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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
  2.1.8 Mupad
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 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, 248, 249, 250, 251, 252, 253, 254 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 70, 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, 129, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 190, 191, 192, 193, 194, 195, 197, 198, 199, 200, 202, 203, 204, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 229, 230, 235, 236, 237, 238, 239, 240, 241, 243, 244, 245, 246, 247, 252, 253, 254 }

B grade: { 11, 40, 42, 44, 61, 72, 136, 138, 140, 158, 160 }

C grade: { 10, 12, 32, 41, 43, 69, 71, 123, 124, 125, 126, 127, 128, 137, 139, 159, 187, 188, 189, 196, 214, 227, 228, 231, 232, 233, 234, 242, 248, 249, 250, 251 }

F grade: { 201, 205 }

2.1.3 Maple

A grade: { 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 19, 20, 21, 22, 24, 25, 26, 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, 87, 105, 106, 107, 108, 112, 130, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 144, 146, 147, 148, 149, 150, 152, 153, 154, 156, 157, 158, 159, 160, 175, 190, 192, 193, 194, 202, 203, 204, 206, 207, 208, 210, 211, 212, 220, 221, 222, 224, 225, 226, 229, 238, 239, 240, 243, 244, 245, 246 }

B grade: { 1, 3, 13, 15, 17, 23, 27, 73, 74, 75, 76, 77, 82, 83, 84, 85, 86, 89, 90, 91, 92, 109, 111, 129, 131, 141, 143, 145, 151, 155, 161, 162, 163, 164, 165, 170, 171, 172, 173, 174, 176, 178, 179, 180, 195, 196, 197, 198, 199, 200, 213, 214, 215, 216, 217, 218, 227, 228, 241, 242 }

C grade: { 78, 93, 97, 98, 99, 100, 101, 102, 103, 115, 116, 117, 118, 119, 121, 166, 181, 185, 186, 230, 231, 232, 233, 234, 235, 247, 248, 249, 250, 251, 252 }

F grade: { 79, 80, 81, 88, 94, 95, 96, 104, 110, 113, 114, 120, 122, 123, 124, 125, 126, 127, 128, 167, 168, 169, 177, 182, 183, 184, 187, 188, 189, 191, 201, 205, 209, 219, 223, 236, 237, 253, 254 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 23, 24, 25, 26, 33, 34, 35, 36, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 51, 59, 60, 61, 62, 63, 64, 66, 129, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 145, 151, 152, 153, 154, 190, 194, 212, 240 }

B grade: { 8, 9, 10, 11, 12, 18, 19, 20, 21, 22, 27, 28, 29, 30, 31, 32, 41, 42, 43, 44, 52, 53, 54, 55, 56, 57, 58, 65, 67, 68, 69, 70, 71, 72, 136, 137, 138, 139, 140, 146, 147, 148, 149, 150, 155, 156, 157, 158, 159, 160, 192, 193, 195, 196, 197, 198, 199, 200, 202, 203, 204, 206, 207, 208, 210, 211, 213, 214, 215, 216, 217, 218, 220, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 238, 239, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252 }

C grade: { }

F grade: { 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, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 201, 205, 209, 219, 223, 236, 237, 253, 254 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 72, 77, 78, 79, 80, 93, 94, 95, 96, 101, 102, 103, 104, 115, 116, 120, 121, 122, 129, 130, 131, 132, 133, 134, 135, 140, 141, 142, 143, 144, 145, 146, 147, 149, 151, 152, 153, 154, 155, 156, 157, 165, 166, 167, 168, 182, 183, 184, 190, 192, 193, 194, 195, 196, 197, 199, 202, 203, 204, 206, 207, 208, 210, 211, 212, 213, 215, 216, 217, 218, 220, 221, 222, 224, 225, 226, 227, 229, 238, 239, 240, 241, 242, 243, 244, 245, 246 }

B grade: { 8, 9, 20, 22, 27, 30, 41, 42, 43, 53, 55, 57, 69, 70, 71, 73, 74, 75, 76, 89, 90, 91, 92, 97, 98, 99, 100, 117, 118, 119, 136, 137, 138, 139, 148, 150, 158, 159, 160, 161, 162, 163, 164, 177, 178, 179, 180, 181, 185, 186, 198, 200, 214, 228, 230, 231, 232, 233, 234, 235, 247, 248, 249, 250, 251, 252 }

C grade: { }

F grade: { 81, 82, 83, 84, 85, 86, 87, 88, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 123, 124, 125, 126, 127, 128, 169, 170, 171, 172, 173, 174, 175, 176, 187, 188, 189, 191, 201, 205, 209, 219, 223, 236, 237, 253, 254 }

2.1.6 Sympy

A grade: { 3, 4, 5, 6, 7, 14, 15, 16, 17, 25, 26, 27, 131, 132, 133, 134, 135, 142, 143, 144, 145, 153, 154, 155, 192, 193, 194, 202, 203, 204, 206, 207, 210, 211, 212, 220, 221, 222, 224, 225, 238, 239, 240, 244, 245 }

B grade: { 40, 195, 196, 213, 214, 227, 228, 241, 242 }

C grade: { }

F grade: { 1, 2, 8, 9, 10, 11, 12, 13, 18, 19, 20, 21, 22, 23, 24, 28, 29, 30, 31, 32, 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, 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, 136, 137, 138, 139, 140, 141, 146, 147, 148, 149, 150, 151, 152, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 197, 198, 199, 200, 201, 205, 208, 209, 215, 216, 217, 218, 219, 223, 226, 229, 230, 231, 232, 233, 234, 235, 236, 237, 243, 246, 247, 248, 249, 250, 251, 252, 253, 254 }

2.1.7 Giac

A grade: { 2, 4, 5, 6, 7, 14, 16, 24, 25, 26, 34, 36, 38, 40, 45, 47, 49, 51, 60, 62, 64, 66, 68, 130, 132, 133, 134, 135, 136, 137, 139, 142, 144, 147, 149, 152, 153, 154, 157, 159, 190, 192, 193, 194, 202, 203, 204, 206, 207, 208, 210, 211, 212, 220, 221, 222, 224, 225, 226, 238, 239, 240, 244, 245, 246 }

B grade: { 1, 3, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 22, 23, 27, 28, 29, 30, 31, 32, 33, 35, 37, 39, 41, 42, 43, 44, 46, 48, 50, 52, 53, 54, 55, 56, 57, 58, 59, 61, 63, 65, 67, 69, 70, 71, 129, 131, 138, 140, 141, 143, 145, 146, 148, 150, 151, 155, 156, 158, 160, 197, 199, 213, 215, 217, 227, 228, 229, 241, 242, 243 }

C grade: { }

F grade: { 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, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 195, 196, 198, 200, 201, 205, 209, 214, 216, 218, 219, 223, 230, 231, 232, 233, 234, 235, 236, 237, 247, 248, 249, 250, 251, 252, 253, 254 }

2.1.8 Mupad

A grade: { }

B 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, 77, 78, 79, 80, 93, 94, 95, 96, 101, 102, 103, 104, 119, 120, 121, 122, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 165, 166, 167, 168, 181, 182, 183, 184, 190, 192, 193, 194, 195, 196, 202, 203, 204, 206, 207, 208, 210, 211, 212, 213, 214, 220, 221, 222, 224, 225, 226, 227, 228, 231, 232, 233, 234, 238, 239, 240, 241, 242, 244, 245, 246, 248, 249, 250, 251 }

C grade: { }

F grade: { 73, 74, 75, 76, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 97, 98, 99, 100, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 123, 124, 125, 126, 127, 128, 161, 162, 163, 164, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 185, 186, 187, 188, 189, 191, 197, 198, 199, 200, 201, 205, 209, 215, 216, 217, 218, 219, 223, 229, 230, 235, 236, 237, 243, 247, 252, 253, 254 }

