[next] [prev] [prev-tail] [tail] [up]

Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 155, 162, 181, 188, 191, 192, 193, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224 }

B grade: { }

C grade: { }

F grade: { 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198}

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 10, 12, 15, 16, 17, 18, 19, 20, 21, 22, 24, 28, 29, 30, 35, 36, 37, 38, 39, 42, 43, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 64, 65, 66, 67, 68, 69, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 153, 155, 157, 158, 165, 167, 169, 170, 171, 172, 173, 181, 184, 185, 186, 187, 189, 190, 191, 193, 194, 195, 196, 198, 199, 200, 201, 202, 205, 206, 208, 211, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224 }

B grade: { 151, 166, 168, 174, 175, 176, 177, 178, 179, 180, 182, 183, 197, 207, 209, 210 }

C grade: { 6, 7, 8, 9, 11, 13, 14, 23, 25, 26, 27, 31, 32, 33, 34, 40, 41, 44, 46, 47, 48, 49, 61, 62, 63, 70, 71, 72, 73, 74, 75, 76, 87, 113, 132, 133, 134, 135, 136, 137, 138, 139, 152, 154, 156, 159, 160, 161, 162, 163, 164, 188, 192, 203, 204, 212 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 20, 21, 29, 30, 31, 32, 40, 41, 42, 43, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 81, 82, 83, 84, 85, 86, 87, 88, 93, 94, 98, 100, 101, 102, 109, 115, 116, 117, 118, 119, 122, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 164, 191, 192, 193, 199, 200, 201, 202, 203, 204, 205, 206, 207, 211, 212, 217, 218, 219, 220, 221, 222, 223, 224 }

B grade: { 33, 34, 35, 36, 37, 38, 77, 78, 79, 80, 89, 90, 91, 92, 95, 96, 97, 99, 103, 104, 105, 106, 107, 108, 110, 111, 112, 114, 120, 121, 123, 124, 125, 126, 140, 141, 152, 154, 155, 156, 162, 181, 188, 213 }

C grade: { 163, 210, 214, 215, 216 }

F grade: { 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 39, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 113, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198, 208, 209 }

2.1.4 Maxima

A grade: { 18, 19, 20, 21, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 64, 65, 66, 67, 68, 69, 80, 81, 82, 85, 86, 89, 90, 91, 92, 93, 94, 97, 99, 102, 105, 106, 107, 108, 109, 110, 114, 116, 119, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 181, 188, 211, 212, 213, 214, 215, 216, 220, 224

B grade: { 61, 62, 63, 77, 78, 79, 83, 84, 95, 96, 104, 111, 112, 191, 192, 193 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 39, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 70, 71, 72, 73, 74, 75, 76, 87, 88, 98, 100, 101, 103, 113, 115, 117, 118, 120, 132, 133, 134, 135, 136, 137, 138, 139, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 217, 218, 219, 221, 222, 223 }

2.1.5 FriCAS

A grade: { 9, 10, 46, 81, 85, 86, 91, 92, 93, 101, 107, 108, 118, 122, 143, 144, 145, 146, 151, 152, 153, 155, 156, 158, 163, 164, 213, 214, 218, 220, 222, 224 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 87, 88, 89, 90, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 147, 148, 149, 150, 154, 157, 159, 160, 161, 162, 181, 188, 191, 192, 193, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 217, 219, 221, 223 }

C grade: { }

F grade: { 15, 16, 17, 27, 28, 39, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198 }

2.1.6 Sympy

A grade: { 61, 62, 63, 64, 77, 78, 79, 80, 81, 85, 86, 144, 145, 146, 147, 148, 149, 162, 220, 224 }

B grade: { 65, 66, 67, 68, 69, 127, 128, 129, 130, 131, 155 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 70, 71, 72, 73, 74, 75, 76, 82, 83, 84, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223 }

2.1.7 Giac

A grade: { 18, 19, 21, 40, 41, 42, 43, 61, 62, 63, 64, 65, 66, 67, 68, 69, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 103, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 188, 192, 211, 212, 213, 214, 215, 216, 220, 224 }

B grade: { 6, 11, 12, 20, 70, 71, 72, 73, 74, 75, 76, 95, 102, 104, 113, 119, 121, 132, 133, 134, 135, 136, 137, 138, 139, 150, 181, 191, 193 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 87, 88, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 189, 190, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 217, 218, 219, 221, 222, 223 }

