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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, 150, 157, 176, 183, 186, 187, 188, 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, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247 }

B grade: { }

C grade: { }

F grade: { 146, 147, 148, 149, 151, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193}

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 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, 148, 150, 152, 153, 154, 155, 156, 157, 158, 159, 160, 162, 164, 165, 166, 176, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 193, 194, 195, 196, 197, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 213, 215, 216, 226, 228, 229, 232, 233, 234, 235, 236, 237, 239, 240, 241, 242, 243, 244, 245, 246, 247 }

B grade: { 41, 42, 146, 161, 163, 169, 170, 171, 172, 173, 174, 175, 177, 178, 190, 192, 230, 231 }

C grade: { 8, 10, 12, 18, 19, 20, 21, 36, 145, 147, 149, 151, 167, 168, 198, 199, 211, 212, 214, 217, 218, 219, 220, 221, 222, 223, 224, 225, 227, 238 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 4, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, 67, 68, 73, 81, 82, 83, 84, 85, 86, 88, 90, 95, 96, 105, 106, 112, 113, 114, 115, 116, 117, 118, 119, 120, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 146, 153, 186, 187, 188, 194, 195, 196, 197, 198, 199, 200, 201, 202, 206, 207, 208, 209, 210, 211, 212, 213, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247 }

B grade: { 3, 5, 6, 7, 8, 10, 45, 57, 58, 59, 60, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 87, 89, 91, 92, 93, 94, 97, 98, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110, 111, 121, 122, 123, 124, 144, 145, 150, 157, 176, 183, 237 }

C grade: { 147, 148, 149, 151, 152, 154, 155, 156, 158, 159, 205, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 234, 235, 236 }

F grade: { 22, 23, 40, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193, 203, 204, 228, 229, 230, 231, 232, 233 }

2.1.4 Maxima

A grade: { 5, 6, 7, 8, 24, 25, 37, 38, 39, 44, 45, 46, 47, 48, 49, 50, 56, 59, 60, 61, 62, 65, 66, 69, 70, 71, 72, 73, 74, 80, 82, 90, 91, 92, 93, 94, 95, 96, 105, 106, 107, 108, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 176, 183, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 224, 225, 234, 235, 236, 237, 238, 239, 243, 247

B grade: { 1, 2, 3, 4, 9, 10, 11, 12, 26, 41, 42, 43, 51, 52, 53, 54, 55, 57, 58, 63, 64, 75, 76, 77, 78, 79, 85, 87, 89, 97, 98, 99, 100, 101, 102, 103, 104, 186, 187, 188 }

C grade: { 27, 28, 29, 30, 31, 32 }

F grade: { 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 33, 34, 35, 36, 40, 67, 68, 81, 83, 84, 86, 88, 109, 110, 111, 112, 113, 114, 125, 126, 127, 128, 129, 130, 131, 132, 144, 145, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 222, 223, 226, 227, 228, 229, 230, 231, 232, 233, 240, 241, 242, 244, 245, 246 }

2.1.5 FriCAS

A grade: { 61, 65, 66, 71, 72, 84, 90, 93, 94, 95, 106, 112, 136, 137, 138, 139, 146, 147, 148, 149, 150, 152, 153, 154, 155, 159, 209, 215, 218, 219, 220, 224, 236, 237, 241, 243, 245, 247 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 67, 68, 69, 70, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 140, 141, 142, 143, 144, 151, 156, 157, 158, 176, 183, 186, 187, 188, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 212, 213, 214, 216, 217, 221, 222, 223, 225, 226, 227, 234, 235, 238, 239, 240, 242, 244, 246 }

C grade: { 27, 28, 29, 30, 31, 32, 145 }

F grade: { 22, 23, 40, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193, 228, 229, 230, 231, 232, 233 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 41, 42, 43, 44, 45, 46, 47, 48, 49, 57, 58, 59, 60, 61, 62, 65, 66, 95, 106, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 150, 157, 176, 186, 187, 196, 197, 247 }

B grade: { 70, 72, 92, 94, 115, 116, 117, 118, 119, 120, 183 }

C grade: { }

F grade: { 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 50, 51, 52, 53, 54, 55, 56, 63, 64, 67, 68, 69, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 114, 121, 122, 123, 124, 133, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 188, 189, 190, 191, 192, 193, 194, 195, 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, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246 }

2.1.7 Giac

A grade: { 1, 2, 3, 10, 12, 24, 33, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 88, 90, 91, 92, 93, 94, 95, 98, 99, 100, 101, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 131, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 183, 187, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 220, 221, 222, 223, 224, 225, 234, 235, 236, 237, 238, 239, 243, 247 }

B grade: { 4, 5, 6, 7, 8, 9, 11, 18, 21, 25, 26, 34, 35, 50, 51, 55, 56, 75, 85, 87, 89, 96, 97, 102, 103, 104, 105, 109, 125, 126, 127, 128, 129, 130, 132, 143, 176, 186, 188, 226, 227 }

C grade: { 27, 28, 29, 30, 31, 32 }

F grade: { 13, 14, 15, 16, 17, 19, 20, 22, 23, 36, 40, 67, 68, 144, 145, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 184, 185, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 218, 219, 228, 229, 230, 231, 232, 233, 240, 241, 242, 244, 245, 246 }