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 Mupad
grade A A A B A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 47 111 91 83 0 110 45
normalized size 1 1.00 0.77 1.82 1.49 1.36 0.00 1.80 0.74
time (sec) N/A 0.057 0.477 1.945 0.367 0.481 0.000 3.139 0.079
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 47 97 80 46 0 96 46
normalized size 1 1.00 0.77 1.59 1.31 0.75 0.00 1.57 0.75
time (sec) N/A 0.058 0.333 0.261 0.349 0.429 0.000 1.906 0.134
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 37 83 69 63 197 82 36
normalized size 1 1.00 0.80 1.80 1.50 1.37 4.28 1.78 0.78
time (sec) N/A 0.055 0.257 1.287 0.339 0.415 124.076 0.709 0.088
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 37 69 58 36 163 68 36
normalized size 1 1.00 0.80 1.50 1.26 0.78 3.54 1.48 0.78
time (sec) N/A 0.055 0.150 0.243 0.336 0.415 40.277 0.449 0.140
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 27 55 47 41 126 54 26
normalized size 1 1.00 0.87 1.77 1.52 1.32 4.06 1.74 0.84
time (sec) N/A 0.050 0.094 0.930 0.339 0.473 11.906 0.374 0.051
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 27 41 36 26 92 40 26
normalized size 1 1.00 0.87 1.32 1.16 0.84 2.97 1.29 0.84
time (sec) N/A 0.050 0.067 0.266 0.338 0.508 3.397 0.353 0.106
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 15 27 26 21 51 26 44
normalized size 1 1.00 0.50 0.90 0.87 0.70 1.70 0.87 1.47
time (sec) N/A 0.011 0.034 0.483 0.321 0.436 0.813 0.321 0.360
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 20 115 28 0 174 12
normalized size 1 1.00 1.00 1.43 8.21 2.00 0.00 12.43 0.86
time (sec) N/A 0.017 0.005 0.681 0.463 0.485 0.000 0.801 0.149
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 50 36 236 52 0 412 26
normalized size 1 1.00 1.79 1.29 8.43 1.86 0.00 14.71 0.93
time (sec) N/A 0.038 0.041 0.975 0.350 0.451 0.000 2.371 0.111
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 29 55 808 85 0 1421 48
normalized size 1 1.00 0.59 1.12 16.49 1.73 0.00 29.00 0.98
time (sec) N/A 0.063 0.019 0.985 0.502 0.494 0.000 4.654 0.121
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 205 78 2174 112 0 3028 60
normalized size 1 1.00 3.11 1.18 32.94 1.70 0.00 45.88 0.91
time (sec) N/A 0.067 0.480 0.866 0.405 0.479 0.000 8.639 0.098
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 31 97 3088 140 0 5647 79
normalized size 1 1.00 0.35 1.09 34.70 1.57 0.00 63.45 0.89
time (sec) N/A 0.069 0.031 0.979 0.619 0.515 0.000 12.384 0.172
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 68 86 72 46 0 85 46
normalized size 1 1.00 1.55 1.95 1.64 1.05 0.00 1.93 1.05
time (sec) N/A 0.069 0.357 0.393 0.333 0.479 0.000 0.761 0.128
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 62 75 65 67 434 74 110
normalized size 1 1.00 0.82 0.99 0.86 0.88 5.71 0.97 1.45
time (sec) N/A 0.068 0.196 0.959 0.335 0.624 117.945 0.599 1.675
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 48 58 50 36 362 57 33
normalized size 1 1.00 1.66 2.00 1.72 1.24 12.48 1.97 1.14
time (sec) N/A 0.059 0.117 0.292 0.327 0.455 40.096 0.502 0.109
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 40 47 41 46 231 46 43
normalized size 1 1.00 0.82 0.96 0.84 0.94 4.71 0.94 0.88
time (sec) N/A 0.056 0.075 0.669 0.329 0.493 11.960 0.418 0.302
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 30 26 24 133 29 13
normalized size 1 1.00 1.00 2.00 1.73 1.60 8.87 1.93 0.87
time (sec) N/A 0.033 0.005 0.142 0.330 0.520 3.298 0.459 0.096
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 13 55 14 0 95 12
normalized size 1 1.00 1.00 0.93 3.93 1.00 0.00 6.79 0.86
time (sec) N/A 0.026 0.013 0.396 0.332 0.444 0.000 0.770 0.084
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 53 19 0 152 11
normalized size 1 1.00 1.00 0.92 4.08 1.46 0.00 11.69 0.85
time (sec) N/A 0.035 0.008 1.071 0.330 0.405 0.000 1.522 0.109
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 36 27 641 56 0 734 35
normalized size 1 1.00 1.20 0.90 21.37 1.87 0.00 24.47 1.17
time (sec) N/A 0.048 0.038 0.872 0.351 0.428 0.000 3.551 0.146
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 48 51 308 43 0 1034 33
normalized size 1 1.00 1.14 1.21 7.33 1.02 0.00 24.62 0.79
time (sec) N/A 0.063 0.056 1.217 0.350 0.393 0.000 2.260 0.135
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 56 69 3164 112 0 2657 74
normalized size 1 1.00 0.93 1.15 52.73 1.87 0.00 44.28 1.23
time (sec) N/A 0.071 0.248 0.922 0.441 0.430 0.000 2.354 0.155
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 37 97 80 73 0 96 36
normalized size 1 1.00 0.80 2.11 1.74 1.59 0.00 2.09 0.78
time (sec) N/A 0.063 0.369 1.478 0.352 0.423 0.000 0.618 0.074
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 47 83 69 46 0 82 46
normalized size 1 1.00 0.77 1.36 1.13 0.75 0.00 1.34 0.75
time (sec) N/A 0.069 0.228 0.305 0.344 0.422 0.000 0.798 0.118
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 27 55 47 53 284 54 26
normalized size 1 1.00 0.87 1.77 1.52 1.71 9.16 1.74 0.84
time (sec) N/A 0.060 0.188 0.882 0.346 0.413 115.462 0.448 0.053
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 37 55 47 36 202 54 36
normalized size 1 1.00 0.80 1.20 1.02 0.78 4.39 1.17 0.78
time (sec) N/A 0.064 0.113 0.302 0.340 0.445 38.634 0.328 0.125
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 41 34 31 117 40 13
normalized size 1 1.00 1.00 2.73 2.27 2.07 7.80 2.67 0.87
time (sec) N/A 0.033 0.008 0.582 0.331 0.458 11.216 0.333 0.099
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 27 32 124 36 0 618 23
normalized size 1 1.00 0.96 1.14 4.43 1.29 0.00 22.07 0.82
time (sec) N/A 0.037 0.014 0.523 0.465 0.489 0.000 0.986 0.124
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 14 83 13 0 319 13
normalized size 1 1.00 1.00 1.08 6.38 1.00 0.00 24.54 1.00
time (sec) N/A 0.035 0.010 0.685 0.326 0.440 0.000 3.869 0.091
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 38 38 480 61 0 1111 36
normalized size 1 1.00 1.12 1.12 14.12 1.79 0.00 32.68 1.06
time (sec) N/A 0.041 0.012 10.773 0.467 0.451 0.000 2.945 0.167
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 61 49 987 67 0 2114 37
normalized size 1 1.00 1.42 1.14 22.95 1.56 0.00 49.16 0.86
time (sec) N/A 0.053 0.029 0.917 0.359 0.484 0.000 6.790 0.075
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 29 76 1805 95 0 4032 67
normalized size 1 1.00 0.41 1.09 25.79 1.36 0.00 57.60 0.96
time (sec) N/A 0.072 0.036 0.916 0.523 0.595 0.000 14.593 0.192
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 119 71 91 46 0 270 46
normalized size 1 1.00 1.95 1.16 1.49 0.75 0.00 4.43 0.75
time (sec) N/A 0.061 0.097 0.834 0.332 0.514 0.000 1.178 0.153
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 48 97 80 73 0 46 45
normalized size 1 1.00 0.79 1.59 1.31 1.20 0.00 0.75 0.74
time (sec) N/A 0.061 0.217 1.262 0.332 0.458 0.000 0.990 0.128
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 89 53 69 36 0 204 36
normalized size 1 1.00 1.93 1.15 1.50 0.78 0.00 4.43 0.78
time (sec) N/A 0.056 0.058 1.009 0.337 0.438 0.000 0.808 0.136
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 38 69 58 53 0 36 36
normalized size 1 1.00 0.83 1.50 1.26 1.15 0.00 0.78 0.78
time (sec) N/A 0.057 0.101 0.972 0.340 0.446 0.000 0.651 0.067
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 59 35 47 26 0 138 26
normalized size 1 1.00 1.90 1.13 1.52 0.84 0.00 4.45 0.84
time (sec) N/A 0.052 0.040 0.662 0.341 0.473 0.000 0.562 0.053
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 28 41 36 33 0 26 26
normalized size 1 1.00 0.90 1.32 1.16 1.06 0.00 0.84 0.84
time (sec) N/A 0.051 0.049 1.049 0.345 0.439 0.000 0.361 0.108
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 14 23 13 0 52 13
normalized size 1 1.00 1.00 0.93 1.53 0.87 0.00 3.47 0.87
time (sec) N/A 0.037 0.007 0.499 0.344 0.438 0.000 0.372 0.034
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 23 12 11 11 3636 11 11
normalized size 1 1.00 2.09 1.09 1.00 1.00 330.55 1.00 1.00
time (sec) N/A 0.017 0.009 0.339 0.344 0.473 21.208 0.362 0.024
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 29 34 233 50 0 484 26
normalized size 1 1.00 1.04 1.21 8.32 1.79 0.00 17.29 0.93
time (sec) N/A 0.041 0.018 0.673 0.476 0.426 0.000 1.696 0.114
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 143 57 974 96 0 1327 49
normalized size 1 1.00 2.92 1.16 19.88 1.96 0.00 27.08 1.00
time (sec) N/A 0.059 0.262 0.915 0.381 0.438 0.000 1.607 0.129
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 31 76 1780 130 0 3033 61
normalized size 1 1.00 0.47 1.15 26.97 1.97 0.00 45.95 0.92