2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 83 80 0 4135 0 0
normalized size 1 1. 0.86 0.82 0. 42.63 0. 0.
time (sec) N/A 0.07 0.232 0.026 0. 2.507 0. 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 68 63 0 2654 0 0
normalized size 1 1. 0.87 0.81 0. 34.03 0. 0.
time (sec) N/A 0.049 0.213 0.01 0. 2.388 0. 0.
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 61 62 0 1754 0 0
normalized size 1 1. 0.81 0.83 0. 23.39 0. 0.
time (sec) N/A 0.05 0.095 0.011 0. 2.272 0. 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 51 47 0 1636 0 0
normalized size 1 1. 0.88 0.81 0. 28.21 0. 0.
time (sec) N/A 0.036 0.042 0.023 0. 2.214 0. 0.
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 49 46 0 1646 0 0
normalized size 1 1. 0.86 0.81 0. 28.88 0. 0.
time (sec) N/A 0.031 0.034 0.033 0. 2.433 0. 0.
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 36 65 0 2576 0 277
normalized size 1 1. 0.46 0.83 0. 33.03 0. 3.55
time (sec) N/A 0.051 0.074 0.013 0. 2.716 0. 1.335
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 38 64 0 3933 0 0
normalized size 1 1. 0.48 0.81 0. 49.78 0. 0.
time (sec) N/A 0.05 0.065 0.011 0. 2.854 0. 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 38 83 0 5797 0 0
normalized size 1 1. 0.38 0.83 0. 57.97 0. 0.
time (sec) N/A 0.071 0.096 0.013 0. 2.599 0. 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 236 236 36 209 0 865 0 0
normalized size 1 1. 0.15 0.89 0. 3.67 0. 0.
time (sec) N/A 0.282 0.026 0.02 0. 1.961 0. 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 218 218 149 193 0 871 0 0
normalized size 1 1. 0.68 0.89 0. 4. 0. 0.
time (sec) N/A 0.294 0.177 0.016 0. 2.047 0. 0.
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 38 115 0 828 0 293
normalized size 1 1. 0.29 0.87 0. 6.27 0. 2.22
time (sec) N/A 0.109 0.041 0.015 0. 2.001 0. 1.687
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 98 115 0 4398 0 292
normalized size 1 1. 0.74 0.87 0. 33.32 0. 2.21
time (sec) N/A 0.104 0.121 0.012 0. 2.23 0. 1.642
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 218 218 36 193 0 991 0 0
normalized size 1 1. 0.17 0.89 0. 4.55 0. 0.
time (sec) N/A 0.235 0.029 0.017 0. 2.01 0. 0.
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 238 238 36 211 0 9677 0 0
normalized size 1 1. 0.15 0.89 0. 40.66 0. 0.
time (sec) N/A 0.316 0.062 0.016 0. 2.449 0. 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 45 0 0 0 0 0
normalized size 1 1. 1.05 0. 0. 0. 0. 0.
time (sec) N/A 0.022 0.063 0.165 0. 0. 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 51 0 0 0 0 0
normalized size 1 1. 1.06 0. 0. 0. 0. 0.
time (sec) N/A 0.027 0.041 0.191 0. 0. 0. 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 47 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.04 0.048 0.247 0. 0. 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 56 53 131 2068 0 122
normalized size 1 1. 0.92 0.87 2.15 33.9 0. 2.
time (sec) N/A 0.037 0.118 0.026 1.604 1.981 0. 1.203
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 39 45 73 304 0 73
normalized size 1 1. 1.26 1.45 2.35 9.81 0. 2.35
time (sec) N/A 0.02 0.045 0.036 1.59 1.934 0. 1.159
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 52 46 309 0 81
normalized size 1 1. 1. 1.68 1.48 9.97 0. 2.61
time (sec) N/A 0.02 0.059 0.04 1.624 1.92 0. 1.2
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 48 79 113 2082 0 149
normalized size 1 1. 0.74 1.22 1.74 32.03 0. 2.29
time (sec) N/A 0.036 0.143 0.02 1.589 1.963 0. 1.242
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 297 297 166 0 0 5673 0 0
normalized size 1 1. 0.56 0. 0. 19.1 0. 0.
time (sec) N/A 0.284 0.338 0.082 0. 2.207 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 289 289 43 0 0 5751 0 0
normalized size 1 1. 0.15 0. 0. 19.9 0. 0.
time (sec) N/A 0.18 0.039 0.079 0. 2.145 0. 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 264 264 151 0 0 4625 0 0
normalized size 1 1. 0.57 0. 0. 17.52 0. 0.
time (sec) N/A 0.212 0.101 0.106 0. 2.082 0. 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 264 264 41 0 0 23547 0 0
normalized size 1 1. 0.16 0. 0. 89.19 0. 0.
time (sec) N/A 0.169 0.054 0.105 0. 3.482 0. 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 289 289 41 0 0 5739 0 0
normalized size 1 1. 0.14 0. 0. 19.86 0. 0.
time (sec) N/A 0.222 0.063 0.079 0. 2.328 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 309 309 43 0 0 0 0 0
normalized size 1 1. 0.14 0. 0. 0. 0. 0.
time (sec) N/A 0.182 0.154 0.079 0. 0. 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 53 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.039 0.041 0.24 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 82 107 0 5846 0 0
normalized size 1 1. 0.61 0.8 0. 43.63 0. 0.
time (sec) N/A 0.06 0.519 0.04 0. 3.087 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 63 86 0 1743 0 0
normalized size 1 1. 0.61 0.83 0. 16.76 0. 0.
time (sec) N/A 0.047 0.096 0.045 0. 2.188 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 41 91 0 2554 0 0
normalized size 1 1. 0.39 0.87 0. 24.32 0. 0.
time (sec) N/A 0.048 0.029 0.041 0. 2.383 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 43 106 0 8204 0 0
normalized size 1 1. 0.3 0.75 0. 58.18 0. 0.
time (sec) N/A 0.061 0.065 0.024 0. 2.947 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 43 145 117 2689 0 0
normalized size 1 1. 0.58 1.96 1.58 36.34 0. 0.
time (sec) N/A 0.034 0.061 0.098 1.757 2.272 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 41 119 46 992 0 0
normalized size 1 1. 0.82 2.38 0.92 19.84 0. 0.
time (sec) N/A 0.024 0.028 0.097 1.617 2.189 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 39 192 69 363 0 0
normalized size 1 1. 1.26 6.19 2.23 11.71 0. 0.
time (sec) N/A 0.02 0.026 0.092 1.741 2.134 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 192 43 460 0 0
normalized size 1 1. 1. 6.19 1.39 14.84 0. 0.
time (sec) N/A 0.02 0.028 0.093 1.711 2.444 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 40 119 50 724 0 0
normalized size 1 1. 0.8 2.38 1. 14.48 0. 0.
time (sec) N/A 0.024 0.06 0.093 1.75 2.237 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 51 149 120 4035 0 0
normalized size 1 1. 0.64 1.86 1.5 50.44 0. 0.
time (sec) N/A 0.035 0.088 0.099 1.77 2.372 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 51 0 0 0 0 0
normalized size 1 1. 0.89 0. 0. 0. 0. 0.
time (sec) N/A 0.039 0.044 0.264 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 43 77 185 9090 0 108