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 B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 53 67 155 717 39 100
normalized size 1 1. 1.23 1.56 3.6 16.67 0.91 2.33
time (sec) N/A 0.024 0.019 0.005 1.043 2.366 0.653 1.199
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 37 56 138 2642 42 99
normalized size 1 1. 0.88 1.33 3.29 62.9 1. 2.36
time (sec) N/A 0.033 0.086 0.004 1.547 2.38 0.471 1.182
Problem 3 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 28 28 38 54 96 327 27 70
normalized size 1 1. 1.36 1.93 3.43 11.68 0.96 2.5
time (sec) N/A 0.016 0.009 0.003 1.055 2.083 0.342 1.192
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 43 82 930 31 73
normalized size 1 1. 1. 1.59 3.04 34.44 1.15 2.7
time (sec) N/A 0.017 0.012 0.003 1.525 2.262 0.243 1.191
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 23 41 34 82 15 38
normalized size 1 1. 1.77 3.15 2.62 6.31 1.15 2.92
time (sec) N/A 0.009 0.007 0.003 1.036 2.328 0.18 1.179
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 30 15 88 17 36
normalized size 1 1. 1. 2.73 1.36 8. 1.55 3.27
time (sec) N/A 0.006 0.005 0.003 1.018 2.19 0.151 1.222
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 19 30 15 88 27 38
normalized size 1 1. 1.73 2.73 1.36 8. 2.45 3.45
time (sec) N/A 0.006 0.009 0.002 1.026 2.447 0.441 1.183
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 27 41 34 82 36 38
normalized size 1 1. 2.08 3.15 2.62 6.31 2.77 2.92
time (sec) N/A 0.008 0.009 0. 1.044 2.277 1.599 1.238
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 34 43 107 930 61 74
normalized size 1 1. 1.26 1.59 3.96 34.44 2.26 2.74
time (sec) N/A 0.018 0.069 0.002 1.029 2.385 4.262 1.221
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 31 54 96 286 49 70
normalized size 1 1. 1.11 1.93 3.43 10.21 1.75 2.5
time (sec) N/A 0.016 0.01 0.002 1.043 2.111 9.256 1.218
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 44 56 165 2642 75 103
normalized size 1 1. 1.05 1.33 3.93 62.9 1.79 2.45
time (sec) N/A 0.033 0.159 0. 1.041 2.391 19.782 1.208
Problem 12 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 43 43 31 67 155 666 63 100
normalized size 1 1. 0.72 1.56 3.6 15.49 1.47 2.33
time (sec) N/A 0.024 0.009 0.002 1.038 2.288 44.837 1.168
Problem 13 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 97 97 83 80 0 4136 0 0
normalized size 1 1. 0.86 0.82 0. 42.64 0. 0.
time (sec) N/A 0.07 0.232 0.032 0. 2.673 0. 0.
Problem 14 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 78 78 68 63 0 2653 0 0
normalized size 1 1. 0.87 0.81 0. 34.01 0. 0.
time (sec) N/A 0.049 0.205 0.018 0. 2.553 0. 0.
Problem 15 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 1755 0 0
normalized size 1 1. 0.81 0.83 0. 23.4 0. 0.
time (sec) N/A 0.051 0.085 0.017 0. 2.582 0. 0.
Problem 16 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 1635 0 0
normalized size 1 1. 0.88 0.81 0. 28.19 0. 0.
time (sec) N/A 0.032 0.038 0.025 0. 2.822 0. 0.
Problem 17 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 1647 0 0
normalized size 1 1. 0.86 0.81 0. 28.89 0. 0.
time (sec) N/A 0.032 0.034 0.033 0. 2.685 0. 0.
Problem 18 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 2574 0 207
normalized size 1 1. 0.46 0.83 0. 33. 0. 2.65
time (sec) N/A 0.048 0.074 0.019 0. 2.709 0. 1.288
Problem 19 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 79 79 38 64 0 3934 0 0
normalized size 1 1. 0.48 0.81 0. 49.8 0. 0.
time (sec) N/A 0.049 0.077 0.02 0. 2.555 0. 0.
Problem 20 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 100 100 38 83 0 5796 0 0
normalized size 1 1. 0.38 0.83 0. 57.96 0. 0.
time (sec) N/A 0.067 0.11 0.02 0. 2.693 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 26 102 0 563 63 258
normalized size 1 1. 0.38 1.48 0. 8.16 0.91 3.74
time (sec) N/A 0.06 0.026 0.023 0. 2.217 2.941 1.243
Problem 22 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 0.045 0.174 0. 0. 0. 0.
Problem 23 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 0.026 0.042 0.176 0. 0. 0. 0.
Problem 24 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 35 35 28 30 57 1368 0 70
normalized size 1 1. 0.8 0.86 1.63 39.09 0. 2.
time (sec) N/A 0.021 0.023 0.025 1.574 2.426 0. 1.209
Problem 25 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 16 16 16 26 26 196 0 42
normalized size 1 1. 1. 1.62 1.62 12.25 0. 2.62
time (sec) N/A 0.015 0.006 0.033 1.574 2.25 0. 1.196
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 29 42 198 0 50
normalized size 1 1. 1. 1.81 2.62 12.38 0. 3.12
time (sec) N/A 0.015 0.008 0.039 1.599 2.27 0. 1.192
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 56 67 153 467 0 192
normalized size 1 1. 0.64 0.76 1.74 5.31 0. 2.18
time (sec) N/A 0.049 0.295 0.026 1.694 2.338 0. 1.36
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 46 53 89 252 0 124
normalized size 1 1. 0.77 0.88 1.48 4.2 0. 2.07
time (sec) N/A 0.032 0.094 0.015 1.601 2.27 0. 1.298
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 45 38 55 0 73
normalized size 1 1. 1. 1.45 1.23 1.77 0. 2.35
time (sec) N/A 0.018 0.033 0.029 1.622 2.344 0. 1.184
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 39 52 61 54 0 85
normalized size 1 1. 1.26 1.68 1.97 1.74 0. 2.74
time (sec) N/A 0.017 0.079 0.027 1.573 2.321 0. 1.229
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 51 79 115 252 0 151
normalized size 1 1. 0.85 1.32 1.92 4.2 0. 2.52
time (sec) N/A 0.031 0.126 0.019 1.63 2.276 0. 1.266
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 63 91 177 466 0 182
normalized size 1 1. 0.72 1.03 2.01 5.3 0. 2.07
time (sec) N/A 0.048 0.236 0.017 1.607 2.328 0. 1.385
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 38 43 0 374 0 74
normalized size 1 1. 0.67 0.75 0. 6.56 0. 1.3
time (sec) N/A 0.038 0.038 0.039 0. 2.233 0. 1.211
Problem 34 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 86 86 55 76 0 4099 0 462
normalized size 1 1. 0.64 0.88 0. 47.66 0. 5.37
time (sec) N/A 0.037 0.059 0.03 0. 2.724 0. 1.31
Problem 35 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 63 63 40 62 0 1237 0 155
normalized size 1 1. 0.63 0.98 0. 19.63 0. 2.46
time (sec) N/A 0.03 0.033 0.036 0. 2.318 0. 1.242
Problem 36 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 64 64 26 65 0 1763 0 0
normalized size 1 1. 0.41 1.02 0. 27.55 0. 0.
time (sec) N/A 0.03 0.017 0.04 0. 2.451 0. 0.
Problem 37 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 69 69 56 46 111 6368 0 61
normalized size 1 1. 0.81 0.67 1.61 92.29 0. 0.88
time (sec) N/A 0.026 0.148 0.026 1.61 2.527 0. 1.185
Problem 38 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 19 32 26 647 0 22
normalized size 1 1. 0.61 1.03 0.84 20.87 0. 0.71
time (sec) N/A 0.014 0.017 0.032 1.603 2.321 0. 1.194
Problem 39 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 19 32 31 668 0 26
normalized size 1 1. 0.61 1.03 1. 21.55 0. 0.84
time (sec) N/A 0.014 0.033 0.039 1.648 2.133 0. 1.261
Problem 40 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 0.039 0.052 3.984 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 202 81 408 2376 95 101
normalized size 1 1. 2.02 0.81 4.08 23.76 0.95 1.01
time (sec) N/A 0.072 1.608 0.006 1.591 2.358 0.616 1.203
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 178 65 265 1470 76 86
normalized size 1 1. 2.31 0.84 3.44 19.09 0.99 1.12