time (sec) N/A 0.063 0.021 0.765 0.532 0.473 0.000 3.944 0.186
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 268 99 3846 148 0 5476 78
normalized size 1 1.00 3.01 1.11 43.21 1.66 0.00 61.53 0.88
time (sec) N/A 0.072 0.514 0.954 0.505 0.494 0.000 10.216 0.122
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 85 111 87 87 0 95 149
normalized size 1 1.00 0.55 0.72 0.56 0.56 0.00 0.61 0.96
time (sec) N/A 0.171 0.255 1.411 0.358 0.458 0.000 1.614 2.272
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 48 53 72 36 0 183 35
normalized size 1 1.00 1.09 1.20 1.64 0.82 0.00 4.16 0.80
time (sec) N/A 0.065 0.175 0.728 0.343 0.424 0.000 0.995 0.149
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 62 83 65 66 0 75 109
normalized size 1 1.00 0.56 0.75 0.59 0.59 0.00 0.68 0.98
time (sec) N/A 0.120 0.199 0.972 0.347 0.458 0.000 1.021 1.690
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 48 35 50 26 0 139 25
normalized size 1 1.00 1.66 1.21 1.72 0.90 0.00 4.79 0.86
time (sec) N/A 0.057 0.125 0.576 0.351 0.418 0.000 0.676 0.052
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 40 55 43 47 0 55 65
normalized size 1 1.00 0.67 0.92 0.72 0.78 0.00 0.92 1.08
time (sec) N/A 0.074 0.103 0.912 0.355 0.459 0.000 0.769 0.490
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 14 26 13 0 69 13
normalized size 1 1.00 1.00 1.08 2.00 1.00 0.00 5.31 1.00
time (sec) N/A 0.041 0.007 0.569 0.340 0.449 0.000 0.490 0.111
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 20 28 18 22 0 29 17
normalized size 1 1.00 0.95 1.33 0.86 1.05 0.00 1.38 0.81
time (sec) N/A 0.034 0.022 0.592 0.340 0.410 0.000 0.494 0.148
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 20 13 81 14 0 55 13
normalized size 1 1.00 1.67 1.08 6.75 1.17 0.00 4.58 1.08
time (sec) N/A 0.020 0.018 0.281 0.352 0.451 0.000 0.986 0.125
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 34 27 656 65 0 813 36
normalized size 1 1.00 1.13 0.90 21.87 2.17 0.00 27.10 1.20
time (sec) N/A 0.042 0.055 0.728 0.372 0.433 0.000 1.007 0.137
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 48 51 308 54 0 1079 37
normalized size 1 1.00 1.14 1.21 7.33 1.29 0.00 25.69 0.88
time (sec) N/A 0.059 0.080 1.107 0.360 0.427 0.000 1.806 0.140
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 54 69 3188 138 0 2808 82
normalized size 1 1.00 0.90 1.15 53.13 2.30 0.00 46.80 1.37
time (sec) N/A 0.067 0.361 0.862 0.450 0.512 0.000 3.364 0.219
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 90 87 1227 86 0 3445 55
normalized size 1 1.00 1.25 1.21 17.04 1.19 0.00 47.85 0.76
time (sec) N/A 0.070 0.055 1.235 0.368 0.417 0.000 2.834 0.381
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 76 111 7650 194 0 6374 114
normalized size 1 1.00 0.84 1.23 85.00 2.16 0.00 70.82 1.27
time (sec) N/A 0.082 0.425 0.842 0.720 0.566 0.000 7.126 0.294
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 132 123 2710 118 0 7477 83
normalized size 1 1.00 1.29 1.21 26.57 1.16 0.00 73.30 0.81
time (sec) N/A 0.084 0.073 1.261 0.479 0.511 0.000 12.221 0.281
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 119 71 91 46 0 314 46
normalized size 1 1.00 1.95 1.16 1.49 0.75 0.00 5.15 0.75
time (sec) N/A 0.072 0.152 0.949 0.347 0.652 0.000 3.297 0.132
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 58 107 91 83 0 56 55
normalized size 1 1.00 0.76 1.41 1.20 1.09 0.00 0.74 0.72
time (sec) N/A 0.077 0.327 1.330 0.833 0.481 0.000 1.931 0.115
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 104 53 80 36 0 248 36
normalized size 1 1.00 2.26 1.15 1.74 0.78 0.00 5.39 0.78
time (sec) N/A 0.067 0.101 0.768 1.018 0.445 0.000 1.344 0.137
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 48 79 69 63 0 46 45
normalized size 1 1.00 0.79 1.30 1.13 1.03 0.00 0.75 0.74
time (sec) N/A 0.071 0.169 0.986 0.754 0.426 0.000 1.339 0.125
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 27 35 47 26 0 182 26
normalized size 1 1.00 0.87 1.13 1.52 0.84 0.00 5.87 0.84
time (sec) N/A 0.061 0.151 0.671 1.046 0.438 0.000 1.443 0.054
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 37 51 47 43 0 36 36
normalized size 1 1.00 0.80 1.11 1.02 0.93 0.00 0.78 0.78
time (sec) N/A 0.066 0.111 0.959 0.447 0.690 0.000 0.776 0.124
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 14 34 13 0 74 13
normalized size 1 1.00 1.00 0.93 2.27 0.87 0.00 4.93 0.87
time (sec) N/A 0.044 0.009 0.582 0.819 0.506 0.000 0.979 0.047
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 28 22 23 21 0 22 24
normalized size 1 1.00 1.04 0.81 0.85 0.78 0.00 0.81 0.89
time (sec) N/A 0.039 0.011 0.819 1.875 0.644 0.000 0.505 0.102
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 44 34 92 38 0 57 22
normalized size 1 1.00 1.83 1.42 3.83 1.58 0.00 2.38 0.92
time (sec) N/A 0.043 0.023 0.568 0.992 0.623 0.000 0.574 0.112
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 14 84 13 0 13 13
normalized size 1 1.00 1.00 1.27 7.64 1.18 0.00 1.18 1.18
time (sec) N/A 0.026 0.011 0.294 0.349 0.518 0.000 0.348 0.038
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 31 47 834 94 0 2096 38
normalized size 1 1.00 0.72 1.09 19.40 2.19 0.00 48.74 0.88
time (sec) N/A 0.049 0.018 0.893 1.145 0.434 0.000 1.075 0.126
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 129 78 2237 132 0 3775 66
normalized size 1 1.00 1.84 1.11 31.96 1.89 0.00 53.93 0.94
time (sec) N/A 0.073 4.470 0.738 0.590 0.443 0.000 4.386 0.150
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 31 97 3095 166 0 6318 71
normalized size 1 1.00 0.38 1.20 38.21 2.05 0.00 78.00 0.88
time (sec) N/A 0.073 0.036 0.706 1.052 0.564 0.000 9.367 0.179
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 278 120 4268 194 0 0 100
normalized size 1 1.00 2.48 1.07 38.11 1.73 0.00 0.00 0.89
time (sec) N/A 0.087 0.846 0.854 1.565 0.554 0.000 0.000 0.227
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 98 183661406 0 291 0 0 -1
normalized size 1 1.00 0.72 1350451.52 0.00 2.14 0.00 0.00 -0.01
time (sec) N/A 0.094 0.297 89.385 0.000 0.622 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 86 65166862 0 280 0 0 -1
normalized size 1 1.00 0.78 592426.02 0.00 2.55 0.00 0.00 -0.01
time (sec) N/A 0.068 0.199 25.674 0.000 0.481 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 72 6214674 0 266 0 0 -1
normalized size 1 1.00 0.86 73984.21 0.00 3.17 0.00 0.00 -0.01
time (sec) N/A 0.043 0.076 2.853 0.000 0.781 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 50 15972263 0 240 0 0 -1
normalized size 1 1.00 0.86 275383.84 0.00 4.14 0.00 0.00 -0.02
time (sec) N/A 0.021 0.053 3.214 0.000 0.494 0.000 0.000 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 22 59119746 0 39 0 0 34
normalized size 1 1.00 0.96 2570423.74 0.00 1.70 0.00 0.00 1.48
time (sec) N/A 0.018 0.020 11.404 0.000 0.473 0.000 0.000 0.284
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 43 597 0 69 0 0 108
normalized size 1 1.00 0.81 11.26 0.00 1.30 0.00 0.00 2.04
time (sec) N/A 0.040 0.109 41.618 0.000 0.451 0.000 0.000 3.080
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 52 0 0 88 0 0 131
normalized size 1 1.00 0.66 0.00 0.00 1.11 0.00 0.00 1.66
time (sec) N/A 0.059 0.195 180.000 0.000 0.432 0.000 0.000 3.391
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 67 0 0 113 0 0 351
normalized size 1 1.00 0.64 0.00 0.00 1.08 0.00 0.00 3.34
time (sec) N/A 0.083 0.146 180.000 0.000 0.453 0.000 0.000 4.335
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 96 0 0 0 0 0 -1
normalized size 1 1.00 0.98 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.060 0.407 180.000 0.000 0.573 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 66 278615779 0 0 0 0 -1
normalized size 1 1.00 0.96 4037909.84 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.047 0.220 167.057 0.000 0.521 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 76 172368074 0 0 0 0 -1
normalized size 1 1.00 1.10 2498088.03 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.047 0.359 71.760 0.000 0.441 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 34 16549859 0 0 0 0 -1
normalized size 1 1.00 0.85 413746.48 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.036 0.087 5.709 0.000 0.468 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 75 53360209 0 0 0 0 -1
normalized size 1 1.00 1.88 1334005.22 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.037 0.245 13.507 0.000 0.448 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 41 83175028 0 0 0 0 -1
normalized size 1 1.00 0.91 1848333.96 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.037 0.098 15.515 0.000 0.449 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 83 123 0 0 0 0 -1
