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 | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 13 | 12 | 13 | 12 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.80 | 0.87 | 0.80 | 0.87 |
time (sec) |
N/A | 0.141 | 0.002 | 0.105 | 0.024 | 0.067 | 0.017 | 0.120 | 0.154 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | B | F | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 49 | 37 | 34 | 41 | 0 | 42 | 41 | 31 | 43 |
N.S. |
1 | 3.27 | 2.47 | 2.27 | 2.73 | 0.00 | 2.80 | 2.73 | 2.07 | 2.87 |
time (sec) |
N/A | 0.271 | 0.020 | 0.214 | 0.025 | 0.000 | 3.959 | 0.128 | 0.155 | 0.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 60 | 73 | 0 | 100 | 0 | 177 | 107 | 204 |
N.S. |
1 | 1.00 | 0.73 | 0.89 | 0.00 | 1.22 | 0.00 | 2.16 | 1.30 | 2.49 |
time (sec) |
N/A | 0.291 | 0.191 | 0.217 | 0.000 | 0.068 | 0.000 | 0.129 | 0.148 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 71 | 52 | 0 | 80 | 0 | 94 | 160 | 0 |
N.S. |
1 | 1.00 | 1.65 | 1.21 | 0.00 | 1.86 | 0.00 | 2.19 | 3.72 | 0.00 |
time (sec) |
N/A | 0.181 | 0.076 | 0.445 | 0.000 | 0.066 | 0.000 | 0.123 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 73 | 115 | 0 | 105 | 0 | 133 | 113 | 82 |
N.S. |
1 | 1.00 | 0.99 | 1.55 | 0.00 | 1.42 | 0.00 | 1.80 | 1.53 | 1.11 |
time (sec) |
N/A | 0.281 | 0.066 | 0.030 | 0.000 | 0.074 | 0.000 | 0.150 | 0.153 | 1.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 70 | 65 | 53 | 89 | 0 | 84 | 24 | 0 |
N.S. |
1 | 1.00 | 1.09 | 1.02 | 0.83 | 1.39 | 0.00 | 1.31 | 0.38 | 0.00 |
time (sec) |
N/A | 0.210 | 0.182 | 0.284 | 0.105 | 0.074 | 0.000 | 0.132 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 55 | 37 | 0 | 83 | 0 | 101 | 157 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.77 | 0.00 | 1.73 | 0.00 | 2.10 | 3.27 | 0.00 |
time (sec) |
N/A | 0.168 | 0.100 | 0.246 | 0.000 | 0.069 | 0.000 | 0.128 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 26 | 21 | 0 | 18 | 53 | 20 | 19 | 21 |
N.S. |
1 | 1.00 | 0.87 | 0.70 | 0.00 | 0.60 | 1.77 | 0.67 | 0.63 | 0.70 |
time (sec) |
N/A | 0.285 | 0.176 | 0.084 | 0.000 | 0.064 | 0.224 | 0.127 | 0.156 | 0.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 365 | 195 | 1206 | 0 | 341 | 0 | 367 | 605 | 0 |
N.S. |
1 | 1.66 | 0.89 | 5.48 | 0.00 | 1.55 | 0.00 | 1.67 | 2.75 | 0.00 |
time (sec) |
N/A | 0.776 | 6.190 | 0.207 | 0.000 | 0.089 | 0.000 | 1.314 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 541 | 195 | 1636 | 0 | 341 | 0 | 358 | 977 | 0 |
N.S. |
1 | 2.46 | 0.89 | 7.44 | 0.00 | 1.55 | 0.00 | 1.63 | 4.44 | 0.00 |
time (sec) |
N/A | 1.128 | 6.324 | 0.809 | 0.000 | 0.082 | 0.000 | 1.417 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 126 | 146 | 0 | 161 | 0 | 547 | 39 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.06 | 0.00 | 1.17 | 0.00 | 3.96 | 0.28 | 0.00 |
time (sec) |
N/A | 0.250 | 3.630 | 0.602 | 0.000 | 0.093 | 0.000 | 0.144 | 180.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 151 | 272 | 0 | 0 | 342 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.21 | 2.18 | 0.00 | 0.00 | 2.74 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.388 | 2.338 | 0.000 | 0.000 | 1.071 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 205 | 0 | 0 | 332 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 2.53 | 0.00 | 0.00 | 4.10 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.347 | 1.086 | 0.000 | 0.000 | 3.270 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 44 | 0 | 0 | 60 | 15 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 1.42 | 0.00 | 0.00 | 1.94 | 0.48 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.225 | 0.132 | 0.000 | 0.000 | 0.207 | 0.906 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 57 | 22 | 0 | 42 | 15 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.73 | 0.67 | 0.00 | 1.27 | 0.45 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.232 | 0.159 | 0.120 | 0.000 | 0.216 | 0.416 | 0.000 | 0.159 | 0.000 |
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 | 19 | 16 | 15 | 28 | 56 | 15 | 26 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 1.47 | 2.95 | 0.79 | 1.37 | 0.79 |
time (sec) |
