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 | F(-2) | B | F(-1) | B | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 974 | 1054 | 1120 | 1422 | 0 | 16082 | 0 | 81273 | 27 | 0 |
N.S. |
1 | 1.08 | 1.15 | 1.46 | 0.00 | 16.51 | 0.00 | 83.44 | 0.03 | 0.00 |
time (sec) |
N/A | 2.959 | 16.314 | 2.438 | 0.000 | 167.754 | 0.000 | 2.942 | 200.038 | 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 | 132 | 152 | 71 | 65 | 109 | 73 | 76 | 69 | 101 | 0 |
N.S. |
1 | 1.15 | 0.54 | 0.49 | 0.83 | 0.55 | 0.58 | 0.52 | 0.77 | 0.00 |
time (sec) |
N/A | 0.523 | 0.577 | 1.567 | 0.109 | 0.082 | 0.564 | 0.360 | 0.187 | 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 | 107 | 122 | 66 | 60 | 92 | 68 | 70 | 64 | 85 | 0 |
N.S. |
1 | 1.14 | 0.62 | 0.56 | 0.86 | 0.64 | 0.65 | 0.60 | 0.79 | 0.00 |
time (sec) |
N/A | 0.440 | 0.450 | 1.573 | 0.109 | 0.086 | 0.550 | 0.359 | 0.190 | 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 | 82 | 92 | 61 | 55 | 75 | 63 | 63 | 59 | 69 | 0 |
N.S. |
1 | 1.12 | 0.74 | 0.67 | 0.91 | 0.77 | 0.77 | 0.72 | 0.84 | 0.00 |
time (sec) |
N/A | 0.389 | 0.364 | 1.565 | 0.112 | 0.086 | 0.530 | 0.381 | 0.220 | 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 | 57 | 62 | 56 | 50 | 58 | 58 | 54 | 54 | 53 | 0 |
N.S. |
1 | 1.09 | 0.98 | 0.88 | 1.02 | 1.02 | 0.95 | 0.95 | 0.93 | 0.00 |
time (sec) |
N/A | 0.314 | 0.278 | 1.405 | 0.106 | 0.082 | 0.622 | 0.446 | 0.206 | 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 | 52 | 57 | 51 | 45 | 43 | 53 | 49 | 49 | 39 | 44 |
N.S. |
1 | 1.10 | 0.98 | 0.87 | 0.83 | 1.02 | 0.94 | 0.94 | 0.75 | 0.85 |
time (sec) |
N/A | 0.296 | 0.195 | 1.398 | 0.109 | 0.080 | 0.433 | 0.346 | 0.198 | 12.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 77 | 61 | 61 | 70 | 90 | 0 | 107 | 82 | 0 |
N.S. |
1 | 1.22 | 0.97 | 0.97 | 1.11 | 1.43 | 0.00 | 1.70 | 1.30 | 0.00 |
time (sec) |
N/A | 0.381 | 0.260 | 1.738 | 0.110 | 0.085 | 0.000 | 0.349 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 64 | 61 | 53 | 64 | 80 | 0 | 127 | 136 | 0 |
N.S. |
1 | 1.08 | 1.03 | 0.90 | 1.08 | 1.36 | 0.00 | 2.15 | 2.31 | 0.00 |
time (sec) |
N/A | 0.321 | 0.312 | 1.612 | 0.153 | 0.079 | 0.000 | 0.377 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 94 | 63 | 68 | 90 | 95 | 0 | 206 | 233 | 0 |
N.S. |
1 | 1.12 | 0.75 | 0.81 | 1.07 | 1.13 | 0.00 | 2.45 | 2.77 | 0.00 |
time (sec) |
N/A | 0.386 | 0.432 | 1.622 | 0.114 | 0.088 | 0.000 | 0.405 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 122 | 68 | 73 | 121 | 110 | 0 | 257 | 323 | 0 |
N.S. |
1 | 1.12 | 0.62 | 0.67 | 1.11 | 1.01 | 0.00 | 2.36 | 2.96 | 0.00 |
time (sec) |
N/A | 0.461 | 0.502 | 1.654 | 0.111 | 0.081 | 0.000 | 1.694 | 0.320 | 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 | 134 | 152 | 73 | 78 | 157 | 125 | 0 | 193 | 413 | 0 |
N.S. |
1 | 1.13 | 0.54 | 0.58 | 1.17 | 0.93 | 0.00 | 1.44 | 3.08 | 0.00 |
time (sec) |
N/A | 0.541 | 0.568 | 1.644 | 0.119 | 0.088 | 0.000 | 0.378 | 0.636 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 182 | 78 | 83 | 198 | 140 | 0 | 359 | 503 | 0 |
N.S. |
1 | 1.14 | 0.49 | 0.52 | 1.25 | 0.88 | 0.00 | 2.26 | 3.16 | 0.00 |
time (sec) |
N/A | 0.620 | 0.632 | 1.664 | 0.115 | 0.095 | 0.000 | 0.372 | 1.529 | 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 | 112 | 127 | 83 | 65 | 109 | 97 | 0 | 67 | 184 | 0 |
N.S. |
1 | 1.13 | 0.74 | 0.58 | 0.97 | 0.87 | 0.00 | 0.60 | 1.64 | 0.00 |