normalized size 1 1.00 1.73 2.56 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.038 0.194 59.888 0.000 0.452 0.000 0.000 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 66 0 0 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.046 0.810 180.000 0.000 0.432 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 98 322540527 0 290 0 0 -1
normalized size 1 1.00 0.72 2371621.52 0.00 2.13 0.00 0.00 -0.01
time (sec) N/A 0.101 0.347 194.690 0.000 0.469 0.000 0.000 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 86 47453403 0 281 0 0 -1
normalized size 1 1.00 0.78 431394.57 0.00 2.55 0.00 0.00 -0.01
time (sec) N/A 0.078 0.220 23.188 0.000 0.507 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 74 155804040 0 268 0 0 -1
normalized size 1 1.00 0.88 1854810.00 0.00 3.19 0.00 0.00 -0.01
time (sec) N/A 0.054 0.144 46.944 0.000 0.488 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 72 149378290 0 296 0 0 -1
normalized size 1 1.00 0.89 1844176.42 0.00 3.65 0.00 0.00 -0.01
time (sec) N/A 0.078 0.095 52.777 0.000 0.464 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 27 727 0 48 0 0 85
normalized size 1 1.00 0.96 25.96 0.00 1.71 0.00 0.00 3.04
time (sec) N/A 0.028 0.055 183.929 0.000 0.450 0.000 0.000 2.194
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 35 0 0 55 0 0 88
normalized size 1 1.00 0.64 0.00 0.00 1.00 0.00 0.00 1.60
time (sec) N/A 0.049 0.095 180.000 0.000 0.486 0.000 0.000 3.260
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 55 0 0 79 0 0 300
normalized size 1 1.00 0.68 0.00 0.00 0.98 0.00 0.00 3.70
time (sec) N/A 0.069 0.109 180.000 0.000 0.429 0.000 0.000 3.713
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 62 0 0 98 0 0 383
normalized size 1 1.00 0.58 0.00 0.00 0.92 0.00 0.00 3.58
time (sec) N/A 0.092 0.167 180.000 0.000 0.447 0.000 0.000 5.161
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 98 973 0 290 0 0 -1
normalized size 1 1.00 0.72 7.15 0.00 2.13 0.00 0.00 -0.01
time (sec) N/A 0.123 0.326 19.859 0.000 0.448 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 86 243 0 281 0 0 -1
normalized size 1 1.00 0.78 2.21 0.00 2.55 0.00 0.00 -0.01
time (sec) N/A 0.095 0.202 20.549 0.000 0.462 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 70 362 0 266 0 0 -1
normalized size 1 1.00 0.86 4.47 0.00 3.28 0.00 0.00 -0.01
time (sec) N/A 0.072 0.086 10.365 0.000 0.474 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 52 157 0 242 0 0 -1
normalized size 1 1.00 0.98 2.96 0.00 4.57 0.00 0.00 -0.02
time (sec) N/A 0.047 0.044 8.587 0.000 0.488 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 23 308 0 39 0 0 24
normalized size 1 1.00 0.96 12.83 0.00 1.62 0.00 0.00 1.00
time (sec) N/A 0.024 0.046 9.957 0.000 0.448 0.000 0.000 0.308
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 43 194 0 74 0 0 103
normalized size 1 1.00 0.81 3.66 0.00 1.40 0.00 0.00 1.94
time (sec) N/A 0.064 0.106 13.100 0.000 0.522 0.000 0.000 2.962
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 52 481 0 103 0 0 136
normalized size 1 1.00 0.66 6.09 0.00 1.30 0.00 0.00 1.72
time (sec) N/A 0.086 0.125 37.234 0.000 0.555 0.000 0.000 3.362
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 67 0 0 118 0 0 350
normalized size 1 1.00 0.64 0.00 0.00 1.12 0.00 0.00 3.33
time (sec) N/A 0.108 0.142 180.000 0.000 0.460 0.000 0.000 4.130
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 66 204 0 0 0 0 -1
normalized size 1 1.00 0.62 1.92 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.058 0.245 29.075 0.000 0.519 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 76 139 0 0 0 0 -1
normalized size 1 1.00 0.72 1.31 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.059 0.268 25.250 0.000 0.460 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 34 137 0 0 0 0 -1
normalized size 1 1.00 0.45 1.83 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.047 0.083 22.392 0.000 0.472 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 73 111 0 0 0 0 -1
normalized size 1 1.00 1.04 1.59 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.048 0.923 15.645 0.000 0.457 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 37 176 0 0 0 0 -1
normalized size 1 1.00 0.84 4.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.036 0.131 17.731 0.000 0.436 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 82 0 0 0 0 0 -1
normalized size 1 1.00 1.71 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.037 0.993 180.000 0.000 0.497 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 64 227 0 0 0 0 -1
normalized size 1 1.00 0.83 2.95 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.047 0.591 59.936 0.000 0.467 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 66 154 0 0 0 0 -1
normalized size 1 1.00 0.86 2.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.048 0.469 90.513 0.000 0.544 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 85 0 0 0 0 0 -1
normalized size 1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.058 0.827 180.000 0.000 0.523 0.000 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 86 0 0 0 0 0 -1
normalized size 1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.059 0.364 180.000 0.000 0.476 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 190 190 100 441 0 291 0 0 -1
normalized size 1 1.00 0.53 2.32 0.00 1.53 0.00 0.00 -0.01
time (sec) N/A 0.186 0.438 211.099 0.000 0.490 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 164 164 84 973 0 280 0 0 -1
normalized size 1 1.00 0.51 5.93 0.00 1.71 0.00 0.00 -0.01
time (sec) N/A 0.156 0.227 81.756 0.000 0.678 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 70 243 0 268 0 0 -1
normalized size 1 1.00 0.55 1.91 0.00 2.11 0.00 0.00 -0.01
time (sec) N/A 0.131 0.139 41.222 0.000 0.574 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 68 542 0 295 0 0 -1
normalized size 1 1.00 0.65 5.21 0.00 2.84 0.00 0.00 -0.01
time (sec) N/A 0.102 0.099 86.501 0.000 0.541 0.000 0.000 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 27 192 0 53 0 0 95
normalized size 1 1.00 0.96 6.86 0.00 1.89 0.00 0.00 3.39
time (sec) N/A 0.028 0.051 31.018 0.000 0.457 0.000 0.000 1.500
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 35 0 0 76 0 0 93
normalized size 1 1.00 0.64 0.00 0.00 1.38 0.00 0.00 1.69
time (sec) N/A 0.053 0.093 180.000 0.000 0.475 0.000 0.000 3.162
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 55 222 0 104 0 0 302
normalized size 1 1.00 0.68 2.74 0.00 1.28 0.00 0.00 3.73
time (sec) N/A 0.092 0.116 107.667 0.000 0.512 0.000 0.000 3.700
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 62 0 0 131 0 0 383
normalized size 1 1.00 0.58 0.00 0.00 1.22 0.00 0.00 3.58
time (sec) N/A 0.116 0.097 180.000 0.000 0.607 0.000 0.000 4.989
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 84 84 602 0 0 0 0 0 -1
normalized size 1 1.00 7.17 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.074 5.726 10.162 0.000 0.508 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 84 84 602 0 0 0 0 0 -1
normalized size 1 1.00 7.17 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.077 3.509 6.229 0.000 0.533 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 82 82 152 0 0 0 0 0 -1
normalized size 1 1.00 1.85 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.064 0.264 5.039 0.000 0.502 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 72 72 254 0 0 0 0 0 -1
normalized size 1 1.00 3.53 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.070 0.866 4.345 0.000 0.575 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 85 85 938 0 0 0 0 0 -1
normalized size 1 1.00 11.04 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.082 5.416 4.280 0.000 0.506 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 85 85 2308 0 0 0 0 0 -1
normalized size 1 1.00 27.15 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.081 19.220 3.849 0.000 0.476 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 47 111 91 46 0 110 46
normalized size 1 1.00 0.77 1.82 1.49 0.75 0.00 1.80 0.75
time (sec) N/A 0.060 0.439 0.413 0.350 0.468 0.000 2.903 0.035
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 47 97 80 73 0 96 45
normalized size 1 1.00 0.77 1.59 1.31 1.20 0.00 1.57 0.74
time (sec) N/A 0.061 0.291 1.760 0.338 0.510 0.000 1.726 0.132
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 37 83 69 36 199 82 36
normalized size 1 1.00 0.80 1.80 1.50 0.78 4.33 1.78 0.78
time (sec) N/A 0.055 0.254 0.458 0.339 0.463 113.174 0.943 0.146
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 37 69 58 53 162 68 36