N/A | 0.421 | 0.009 | 0.243 | 0.027 | 0.076 | 0.658 | 0.136 | 0.148 | 0.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 51 | 43 | 120 | 0 | 32 | 2236 | 0 | 30 | 0 |
N.S. |
1 | 0.98 | 0.83 | 2.31 | 0.00 | 0.62 | 43.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.204 | 0.128 | 0.042 | 0.000 | 0.094 | 1.506 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 55 | 50 | 0 | 0 | 33 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.98 | 0.89 | 0.00 | 0.00 | 0.59 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.208 | 0.137 | 0.000 | 0.000 | 0.091 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 0 | 15 | 311 | 15 | 14 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 0.88 | 18.29 | 0.88 | 0.82 | 0.88 |
time (sec) |
N/A | 0.215 | 0.025 | 0.093 | 0.000 | 0.074 | 1.309 | 0.120 | 0.155 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 0 | 18 | 41 | 18 | 23 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.00 | 0.90 | 2.05 | 0.90 | 1.15 | 0.90 |
time (sec) |
N/A | 0.230 | 0.024 | 0.153 | 0.000 | 0.079 | 0.846 | 0.123 | 0.148 | 0.188 |
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 | 42 | 45 | 39 | 43 | 40 | 52 | 36 | 41 | 71 | 58 |
N.S. |
1 | 1.07 | 0.93 | 1.02 | 0.95 | 1.24 | 0.86 | 0.98 | 1.69 | 1.38 |
time (sec) |
N/A | 0.211 | 0.040 | 0.056 | 0.042 | 0.075 | 0.056 | 0.120 | 0.154 | 0.243 |
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 | 22 | 22 | 22 | 20 | 20 | 19 | 20 | 19 | 26 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.91 | 0.86 | 0.91 | 0.86 | 1.18 | 1.09 |
time (sec) |
N/A | 0.181 | 0.021 | 0.060 | 0.034 | 0.067 | 0.043 | 0.122 | 0.157 | 0.223 |
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 | 62 | 62 | 49 | 50 | 51 | 58 | 51 | 74 | 69 | 47 |
N.S. |
1 | 1.00 | 0.79 | 0.81 | 0.82 | 0.94 | 0.82 | 1.19 | 1.11 | 0.76 |
time (sec) |
N/A | 0.308 | 0.070 | 0.119 | 0.042 | 0.074 | 0.072 | 0.123 | 0.155 | 0.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 94 | 239 | 158 | 0 | 245 | 0 | 304 | 283 | 0 |
N.S. |
1 | 1.09 | 2.78 | 1.84 | 0.00 | 2.85 | 0.00 | 3.53 | 3.29 | 0.00 |
time (sec) |
N/A | 0.308 | 0.300 | 1.258 | 0.000 | 0.081 | 0.000 | 0.143 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 16 | 0 | 15 | 15 | 15 | 13 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 0.79 | 0.79 | 0.79 | 0.68 | 0.79 |
time (sec) |
N/A | 0.205 | 0.031 | 0.111 | 0.000 | 0.065 | 0.082 | 0.126 | 0.157 | 0.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 23 | 0 | 22 | 27 | 22 | 20 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.85 | 1.04 | 0.85 | 0.77 | 0.85 |
time (sec) |
N/A | 0.226 | 0.042 | 0.144 | 0.000 | 0.072 | 0.396 | 0.119 | 0.162 | 0.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 69 | 56 | 0 | 0 | 237 | 46 | 0 | 102 | 0 |
N.S. |
1 | 1.10 | 0.89 | 0.00 | 0.00 | 3.76 | 0.73 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 0.344 | 0.066 | 0.000 | 0.000 | 0.089 | 1.032 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 92 | 82 | 25 | 0 | 257 | 51 | 0 | 117 | 0 |
N.S. |
1 | 1.12 | 1.00 | 0.30 | 0.00 | 3.13 | 0.62 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.229 | 0.062 | 0.029 | 0.000 | 0.088 | 1.654 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 606 | 741 | 412 | 0 | 518 | 0 | 0 | 0 | 425 | 0 |
N.S. |
1 | 1.22 | 0.68 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 4.787 | 0.184 | 0.000 | 0.054 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 0 | 15 | 311 | 15 | 14 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 0.88 | 18.29 | 0.88 | 0.82 | 0.88 |
time (sec) |
N/A | 0.190 | 0.026 | 0.118 | 0.000 | 0.069 | 1.223 | 0.118 | 0.147 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 51 | 46 | 120 | 0 | 32 | 2236 | 0 | 30 | 0 |
N.S. |
1 | 0.98 | 0.88 | 2.31 | 0.00 | 0.62 | 43.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.191 | 0.133 | 0.039 | 0.000 | 0.094 | 1.164 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 33 | 44 | 48 | 48 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.29 | 1.41 | 1.41 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.224 | 0.124 | 0.878 | 0.098 | 0.080 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 61 | 77 | 63 | 62 | 64 | 36 | 64 | 15 | 86 |