time (sec) N/A 0.053 1.088 0.003 1.658 2.341 0.422 1.175
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 103 49 157 780 61 72
normalized size 1 1. 1.84 0.88 2.8 13.93 1.09 1.29
time (sec) N/A 0.036 0.898 0.001 1.612 2.156 0.28 1.171
Problem 44 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 36 36 58 33 68 308 44 53
normalized size 1 1. 1.61 0.92 1.89 8.56 1.22 1.47
time (sec) N/A 0.021 0.505 0.003 1.08 2.199 0.296 1.162
Problem 45 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 28 28 39 54 42 136 73 36
normalized size 1 1. 1.39 1.93 1.5 4.86 2.61 1.29
time (sec) N/A 0.013 0.101 0.017 1.084 2.19 0.827 1.189
Problem 46 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 51 51 60 72 58 270 223 54
normalized size 1 1. 1.18 1.41 1.14 5.29 4.37 1.06
time (sec) N/A 0.028 0.171 0.018 1.081 2.224 1.645 1.17
Problem 47 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 73 73 83 90 76 428 430 69
normalized size 1 1. 1.14 1.23 1.04 5.86 5.89 0.95
time (sec) N/A 0.044 0.246 0.019 1.136 2.118 2.017 1.196
Problem 48 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 96 96 88 108 90 594 694 84
normalized size 1 1. 0.92 1.12 0.94 6.19 7.23 0.88
time (sec) N/A 0.062 0.249 0.02 1.078 2.156 2.608 1.186
Problem 49 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 121 121 109 126 105 798 1018 99
normalized size 1 1. 0.9 1.04 0.87 6.6 8.41 0.82
time (sec) N/A 0.082 0.276 0.027 1.096 2.197 4.176 1.204
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 65 43 112 1470 0 189
normalized size 1 1. 1.14 0.75 1.96 25.79 0. 3.32
time (sec) N/A 0.041 0.201 0.019 1.633 2.344 0. 1.277
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 39 35 95 871 0 130
normalized size 1 1. 0.87 0.78 2.11 19.36 0. 2.89
time (sec) N/A 0.031 0.164 0.013 1.589 2.327 0. 1.174
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 33 27 77 451 0 70
normalized size 1 1. 1. 0.82 2.33 13.67 0. 2.12
time (sec) N/A 0.021 0.067 0.013 1.566 2.255 0. 1.173
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 21 17 58 182 0 36
normalized size 1 1. 1. 0.81 2.76 8.67 0. 1.71
time (sec) N/A 0.011 0.045 0.032 1.601 2.22 0. 1.202
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 32 27 77 301 0 68
normalized size 1 1. 1. 0.84 2.41 9.41 0. 2.12
time (sec) N/A 0.023 0.072 0.033 1.586 2.291 0. 1.182
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 53 35 93 579 0 130
normalized size 1 1. 1.08 0.71 1.9 11.82 0. 2.65
time (sec) N/A 0.031 0.133 0.014 1.607 2.34 0. 1.204
Problem 56 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 61 61 62 43 107 921 0 189
normalized size 1 1. 1.02 0.7 1.75 15.1 0. 3.1
time (sec) N/A 0.041 0.229 0.017 1.64 2.228 0. 1.246
Problem 57 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 142 142 114 322 419 6413 211 305
normalized size 1 1. 0.8 2.27 2.95 45.16 1.49 2.15
time (sec) N/A 0.211 0.64 0.005 1.655 2.616 0.757 1.217
Problem 58 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 91 246 271 3318 144 209
normalized size 1 1. 0.9 2.44 2.68 32.85 1.43 2.07
time (sec) N/A 0.124 0.334 0.006 1.871 2.462 0.527 1.199
Problem 59 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 69 69 67 173 159 1563 100 138
normalized size 1 1. 0.97 2.51 2.3 22.65 1.45 2.
time (sec) N/A 0.065 0.327 0.004 1.783 2.293 0.341 1.237
Problem 60 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 54 116 66 535 54 82
normalized size 1 1. 1.42 3.05 1.74 14.08 1.42 2.16
time (sec) N/A 0.023 0.095 0.004 1.127 2.215 0.224 1.238
Problem 61 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 76 149 224 85
normalized size 1 1. 1.28 1.52 1.52 2.98 4.48 1.7
time (sec) N/A 0.054 0.082 0.019 1.177 2.322 2.365 1.241
Problem 62 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 85 85 94 101 171 980 3599 188
normalized size 1 1. 1.11 1.19 2.01 11.53 42.34 2.21
time (sec) N/A 0.09 1.059 0.027 1.158 2.393 32.424 1.215
Problem 63 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 129 129 122 166 439 3182 0 288
normalized size 1 1. 0.95 1.29 3.4 24.67 0. 2.23
time (sec) N/A 0.178 2.291 0.03 1.429 2.575 0. 1.25
Problem 64 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 169 169 160 230 709 8128 0 427
normalized size 1 1. 0.95 1.36 4.2 48.09 0. 2.53
time (sec) N/A 0.269 3.257 0.035 1.416 2.897 0. 1.272
Problem 65 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 42
normalized size 1 1. 1.71 1.48 1.23 4.19 1.35 1.35
time (sec) N/A 0.044 0.033 0.017 1.113 2.258 0.634 1.181
Problem 66 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 39 127 42 39
normalized size 1 1. 1.71 1.48 1.26 4.1 1.35 1.26
time (sec) N/A 0.042 0.032 0.017 1.112 2.265 0.572 1.188
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 74 63 0 5682 0 0
normalized size 1 1. 1. 0.85 0. 76.78 0. 0.
time (sec) N/A 0.072 0.088 0.052 0. 2.912 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 74 62 0 5844 0 0
normalized size 1 1. 1. 0.84 0. 78.97 0. 0.
time (sec) N/A 0.069 0.064 0.039 0. 2.845 0. 0.
Problem 69 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 98 49 319 0 57
normalized size 1 1. 0.7 1.63 0.82 5.32 0. 0.95
time (sec) N/A 0.072 0.076 0.031 1.121 2.249 0. 1.22
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 34 72 36 200 134 34
normalized size 1 1. 1.36 2.88 1.44 8. 5.36 1.36
time (sec) N/A 0.167 0.059 0.027 1.182 2.198 1.597 1.194
Problem 71 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 68 30 176 0 41
normalized size 1 1. 0.63 1.79 0.79 4.63 0. 1.08
time (sec) N/A 0.059 0.037 0.027 1.139 2.314 0. 1.227
Problem 72 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 17 17 19 42 15 90 48 15
normalized size 1 1. 1.12 2.47 0.88 5.29 2.82 0.88
time (sec) N/A 0.111 0.016 0.023 1.156 2.439 0.436 1.187
Problem 73 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 12 12 14 17 28 167 0 24
normalized size 1 1. 1.17 1.42 2.33 13.92 0. 2.
time (sec) N/A 0.11 0.021 0.023 1.143 2.631 0. 1.281
Problem 74 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 11 32 39 267 0 39
normalized size 1 1. 0.73 2.13 2.6 17.8 0. 2.6
time (sec) N/A 0.039 0.029 0.026 1.121 2.633 0. 1.176
Problem 75 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 18 18 20 39 65 733 0 46
normalized size 1 1. 1.11 2.17 3.61 40.72 0. 2.56
time (sec) N/A 0.161 0.079 0.027 1.115 2.644 0. 1.213
Problem 76 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 20 48 101 286 0 24
normalized size 1 1. 1.18 2.82 5.94 16.82 0. 1.41
time (sec) N/A 0.044 0.048 0.03 1.165 2.284 0. 1.227
Problem 77 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 34 34 49 55 100 2136 0 66
normalized size 1 1. 1.44 1.62 2.94 62.82 0. 1.94
time (sec) N/A 0.192 0.119 0.033 1.079 2.189 0. 1.32
Problem 78 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 33 33 27 80 201 626 0 32
normalized size 1 1. 0.82 2.42 6.09 18.97 0. 0.97
time (sec) N/A 0.054 0.051 0.033 1.105 1.985 0. 1.216
Problem 79 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 44 44 68 103 132 4358 0 82
normalized size 1 1. 1.55 2.34 3. 99.05 0. 1.86
time (sec) N/A 0.211 0.264 0.033 1.213 2.318 0. 1.288
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 144 320 220 2747 0 289
normalized size 1 1. 0.98 2.18 1.5 18.69 0. 1.97
time (sec) N/A 0.346 0.54 0.046 1.161 2.541 0. 1.187
Problem 81 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 137 137 180 166 0 4208 0 220
