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

Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
  2.1.8 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, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 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, 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, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 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, 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, 239, 240, 241, 242, 243, 244, 245, 246, 248, 249, 250, 251, 252, 254, 255, 256, 259, 260, 261, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 276, 277, 278, 281, 282, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 326, 327, 330, 331, 333, 334 }

B grade: { 1, 75, 247, 262, 325, 328, 329 }

C grade: { 9, 13, 17, 21, 130, 143, 210, 253, 257, 258, 275, 279, 280, 283, 284, 332, 335, 336 }

F grade: { 238 }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 12, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 104, 105, 106, 111, 112, 113, 115, 117, 118, 121, 122, 123, 124, 134, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 159, 160, 161, 162, 163, 164, 171, 172, 173, 174, 175, 176, 177, 178, 182, 183, 184, 185, 186, 188, 190, 191, 192, 193, 194, 195, 196, 197, 198, 200, 201, 203, 204, 205, 207, 208, 209, 216, 217, 220, 221, 225, 226, 227, 232, 233, 238, 247, 248, 249, 250, 251, 256, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 277, 278, 281, 282, 285, 286, 287, 299, 300, 301, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 333, 334, 335, 336 }

B grade: { 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 40, 45, 46, 47, 54, 55, 61, 79, 80, 81, 82, 83, 84, 85, 101, 102, 103, 107, 108, 109, 110, 114, 116, 119, 120, 125, 126, 127, 135, 136, 137, 152, 153, 154, 155, 156, 157, 158, 165, 166, 167, 168, 169, 170, 179, 180, 181, 187, 189, 199, 202, 206, 210, 211, 212, 218, 219, 224, 230, 231, 236, 237, 252, 253, 254, 255, 257, 262, 263 }

C grade: { 275, 276, 279, 280, 283, 284, 302 }

F grade: { 23, 128, 129, 130, 131, 132, 133, 213, 214, 215, 222, 223, 228, 229, 234, 235, 239, 240, 241, 242, 243, 244, 245, 246, 258, 259, 260, 261, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 329, 330, 331, 332 }

2.1.4 Maxima

A grade: { 1, 2, 4, 6, 24, 25, 26, 27, 28, 29, 30, 32, 36, 42, 43, 44, 62, 63, 64, 65, 66, 71, 72, 73, 74, 75, 76, 77, 78, 93, 97, 117, 121, 122, 123, 124, 125, 126, 127, 134, 135, 136, 137, 140, 141, 142, 143, 145, 146, 147, 151, 153, 155, 158, 159, 171, 172, 174, 180, 182, 183, 185, 191, 192, 193, 200, 201, 216, 217, 220, 221, 225, 226, 227, 232, 233, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 250, 264, 265, 266, 267, 268, 269, 271, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 285, 286, 287, 292, 293, 294, 295, 296, 297, 300, 301, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 333, 334 }

B grade: { 3, 5, 31, 33, 34, 35, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 87, 88, 89, 90, 91, 92, 94, 95, 96, 98, 99, 100, 101, 102, 103, 138, 139, 144, 148, 149, 150, 152, 154, 156, 157, 160, 161, 162, 163, 164, 165, 167, 169, 176, 187, 188, 189, 190, 194, 195, 196, 237, 249, 251, 270, 272, 298 }

C grade: { 302 }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 67, 68, 69, 70, 79, 80, 81, 82, 83, 84, 85, 86, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 119, 120, 128, 129, 130, 131, 132, 133, 166, 168, 170, 173, 175, 177, 178, 179, 181, 184, 186, 197, 198, 199, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 218, 219, 222, 223, 224, 228, 229, 230, 231, 234, 235, 236, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 283, 284, 288, 289, 290, 291, 299, 329, 330, 331, 332, 335, 336 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 25, 26, 27, 28, 32, 36, 40, 44, 45, 50, 51, 57, 58, 62, 63, 64, 65, 66, 67, 71, 75, 93, 94, 97, 98, 101, 110, 114, 115, 117, 142, 143, 154, 155, 156, 157, 158, 159, 172, 182, 183, 192, 203, 204, 205, 206, 216, 217, 220, 221, 226, 227, 232, 233, 238, 239, 240, 241, 242, 243, 244, 247, 248, 249, 250, 251, 258, 259, 260, 261, 262, 264, 266, 268, 274, 275, 279, 280, 292, 293, 294, 295, 299, 300, 301, 302, 303, 304, 312, 333, 334 }

B grade: { 24, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 48, 49, 52, 53, 54, 55, 56, 59, 60, 61, 68, 69, 70, 72, 73, 74, 76, 77, 78, 87, 88, 89, 90, 91, 92, 95, 96, 99, 100, 102, 103, 104, 105, 106, 111, 112, 113, 116, 121, 122, 123, 124, 125, 126, 127, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 174, 175, 176, 177, 178, 179, 180, 181, 184, 185, 186, 187, 188, 189, 190, 191, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 207, 208, 209, 210, 218, 219, 224, 225, 230, 231, 236, 237, 245, 246, 263, 265, 267, 269, 270, 271, 272, 273, 276, 277, 278, 281, 282, 283, 284, 285, 286, 287, 296, 297, 298, 305, 306, 307, 308, 309, 310, 311, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 330, 335, 336 }

C grade: { 211, 212, 222, 223, 228, 229, 234, 235 }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 79, 80, 81, 82, 83, 84, 85, 86, 107, 108, 109, 118, 119, 120, 128, 129, 130, 131, 132, 133, 213, 214, 215, 252, 253, 254, 255, 256, 257, 288, 289, 290, 291, 329, 331, 332 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 27, 32, 33, 34, 35, 36, 37, 38, 39, 56, 57, 62, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75, 76, 77, 78, 93, 94, 95, 96, 97, 98, 99, 100, 110, 114, 115, 117, 124, 140, 141, 142, 143, 146, 147, 148, 149, 159, 170, 171, 199, 200, 201, 206, 216, 217, 221, 225, 226, 227, 231, 232, 233, 238, 247, 249, 251, 264, 265, 266, 267, 274, 278, 282, 286, 287, 294, 299, 333, 334 }

B grade: { 24, 25, 26, 116, 144, 145, 150, 151, 152, 153, 154, 155, 156, 157, 158, 273, 277, 281 }

C grade: { }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 68, 69, 70, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 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, 202, 203, 204, 205, 207, 208, 209, 210, 211, 212, 213, 214, 215, 218, 219, 220, 222, 223, 224, 228, 229, 230, 234, 235, 236, 237, 239, 240, 241, 242, 243, 244, 245, 246, 248, 250, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 268, 269, 270, 271, 272, 275, 276, 279, 280, 283, 284, 285, 288, 289, 290, 291, 292, 293, 295, 296, 297, 298, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 335, 336 }

2.1.7 Giac

A grade: { 2, 4, 6, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 87, 93, 94, 95, 96, 97, 98, 99, 100, 102, 103, 110, 111, 114, 115, 117, 121, 122, 123, 124, 126, 127, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 161, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 175, 178, 179, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 199, 200, 201, 202, 203, 204, 205, 206, 207, 216, 217, 220, 221, 225, 226, 227, 231, 232, 233, 237, 238, 239, 240, 250, 251, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 303, 304, 305, 307, 308, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 333, 334 }

B grade: { 1, 3, 5, 48, 49, 50, 66, 88, 89, 90, 91, 92, 105, 106, 112, 113, 116, 144, 160, 162, 174, 176, 177, 180, 195, 208, 209, 241, 242, 243, 244, 245, 246, 247, 248, 249, 262, 263 }

C grade: { 40, 41, 101, 104, 285, 286, 287, 302, 306, 309 }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 79, 80, 81, 82, 83, 84, 85, 86, 107, 108, 109, 118, 119, 120, 125, 128, 129, 130, 131, 132, 133, 197, 198, 210, 211, 212, 213, 214, 215, 218, 219, 222, 223, 224, 228, 229, 230, 234, 235, 236, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 288, 289, 290, 291, 329, 330, 331, 332, 335, 336 }