time (sec) |
N/A | 0.440 | 0.532 | 1.595 | 0.116 | 0.092 | 0.000 | 0.320 | 0.248 | 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 | 87 | 97 | 78 | 60 | 92 | 92 | 0 | 62 | 168 | 0 |
N.S. |
1 | 1.11 | 0.90 | 0.69 | 1.06 | 1.06 | 0.00 | 0.71 | 1.93 | 0.00 |
time (sec) |
N/A | 0.379 | 0.469 | 1.602 | 0.112 | 0.123 | 0.000 | 0.372 | 0.240 | 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 | 78 | 86 | 59 | 55 | 75 | 87 | 0 | 58 | 153 | 0 |
N.S. |
1 | 1.10 | 0.76 | 0.71 | 0.96 | 1.12 | 0.00 | 0.74 | 1.96 | 0.00 |
time (sec) |
N/A | 0.369 | 0.375 | 1.590 | 0.111 | 0.117 | 0.000 | 0.310 | 0.207 | 0.000 |
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 | 57 | 62 | 55 | 50 | 58 | 81 | 0 | 54 | 137 | 78 |
N.S. |
1 | 1.09 | 0.96 | 0.88 | 1.02 | 1.42 | 0.00 | 0.95 | 2.40 | 1.37 |
time (sec) |
N/A | 0.307 | 0.316 | 1.447 | 0.111 | 0.112 | 0.000 | 0.322 | 0.240 | 13.106 |
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 | 21 | 21 | 21 | 20 | 30 | 19 | 0 | 19 | 58 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.43 | 0.90 | 0.00 | 0.90 | 2.76 | 0.90 |
time (sec) |
N/A | 0.233 | 0.184 | 1.405 | 0.026 | 0.106 | 0.000 | 0.335 | 0.235 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 62 | 68 | 51 | 72 | 95 | 0 | 93 | 234 | 0 |
N.S. |
1 | 1.09 | 1.19 | 0.89 | 1.26 | 1.67 | 0.00 | 1.63 | 4.11 | 0.00 |
time (sec) |
N/A | 0.314 | 0.343 | 1.655 | 0.108 | 0.126 | 0.000 | 0.351 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 99 | 80 | 63 | 106 | 110 | 0 | 170 | 324 | 0 |
N.S. |
1 | 1.21 | 0.98 | 0.77 | 1.29 | 1.34 | 0.00 | 2.07 | 3.95 | 0.00 |
time (sec) |
N/A | 0.386 | 0.435 | 1.658 | 0.116 | 0.129 | 0.000 | 0.404 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 127 | 85 | 68 | 157 | 125 | 0 | 225 | 413 | 0 |
N.S. |
1 | 1.21 | 0.81 | 0.65 | 1.50 | 1.19 | 0.00 | 2.14 | 3.93 | 0.00 |
time (sec) |
N/A | 0.464 | 0.481 | 1.704 | 0.113 | 0.124 | 0.000 | 0.360 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 157 | 90 | 73 | 225 | 140 | 0 | 276 | 503 | 0 |
N.S. |
1 | 1.19 | 0.68 | 0.55 | 1.70 | 1.06 | 0.00 | 2.09 | 3.81 | 0.00 |
time (sec) |
N/A | 0.545 | 0.541 | 1.641 | 0.110 | 0.127 | 0.000 | 0.389 | 0.538 | 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 | 157 | 187 | 95 | 78 | 310 | 155 | 0 | 235 | 593 | 0 |
N.S. |
1 | 1.19 | 0.61 | 0.50 | 1.97 | 0.99 | 0.00 | 1.50 | 3.78 | 0.00 |
time (sec) |
N/A | 0.619 | 0.607 | 1.643 | 0.116 | 0.126 | 0.000 | 0.408 | 1.073 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 121 | 83 | 65 | 214 | 117 | 0 | 68 | 27 | 0 |
N.S. |
1 | 1.10 | 0.75 | 0.59 | 1.95 | 1.06 | 0.00 | 0.62 | 0.25 | 0.00 |
time (sec) |
N/A | 0.421 | 0.460 | 1.671 | 0.119 | 0.123 | 0.000 | 0.367 | 200.037 | 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 | 87 | 93 | 78 | 60 | 197 | 112 | 0 | 63 | 249 | 0 |
N.S. |
1 | 1.07 | 0.90 | 0.69 | 2.26 | 1.29 | 0.00 | 0.72 | 2.86 | 0.00 |
time (sec) |
N/A | 0.370 | 0.409 | 1.619 | 0.118 | 0.117 | 0.000 | 0.389 | 0.194 | 0.000 |
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 | 52 | 54 | 45 | 30 | 76 | 51 | 0 | 28 | 114 | 48 |
N.S. |
1 | 1.04 | 0.87 | 0.58 | 1.46 | 0.98 | 0.00 | 0.54 | 2.19 | 0.92 |
time (sec) |
N/A | 0.297 | 0.304 | 1.559 | 0.032 | 0.113 | 0.000 | 0.378 | 0.221 | 0.121 |
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 | 43 | 30 | 59 | 51 | 0 | 28 | 114 | 48 |
N.S. |
1 | 1.00 | 0.91 | 0.64 | 1.26 | 1.09 | 0.00 | 0.60 | 2.43 | 1.02 |