normalized size 1 1. 1.31 1.21 0. 30.72 0. 1.61
time (sec) N/A 0.279 1.148 0.042 0. 2.452 0. 1.217
Problem 82 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 84 84 73 145 112 826 0 136
normalized size 1 1. 0.87 1.73 1.33 9.83 0. 1.62
time (sec) N/A 0.162 0.222 0.039 1.168 2.633 0. 1.213
Problem 83 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 1103 0 81
normalized size 1 1. 1.1 1.28 0. 15.32 0. 1.12
time (sec) N/A 0.116 0.221 0.03 0. 2.519 0. 1.187
Problem 84 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 52 52 59 53 0 675 0 81
normalized size 1 1. 1.13 1.02 0. 12.98 0. 1.56
time (sec) N/A 0.143 0.09 0.033 0. 2.451 0. 1.213
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 28 56 88 360 0 105
normalized size 1 1. 0.97 1.93 3.03 12.41 0. 3.62
time (sec) N/A 0.054 0.083 0.039 1.04 2.26 0. 1.199
Problem 86 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 82 82 123 110 0 3212 0 169
normalized size 1 1. 1.5 1.34 0. 39.17 0. 2.06
time (sec) N/A 0.293 0.346 0.042 0. 2.78 0. 1.184
Problem 87 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 78 78 70 166 217 2186 0 273
normalized size 1 1. 0.9 2.13 2.78 28.03 0. 3.5
time (sec) N/A 0.1 0.239 0.045 1.122 2.464 0. 1.295
Problem 88 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 255 255 296 311 0 12964 0 369
normalized size 1 1. 1.16 1.22 0. 50.84 0. 1.45
time (sec) N/A 0.548 0.847 0.047 0. 3.802 0. 1.252
Problem 89 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 130 130 119 333 416 7144 0 556
normalized size 1 1. 0.92 2.56 3.2 54.95 0. 4.28
time (sec) N/A 0.154 0.582 0.051 1.111 2.747 0. 1.219
Problem 90 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 33 33 46 29 46 180 0 38
normalized size 1 1. 1.39 0.88 1.39 5.45 0. 1.15
time (sec) N/A 0.102 0.068 0.036 1.563 2.322 0. 1.226
Problem 91 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 42 116 49 323 0 57
normalized size 1 1. 0.7 1.93 0.82 5.38 0. 0.95
time (sec) N/A 0.061 0.045 0.033 1.114 2.198 0. 1.251
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 36 80 45 221 134 42
normalized size 1 1. 1.24 2.76 1.55 7.62 4.62 1.45
time (sec) N/A 0.042 0.047 0.032 1.063 2.061 1.591 1.178
Problem 93 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 76 30 178 0 41
normalized size 1 1. 0.79 2. 0.79 4.68 0. 1.08
time (sec) N/A 0.049 0.03 0.032 1.018 2.149 0. 1.208
Problem 94 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 19 19 23 40 23 99 48 26
normalized size 1 1. 1.21 2.11 1.21 5.21 2.53 1.37
time (sec) N/A 0.03 0.027 0.027 1.01 2.218 0.436 1.259
Problem 95 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 10 10 7 11 8 32 8 8
normalized size 1 1. 0.7 1.1 0.8 3.2 0.8 0.8
time (sec) N/A 0.02 0.003 0.003 1.179 2.231 0.382 1.19
Problem 96 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 5 5 7 6 7 57 0 18
normalized size 1 1. 1.4 1.2 1.4 11.4 0. 3.6
time (sec) N/A 0.033 0.004 0.018 1.167 2.316 0. 1.267
Problem 97 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 6 6 12 21 30 198 0 24
normalized size 1 1. 2. 3.5 5. 33. 0. 4.
time (sec) N/A 0.035 0.025 0.022 1.583 2.082 0. 1.222
Problem 98 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 34 50 181 0 14
normalized size 1 1. 1. 3.09 4.55 16.45 0. 1.27
time (sec) N/A 0.033 0.024 0.025 1.183 2.022 0. 1.255
Problem 99 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 24 24 24 41 66 968 0 42
normalized size 1 1. 1. 1.71 2.75 40.33 0. 1.75
time (sec) N/A 0.042 0.027 0.026 1.637 2.215 0. 1.229
Problem 100 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 25 25 20 56 126 467 0 24
normalized size 1 1. 0.8 2.24 5.04 18.68 0. 0.96
time (sec) N/A 0.041 0.03 0.024 1.118 2.153 0. 1.204
Problem 101 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 34 34 34 67 99 2298 0 61
normalized size 1 1. 1. 1.97 2.91 67.59 0. 1.79
time (sec) N/A 0.048 0.033 0.028 1.745 2.156 0. 1.227
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 137 925 521 12186 0 801
normalized size 1 1. 0.98 6.61 3.72 87.04 0. 5.72
time (sec) N/A 0.158 0.551 0.056 1.73 3.166 0. 1.231
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 92 438 275 4520 0 427
normalized size 1 1. 1.11 5.28 3.31 54.46 0. 5.14
time (sec) N/A 0.111 0.347 0.046 1.615 2.643 0. 1.257
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 49 143 120 1088 0 140
normalized size 1 1. 1.22 3.58 3. 27.2 0. 3.5
time (sec) N/A 0.066 0.157 0.039 1.679 2.434 0. 1.207
Problem 105 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 11 11 20 12 15 126 0 61
normalized size 1 1. 1.82 1.09 1.36 11.45 0. 5.55
time (sec) N/A 0.042 0.044 0.023 1.166 2.311 0. 1.21
Problem 106 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 55 108 146 58
normalized size 1 1. 0.74 1.41 1.41 2.77 3.74 1.49
time (sec) N/A 0.046 0.045 0.011 1.14 2.359 0.743 1.214
Problem 107 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 91 91 75 175 116 818 0 150
normalized size 1 1. 0.82 1.92 1.27 8.99 0. 1.65
time (sec) N/A 0.146 0.113 0.046 1.226 2.304 0. 1.21
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 156 354 223 2882 0 306
normalized size 1 1. 1.01 2.28 1.44 18.59 0. 1.97
time (sec) N/A 0.236 0.194 0.049 1.168 2.393 0. 1.24
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 157 187 166 715 0 16338 0 440
normalized size 1 1.19 1.06 4.55 0. 104.06 0. 2.8
time (sec) N/A 0.273 0.496 0.053 0. 4.489 0. 1.236
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 109 116 316 0 5131 0 205
normalized size 1 1.07 1.14 3.1 0. 50.3 0. 2.01
time (sec) N/A 0.166 0.259 0.042 0. 3.163 0. 1.265
Problem 111 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 56 56 65 110 0 1000 0 85
normalized size 1 1. 1.16 1.96 0. 17.86 0. 1.52
time (sec) N/A 0.088 0.084 0.03 0. 2.56 0. 1.248
Problem 112 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 37 37 46 39 0 423 0 47
normalized size 1 1. 1.24 1.05 0. 11.43 0. 1.27
time (sec) N/A 0.032 0.029 0.018 0. 2.165 0. 1.293
Problem 113 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 1106 0 82
normalized size 1 1. 1.1 1.27 0. 15.15 0. 1.12
time (sec) N/A 0.09 0.225 0.038 0. 2.496 0. 1.211
Problem 114 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 132 132 258 198 0 4251 0 219
normalized size 1 1. 1.95 1.5 0. 32.2 0. 1.66
time (sec) N/A 0.156 0.459 0.044 0. 2.566 0. 1.269
Problem 115 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 43 43 40 40 74 1897 104 63
normalized size 1 1. 0.93 0.93 1.72 44.12 2.42 1.47
time (sec) N/A 0.089 0.095 0.023 1.646 2.368 0.637 1.239
Problem 116 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 58 1168 85 53
normalized size 1 1. 0.89 0.86 1.57 31.57 2.3 1.43
time (sec) N/A 0.066 0.052 0.019 1.762 2.322 0.539 1.271
Problem 117 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 39 632 75 47
normalized size 1 1. 0.87 0.9 1.26 20.39 2.42 1.52
time (sec) N/A 0.051 0.045 0.017 1.921 2.282 0.47 1.2
Problem 118 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 23 259 61 23
normalized size 1 1. 1.21 1.26 1.21 13.63 3.21 1.21
time (sec) N/A 0.038 0.028 0.016 1.85 2.322 0.428 1.209
Problem 119 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 0.02 0.026 0.016 1.267 2.211 0.388 1.206
Problem 120 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 0.015 0.014 1.181 2.104 0.396 1.197