2.1.8 Mupad

A grade: { 216, 217, 221, 226, 227, 232, 233, 238 }

B grade: { 1, 2, 3, 4, 5, 6, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 44, 50, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77, 78, 93, 94, 95, 96, 97, 98, 99, 100, 110, 111, 114, 115, 116, 117, 124, 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, 199, 200, 201, 202, 203, 204, 205, 206, 207, 218, 225, 231, 237, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 294, 296, 297, 298, 299, 329, 330, 331, 333, 334 }

C grade: { }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 69, 70, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 101, 102, 103, 104, 105, 106, 107, 108, 109, 112, 113, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 197, 198, 208, 209, 210, 211, 212, 213, 214, 215, 219, 220, 222, 223, 224, 228, 229, 230, 234, 235, 236, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 288, 289, 290, 291, 292, 293, 295, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 332, 335, 336 }

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 B A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 21 11 10 10 12 26 10
normalized size 1 1.00 2.10 1.10 1.00 1.00 1.20 2.60 1.00
time (sec) N/A 0.005 0.011 0.041 0.317 0.591 0.133 0.135 0.045
Problem 2 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 25 25 23 27 32 22 46 32 18
normalized size 1 1.00 0.92 1.08 1.28 0.88 1.84 1.28 0.72
time (sec) N/A 0.010 0.022 0.085 0.315 0.564 0.207 0.134 0.882
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 26 23 54 32 36 54 22
normalized size 1 1.00 1.00 0.88 2.08 1.23 1.38 2.08 0.85
time (sec) N/A 0.012 0.008 0.205 0.311 0.734 0.407 0.122 0.885
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 33 39 60 49 95 60 31
normalized size 1 1.00 0.72 0.85 1.30 1.07 2.07 1.30 0.67
time (sec) N/A 0.020 0.045 0.213 0.309 0.812 0.847 0.121 0.083
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 41 33 82 66 58 82 31
normalized size 1 1.00 1.00 0.80 2.00 1.61 1.41 2.00 0.76
time (sec) N/A 0.013 0.015 0.215 0.315 0.469 1.568 0.141 0.918
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 67 67 43 49 86 90 139 88 42
normalized size 1 1.00 0.64 0.73 1.28 1.34 2.07 1.31 0.63
time (sec) N/A 0.033 0.041 0.223 0.312 0.613 2.988 0.136 0.966
Problem 7 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 69 69 55 201 0 0 0 0 -1
normalized size 1 1.00 0.80 2.91 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.033 0.116 0.353 0.000 0.464 0.000 0.000 0.000
Problem 8 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 44 188 0 0 0 0 -1
normalized size 1 1.00 0.96 4.09 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.020 0.056 0.298 0.000 0.540 0.000 0.000 0.000
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 81 174 0 0 0 0 -1
normalized size 1 1.00 1.76 3.78 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.019 0.112 0.293 0.000 0.499 0.000 0.000 0.000
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 135 0 0 0 0 -1
normalized size 1 1.00 1.00 6.75 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.009 0.030 0.261 0.000 0.487 0.000 0.000 0.000
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 135 0 0 0 0 -1
normalized size 1 1.00 1.00 6.75 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.009 0.029 0.289 0.000 0.490 0.000 0.000 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 42 103 0 0 0 0 -1
normalized size 1 1.00 1.00 2.45 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.019 0.063 0.355 0.000 0.518 0.000 0.000 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 84 217 0 0 0 0 -1
normalized size 1 1.00 1.83 4.72 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.019 0.072 0.334 0.000 0.484 0.000 0.000 0.000
Problem 14 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 69 69 63 363 0 0 0 0 -1
normalized size 1 1.00 0.91 5.26 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.030 0.142 0.628 0.000 0.454 0.000 0.000 0.000
Problem 15 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 65 65 53 145 0 0 0 0 -1
normalized size 1 1.00 0.82 2.23 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.037 0.053 0.349 0.000 0.475 0.000 0.000 0.000
Problem 16 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 48 48 41 184 0 0 0 0 -1
normalized size 1 1.00 0.85 3.83 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.025 0.046 0.368 0.000 0.462 0.000 0.000 0.000
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 57 130 0 0 0 0 -1
normalized size 1 1.00 1.19 2.71 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.024 0.064 0.376 0.000 0.549 0.000 0.000 0.000
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 118 0 0 0 0 -1
normalized size 1 1.00 1.00 4.37 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.015 0.010 0.373 0.000 0.580 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 100 0 0 0 0 -1
normalized size 1 1.00 1.00 3.70 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.015 0.013 0.253 0.000 0.494 0.000 0.000 0.000
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 34 159 0 0 0 0 -1
normalized size 1 1.00 0.74 3.46 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.025 0.026 0.368 0.000 0.662 0.000 0.000 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 56 177 0 0 0 0 -1
normalized size 1 1.00 1.12 3.54 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.027 0.043 0.344 0.000 0.517 0.000 0.000 0.000
Problem 22 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 67 67 43 254 0 0 0 0 -1
normalized size 1 1.00 0.64 3.79 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.039 0.051 0.602 0.000 0.688 0.000 0.000 0.000
Problem 23 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 71 71 65 0 0 0 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.019 0.067 0.269 0.000 0.997 0.000 0.000 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 53 111 66 100 337 70 70
normalized size 1 1.00 0.98 2.06 1.22 1.85 6.24 1.30 1.30
time (sec) N/A 0.076 0.086 0.066 0.372 0.515 1.893 0.122 0.961
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 45 87 56 70 189 51 52
normalized size 1 1.00 1.05 2.02 1.30 1.63 4.40 1.19 1.21
time (sec) N/A 0.051 0.056 0.068 0.350 3.488 1.113 0.116 0.917
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 32 59 41 47 63 35 34
normalized size 1 1.00 1.28 2.36 1.64 1.88 2.52 1.40 1.36
time (sec) N/A 0.069 0.059 0.068 0.370 1.463 0.600 0.120 0.901
Problem 27 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 18 18 14 34 18 24 8 17 17
normalized size 1 1.00 0.78 1.89 1.00 1.33 0.44 0.94 0.94
time (sec) N/A 0.032 0.029 0.054 0.309 0.379 0.335 0.122 0.875
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 22 21 23 29 0 20 31
normalized size 1 1.00 1.10 1.05 1.15 1.45 0.00 1.00 1.55
time (sec) N/A 0.042 0.026 0.065 0.397 0.607 0.000 0.122 0.878
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 43 39 45 127 0 36 58
normalized size 1 1.00 1.54 1.39 1.61 4.54 0.00 1.29 2.07
time (sec) N/A 0.068 0.088 0.088 0.802 0.459 0.000 0.147 0.895
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 49 61 73 325 0 48 73