N.S. |
1 | 1.05 | 1.33 | 1.09 | 1.07 | 1.10 | 0.62 | 1.10 | 0.26 | 1.48 |
time (sec) |
N/A | 0.178 | 0.044 | 1.589 | 0.118 | 0.071 | 0.399 | 0.127 | 0.157 | 0.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 62 | 77 | 48 | 62 | 64 | 37 | 64 | 15 | 76 |
N.S. |
1 | 1.07 | 1.33 | 0.83 | 1.07 | 1.10 | 0.64 | 1.10 | 0.26 | 1.31 |
time (sec) |
N/A | 0.177 | 0.035 | 1.627 | 0.113 | 0.069 | 0.432 | 0.131 | 0.161 | 0.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 86 | 12 | 78 | 82 | 29 | 0 | 11 | 10 |
N.S. |
1 | 1.00 | 1.76 | 0.24 | 1.59 | 1.67 | 0.59 | 0.00 | 0.22 | 0.20 |
time (sec) |
N/A | 0.148 | 0.028 | 2.067 | 0.111 | 0.082 | 0.392 | 0.000 | 0.156 | 0.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 61 | 79 | 63 | 62 | 64 | 32 | 63 | 15 | 80 |
N.S. |
1 | 1.11 | 1.44 | 1.15 | 1.13 | 1.16 | 0.58 | 1.15 | 0.27 | 1.45 |
time (sec) |
N/A | 0.180 | 0.034 | 2.253 | 0.111 | 0.068 | 0.405 | 0.132 | 0.158 | 0.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 148 | 1143 | 0 | 298 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.53 | 11.78 | 0.00 | 3.07 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.208 | 0.938 | 7.403 | 0.000 | 1.759 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 0 | 1421 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.00 | 9.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.312 | 0.000 | 16.865 | 0.000 | 0.000 | 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 | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 120 | 162 | 1592 | 0 | 274 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.09 | 1.47 | 14.47 | 0.00 | 2.49 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.193 | 0.172 | 7.765 | 0.000 | 0.998 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 86 | 85 | 653 | 0 | 120 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.06 | 1.05 | 8.06 | 0.00 | 1.48 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.217 | 0.010 | 1.166 | 0.000 | 0.230 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 86 | 130 | 92 | 0 | 415 | 0 | 67 | 15 | 37 |
N.S. |
1 | 1.30 | 1.97 | 1.39 | 0.00 | 6.29 | 0.00 | 1.02 | 0.23 | 0.56 |
time (sec) |
N/A | 0.227 | 0.571 | 0.752 | 0.000 | 0.768 | 0.000 | 0.127 | 0.169 | 0.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 94 | 145 | 0 | 0 | 665 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.19 | 1.84 | 0.00 | 0.00 | 8.42 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.233 | 0.647 | 0.000 | 0.000 | 0.628 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 0 | 189 | 0 | 0 | 1496 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.00 | 1.60 | 0.00 | 0.00 | 12.68 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.000 | 2.089 | 0.000 | 0.000 | 13.548 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 128 | 111 | 0 | 0 | 0 | 0 | 210 | 0 |
N.S. |
1 | 0.00 | 1.15 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.89 | 0.00 |
time (sec) |
N/A | 0.000 | 15.185 | 1.243 | 0.000 | 0.000 | 0.000 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | B | F | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 0 | 0 | 0 | 0 | 932 | 0 | 0 | 140 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 5.30 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 52.261 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 493 | 570 | 0 | 0 | 0 | 0 | 0 | 0 | 130 | 0 |
N.S. |
1 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.777 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 407 | 506 | 178 | 277 | 0 | 636 | 0 | 795 | 4694 | 343 |
N.S. |
1 | 1.24 | 0.44 | 0.68 | 0.00 | 1.56 | 0.00 | 1.95 | 11.53 | 0.84 |
time (sec) |
N/A | 0.878 | 4.255 | 2.543 | 0.000 | 0.095 | 0.000 | 0.447 | 0.167 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 648 | 0 | 253 | 352 | 0 | 1086 | 0 | 1000 | 10154 | 567 |
N.S. |
1 | 0.00 | 0.39 | 0.54 | 0.00 | 1.68 | 0.00 | 1.54 | 15.67 | 0.88 |
time (sec) |
N/A | 0.000 | 6.725 | 3.135 | 0.000 | 0.121 | 0.000 | 0.598 | 0.220 | 0.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1058 | 0 | 1242 | 502 | 0 | 1986 | 0 | 1410 | 21074 | 1017 |
