[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, 68, 71, 72, 73, 74, 75, 76, 79, 82, 83, 84, 85, 86, 87, 88, 89, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 120, 127, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 147, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 173, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 199, 206, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243 }

B grade: { 65, 67, 69, 77, 78, 117, 119, 121, 123, 124, 125, 126, 144, 146, 148, 155, 172, 174 }

C grade: { 64, 66, 70, 116, 118, 122, 143, 145, 149, 171, 175 }

F grade: { 80, 81, 90, 91, 92, 93, 128, 129, 150, 151, 152, 153, 156, 195, 196, 197, 198, 200, 201, 202, 203, 204, 205, 207, 208, 221, 223}

2.1.2 Mathematica

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, 32, 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, 73, 74, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 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, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 178, 179, 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, 220, 221, 222, 223, 224, 225, 226, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 240, 241, 242, 243 }

B grade: { }

C grade: { 31, 33, 80, 128, 151, 153, 227, 236 }

F grade: { 71, 72, 75, 76, 90, 91, 92, 93, 176, 177, 180, 181}

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 18, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67, 82, 83, 84, 85, 86, 87, 88, 89, 94, 95, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 119, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 148, 157, 158, 159, 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 174, 182, 183, 185, 186, 187, 188, 189, 190, 192, 193, 194, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 231, 232, 234, 235, 238, 239, 240, 242, 243 }

B grade: { 7, 13, 14, 15, 16, 17, 20, 21, 22, 23, 29, 54, 66, 70, 78, 118, 122, 126, 139, 143, 144, 145, 146, 149, 155, 161, 175, 191, 195, 196, 197, 198, 200, 201, 217, 221, 227, 236 }

C grade: { 19, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 77, 103, 125, 147, 150, 151, 152, 153, 154, 156, 199, 202, 203, 204, 205, 206, 207, 208, 222, 233, 237 }

F grade: { 45, 64, 65, 68, 69, 71, 72, 73, 74, 75, 76, 79, 80, 81, 90, 91, 92, 93, 96, 116, 117, 120, 121, 123, 124, 127, 128, 129, 132, 171, 172, 173, 176, 177, 178, 179, 180, 181, 184, 223, 224, 225, 226, 228, 229, 230, 241 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 64, 97, 98, 99, 100, 101, 102, 104, 105, 106, 108, 110, 112, 114, 116, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 145, 157, 158, 159, 160, 162, 163, 164, 171, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 209, 210, 211, 212, 214, 220, 231, 232, 234, 235, 238, 242, 243

B grade: { 17, 21, 23, 66, 70, 118, 122, 149, 175, 191, 197, 198, 200, 201, 202, 203, 204, 207, 208, 217, 221, 223, 236, 237 }

C grade: { }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 54, 58, 59, 60, 61, 62, 63, 65, 67, 68, 69, 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, 103, 107, 109, 111, 113, 115, 117, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 139, 144, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 161, 165, 166, 167, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 199, 205, 206, 213, 215, 216, 218, 219, 222, 224, 225, 226, 227, 228, 229, 230, 233, 239, 240, 241 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 66, 70, 82, 83, 84, 85, 86, 87, 88, 89, 94, 95, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 122, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 145, 149, 157, 158, 159, 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 175, 182, 183, 185, 186, 187, 188, 189, 190, 192, 193, 194, 195, 196, 197, 201, 209, 210, 211, 212, 214, 218, 219, 220, 231, 232, 234, 235, 238, 239, 240, 242, 243 }

B grade: { 60, 198, 200, 221, 223, 227, 236 }

C grade: { 213, 215, 216 }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 45, 49, 54, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 90, 91, 92, 93, 96, 103, 117, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 132, 139, 144, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 161, 172, 173, 174, 176, 177, 178, 179, 180, 181, 184, 191, 199, 202, 203, 204, 205, 206, 207, 208, 217, 222, 224, 225, 226, 228, 229, 230, 233, 237, 241 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 43, 44, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 70, 135, 136, 137, 138, 140, 141, 142, 143, 145, 149, 157, 159, 162, 163, 164, 165, 166, 167, 168, 169, 170, 175, 192, 193, 200, 201, 210, 232, 234, 238 }

B grade: { 209, 211, 212 }

C grade: { 37, 158, 160, 171 }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 45, 49, 54, 65, 67, 68, 69, 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, 139, 144, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 161, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 194, 195, 196, 197, 198, 199, 202, 203, 204, 205, 206, 207, 208, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 236, 237, 239, 240, 241, 242, 243 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 63, 64, 66, 94, 95, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 145, 157, 158, 159, 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 182, 183, 185, 186, 187, 188, 189, 190, 192, 193, 194, 209, 210, 211, 212, 214, 216, 218, 219, 220, 231, 232, 234, 235, 238, 239, 240, 242, 243 }

B grade: { 60, 61, 62, 85, 86, 87, 88, 89 }

C grade: { 213 }

F grade: { 7, 14, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 45, 54, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 90, 91, 92, 93, 96, 103, 117, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 139, 144, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 161, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 184, 191, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 215, 217, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 233, 236, 237, 241 }