normalized size 1 1.00 1.14 1.42 1.70 7.56 0.00 1.12 1.70
time (sec) N/A 0.074 0.092 0.089 0.455 0.487 0.000 0.146 0.909
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 60 81 101 600 0 57 107
normalized size 1 1.00 1.07 1.45 1.80 10.71 0.00 1.02 1.91
time (sec) N/A 0.077 0.195 0.092 0.409 0.522 0.000 0.140 0.897
Problem 32 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 20 20 14 14 18 22 17 15 15
normalized size 1 1.00 0.70 0.70 0.90 1.10 0.85 0.75 0.75
time (sec) N/A 0.010 0.017 0.053 0.308 0.427 0.518 0.141 0.895
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 34 30 90 113 36 25 25
normalized size 1 1.00 0.72 0.64 1.91 2.40 0.77 0.53 0.53
time (sec) N/A 0.022 0.031 0.062 0.308 0.449 1.005 0.129 0.059
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 44 43 205 174 51 36 36
normalized size 1 1.00 0.63 0.61 2.93 2.49 0.73 0.51 0.51
time (sec) N/A 0.036 0.061 0.059 0.354 0.501 2.166 0.142 0.934
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 93 54 56 364 347 68 47 283
normalized size 1 1.00 0.58 0.60 3.91 3.73 0.73 0.51 3.04
time (sec) N/A 0.054 0.087 0.054 0.487 0.522 5.187 0.138 0.919
Problem 36 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 23 23 14 16 18 24 32 15 15
normalized size 1 1.00 0.61 0.70 0.78 1.04 1.39 0.65 0.65
time (sec) N/A 0.011 0.026 0.063 0.388 0.584 0.626 0.136 0.893
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 31 32 90 117 53 25 25
normalized size 1 1.00 0.61 0.63 1.76 2.29 1.04 0.49 0.49
time (sec) N/A 0.025 0.030 0.073 0.879 0.768 1.226 0.119 0.059
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 41 45 205 174 70 36 36
normalized size 1 1.00 0.54 0.59 2.70 2.29 0.92 0.47 0.47
time (sec) N/A 0.040 0.056 0.076 0.408 0.485 2.525 0.125 0.911
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 51 58 364 347 87 47 283
normalized size 1 1.00 0.50 0.57 3.60 3.44 0.86 0.47 2.80
time (sec) N/A 0.057 0.080 0.076 0.332 0.544 5.607 0.133 0.085
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 34 92 114 62 0 46 -1
normalized size 1 1.00 0.67 1.80 2.24 1.22 0.00 0.90 -0.02
time (sec) N/A 0.045 0.023 0.268 1.111 0.520 0.000 0.173 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 35 40 0 92 0 90 -1
normalized size 1 1.00 0.66 0.75 0.00 1.74 0.00 1.70 -0.02
time (sec) N/A 0.049 0.031 0.338 0.000 0.553 0.000 0.159 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 71 73 121 327 0 105 -1
normalized size 1 1.00 0.80 0.82 1.36 3.67 0.00 1.18 -0.01
time (sec) N/A 0.047 0.135 0.283 1.058 0.612 0.000 0.153 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 55 58 81 140 0 75 -1
normalized size 1 1.00 0.93 0.98 1.37 2.37 0.00 1.27 -0.02
time (sec) N/A 0.029 0.067 0.169 0.606 0.460 0.000 0.128 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 29 43 40 41 0 35 26
normalized size 1 1.00 1.12 1.65 1.54 1.58 0.00 1.35 1.00
time (sec) N/A 0.013 0.033 0.137 0.408 0.496 0.000 0.115 0.115
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 40 103 86 149 0 21 -1
normalized size 1 1.00 0.87 2.24 1.87 3.24 0.00 0.46 -0.02
time (sec) N/A 0.023 0.017 0.189 0.472 0.777 0.000 0.142 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 63 144 170 219 0 67 -1
normalized size 1 1.00 0.82 1.87 2.21 2.84 0.00 0.87 -0.01
time (sec) N/A 0.041 0.090 0.273 0.502 0.529 0.000 0.199 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 91 178 250 522 0 97 -1
normalized size 1 1.00 0.85 1.66 2.34 4.88 0.00 0.91 -0.01
time (sec) N/A 0.062 0.283 0.286 0.512 0.419 0.000 0.270 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 72 71 190 328 0 189 -1
normalized size 1 1.00 0.78 0.77 2.07 3.57 0.00 2.05 -0.01
time (sec) N/A 0.052 0.145 0.257 0.421 0.511 0.000 0.161 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 56 56 124 139 0 119 -1
normalized size 1 1.00 0.92 0.92 2.03 2.28 0.00 1.95 -0.02
time (sec) N/A 0.031 0.094 0.250 0.434 0.515 0.000 0.162 0.000
Problem 50 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 27 27 30 41 58 42 0 61 27
normalized size 1 1.00 1.11 1.52 2.15 1.56 0.00 2.26 1.00
time (sec) N/A 0.014 0.035 0.215 0.425 0.399 0.000 0.150 0.941
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 41 41 0 154 0 40 -1
normalized size 1 1.00 0.85 0.85 0.00 3.21 0.00 0.83 -0.02
time (sec) N/A 0.025 0.032 0.219 0.000 0.526 0.000 0.140 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 85 87 0 274 0 107 -1
normalized size 1 1.00 1.08 1.10 0.00 3.47 0.00 1.35 -0.01
time (sec) N/A 0.041 0.175 0.369 0.000 0.610 0.000 0.245 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 115 137 0 580 0 164 -1
normalized size 1 1.00 1.05 1.25 0.00 5.27 0.00 1.49 -0.01
time (sec) N/A 0.063 0.199 0.336 0.000 1.254 0.000 0.301 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 99 264 0 1625 0 133 209
normalized size 1 1.00 0.88 2.36 0.00 14.51 0.00 1.19 1.87
time (sec) N/A 0.309 0.200 0.067 0.000 0.801 0.000 0.125 1.263
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 78 174 0 903 0 92 167
normalized size 1 1.00 0.92 2.05 0.00 10.62 0.00 1.08 1.96
time (sec) N/A 0.169 0.132 0.063 0.000 0.892 0.000 0.120 1.117
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 57 94 0 449 1275 62 139
normalized size 1 1.00 0.92 1.52 0.00 7.24 20.56 1.00 2.24
time (sec) N/A 0.106 0.113 0.060 0.000 0.776 93.904 0.150 1.041
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 48 64 0 218 241 42 109
normalized size 1 1.00 0.92 1.23 0.00 4.19 4.63 0.81 2.10
time (sec) N/A 0.053 0.048 0.057 0.000 0.485 25.019 0.122 0.219
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 51 0 227 0 45 286
normalized size 1 1.00 1.00 0.94 0.00 4.20 0.00 0.83 5.30
time (sec) N/A 0.067 0.053 0.076 0.000 0.634 0.000 0.147 3.456
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 63 73 0 515 0 61 294
normalized size 1 1.00 0.98 1.14 0.00 8.05 0.00 0.95 4.59
time (sec) N/A 0.117 0.110 0.087 0.000 0.652 0.000 0.145 3.098
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 82 146 0 1370 0 89 476
normalized size 1 1.00 0.94 1.68 0.00 15.75 0.00 1.02 5.47
time (sec) N/A 0.300 0.210 0.091 0.000 0.850 0.000 0.146 4.126
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 101 239 0 2483 0 123 547
normalized size 1 1.00 0.89 2.10 0.00 21.78 0.00 1.08 4.80
time (sec) N/A 0.472 0.427 0.112 0.000 1.112 0.000 0.120 4.533
Problem 62 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 183 183 133 155 273 190 314 263 160
normalized size 1 1.00 0.73 0.85 1.49 1.04 1.72 1.44 0.87
time (sec) N/A 0.260 0.367 0.303 0.364 0.510 2.253 0.155 1.144
Problem 63 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 137 137 104 119 183 123 240 196 114
normalized size 1 1.00 0.76 0.87 1.34 0.90 1.75 1.43 0.83
time (sec) N/A 0.151 0.223 0.254 0.300 0.871 1.102 0.132 0.191
Problem 64 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 90 90 80 77 116 78 128 131 73
normalized size 1 1.00 0.89 0.86 1.29 0.87 1.42 1.46 0.81
time (sec) N/A 0.068 0.132 0.204 0.301 0.628 0.537 0.141 0.955
Problem 65 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 50 50 46 51 55 40 78 75 41
normalized size 1 1.00 0.92 1.02 1.10 0.80 1.56 1.50 0.82