normalized size 1 1.00 0.80 1.50 1.26 1.15 3.52 1.48 0.78
time (sec) N/A 0.054 0.135 1.223 0.336 0.410 38.308 2.925 0.141
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 27 55 47 26 128 54 26
normalized size 1 1.00 0.87 1.77 1.52 0.84 4.13 1.74 0.84
time (sec) N/A 0.050 0.093 0.409 0.330 0.452 11.275 0.290 0.032
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 27 41 36 33 90 40 26
normalized size 1 1.00 0.87 1.32 1.16 1.06 2.90 1.29 0.84
time (sec) N/A 0.048 0.064 0.622 0.328 0.420 3.117 0.455 0.028
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 15 27 26 13 53 26 43
normalized size 1 1.00 0.50 0.90 0.87 0.43 1.77 0.87 1.43
time (sec) N/A 0.011 0.006 0.219 0.317 0.480 0.760 0.278 0.192
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 42 22 84 30 0 16 12
normalized size 1 1.00 3.00 1.57 6.00 2.14 0.00 1.14 0.86
time (sec) N/A 0.016 0.012 0.551 0.337 0.597 0.000 0.223 0.022
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 29 34 233 50 0 38 26
normalized size 1 1.00 1.04 1.21 8.32 1.79 0.00 1.36 0.93
time (sec) N/A 0.038 0.019 0.861 0.465 0.474 0.000 0.271 0.024
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 143 57 974 96 0 140 49
normalized size 1 1.00 2.92 1.16 19.88 1.96 0.00 2.86 1.00
time (sec) N/A 0.055 0.255 0.947 0.352 0.468 0.000 0.412 0.083
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 31 76 1780 130 0 72 61
normalized size 1 1.00 0.47 1.15 26.97 1.97 0.00 1.09 0.92
time (sec) N/A 0.059 0.023 1.113 0.528 0.466 0.000 0.437 0.098
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 268 99 3846 148 0 209 78
normalized size 1 1.00 3.01 1.11 43.21 1.66 0.00 2.35 0.88
time (sec) N/A 0.067 0.476 0.963 0.502 0.477 0.000 0.643 0.119
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 68 86 72 36 0 85 35
normalized size 1 1.00 1.55 1.95 1.64 0.82 0.00 1.93 0.80
time (sec) N/A 0.067 0.412 0.339 0.338 0.459 0.000 0.493 0.175
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 62 75 65 66 434 74 109
normalized size 1 1.00 0.82 0.99 0.86 0.87 5.71 0.97 1.43
time (sec) N/A 0.064 0.185 1.652 0.341 0.465 116.231 0.398 1.727
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 48 58 50 26 359 57 26
normalized size 1 1.00 1.71 2.07 1.79 0.93 12.82 2.04 0.93
time (sec) N/A 0.057 0.116 0.416 0.337 0.652 39.276 0.320 0.144
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 40 47 43 47 231 46 43
normalized size 1 1.00 0.82 0.96 0.88 0.96 4.71 0.94 0.88
time (sec) N/A 0.054 0.096 0.962 0.339 0.501 11.677 0.191 0.313
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 30 26 13 131 29 13
normalized size 1 1.00 1.00 2.00 1.73 0.87 8.73 1.93 0.87
time (sec) N/A 0.033 0.005 0.240 0.335 0.518 3.241 0.496 0.153
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 22 13 82 14 0 56 14
normalized size 1 1.00 1.57 0.93 5.86 1.00 0.00 4.00 1.00
time (sec) N/A 0.025 0.016 0.644 0.332 0.518 0.000 0.224 0.157
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 53 19 0 13 11
normalized size 1 1.00 1.00 0.92 4.08 1.46 0.00 1.00 0.85
time (sec) N/A 0.033 0.013 1.128 0.333 0.515 0.000 0.230 0.142
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 34 27 656 65 0 119 36
normalized size 1 1.00 1.13 0.90 21.87 2.17 0.00 3.97 1.20
time (sec) N/A 0.047 0.049 1.075 0.351 0.585 0.000 0.361 0.178
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 48 51 308 54 0 35 37
normalized size 1 1.00 1.14 1.21 7.33 1.29 0.00 0.83 0.88
time (sec) N/A 0.060 0.052 1.625 0.343 0.459 0.000 0.495 0.184
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 54 69 3188 138 0 232 82
normalized size 1 1.00 0.90 1.15 53.13 2.30 0.00 3.87 1.37
time (sec) N/A 0.068 0.351 1.265 0.437 0.466 0.000 0.739 0.144
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 37 97 80 36 0 96 36
normalized size 1 1.00 0.80 2.11 1.74 0.78 0.00 2.09 0.78
time (sec) N/A 0.061 0.390 0.397 0.336 0.446 0.000 0.598 0.071
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 47 83 69 63 0 82 45
normalized size 1 1.00 0.77 1.36 1.13 1.03 0.00 1.34 0.74
time (sec) N/A 0.065 0.213 1.251 0.340 0.484 0.000 0.371 0.061
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 27 55 47 26 284 54 26
normalized size 1 1.00 0.87 1.77 1.52 0.84 9.16 1.74 0.84
time (sec) N/A 0.056 0.137 0.454 0.329 0.423 113.547 0.374 0.152
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 37 55 47 43 202 54 36
normalized size 1 1.00 0.80 1.20 1.02 0.93 4.39 1.17 0.78
time (sec) N/A 0.060 0.093 0.987 0.330 0.414 38.318 0.226 0.160
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 41 34 13 117 40 13
normalized size 1 1.00 1.00 2.73 2.27 0.87 7.80 2.67 0.87
time (sec) N/A 0.033 0.008 0.169 0.326 0.455 11.227 0.178 0.142
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 46 34 92 38 0 57 22
normalized size 1 1.00 1.64 1.21 3.29 1.36 0.00 2.04 0.79
time (sec) N/A 0.035 0.020 0.565 0.343 0.495 0.000 0.691 0.053
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 14 84 13 0 13 13
normalized size 1 1.00 1.00 1.08 6.46 1.00 0.00 1.00 1.00
time (sec) N/A 0.035 0.012 0.472 0.337 0.463 0.000 0.250 0.023
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 79 40 558 72 0 92 36
normalized size 1 1.00 2.32 1.18 16.41 2.12 0.00 2.71 1.06
time (sec) N/A 0.041 0.015 0.857 0.345 0.478 0.000 0.657 0.059
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 31 47 834 94 0 52 38
normalized size 1 1.00 0.72 1.09 19.40 2.19 0.00 1.21 0.88
time (sec) N/A 0.051 0.018 1.214 0.656 0.447 0.000 0.929 0.064
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 195 78 2237 132 0 163 66
normalized size 1 1.00 2.79 1.11 31.96 1.89 0.00 2.33 0.94
time (sec) N/A 0.070 0.333 1.120 0.415 0.435 0.000 0.825 0.186
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 98 199880292 0 290 0 0 -1
normalized size 1 1.00 0.72 1469708.03 0.00 2.13 0.00 0.00 -0.01
time (sec) N/A 0.091 0.345 91.921 0.000 0.496 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 86 74316382 0 281 0 0 -1
normalized size 1 1.00 0.78 675603.47 0.00 2.55 0.00 0.00 -0.01
time (sec) N/A 0.067 0.190 24.515 0.000 0.497 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 70 5342284 0 266 0 0 -1
normalized size 1 1.00 0.83 63598.62 0.00 3.17 0.00 0.00 -0.01
time (sec) N/A 0.043 0.098 2.750 0.000 0.533 0.000 0.000 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 52 16154758 0 242 0 0 -1
normalized size 1 1.00 0.90 278530.31 0.00 4.17 0.00 0.00 -0.02
time (sec) N/A 0.021 0.049 3.185 0.000 0.441 0.000 0.000 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 23 55902198 0 39 0 0 24
normalized size 1 1.00 0.96 2329258.25 0.00 1.62 0.00 0.00 1.00
time (sec) N/A 0.018 0.023 10.737 0.000 0.503 0.000 0.000 0.192
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 43 194 0 74 0 0 104
normalized size 1 1.00 0.81 3.66 0.00 1.40 0.00 0.00 1.96
time (sec) N/A 0.038 0.108 33.699 0.000 0.592 0.000 0.000 3.168
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 52 0 0 103 0 0 136
normalized size 1 1.00 0.66 0.00 0.00 1.30 0.00 0.00 1.72
time (sec) N/A 0.059 0.125 180.000 0.000 0.458 0.000 0.000 3.233
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 67 0 0 118 0 0 350
normalized size 1 1.00 0.64 0.00 0.00 1.12 0.00 0.00 3.33
time (sec) N/A 0.080 0.143 180.000 0.000 0.433 0.000 0.000 3.866
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 96 0 0 0 0 0 -1
normalized size 1 1.00 0.98 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.057 0.390 180.000 0.000 0.555 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 66 336654856 0 0 0 0 -1
normalized size 1 1.00 0.96 4879055.88 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.045 0.205 196.388 0.000 0.551 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 76 174364216 0 0 0 0 -1
normalized size 1 1.00 1.10 2527017.62 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.045 0.348 61.350 0.000 0.484 0.000 0.000 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 34 24858211 0 0 0 0 -1
normalized size 1 1.00 0.85 621455.28 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.035 0.057 7.574 0.000 0.542 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 76 59624230 0 0 0 0 -1
normalized size 1 1.00 1.90 1490605.75 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.035 0.890 15.386 0.000 0.600 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 39 94273592 0 0 0 0 -1
normalized size 1 1.00 0.85 2049425.91 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.036 0.112 17.328 0.000 0.616 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 82 123 0 0 0 0 -1