time (sec) |
N/A | 0.285 | 0.300 | 1.460 | 0.028 | 0.113 | 0.000 | 0.380 | 0.194 | 0.096 |
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 | 43 | 30 | 59 | 51 | 0 | 29 | 114 | 36 |
N.S. |
1 | 1.00 | 0.91 | 0.64 | 1.26 | 1.09 | 0.00 | 0.62 | 2.43 | 0.77 |
time (sec) |
N/A | 0.270 | 0.271 | 1.488 | 0.031 | 0.105 | 0.000 | 0.380 | 0.202 | 12.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 90 | 78 | 80 | 101 | 125 | 0 | 102 | 414 | 0 |
N.S. |
1 | 1.12 | 0.98 | 1.00 | 1.26 | 1.56 | 0.00 | 1.28 | 5.18 | 0.00 |
time (sec) |
N/A | 0.382 | 0.421 | 1.629 | 0.109 | 0.121 | 0.000 | 0.397 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 130 | 90 | 73 | 135 | 140 | 0 | 235 | 504 | 0 |
N.S. |
1 | 1.24 | 0.86 | 0.70 | 1.29 | 1.33 | 0.00 | 2.24 | 4.80 | 0.00 |
time (sec) |
N/A | 0.473 | 0.469 | 1.623 | 0.113 | 0.127 | 0.000 | 0.395 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 162 | 95 | 78 | 186 | 155 | 0 | 234 | 594 | 0 |
N.S. |
1 | 1.25 | 0.73 | 0.60 | 1.43 | 1.19 | 0.00 | 1.80 | 4.57 | 0.00 |
time (sec) |
N/A | 0.561 | 0.543 | 1.639 | 0.114 | 0.131 | 0.000 | 0.408 | 0.456 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 192 | 100 | 83 | 254 | 170 | 0 | 285 | 684 | 0 |
N.S. |
1 | 1.24 | 0.65 | 0.54 | 1.64 | 1.10 | 0.00 | 1.84 | 4.41 | 0.00 |
time (sec) |
N/A | 0.646 | 0.587 | 1.654 | 0.128 | 0.132 | 0.000 | 0.410 | 0.983 | 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 | 35 | 35 | 39 | 32 | 41 | 50 | 0 | 52 | 64 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.91 | 1.17 | 1.43 | 0.00 | 1.49 | 1.83 | 0.00 |
time (sec) |
N/A | 0.335 | 0.149 | 2.592 | 0.158 | 0.122 | 0.000 | 0.360 | 0.193 | 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 | 224 | 240 | 208 | 156 | 0 | 67 | 0 | 0 | 187 | 0 |
N.S. |
1 | 1.07 | 0.93 | 0.70 | 0.00 | 0.30 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.721 | 31.447 | 1.861 | 0.000 | 0.111 | 0.000 | 0.000 | 0.437 | 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 | 197 | 208 | 203 | 151 | 0 | 62 | 0 | 0 | 165 | 0 |
N.S. |
1 | 1.06 | 1.03 | 0.77 | 0.00 | 0.31 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.639 | 31.407 | 1.768 | 0.000 | 0.115 | 0.000 | 0.000 | 0.414 | 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 | 170 | 176 | 198 | 146 | 0 | 57 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.04 | 1.16 | 0.86 | 0.00 | 0.34 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.612 | 30.116 | 1.774 | 0.000 | 0.130 | 0.000 | 0.000 | 0.396 | 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 | 143 | 144 | 193 | 141 | 0 | 52 | 0 | 0 | 121 | 0 |
N.S. |
1 | 1.01 | 1.35 | 0.99 | 0.00 | 0.36 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.467 | 28.418 | 1.585 | 0.000 | 0.109 | 0.000 | 0.000 | 0.429 | 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 | 141 | 142 | 185 | 136 | 0 | 69 | 0 | 0 | 232 | 0 |
N.S. |
1 | 1.01 | 1.31 | 0.96 | 0.00 | 0.49 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 0.480 | 28.034 | 2.029 | 0.000 | 0.122 | 0.000 | 0.000 | 0.580 | 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 | 143 | 144 | 182 | 203 | 0 | 86 | 0 | 0 | 364 | 0 |
N.S. |
1 | 1.01 | 1.27 | 1.42 | 0.00 | 0.60 | 0.00 | 0.00 | 2.55 | 0.00 |
time (sec) |
N/A | 0.473 | 31.372 | 1.697 | 0.000 | 0.117 | 0.000 | 0.000 | 0.632 | 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 | 170 | 176 | 182 | 246 | 0 | 106 | 0 | 0 | 516 | 0 |