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 A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 81 67 95 153 63 104
normalized size 1 1. 1.37 1.14 1.61 2.59 1.07 1.76
time (sec) N/A 0.033 0.01 0.007 0.969 1.954 2.132 1.173
Problem 2 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 57 57 62 60 74 153 68 84
normalized size 1 1. 1.09 1.05 1.3 2.68 1.19 1.47
time (sec) N/A 0.043 0.009 0.007 0.966 2.056 1.616 1.156
Problem 3 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 48 48 70 58 82 127 53 92
normalized size 1 1. 1.46 1.21 1.71 2.65 1.1 1.92
time (sec) N/A 0.029 0.009 0.007 0.96 2.025 1.167 1.235
Problem 4 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 46 46 51 51 59 127 58 72
normalized size 1 1. 1.11 1.11 1.28 2.76 1.26 1.57
time (sec) N/A 0.035 0.008 0.007 0.968 1.969 0.945 1.232
Problem 5 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 37 37 59 49 68 104 42 80
normalized size 1 1. 1.59 1.32 1.84 2.81 1.14 2.16
time (sec) N/A 0.017 0.007 0.007 0.985 1.908 0.592 1.209
Problem 6 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 30 30 30 29 41 97 27 54
normalized size 1 1. 1. 0.97 1.37 3.23 0.9 1.8
time (sec) N/A 0.013 0.003 0.002 0.976 1.947 0.387 1.172
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 24 47 0 0 0 0
normalized size 1 1. 0.92 1.81 0. 0. 0. 0.
time (sec) N/A 0.015 0.009 0.013 0. 0. 0. 0.
Problem 8 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 36 36 39 45 53 116 41 63
normalized size 1 1. 1.08 1.25 1.47 3.22 1.14 1.75
time (sec) N/A 0.026 0.008 0.01 0.976 1.87 0.946 1.152
Problem 9 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 37 37 59 49 61 95 36 77
normalized size 1 1. 1.59 1.32 1.65 2.57 0.97 2.08
time (sec) N/A 0.022 0.008 0.01 0.979 1.933 0.74 1.202
Problem 10 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 54 54 59 59 66 140 70 80
normalized size 1 1. 1.09 1.09 1.22 2.59 1.3 1.48
time (sec) N/A 0.036 0.008 0.01 0.967 1.928 1.561 1.206
Problem 11 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 48 48 70 58 81 117 46 92
normalized size 1 1. 1.46 1.21 1.69 2.44 0.96 1.92
time (sec) N/A 0.027 0.008 0.01 0.987 1.926 1.166 1.214
Problem 12 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 65 65 70 68 82 166 80 92
normalized size 1 1. 1.08 1.05 1.26 2.55 1.23 1.42
time (sec) N/A 0.041 0.009 0.01 0.973 1.979 2.782 1.222
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 164 314 290 437 211 259
normalized size 1 1. 1.13 2.17 2. 3.01 1.46 1.79
time (sec) N/A 0.327 0.068 0.023 1.013 2.188 4.115 1.302
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 162 162 161 306 0 0 0 0
normalized size 1 1. 0.99 1.89 0. 0. 0. 0.
time (sec) N/A 0.302 0.452 0.016 0. 0. 0. 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 132 278 255 354 168 215
normalized size 1 1. 1.17 2.46 2.26 3.13 1.49 1.9
time (sec) N/A 0.223 0.059 0.015 0.977 2.097 2.244 1.257
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 130 130 122 270 0 0 0 0
normalized size 1 1. 0.94 2.08 0. 0. 0. 0.
time (sec) N/A 0.201 0.257 0.013 0. 0. 0. 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 90 239 213 269 114 163
normalized size 1 1. 1.2 3.19 2.84 3.59 1.52 2.17
time (sec) N/A 0.114 0.062 0.016 0.994 2.233 1.089 1.213
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 74 74 82 123 0 0 0 0
normalized size 1 1. 1.11 1.66 0. 0. 0. 0.
time (sec) N/A 0.101 0.143 0.049 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 120 701 0 0 0 0
normalized size 1 1. 1.03 5.99 0. 0. 0. 0.
time (sec) N/A 0.264 0.072 0.214 0. 0. 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 71 71 94 248 0 0 0 0
normalized size 1 1. 1.32 3.49 0. 0. 0. 0.
time (sec) N/A 0.145 0.144 0.021 0. 0. 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 101 253 204 300 126 0
normalized size 1 1. 1.26 3.16 2.55 3.75 1.58 0.
time (sec) N/A 0.133 0.068 0.019 1.004 2.367 1.455 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 130 130 145 339 0 0 0 0
normalized size 1 1. 1.12 2.61 0. 0. 0. 0.
time (sec) N/A 0.231 0.344 0.02 0. 0. 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 164 290 302 386 184 0
normalized size 1 1. 1.4 2.48 2.58 3.3 1.57 0.
time (sec) N/A 0.228 0.069 0.026 0.998 2.38 2.601 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 247 247 305 1330 0 0 0 0
normalized size 1 1. 1.23 5.38 0. 0. 0. 0.
time (sec) N/A 0.964 0.704 0.754 0. 0. 0. 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 262 262 383 1275 0 0 0 0
normalized size 1 1. 1.46 4.87 0. 0. 0. 0.
time (sec) N/A 0.774 0.735 0.823 0. 0. 0. 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 185 185 245 1245 0 0 0 0
normalized size 1 1. 1.32 6.73 0. 0. 0. 0.
time (sec) N/A 0.569 0.492 0.602 0. 0. 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 197 197 250 1177 0 0 0 0
normalized size 1 1. 1.27 5.97 0. 0. 0. 0.
time (sec) N/A 0.449 0.52 0.477 0. 0. 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 123 123 161 6097 0 0 0 0
normalized size 1 1. 1.31 49.57 0. 0. 0. 0.
time (sec) N/A 0.25 0.284 0.342 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 108 108 161 261 0 0 0 0
normalized size 1 1. 1.49 2.42 0. 0. 0. 0.
time (sec) N/A 0.217 0.26 0.082 0. 0. 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 184 184 178 1470 0 0 0 0
normalized size 1 1. 0.97 7.99 0. 0. 0. 0.
time (sec) N/A 0.449 0.128 0.113 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 102 102 196 1583 0 0 0 0
normalized size 1 1. 1.92 15.52 0. 0. 0. 0.
time (sec) N/A 0.268 0.321 0.183 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 123 123 192 5098 0 0 0 0
normalized size 1 1. 1.56 41.45 0. 0. 0. 0.
time (sec) N/A 0.294 0.272 0.316 0. 0. 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 200 200 323 1838 0 0 0 0
normalized size 1 1. 1.62 9.19 0. 0. 0. 0.
time (sec) N/A 0.498 0.861 0.849 0. 0. 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 187 187 295 1281 0 0 0 0
normalized size 1 1. 1.58 6.85 0. 0. 0. 0.
time (sec) N/A 0.626 0.639 0.873 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 128 107 0 660 0 0
normalized size 1 1. 1.03 0.86 0. 5.32 0. 0.
time (sec) N/A 0.086 0.073 0.036 0. 2.339 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 115 93 0 586 0 0
normalized size 1 1. 1.08 0.88 0. 5.53 0. 0.
time (sec) N/A 0.067 0.055 0.011 0. 2.253 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 114 89 0 509 586 0
normalized size 1 1. 1.08 0.84 0. 4.8 5.53 0.
time (sec) N/A 0.061 0.05 0.012 0. 2.229 20.006 0.
Problem 38 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 85 85 98 70 0 487 0 119
normalized size 1 1. 1.15 0.82 0. 5.73 0. 1.4
time (sec) N/A 0.052 0.032 0.013 0. 2.324 0. 1.162
Problem 39 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 85 85 99 78 0 494 0 127
normalized size 1 1. 1.16 0.92 0. 5.81 0. 1.49
time (sec) N/A 0.055 0.043 0.013 0. 2.16 0. 1.27
Problem 40 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 107 107 107 94 0 558 0 163
normalized size 1 1. 1. 0.88 0. 5.21 0. 1.52
time (sec) N/A 0.063 0.06 0.014 0. 2.212 0. 1.343