normalized size 1 1.00 1.71 2.56 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.036 1.002 59.046 0.000 0.520 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 64 227 0 0 0 0 -1
normalized size 1 1.00 0.83 2.95 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.046 0.561 212.846 0.000 0.554 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 99 0 0 291 0 0 -1
normalized size 1 1.00 0.73 0.00 0.00 2.14 0.00 0.00 -0.01
time (sec) N/A 0.099 0.336 180.000 0.000 0.459 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 84 88680892 0 280 0 0 -1
normalized size 1 1.00 0.76 806189.93 0.00 2.55 0.00 0.00 -0.01
time (sec) N/A 0.076 0.187 32.658 0.000 0.565 0.000 0.000 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 73 191110780 0 268 0 0 -1
normalized size 1 1.00 0.87 2275128.33 0.00 3.19 0.00 0.00 -0.01
time (sec) N/A 0.052 0.107 69.299 0.000 0.725 0.000 0.000 0.000
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 70 179323229 0 295 0 0 -1
normalized size 1 1.00 0.85 2186868.65 0.00 3.60 0.00 0.00 -0.01
time (sec) N/A 0.076 0.092 32.122 0.000 0.542 0.000 0.000 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 27 192 0 53 0 0 94
normalized size 1 1.00 0.96 6.86 0.00 1.89 0.00 0.00 3.36
time (sec) N/A 0.027 0.054 167.451 0.000 0.645 0.000 0.000 1.168
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 35 0 0 76 0 0 93
normalized size 1 1.00 0.64 0.00 0.00 1.38 0.00 0.00 1.69
time (sec) N/A 0.047 0.092 180.000 0.000 0.470 0.000 0.000 3.075
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 55 0 0 104 0 0 302
normalized size 1 1.00 0.68 0.00 0.00 1.28 0.00 0.00 3.73
time (sec) N/A 0.068 0.116 180.000 0.000 0.518 0.000 0.000 3.661
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F A F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 62 0 0 131 0 0 383
normalized size 1 1.00 0.58 0.00 0.00 1.22 0.00 0.00 3.58
time (sec) N/A 0.090 0.093 180.000 0.000 0.482 0.000 0.000 4.881
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 29 98 0 137 0 0 -1
normalized size 1 1.00 0.94 3.16 0.00 4.42 0.00 0.00 -0.03
time (sec) N/A 0.013 0.025 0.814 0.000 0.487 0.000 0.000 0.000
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 99 0 137 0 0 -1
normalized size 1 1.00 1.00 3.96 0.00 5.48 0.00 0.00 -0.04
time (sec) N/A 0.030 0.016 2.461 0.000 0.453 0.000 0.000 0.000
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 85 85 2472 0 0 0 0 0 -1
normalized size 1 1.00 29.08 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.071 13.248 6.181 0.000 0.432 0.000 0.000 0.000
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 85 85 890 0 0 0 0 0 -1
normalized size 1 1.00 10.47 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.071 7.809 5.900 0.000 0.431 0.000 0.000 0.000
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 83 83 149 0 0 0 0 0 -1
normalized size 1 1.00 1.80 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.061 0.258 5.358 0.000 0.477 0.000 0.000 0.000
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 37 69 58 36 0 68 36
normalized size 1 1.00 0.80 1.50 1.26 0.78 0.00 1.48 0.78
time (sec) N/A 0.097 0.156 0.426 0.341 0.531 0.000 0.638 0.205
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 293 293 209 0 0 0 0 0 -1
normalized size 1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.848 0.895 14.316 0.000 0.450 0.000 0.000 0.000
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 86 84 916 122 921 84 311
normalized size 1 1.00 0.95 0.92 10.07 1.34 10.12 0.92 3.42
time (sec) N/A 0.076 0.545 0.856 0.414 0.572 32.888 0.745 1.567
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 69 57 414 71 408 56 98
normalized size 1 1.00 1.11 0.92 6.68 1.15 6.58 0.90 1.58
time (sec) N/A 0.053 0.714 0.200 0.348 0.426 6.696 0.188 0.736
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 43 40 40 42 153 40 84
normalized size 1 1.00 1.00 0.93 0.93 0.98 3.56 0.93 1.95
time (sec) N/A 0.035 0.194 0.418 0.319 0.428 1.486 0.363 1.063
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 26 325 108 31 333 0 111
normalized size 1 1.00 1.00 12.50 4.15 1.19 12.81 0.00 4.27
time (sec) N/A 0.027 0.151 1.549 0.396 0.424 8.199 0.000 0.869
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 90 890 454 71 3266 0 252
normalized size 1 1.00 2.50 24.72 12.61 1.97 90.72 0.00 7.00
time (sec) N/A 0.033 0.099 2.226 0.363 0.509 101.783 0.000 5.209
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-1) B F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 35 120 399 47 0 145 -1
normalized size 1 1.00 0.90 3.08 10.23 1.21 0.00 3.72 -0.03
time (sec) N/A 0.044 0.202 2.343 0.336 0.433 0.000 0.215 0.000
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 67 14880 1773 141 0 0 -1
normalized size 1 1.00 1.00 222.09 26.46 2.10 0.00 0.00 -0.01
time (sec) N/A 0.046 0.576 4.898 0.423 0.651 0.000 0.000 0.000
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-1) B F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 58 321 1076 75 0 301 -1
normalized size 1 1.00 0.97 5.35 17.93 1.25 0.00 5.02 -0.02
time (sec) N/A 0.047 0.381 4.635 0.349 0.573 0.000 3.250 0.000
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 79 97954 3879 197 0 0 -1
normalized size 1 1.00 0.84 1042.06 41.27 2.10 0.00 0.00 -0.01
time (sec) N/A 0.058 1.160 14.958 0.569 0.492 0.000 0.000 0.000
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 410 410 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.973 0.403 7.184 0.000 0.432 0.000 0.000 0.000
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 80 63 371 69 408 61 105
normalized size 1 1.00 1.18 0.93 5.46 1.01 6.00 0.90 1.54
time (sec) N/A 0.054 0.342 0.152 0.351 0.465 6.514 0.202 0.751
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 106 83 620 118 1027 80 177
normalized size 1 1.00 1.20 0.94 7.05 1.34 11.67 0.91 2.01
time (sec) N/A 0.065 0.761 1.078 0.378 0.468 22.695 0.184 0.886
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 158 133 1362 192 1999 129 469
normalized size 1 1.00 1.10 0.92 9.46 1.33 13.88 0.90 3.26
time (sec) N/A 0.097 1.568 0.276 0.423 0.612 113.790 2.527 1.873
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 600 600 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.722 0.579 6.415 0.000 0.658 0.000 0.000 0.000
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 91 90 789 115 933 89 494
normalized size 1 1.00 0.94 0.93 8.13 1.19 9.62 0.92 5.09
time (sec) N/A 0.075 0.537 0.993 0.403 0.565 31.735 1.460 1.717
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 153 127 1360 189 2030 124 437
normalized size 1 1.00 1.11 0.92 9.86 1.37 14.71 0.90 3.17
time (sec) N/A 0.098 1.598 0.293 0.433 0.473 113.351 0.183 2.127
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 195 177 184 2612 291 0 181 997
normalized size 1 1.00 0.91 0.94 13.39 1.49 0.00 0.93 5.11
time (sec) N/A 0.132 1.661 2.019 0.574 0.590 0.000 0.178 4.315
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 277 277 202 0 0 0 0 0 -1
normalized size 1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.589 1.025 3.262 0.000 0.579 0.000 0.000 0.000
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 87 84 912 106 918 84 297
normalized size 1 1.00 0.96 0.92 10.02 1.16 10.09 0.92 3.26
time (sec) N/A 0.066 0.505 0.173 0.391 0.416 32.160 1.920 1.615
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 71 57 414 66 405 56 97
normalized size 1 1.00 1.15 0.92 6.68 1.06 6.53 0.90 1.56
time (sec) N/A 0.047 0.778 0.169 0.348 0.502 6.539 5.904 0.767
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 43 40 40 42 155 40 85
normalized size 1 1.00 1.00 0.93 0.93 0.98 3.60 0.93 1.98
time (sec) N/A 0.036 0.187 0.176 0.312 0.463 1.454 0.262 0.842
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 563 73 31 435 158 112
normalized size 1 1.00 1.00 20.85 2.70 1.15 16.11 5.85 4.15
time (sec) N/A 0.018 0.150 1.558 0.342 0.457 10.125 0.203 0.894
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 88 888 387 69 5552 0 254
normalized size 1 1.00 2.59 26.12 11.38 2.03 163.29 0.00 7.47
time (sec) N/A 0.027 0.100 1.969 0.519 0.480 165.058 0.000 5.345
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-2) B F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 34 150 391 42 0 174 -1
normalized size 1 1.00 0.89 3.95 10.29 1.11 0.00 4.58 -0.03
time (sec) N/A 0.037 0.176 3.140 0.343 0.536 0.000 3.852 0.000
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 64 14825 1424 94 0 0 -1
normalized size 1 1.00 0.96 221.27 21.25 1.40 0.00 0.00 -0.01
time (sec) N/A 0.042 0.443 8.843 0.577 0.526 0.000 0.000 0.000
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-1) B F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 48 333 1074 53 0 327 -1