N.S. |
1 | 0.00 | 1.17 | 0.47 | 0.00 | 1.88 | 0.00 | 1.33 | 19.92 | 0.96 |
time (sec) |
N/A | 0.000 | 36.087 | 8.081 | 0.000 | 0.317 | 0.000 | 0.933 | 0.593 | 0.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 378 | 424 | 733 | 452 | 0 | 1014 | 0 | 2509 | 124 | 0 |
N.S. |
1 | 1.12 | 1.94 | 1.20 | 0.00 | 2.68 | 0.00 | 6.64 | 0.33 | 0.00 |
time (sec) |
N/A | 1.327 | 2.582 | 2.503 | 0.000 | 0.101 | 0.000 | 34.719 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 638 | 0 | 1431 | 552 | 0 | 1714 | 0 | 0 | 224 | 0 |
N.S. |
1 | 0.00 | 2.24 | 0.87 | 0.00 | 2.69 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.000 | 21.416 | 5.678 | 0.000 | 0.182 | 0.000 | 0.000 | 0.437 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 429 | 99 | 787 | 0 | 546 | 0 | 0 | 337 | 0 |
N.S. |
1 | 6.50 | 1.50 | 11.92 | 0.00 | 8.27 | 0.00 | 0.00 | 5.11 | 0.00 |
time (sec) |
N/A | 1.204 | 1.313 | 1.842 | 0.000 | 0.122 | 0.000 | 0.000 | 0.987 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 203 | 145 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.03 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.284 | 10.154 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 1072 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 5.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.268 | 9.752 | 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 | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 168 | 1593 | 0 | 171 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 1.73 | 16.42 | 0.00 | 1.76 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.172 | 0.184 | 12.414 | 0.000 | 1.066 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 76 | 99 | 15 | 105 | 96 | 32 | 0 | 37 | 0 |
N.S. |
1 | 1.04 | 1.36 | 0.21 | 1.44 | 1.32 | 0.44 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.167 | 0.146 | 1.512 | 0.116 | 0.070 | 0.497 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 75 | 88 | 49 | 71 | 73 | 37 | 72 | 33 | 83 |
N.S. |
1 | 1.12 | 1.31 | 0.73 | 1.06 | 1.09 | 0.55 | 1.07 | 0.49 | 1.24 |
time (sec) |
N/A | 0.187 | 0.048 | 1.952 | 0.105 | 0.069 | 0.518 | 0.123 | 0.155 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 482 | 482 | 0 | 0 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.665 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 408 | 0 | 925 | 0 | 3744 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.46 | 0.00 | 3.30 | 0.00 | 13.37 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.557 | 0.000 | 9.348 | 0.000 | 5.063 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 232 | 0 | 0 | 0 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.395 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
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 | 168 | 168 | 0 | 0 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.344 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 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 | 25 | 25 | 25 | 22 | 23 | 23 | 22 | 23 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.92 | 0.92 | 0.88 | 0.92 | 0.92 | 0.92 |
time (sec) |
N/A | 0.171 | 0.005 | 0.065 | 0.026 | 0.062 | 0.035 | 0.122 | 0.154 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 86 | 52 | 0 | 43 | 73 | 40 | 85 | 53 |
N.S. |
1 | 1.00 | 1.46 | 0.88 | 0.00 | 0.73 | 1.24 | 0.68 | 1.44 | 0.90 |
time (sec) |
N/A | 0.184 | 0.014 | 0.099 | 0.000 | 0.068 | 0.066 | 0.129 | 0.159 | 0.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 85 | 99 | 70 | 0 | 66 | 100 | 64 | 108 | 76 |
N.S. |
1 | 1.09 | 1.27 | 0.90 | 0.00 | 0.85 | 1.28 | 0.82 | 1.38 | 0.97 |
time (sec) |