time (sec) N/A 0.017 0.079 0.074 0.504 0.519 0.265 0.137 0.923
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 26 16 15 17 17 32 15
normalized size 1 1.00 1.73 1.07 1.00 1.13 1.13 2.13 1.00
time (sec) N/A 0.008 0.009 0.028 0.294 0.386 0.132 0.110 0.057
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 48 44 0 237 163 39 53
normalized size 1 1.00 0.98 0.90 0.00 4.84 3.33 0.80 1.08
time (sec) N/A 0.035 0.053 0.065 0.000 0.584 4.620 0.135 1.225
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 84 118 0 743 0 99 215
normalized size 1 1.00 0.98 1.37 0.00 8.64 0.00 1.15 2.50
time (sec) N/A 0.084 0.227 0.076 0.000 0.727 0.000 0.140 1.301
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 133 133 113 186 0 2591 0 195 -1
normalized size 1 1.00 0.85 1.40 0.00 19.48 0.00 1.47 -0.01
time (sec) N/A 0.147 0.410 0.086 0.000 0.547 0.000 0.149 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 184 184 160 284 0 5705 0 329 -1
normalized size 1 1.00 0.87 1.54 0.00 31.01 0.00 1.79 -0.01
time (sec) N/A 0.253 1.101 0.094 0.000 0.679 0.000 0.137 0.000
Problem 71 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 22 22 23 18 19 24 24 16 34
normalized size 1 1.00 1.05 0.82 0.86 1.09 1.09 0.73 1.55
time (sec) N/A 0.015 0.039 0.063 0.408 0.526 0.777 0.135 0.125
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 45 48 64 147 316 54 74
normalized size 1 1.00 0.94 1.00 1.33 3.06 6.58 1.12 1.54
time (sec) N/A 0.032 0.105 0.069 0.399 0.598 2.519 0.120 0.939
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 55 79 108 408 530 76 137
normalized size 1 1.00 0.75 1.08 1.48 5.59 7.26 1.04 1.88
time (sec) N/A 0.065 0.165 0.072 0.447 0.457 6.592 0.120 0.959
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 65 110 152 793 809 98 223
normalized size 1 1.00 0.66 1.12 1.55 8.09 8.26 1.00 2.28
time (sec) N/A 0.097 0.273 0.072 0.406 0.673 14.132 0.145 0.949
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 77 36 37 42 41 28 40
normalized size 1 1.00 2.48 1.16 1.19 1.35 1.32 0.90 1.29
time (sec) N/A 0.013 0.032 0.085 0.662 1.604 0.633 0.119 0.943
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 45 72 81 212 199 65 77
normalized size 1 1.00 0.80 1.29 1.45 3.79 3.55 1.16 1.38
time (sec) N/A 0.036 0.121 0.073 0.311 1.026 1.652 0.139 0.938
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 58 108 125 563 445 87 141
normalized size 1 1.00 0.72 1.33 1.54 6.95 5.49 1.07 1.74
time (sec) N/A 0.063 0.199 0.072 0.335 0.495 3.669 0.125 0.954
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 68 144 169 1078 784 109 226
normalized size 1 1.00 0.64 1.36 1.59 10.17 7.40 1.03 2.13
time (sec) N/A 0.097 0.265 0.084 0.336 0.660 7.954 0.122 0.114
Problem 79 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 153 153 150 685 0 0 0 0 -1
normalized size 1 1.00 0.98 4.48 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.244 0.547 0.494 0.000 0.687 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 111 458 0 0 0 0 -1
normalized size 1 1.00 0.90 3.69 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.157 0.244 0.527 0.000 1.232 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 61 276 0 0 0 0 -1
normalized size 1 1.00 1.00 4.52 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.039 0.093 0.431 0.000 0.809 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 F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 46 146 0 0 0 0 -1
normalized size 1 1.00 1.00 3.17 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.034 0.039 0.358 0.000 1.323 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 F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 68 296 0 0 0 0 -1
normalized size 1 1.00 0.81 3.52 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.057 0.128 0.498 0.000 0.881 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 F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 177 177 135 459 0 0 0 0 -1
normalized size 1 1.00 0.76 2.59 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.207 0.574 0.842 0.000 0.885 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 F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 227 227 165 566 0 0 0 0 -1
normalized size 1 1.00 0.73 2.49 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.313 0.719 1.115 0.000 1.014 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 73 181 0 0 0 0 -1
normalized size 1 1.00 0.73 1.81 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.107 0.383 0.422 0.000 0.751 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 60 71 237 563 0 153 -1
normalized size 1 1.00 0.64 0.76 2.52 5.99 0.00 1.63 -0.01
time (sec) N/A 0.092 0.135 0.224 0.494 0.700 0.000 0.145 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 46 57 163 279 0 113 -1
normalized size 1 1.00 0.68 0.84 2.40 4.10 0.00 1.66 -0.01
time (sec) N/A 0.074 0.093 0.205 0.463 0.510 0.000 0.128 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 31 39 90 100 0 71 -1
normalized size 1 1.00 0.78 0.98 2.25 2.50 0.00 1.78 -0.02
time (sec) N/A 0.052 0.040 0.234 0.457 0.495 0.000 0.145 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 61 69 288 564 0 295 -1
normalized size 1 1.00 0.62 0.70 2.94 5.76 0.00 3.01 -0.01
time (sec) N/A 0.104 0.148 0.261 0.468 0.517 0.000 0.191 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 47 55 199 279 0 212 -1
normalized size 1 1.00 0.66 0.77 2.80 3.93 0.00 2.99 -0.01
time (sec) N/A 0.080 0.106 0.316 0.466 0.524 0.000 0.153 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 32 39 109 107 0 131 -1
normalized size 1 1.00 0.73 0.89 2.48 2.43 0.00 2.98 -0.02
time (sec) N/A 0.058 0.055 0.270 0.465 0.494 0.000 0.151 0.000
Problem 93 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 18 18 23 34 26 29 15 17 19
normalized size 1 1.00 1.28 1.89 1.44 1.61 0.83 0.94 1.06
time (sec) N/A 0.036 0.059 0.043 0.311 0.837 0.336 0.118 0.046
Problem 94 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 35 35 25 34 129 50 36 30 30
normalized size 1 1.00 0.71 0.97 3.69 1.43 1.03 0.86 0.86
time (sec) N/A 0.038 0.059 0.044 0.322 0.845 0.612 0.118 0.076
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 42 38 263 127 46 46 141
normalized size 1 1.00 0.75 0.68 4.70 2.27 0.82 0.82 2.52
time (sec) N/A 0.048 0.095 0.040 0.336 1.104 1.198 0.116 0.920
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 57 55 449 175 78 60 231
normalized size 1 1.00 0.76 0.73 5.99 2.33 1.04 0.80 3.08
time (sec) N/A 0.059 0.111 0.040 0.340 0.731 2.362 0.120 0.917
Problem 97 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 20 20 35 37 27 31 15 16 19
normalized size 1 1.00 1.75 1.85 1.35 1.55 0.75 0.80 0.95
time (sec) N/A 0.040 0.058 0.059 0.312 0.722 0.488 0.130 0.053
Problem 98 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 37 37 25 26 131 48 36 32 32
normalized size 1 1.00 0.68 0.70 3.54 1.30 0.97 0.86 0.86
time (sec) N/A 0.041 0.059 0.059 0.322 1.204 0.842 0.114 0.933
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 42 39 267 127 46 46 143
normalized size 1 1.00 0.70 0.65 4.45 2.12 0.77 0.77 2.38
time (sec) N/A 0.055 0.085 0.061 0.331 1.487 1.461 0.113 0.081