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 108 94 0 583 0 159
normalized size 1 1. 1.01 0.88 0. 5.45 0. 1.49
time (sec) N/A 0.066 0.048 0.014 0. 2.28 0. 1.265
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 122 108 0 628 0 188
normalized size 1 1. 0.98 0.86 0. 5.02 0. 1.5
time (sec) N/A 0.078 0.066 0.015 0. 2.452 0. 1.423
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 3.519 1.024 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 2.321 0.914 0. 0. 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 59 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.032 0.067 0.925 0. 0. 0. 0.
Problem 46 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 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.027 0.253 0.654 0. 0. 0. 0.
Problem 47 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 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.5 0.658 0. 0. 0. 0.
Problem 48 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.005 0.441 0.201 0. 0. 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 0.326 0.378 0. 0. 0. 0.
Problem 50 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 54 54 78 66 93 135 58 105
normalized size 1 1. 1.44 1.22 1.72 2.5 1.07 1.94
time (sec) N/A 0.039 0.016 0.022 0.953 1.999 29.879 1.206
Problem 51 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 48 48 53 45 62 134 85 77
normalized size 1 1. 1.1 0.94 1.29 2.79 1.77 1.6
time (sec) N/A 0.035 0.014 0.009 0.982 2.059 21.035 1.17
Problem 52 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 43 43 67 57 78 112 48 93
normalized size 1 1. 1.56 1.33 1.81 2.6 1.12 2.16
time (sec) N/A 0.03 0.013 0.012 0.955 2.02 14.08 1.184
Problem 53 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 37 37 42 37 50 108 71 66
normalized size 1 1. 1.14 1. 1.35 2.92 1.92 1.78
time (sec) N/A 0.015 0.007 0.003 0.956 2.065 10.068 1.188
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 28 124 0 0 0 0
normalized size 1 1. 0.93 4.13 0. 0. 0. 0.
time (sec) N/A 0.033 0.013 0.029 0. 0. 0. 0.
Problem 55 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 40 40 45 49 55 130 80 69
normalized size 1 1. 1.12 1.22 1.38 3.25 2. 1.72
time (sec) N/A 0.026 0.011 0.013 0.981 2.002 17.27 1.172
Problem 56 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 41 41 65 55 69 103 41 90
normalized size 1 1. 1.59 1.34 1.68 2.51 1. 2.2
time (sec) N/A 0.027 0.011 0.013 0.959 1.939 12.464 1.195
Problem 57 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 56 56 61 63 69 150 97 88
normalized size 1 1. 1.09 1.12 1.23 2.68 1.73 1.57
time (sec) N/A 0.034 0.011 0.015 0.975 2.11 34.431 1.333
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 93 53 0 473 185 103
normalized size 1 1. 1.43 0.82 0. 7.28 2.85 1.58
time (sec) N/A 0.035 0.024 0.011 0. 2.009 19.363 1.274
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 91 51 0 448 581 101
normalized size 1 1. 1.44 0.81 0. 7.11 9.22 1.6
time (sec) N/A 0.033 0.019 0.01 0. 2.229 12.964 1.277
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 57 37 0 394 139 112
normalized size 1 1. 1.3 0.84 0. 8.95 3.16 2.55
time (sec) N/A 0.024 0.02 0.007 0. 2.074 8.394 1.195
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 75 42 0 385 699 107
normalized size 1 1. 1.63 0.91 0. 8.37 15.2 2.33
time (sec) N/A 0.026 0.017 0.013 0. 2.125 15.145 1.225
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 91 51 0 440 813 132
normalized size 1 1. 1.44 0.81 0. 6.98 12.9 2.1
time (sec) N/A 0.033 0.027 0.014 0. 2.134 21.291 1.352
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 91 51 0 458 833 123
normalized size 1 1. 1.44 0.81 0. 7.27 13.22 1.95
time (sec) N/A 0.032 0.027 0.013 0. 2.141 30.884 1.533
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A F A A A A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 125 636 146 0 293 375 206 236
normalized size 1 5.09 1.17 0. 2.34 3. 1.65 1.89
time (sec) N/A 1.547 0.073 180. 1.007 2.043 39.731 1.503
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 146 536 132 0 0 0 0 0
normalized size 1 3.67 0.9 0. 0. 0. 0. 0.
time (sec) N/A 1.296 0.278 180. 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A B B A A A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 91 524 106 247 251 292 163 186
normalized size 1 5.76 1.16 2.71 2.76 3.21 1.79 2.04
time (sec) N/A 0.965 0.06 0.163 0.976 2.113 19.12 1.382
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A A F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 94 207 99 144 0 0 0 0
normalized size 1 2.2 1.05 1.53 0. 0. 0. 0.
time (sec) N/A 0.514 0.066 0.035 0. 0. 0. 0.
Problem 68 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 137 137 141 0 0 0 0 0
normalized size 1 1. 1.03 0. 0. 0. 0. 0.
time (sec) N/A 0.336 0.101 0.133 0. 0. 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 87 237 119 0 0 0 0 0
normalized size 1 2.72 1.37 0. 0. 0. 0. 0.
time (sec) N/A 0.632 0.157 180. 0. 0. 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A B B A A F
verified N/A NO Yes TBD TBD TBD TBD TBD
size 88 360 111 257 236 324 175 0
normalized size 1 4.09 1.26 2.92 2.68 3.68 1.99 0.
time (sec) N/A 1.057 0.083 0.188 1.003 2.164 26.066 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1173 1173 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.334 9.308 0.216 0. 0. 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1129 1129 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.061 9.058 0.184 0. 0. 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 958 958 566 0 0 0 0 0
normalized size 1 1. 0.59 0. 0. 0. 0. 0.
time (sec) N/A 1.468 2.562 0.125 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 942 942 566 0 0 0 0 0
normalized size 1 1. 0.6 0. 0. 0. 0. 0.
time (sec) N/A 1.335 3.369 0.175 0. 0. 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1102 1102 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.842 2.554 0.175 0. 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1176 1176 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.99 3.012 0.167 0. 0. 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A C F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 141 479 185 751 0 0 0 0
normalized size 1 3.4 1.31 5.33 0. 0. 0. 0.
time (sec) N/A 4.216 0.464 0.269 0. 0. 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 134 390 213 298 0 0 0 0
normalized size 1 2.91 1.59 2.22 0. 0. 0. 0.
time (sec) N/A 2.323 0.222 0.007 0. 0. 0. 0.
Problem 79 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 207 207 211 0 0 0 0 0
normalized size 1 1. 1.02 0. 0. 0. 0. 0.
time (sec) N/A 0.56 0.191 0.138 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 125 0 222 0 0 0 0 0
normalized size 1 0. 1.78 0. 0. 0. 0. 0.
time (sec) N/A 0.78 0.414 0.194 0. 0. 0. 0.
Problem 81 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 139 0 218 0 0 0 0 0
normalized size 1 0. 1.57 0. 0. 0. 0. 0.
time (sec) N/A 1.558 0.29 0.231 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 317 317 241 302 0 124 0 0
normalized size 1 1. 0.76 0.95 0. 0.39 0. 0.