Problem 121 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 43 32 259 0 24
normalized size 1 1. 1.21 2.26 1.68 13.63 0. 1.26
time (sec) N/A 0.04 0.028 0.027 1.27 2.375 0. 1.205
Problem 122 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 59 51 632 0 49
normalized size 1 1. 0.93 2.03 1.76 21.79 0. 1.69
time (sec) N/A 0.068 0.043 0.029 1.218 2.254 0. 1.208
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 37 37 33 75 73 1168 0 54
normalized size 1 1. 0.89 2.03 1.97 31.57 0. 1.46
time (sec) N/A 0.089 0.059 0.032 1.398 2.218 0. 1.183
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 43 43 42 91 86 1897 0 65
normalized size 1 1. 0.98 2.12 2. 44.12 0. 1.51
time (sec) N/A 0.101 0.128 0.036 1.142 2.211 0. 1.271
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 39 35 0 871 82 130
normalized size 1 1. 0.87 0.78 0. 19.36 1.82 2.89
time (sec) N/A 0.048 0.18 0.011 0. 2.34 11.353 1.355
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 32 26 0 456 70 72
normalized size 1 1. 1. 0.81 0. 14.25 2.19 2.25
time (sec) N/A 0.035 0.044 0.026 0. 2.298 2.139 1.264
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 30 25 0 301 66 78
normalized size 1 1. 1. 0.83 0. 10.03 2.2 2.6
time (sec) N/A 0.037 0.054 0.043 0. 2.157 2.408 1.267
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 51 35 0 579 82 100
normalized size 1 1. 1.04 0.71 0. 11.82 1.67 2.04
time (sec) N/A 0.049 0.119 0.016 0. 2.247 10.032 1.269
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 53 35 0 1450 82 189
normalized size 1 1. 1.18 0.78 0. 32.22 1.82 4.2
time (sec) N/A 0.058 0.198 0.019 0. 2.348 17.353 1.291
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 34 26 0 818 71 130
normalized size 1 1. 1. 0.76 0. 24.06 2.09 3.82
time (sec) N/A 0.044 0.068 0.034 0. 2.206 2.999 1.223
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 37 35 0 639 78 73
normalized size 1 1. 0.88 0.83 0. 15.21 1.86 1.74
time (sec) N/A 0.056 0.088 0.039 0. 2.35 3.403 1.26
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 53 35 0 579 82 136
normalized size 1 1. 1.08 0.71 0. 11.82 1.67 2.78
time (sec) N/A 0.08 0.096 0.021 0. 2.264 11.425 1.268
Problem 133 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 94 94 105 96 203 3089 0 192
normalized size 1 1. 1.12 1.02 2.16 32.86 0. 2.04
time (sec) N/A 0.367 0.453 0.023 1.765 2.626 0. 1.21
Problem 134 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 76 135 1538 442 132
normalized size 1 1. 1.16 1. 1.78 20.24 5.82 1.74
time (sec) N/A 0.213 0.274 0.022 1.83 2.514 105.921 1.311
Problem 135 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 65 67 96 662 330 101
normalized size 1 1. 1.02 1.05 1.5 10.34 5.16 1.58
time (sec) N/A 0.129 0.12 0.02 1.846 2.495 1.36 1.204
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 63 63 49 60 76 186 243 78
normalized size 1 1. 0.78 0.95 1.21 2.95 3.86 1.24
time (sec) N/A 0.092 0.075 0.017 1.815 2.287 0.871 1.181
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 29 55 54 109 141 58
normalized size 1 1. 0.74 1.41 1.38 2.79 3.62 1.49
time (sec) N/A 0.059 0.054 0.019 1.277 2.164 0.702 1.19
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 39 39 29 55 55 108 146 58
normalized size 1 1. 0.74 1.41 1.41 2.77 3.74 1.49
time (sec) N/A 0.046 0.041 0. 1.142 2.172 0.687 1.167
Problem 139 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 78 88 185 0 78
normalized size 1 1. 0.9 1.53 1.73 3.63 0. 1.53
time (sec) N/A 0.079 0.077 0.039 1.261 2.357 0. 1.18
Problem 140 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 64 100 116 662 0 101
normalized size 1 1. 1.07 1.67 1.93 11.03 0. 1.68
time (sec) N/A 0.182 0.123 0.042 1.259 2.481 0. 1.152
Problem 141 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 76 76 91 134 163 1539 0 131
normalized size 1 1. 1.2 1.76 2.14 20.25 0. 1.72
time (sec) N/A 0.309 0.184 0.046 1.278 2.837 0. 1.18
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 97 97 108 185 234 3087 0 192
normalized size 1 1. 1.11 1.91 2.41 31.82 0. 1.98
time (sec) N/A 0.494 0.285 0.049 1.187 3.081 0. 1.187
Problem 143 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 55 55 49 73 92 491 0 235
normalized size 1 1. 0.89 1.33 1.67 8.93 0. 4.27
time (sec) N/A 0.085 0.166 0.111 2.044 2.713 0. 1.188
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 231 231 250 953 0 3791 0 0
normalized size 1 1. 1.08 4.13 0. 16.41 0. 0.
time (sec) N/A 0.541 2.446 0.155 0. 2.822 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 351 351 316 1186 0 5269 0 0
normalized size 1 1. 0.9 3.38 0. 15.01 0. 0.
time (sec) N/A 0.867 2.302 0.134 0. 3.123 0. 0.
Problem 146 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 29 0 64 24 31 72 0 31
normalized size 1 0. 2.21 0.83 1.07 2.48 0. 1.07
time (sec) N/A 0.029 0.025 0.021 1.237 2.447 0. 1.165
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C C A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 151 0 64 37 173 506 0 166
normalized size 1 0. 0.42 0.25 1.15 3.35 0. 1.1
time (sec) N/A 0.022 0.251 0.022 1.799 2.512 0. 1.2
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 23 0 35 41 26 57 0 26
normalized size 1 0. 1.52 1.78 1.13 2.48 0. 1.13
time (sec) N/A 0.016 0.187 0.035 1.914 1.839 0. 1.235
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C C A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 145 0 58 33 167 498 0 161
normalized size 1 0. 0.4 0.23 1.15 3.43 0. 1.11
time (sec) N/A 0.007 0.165 0.012 1.808 2.148 0. 1.166
Problem 150 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 12 12 12 26 14 47 15 27
normalized size 1 1. 1. 2.17 1.17 3.92 1.25 2.25
time (sec) N/A 0.014 0.025 0.003 1.219 1.969 0.297 1.157
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C C A B F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 147 0 59 42 169 597 0 163
normalized size 1 0. 0.4 0.29 1.15 4.06 0. 1.11
time (sec) N/A 0.024 0.159 0.027 1.901 2.199 0. 1.185
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 20 0 40 44 26 55 0 22
normalized size 1 0. 2. 2.2 1.3 2.75 0. 1.1
time (sec) N/A 0.024 0.153 0.027 1.621 2.095 0. 1.206
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 47 0 86 42 54 140 0 53
normalized size 1 0. 1.83 0.89 1.15 2.98 0. 1.13
time (sec) N/A 0.068 0.104 0.019 1.541 1.885 0. 1.18
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 173 0 174 53 194 693 0 188
normalized size 1 0. 1.01 0.31 1.12 4.01 0. 1.09
time (sec) N/A 0.048 0.649 0.022 1.778 2.146 0. 1.184
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 40 0 41 57 47 120 0 47
normalized size 1 0. 1.02 1.42 1.18 3. 0. 1.18
time (sec) N/A 0.03 0.378 0.033 1.864 2.03 0. 1.239
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C A B F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 165 0 146 47 186 680 0 180
normalized size 1 0. 0.88 0.28 1.13 4.12 0. 1.09
time (sec) N/A 0.01 0.531 0.02 1.702 2.203 0. 1.453
Problem 157 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 14 14 24 35 28 68 12 26
normalized size 1 1. 1.71 2.5 2. 4.86 0.86 1.86
time (sec) N/A 0.024 0.038 0.003 1.148 1.977 0.5 1.472
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C A B F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 190 0 181 64 197 771 0 193
normalized size 1 0. 0.95 0.34 1.04 4.06 0. 1.02
time (sec) N/A 0.045 0.736 0.026 1.931 2.145 0. 1.45