N.S. |
1 | 1.04 | 1.07 | 1.45 | 0.00 | 0.62 | 0.00 | 0.00 | 3.04 | 0.00 |
time (sec) |
N/A | 0.556 | 31.357 | 1.712 | 0.000 | 0.115 | 0.000 | 0.000 | 0.786 | 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 | 197 | 208 | 217 | 270 | 0 | 126 | 0 | 0 | 688 | 0 |
N.S. |
1 | 1.06 | 1.10 | 1.37 | 0.00 | 0.64 | 0.00 | 0.00 | 3.49 | 0.00 |
time (sec) |
N/A | 0.639 | 31.464 | 1.711 | 0.000 | 0.124 | 0.000 | 0.000 | 1.073 | 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 | 256 | 277 | 218 | 166 | 0 | 77 | 0 | 0 | 231 | 0 |
N.S. |
1 | 1.08 | 0.85 | 0.65 | 0.00 | 0.30 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.790 | 31.452 | 1.905 | 0.000 | 0.119 | 0.000 | 0.000 | 0.555 | 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 | 229 | 245 | 213 | 161 | 0 | 72 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.07 | 0.93 | 0.70 | 0.00 | 0.31 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.729 | 31.431 | 1.812 | 0.000 | 0.116 | 0.000 | 0.000 | 0.485 | 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 | 202 | 213 | 208 | 156 | 0 | 67 | 0 | 0 | 187 | 0 |
N.S. |
1 | 1.05 | 1.03 | 0.77 | 0.00 | 0.33 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.650 | 31.416 | 1.836 | 0.000 | 0.113 | 0.000 | 0.000 | 0.473 | 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 | 175 | 181 | 203 | 151 | 0 | 62 | 0 | 0 | 165 | 0 |
N.S. |
1 | 1.03 | 1.16 | 0.86 | 0.00 | 0.35 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.550 | 31.411 | 1.803 | 0.000 | 0.115 | 0.000 | 0.000 | 0.486 | 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 | 173 | 179 | 192 | 146 | 0 | 81 | 0 | 0 | 276 | 0 |
N.S. |
1 | 1.03 | 1.11 | 0.84 | 0.00 | 0.47 | 0.00 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.552 | 30.391 | 1.662 | 0.000 | 0.123 | 0.000 | 0.000 | 0.639 | 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 | 175 | 178 | 195 | 213 | 0 | 96 | 0 | 0 | 408 | 0 |
N.S. |
1 | 1.02 | 1.11 | 1.22 | 0.00 | 0.55 | 0.00 | 0.00 | 2.33 | 0.00 |
time (sec) |
N/A | 0.571 | 31.394 | 1.740 | 0.000 | 0.120 | 0.000 | 0.000 | 0.798 | 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 | 175 | 179 | 192 | 265 | 0 | 111 | 0 | 0 | 560 | 0 |
N.S. |
1 | 1.02 | 1.10 | 1.51 | 0.00 | 0.63 | 0.00 | 0.00 | 3.20 | 0.00 |
time (sec) |
N/A | 0.543 | 31.404 | 1.688 | 0.000 | 0.121 | 0.000 | 0.000 | 0.942 | 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 | 175 | 181 | 192 | 270 | 0 | 126 | 0 | 0 | 732 | 0 |
N.S. |
1 | 1.03 | 1.10 | 1.54 | 0.00 | 0.72 | 0.00 | 0.00 | 4.18 | 0.00 |
time (sec) |
N/A | 0.547 | 31.401 | 1.631 | 0.000 | 0.119 | 0.000 | 0.000 | 1.173 | 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 | 202 | 213 | 192 | 294 | 0 | 146 | 0 | 0 | 924 | 0 |
N.S. |
1 | 1.05 | 0.95 | 1.46 | 0.00 | 0.72 | 0.00 | 0.00 | 4.57 | 0.00 |
time (sec) |
N/A | 0.640 | 31.525 | 1.761 | 0.000 | 0.130 | 0.000 | 0.000 | 1.535 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 245 | 227 | 318 | 0 | 166 | 0 | 0 | 1136 | 0 |
N.S. |
1 | 1.07 | 0.99 | 1.39 | 0.00 | 0.72 | 0.00 | 0.00 | 4.96 | 0.00 |
time (sec) |
N/A | 0.734 | 31.605 | 2.001 | 0.000 | 0.123 | 0.000 | 0.000 | 2.278 | 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 | 288 | 314 | 228 | 176 | 0 | 87 | 0 | 0 | 275 | 0 |
N.S. |
1 | 1.09 | 0.79 | 0.61 | 0.00 | 0.30 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.902 | 31.488 | 2.220 | 0.000 | 0.112 | 0.000 | 0.000 | 0.576 | 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 | 261 | 282 | 223 | 171 | 0 | 82 | 0 | 0 | 253 | 0 |