time (sec) N/A 0.334 0.125 0.022 0. 2.293 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 317 317 240 292 0 109 0 0
normalized size 1 1. 0.76 0.92 0. 0.34 0. 0.
time (sec) N/A 0.3 0.093 0.016 0. 2.272 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 301 301 227 280 0 80 0 0
normalized size 1 1. 0.75 0.93 0. 0.27 0. 0.
time (sec) N/A 0.251 0.072 0.011 0. 2.16 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 285 285 227 273 0 72 0 666
normalized size 1 1. 0.8 0.96 0. 0.25 0. 2.34
time (sec) N/A 0.242 0.059 0.013 0. 2.229 0. 1.243
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 285 285 268 272 0 81 0 682
normalized size 1 1. 0.94 0.95 0. 0.28 0. 2.39
time (sec) N/A 0.248 0.103 0.013 0. 2.266 0. 1.906
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 301 301 268 280 0 89 0 698
normalized size 1 1. 0.89 0.93 0. 0.3 0. 2.32
time (sec) N/A 0.25 0.106 0.01 0. 2.268 0. 3.186
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 317 317 275 292 0 105 0 717
normalized size 1 1. 0.87 0.92 0. 0.33 0. 2.26
time (sec) N/A 0.278 0.086 0.016 0. 2.237 0. 9.78
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 317 317 281 302 0 109 0 720
normalized size 1 1. 0.89 0.95 0. 0.34 0. 2.27
time (sec) N/A 0.287 0.098 0.014 0. 2.236 0. 25.291
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F F F F(-2) F F(-1) F
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 6327 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 61.946 0.313 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F F F F(-2) F F F
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 6177 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 59.351 0.213 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F F F F(-2) F F(-1) F
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 6334 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.029 94.015 0.272 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F F F F(-2) F F(-1) F
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 6520 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.03 50.738 0.275 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 1.751 0.122 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 1.167 0.119 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 64 0 0 0 0 0
normalized size 1 1. 0.86 0. 0. 0. 0. 0.
time (sec) N/A 0.04 0.066 0.117 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.029 0.348 0.063 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.027 0.414 0.068 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 78 66 93 138 0 105
normalized size 1 1. 1.44 1.22 1.72 2.56 0. 1.94
time (sec) N/A 0.038 0.02 0.009 0.953 2.042 0. 1.202
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 53 45 62 134 0 77
normalized size 1 1. 1.1 0.94 1.29 2.79 0. 1.6
time (sec) N/A 0.036 0.016 0.008 1.021 1.916 0. 1.196
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 67 57 78 113 0 93
normalized size 1 1. 1.56 1.33 1.81 2.63 0. 2.16
time (sec) N/A 0.03 0.016 0.012 0.98 1.799 0. 1.149
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 42 37 50 108 0 66
normalized size 1 1. 1.14 1. 1.35 2.92 0. 1.78
time (sec) N/A 0.02 0.008 0.003 1.011 1.961 0. 1.169
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 28 92 0 0 0 0
normalized size 1 1. 0.93 3.07 0. 0. 0. 0.
time (sec) N/A 0.034 0.014 0.029 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 45 49 55 130 0 69
normalized size 1 1. 1.12 1.22 1.38 3.25 0. 1.72
time (sec) N/A 0.027 0.012 0.013 1.021 1.98 0. 1.134
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 65 55 69 104 0 90
normalized size 1 1. 1.59 1.34 1.68 2.54 0. 2.2
time (sec) N/A 0.027 0.018 0.013 1.013 1.936 0. 1.162
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 61 63 69 150 0 88
normalized size 1 1. 1.09 1.12 1.23 2.68 0. 1.57
time (sec) N/A 0.036 0.012 0.014 0.965 2.157 0. 1.171
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 196 184 0 2611 0 279
normalized size 1 1. 1.13 1.06 0. 15.01 0. 1.6
time (sec) N/A 0.22 0.042 0.015 0. 2.077 0. 1.317
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 136 99 143 674 0 147
normalized size 1 1. 1.35 0.98 1.42 6.67 0. 1.46
time (sec) N/A 0.097 0.043 0.006 1.448 1.869 0. 1.184
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 165 187 159 0 598 0 223
normalized size 1 1. 1.13 0.96 0. 3.62 0. 1.35
time (sec) N/A 0.197 0.052 0.01 0. 1.927 0. 1.298
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 196 172 144 367 0 169
normalized size 1 1. 1.7 1.5 1.25 3.19 0. 1.47
time (sec) N/A 0.095 0.05 0.014 1.449 1.767 0. 1.218
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 176 176 198 186 0 659 0 281
normalized size 1 1. 1.12 1.06 0. 3.74 0. 1.6
time (sec) N/A 0.284 0.03 0.013 0. 1.884 0. 1.493
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 198 114 161 414 0 170
normalized size 1 1. 1.69 0.97 1.38 3.54 0. 1.45
time (sec) N/A 0.097 0.028 0.007 1.501 1.791 0. 1.186
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 165 187 177 0 622 0 269
normalized size 1 1. 1.13 1.07 0. 3.77 0. 1.63
time (sec) N/A 0.249 0.026 0.01 0. 1.858 0. 1.31
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 183 105 149 312 0 143
normalized size 1 1. 1.76 1.01 1.43 3. 0. 1.38
time (sec) N/A 0.083 0.029 0.005 1.528 1.829 0. 1.183
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 196 172 0 547 0 261
normalized size 1 1. 1.13 0.99 0. 3.14 0. 1.5
time (sec) N/A 0.267 0.052 0.013 0. 1.673 0. 2.087
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A F A A F(-1) A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 125 636 146 0 293 381 0 236
normalized size 1 5.09 1.17 0. 2.34 3.05 0. 1.89
time (sec) N/A 1.546 0.076 180. 0.986 1.855 0. 1.289
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F(-2) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 146 536 132 0 0 0 0 0
normalized size 1 3.67 0.9 0. 0. 0. 0. 0.
time (sec) N/A 1.309 0.272 180. 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A B B A F(-2) A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 91 524 106 247 251 292 0 186
normalized size 1 5.76 1.16 2.71 2.76 3.21 0. 2.04
time (sec) N/A 0.985 0.056 0.18 1.123 1.689 0. 1.198
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A A F F F(-2) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 96 207 99 145 0 0 0 0
normalized size 1 2.16 1.03 1.51 0. 0. 0. 0.
time (sec) N/A 0.592 0.152 0.004 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 143 0 0 0 0 0
normalized size 1 1. 1.02 0. 0. 0. 0. 0.
time (sec) N/A 0.335 0.111 0.144 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F(-2) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 90 237 117 0 0 0 0 0
normalized size 1 2.63 1.3 0. 0. 0. 0. 0.
time (sec) N/A 0.619 0.158 180. 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A B B A F(-1) F
verified N/A NO Yes TBD TBD TBD TBD TBD
size 88 360 111 257 236 324 0 0
normalized size 1 4.09 1.26 2.92 2.68 3.68 0. 0.
time (sec) N/A 1.06 0.083 0.201 0.997 1.771 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 144 420 159 0 0 0 0 0