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 57 56 451 175 78 60 233
normalized size 1 1.00 0.70 0.69 5.57 2.16 0.96 0.74 2.88
time (sec) N/A 0.066 0.104 0.062 0.341 0.837 2.725 0.116 0.917
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 41 128 174 72 0 61 -1
normalized size 1 1.00 0.73 2.29 3.11 1.29 0.00 1.09 -0.02
time (sec) N/A 0.066 0.037 0.321 0.622 3.967 0.000 0.153 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 44 159 300 189 0 78 -1
normalized size 1 1.00 0.68 2.45 4.62 2.91 0.00 1.20 -0.02
time (sec) N/A 0.068 0.084 0.331 0.577 1.036 0.000 0.176 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 93 57 209 427 509 0 118 -1
normalized size 1 1.00 0.61 2.25 4.59 5.47 0.00 1.27 -0.01
time (sec) N/A 0.089 0.170 0.406 0.929 0.854 0.000 0.225 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 40 63 0 99 0 103 -1
normalized size 1 1.00 0.70 1.11 0.00 1.74 0.00 1.81 -0.02
time (sec) N/A 0.065 0.060 0.370 0.000 0.863 0.000 0.157 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 71 83 0 217 0 111 -1
normalized size 1 1.00 1.09 1.28 0.00 3.34 0.00 1.71 -0.02
time (sec) N/A 0.073 0.162 0.342 0.000 0.900 0.000 0.188 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 108 118 0 548 0 189 -1
normalized size 1 1.00 1.15 1.26 0.00 5.83 0.00 2.01 -0.01
time (sec) N/A 0.096 0.387 0.351 0.000 1.124 0.000 0.240 0.000
Problem 107 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 233 233 203 1365 0 0 0 0 -1
normalized size 1 1.00 0.87 5.86 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.454 0.626 0.553 0.000 0.778 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 181 181 124 973 0 0 0 0 -1
normalized size 1 1.00 0.69 5.38 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.322 0.705 0.578 0.000 0.606 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 F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 123 605 0 0 0 0 -1
normalized size 1 1.00 0.89 4.38 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.206 0.354 0.525 0.000 1.430 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 59 103 0 240 403 50 242
normalized size 1 1.00 0.98 1.72 0.00 4.00 6.72 0.83 4.03
time (sec) N/A 0.068 0.103 0.062 0.000 0.771 27.029 0.121 1.123
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 81 108 0 828 0 107 246
normalized size 1 1.00 0.99 1.32 0.00 10.10 0.00 1.30 3.00
time (sec) N/A 0.078 0.201 0.065 0.000 1.380 0.000 0.119 1.420
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 134 207 0 3166 0 249 -1
normalized size 1 1.00 0.99 1.53 0.00 23.45 0.00 1.84 -0.01
time (sec) N/A 0.169 0.428 0.069 0.000 0.819 0.000 0.135 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 197 197 196 342 0 7603 0 453 -1
normalized size 1 1.00 0.99 1.74 0.00 38.59 0.00 2.30 -0.01
time (sec) N/A 0.348 0.830 0.076 0.000 1.989 0.000 0.154 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 56 107 0 190 170 57 205
normalized size 1 1.00 1.00 1.91 0.00 3.39 3.04 1.02 3.66
time (sec) N/A 0.078 0.075 0.067 0.000 1.796 28.168 0.139 0.494
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 6 6 6 7 0 6 3 6 6
normalized size 1 1.00 1.00 1.17 0.00 1.00 0.50 1.00 1.00
time (sec) N/A 0.001 0.000 0.006 0.000 0.697 0.296 0.124 0.020
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 29 0 54 26 26 51
normalized size 1 1.00 1.00 2.64 0.00 4.91 2.36 2.36 4.64
time (sec) N/A 0.029 0.054 0.056 0.000 1.783 146.491 0.129 1.020
Problem 117 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 36 36 24 32 34 45 44 37 48
normalized size 1 1.00 0.67 0.89 0.94 1.25 1.22 1.03 1.33
time (sec) N/A 0.050 0.077 0.063 0.408 2.705 0.793 0.138 0.111
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 80 218 0 0 0 0 -1
normalized size 1 1.00 0.74 2.02 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.112 0.484 0.458 0.000 0.719 0.000 0.000 0.000
Problem 119 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 152 152 133 483 0 0 0 0 -1
normalized size 1 1.00 0.88 3.18 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.205 0.381 1.046 0.000 0.767 0.000 0.000 0.000
Problem 120 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 231 231 172 797 0 0 0 0 -1
normalized size 1 1.00 0.74 3.45 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.350 0.922 1.551 0.000 0.965 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 42 38 71 817 0 79 -1
normalized size 1 1.00 0.58 0.53 0.99 11.35 0.00 1.10 -0.01
time (sec) N/A 0.055 0.027 0.164 0.430 2.764 0.000 0.120 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 36 32 53 501 0 61 -1
normalized size 1 1.00 0.68 0.60 1.00 9.45 0.00 1.15 -0.02
time (sec) N/A 0.036 0.019 0.177 0.441 0.862 0.000 0.119 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 26 24 35 222 0 29 -1
normalized size 1 1.00 0.76 0.71 1.03 6.53 0.00 0.85 -0.03
time (sec) N/A 0.023 0.009 0.178 0.419 0.808 0.000 0.121 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 15 17 69 19 14 17
normalized size 1 1.00 1.00 1.15 1.31 5.31 1.46 1.08 1.31
time (sec) N/A 0.012 0.004 0.146 0.423 1.055 0.450 0.127 0.053
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 21 55 8 186 0 0 -1
normalized size 1 1.00 1.31 3.44 0.50 11.62 0.00 0.00 -0.06
time (sec) N/A 0.015 0.007 0.218 0.460 1.321 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 31 82 41 299 0 56 -1
normalized size 1 1.00 0.74 1.95 0.98 7.12 0.00 1.33 -0.02
time (sec) N/A 0.025 0.016 0.300 0.460 1.263 0.000 0.141 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 40 102 75 837 0 67 -1
normalized size 1 1.00 0.66 1.67 1.23 13.72 0.00 1.10 -0.02
time (sec) N/A 0.039 0.037 0.304 0.468 1.000 0.000 0.166 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 65 0 0 0 0 0 -1
normalized size 1 1.00 0.54 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.054 0.121 0.192 0.000 1.704 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 54 0 0 0 0 0 -1
normalized size 1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.034 0.075 0.217 0.000 1.980 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 59 0 0 0 0 0 -1
normalized size 1 1.00 1.23 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.024 0.046 0.229 0.000 0.846 0.000 0.000 0.000
Problem 131 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 46 46 36 0 0 0 0 0 -1
normalized size 1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.024 0.023 0.181 0.000 0.999 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 48 0 0 0 0 0 -1
normalized size 1 1.00 0.64 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.034 0.064 0.172 0.000 1.769 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 61 0 0 0 0 0 -1
normalized size 1 1.00 0.50 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.052 0.109 0.176 0.000 1.652 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 53 177 100 1597 0 114 -1
normalized size 1 1.00 0.40 1.34 0.76 12.10 0.00 0.86 -0.01
time (sec) N/A 0.053 0.125 0.593 0.414 0.867 0.000 0.126 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 38 131 62 659 0 52 -1
normalized size 1 1.00 0.49 1.68 0.79 8.45 0.00 0.67 -0.01
time (sec) N/A 0.035 0.070 0.500 0.415 0.830 0.000 0.144 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 25 89 27 180 0 28 -1