N.S. |
1 | 1.08 | 0.85 | 0.66 | 0.00 | 0.31 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.824 | 31.467 | 1.936 | 0.000 | 0.113 | 0.000 | 0.000 | 0.557 | 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 | 234 | 250 | 218 | 166 | 0 | 77 | 0 | 0 | 231 | 0 |
N.S. |
1 | 1.07 | 0.93 | 0.71 | 0.00 | 0.33 | 0.00 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.723 | 31.452 | 1.843 | 0.000 | 0.119 | 0.000 | 0.000 | 0.496 | 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 | 207 | 218 | 213 | 161 | 0 | 72 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.05 | 1.03 | 0.78 | 0.00 | 0.35 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.635 | 31.419 | 1.793 | 0.000 | 0.114 | 0.000 | 0.000 | 0.542 | 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 | 205 | 216 | 205 | 156 | 0 | 91 | 0 | 0 | 320 | 0 |
N.S. |
1 | 1.05 | 1.00 | 0.76 | 0.00 | 0.44 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.662 | 31.517 | 1.607 | 0.000 | 0.121 | 0.000 | 0.000 | 0.668 | 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 | 207 | 216 | 202 | 223 | 0 | 106 | 0 | 0 | 452 | 0 |
N.S. |
1 | 1.04 | 0.98 | 1.08 | 0.00 | 0.51 | 0.00 | 0.00 | 2.18 | 0.00 |
time (sec) |
N/A | 0.634 | 31.410 | 1.674 | 0.000 | 0.130 | 0.000 | 0.000 | 0.945 | 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 | 207 | 216 | 202 | 307 | 0 | 121 | 0 | 0 | 604 | 0 |
N.S. |
1 | 1.04 | 0.98 | 1.48 | 0.00 | 0.58 | 0.00 | 0.00 | 2.92 | 0.00 |
time (sec) |
N/A | 0.656 | 31.545 | 1.714 | 0.000 | 0.124 | 0.000 | 0.000 | 1.128 | 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 | 207 | 215 | 202 | 309 | 0 | 136 | 0 | 0 | 776 | 0 |
N.S. |
1 | 1.04 | 0.98 | 1.49 | 0.00 | 0.66 | 0.00 | 0.00 | 3.75 | 0.00 |
time (sec) |
N/A | 0.655 | 31.466 | 1.769 | 0.000 | 0.126 | 0.000 | 0.000 | 1.631 | 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 | 207 | 218 | 227 | 313 | 0 | 151 | 0 | 0 | 968 | 0 |
N.S. |
1 | 1.05 | 1.10 | 1.51 | 0.00 | 0.73 | 0.00 | 0.00 | 4.68 | 0.00 |
time (sec) |
N/A | 0.661 | 31.564 | 1.865 | 0.000 | 0.131 | 0.000 | 0.000 | 1.884 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 218 | 227 | 318 | 0 | 166 | 0 | 0 | 1180 | 0 |
N.S. |
1 | 1.05 | 1.10 | 1.54 | 0.00 | 0.80 | 0.00 | 0.00 | 5.70 | 0.00 |
time (sec) |
N/A | 0.649 | 31.553 | 1.937 | 0.000 | 0.129 | 0.000 | 0.000 | 2.655 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 250 | 232 | 342 | 0 | 186 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.99 | 1.46 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.751 | 31.657 | 2.141 | 0.000 | 0.121 | 0.000 | 0.000 | 2.954 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 282 | 237 | 366 | 0 | 206 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.91 | 1.40 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.820 | 21.895 | 2.227 | 0.000 | 0.122 | 0.000 | 0.000 | 4.467 | 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 | 192 | 203 | 198 | 146 | 0 | 57 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.06 | 1.03 | 0.76 | 0.00 | 0.30 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.617 | 31.412 | 1.744 | 0.000 | 0.119 | 0.000 | 0.000 | 0.416 | 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 | 165 | 171 | 193 | 141 | 0 | 52 | 0 | 0 | 121 | 0 |
N.S. |