normalized size 1 2.92 1.1 0. 0. 0. 0. 0.
time (sec) N/A 1.311 0.363 0.181 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 231 1421 334 0 0 0 0 0
normalized size 1 6.15 1.45 0. 0. 0. 0. 0.
time (sec) N/A 6.35 0.47 0.217 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A C F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 139 479 185 750 0 0 0 0
normalized size 1 3.45 1.33 5.4 0. 0. 0. 0.
time (sec) N/A 4.204 0.299 0.316 0. 0. 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F F F(-2) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 130 390 191 295 0 0 0 0
normalized size 1 3. 1.47 2.27 0. 0. 0. 0.
time (sec) N/A 2.467 0.282 0.006 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 210 210 214 0 0 0 0 0
normalized size 1 1. 1.02 0. 0. 0. 0. 0.
time (sec) N/A 0.565 0.18 0.151 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C F F F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 120 0 223 0 0 0 0 0
normalized size 1 0. 1.86 0. 0. 0. 0. 0.
time (sec) N/A 0.779 0.395 0.208 0. 0. 0. 0.
Problem 129 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 136 0 218 0 0 0 0 0
normalized size 1 0. 1.6 0. 0. 0. 0. 0.
time (sec) N/A 1.575 0.279 0.23 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 1.81 0.125 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 1.174 0.125 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 64 0 0 0 0 0
normalized size 1 1. 0.86 0. 0. 0. 0. 0.
time (sec) N/A 0.043 0.062 0.119 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 0.349 0.07 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.027 0.361 0.069 0. 0. 0. 0.
Problem 135 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 67 62 77 113 46 84
normalized size 1 1. 1.34 1.24 1.54 2.26 0.92 1.68
time (sec) N/A 0.032 0.01 0.013 0.979 1.668 1.759 1.168
Problem 136 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 45 45 50 67 57 117 49 66
normalized size 1 1. 1.11 1.49 1.27 2.6 1.09 1.47
time (sec) N/A 0.033 0.008 0.013 0.961 1.769 1.109 1.168
Problem 137 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 56 53 59 90 36 72
normalized size 1 1. 1.44 1.36 1.51 2.31 0.92 1.85
time (sec) N/A 0.02 0.008 0.01 0.97 1.687 0.487 1.141
Problem 138 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 29 29 29 48 39 85 24 57
normalized size 1 1. 1. 1.66 1.34 2.93 0.83 1.97
time (sec) N/A 0.013 0.003 0.01 0.95 1.679 0.317 1.131
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 28 63 0 0 0 0
normalized size 1 1. 0.93 2.1 0. 0. 0. 0.
time (sec) N/A 0.032 0.012 0.014 0. 0. 0. 0.
Problem 140 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 35 35 38 37 50 115 39 66
normalized size 1 1. 1.09 1.06 1.43 3.29 1.11 1.89
time (sec) N/A 0.021 0.008 0.004 0.957 1.694 1.852 1.133
Problem 141 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 43 43 60 57 70 103 44 77
normalized size 1 1. 1.4 1.33 1.63 2.4 1.02 1.79
time (sec) N/A 0.027 0.009 0.007 0.955 1.761 2.114 1.164
Problem 142 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 57 57 62 57 74 144 68 85
normalized size 1 1. 1.09 1. 1.3 2.53 1.19 1.49
time (sec) N/A 0.041 0.009 0.007 0.962 1.672 3.641 1.129
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A B A A A A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 123 812 131 328 255 350 158 209
normalized size 1 6.6 1.07 2.67 2.07 2.85 1.28 1.7
time (sec) N/A 1.703 0.061 0.007 0.982 1.677 3.443 1.222
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 142 695 145 391 0 0 0 0
normalized size 1 4.89 1.02 2.75 0. 0. 0. 0.
time (sec) N/A 1.389 0.303 0.032 0. 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A B A A A A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 83 574 92 287 184 254 104 159
normalized size 1 6.92 1.11 3.46 2.22 3.06 1.25 1.92
time (sec) N/A 1.041 0.047 0.025 0.976 1.762 1.05 1.211
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 74 370 97 282 0 0 0 0
normalized size 1 5. 1.31 3.81 0. 0. 0. 0.
time (sec) N/A 0.402 0.122 0.012 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 133 133 114 780 0 0 0 0
normalized size 1 1. 0.86 5.86 0. 0. 0. 0.
time (sec) N/A 0.314 0.092 0.162 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A A F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 87 205 101 144 0 0 0 0
normalized size 1 2.36 1.16 1.66 0. 0. 0. 0.
time (sec) N/A 0.507 0.097 0.004 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A B B A A F
verified N/A NO Yes TBD TBD TBD TBD TBD
size 87 707 119 284 223 288 124 0
normalized size 1 8.13 1.37 3.26 2.56 3.31 1.43 0.
time (sec) N/A 1.247 0.067 0.016 0.989 1.867 1.962 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 203 0 286 1410 0 0 0 0
normalized size 1 0. 1.41 6.95 0. 0. 0. 0.
time (sec) N/A 4.39 0.603 0.332 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C C F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 217 0 316 2033 0 0 0 0
normalized size 1 0. 1.46 9.37 0. 0. 0. 0.
time (sec) N/A 3.302 0.744 0.02 0. 0. 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 135 0 193 5536 0 0 0 0
normalized size 1 0. 1.43 41.01 0. 0. 0. 0.
time (sec) N/A 2.245 0.318 0.278 0. 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C C F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 108 0 198 1756 0 0 0 0
normalized size 1 0. 1.83 16.26 0. 0. 0. 0.
time (sec) N/A 0.701 0.263 0.121 0. 0. 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 208 208 171 1631 0 0 0 0
normalized size 1 1. 0.82 7.84 0. 0. 0. 0.
time (sec) N/A 0.509 0.191 0.07 0. 0. 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 126 387 205 298 0 0 0 0
normalized size 1 3.07 1.63 2.37 0. 0. 0. 0.
time (sec) N/A 2.237 0.122 0.004 0. 0. 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 139 0 195 6645 0 0 0 0
normalized size 1 0. 1.4 47.81 0. 0. 0. 0.
time (sec) N/A 2.102 0.334 0.266 0. 0. 0. 0.
Problem 157 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 54 54 73 64 84 122 51 96
normalized size 1 1. 1.35 1.19 1.56 2.26 0.94 1.78
time (sec) N/A 0.042 0.014 0.016 0.99 1.75 18.497 1.332
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 50 65 57 124 75 70
normalized size 1 1. 1.11 1.44 1.27 2.76 1.67 1.56
time (sec) N/A 0.033 0.012 0.019 0.968 1.711 13.194 1.245
Problem 159 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 43 43 62 55 66 97 41 84
normalized size 1 1. 1.44 1.28 1.53 2.26 0.95 1.95
time (sec) N/A 0.03 0.011 0.006 0.96 1.585 15.366 1.254
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 39 52 46 99 61 63
normalized size 1 1. 1.15 1.53 1.35 2.91 1.79 1.85
time (sec) N/A 0.018 0.007 0.016 0.982 1.647 10.123 1.386
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 28 154 0 0 0 0
normalized size 1 1. 0.93 5.13 0. 0. 0. 0.
time (sec) N/A 0.033 0.014 0.03 0. 0. 0. 0.
Problem 162 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 37 37 42 37 50 126 76 70
normalized size 1 1. 1.14 1. 1.35 3.41 2.05 1.89
time (sec) N/A 0.02 0.009 0.004 0.969 1.775 18.503 1.275
Problem 163 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 45 45 64 57 76 109 49 89