normalized size 1 1.00 0.69 2.47 0.75 5.00 0.00 0.78 -0.03
time (sec) N/A 0.016 0.015 0.446 0.431 0.853 0.000 0.150 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 56 16 116 0 13 39
normalized size 1 1.00 1.00 3.73 1.07 7.73 0.00 0.87 2.60
time (sec) N/A 0.017 0.006 0.372 0.422 2.328 0.000 0.133 0.065
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 30 80 165 1137 0 27 48
normalized size 1 1.00 0.45 1.19 2.46 16.97 0.00 0.40 0.72
time (sec) N/A 0.025 0.028 0.386 0.427 1.329 0.000 0.161 0.970
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 47 96 457 3065 0 39 256
normalized size 1 1.00 0.40 0.82 3.91 26.20 0.00 0.33 2.19
time (sec) N/A 0.035 0.050 0.361 0.426 0.642 0.000 0.209 0.986
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 12 9 8 31 7 10 8
normalized size 1 1.00 1.50 1.12 1.00 3.88 0.88 1.25 1.00
time (sec) N/A 0.021 0.011 0.031 0.301 1.535 0.335 0.142 0.074
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 12 9 8 31 7 10 8
normalized size 1 1.00 1.50 1.12 1.00 3.88 0.88 1.25 1.00
time (sec) N/A 0.022 0.010 0.033 0.305 0.401 0.543 0.124 0.908
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 12 12 18 24 12 20 7 10 10
normalized size 1 1.00 1.50 2.00 1.00 1.67 0.58 0.83 0.83
time (sec) N/A 0.031 0.007 0.049 0.309 2.085 0.545 0.130 0.897
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 24 26 12 22 7 10 10
normalized size 1 1.00 1.71 1.86 0.86 1.57 0.50 0.71 0.71
time (sec) N/A 0.031 0.011 0.071 0.309 2.154 1.045 0.158 0.045
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 13 11 23 48 58 21 10
normalized size 1 1.00 1.30 1.10 2.30 4.80 5.80 2.10 1.00
time (sec) N/A 0.038 0.020 0.041 0.303 2.698 0.519 0.122 0.940
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 13 11 23 54 58 22 10
normalized size 1 1.00 1.08 0.92 1.92 4.50 4.83 1.83 0.83
time (sec) N/A 0.037 0.018 0.062 0.314 1.087 0.528 0.131 0.944
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 12 9 8 55 15 12 8
normalized size 1 1.00 1.20 0.90 0.80 5.50 1.50 1.20 0.80
time (sec) N/A 0.021 0.010 0.030 0.295 0.816 0.635 0.120 0.920
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 11 8 55 14 12 8
normalized size 1 1.00 1.00 0.92 0.67 4.58 1.17 1.00 0.67
time (sec) N/A 0.021 0.012 0.029 0.296 1.710 0.583 0.132 0.076
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 12 9 49 33 7 16 16
normalized size 1 1.00 0.86 0.64 3.50 2.36 0.50 1.14 1.14
time (sec) N/A 0.032 0.028 0.050 0.309 0.496 0.960 0.128 0.925
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 12 9 49 33 8 16 16
normalized size 1 1.00 0.75 0.56 3.06 2.06 0.50 1.00 1.00
time (sec) N/A 0.033 0.029 0.056 0.311 3.354 1.492 0.140 0.922
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 20 15 31 89 126 21 14
normalized size 1 1.00 1.43 1.07 2.21 6.36 9.00 1.50 1.00
time (sec) N/A 0.040 0.010 0.051 0.302 0.553 0.591 0.123 0.984
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 27 17 35 90 126 20 16
normalized size 1 1.00 1.35 0.85 1.75 4.50 6.30 1.00 0.80
time (sec) N/A 0.040 0.014 0.075 0.304 0.697 0.598 0.144 0.994
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 51 208 102 101 1253 90 131
normalized size 1 1.00 0.89 3.65 1.79 1.77 21.98 1.58 2.30
time (sec) N/A 0.059 0.072 0.096 0.310 1.115 8.767 0.122 1.262
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 27 107 84 94 284 75 107
normalized size 1 1.00 0.59 2.33 1.83 2.04 6.17 1.63 2.33
time (sec) N/A 0.065 0.033 0.089 0.316 1.383 5.623 0.118 1.133
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 39 156 78 57 692 66 95
normalized size 1 1.00 0.89 3.55 1.77 1.30 15.73 1.50 2.16
time (sec) N/A 0.054 0.055 0.085 0.306 1.039 3.712 0.133 1.045
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 21 87 60 52 150 51 71
normalized size 1 1.00 0.64 2.64 1.82 1.58 4.55 1.55 2.15
time (sec) N/A 0.056 0.022 0.082 0.315 0.629 2.220 0.126 0.979
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 25 103 54 27 294 40 59
normalized size 1 1.00 0.81 3.32 1.74 0.87 9.48 1.29 1.90
time (sec) N/A 0.046 0.037 0.080 0.321 2.017 1.303 0.138 0.942
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 13 47 36 18 49 27 35
normalized size 1 1.00 0.68 2.47 1.89 0.95 2.58 1.42 1.84
time (sec) N/A 0.043 0.013 0.072 0.313 0.729 0.734 0.133 0.936
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 17 51 23 11 46 17 23
normalized size 1 1.00 1.31 3.92 1.77 0.85 3.54 1.31 1.77
time (sec) N/A 0.039 0.009 0.070 0.311 1.689 0.410 0.117 0.913
Problem 159 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 9 9 12 12 11 16 7 17 9
normalized size 1 1.00 1.33 1.33 1.22 1.78 0.78 1.89 1.00
time (sec) N/A 0.024 0.006 0.036 0.304 0.784 0.132 0.160 0.888
Problem 160 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 23 23 42 23 47 103 0 52 51
normalized size 1 1.00 1.83 1.00 2.04 4.48 0.00 2.26 2.22
time (sec) N/A 0.052 0.032 0.072 0.300 1.748 0.000 0.153 0.928
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 30 29 59 94 0 35 89
normalized size 1 1.00 1.25 1.21 2.46 3.92 0.00 1.46 3.71
time (sec) N/A 0.048 0.050 0.081 0.304 1.617 0.000 0.153 0.919
Problem 162 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 49 49 60 45 103 631 0 94 114
normalized size 1 1.00 1.22 0.92 2.10 12.88 0.00 1.92 2.33
time (sec) N/A 0.081 0.170 0.092 0.312 0.867 0.000 0.178 0.933
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 38 45 233 250 0 59 263
normalized size 1 1.00 1.03 1.22 6.30 6.76 0.00 1.59 7.11
time (sec) N/A 0.051 0.057 0.092 0.314 1.091 0.000 0.147 0.953
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 89 67 155 1551 0 116 244
normalized size 1 1.00 1.14 0.86 1.99 19.88 0.00 1.49 3.13
time (sec) N/A 0.106 0.287 0.096 0.326 0.827 0.000 0.136 1.048
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 144 1039 310 2134 0 229 289
normalized size 1 1.00 1.03 7.42 2.21 15.24 0.00 1.64 2.06
time (sec) N/A 0.167 0.187 0.078 0.321 0.839 0.000 0.169 1.715
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 154 679 0 2913 0 266 348
normalized size 1 1.00 1.00 4.41 0.00 18.92 0.00 1.73 2.26
time (sec) N/A 0.425 0.244 0.085 0.000 1.508 0.000 0.164 1.701
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 84 599 178 866 0 124 169
normalized size 1 1.00 1.01 7.22 2.14 10.43 0.00 1.49 2.04
time (sec) N/A 0.107 0.115 0.069 0.335 1.029 0.000 0.129 1.310
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 95 338 0 1099 0 146 222
normalized size 1 1.00 0.91 3.25 0.00 10.57 0.00 1.40 2.13
time (sec) N/A 0.241 0.190 0.085 0.000 2.778 0.000 0.125 1.310
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 283 84 234 0 56 79
normalized size 1 1.00 1.00 7.08 2.10 5.85 0.00 1.40 1.98
time (sec) N/A 0.069 0.060 0.060 0.312 1.416 0.000 0.127 1.044
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 54 129 0 279 892 68 139
normalized size 1 1.00 0.92 2.19 0.00 4.73 15.12 1.15 2.36
time (sec) N/A 0.112 0.086 0.062 0.000 1.288 93.140 0.133 1.045
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 12 11 27 14 19 11
normalized size 1 1.00 1.00 1.09 1.00 2.45 1.27 1.73 1.00