1 | 1.04 | 1.17 | 0.85 | 0.00 | 0.32 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.547 | 31.353 | 1.730 | 0.000 | 0.118 | 0.000 | 0.000 | 0.382 | 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 | 138 | 139 | 188 | 136 | 0 | 47 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.01 | 1.36 | 0.99 | 0.00 | 0.34 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.472 | 31.379 | 1.745 | 0.000 | 0.113 | 0.000 | 0.000 | 0.388 | 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 | 107 | 107 | 177 | 67 | 0 | 26 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.00 | 1.65 | 0.63 | 0.00 | 0.24 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.409 | 31.505 | 1.558 | 0.000 | 0.110 | 0.000 | 0.000 | 0.395 | 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 | 136 | 139 | 104 | 131 | 0 | 66 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.02 | 0.76 | 0.96 | 0.00 | 0.49 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.467 | 31.237 | 1.561 | 0.000 | 0.117 | 0.000 | 0.000 | 0.565 | 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 | 165 | 171 | 183 | 203 | 0 | 86 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.04 | 1.11 | 1.23 | 0.00 | 0.52 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.557 | 31.374 | 1.601 | 0.000 | 0.129 | 0.000 | 0.000 | 0.615 | 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 | 192 | 203 | 182 | 246 | 0 | 106 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.06 | 0.95 | 1.28 | 0.00 | 0.55 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.636 | 31.354 | 1.685 | 0.000 | 0.112 | 0.000 | 0.000 | 0.664 | 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 | 197 | 208 | 192 | 141 | 0 | 96 | 0 | 0 | 408 | 0 |
N.S. |
1 | 1.06 | 0.97 | 0.72 | 0.00 | 0.49 | 0.00 | 0.00 | 2.07 | 0.00 |
time (sec) |
N/A | 0.636 | 31.418 | 1.653 | 0.000 | 0.122 | 0.000 | 0.000 | 0.506 | 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 | 170 | 176 | 187 | 136 | 0 | 91 | 0 | 0 | 386 | 0 |
N.S. |
1 | 1.04 | 1.10 | 0.80 | 0.00 | 0.54 | 0.00 | 0.00 | 2.27 | 0.00 |
time (sec) |
N/A | 0.549 | 31.403 | 1.549 | 0.000 | 0.129 | 0.000 | 0.000 | 0.475 | 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 | 143 | 144 | 183 | 131 | 0 | 86 | 0 | 0 | 364 | 0 |
N.S. |
1 | 1.01 | 1.28 | 0.92 | 0.00 | 0.60 | 0.00 | 0.00 | 2.55 | 0.00 |
time (sec) |
N/A | 0.475 | 31.400 | 1.650 | 0.000 | 0.118 | 0.000 | 0.000 | 0.460 | 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 | 137 | 140 | 178 | 131 | 0 | 86 | 0 | 0 | 344 | 0 |
N.S. |
1 | 1.02 | 1.30 | 0.96 | 0.00 | 0.63 | 0.00 | 0.00 | 2.51 | 0.00 |
time (sec) |
N/A | 0.486 | 31.386 | 1.580 | 0.000 | 0.110 | 0.000 | 0.000 | 0.429 | 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 | 141 | 144 | 178 | 131 | 0 | 86 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.02 | 1.26 | 0.93 | 0.00 | 0.61 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.475 | 31.381 | 1.556 | 0.000 | 0.120 | 0.000 | 0.000 | 0.507 | 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 | 170 | 176 | 172 | 131 | 0 | 106 | 0 | 0 | 501 | 0 |
N.S. |
1 | 1.04 | 1.01 | 0.77 | 0.00 | 0.62 | 0.00 | 0.00 | 2.95 | 0.00 |
time (sec) |
N/A | 0.553 | 31.386 | 1.764 | 0.000 | 0.120 | 0.000 | 0.000 | 0.692 | 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 | 197 | 208 | 177 | 203 | 0 | 126 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.06 | 0.90 | 1.03 | 0.00 | 0.64 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.633 | 31.432 | 1.724 | 0.000 | 0.117 | 0.000 | 0.000 | 0.749 | 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 | 224 | 240 | 182 | 274 | 0 | 146 | 0 | 0 | 130 | 0 |