normalized size 1 1.00 0.81 5.64 18.20 0.90 0.00 5.54 -0.02
time (sec) N/A 0.051 0.343 13.273 0.352 0.483 0.000 0.230 0.000
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 78 97703 3096 107 0 0 -1
normalized size 1 1.00 0.83 1039.39 32.94 1.14 0.00 0.00 -0.01
time (sec) N/A 0.070 0.986 14.867 0.686 0.496 0.000 0.000 0.000
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 386 386 242 0 0 0 0 0 -1
normalized size 1 1.00 0.63 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.700 1.832 5.432 0.000 0.489 0.000 0.000 0.000
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 76 63 371 70 408 61 105
normalized size 1 1.00 1.12 0.93 5.46 1.03 6.00 0.90 1.54
time (sec) N/A 0.051 0.793 0.631 0.350 0.455 6.697 0.196 0.809
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 108 83 620 108 1027 80 177
normalized size 1 1.00 1.23 0.94 7.05 1.23 11.67 0.91 2.01
time (sec) N/A 0.068 0.730 1.231 0.379 0.435 22.977 0.198 0.929
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 158 133 1362 174 1999 129 495
normalized size 1 1.00 1.10 0.92 9.46 1.21 13.88 0.90 3.44
time (sec) N/A 0.096 1.759 1.194 0.431 0.432 115.103 0.278 1.969
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 568 568 329 0 0 0 0 0 -1
normalized size 1 1.00 0.58 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.180 23.938 5.522 0.000 0.540 0.000 0.000 0.000
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 90 90 785 116 933 89 471
normalized size 1 1.00 0.93 0.93 8.09 1.20 9.62 0.92 4.86
time (sec) N/A 0.068 0.527 0.266 0.383 0.441 32.622 0.249 1.613
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 153 127 1360 179 2020 124 438
normalized size 1 1.00 1.11 0.92 9.86 1.30 14.64 0.90 3.17
time (sec) N/A 0.096 1.574 0.288 0.420 0.438 117.133 0.195 2.032
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 195 176 184 2612 264 0 181 951
normalized size 1 1.00 0.90 0.94 13.39 1.35 0.00 0.93 4.88
time (sec) N/A 0.124 1.546 0.312 0.540 0.497 0.000 0.282 4.136
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 58 325 106 30 333 482 115
normalized size 1 1.00 2.15 12.04 3.93 1.11 12.33 17.85 4.26
time (sec) N/A 0.017 0.179 1.935 0.359 0.478 8.034 1.556 0.703
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 90 1062 450 71 3266 893 252
normalized size 1 1.00 2.57 30.34 12.86 2.03 93.31 25.51 7.20
time (sec) N/A 0.028 0.102 2.163 0.376 0.473 102.513 0.466 5.210
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) B F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 35 55 395 45 0 327 -1
normalized size 1 1.00 0.92 1.45 10.39 1.18 0.00 8.61 -0.03
time (sec) N/A 0.043 0.210 12.388 0.345 0.471 0.000 0.285 0.000
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B B F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 70 186 1027 376 0 0 -1
normalized size 1 1.00 0.97 2.58 14.26 5.22 0.00 0.00 -0.01
time (sec) N/A 0.071 0.372 1.005 0.546 0.535 0.000 0.000 0.000
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C B B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 109 143 520 315 0 0 294
normalized size 1 1.00 2.48 3.25 11.82 7.16 0.00 0.00 6.68
time (sec) N/A 0.036 0.096 0.792 0.530 0.467 0.000 0.000 5.306
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C B B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 94 99 131 188 0 0 227
normalized size 1 1.00 3.24 3.41 4.52 6.48 0.00 0.00 7.83
time (sec) N/A 0.016 0.048 0.515 0.515 0.451 0.000 0.000 5.487
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C B B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 93 95 105 197 0 0 233
normalized size 1 1.00 3.21 3.28 3.62 6.79 0.00 0.00 8.03
time (sec) N/A 0.016 0.057 0.799 0.351 0.447 0.000 0.000 4.846
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C B B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 111 143 612 316 0 0 290
normalized size 1 1.00 2.41 3.11 13.30 6.87 0.00 0.00 6.30
time (sec) N/A 0.040 0.096 1.007 0.371 0.451 0.000 0.000 5.262
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B B F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 71 184 1254 372 0 0 -1
normalized size 1 1.00 0.96 2.49 16.95 5.03 0.00 0.00 -0.01
time (sec) N/A 0.072 0.374 0.880 0.396 0.508 0.000 0.000 0.000
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 143 143 116 0 0 0 0 0 -1
normalized size 1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.112 1.806 1.465 0.000 0.477 0.000 0.000 0.000
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 139 139 260 0 0 0 0 0 -1
normalized size 1 1.00 1.87 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.111 3.615 1.770 0.000 0.540 0.000 0.000 0.000
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 85 84 914 109 918 84 313
normalized size 1 1.00 0.93 0.92 10.04 1.20 10.09 0.92 3.44
time (sec) N/A 0.065 0.518 0.942 0.405 0.431 32.436 5.945 1.949
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 69 57 416 63 405 56 98
normalized size 1 1.00 1.11 0.92 6.71 1.02 6.53 0.90 1.58
time (sec) N/A 0.045 0.756 0.648 0.372 0.454 6.680 0.196 1.017
Problem 240 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 43 40 40 42 153 40 84
normalized size 1 1.00 1.00 0.93 0.93 0.98 3.56 0.93 1.95
time (sec) N/A 0.033 0.184 0.663 0.333 0.448 1.476 0.820 1.295
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 26 461 74 31 435 440 109
normalized size 1 1.00 1.00 17.73 2.85 1.19 16.73 16.92 4.19
time (sec) N/A 0.013 0.121 1.572 0.343 0.536 10.435 0.261 1.039
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 89 1049 391 69 5552 1341 246
normalized size 1 1.00 2.54 29.97 11.17 1.97 158.63 38.31 7.03
time (sec) N/A 0.029 0.090 2.252 0.524 0.458 160.750 1.829 6.525
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-2) B F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 35 56 382 40 0 315 -1
normalized size 1 1.00 0.92 1.47 10.05 1.05 0.00 8.29 -0.03
time (sec) N/A 0.039 0.197 3.672 0.333 0.505 0.000 5.752 0.000
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 158 133 1362 163 2009 129 495
normalized size 1 1.00 1.10 0.92 9.46 1.13 13.95 0.90 3.44
time (sec) N/A 0.089 1.574 1.286 0.426 0.631 114.287 4.935 2.445
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 105 83 620 105 1027 80 177
normalized size 1 1.00 1.19 0.94 7.05 1.19 11.67 0.91 2.01
time (sec) N/A 0.069 0.723 1.689 0.371 0.444 23.830 1.985 1.058
Problem 246 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 195 176 184 2614 240 0 181 999
normalized size 1 1.00 0.90 0.94 13.41 1.23 0.00 0.93 5.12
time (sec) N/A 0.135 1.637 1.999 0.582 0.480 0.000 0.174 4.542
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B B F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 70 181 1027 366 0 0 -1
normalized size 1 1.00 0.97 2.51 14.26 5.08 0.00 0.00 -0.01
time (sec) N/A 0.078 0.372 0.958 0.542 0.490 0.000 0.000 0.000
Problem 248 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C B B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 111 149 526 316 0 0 285
normalized size 1 1.00 2.41 3.24 11.43 6.87 0.00 0.00 6.20
time (sec) N/A 0.039 0.094 0.859 0.520 0.509 0.000 0.000 5.243
Problem 249 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C B B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 93 97 131 196 0 0 237
normalized size 1 1.00 3.10 3.23 4.37 6.53 0.00 0.00 7.90
time (sec) N/A 0.018 0.053 0.608 0.510 0.467 0.000 0.000 4.727
Problem 250 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C B B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 94 93 105 190 0 0 231
normalized size 1 1.00 3.24 3.21 3.62 6.55 0.00 0.00 7.97
time (sec) N/A 0.021 0.052 0.753 0.346 0.459 0.000 0.000 5.386
Problem 251 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C B B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 112 145 613 316 0 0 289
normalized size 1 1.00 2.43 3.15 13.33 6.87 0.00 0.00 6.28
time (sec) N/A 0.041 0.101 0.842 0.359 0.493 0.000 0.000 5.439
Problem 252 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B B F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 71 179 1254 385 0 0 -1
normalized size 1 1.00 0.97 2.45 17.18 5.27 0.00 0.00 -0.01
time (sec) N/A 0.077 0.342 1.006 0.404 0.514 0.000 0.000 0.000
Problem 253 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 114 0 0 0 0 0 -1
normalized size 1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.119 1.660 1.591 0.000 0.455 0.000 0.000 0.000
Problem 254 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 108 0 0 0 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.120 1.795 1.766 0.000 0.411 0.000 0.000 0.000