time (sec) N/A 0.027 0.016 0.029 0.301 0.843 0.312 0.142 0.058
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 37 52 59 58 0 67 160
normalized size 1 1.00 0.70 0.98 1.11 1.09 0.00 1.26 3.02
time (sec) N/A 0.077 0.071 0.072 0.378 0.620 0.000 0.149 1.286
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 77 78 0 470 0 76 327
normalized size 1 1.00 1.15 1.16 0.00 7.01 0.00 1.13 4.88
time (sec) N/A 0.090 0.212 0.083 0.000 0.602 0.000 0.139 1.479
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 100 97 154 818 0 179 291
normalized size 1 1.00 1.10 1.07 1.69 8.99 0.00 1.97 3.20
time (sec) N/A 0.159 0.280 0.086 0.351 0.555 0.000 0.146 1.477
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 141 127 0 2339 0 156 642
normalized size 1 1.00 1.28 1.15 0.00 21.26 0.00 1.42 5.84
time (sec) N/A 0.246 0.571 0.092 0.000 0.496 0.000 0.132 1.975
Problem 176 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 151 151 148 191 348 3450 0 338 559
normalized size 1 1.00 0.98 1.26 2.30 22.85 0.00 2.24 3.70
time (sec) N/A 0.254 0.910 0.089 0.402 0.591 0.000 0.161 1.831
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 159 159 201 213 0 6381 0 303 1031
normalized size 1 1.00 1.26 1.34 0.00 40.13 0.00 1.91 6.48
time (sec) N/A 0.477 1.813 0.094 0.000 0.649 0.000 0.187 2.605
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 61 99 0 700 0 68 139
normalized size 1 1.00 0.91 1.48 0.00 10.45 0.00 1.01 2.07
time (sec) N/A 0.104 0.109 0.068 0.000 0.585 0.000 0.152 1.123
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 100 315 0 2003 0 144 722
normalized size 1 1.00 0.88 2.79 0.00 17.73 0.00 1.27 6.39
time (sec) N/A 0.406 0.444 0.098 0.000 1.575 0.000 0.155 5.941
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 46 140 96 450 0 115 1221
normalized size 1 1.00 0.81 2.46 1.68 7.89 0.00 2.02 21.42
time (sec) N/A 0.099 0.104 0.095 0.443 0.710 0.000 0.128 1.610
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 61 108 0 326 0 67 285
normalized size 1 1.00 1.00 1.77 0.00 5.34 0.00 1.10 4.67
time (sec) N/A 0.232 0.121 0.086 0.000 0.632 0.000 0.130 3.533
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 21 33 40 0 33 201
normalized size 1 1.00 1.00 1.05 1.65 2.00 0.00 1.65 10.05
time (sec) N/A 0.042 0.009 0.073 0.453 1.435 0.000 0.122 0.425
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 38 53 59 60 0 67 148
normalized size 1 1.00 0.70 0.98 1.09 1.11 0.00 1.24 2.74
time (sec) N/A 0.070 0.074 0.086 0.303 0.556 0.000 0.123 0.427
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 77 78 0 470 0 76 337
normalized size 1 1.00 1.00 1.01 0.00 6.10 0.00 0.99 4.38
time (sec) N/A 0.094 0.207 0.093 0.000 0.415 0.000 0.145 1.338
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 101 97 156 839 0 178 291
normalized size 1 1.00 1.07 1.03 1.66 8.93 0.00 1.89 3.10
time (sec) N/A 0.199 0.225 0.096 0.322 0.437 0.000 0.128 1.519
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 131 127 0 2417 0 172 666
normalized size 1 1.00 0.96 0.93 0.00 17.64 0.00 1.26 4.86
time (sec) N/A 0.196 0.542 0.109 0.000 0.635 0.000 0.147 1.806
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 58 115 89 750 0 58 183
normalized size 1 1.00 1.26 2.50 1.93 16.30 0.00 1.26 3.98
time (sec) N/A 0.093 0.091 0.128 0.498 0.525 0.000 0.149 1.062
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 25 30 223 174 0 48 117
normalized size 1 1.00 0.83 1.00 7.43 5.80 0.00 1.60 3.90
time (sec) N/A 0.086 0.030 0.112 0.369 0.464 0.000 0.148 1.013
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 46 71 57 315 0 39 95
normalized size 1 1.00 1.39 2.15 1.73 9.55 0.00 1.18 2.88
time (sec) N/A 0.080 0.065 0.099 0.424 0.482 0.000 0.131 0.962
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 17 18 70 66 0 22 25
normalized size 1 1.00 0.89 0.95 3.68 3.47 0.00 1.16 1.32
time (sec) N/A 0.066 0.023 0.101 0.342 0.637 0.000 0.129 0.919
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 18 31 23 50 0 22 33
normalized size 1 1.00 1.20 2.07 1.53 3.33 0.00 1.47 2.20
time (sec) N/A 0.049 0.050 0.085 0.434 0.539 0.000 0.141 0.921
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 12 19 24 28 0 22 26
normalized size 1 1.00 0.67 1.06 1.33 1.56 0.00 1.22 1.44
time (sec) N/A 0.040 0.019 0.084 0.330 0.520 0.000 0.140 0.076
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 42 23 48 103 0 52 51
normalized size 1 1.00 1.27 0.70 1.45 3.12 0.00 1.58 1.55
time (sec) N/A 0.065 0.043 0.099 0.328 0.530 0.000 0.128 0.922
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 25 29 121 91 0 35 92
normalized size 1 1.00 0.83 0.97 4.03 3.03 0.00 1.17 3.07
time (sec) N/A 0.079 0.052 0.090 0.333 0.447 0.000 0.148 0.927
Problem 195 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 46 46 60 45 103 631 0 94 132
normalized size 1 1.00 1.30 0.98 2.24 13.72 0.00 2.04 2.87
time (sec) N/A 0.107 0.134 0.101 0.335 0.526 0.000 0.148 0.962
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 41 45 469 224 0 59 263
normalized size 1 1.00 1.00 1.10 11.44 5.46 0.00 1.44 6.41
time (sec) N/A 0.081 0.078 0.099 0.345 0.436 0.000 0.159 1.029
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 37 30 0 376 0 0 -1
normalized size 1 1.00 1.00 0.81 0.00 10.16 0.00 0.00 -0.03
time (sec) N/A 0.063 0.024 0.063 0.000 0.722 0.000 0.000 0.000
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 19 0 356 0 0 -1
normalized size 1 1.00 1.00 0.79 0.00 14.83 0.00 0.00 -0.04
time (sec) N/A 0.057 0.012 0.074 0.000 0.652 0.000 0.000 0.000
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 55 137 0 291 741 60 197
normalized size 1 1.00 0.98 2.45 0.00 5.20 13.23 1.07 3.52
time (sec) N/A 0.128 0.091 0.067 0.000 0.549 27.721 0.134 2.982
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 19 28 19 46 20 22 22
normalized size 1 1.00 1.06 1.56 1.06 2.56 1.11 1.22 1.22
time (sec) N/A 0.077 0.035 0.047 0.373 0.486 0.342 0.121 0.056
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 19 36 20 48 31 22 21
normalized size 1 1.00 0.79 1.50 0.83 2.00 1.29 0.92 0.88
time (sec) N/A 0.086 0.050 0.071 0.374 0.483 0.507 0.123 0.909
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 61 125 0 315 0 66 160
normalized size 1 1.00 0.94 1.92 0.00 4.85 0.00 1.02 2.46
time (sec) N/A 0.148 0.158 0.102 0.000 0.581 0.000 0.124 12.141
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 81 139 0 303 0 90 974
normalized size 1 1.00 0.81 1.39 0.00 3.03 0.00 0.90 9.74
time (sec) N/A 0.166 0.262 0.106 0.000 2.754 0.000 0.129 3.679
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 63 89 0 249 0 53 636
normalized size 1 1.00 1.02 1.44 0.00 4.02 0.00 0.85 10.26
time (sec) N/A 0.133 0.125 0.095 0.000 0.984 0.000 0.126 6.413
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 81 138 0 298 0 90 983
normalized size 1 1.00 0.82 1.39 0.00 3.01 0.00 0.91 9.93
time (sec) N/A 0.305 0.200 0.115 0.000 3.246 0.000 0.154 3.328
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 81 276 0 405 695 97 653
normalized size 1 1.00 0.94 3.21 0.00 4.71 8.08 1.13 7.59
time (sec) N/A 0.154 0.256 0.173 0.000 0.474 31.240 0.158 2.188