normalized size 1 1. 1.42 1.27 1.69 2.42 1.09 1.98
time (sec) N/A 0.032 0.011 0.009 0.967 1.546 45.385 1.214
Problem 164 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 57 57 62 45 74 151 94 88
normalized size 1 1. 1.09 0.79 1.3 2.65 1.65 1.54
time (sec) N/A 0.04 0.013 0.006 0.98 1.678 47.101 1.16
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 88 53 0 440 588 90
normalized size 1 1. 1.4 0.84 0. 6.98 9.33 1.43
time (sec) N/A 0.035 0.021 0.014 0. 1.836 42.206 1.303
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 86 51 0 421 624 93
normalized size 1 1. 1.41 0.84 0. 6.9 10.23 1.52
time (sec) N/A 0.033 0.018 0.008 0. 1.774 22.228 1.258
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 54 39 0 351 473 77
normalized size 1 1. 1.23 0.89 0. 7.98 10.75 1.75
time (sec) N/A 0.024 0.016 0.01 0. 1.764 16.727 1.215
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 72 44 0 385 593 84
normalized size 1 1. 1.57 0.96 0. 8.37 12.89 1.83
time (sec) N/A 0.031 0.018 0.01 0. 1.774 13.88 1.232
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 90 55 0 451 706 97
normalized size 1 1. 1.38 0.85 0. 6.94 10.86 1.49
time (sec) N/A 0.037 0.031 0.012 0. 1.848 25.699 1.301
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 90 55 0 468 668 100
normalized size 1 1. 1.38 0.85 0. 7.2 10.28 1.54
time (sec) N/A 0.038 0.024 0.011 0. 1.785 52.415 1.314
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A F A A C A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 94 599 104 0 212 278 151 180
normalized size 1 6.37 1.11 0. 2.26 2.96 1.61 1.91
time (sec) N/A 1.296 0.06 180. 0.978 1.817 14.765 1.275
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 94 404 107 0 0 0 0 0
normalized size 1 4.3 1.14 0. 0. 0. 0. 0.
time (sec) N/A 0.696 0.134 180. 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 144 144 177 0 0 0 0 0
normalized size 1 1. 1.23 0. 0. 0. 0. 0.
time (sec) N/A 0.324 0.066 0.483 0. 0. 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A A F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 99 207 114 144 0 0 0 0
normalized size 1 2.09 1.15 1.45 0. 0. 0. 0.
time (sec) N/A 0.529 0.09 0.004 0. 0. 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A B B A A F
verified N/A NO Yes TBD TBD TBD TBD TBD
size 97 770 131 682002 247 308 172 0
normalized size 1 7.94 1.35 7030.95 2.55 3.18 1.77 0.
time (sec) N/A 1.53 0.081 88.027 1.057 1.799 41.77 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1214 1214 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.712 5.646 0.685 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1172 1172 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.208 2.978 0.641 0. 0. 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1549 1549 565 0 0 0 0 0
normalized size 1 1. 0.36 0. 0. 0. 0. 0.
time (sec) N/A 2.249 3.406 0.549 0. 0. 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1117 1117 568 0 0 0 0 0
normalized size 1 1. 0.51 0. 0. 0. 0. 0.
time (sec) N/A 2.15 3.037 0.656 0. 0. 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1263 1263 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.585 2.662 0.603 0. 0. 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1337 1337 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.79 2.61 0.665 0. 0. 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 2.437 0.664 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 1.625 0.38 0. 0. 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 68 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.056 0.067 0.294 0. 0. 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 0.403 0.185 0. 0. 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.39 0.146 0. 0. 0. 0.
Problem 187 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 88 88 114 84 116 213 0 142
normalized size 1 1. 1.3 0.95 1.32 2.42 0. 1.61
time (sec) N/A 0.042 0.031 0.026 1.023 1.787 0. 1.204
Problem 188 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 75 75 101 75 105 185 0 131
normalized size 1 1. 1.35 1. 1.4 2.47 0. 1.75
time (sec) N/A 0.035 0.024 0.026 0.958 1.779 0. 1.17
Problem 189 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 62 62 88 66 93 159 0 119
normalized size 1 1. 1.42 1.06 1.5 2.56 0. 1.92
time (sec) N/A 0.024 0.021 0.027 1.002 1.761 0. 1.194
Problem 190 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 39 39 42 50 72 131 0 90
normalized size 1 1. 1.08 1.28 1.85 3.36 0. 2.31
time (sec) N/A 0.02 0.024 0.024 0.971 1.719 0. 1.22
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 29 63 82 0 0 0
normalized size 1 1. 1. 2.17 2.83 0. 0. 0.
time (sec) N/A 0.032 0.011 0.036 1.493 0. 0. 0.
Problem 192 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 40 40 67 55 69 122 231 90
normalized size 1 1. 1.68 1.38 1.72 3.05 5.78 2.25
time (sec) N/A 0.023 0.024 0.033 0.961 1.746 40.854 1.332
Problem 193 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 60 60 86 64 86 149 342 105
normalized size 1 1. 1.43 1.07 1.43 2.48 5.7 1.75
time (sec) N/A 0.026 0.026 0.033 0.956 1.652 179.21 1.327
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 99 73 97 174 0 119
normalized size 1 1. 1.36 1. 1.33 2.38 0. 1.63
time (sec) N/A 0.034 0.03 0.037 0.957 1.627 0. 1.399
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A B A A F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 211 0 224 396 358 662 0 0
normalized size 1 0. 1.06 1.88 1.7 3.14 0. 0.
time (sec) N/A 0.025 0.112 0.056 0.988 2.126 0. 0.
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A B A A F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 173 0 194 358 325 567 0 0
normalized size 1 0. 1.12 2.07 1.88 3.28 0. 0.
time (sec) N/A 0.024 0.104 0.049 1.005 2.187 0. 0.
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A B B A F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 129 0 160 317 290 479 0 0
normalized size 1 0. 1.24 2.46 2.25 3.71 0. 0.
time (sec) N/A 0.014 0.086 0.051 1.027 2.204 0. 0.
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A B B B F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 85 0 115 272 236 382 0 0
normalized size 1 0. 1.35 3.2 2.78 4.49 0. 0.
time (sec) N/A 0.006 0.061 0.05 1.014 1.991 0. 0.
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 164 742 0 0 0 0
normalized size 1 1. 1.13 5.12 0. 0. 0. 0.
time (sec) N/A 0.317 0.083 0.316 0. 0. 0. 0.
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A B B B A F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 85 0 129 292 235 375 680 0
normalized size 1 0. 1.52 3.44 2.76 4.41 8. 0.
time (sec) N/A 0.024 0.11 0.054 1.02 1.834 42.93 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A B B A A F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 133 0 178 332 316 471 972 0
normalized size 1 0. 1.34 2.5 2.38 3.54 7.31 0.
time (sec) N/A 0.024 0.128 0.062 0.985 1.924 179.052 0.
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C B F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 374 0 418 1518 2662 0 0 0
normalized size 1 0. 1.12 4.06 7.12 0. 0. 0.