N/A | 0.255 | 0.013 | 0.093 | 0.000 | 0.068 | 0.074 | 0.133 | 0.151 | 0.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 57 | 56 | 0 | 56 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.14 | 0.00 | 1.14 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.149 | 0.143 | 1.790 | 0.000 | 0.107 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 44 | 62 | 0 | 61 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.17 | 0.00 | 1.15 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.154 | 0.172 | 1.550 | 0.000 | 0.107 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 101 | 79 | 89 | 0 | 345 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.35 | 1.05 | 1.19 | 0.00 | 4.60 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.258 | 0.250 | 2.428 | 0.000 | 0.143 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 92 | 107 | 0 | 229 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.54 | 0.63 | 0.00 | 1.34 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.283 | 0.241 | 1.343 | 0.000 | 0.154 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 88 | 157 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.10 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.211 | 10.192 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 96 | 162 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.09 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.210 | 10.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 151 | 144 | 0 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.01 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.221 | 10.188 | 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 | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 137 | 152 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.01 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.210 | 10.142 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 28 | 164 | 0 | 1019 | 0 | 0 | 24 | 653 |
N.S. |
1 | 1.00 | 0.22 | 1.29 | 0.00 | 8.02 | 0.00 | 0.00 | 0.19 | 5.14 |
time (sec) |
N/A | 0.182 | 10.019 | 11.852 | 0.000 | 0.145 | 0.000 | 0.000 | 0.162 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | B |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 54 | 240 | 0 | 1669 | 0 | 0 | 31 | 331 |
N.S. |
1 | 1.00 | 0.34 | 1.53 | 0.00 | 10.63 | 0.00 | 0.00 | 0.20 | 2.11 |
time (sec) |
N/A | 0.203 | 10.024 | 0.883 | 0.000 | 0.212 | 0.000 | 0.000 | 0.162 | 8.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 48 | 421 | 0 | 261 | 0 | 0 | 22 | 533 |
N.S. |
1 | 1.00 | 0.65 | 5.69 | 0.00 | 3.53 | 0.00 | 0.00 | 0.30 | 7.20 |
time (sec) |
N/A | 0.422 | 10.021 | 8.427 | 0.000 | 0.129 | 0.000 | 0.000 | 0.151 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 32 | 383 | 0 | 491 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.31 | 3.72 | 0.00 | 4.77 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.642 | 10.023 | 1.681 | 0.000 | 0.237 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 126 | 438 | 0 | 956 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.56 | 5.41 | 0.00 | 11.80 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.157 | 4.158 | 8.730 | 0.000 | 1.100 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 126 | 443 | 0 | 345 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.56 | 5.47 | 0.00 | 4.26 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.162 | 3.923 | 2.066 | 0.000 | 0.859 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 118 | 938 | 0 | 1132 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.04 | 8.30 | 0.00 | 10.02 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.170 | 3.925 | 14.201 | 0.000 | 0.501 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 124 | 0 | 0 | 1103 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 10.12 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.169 | 4.052 | 0.000 | 0.000 | 0.492 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 29 | 33 | 0 | 85 | 0 | 0 | 130 | 217 |
N.S. |
1 | 1.00 | 0.33 | 0.38 | 0.00 | 0.98 | 0.00 | 0.00 | 1.49 | 2.49 |
time (sec) |
N/A | 0.495 | 10.357 | 1.063 | 0.000 | 0.097 | 0.000 | 0.000 | 1.371 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | F | C | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 546 | 46 | 317 | 0 | 70 | 0 | 0 | 228 | 207 |
N.S. |
1 | 7.69 | 0.65 | 4.46 | 0.00 | 0.99 | 0.00 | 0.00 | 3.21 | 2.92 |
time (sec) |
N/A | 1.170 | 10.360 | 0.759 | 0.000 | 0.085 | 0.000 | 0.000 | 5.843 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 233 | 52 | 367 | 0 | 63 | 0 | 0 | 51 | 0 |
N.S. |