normalized size 1 1. 0.39 0.7 1.68 82.64 0. 0.98
time (sec) N/A 0.045 0.063 0.036 1.735 2.65 0. 1.183
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 41 55 46 1046 0 43
normalized size 1 1. 0.82 1.1 0.92 20.92 0. 0.86
time (sec) N/A 0.023 0.031 0.041 1.82 2.158 0. 1.145
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 40 59 49 1079 0 46
normalized size 1 1. 0.8 1.18 0.98 21.58 0. 0.92
time (sec) N/A 0.023 0.073 0.037 1.736 2.193 0. 1.169
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 68 84 209 9179 0 138
normalized size 1 1. 0.58 0.71 1.77 77.79 0. 1.17
time (sec) N/A 0.046 0.233 0.022 1.801 2.677 0. 1.251
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 353 353 68 0 0 7973 0 0
normalized size 1 1. 0.19 0. 0. 22.59 0. 0.
time (sec) N/A 0.196 0.139 0.099 0. 2.938 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 291 291 166 0 0 1783 0 0
normalized size 1 1. 0.57 0. 0. 6.13 0. 0.
time (sec) N/A 0.215 0.409 0.094 0. 2.264 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 289 289 43 0 0 855 0 0
normalized size 1 1. 0.15 0. 0. 2.96 0. 0.
time (sec) N/A 0.176 0.036 0.099 0. 2.267 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 289 289 41 0 0 9634 0 0
normalized size 1 1. 0.14 0. 0. 33.34 0. 0.
time (sec) N/A 0.218 0.053 0.093 0. 2.911 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 291 291 43 0 0 3221 0 0
normalized size 1 1. 0.15 0. 0. 11.07 0. 0.
time (sec) N/A 0.185 0.051 0.094 0. 2.487 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 369 369 43 0 0 0 0 0
normalized size 1 1. 0.12 0. 0. 0. 0. 0.
time (sec) N/A 0.245 0.042 0.101 0. 0. 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 55 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.042 0.048 2.588 0. 0. 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 58 0 0 0 0 0
normalized size 1 1. 0.92 0. 0. 0. 0. 0.
time (sec) N/A 0.045 0.075 0.341 0. 0. 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 54 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.041 0.04 0.186 0. 0. 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 58 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.047 0.047 0.195 0. 0. 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 58 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.048 0.066 0.168 0. 0. 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 60 0 0 0 0 0
normalized size 1 1. 0.92 0. 0. 0. 0. 0.
time (sec) N/A 0.045 0.07 0.112 0. 0. 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 60 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.043 0.042 0.113 0. 0. 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 54 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.044 0.039 0.114 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 58 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.043 0.039 0.112 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 60 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.045 0.04 0.142 0. 0. 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 60 0 0 0 0 0
normalized size 1 1. 0.87 0. 0. 0. 0. 0.
time (sec) N/A 0.047 0.066 0.112 0. 0. 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 94 31 189 1481 48 55
normalized size 1 1. 2.29 0.76 4.61 36.12 1.17 1.34
time (sec) N/A 0.039 0.238 0.007 1.061 2.049 2.589 1.183
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 84 25 128 915 37 47
normalized size 1 1. 2.71 0.81 4.13 29.52 1.19 1.52
time (sec) N/A 0.031 0.18 0.004 1.101 2.069 1.884 1.195
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 61 19 74 479 31 39
normalized size 1 1. 2.65 0.83 3.22 20.83 1.35 1.7
time (sec) N/A 0.021 0.149 0.002 1.04 2.039 1.18 1.17
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 13 26 189 22 28
normalized size 1 1. 1. 1. 2. 14.54 1.69 2.15
time (sec) N/A 0.013 0.004 0.003 1.13 1.957 0.746 1.187
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 18 24 14 88 27 14
normalized size 1 1. 1.12 1.5 0.88 5.5 1.69 0.88
time (sec) N/A 0.009 0.031 0.016 1.014 2.012 0.577 1.147
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 30 32 22 173 88 24
normalized size 1 1. 1.15 1.23 0.85 6.65 3.38 0.92
time (sec) N/A 0.017 0.058 0.017 1.029 2.395 0.99 1.156
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 44 40 30 278 182 32
normalized size 1 1. 1.22 1.11 0.83 7.72 5.06 0.89
time (sec) N/A 0.027 0.087 0.017 1.05 2.269 1.472 1.148
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 53 48 38 394 299 41
normalized size 1 1. 1.15 1.04 0.83 8.57 6.5 0.89
time (sec) N/A 0.036 0.121 0.017 1.179 2.377 2.555 1.152
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 62 56 46 540 444 49
normalized size 1 1. 1.11 1. 0.82 9.64 7.93 0.88
time (sec) N/A 0.046 0.138 0.024 1.038 2.272 3.234 1.142
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 101 43 0 1469 0 216
normalized size 1 1. 1.77 0.75 0. 25.77 0. 3.79
time (sec) N/A 0.042 0.259 0.016 0. 2.418 0. 1.17
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 92 35 0 869 0 151
normalized size 1 1. 2.04 0.78 0. 19.31 0. 3.36
time (sec) N/A 0.032 0.153 0.013 0. 2.39 0. 1.174
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 69 27 0 450 0 85
normalized size 1 1. 2.09 0.82 0. 13.64 0. 2.58
time (sec) N/A 0.022 0.106 0.013 0. 2.487 0. 1.164
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 45 17 0 181 0 50
normalized size 1 1. 2.14 0.81 0. 8.62 0. 2.38
time (sec) N/A 0.012 0.074 0.036 0. 2.316 0. 1.177
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 51 27 0 300 0 89
normalized size 1 1. 1.59 0.84 0. 9.38 0. 2.78
time (sec) N/A 0.023 0.292 0.036 0. 2.361 0. 1.154
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 86 35 0 578 0 177
normalized size 1 1. 1.76 0.71 0. 11.8 0. 3.61
time (sec) N/A 0.031 0.308 0.011 0. 2.367 0. 1.191
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 94 43 0 919 0 242
normalized size 1 1. 1.54 0.7 0. 15.07 0. 3.97
time (sec) N/A 0.042 0.758 0.013 0. 2.456 0. 1.223
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 141 322 470 6413 325 308
normalized size 1 1. 0.99 2.27 3.31 45.16 2.29 2.17
time (sec) N/A 0.209 0.799 0.006 1.081 2.763 22.938 1.155
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 109 246 296 3318 233 211
normalized size 1 1. 1.08 2.44 2.93 32.85 2.31 2.09
time (sec) N/A 0.123 0.905 0.004 1.114 2.535 10.181 1.137
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 86 173 184 1563 175 140