N.S. |
1 | 1.07 | 0.81 | 1.22 | 0.00 | 0.65 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.717 | 31.476 | 1.856 | 0.000 | 0.116 | 0.000 | 0.000 | 0.797 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 209 | 220 | 250 | 0 | 131 | 0 | 0 | 754 | 0 |
N.S. |
1 | 1.03 | 1.09 | 1.24 | 0.00 | 0.65 | 0.00 | 0.00 | 3.73 | 0.00 |
time (sec) |
N/A | 0.648 | 31.638 | 1.715 | 0.000 | 0.122 | 0.000 | 0.000 | 0.566 | 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 | 175 | 181 | 196 | 231 | 0 | 126 | 0 | 0 | 732 | 0 |
N.S. |
1 | 1.03 | 1.12 | 1.32 | 0.00 | 0.72 | 0.00 | 0.00 | 4.18 | 0.00 |
time (sec) |
N/A | 0.552 | 31.442 | 1.583 | 0.000 | 0.124 | 0.000 | 0.000 | 0.574 | 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 | 175 | 177 | 196 | 231 | 0 | 126 | 0 | 0 | 710 | 0 |
N.S. |
1 | 1.01 | 1.12 | 1.32 | 0.00 | 0.72 | 0.00 | 0.00 | 4.06 | 0.00 |
time (sec) |
N/A | 0.565 | 31.435 | 1.769 | 0.000 | 0.119 | 0.000 | 0.000 | 0.499 | 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 | 175 | 177 | 196 | 231 | 0 | 126 | 0 | 0 | 688 | 0 |
N.S. |
1 | 1.01 | 1.12 | 1.32 | 0.00 | 0.72 | 0.00 | 0.00 | 3.93 | 0.00 |
time (sec) |
N/A | 0.542 | 31.425 | 1.744 | 0.000 | 0.115 | 0.000 | 0.000 | 0.454 | 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 | 173 | 181 | 196 | 231 | 0 | 126 | 0 | 0 | 668 | 0 |
N.S. |
1 | 1.05 | 1.13 | 1.34 | 0.00 | 0.73 | 0.00 | 0.00 | 3.86 | 0.00 |
time (sec) |
N/A | 0.557 | 31.420 | 1.728 | 0.000 | 0.124 | 0.000 | 0.000 | 0.432 | 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 | 175 | 181 | 196 | 231 | 0 | 126 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.03 | 1.12 | 1.32 | 0.00 | 0.72 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.563 | 31.404 | 1.798 | 0.000 | 0.125 | 0.000 | 0.000 | 0.487 | 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 | 202 | 213 | 215 | 259 | 0 | 146 | 0 | 0 | 130 | 0 |
N.S. |
1 | 1.05 | 1.06 | 1.28 | 0.00 | 0.72 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.682 | 31.493 | 1.917 | 0.000 | 0.121 | 0.000 | 0.000 | 0.535 | 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 | 229 | 245 | 222 | 242 | 0 | 166 | 0 | 0 | 140 | 0 |
N.S. |
1 | 1.07 | 0.97 | 1.06 | 0.00 | 0.72 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.730 | 31.661 | 1.968 | 0.000 | 0.112 | 0.000 | 0.000 | 0.790 | 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 | 256 | 277 | 229 | 307 | 0 | 186 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.08 | 0.89 | 1.20 | 0.00 | 0.73 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.827 | 31.656 | 2.135 | 0.000 | 0.124 | 0.000 | 0.000 | 0.852 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 525 | 556 | 978 | 979 | 0 | 555 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.06 | 1.86 | 1.86 | 0.00 | 1.06 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.719 | 32.391 | 7.553 | 0.000 | 0.144 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 432 | 456 | 653 | 821 | 0 | 447 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.06 | 1.51 | 1.90 | 0.00 | 1.03 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.047 | 29.011 | 4.526 | 0.000 | 0.125 | 0.000 | 0.000 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 