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C A A F A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 59 0 40 66 50 122 0 53
normalized size 1 0. 0.68 1.12 0.85 2.07 0. 0.9
time (sec) N/A 0.053 0.355 0.029 1.819 1.886 0. 1.401
Problem 160 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 60 0 47 0 0 0 0 0
normalized size 1 0. 0.78 0. 0. 0. 0. 0.
time (sec) N/A 0.039 0.09 0.036 0. 0. 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 79 0 168 0 0 0 0 0
normalized size 1 0. 2.13 0. 0. 0. 0. 0.
time (sec) N/A 0.069 0.364 0.027 0. 0. 0. 0.
Problem 162 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 176 0 218 0 0 0 0 0
normalized size 1 0. 1.24 0. 0. 0. 0. 0.
time (sec) N/A 0.074 0.817 0.033 0. 0. 0. 0.
Problem 163 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 0.023 1.907 0.106 0. 0. 0. 0.
Problem 164 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 99 0 126 0 0 0 0 0
normalized size 1 0. 1.27 0. 0. 0. 0. 0.
time (sec) N/A 0.114 2.978 0.03 0. 0. 0. 0.
Problem 165 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 51 0 76 0 0 0 0 0
normalized size 1 0. 1.49 0. 0. 0. 0. 0.
time (sec) N/A 0.047 2.904 0.033 0. 0. 0. 0.
Problem 166 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 106 0 121 0 0 0 0 0
normalized size 1 0. 1.14 0. 0. 0. 0. 0.
time (sec) N/A 0.053 2.904 0.029 0. 0. 0. 0.
Problem 167 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 158 0 177 0 0 0 0 0
normalized size 1 0. 1.12 0. 0. 0. 0. 0.
time (sec) N/A 0.052 4.096 0.03 0. 0. 0. 0.
Problem 168 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 190 0 177 0 0 0 0 0
normalized size 1 0. 0.93 0. 0. 0. 0. 0.
time (sec) N/A 0.052 3.17 0.029 0. 0. 0. 0.
Problem 169 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 0.016 1.544 0.048 0. 0. 0. 0.
Problem 170 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 1.775 0.046 0. 0. 0. 0.
Problem 171 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 1.782 0.052 0. 0. 0. 0.
Problem 172 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 59 0 127 0 0 0 0 0
normalized size 1 0. 2.15 0. 0. 0. 0. 0.
time (sec) N/A 0.042 7.671 0.894 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 63 0 136 0 0 0 0 0
normalized size 1 0. 2.16 0. 0. 0. 0. 0.
time (sec) N/A 0.03 7.56 0.784 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 Yes TBD TBD TBD TBD TBD
size 55 0 122 0 0 0 0 0
normalized size 1 0. 2.22 0. 0. 0. 0. 0.
time (sec) N/A 0.024 7.585 0.783 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 Yes TBD TBD TBD TBD TBD
size 53 0 126 0 0 0 0 0
normalized size 1 0. 2.38 0. 0. 0. 0. 0.
time (sec) N/A 0.011 8.558 0.717 0. 0. 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 24 56 32 205 36 99
normalized size 1 1. 0.96 2.24 1.28 8.2 1.44 3.96
time (sec) N/A 0.02 0.046 0.004 1.086 2.146 5.9 1.37
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 59 0 126 0 0 0 0 0
normalized size 1 0. 2.14 0. 0. 0. 0. 0.
time (sec) N/A 0.029 3.212 0.796 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 Yes TBD TBD TBD TBD TBD
size 56 0 120 0 0 0 0 0
normalized size 1 0. 2.14 0. 0. 0. 0. 0.
time (sec) N/A 0.029 3.121 0.818 0. 0. 0. 0.
Problem 179 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 133 0 159 0 0 0 0 0
normalized size 1 0. 1.2 0. 0. 0. 0. 0.
time (sec) N/A 0.086 8.162 0.809 0. 0. 0. 0.
Problem 180 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 137 0 169 0 0 0 0 0
normalized size 1 0. 1.23 0. 0. 0. 0. 0.
time (sec) N/A 0.06 7.78 0.317 0. 0. 0. 0.
Problem 181 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 131 0 155 0 0 0 0 0
normalized size 1 0. 1.18 0. 0. 0. 0. 0.
time (sec) N/A 0.043 7.733 0.098 0. 0. 0. 0.
Problem 182 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 127 0 163 0 0 0 0 0
normalized size 1 0. 1.28 0. 0. 0. 0. 0.
time (sec) N/A 0.014 8.807 0.099 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 51 80 49 197 70 50
normalized size 1 1. 1.82 2.86 1.75 7.04 2.5 1.79
time (sec) N/A 0.029 0.078 0.006 1.396 2.148 14.908 1.515
Problem 184 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 135 0 162 0 0 0 0 0
normalized size 1 0. 1.2 0. 0. 0. 0. 0.
time (sec) N/A 0.052 3.416 0.102 0. 0. 0. 0.
Problem 185 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 136 0 159 0 0 0 0 0
normalized size 1 0. 1.17 0. 0. 0. 0. 0.
time (sec) N/A 0.052 3.377 0.109 0. 0. 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 43 67 410 1841 75 170
normalized size 1 1. 1. 1.56 9.53 42.81 1.74 3.95
time (sec) N/A 0.041 0.134 0.007 1.505 2.051 5.78 1.381
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 62 86 667 630 71 90
normalized size 1 1. 1.38 1.91 14.82 14. 1.58 2.
time (sec) N/A 0.039 0.103 0.004 1.531 2.004 28.884 1.363
Problem 188 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 55 88 1119 5060 0 216
normalized size 1 1. 0.83 1.33 16.95 76.67 0. 3.27
time (sec) N/A 0.057 0.208 0.006 1.757 2.324 0. 1.425
Problem 189 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 88 0 160 0 0 0 0 0
normalized size 1 0. 1.82 0. 0. 0. 0. 0.
time (sec) N/A 0.046 13.584 1.214 0. 0. 0. 0.
Problem 190 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 169 0 516 0 0 0 0 0
normalized size 1 0. 3.05 0. 0. 0. 0. 0.
time (sec) N/A 0.077 16.539 0.218 0. 0. 0. 0.
Problem 191 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 307 0 606 0 0 0 0 0
normalized size 1 0. 1.97 0. 0. 0. 0. 0.
time (sec) N/A 0.071 16.76 0.218 0. 0. 0. 0.
Problem 192 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 115 0 387 0 0 0 0 0
normalized size 1 0. 3.37 0. 0. 0. 0. 0.
time (sec) N/A 0.014 3.824 0.088 0. 0. 0. 0.
Problem 193 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 0.099 4.999 0.057 0. 0. 0. 0.
Problem 194 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 2091 0 0
normalized size 1 1. 0.88 1.27 0. 28.64 0. 0.
time (sec) N/A 0.053 0.285 0.023 0. 2.235 0. 0.
Problem 195 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 0.052 0.133 0.013 0. 2.123 0. 0.
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 48 72 0 1000 66 0
normalized size 1 1. 1. 1.5 0. 20.83 1.38 0.
time (sec) N/A 0.041 0.076 0.015 0. 2.115 3.235 0.
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 47 44 0 999 66 0
normalized size 1 1. 1. 0.94 0. 21.26 1.4 0.
time (sec) N/A 0.04 0.109 0.017 0. 2.069 7.105 0.
Problem 198 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 71 71 44 93 0 2088 0 0
normalized size 1 1. 0.62 1.31 0. 29.41 0. 0.
time (sec) N/A 0.052 0.158 0.017 0. 2.1 0. 0.
Problem 199 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 0.05 0.203 0.016 0. 2.216 0. 0.
Problem 200 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 135 135 136 149 0 24521 0 0
normalized size 1 1. 1.01 1.1 0. 181.64 0. 0.
time (sec) N/A 0.358 1.305 0.168 0. 15.786 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 105 105 105 90 0 18436 0 0
normalized size 1 1. 1. 0.86 0. 175.58 0. 0.
time (sec) N/A 0.225 0.074 0.057 0. 12.276 0. 0.
Problem 202 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 58 58 58 52 0 4811 0 0
normalized size 1 1. 1. 0.9 0. 82.95 0. 0.
time (sec) N/A 0.12 0.032 0.075 0. 8.646 0. 0.
Problem 203 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 106 106 109 0 0 18421 0 0
normalized size 1 1. 1.03 0. 0. 173.78 0. 0.
time (sec) N/A 0.249 0.328 0.218 0. 12.137 0. 0.