normalized size 1 1. 1.25 2.51 2.67 22.65 2.54 2.03
time (sec) N/A 0.064 0.402 0.004 1.111 2.644 4.431 1.143
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 65 116 66 535 104 84
normalized size 1 1. 1.71 3.05 1.74 14.08 2.74 2.21
time (sec) N/A 0.024 0.128 0.005 1.013 2.854 1.866 1.124
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 64 76 70 149 236 85
normalized size 1 1. 1.28 1.52 1.4 2.98 4.72 1.7
time (sec) N/A 0.054 0.079 0.019 1.122 2.886 3.149 1.143
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 100 101 167 980 0 185
normalized size 1 1. 1.18 1.19 1.96 11.53 0. 2.18
time (sec) N/A 0.095 1.42 0.025 1.165 2.676 0. 1.155
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 129 129 134 166 435 3182 0 285
normalized size 1 1. 1.04 1.29 3.37 24.67 0. 2.21
time (sec) N/A 0.18 3.432 0.031 1.184 3.204 0. 1.18
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 169 169 214 230 705 8128 0 424
normalized size 1 1. 1.27 1.36 4.17 48.09 0. 2.51
time (sec) N/A 0.264 6.208 0.034 1.345 3.468 0. 1.216
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 53 46 38 130 42 41
normalized size 1 1. 1.71 1.48 1.23 4.19 1.35 1.32
time (sec) N/A 0.044 0.039 0.017 1.101 2.554 1.362 1.179
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 53 46 39 126 42 38
normalized size 1 1. 1.71 1.48 1.26 4.06 1.35 1.23
time (sec) N/A 0.042 0.037 0.016 1.058 2.498 1.183 1.192
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 128 63 0 5682 0 0
normalized size 1 1. 1.73 0.85 0. 76.78 0. 0.
time (sec) N/A 0.07 3.216 0.053 0. 3.212 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 73 62 0 5844 0 0
normalized size 1 1. 0.99 0.84 0. 78.97 0. 0.
time (sec) N/A 0.068 0.142 0.046 0. 3.265 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 42 110 49 321 0 57
normalized size 1 1. 0.7 1.83 0.82 5.35 0. 0.95
time (sec) N/A 0.063 0.103 0.033 1.069 2.543 0. 1.199
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 36 80 45 221 0 42
normalized size 1 1. 1.24 2.76 1.55 7.62 0. 1.45
time (sec) N/A 0.047 0.076 0.03 1.059 2.402 0. 1.154
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 30 70 30 176 0 41
normalized size 1 1. 0.79 1.84 0.79 4.63 0. 1.08
time (sec) N/A 0.052 0.052 0.03 1.083 2.454 0. 1.128
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 21 40 23 99 0 26
normalized size 1 1. 1.11 2.11 1.21 5.21 0. 1.37
time (sec) N/A 0.036 0.048 0.027 1.102 2.478 0. 1.125
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 7 11 8 32 0 8
normalized size 1 1. 0.7 1.1 0.8 3.2 0. 0.8
time (sec) N/A 0.022 0.003 0.001 1.063 2.515 0. 1.153
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 7 7 7 8 9 58 0 16
normalized size 1 1. 1. 1.14 1.29 8.29 0. 2.29
time (sec) N/A 0.036 0.003 0.017 1.051 2.592 0. 1.158
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 8 8 14 23 42 306 0 35
normalized size 1 1. 1.75 2.88 5.25 38.25 0. 4.38
time (sec) N/A 0.04 0.037 0.019 1.088 2.592 0. 1.144
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 32 55 181 0 14
normalized size 1 1. 1. 2.91 5. 16.45 0. 1.27
time (sec) N/A 0.034 0.025 0.023 1.102 2.372 0. 1.151
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 156 354 224 2882 0 309
normalized size 1 1. 1.01 2.28 1.45 18.59 0. 1.99
time (sec) N/A 0.24 0.266 0.049 1.108 2.847 0. 1.175
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 171 197 0 4251 0 220
normalized size 1 1. 1.28 1.47 0. 31.72 0. 1.64
time (sec) N/A 0.237 0.788 0.044 0. 2.964 0. 1.135
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 75 175 112 818 0 154
normalized size 1 1. 0.82 1.9 1.22 8.89 0. 1.67
time (sec) N/A 0.142 0.152 0.039 1.177 2.695 0. 1.173
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 80 93 0 1103 0 97
normalized size 1 1. 1.1 1.27 0. 15.11 0. 1.33
time (sec) N/A 0.107 0.436 0.032 0. 2.66 0. 1.154
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 46 39 0 420 0 47
normalized size 1 1. 1.21 1.03 0. 11.05 0. 1.24
time (sec) N/A 0.036 0.031 0.017 0. 2.652 0. 1.18
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 20 13 16 127 0 62
normalized size 1 1. 1.67 1.08 1.33 10.58 0. 5.17
time (sec) N/A 0.044 0.05 0.019 1.175 2.702 0. 1.19
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 65 115 0 1230 0 115
normalized size 1 1. 1.14 2.02 0. 21.58 0. 2.02
time (sec) N/A 0.109 0.105 0.028 0. 2.926 0. 1.149
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 50 116 149 1087 0 143
normalized size 1 1. 1.25 2.9 3.72 27.18 0. 3.58
time (sec) N/A 0.067 0.137 0.031 1.033 2.723 0. 1.176
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 42 118 49 319 0 57
normalized size 1 1. 0.7 1.97 0.82 5.32 0. 0.95
time (sec) N/A 0.067 0.088 0.032 0.998 2.506 0. 1.177
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 34 82 36 200 0 34
normalized size 1 1. 1.36 3.28 1.44 8. 0. 1.36
time (sec) N/A 0.177 0.058 0.028 1.031 2.536 0. 1.187
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 24 78 30 176 0 41
normalized size 1 1. 0.63 2.05 0.79 4.63 0. 1.08
time (sec) N/A 0.059 0.047 0.029 1.03 2.536 0. 1.113
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 19 42 15 90 0 15
normalized size 1 1. 1.12 2.47 0.88 5.29 0. 0.88
time (sec) N/A 0.113 0.017 0.024 1.015 2.486 0. 1.13
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 16 19 16 101 0 14
normalized size 1 1. 1.6 1.9 1.6 10.1 0. 1.4
time (sec) N/A 0.114 0.023 0.023 1.534 2.58 0. 1.163
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 9 36 24 269 0 36
normalized size 1 1. 0.6 2.4 1.6 17.93 0. 2.4
time (sec) N/A 0.041 0.03 0.028 1.564 2.698 0. 1.188
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 20 45 45 508 0 34
normalized size 1 1. 1. 2.25 2.25 25.4 0. 1.7
time (sec) N/A 0.167 0.039 0.029 1.523 2.507 0. 1.149
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 38 101 286 0 24
normalized size 1 1. 1. 2.24 5.94 16.82 0. 1.41
time (sec) N/A 0.045 0.05 0.029 1.035 2.523 0. 1.144
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 160 0 0 813 0 201
normalized size 1 1. 7.62 0. 0. 38.71 0. 9.57
time (sec) N/A 0.046 5.006 0.177 0. 2.552 0. 1.162
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 144 319 208 2747 0 292
normalized size 1 1. 0.98 2.17 1.41 18.69 0. 1.99
time (sec) N/A 0.339 0.522 0.047 1.199 2.856 0. 1.16
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 167 200 0 4208 0 221
normalized size 1 1. 1.24 1.48 0. 31.17 0. 1.64
time (sec) N/A 0.251 1.403 0.041 0. 3.019 0. 1.164