time (sec) N/A 0.023 1.194 1.179 4.152 0. 0. 0.
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C B F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 304 0 351 1423 2132 0 0 0
normalized size 1 0. 1.15 4.68 7.01 0. 0. 0.
time (sec) N/A 0.024 0.789 0.326 3.732 0. 0. 0.
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C B F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 234 0 285 1339 1598 0 0 0
normalized size 1 0. 1.22 5.72 6.83 0. 0. 0.
time (sec) N/A 0.014 0.527 0.286 3.391 0. 0. 0.
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 142 0 201 6235 0 0 0 0
normalized size 1 0. 1.42 43.91 0. 0. 0. 0.
time (sec) N/A 0.006 0.277 0.388 0. 0. 0. 0.
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 224 224 248 1542 0 0 0 0
normalized size 1 1. 1.11 6.88 0. 0. 0. 0.
time (sec) N/A 0.512 0.199 0.173 0. 0. 0. 0.
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C B F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 142 0 230 5199 713 0 0 0
normalized size 1 0. 1.62 36.61 5.02 0. 0. 0.
time (sec) N/A 0.022 0.307 0.412 5.865 0. 0. 0.
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C B F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 234 0 333 1365 949 0 0 0
normalized size 1 0. 1.42 5.83 4.06 0. 0. 0.
time (sec) N/A 0.023 0.692 0.31 6.649 0. 0. 0.
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 31 35 32 112 128 49
normalized size 1 1. 0.82 0.92 0.84 2.95 3.37 1.29
time (sec) N/A 0.016 0.016 0.024 0.971 1.653 18.109 1.179
Problem 210 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 25 30 26 97 39 42
normalized size 1 1. 0.81 0.97 0.84 3.13 1.26 1.35
time (sec) N/A 0.013 0.011 0.024 0.977 1.706 1.717 1.168
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 20 17 22 76 87 34
normalized size 1 1. 1. 0.85 1.1 3.8 4.35 1.7
time (sec) N/A 0.009 0.008 0.025 0.954 1.708 0.892 1.182
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 24 29 24 100 126 41
normalized size 1 1. 1. 1.21 1. 4.17 5.25 1.71
time (sec) N/A 0.01 0.018 0.03 0.958 1.808 2.417 1.164
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) C F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 190 190 222 194 0 4629 0 296
normalized size 1 1. 1.17 1.02 0. 24.36 0. 1.56
time (sec) N/A 0.301 0.053 0.036 0. 10.99 0. 1.492
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 75 57 78 142 0 97
normalized size 1 1. 1.53 1.16 1.59 2.9 0. 1.98
time (sec) N/A 0.034 0.026 0.029 0.995 1.856 0. 1.228
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 190 190 222 194 0 4730 0 0
normalized size 1 1. 1.17 1.02 0. 24.89 0. 0.
time (sec) N/A 0.238 0.034 0.036 0. 10.529 0. 0.
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) C F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 170 170 141 179 0 4289 0 251
normalized size 1 1. 0.83 1.05 0. 25.23 0. 1.48
time (sec) N/A 0.287 0.101 0.032 0. 10.769 0. 1.199
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 32 63 84 0 0 0
normalized size 1 1. 0.94 1.85 2.47 0. 0. 0.
time (sec) N/A 0.033 0.02 0.036 1.594 0. 0. 0.
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 172 172 205 167 0 647 0 232
normalized size 1 1. 1.19 0.97 0. 3.76 0. 1.35
time (sec) N/A 0.221 0.034 0.034 0. 1.933 0. 1.47
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 188 188 220 180 0 618 0 270
normalized size 1 1. 1.17 0.96 0. 3.29 0. 1.44
time (sec) N/A 0.287 0.058 0.037 0. 1.996 0. 1.514
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 73 55 69 132 0 90
normalized size 1 1. 1.55 1.17 1.47 2.81 0. 1.91
time (sec) N/A 0.032 0.029 0.036 0.985 1.878 0. 1.212
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A B B B F(-1) F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 101 0 122 284 251 402 0 0
normalized size 1 0. 1.21 2.81 2.49 3.98 0. 0.
time (sec) N/A 0.024 0.093 0.049 1.009 1.998 0. 0.
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 156 167 785 0 0 0 0
normalized size 1 1. 1.07 5.03 0. 0. 0. 0.
time (sec) N/A 0.32 0.132 0.334 0. 0. 0. 0.
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F B B F(-1) F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 96 0 123 0 236 402 0 0
normalized size 1 0. 1.28 0. 2.46 4.19 0. 0.
time (sec) N/A 0.024 0.139 0.28 0.998 1.891 0. 0.
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 73 0 0 0 0 0
normalized size 1 1. 1.11 0. 0. 0. 0. 0.
time (sec) N/A 0.031 0.052 0.12 0. 0. 0. 0.
Problem 225 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 67 67 73 0 0 0 0 0
normalized size 1 1. 1.09 0. 0. 0. 0. 0.
time (sec) N/A 0.024 0.045 0.21 0. 0. 0. 0.
Problem 226 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 58 58 58 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 0.032 0.191 0. 0. 0. 0.
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 39 76 0 456 0 0
normalized size 1 1. 1.08 2.11 0. 12.67 0. 0.
time (sec) N/A 0.035 0.075 0.036 0. 1.819 0. 0.
Problem 228 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 67 67 66 0 0 0 0 0
normalized size 1 1. 0.99 0. 0. 0. 0. 0.
time (sec) N/A 0.032 0.061 0.102 0. 0. 0. 0.
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 73 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.031 0.041 0.109 0. 0. 0. 0.
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 73 0 0 0 0 0
normalized size 1 1. 1.01 0. 0. 0. 0. 0.
time (sec) N/A 0.034 0.042 0.112 0. 0. 0. 0.
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 8.618 0.162 0. 0. 0. 0.
Problem 232 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.006 1.897 0.187 0. 0. 0. 0.
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 148 148 146 880 0 0 0 0
normalized size 1 1. 0.99 5.95 0. 0. 0. 0.
time (sec) N/A 0.313 0.128 0.33 0. 0. 0. 0.
Problem 234 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 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 12.352 0.109 0. 0. 0. 0.
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 12.317 0.109 0. 0. 0. 0.
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 33 61 198 423 0 0
normalized size 1 1. 1.1 2.03 6.6 14.1 0. 0.
time (sec) N/A 0.021 0.039 0.034 1.266 1.731 0. 0.
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 22 85 140 0 0 0
normalized size 1 1. 0.92 3.54 5.83 0. 0. 0.
time (sec) N/A 0.021 0.011 0.095 0.989 0. 0. 0.
Problem 238 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 19 19 17 30 20 63 15 38
normalized size 1 1. 0.89 1.58 1.05 3.32 0.79 2.
time (sec) N/A 0.006 0.002 0.043 0.955 1.607 0.258 1.18
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 7.971 0.232 0. 0. 0. 0.
Problem 240 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 5.791 0.214 0. 0. 0. 0.
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 88 77 0 0 0 0 0
normalized size 1 1.05 0.92 0. 0. 0. 0. 0.
time (sec) N/A 0.044 0.087 0.279 0. 0. 0. 0.
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.027 0.373 0.058 0. 0. 0. 0.
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 1.753 0.275 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 [178] had the largest ratio of [ 2.417 ]