1 | 5.07 | 1.13 | 7.98 | 0.00 | 1.37 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.833 | 10.851 | 0.920 | 0.000 | 0.088 | 0.000 | 0.000 | 180.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-2) | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 112 | 0 | 0 | 0 | 0 | 54 | 67 |
N.S. |
1 | 1.00 | 1.06 | 3.50 | 0.00 | 0.00 | 0.00 | 0.00 | 1.69 | 2.09 |
time (sec) |
N/A | 0.234 | 1.209 | 3.578 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 31 | 44 | 0 | 44 | 0 | 0 | 24 | 204 |
N.S. |
1 | 1.00 | 1.35 | 1.91 | 0.00 | 1.91 | 0.00 | 0.00 | 1.04 | 8.87 |
time (sec) |
N/A | 0.192 | 0.868 | 0.542 | 0.000 | 0.079 | 0.000 | 0.000 | 0.160 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 218 | 47 | 351 | 0 | 511 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.22 | 1.61 | 0.00 | 2.34 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.237 | 10.044 | 70.818 | 0.000 | 0.205 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 50 | 350 | 0 | 657 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.24 | 1.67 | 0.00 | 3.13 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.233 | 10.053 | 72.366 | 0.000 | 0.212 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 222 | 65 | 347 | 0 | 659 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.29 | 1.56 | 0.00 | 2.97 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.218 | 10.053 | 61.048 | 0.000 | 0.215 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 214 | 68 | 350 | 0 | 516 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.32 | 1.64 | 0.00 | 2.41 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.222 | 10.049 | 61.290 | 0.000 | 0.199 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 73 | 77 | 327 | 0 | 323 | 0 | 0 | 261 | 0 |
N.S. |
1 | 1.12 | 1.18 | 5.03 | 0.00 | 4.97 | 0.00 | 0.00 | 4.02 | 0.00 |
time (sec) |
N/A | 0.267 | 8.545 | 2.500 | 0.000 | 0.161 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 70 | 77 | 311 | 0 | 112 | 0 | 0 | 261 | 0 |
N.S. |
1 | 1.11 | 1.22 | 4.94 | 0.00 | 1.78 | 0.00 | 0.00 | 4.14 | 0.00 |
time (sec) |
N/A | 0.276 | 8.471 | 2.625 | 0.000 | 0.156 | 0.000 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 92 | 818 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.74 | 15.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.206 | 0.747 | 2.490 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 111 | 0 | 1421 | 0 | 267 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.03 | 0.00 | 13.16 | 0.00 | 2.47 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.278 | 0.000 | 5.063 | 0.000 | 0.771 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 189 | 111 | 0 | 1252 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.93 | 1.13 | 0.00 | 12.78 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.174 | 0.883 | 1.144 | 0.000 | 101.790 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 154 | 0 | 0 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.408 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 100 | 182 | 92 | 110 | 387 | 0 | 113 | 35 | 157 |
N.S. |
1 | 1.04 | 1.90 | 0.96 | 1.15 | 4.03 | 0.00 | 1.18 | 0.36 | 1.64 |
time (sec) |
N/A | 0.214 | 0.339 | 0.832 | 0.125 | 0.093 | 0.000 | 3.443 | 0.179 | 0.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 114 | 95 | 0 | 246 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 1.30 | 1.08 | 0.00 | 2.80 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.168 | 0.235 | 3.100 | 0.000 | 1.544 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 249 | 283 | 0 | 0 | 336 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.07 | 1.21 | 0.00 | 0.00 | 1.44 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.390 | 0.720 | 0.000 | 0.000 | 1.565 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 86 | 104 | 80 | 86 | 84 | 0 | 87 | 31 | 100 |
N.S. |
1 | 1.05 | 1.27 | 0.98 | 1.05 | 1.02 | 0.00 | 1.06 | 0.38 | 1.22 |
time (sec) |
N/A | 0.199 | 0.092 | 3.595 | 0.108 | 0.082 | 0.000 | 0.138 | 0.149 | 0.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 383 | 145 | 720 | 0 | 287 | 0 | 0 | 81 | 0 |
N.S. |
1 | 2.84 | 1.07 | 5.33 | 0.00 | 2.13 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.574 | 1.098 | 7.268 | 0.000 | 5.654 | 0.000 | 0.000 | 0.160 | 0.000 |