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 73 146 108 826 0 140
normalized size 1 1. 0.86 1.72 1.27 9.72 0. 1.65
time (sec) N/A 0.164 0.229 0.041 1.156 2.651 0. 1.149
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 79 92 0 1106 0 96
normalized size 1 1. 1.1 1.28 0. 15.36 0. 1.33
time (sec) N/A 0.112 0.301 0.033 0. 2.871 0. 1.13
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 60 54 0 564 0 65
normalized size 1 1. 1.2 1.08 0. 11.28 0. 1.3
time (sec) N/A 0.138 0.113 0.033 0. 2.863 0. 1.145
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 27 59 62 362 0 103
normalized size 1 1. 0.93 2.03 2.14 12.48 0. 3.55
time (sec) N/A 0.055 0.081 0.04 1.766 2.617 0. 1.147
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 85 187 0 2423 0 138
normalized size 1 1. 1.02 2.25 0. 29.19 0. 1.66
time (sec) N/A 0.237 0.182 0.047 0. 3.13 0. 1.154
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 68 257 180 2187 0 271
normalized size 1 1. 0.86 3.25 2.28 27.68 0. 3.43
time (sec) N/A 0.1 0.258 0.053 1.705 2.768 0. 1.148
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 38 41 57 169 0 35
normalized size 1 1. 1.23 1.32 1.84 5.45 0. 1.13
time (sec) N/A 0.103 0.051 0.052 1.708 2.796 0. 1.134
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 40 96 74 1897 0 63
normalized size 1 1. 0.93 2.23 1.72 44.12 0. 1.47
time (sec) N/A 0.115 0.096 0.043 1.701 2.654 0. 1.11
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 33 80 58 1168 0 53
normalized size 1 1. 0.89 2.16 1.57 31.57 0. 1.43
time (sec) N/A 0.099 0.053 0.037 1.54 2.648 0. 1.117
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 27 65 39 632 0 47
normalized size 1 1. 0.93 2.24 1.34 21.79 0. 1.62
time (sec) N/A 0.074 0.046 0.035 1.675 2.697 0. 1.145
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 23 47 23 259 0 23
normalized size 1 1. 1.21 2.47 1.21 13.63 0. 1.21
time (sec) N/A 0.042 0.028 0.029 1.672 2.959 0. 1.158
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 18 24 14 88 27 14
normalized size 1 1. 1.12 1.5 0.88 5.5 1.69 0.88
time (sec) N/A 0.008 0.025 0. 1.126 2.769 0.614 1.14
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 18 24 14 88 27 14
normalized size 1 1. 1.12 1.5 0.88 5.5 1.69 0.88
time (sec) N/A 0.022 0.015 0.018 1.136 2.805 0.597 1.112
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 23 24 32 259 92 24
normalized size 1 1. 1.21 1.26 1.68 13.63 4.84 1.26
time (sec) N/A 0.038 0.029 0.017 1.109 3.092 0.906 1.124
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 27 28 51 632 162 49
normalized size 1 1. 0.87 0.9 1.65 20.39 5.23 1.58
time (sec) N/A 0.055 0.041 0.017 1.093 3.02 1.381 1.133
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 33 32 73 1168 197 54
normalized size 1 1. 0.89 0.86 1.97 31.57 5.32 1.46
time (sec) N/A 0.068 0.058 0.02 1.112 3.043 1.859 1.114
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 90 35 0 869 0 182
normalized size 1 1. 2. 0.78 0. 19.31 0. 4.04
time (sec) N/A 0.052 0.136 0.014 0. 3.052 0. 1.185
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 53 26 0 455 0 96
normalized size 1 1. 1.66 0.81 0. 14.22 0. 3.
time (sec) N/A 0.038 0.119 0.036 0. 2.891 0. 1.166
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 97 25 0 300 0 119
normalized size 1 1. 3.23 0.83 0. 10. 0. 3.97
time (sec) N/A 0.039 0.195 0.039 0. 2.99 0. 1.162
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 84 35 0 578 0 144
normalized size 1 1. 1.71 0.71 0. 11.8 0. 2.94
time (sec) N/A 0.051 0.332 0.013 0. 2.957 0. 1.184
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 70 35 0 1449 0 266
normalized size 1 1. 1.56 0.78 0. 32.2 0. 5.91
time (sec) N/A 0.063 0.254 0.019 0. 2.953 0. 1.2
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 61 26 0 817 0 180
normalized size 1 1. 1.79 0.76 0. 24.03 0. 5.29
time (sec) N/A 0.048 0.169 0.039 0. 3.169 0. 1.181
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 81 35 0 637 0 119
normalized size 1 1. 1.93 0.83 0. 15.17 0. 2.83
time (sec) N/A 0.059 0.359 0.041 0. 3.119 0. 1.206
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 86 35 0 578 0 182
normalized size 1 1. 1.76 0.71 0. 11.8 0. 3.71
time (sec) N/A 0.082 0.349 0.017 0. 2.929 0. 1.209
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 105 283 197 3087 0 190
normalized size 1 1. 1.08 2.92 2.03 31.82 0. 1.96
time (sec) N/A 0.525 0.328 0.056 1.752 3.182 0. 1.131
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 88 167 127 1539 0 131
normalized size 1 1. 1.16 2.2 1.67 20.25 0. 1.72
time (sec) N/A 0.326 0.303 0.053 1.733 3.245 0. 1.176
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 64 110 90 660 0 100
normalized size 1 1. 1.07 1.83 1.5 11. 0. 1.67
time (sec) N/A 0.193 0.132 0.046 1.785 2.986 0. 1.134
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 46 88 68 185 0 77
normalized size 1 1. 0.9 1.73 1.33 3.63 0. 1.51
time (sec) N/A 0.082 0.076 0.039 1.742 2.817 0. 1.199
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 29 55 50 108 148 58
normalized size 1 1. 0.74 1.41 1.28 2.77 3.79 1.49
time (sec) N/A 0.046 0.053 0.013 1.269 2.539 1.227 1.13
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 29 55 49 109 134 58
normalized size 1 1. 0.74 1.41 1.26 2.79 3.44 1.49
time (sec) N/A 0.058 0.045 0.017 1.238 2.573 1.342 1.127
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 49 60 85 186 372 80
normalized size 1 1. 0.78 0.95 1.35 2.95 5.9 1.27
time (sec) N/A 0.092 0.076 0.019 1.276 2.803 2.94 1.148
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 64 67 111 660 639 103
normalized size 1 1. 1. 1.05 1.73 10.31 9.98 1.61
time (sec) N/A 0.13 0.12 0.022 1.171 2.83 5.45 1.115
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 88 76 161 1538 882 135
normalized size 1 1. 1.16 1. 2.12 20.24 11.61 1.78
time (sec) N/A 0.221 0.201 0.021 1.195 2.93 7.993 1.179
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 108 96 228 3089 1013 193
normalized size 1 1. 1.15 1.02 2.43 32.86 10.78 2.05
time (sec) N/A 0.392 0.287 0.023 1.264 3.096 13.074 1.176
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 49 73 92 491 0 228
normalized size 1 1. 0.91 1.35 1.7 9.09 0. 4.22
time (sec) N/A 0.085 0.159 0.112 1.952 2.684 0. 1.174
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B A A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 30 0 64 24 49 72 0 32
normalized size 1 0. 2.13 0.8 1.63 2.4 0. 1.07
time (sec) N/A 0.029 0.024 0.026 1.215 2.535 0. 1.143
