.033 | 1.271 | 0.000 | 0.082 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 76 | 51 | 93 | 0 | 84 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.13 | 0.76 | 1.39 | 0.00 | 1.25 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.376 | 0.170 | 1.595 | 0.000 | 0.091 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 76 | 57 | 206 | 0 | 92 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.09 | 0.81 | 2.94 | 0.00 | 1.31 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.388 | 0.130 | 2.704 | 0.000 | 0.085 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 112 | 63 | 107 | 0 | 97 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.18 | 0.66 | 1.13 | 0.00 | 1.02 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.499 | 0.152 | 3.369 | 0.000 | 0.099 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 112 | 71 | 228 | 0 | 105 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.14 | 0.72 | 2.33 | 0.00 | 1.07 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.491 | 0.265 | 5.662 | 0.000 | 0.086 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 108 | 64 | 104 | 0 | 117 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.14 | 0.67 | 1.09 | 0.00 | 1.23 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.473 | 0.262 | 3.793 | 0.000 | 0.089 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 104 | 64 | 205 | 0 | 121 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 0.65 | 2.09 | 0.00 | 1.23 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.471 | 0.184 | 2.894 | 0.000 | 0.086 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 74 | 49 | 88 | 0 | 99 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.10 | 0.73 | 1.31 | 0.00 | 1.48 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.354 | 0.066 | 2.181 | 0.000 | 0.090 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 48 | 182 | 0 | 84 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.73 | 2.76 | 0.00 | 1.27 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.346 | 0.008 | 1.833 | 0.000 | 0.083 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 78 | 0 | 57 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 0.00 | 1.46 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.280 | 0.006 | 1.318 | 0.000 | 0.078 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 189 | 0 | 63 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.61 | 0.00 | 1.54 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.279 | 0.019 | 1.196 | 0.000 | 0.086 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 76 | 52 | 95 | 0 | 85 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.09 | 0.74 | 1.36 | 0.00 | 1.21 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.377 | 0.116 | 1.644 | 0.000 | 0.087 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 76 | 58 | 207 | 0 | 93 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 0.81 | 2.88 | 0.00 | 1.29 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.383 | 0.109 | 2.742 | 0.000 | 0.086 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 112 | 64 | 108 | 0 | 99 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.14 | 0.65 | 1.10 | 0.00 | 1.01 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.488 | 0.171 | 3.467 | 0.000 | 0.087 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 112 | 72 | 229 | 0 | 107 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.12 | 0.72 | 2.29 | 0.00 | 1.07 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.495 | 0.311 | 5.826 | 0.000 | 0.087 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 108 | 61 | 106 | 0 | 121 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.10 | 0.62 | 1.08 | 0.00 | 1.23 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.469 | 0.281 | 8.171 | 0.000 | 0.125 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 104 | 61 | 210 | 0 | 125 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.07 | 0.63 | 2.16 | 0.00 | 1.29 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.483 | 0.148 | 4.025 | 0.000 | 0.084 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 51 | 90 | 0 | 101 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.73 | 1.29 | 0.00 | 1.44 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.327 | 0.040 | 2.516 | 0.000 | 0.080 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 50 | 184 | 0 | 86 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.74 | 2.71 | 0.00 | 1.26 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.362 | 0.013 | 8.410 | 0.000 | 0.103 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 80 | 0 | 57 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.95 | 0.00 | 1.39 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.277 | 0.011 | 30.096 | 0.000 | 0.080 | 0.000 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 38 | 191 | 0 | 63 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.93 | 4.66 | 0.00 | 1.54 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.301 | 0.123 | 104.040 | 0.000 | 0.081 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 76 | 54 | 96 | 0 | 87 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.06 | 0.75 | 1.33 | 0.00 | 1.21 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.375 | 0.146 | 1.181 | 0.000 | 0.086 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 76 | 60 | 209 | 0 | 95 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.06 | 0.83 | 2.90 | 0.00 | 1.32 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.379 | 0.125 | 11.629 | 0.000 | 0.088 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 112 | 66 | 110 | 0 | 103 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.12 | 0.66 | 1.10 | 0.00 | 1.03 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.502 | 0.217 | 2.820 | 0.000 | 0.129 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 112 | 74 | 231 | 0 | 111 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.12 | 0.74 | 2.31 | 0.00 | 1.11 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.487 | 0.360 | 4.918 | 0.000 | 0.089 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 100 | 62 | 210 | 0 | 125 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.02 | 0.63 | 2.14 | 0.00 | 1.28 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.438 | 0.021 | 3.103 | 0.000 | 0.084 | 0.000 | 0.000 | 0.183 | 0.000 |