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 183 183 142 0 0 24602 0 0
normalized size 1 1. 0.78 0. 0. 134.44 0. 0.
time (sec) N/A 0.337 0.576 0.193 0. 15.907 0. 0.
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 131 559 0 22316 0 0
normalized size 1 1. 0.99 4.23 0. 169.06 0. 0.
time (sec) N/A 0.231 0.324 0.082 0. 20.853 0. 0.
Problem 206 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 107 107 76 143 127 1685 0 92
normalized size 1 1. 0.71 1.34 1.19 15.75 0. 0.86
time (sec) N/A 0.069 0.132 0.013 1.575 2.24 0. 1.804
Problem 207 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 77 77 60 102 93 956 0 70
normalized size 1 1. 0.78 1.32 1.21 12.42 0. 0.91
time (sec) N/A 0.05 0.089 0.012 1.583 2.111 0. 2.134
Problem 208 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 51 51 40 56 63 433 0 55
normalized size 1 1. 0.78 1.1 1.24 8.49 0. 1.08
time (sec) N/A 0.035 0.088 0.007 1.592 1.986 0. 2.209
Problem 209 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 25 25 22 34 31 105 0 31
normalized size 1 1. 0.88 1.36 1.24 4.2 0. 1.24
time (sec) N/A 0.015 0.014 0.01 1.615 1.921 0. 1.526
Problem 210 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 25 25 22 27 51 158 0 43
normalized size 1 1. 0.88 1.08 2.04 6.32 0. 1.72
time (sec) N/A 0.017 0.017 0.011 1.039 2.046 0. 1.604
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 53 53 179 47 84 585 0 76
normalized size 1 1. 3.38 0.89 1.58 11.04 0. 1.43
time (sec) N/A 0.038 1.721 0.01 1.042 2.067 0. 1.291
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 81 81 286 88 119 1291 0 97
normalized size 1 1. 3.53 1.09 1.47 15.94 0. 1.2
time (sec) N/A 0.052 2.454 0.017 1.05 2.051 0. 1.227
Problem 213 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 113 113 115 123 149 2221 0 112
normalized size 1 1. 1.02 1.09 1.32 19.65 0. 0.99
time (sec) N/A 0.072 10.105 0.014 1.166 2.117 0. 1.291
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 48 35 120 510 0 120
normalized size 1 1. 0.42 0.31 1.06 4.51 0. 1.06
time (sec) N/A 0.087 0.043 0.059 1.576 2.295 0. 1.208
Problem 215 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 95 95 95 24 105 360 0 105
normalized size 1 1. 1. 0.25 1.11 3.79 0. 1.11
time (sec) N/A 0.062 0.03 0.052 1.588 2.435 0. 1.275
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 36 30 154 0 31
normalized size 1 1. 1. 2.25 1.88 9.62 0. 1.94
time (sec) N/A 0.014 0.012 0.063 1.532 2.389 0. 1.283
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 35 35 113 48 46 837 0 47
normalized size 1 1. 3.23 1.37 1.31 23.91 0. 1.34
time (sec) N/A 0.029 1.466 0.072 1.544 2.361 0. 1.268
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 97 59 109 490 0 0
normalized size 1 1. 0.86 0.52 0.96 4.34 0. 0.
time (sec) N/A 0.212 0.076 0.106 1.57 2.314 0. 0.
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 24 47 93 350 0 0
normalized size 1 1. 0.25 0.48 0.96 3.61 0. 0.
time (sec) N/A 0.186 0.012 0.071 1.59 2.299 0. 0.
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 22 138 101 454 0 103
normalized size 1 1. 0.26 1.62 1.19 5.34 0. 1.21
time (sec) N/A 0.122 0.015 0.076 1.605 2.16 0. 1.205
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 108 108 113 150 117 2221 0 119
normalized size 1 1. 1.05 1.39 1.08 20.56 0. 1.1
time (sec) N/A 0.147 1.716 0.1 1.643 2.165 0. 1.29
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 382 382 51 36 0 4162 0 355
normalized size 1 1. 0.13 0.09 0. 10.9 0. 0.93
time (sec) N/A 0.405 0.048 0.095 0. 2.643 0. 1.332
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 366 366 24 24 0 3330 0 339
normalized size 1 1. 0.07 0.07 0. 9.1 0. 0.93
time (sec) N/A 0.244 0.012 0.059 0. 2.396 0. 1.448
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 22 56 131 447 0 132
normalized size 1 1. 0.19 0.48 1.13 3.85 0. 1.14
time (sec) N/A 0.078 0.016 0.07 1.692 2.109 0. 1.304
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 134 134 113 68 147 637 0 149
normalized size 1 1. 0.84 0.51 1.1 4.75 0. 1.11
time (sec) N/A 0.101 1.645 0.105 1.779 2.332 0. 1.506
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 81 70 0 1037 0 443
normalized size 1 1. 0.76 0.65 0. 9.69 0. 4.14
time (sec) N/A 0.126 0.077 0.17 0. 2.258 0. 1.29
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 152 152 107 476 0 2920 0 616
normalized size 1 1. 0.7 3.13 0. 19.21 0. 4.05
time (sec) N/A 0.176 0.139 0.194 0. 2.348 0. 1.271
Problem 228 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 167 167 205 0 0 0 0 0
normalized size 1 1. 1.23 0. 0. 0. 0. 0.
time (sec) N/A 0.188 4.129 0.105 0. 0. 0. 0.
Problem 229 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 117 117 169 0 0 0 0 0
normalized size 1 1. 1.44 0. 0. 0. 0. 0.
time (sec) N/A 0.127 3.257 0.068 0. 0. 0. 0.
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 141 0 0 0 0 0
normalized size 1 1. 2.1 0. 0. 0. 0. 0.
time (sec) N/A 0.071 1.808 0.045 0. 0. 0. 0.
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 134 0 0 0 0 0
normalized size 1 1. 2.06 0. 0. 0. 0. 0.
time (sec) N/A 0.071 2.388 0.059 0. 0. 0. 0.
Problem 232 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 113 113 145 0 0 0 0 0
normalized size 1 1. 1.28 0. 0. 0. 0. 0.
time (sec) N/A 0.126 3.047 0.073 0. 0. 0. 0.
Problem 233 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 161 161 185 0 0 0 0 0
normalized size 1 1. 1.15 0. 0. 0. 0. 0.
time (sec) N/A 0.176 3.313 0.113 0. 0. 0. 0.
Problem 234 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 0 248
normalized size 1 1. 0.43 1.04 0.63 10.24 0. 0.8
time (sec) N/A 0.902 0.217 0.277 1.704 2.118 0. 1.333
Problem 235 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 0 174
normalized size 1 1. 0.54 1.56 0.63 6.09 0. 0.9
time (sec) N/A 0.28 0.155 0.185 1.771 2.151 0. 1.274
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-1) 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 0.15 0.052 0.23 1.774 1.994 0. 1.23
Problem 237 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 83 83 51 213 76 196 0 119
normalized size 1 1. 0.61 2.57 0.92 2.36 0. 1.43
time (sec) N/A 0.199 0.123 0.227 1.772 2.035 0. 1.302
Problem 238 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 0 217
normalized size 1 1. 1.7 1.51 0.77 7.99 0. 1.1
time (sec) N/A 0.865 7.586 0.193 1.752 2.007 0. 1.507
Problem 239 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 0 290
normalized size 1 1. 0.51 1. 0.71 13.09 0. 0.91
time (sec) N/A 1.77 10.657 0.197 1.682 2.216 0. 1.648
Problem 240 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 0.395 0.214 0.026 0. 2.341 0. 0.
Problem 241 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 0.266 0.141 0.023 0. 2.211 0. 0.
Problem 242 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 0.146 0.125 0.017 0. 2.201 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 65 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.077 2.634 0.239 0. 0. 0. 0.
Problem 244 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 0.263 0.023 0. 2.511 0. 0.
Problem 245 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 0.25 0.158 0.022 0. 2.202 0. 0.
Problem 246 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 0.139 0.104 0.02 0. 2.18 0. 0.
Problem 247 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 4.66 0.095 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 [224] had the largest ratio of [ 1.5 ]