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C B A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 45 0 64 83 65 171 0 73
normalized size 1 0. 1.42 1.84 1.44 3.8 0. 1.62
time (sec) N/A 0.021 0.232 0.048 1.757 2.685 0. 1.141
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A A A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 23 0 26 37 49 81 0 50
normalized size 1 0. 1.13 1.61 2.13 3.52 0. 2.17
time (sec) N/A 0.016 0.182 0.024 1.044 2.594 0. 1.117
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C B A B F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 40 0 58 71 61 159 0 69
normalized size 1 0. 1.45 1.78 1.52 3.98 0. 1.72
time (sec) N/A 0.007 0.179 0.045 1.609 2.582 0. 1.121
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 21 26 14 47 27 28
normalized size 1 1. 1.75 2.17 1.17 3.92 2.25 2.33
time (sec) N/A 0.014 0.027 0.003 1.051 2.535 1.689 1.095
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C B A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 41 0 62 93 63 149 0 70
normalized size 1 0. 1.51 2.27 1.54 3.63 0. 1.71
time (sec) N/A 0.022 0.162 0.042 1.733 2.656 0. 1.158
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A A A B F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 21 0 27 35 41 92 0 45
normalized size 1 0. 1.29 1.67 1.95 4.38 0. 2.14
time (sec) N/A 0.021 0.156 0.026 1.03 2.584 0. 1.108
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A A A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 47 0 86 41 72 140 0 54
normalized size 1 0. 1.83 0.87 1.53 2.98 0. 1.15
time (sec) N/A 0.066 0.103 0.018 1.051 2.468 0. 1.122
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C A A B F A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 68 0 154 100 89 266 0 97
normalized size 1 0. 2.26 1.47 1.31 3.91 0. 1.43
time (sec) N/A 0.048 2.899 0.046 1.624 2.596 0. 1.144
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C A A B F A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 41 0 163 54 72 169 0 73
normalized size 1 0. 3.98 1.32 1.76 4.12 0. 1.78
time (sec) N/A 0.03 2.933 0.02 1.061 2.572 0. 1.111
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C A A B F A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 60 0 153 86 81 246 0 89
normalized size 1 0. 2.55 1.43 1.35 4.1 0. 1.48
time (sec) N/A 0.01 1.951 0.043 1.57 2.641 0. 1.119
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 28 35 26 68 32 28
normalized size 1 1. 2. 2.5 1.86 4.86 2.29 2.
time (sec) N/A 0.024 0.054 0.003 1.032 2.521 17.227 1.116
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C C A A F A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 86 0 153 101 93 236 0 104
normalized size 1 0. 1.78 1.17 1.08 2.74 0. 1.21
time (sec) N/A 0.045 3.127 0.033 1.564 2.604 0. 1.121
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C A A A F A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 60 0 155 55 68 178 0 77
normalized size 1 0. 2.58 0.92 1.13 2.97 0. 1.28
time (sec) N/A 0.046 2.863 0.023 1.078 2.581 0. 1.152
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 59 0 46 0 0 0 0 0
normalized size 1 0. 0.78 0. 0. 0. 0. 0.
time (sec) N/A 0.039 0.093 0.038 0. 0. 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F(-1) F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 79 0 165 0 0 0 0 0
normalized size 1 0. 2.09 0. 0. 0. 0. 0.
time (sec) N/A 0.068 0.369 0.027 0. 0. 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 177 0 215 0 0 0 0 0
normalized size 1 0. 1.21 0. 0. 0. 0. 0.
time (sec) N/A 0.073 0.825 0.037 0. 0. 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 79 0 259 0 0 0 0 0
normalized size 1 0. 3.28 0. 0. 0. 0. 0.
time (sec) N/A 0.022 1.889 0.106 0. 0. 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 99 0 126 0 0 0 0 0
normalized size 1 0. 1.27 0. 0. 0. 0. 0.
time (sec) N/A 0.116 2.977 0.03 0. 0. 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 52 0 83 0 0 0 0 0
normalized size 1 0. 1.6 0. 0. 0. 0. 0.
time (sec) N/A 0.046 0.391 0.036 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 108 0 125 0 0 0 0 0
normalized size 1 0. 1.16 0. 0. 0. 0. 0.
time (sec) N/A 0.051 0.527 0.027 0. 0. 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 162 0 142 0 0 0 0 0
normalized size 1 0. 0.88 0. 0. 0. 0. 0.
time (sec) N/A 0.05 0.561 0.027 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 194 0 223 0 0 0 0 0
normalized size 1 0. 1.15 0. 0. 0. 0. 0.
time (sec) N/A 0.051 0.907 0.024 0. 0. 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 61 0 171 0 0 0 0 0
normalized size 1 0. 2.8 0. 0. 0. 0. 0.
time (sec) N/A 0.015 1.548 0.05 0. 0. 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 61 0 171 0 0 0 0 0
normalized size 1 0. 2.8 0. 0. 0. 0. 0.
time (sec) N/A 0.011 1.734 0.052 0. 0. 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 61 0 171 0 0 0 0 0
normalized size 1 0. 2.8 0. 0. 0. 0. 0.
time (sec) N/A 0.018 1.814 0.05 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 58 0 198 0 0 0 0 0
normalized size 1 0. 3.41 0. 0. 0. 0. 0.
time (sec) N/A 0.039 7.015 1.095 0. 0. 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 62 0 207 0 0 0 0 0
normalized size 1 0. 3.34 0. 0. 0. 0. 0.
time (sec) N/A 0.03 4.896 1.046 0. 0. 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 54 0 193 0 0 0 0 0
normalized size 1 0. 3.57 0. 0. 0. 0. 0.
time (sec) N/A 0.024 6.939 1. 0. 0. 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 52 0 198 0 0 0 0 0
normalized size 1 0. 3.81 0. 0. 0. 0. 0.
time (sec) N/A 0.011 8.329 0.915 0. 0. 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 40 56 32 205 0 99
normalized size 1 1. 1.6 2.24 1.28 8.2 0. 3.96
time (sec) N/A 0.021 0.057 0.004 1.158 2.914 0. 1.241
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 58 0 197 0 0 0 0 0
normalized size 1 0. 3.4 0. 0. 0. 0. 0.
time (sec) N/A 0.031 3.83 1.026 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 55 0 191 0 0 0 0 0
normalized size 1 0. 3.47 0. 0. 0. 0. 0.
time (sec) N/A 0.03 3.678 1.026 0. 0. 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 132 0 155 0 0 0 0 0
normalized size 1 0. 1.17 0. 0. 0. 0. 0.
time (sec) N/A 0.086 6.606 0.365 0. 0. 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 136 0 165 0 0 0 0 0
normalized size 1 0. 1.21 0. 0. 0. 0. 0.
time (sec) N/A 0.058 4.532 0.113 0. 0. 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 130 0 151 0 0 0 0 0
normalized size 1 0. 1.16 0. 0. 0. 0. 0.