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 4 3 1. 12 0.25
2 A 4 3 1. 12 0.25
3 A 4 3 1. 12 0.25
4 A 4 3 1. 12 0.25
5 A 3 3 1. 10 0.3
6 A 3 2 1. 8 0.25
7 A 1 1 1. 12 0.083
8 A 5 5 1. 12 0.417
9 A 3 3 1. 12 0.25
10 A 4 3 1. 12 0.25
11 A 4 3 1. 12 0.25
12 A 4 3 1. 12 0.25
13 A 16 7 1. 14 0.5
14 A 14 9 1. 14 0.643
15 A 11 7 1. 14 0.5
16 A 9 8 1. 14 0.571
17 A 6 5 1. 12 0.417
18 A 5 5 1. 10 0.5
19 A 6 5 1. 14 0.357
20 A 4 4 1. 14 0.286
21 A 8 7 1. 14 0.5
22 A 8 7 1. 14 0.5
23 A 13 8 1. 14 0.571
24 A 33 11 1. 14 0.786
25 A 24 11 1. 14 0.786
26 A 18 10 1. 14 0.714
27 A 12 9 1. 14 0.643
28 A 8 8 1. 12 0.667
29 A 5 6 1. 10 0.6
30 A 8 6 1. 14 0.429
31 A 5 6 1. 14 0.429
32 A 7 6 1. 14 0.429
33 A 14 11 1. 14 0.786
34 A 16 8 1. 14 0.571
35 A 7 6 1. 16 0.375
36 A 6 6 1. 16 0.375
37 A 6 6 1. 16 0.375
38 A 5 5 1. 16 0.312
39 A 5 5 1. 16 0.312
40 A 6 6 1. 16 0.375
41 A 6 6 1. 16 0.375
42 A 7 6 1. 16 0.375
43 A 0 0 0. 0 0.
44 A 0 0 0. 0 0.
45 A 2 2 1. 14 0.143
46 A 0 0 0. 0 0.
47 A 0 0 0. 0 0.
48 A 0 0 0. 0 0.
49 A 0 0 0. 0 0.
50 A 5 4 1. 14 0.286
51 A 4 3 1. 14 0.214
52 A 4 4 1. 14 0.286
53 A 2 2 1. 12 0.167
54 A 2 2 1. 14 0.143
55 A 5 5 1. 14 0.357
56 A 4 4 1. 14 0.286
57 A 4 3 1. 14 0.214
58 A 5 5 1. 14 0.357
59 A 5 5 1. 14 0.357
60 A 5 4 1. 10 0.4
61 A 4 4 1. 14 0.286
62 A 5 5 1. 14 0.357
63 A 5 5 1. 14 0.357
64 C 62 19 5.09 16 1.187
65 B 53 19 3.67 16 1.187
66 C 44 16 5.76 16 1.
67 B 28 12 2.2 14 0.857
68 A 7 6 1. 16 0.375
69 B 24 13 2.72 16 0.812
70 C 46 23 4.09 16 1.438
71 A 102 26 1. 16 1.625
72 A 86 26 1. 16 1.625
73 A 69 21 1. 12 1.75
74 A 47 21 1. 16 1.313
75 A 64 24 1. 16 1.5
76 A 77 24 1. 16 1.5
77 B 155 30 3.4 16 1.875
78 B 82 23 2.91 14 1.643
79 A 9 7 1. 16 0.438
80 F 0 0 N/A 0 N/A
81 F 0 0 N/A 0 N/A
82 A 17 14 1. 18 0.778
83 A 17 14 1. 18 0.778
84 A 16 13 1. 18 0.722
85 A 16 13 1. 18 0.722
86 A 16 13 1. 18 0.722
87 A 16 13 1. 18 0.722
88 A 17 14 1. 18 0.778
89 A 17 14 1. 18 0.778
90 F 0 0 N/A 0 N/A
91 F 0 0 N/A 0 N/A
92 F 0 0 N/A 0 N/A
93 F 0 0 N/A 0 N/A
94 A 0 0 0. 0 0.
95 A 0 0 0. 0 0.
96 A 3 3 1. 16 0.188
97 A 0 0 0. 0 0.
98 A 0 0 0. 0 0.
99 A 5 4 1. 14 0.286
100 A 4 3 1. 14 0.214
101 A 4 4 1. 14 0.286
102 A 2 2 1. 14 0.143
103 A 2 2 1. 14 0.143
104 A 5 5 1. 14 0.357
105 A 4 4 1. 14 0.286
106 A 4 3 1. 14 0.214
107 A 12 8 1. 14 0.571
108 A 9 8 1. 10 0.8
109 A 11 7 1. 14 0.5
110 A 9 9 1. 14 0.643
111 A 12 8 1. 14 0.571
112 A 9 9 1. 14 0.643
113 A 11 7 1. 12 0.583
114 A 8 8 1. 14 0.571
115 A 12 8 1. 14 0.571
116 C 62 19 5.09 16 1.187
117 B 53 19 3.67 16 1.187
118 C 44 16 5.76 16 1.
119 B 28 12 2.16 16 0.75
120 A 7 6 1. 16 0.375
121 B 24 13 2.63 16 0.812
122 C 46 23 4.09 16 1.438
123 B 59 24 2.92 16 1.5
124 B 239 32 6.15 16 2.
125 B 155 30 3.45 16 1.875
126 B 82 23 3. 16 1.438
127 A 9 7 1. 16 0.438
128 F 0 0 N/A 0 N/A
129 F 0 0 N/A 0 N/A
130 A 0 0 0. 0 0.
131 A 0 0 0. 0 0.
132 A 3 3 1. 16 0.188
133 A 0 0 0. 0 0.
134 A 0 0 0. 0 0.
135 A 5 4 1. 14 0.286
136 A 5 4 1. 14 0.286
137 A 4 4 1. 12 0.333
138 A 4 3 1. 10 0.3
139 A 2 2 1. 14 0.143
140 A 2 2 1. 14 0.143
141 A 4 4 1. 14 0.286
142 A 5 4 1. 14 0.286
143 C 88 34 6.6 16 2.125
144 B 73 34 4.89 16 2.125
145 C 58 32 6.92 14 2.286
146 B 31 14 5. 12 1.167
147 A 7 6 1. 16 0.375
148 B 28 12 2.36 16 0.75
149 C 66 23 8.13 16 1.438
150 F 0 0 N/A 0 N/A
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 A 9 7 1. 16 0.438
155 B 82 23 3.07 16 1.438
156 F 0 0 N/A 0 N/A
157 A 6 5 1. 14 0.357
158 A 5 4 1. 14 0.286
159 A 5 5 1. 14 0.357
160 A 3 3 1. 12 0.25
161 A 2 2 1. 14 0.143
162 A 2 2 1. 14 0.143
163 A 5 5 1. 14 0.357
164 A 5 4 1. 14 0.286
165 A 6 6 1. 14 0.429
166 A 6 6 1. 14 0.429
167 A 6 5 1. 10 0.5
168 A 5 5 1. 14 0.357
169 A 6 6 1. 14 0.429
170 A 6 6 1. 14 0.429
171 C 59 33 6.37 16 2.063
172 B 34 19 4.3 14 1.357
173 A 7 6 1. 16 0.375
174 B 28 12 2.09 16 0.75
175 C 67 23 7.94 16 1.438
176 A 97 33 1. 16 2.063
177 A 79 33 1. 16 2.063
178 A 99 29 1. 12 2.417
179 A 71 29 1. 16 1.812
180 A 104 30 1. 16 1.875
181 A 129 30 1. 16 1.875
182 A 0 0 0. 0 0.
183 A 0 0 0. 0 0.
184 A 4 4 1. 16 0.25
185 A 0 0 0. 0 0.
186 A 0 0 0. 0 0.
187 A 7 4 1. 16 0.25
188 A 6 4 1. 16 0.25
189 A 5 4 1. 14 0.286
190 A 5 4 1. 12 0.333
191 A 2 2 1. 16 0.125
192 A 4 4 1. 16 0.25
193 A 5 4 1. 16 0.25
194 A 6 4 1. 16 0.25
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. 18 0.333
200 F 0 0 N/A 0 N/A
201 F 0 0 N/A 0 N/A
202 F 0 0 N/A 0 N/A
203 F 0 0 N/A 0 N/A
204 F 0 0 N/A 0 N/A
205 F 0 0 N/A 0 N/A
206 A 9 7 1. 18 0.389
207 F 0 0 N/A 0 N/A
208 F 0 0 N/A 0 N/A
209 A 3 2 1. 12 0.167
210 A 3 2 1. 12 0.167
211 A 2 2 1. 12 0.167
212 A 4 4 1. 12 0.333
213 A 13 9 1. 16 0.562
214 A 5 5 1. 16 0.312
215 A 13 9 1. 14 0.643
216 A 13 8 1. 12 0.667
217 A 2 2 1. 16 0.125
218 A 12 8 1. 16 0.5
219 A 13 9 1. 16 0.562
220 A 5 5 1. 16 0.312
221 F 0 0 N/A 0 N/A
222 A 7 6 1. 18 0.333
223 F 0 0 N/A 0 N/A
224 A 2 2 1. 14 0.143
225 A 2 2 1. 12 0.167
226 A 3 2 1. 10 0.2
227 A 2 2 1. 14 0.143
228 A 2 2 1. 14 0.143
229 A 2 2 1. 14 0.143
230 A 2 2 1. 14 0.143
231 A 0 0 0. 0 0.
232 A 0 0 0. 0 0.
233 A 7 6 1. 16 0.375
234 A 0 0 0. 0 0.
235 A 0 0 0. 0 0.
236 A 2 2 1. 10 0.2
237 A 2 2 1. 10 0.2
238 A 3 3 1. 4 0.75
239 A 0 0 0. 0 0.
240 A 0 0 0. 0 0.
241 A 3 3 1.05 16 0.188
242 A 0 0 0. 0 0.
243 A 0 0 0. 0 0.

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