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 2 1. 8 0.25
2 A 3 2 1. 8 0.25
3 A 3 2 1. 8 0.25
4 A 2 2 1. 8 0.25
5 A 2 2 1. 8 0.25
6 A 1 1 1. 6 0.167
7 A 1 1 1. 6 0.167
8 A 2 2 1. 8 0.25
9 A 2 2 1. 8 0.25
10 A 3 2 1. 8 0.25
11 A 3 2 1. 8 0.25
12 A 4 2 1. 8 0.25
13 A 7 6 1. 12 0.5
14 A 6 6 1. 12 0.5
15 A 6 6 1. 12 0.5
16 A 5 5 1. 12 0.417
17 A 5 5 1. 12 0.417
18 A 6 6 1. 12 0.5
19 A 6 6 1. 12 0.5
20 A 7 6 1. 12 0.5
21 A 9 9 1. 8 1.125
22 A 2 2 1. 8 0.25
23 A 2 2 1. 10 0.2
24 A 3 3 1. 10 0.3
25 A 2 2 1. 10 0.2
26 A 2 2 1. 10 0.2
27 A 4 3 1. 14 0.214
28 A 3 3 1. 14 0.214
29 A 2 2 1. 14 0.143
30 A 2 2 1. 14 0.143
31 A 3 3 1. 14 0.214
32 A 4 3 1. 14 0.214
33 A 7 7 1. 8 0.875
34 A 8 7 1. 10 0.7
35 A 7 7 1. 10 0.7
36 A 7 7 1. 10 0.7
37 A 5 3 1. 10 0.3
38 A 3 3 1. 10 0.3
39 A 3 3 1. 10 0.3
40 A 3 3 1. 12 0.25
41 A 5 3 1. 12 0.25
42 A 4 3 1. 12 0.25
43 A 3 3 1. 12 0.25
44 A 2 2 1. 12 0.167
45 A 2 2 1. 12 0.167
46 A 3 2 1. 12 0.167
47 A 4 2 1. 12 0.167
48 A 5 2 1. 12 0.167
49 A 6 2 1. 12 0.167
50 A 5 3 1. 8 0.375
51 A 4 3 1. 8 0.375
52 A 3 3 1. 8 0.375
53 A 2 2 1. 8 0.25
54 A 3 3 1. 8 0.375
55 A 4 3 1. 8 0.375
56 A 5 3 1. 8 0.375
57 A 5 4 1. 12 0.333
58 A 4 4 1. 12 0.333
59 A 3 3 1. 12 0.25
60 A 2 2 1. 12 0.167
61 A 2 2 1. 12 0.167
62 A 3 3 1. 12 0.25
63 A 4 4 1. 12 0.333
64 A 5 4 1. 12 0.333
65 A 2 2 1. 12 0.167
66 A 2 2 1. 12 0.167
67 A 5 4 1. 14 0.286
68 A 5 4 1. 14 0.286
69 A 5 4 1. 11 0.364
70 A 9 7 1. 11 0.636
71 A 5 4 1. 11 0.364
72 A 8 6 1. 9 0.667
73 A 8 7 1. 9 0.778
74 A 3 2 1. 11 0.182
75 A 8 7 1. 11 0.636
76 A 4 3 1. 11 0.273
77 A 9 8 1. 11 0.727
78 A 4 3 1. 11 0.273
79 A 10 8 1. 11 0.727
80 A 5 3 1. 13 0.231
81 A 10 9 1. 13 0.692
82 A 4 3 1. 13 0.231
83 A 6 6 1. 11 0.546
84 A 6 5 1. 11 0.454
85 A 3 2 1. 13 0.154
86 A 15 11 1. 13 0.846
87 A 3 2 1. 13 0.154
88 A 29 13 1. 13 1.
89 A 3 2 1. 13 0.154
90 A 6 5 1. 11 0.454
91 A 4 3 1. 11 0.273
92 A 3 2 1. 11 0.182
93 A 4 3 1. 11 0.273
94 A 2 2 1. 9 0.222
95 A 1 1 1. 9 0.111
96 A 2 2 1. 11 0.182
97 A 2 2 1. 11 0.182
98 A 2 1 1. 11 0.091
99 A 3 3 1. 11 0.273
100 A 3 2 1. 11 0.182
101 A 4 3 1. 11 0.273
102 A 3 2 1. 13 0.154
103 A 3 2 1. 13 0.154
104 A 3 2 1. 13 0.154
105 A 2 2 1. 13 0.154
106 A 2 2 1. 8 0.25
107 A 4 3 1. 13 0.231
108 A 5 4 1. 13 0.308
109 A 14 6 1.19 13 0.462
110 A 9 6 1.07 13 0.462
111 A 5 5 1. 13 0.385
112 A 2 2 1. 11 0.182
113 A 5 5 1. 11 0.454
114 A 9 6 1. 13 0.462
115 A 5 4 1. 11 0.364
116 A 4 4 1. 11 0.364
117 A 3 3 1. 11 0.273
118 A 3 2 1. 11 0.182
119 A 2 2 1. 9 0.222
120 A 2 2 1. 6 0.333
121 A 4 4 1. 9 0.444
122 A 4 4 1. 11 0.364
123 A 5 4 1. 11 0.364
124 A 6 4 1. 11 0.364
125 A 4 4 1. 11 0.364
126 A 3 3 1. 11 0.273
127 A 3 3 1. 11 0.273
128 A 4 4 1. 11 0.364
129 A 4 4 1. 13 0.308
130 A 3 3 1. 13 0.231
131 A 4 4 1. 13 0.308
132 A 4 4 1. 13 0.308
133 A 7 7 1. 13 0.538
134 A 6 6 1. 13 0.462
135 A 5 5 1. 13 0.385
136 A 4 4 1. 13 0.308
137 A 2 2 1. 11 0.182
138 A 2 2 1. 8 0.25
139 A 3 3 1. 11 0.273
140 A 4 4 1. 13 0.308
141 A 5 5 1. 13 0.385
142 A 6 6 1. 13 0.462
143 A 3 3 1. 14 0.214
144 A 9 6 1. 24 0.25
145 A 11 7 1. 26 0.269
146 F 0 0 N/A 0 N/A
147 F 0 0 N/A 0 N/A
148 F 0 0 N/A 0 N/A
149 F 0 0 N/A 0 N/A
150 A 2 1 1. 11 0.091
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 F 0 0 N/A 0 N/A
156 F 0 0 N/A 0 N/A
157 A 3 2 1. 13 0.154
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 F 0 0 N/A 0 N/A
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 A 2 1 1. 17 0.059
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 F 0 0 N/A 0 N/A
182 F 0 0 N/A 0 N/A
183 A 3 2 1. 19 0.105
184 F 0 0 N/A 0 N/A
185 F 0 0 N/A 0 N/A
186 A 3 2 1. 17 0.118
187 A 4 2 1. 17 0.118
188 A 4 2 1. 17 0.118
189 F 0 0 N/A 0 N/A
190 F 0 0 N/A 0 N/A
191 F 0 0 N/A 0 N/A
192 F 0 0 N/A 0 N/A
193 F 0 0 N/A 0 N/A
194 A 7 6 1. 19 0.316
195 A 7 6 1. 19 0.316
196 A 6 5 1. 19 0.263
197 A 6 5 1. 19 0.263
198 A 7 6 1. 19 0.316
199 A 7 6 1. 19 0.316
200 A 8 7 1. 23 0.304
201 A 7 6 1. 23 0.261
202 A 4 4 1. 21 0.19
203 A 8 5 1. 21 0.238
204 A 11 6 1. 23 0.261
205 A 8 7 1. 21 0.333
206 A 7 6 1. 16 0.375
207 A 7 6 1. 16 0.375
208 A 5 4 1. 16 0.25
209 A 3 3 1. 14 0.214
210 A 3 3 1. 14 0.214
211 A 5 4 1. 16 0.25
212 A 7 6 1. 16 0.375
213 A 7 6 1. 16 0.375
214 A 13 9 1. 10 0.9
215 A 11 8 1. 8 1.
216 A 5 5 1. 8 0.625
217 A 7 6 1. 10 0.6
218 A 14 9 1. 10 0.9
219 A 12 8 1. 8 1.
220 A 12 8 1. 8 1.
221 A 14 9 1. 10 0.9
222 A 23 9 1. 10 0.9
223 A 21 8 1. 8 1.
224 A 15 12 1. 8 1.5
225 A 17 13 1. 10 1.3
226 A 5 5 1. 14 0.357
227 A 7 6 1. 14 0.429
228 A 6 3 1. 18 0.167
229 A 5 3 1. 18 0.167
230 A 4 3 1. 16 0.188
231 A 4 3 1. 16 0.188
232 A 5 3 1. 18 0.167
233 A 6 3 1. 18 0.167
234 A 9 7 1. 25 0.28
235 A 8 7 1. 25 0.28
236 A 4 4 1. 25 0.16
237 A 4 4 1. 25 0.16
238 A 8 7 1. 25 0.28
239 A 9 7 1. 25 0.28
240 A 19 5 1. 9 0.556
241 A 13 5 1. 9 0.556
242 A 9 4 1. 7 0.571
243 A 0 0 0. 0 0.
244 A 19 5 1. 9 0.556
245 A 13 5 1. 9 0.556
246 A 9 4 1. 7 0.571
247 A 0 0 0. 0 0.

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