time (sec) N/A 0.043 6.481 0.11 0. 0. 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 126 0 160 0 0 0 0 0
normalized size 1 0. 1.27 0. 0. 0. 0. 0.
time (sec) N/A 0.014 7.686 0.099 0. 0. 0. 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 49 80 50 197 0 50
normalized size 1 1. 1.75 2.86 1.79 7.04 0. 1.79
time (sec) N/A 0.029 0.104 0.005 1.3 2.512 0. 1.33
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 134 0 158 0 0 0 0 0
normalized size 1 0. 1.18 0. 0. 0. 0. 0.
time (sec) N/A 0.051 3.563 0.12 0. 0. 0. 0.
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 135 0 156 0 0 0 0 0
normalized size 1 0. 1.16 0. 0. 0. 0. 0.
time (sec) N/A 0.053 3.554 0.127 0. 0. 0. 0.
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 52 67 446 1841 0 170
normalized size 1 1. 1.21 1.56 10.37 42.81 0. 3.95
time (sec) N/A 0.04 0.207 0.009 1.372 2.673 0. 1.429
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 44 86 674 541 0 90
normalized size 1 1. 0.98 1.91 14.98 12.02 0. 2.
time (sec) N/A 0.037 0.114 0.003 1.511 2.508 0. 1.434
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 67 88 1154 5060 0 216
normalized size 1 1. 1.02 1.33 17.48 76.67 0. 3.27
time (sec) N/A 0.057 0.28 0.003 1.639 2.687 0. 1.344
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 87 0 158 0 0 0 0 0
normalized size 1 0. 1.82 0. 0. 0. 0. 0.
time (sec) N/A 0.046 13.231 1.436 0. 0. 0. 0.
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 168 0 312 0 0 0 0 0
normalized size 1 0. 1.86 0. 0. 0. 0. 0.
time (sec) N/A 0.077 14.437 0.221 0. 0. 0. 0.
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 306 0 600 0 0 0 0 0
normalized size 1 0. 1.96 0. 0. 0. 0. 0.
time (sec) N/A 0.069 16.586 0.24 0. 0. 0. 0.
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 115 0 387 0 0 0 0 0
normalized size 1 0. 3.37 0. 0. 0. 0. 0.
time (sec) N/A 0.015 3.629 0.081 0. 0. 0. 0.
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 135 0 174 0 0 0 0 0
normalized size 1 0. 1.29 0. 0. 0. 0. 0.
time (sec) N/A 0.097 5.072 0.069 0. 0. 0. 0.
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 64 93 0 2090 0 0
normalized size 1 1. 0.88 1.27 0. 28.63 0. 0.
time (sec) N/A 0.051 0.286 0.028 0. 2.436 0. 0.
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 57 92 0 1100 0 0
normalized size 1 1. 0.81 1.31 0. 15.71 0. 0.
time (sec) N/A 0.05 0.146 0.015 0. 2.512 0. 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 48 72 0 999 0 0
normalized size 1 1. 1. 1.5 0. 20.81 0. 0.
time (sec) N/A 0.039 0.075 0.013 0. 2.441 0. 0.
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 47 44 0 1000 0 0
normalized size 1 1. 1. 0.94 0. 21.28 0. 0.
time (sec) N/A 0.04 0.111 0.015 0. 2.348 0. 0.
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 44 93 0 2087 0 0
normalized size 1 1. 0.62 1.31 0. 29.39 0. 0.
time (sec) N/A 0.052 0.144 0.015 0. 2.842 0. 0.
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 46 92 0 3644 0 0
normalized size 1 1. 0.64 1.28 0. 50.61 0. 0.
time (sec) N/A 0.051 0.2 0.013 0. 2.889 0. 0.
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 266 149 0 24521 0 0
normalized size 1 1. 1.97 1.1 0. 181.64 0. 0.
time (sec) N/A 0.353 9.015 0.104 0. 18.619 0. 0.
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 199 90 0 18436 0 0
normalized size 1 1. 1.9 0.86 0. 175.58 0. 0.
time (sec) N/A 0.217 25.823 0.063 0. 14.573 0. 0.
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 141 52 0 4811 0 0
normalized size 1 1. 2.43 0.9 0. 82.95 0. 0.
time (sec) N/A 0.117 18.196 0.065 0. 9.668 0. 0.
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 203 0 0 18421 0 0
normalized size 1 1. 1.92 0. 0. 173.78 0. 0.
time (sec) N/A 0.24 7.83 0.304 0. 13.848 0. 0.
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 183 183 2574 0 0 24602 0 0
normalized size 1 1. 14.07 0. 0. 134.44 0. 0.
time (sec) N/A 0.332 20.687 0.274 0. 19.634 0. 0.
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 304 559 0 22316 0 0
normalized size 1 1. 2.3 4.23 0. 169.06 0. 0.
time (sec) N/A 0.231 7.991 0.061 0. 24.07 0. 0.
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 319 319 164 320 225 4176 0 244
normalized size 1 1. 0.51 1. 0.71 13.09 0. 0.76
time (sec) N/A 0.912 10.266 0.255 1.609 2.677 0. 1.432
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 197 197 334 298 151 1574 0 209
normalized size 1 1. 1.7 1.51 0.77 7.99 0. 1.06
time (sec) N/A 0.284 3.77 0.199 1.826 2.422 0. 1.27
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 51 213 76 196 0 127
normalized size 1 1. 0.61 2.57 0.92 2.36 0. 1.53
time (sec) N/A 0.144 0.058 0.238 1.705 2.373 0. 1.192
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 51 218 47 132 0 81
normalized size 1 1. 0.61 2.63 0.57 1.59 0. 0.98
time (sec) N/A 0.194 0.118 0.231 1.72 2.26 0. 1.183
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 193 193 104 301 122 1175 0 176
normalized size 1 1. 0.54 1.56 0.63 6.09 0. 0.91
time (sec) N/A 0.864 0.297 0.209 1.666 2.542 0. 1.218
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 311 311 133 324 196 3186 0 250
normalized size 1 1. 0.43 1.04 0.63 10.24 0. 0.8
time (sec) N/A 1.743 0.461 0.22 1.762 2.616 0. 1.253
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 157 157 124 118 0 929 0 0
normalized size 1 1. 0.79 0.75 0. 5.92 0. 0.
time (sec) N/A 0.375 0.242 0.025 0. 2.75 0. 0.
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 88 102 0 474 0 0
normalized size 1 1. 0.77 0.89 0. 4.12 0. 0.
time (sec) N/A 0.262 0.167 0.02 0. 2.526 0. 0.
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 59 58 0 464 0 0
normalized size 1 1. 0.77 0.75 0. 6.03 0. 0.
time (sec) N/A 0.144 0.128 0.016 0. 2.438 0. 0.
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 65 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.077 2.68 0.165 0. 0. 0. 0.
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 157 157 124 118 0 929 0 0
normalized size 1 1. 0.79 0.75 0. 5.92 0. 0.
time (sec) N/A 0.373 0.244 0.023 0. 2.968 0. 0.
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 88 102 0 474 0 0
normalized size 1 1. 0.77 0.89 0. 4.12 0. 0.
time (sec) N/A 0.251 0.166 0.021 0. 2.78 0. 0.
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 62 58 0 463 0 0
normalized size 1 1. 0.81 0.75 0. 6.01 0. 0.
time (sec) N/A 0.14 0.106 0.022 0. 2.698 0. 0.
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 65 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.077 5.484 0.067 0. 0. 0. 0.