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 [201] had the largest ratio of [.5882]

Table 2.1:Rubi 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 1.00 18 0.167
2 A 4 3 1.00 18 0.167
3 A 4 3 1.00 18 0.167
4 A 4 3 1.00 18 0.167
5 A 4 3 1.00 18 0.167
6 A 4 3 1.00 18 0.167
7 A 1 1 1.00 16 0.062
8 A 2 2 1.00 16 0.125
9 A 4 4 1.00 18 0.222
10 A 5 5 1.00 18 0.278
11 A 6 5 1.00 18 0.278
12 A 7 5 1.00 18 0.278
13 A 5 4 1.00 20 0.200
14 A 6 5 1.00 20 0.250
15 A 4 3 1.00 20 0.150
16 A 5 5 1.00 20 0.250
17 A 3 3 1.00 18 0.167
18 A 2 2 1.00 18 0.111
19 A 3 3 1.00 20 0.150
20 A 4 3 1.00 20 0.150
21 A 4 3 1.00 20 0.150
22 A 5 4 1.00 20 0.200
23 A 4 3 1.00 20 0.150
24 A 4 3 1.00 20 0.150
25 A 4 3 1.00 20 0.150
26 A 4 3 1.00 20 0.150
27 A 3 3 1.00 18 0.167
28 A 4 4 1.00 18 0.222
29 A 3 3 1.00 20 0.150
30 A 3 3 1.00 20 0.150
31 A 5 4 1.00 20 0.200
32 A 6 5 1.00 20 0.250
33 A 4 3 1.00 18 0.167
34 A 4 3 1.00 18 0.167
35 A 4 3 1.00 18 0.167
36 A 4 3 1.00 18 0.167
37 A 4 3 1.00 18 0.167
38 A 4 3 1.00 18 0.167
39 A 3 3 1.00 18 0.167
40 A 2 2 1.00 16 0.125
41 A 4 4 1.00 16 0.250
42 A 5 5 1.00 18 0.278
43 A 6 5 1.00 18 0.278
44 A 7 5 1.00 18 0.278
45 A 9 4 1.00 20 0.200
46 A 5 4 1.00 20 0.200
47 A 7 4 1.00 20 0.200
48 A 4 3 1.00 20 0.150
49 A 5 4 1.00 20 0.200
50 A 3 3 1.00 20 0.150
51 A 3 3 1.00 20 0.150
52 A 2 2 1.00 18 0.111
53 A 4 3 1.00 18 0.167
54 A 4 3 1.00 20 0.150
55 A 5 4 1.00 20 0.200
56 A 4 3 1.00 20 0.150
57 A 5 4 1.00 20 0.200
58 A 4 3 1.00 20 0.150
59 A 4 3 1.00 20 0.150
60 A 4 3 1.00 20 0.150
61 A 4 3 1.00 20 0.150
62 A 4 3 1.00 20 0.150
63 A 4 3 1.00 20 0.150
64 A 4 3 1.00 20 0.150
65 A 3 3 1.00 20 0.150
66 A 3 2 1.00 20 0.100
67 A 4 4 1.00 20 0.200
68 A 3 3 1.00 18 0.167
69 A 5 4 1.00 18 0.222
70 A 6 5 1.00 20 0.250
71 A 6 5 1.00 20 0.250
72 A 8 5 1.00 20 0.250
73 A 4 3 1.00 20 0.150
74 A 3 3 1.00 20 0.150
75 A 2 2 1.00 20 0.100
76 A 1 1 1.00 20 0.050
77 A 1 1 1.00 20 0.050
78 A 2 2 1.00 20 0.100
79 A 3 3 1.00 20 0.150
80 A 4 3 1.00 20 0.150
81 A 4 3 1.00 22 0.136
82 A 3 3 1.00 22 0.136
83 A 3 3 1.00 22 0.136
84 A 2 2 1.00 22 0.091
85 A 2 2 1.00 22 0.091
86 A 2 2 1.00 22 0.091
87 A 2 2 1.00 22 0.091
88 A 3 3 1.00 22 0.136
89 A 4 4 1.00 22 0.182
90 A 3 3 1.00 22 0.136
91 A 2 2 1.00 22 0.091
92 A 3 3 1.00 22 0.136
93 A 1 1 1.00 22 0.045
94 A 2 2 1.00 22 0.091
95 A 3 3 1.00 22 0.136
96 A 4 4 1.00 22 0.182
97 A 5 4 1.00 20 0.200
98 A 4 4 1.00 20 0.200
99 A 3 3 1.00 20 0.150
100 A 2 2 1.00 20 0.100
101 A 1 1 1.00 20 0.050
102 A 3 3 1.00 20 0.150
103 A 4 4 1.00 20 0.200
104 A 5 4 1.00 20 0.200
105 A 4 3 1.00 22 0.136
106 A 4 3 1.00 22 0.136
107 A 3 3 1.00 22 0.136
108 A 3 3 1.00 22 0.136
109 A 2 2 1.00 22 0.091
110 A 2 2 1.00 22 0.091
111 A 3 3 1.00 22 0.136
112 A 3 3 1.00 22 0.136
113 A 4 3 1.00 22 0.136
114 A 4 3 1.00 22 0.136
115 A 7 5 1.00 22 0.227
116 A 6 5 1.00 22 0.227
117 A 5 5 1.00 22 0.227
118 A 4 4 1.00 22 0.182
119 A 1 1 1.00 22 0.045
120 A 2 2 1.00 22 0.091
121 A 4 4 1.00 22 0.182
122 A 5 5 1.00 22 0.227
123 A 2 2 1.00 20 0.100
124 A 2 2 1.00 20 0.100
125 A 2 2 1.00 18 0.111
126 A 2 2 1.00 18 0.111
127 A 2 2 1.00 20 0.100
128 A 2 2 1.00 20 0.100
129 A 4 3 1.00 18 0.167
130 A 4 3 1.00 18 0.167
131 A 4 3 1.00 18 0.167
132 A 4 3 1.00 18 0.167
133 A 4 3 1.00 18 0.167
134 A 4 3 1.00 18 0.167
135 A 1 1 1.00 16 0.062
136 A 2 2 1.00 16 0.125
137 A 4 4 1.00 18 0.222
138 A 5 5 1.00 18 0.278
139 A 6 5 1.00 18 0.278
140 A 7 5 1.00 18 0.278
141 A 5 4 1.00 20 0.200
142 A 6 5 1.00 20 0.250
143 A 4 3 1.00 20 0.150
144 A 5 5 1.00 20 0.250
145 A 3 3 1.00 18 0.167
146 A 2 2 1.00 18 0.111
147 A 3 3 1.00 20 0.150
148 A 4 3 1.00 20 0.150
149 A 4 3 1.00 20 0.150
150 A 5 4 1.00 20 0.200
151 A 4 3 1.00 20 0.150
152 A 4 3 1.00 20 0.150
153 A 4 3 1.00 20 0.150
154 A 4 3 1.00 20 0.150
155 A 3 3 1.00 18 0.167
156 A 4 4 1.00 18 0.222
157 A 3 3 1.00 20 0.150
158 A 3 3 1.00 20 0.150
159 A 5 4 1.00 20 0.200
160 A 6 5 1.00 20 0.250
161 A 4 3 1.00 20 0.150
162 A 3 3 1.00 20 0.150
163 A 2 2 1.00 20 0.100
164 A 1 1 1.00 20 0.050
165 A 1 1 1.00 20 0.050
166 A 2 2 1.00 20 0.100
167 A 3 3 1.00 20 0.150
168 A 4 3 1.00 20 0.150
169 A 4 3 1.00 22 0.136
170 A 3 3 1.00 22 0.136
171 A 3 3 1.00 22 0.136
172 A 2 2 1.00 22 0.091
173 A 2 2 1.00 22 0.091
174 A 2 2 1.00 22 0.091
175 A 2 2 1.00 22 0.091
176 A 3 3 1.00 22 0.136
177 A 4 4 1.00 22 0.182
178 A 3 3 1.00 22 0.136
179 A 2 2 1.00 22 0.091
180 A 3 3 1.00 22 0.136
181 A 1 1 1.00 22 0.045
182 A 2 2 1.00 22 0.091
183 A 3 3 1.00 22 0.136
184 A 4 4 1.00 22 0.182
185 A 1 1 1.00 11 0.091
186 A 2 2 1.00 11 0.182
187 A 2 2 1.00 20 0.100
188 A 2 2 1.00 20 0.100
189 A 2 2 1.00 18 0.111
190 A 4 3 1.00 28 0.107
191 A 10 5 1.00 15 0.333
192 A 6 2 1.00 15 0.133
193 A 5 2 1.00 15 0.133
194 A 4 2 1.00 13 0.154
195 A 3 3 1.00 13 0.231
196 A 4 4 1.00 15 0.267
197 A 5 5 1.00 15 0.333
198 A 5 5 1.00 15 0.333
199 A 5 4 1.00 15 0.267
200 A 6 5 1.00 15 0.333
201 A 15 10 1.00 17 0.588
202 A 5 2 1.00 15 0.133
203 A 6 2 1.00 17 0.118
204 A 8 2 1.00 17 0.118
205 A 18 5 1.00 17 0.294
206 A 6 2 1.00 15 0.133
207 A 8 2 1.00 17 0.118
208 A 10 2 1.00 17 0.118
209 A 8 4 1.00 15 0.267
210 A 6 2 1.00 15 0.133
211 A 5 2 1.00 15 0.133
212 A 4 2 1.00 13 0.154
213 A 3 3 1.00 13 0.231
214 A 4 4 1.00 15 0.267
215 A 5 5 1.00 15 0.333
216 A 5 5 1.00 15 0.333
217 A 5 4 1.00 15 0.267
218 A 6 5 1.00 15 0.333
219 A 11 7 1.00 17 0.412
220 A 5 2 1.00 15 0.133
221 A 6 2 1.00 17 0.118
222 A 8 2 1.00 17 0.118
223 A 14 4 1.00 17 0.235
224 A 6 2 1.00 15 0.133
225 A 8 2 1.00 17 0.118
226 A 10 2 1.00 17 0.118
227 A 3 3 1.00 13 0.231
228 A 4 4 1.00 15 0.267
229 A 5 5 1.00 15 0.333
230 A 9 7 1.00 15 0.467
231 A 6 6 1.00 15 0.400
232 A 3 3 1.00 13 0.231
233 A 3 3 1.00 13 0.231
234 A 6 6 1.00 15 0.400
235 A 9 7 1.00 15 0.467
236 A 6 3 1.00 13 0.231
237 A 6 3 1.00 13 0.231
238 A 6 2 1.00 15 0.133
239 A 5 2 1.00 15 0.133
240 A 4 2 1.00 13 0.154
241 A 3 3 1.00 13 0.231
242 A 4 4 1.00 15 0.267
243 A 5 5 1.00 15 0.333
244 A 8 2 1.00 17 0.118
245 A 6 2 1.00 17 0.118
246 A 10 2 1.00 17 0.118
247 A 9 7 1.00 15 0.467
248 A 6 6 1.00 15 0.400
249 A 3 3 1.00 13 0.231
250 A 3 3 1.00 13 0.231
251 A 6 6 1.00 15 0.400
252 A 9 7 1.00 15 0.467
253 A 6 3 1.00 13 0.231
254 A 6 3 1.00 13 0.231

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