393 | 814 | 746 | 0 | 365 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.05 | 2.18 | 2.00 | 0.00 | 0.98 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.826 | 27.714 | 5.630 | 0.000 | 0.128 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 440 | 478 | 550 | 913 | 0 | 539 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.09 | 1.25 | 2.08 | 0.00 | 1.22 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.079 | 26.805 | 7.596 | 0.000 | 0.145 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 567 | 612 | 992 | 1109 | 0 | 1028 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.08 | 1.75 | 1.96 | 0.00 | 1.81 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.520 | 31.574 | 10.097 | 0.000 | 0.196 | 0.000 | 0.000 | 200.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 663 | 692 | 1287 | 1570 | 0 | 1325 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.04 | 1.94 | 2.37 | 0.00 | 2.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.953 | 34.214 | 12.181 | 0.000 | 0.184 | 0.000 | 0.000 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 515 | 552 | 932 | 1140 | 0 | 912 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.07 | 1.81 | 2.21 | 0.00 | 1.77 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.307 | 31.546 | 6.036 | 0.000 | 0.195 | 0.000 | 0.000 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 440 | 479 | 962 | 951 | 0 | 628 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.09 | 2.19 | 2.16 | 0.00 | 1.43 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.036 | 31.046 | 2.668 | 0.000 | 0.153 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 508 | 563 | 893 | 1277 | 0 | 956 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.11 | 1.76 | 2.51 | 0.00 | 1.88 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.251 | 30.845 | 7.891 | 0.000 | 0.171 | 0.000 | 0.000 | 200.046 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 680 | 738 | 1267 | 2169 | 0 | 2251 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.09 | 1.86 | 3.19 | 0.00 | 3.31 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.919 | 33.271 | 10.276 | 0.000 | 0.269 | 0.000 | 0.000 | 200.030 | 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 | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 380 | 454 | 291 | 0 | 0 | 0 | 0 | 0 | 1083 | 0 |
N.S. |
1 | 1.19 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.85 | 0.00 |
time (sec) |
N/A | 0.995 | 11.260 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.959 | 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 | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 335 | 190 | 0 | 0 | 0 | 0 | 0 | 524 | 0 |
N.S. |
1 | 1.46 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.28 | 0.00 |
time (sec) |
N/A | 0.665 | 10.326 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.151 | 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 | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 290 | 140 | 0 | 0 | 0 | 0 | 0 | 190 | 0 |
N.S. |
1 | 1.78 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.560 | 9.878 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.594 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 897 | 1074 | 686 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.20 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 3.517 | 13.320 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.035 | 0.000 |