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [109] had the largest ratio of [ 0.7778 ]

Table 2.1Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\)
1 A 7 6 1. 12 0.5
2 A 6 6 1. 12 0.5
3 A 6 6 1. 12 0.5
4 A 5 5 1. 12 0.417
5 A 5 5 1. 12 0.417
6 A 6 6 1. 12 0.5
7 A 6 6 1. 12 0.5
8 A 7 6 1. 12 0.5
9 A 13 9 1. 12 0.75
10 A 12 8 1. 12 0.667
11 A 9 9 1. 12 0.75
12 A 9 9 1. 12 0.75
13 A 12 8 1. 12 0.667
14 A 13 9 1. 12 0.75
15 A 2 2 1. 8 0.25
16 A 2 2 1. 10 0.2
17 A 3 3 1. 12 0.25
18 A 3 3 1. 14 0.214
19 A 2 2 1. 14 0.143
20 A 2 2 1. 14 0.143
21 A 3 3 1. 14 0.214
22 A 14 10 1. 14 0.714
23 A 14 10 1. 14 0.714
24 A 13 9 1. 14 0.643
25 A 13 9 1. 14 0.643
26 A 14 10 1. 14 0.714
27 A 14 10 1. 14 0.714
28 A 3 3 1. 12 0.25
29 A 8 7 1. 14 0.5
30 A 7 7 1. 14 0.5
31 A 7 7 1. 14 0.5
32 A 8 7 1. 14 0.5
33 A 4 3 1. 14 0.214
34 A 3 3 1. 14 0.214
35 A 2 2 1. 14 0.143
36 A 2 2 1. 14 0.143
37 A 3 3 1. 14 0.214
38 A 4 3 1. 14 0.214
39 A 3 3 1. 12 0.25
40 A 5 3 1. 14 0.214
41 A 3 3 1. 14 0.214
42 A 3 3 1. 14 0.214
43 A 5 3 1. 14 0.214
44 A 16 10 1. 14 0.714
45 A 14 10 1. 14 0.714
46 A 14 10 1. 14 0.714
47 A 14 10 1. 14 0.714
48 A 14 10 1. 14 0.714
49 A 16 10 1. 14 0.714
50 A 3 3 1. 12 0.25
51 A 3 3 1. 14 0.214
52 A 3 3 1. 14 0.214
53 A 3 3 1. 14 0.214
54 A 3 3 1. 14 0.214
55 A 3 3 1. 14 0.214
56 A 3 3 1. 14 0.214
57 A 3 3 1. 14 0.214
58 A 3 3 1. 14 0.214
59 A 3 3 1. 14 0.214
60 A 3 3 1. 14 0.214
61 A 5 3 1. 6 0.5
62 A 4 3 1. 6 0.5
63 A 3 3 1. 6 0.5
64 A 2 2 1. 6 0.333
65 A 2 2 1. 6 0.333
66 A 3 2 1. 6 0.333
67 A 4 2 1. 6 0.333
68 A 5 2 1. 6 0.333
69 A 6 2 1. 6 0.333
70 A 5 3 1. 8 0.375
71 A 4 3 1. 8 0.375
72 A 3 3 1. 8 0.375
73 A 2 2 1. 8 0.25
74 A 3 3 1. 8 0.375
75 A 4 3 1. 8 0.375
76 A 5 3 1. 8 0.375
77 A 5 4 1. 12 0.333
78 A 4 4 1. 12 0.333
79 A 3 3 1. 12 0.25
80 A 2 2 1. 12 0.167
81 A 2 2 1. 12 0.167
82 A 3 3 1. 12 0.25
83 A 4 4 1. 12 0.333
84 A 5 4 1. 12 0.333
85 A 2 2 1. 12 0.167
86 A 2 2 1. 12 0.167
87 A 5 4 1. 14 0.286
88 A 5 4 1. 14 0.286
89 A 4 3 1. 11 0.273
90 A 3 2 1. 11 0.182
91 A 4 3 1. 11 0.273
92 A 2 2 1. 9 0.222
93 A 1 1 1. 9 0.111
94 A 2 2 1. 11 0.182
95 A 2 2 1. 11 0.182
96 A 2 1 1. 11 0.091
97 A 5 4 1. 13 0.308
98 A 9 6 1. 13 0.462
99 A 4 3 1. 13 0.231
100 A 5 5 1. 11 0.454
101 A 2 2 1. 11 0.182
102 A 2 2 1. 13 0.154
103 A 5 5 1. 13 0.385
104 A 3 2 1. 13 0.154
105 A 5 4 1. 11 0.364
106 A 9 7 1. 11 0.636
107 A 5 4 1. 11 0.364
108 A 8 6 1. 9 0.667
109 A 8 7 1. 9 0.778
110 A 3 2 1. 11 0.182
111 A 8 7 1. 11 0.636
112 A 4 3 1. 11 0.273
113 A 4 4 1. 13 0.308
114 A 5 3 1. 13 0.231
115 A 10 9 1. 13 0.692
116 A 4 3 1. 13 0.231
117 A 6 6 1. 11 0.546
118 A 6 5 1. 11 0.454
119 A 3 2 1. 13 0.154
120 A 9 7 1. 13 0.538
121 A 3 2 1. 13 0.154
122 A 6 5 1. 13 0.385
123 A 6 4 1. 11 0.364
124 A 5 4 1. 11 0.364
125 A 4 4 1. 11 0.364
126 A 4 4 1. 9 0.444
127 A 2 2 1. 6 0.333
128 A 2 2 1. 9 0.222
129 A 3 2 1. 11 0.182
130 A 3 3 1. 11 0.273
131 A 4 4 1. 11 0.364
132 A 4 4 1. 11 0.364
133 A 3 3 1. 11 0.273
134 A 3 3 1. 11 0.273
135 A 4 4 1. 11 0.364
136 A 4 4 1. 13 0.308
137 A 3 3 1. 13 0.231
138 A 4 4 1. 13 0.308
139 A 4 4 1. 13 0.308
140 A 6 6 1. 13 0.462
141 A 5 5 1. 13 0.385
142 A 4 4 1. 13 0.308
143 A 3 3 1. 11 0.273
144 A 2 2 1. 8 0.25
145 A 2 2 1. 11 0.182
146 A 4 4 1. 13 0.308
147 A 5 5 1. 13 0.385
148 A 6 6 1. 13 0.462
149 A 7 7 1. 13 0.538
150 A 3 3 1. 14 0.214
151 F 0 0 N/A 0 N/A
152 F 0 0 N/A 0 N/A
153 F 0 0 N/A 0 N/A
154 F 0 0 N/A 0 N/A
155 A 2 1 1. 11 0.091
156 F 0 0 N/A 0 N/A
157 F 0 0 N/A 0 N/A
158 F 0 0 N/A 0 N/A
159 F 0 0 N/A 0 N/A
160 F 0 0 N/A 0 N/A
161 F 0 0 N/A 0 N/A
162 A 3 2 1. 13 0.154
163 F 0 0 N/A 0 N/A
164 F 0 0 N/A 0 N/A
165 F 0 0 N/A 0 N/A
166 F 0 0 N/A 0 N/A
167 F 0 0 N/A 0 N/A
168 F 0 0 N/A 0 N/A
169 F 0 0 N/A 0 N/A
170 F 0 0 N/A 0 N/A
171 F 0 0 N/A 0 N/A
172 F 0 0 N/A 0 N/A
173 F 0 0 N/A 0 N/A
174 F 0 0 N/A 0 N/A
175 F 0 0 N/A 0 N/A
176 F 0 0 N/A 0 N/A
177 F 0 0 N/A 0 N/A
178 F 0 0 N/A 0 N/A
179 F 0 0 N/A 0 N/A
180 F 0 0 N/A 0 N/A
181 A 2 1 1. 17 0.059
182 F 0 0 N/A 0 N/A
183 F 0 0 N/A 0 N/A
184 F 0 0 N/A 0 N/A
185 F 0 0 N/A 0 N/A
186 F 0 0 N/A 0 N/A
187 F 0 0 N/A 0 N/A
188 A 3 2 1. 19 0.105
189 F 0 0 N/A 0 N/A
190 F 0 0 N/A 0 N/A
191 A 3 2 1. 17 0.118
192 A 4 2 1. 17 0.118
193 A 4 2 1. 17 0.118
194 F 0 0 N/A 0 N/A
195 F 0 0 N/A 0 N/A
196 F 0 0 N/A 0 N/A
197 F 0 0 N/A 0 N/A
198 F 0 0 N/A 0 N/A
199 A 7 6 1. 19 0.316
200 A 7 6 1. 19 0.316
201 A 6 5 1. 19 0.263
202 A 6 5 1. 19 0.263
203 A 7 6 1. 19 0.316
204 A 7 6 1. 19 0.316
205 A 8 7 1. 23 0.304
206 A 7 6 1. 23 0.261
207 A 4 4 1. 21 0.19
208 A 8 5 1. 21 0.238
209 A 11 6 1. 23 0.261
210 A 8 7 1. 21 0.333
211 A 9 7 1. 25 0.28
212 A 8 7 1. 25 0.28
213 A 4 4 1. 25 0.16
214 A 4 4 1. 25 0.16
215 A 8 7 1. 25 0.28
216 A 9 7 1. 25 0.28
217 A 19 5 1. 9 0.556
218 A 13 5 1. 9 0.556
219 A 9 4 1. 7 0.571
220 A 0 0 0. 0 0.
221 A 19 5 1. 9 0.556
222 A 13 5 1. 9 0.556
223 A 9 4 1. 7 0.571
224 A 0 0 0. 0 0.

[next] [prev] [prev-tail] [front] [up]