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 115 144 0 1044 0 161 301
normalized size 1 1.00 0.95 1.19 0.00 8.63 0.00 1.33 2.49
time (sec) N/A 0.176 0.446 0.172 0.000 0.754 0.000 0.185 1.588
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 187 187 175 273 0 3636 0 387 -1
normalized size 1 1.00 0.94 1.46 0.00 19.44 0.00 2.07 -0.01
time (sec) N/A 0.264 0.849 0.166 0.000 0.658 0.000 0.212 0.000
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 260 260 245 459 0 8531 0 688 -1
normalized size 1 1.00 0.94 1.77 0.00 32.81 0.00 2.65 -0.00
time (sec) N/A 0.448 2.574 0.176 0.000 0.690 0.000 0.246 0.000
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 191 191 536 487 0 780 0 0 -1
normalized size 1 1.00 2.81 2.55 0.00 4.08 0.00 0.00 -0.01
time (sec) N/A 0.377 0.634 0.129 0.000 0.558 0.000 0.000 0.000
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 291 291 221 686 0 1162 0 0 -1
normalized size 1 1.00 0.76 2.36 0.00 3.99 0.00 0.00 -0.00
time (sec) N/A 0.567 0.774 0.124 0.000 1.380 0.000 0.000 0.000
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 391 391 295 889 0 1542 0 0 -1
normalized size 1 1.00 0.75 2.27 0.00 3.94 0.00 0.00 -0.00
time (sec) N/A 0.599 0.693 0.126 0.000 0.569 0.000 0.000 0.000
Problem 213 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 58 58 55 0 0 0 0 0 -1
normalized size 1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.119 0.084 0.602 0.000 0.720 0.000 0.000 0.000
Problem 214 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 58 58 57 0 0 0 0 0 -1
normalized size 1 1.00 0.98 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.081 0.038 0.346 0.000 0.924 0.000 0.000 0.000
Problem 215 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 26 26 26 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.039 0.035 0.197 0.000 0.715 0.000 0.000 0.000
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 40 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.038 6.337 0.201 0.000 0.565 0.000 0.000 0.000
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 42 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.080 26.141 0.198 0.000 0.444 0.000 0.000 0.000
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 59 138 0 480 0 0 110
normalized size 1 1.00 0.98 2.30 0.00 8.00 0.00 0.00 1.83
time (sec) N/A 0.057 0.136 0.176 0.000 0.504 0.000 0.000 1.091
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 87 231 0 1692 0 0 -1
normalized size 1 1.00 1.00 2.66 0.00 19.45 0.00 0.00 -0.01
time (sec) N/A 0.089 0.264 0.229 0.000 0.522 0.000 0.000 0.000
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 41 47 42 67 0 42 -1
normalized size 1 1.00 0.87 1.00 0.89 1.43 0.00 0.89 -0.02
time (sec) N/A 0.462 0.113 0.292 0.433 0.500 0.000 0.142 0.000
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.038 5.528 0.140 0.000 2.070 0.000 0.000 0.000
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 327 327 326 0 0 624 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 1.91 0.00 0.00 -0.00
time (sec) N/A 0.479 0.036 0.562 0.000 0.570 0.000 0.000 0.000
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 245 245 244 0 0 497 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 2.03 0.00 0.00 -0.00
time (sec) N/A 0.390 0.023 0.533 0.000 0.654 0.000 0.000 0.000
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 160 368 0 354 0 0 -1
normalized size 1 1.00 0.99 2.29 0.00 2.20 0.00 0.00 -0.01
time (sec) N/A 0.242 0.013 0.210 0.000 1.633 0.000 0.000 0.000
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 19 18 44 41 31 18
normalized size 1 1.00 1.00 1.06 1.00 2.44 2.28 1.72 1.00
time (sec) N/A 0.032 0.038 0.027 0.319 1.003 0.970 0.144 0.072
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.036 14.214 0.385 0.000 0.613 0.000 0.000 0.000
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 27 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.061 25.213 0.304 0.000 0.526 0.000 0.000 0.000
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 495 495 386 0 0 1174 0 0 -1
normalized size 1 1.00 0.78 0.00 0.00 2.37 0.00 0.00 -0.00
time (sec) N/A 0.839 1.513 0.422 0.000 0.687 0.000 0.000 0.000
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 370 370 293 0 0 937 0 0 -1
normalized size 1 1.00 0.79 0.00 0.00 2.53 0.00 0.00 -0.00
time (sec) N/A 0.704 1.305 0.426 0.000 1.701 0.000 0.000 0.000
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 244 244 187 862 0 669 0 0 -1
normalized size 1 1.00 0.77 3.53 0.00 2.74 0.00 0.00 -0.00
time (sec) N/A 0.418 1.030 0.287 0.000 0.733 0.000 0.000 0.000
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 69 177 0 415 1122 89 176
normalized size 1 1.00 0.95 2.42 0.00 5.68 15.37 1.22 2.41
time (sec) N/A 0.123 0.180 0.079 0.000 0.502 122.503 0.140 1.115
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 27 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.057 116.728 0.290 0.000 0.583 0.000 0.000 0.000
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 27 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.064 32.313 0.209 0.000 0.444 0.000 0.000 0.000
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 586 586 1082 0 0 2025 0 0 -1
normalized size 1 1.00 1.85 0.00 0.00 3.46 0.00 0.00 -0.00
time (sec) N/A 0.686 11.572 0.743 0.000 0.529 0.000 0.000 0.000
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F C F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 432 432 831 0 0 1622 0 0 -1
normalized size 1 1.00 1.92 0.00 0.00 3.75 0.00 0.00 -0.00
time (sec) N/A 0.563 8.423 0.655 0.000 0.698 0.000 0.000 0.000
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 288 288 414 860 0 1196 0 0 -1
normalized size 1 1.00 1.44 2.99 0.00 4.15 0.00 0.00 -0.00
time (sec) N/A 0.336 2.961 0.300 0.000 0.526 0.000 0.000 0.000
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 55 415 130 340 0 88 122
normalized size 1 1.00 0.90 6.80 2.13 5.57 0.00 1.44 2.00
time (sec) N/A 0.073 0.110 0.081 0.328 0.645 0.000 0.150 1.065
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A F(-1) A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 27 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.055 180.000 0.505 0.000 1.352 0.000 0.000 0.000
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 41 0 51 44 0 47 44
normalized size 1 1.00 0.76 0.00 0.94 0.81 0.00 0.87 0.81
time (sec) N/A 0.012 0.072 0.100 0.337 0.970 0.000 0.124 0.995
Problem 240 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 56 0 67 90 0 169 53
normalized size 1 1.00 0.64 0.00 0.76 1.02 0.00 1.92 0.60
time (sec) N/A 0.020 0.106 0.498 0.343 0.535 0.000 0.174 1.006
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 117 0 115 199 0 665 94
normalized size 1 1.00 0.79 0.00 0.77 1.34 0.00 4.46 0.63
time (sec) N/A 0.039 0.562 0.502 0.382 0.495 0.000 0.218 1.047
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 191 191 167 0 129 293 0 777 102
normalized size 1 1.00 0.87 0.00 0.68 1.53 0.00 4.07 0.53
time (sec) N/A 0.051 0.448 0.545 0.397 0.564 0.000 0.238 1.038
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 54 0 64 99 0 235 55
normalized size 1 1.00 0.74 0.00 0.88 1.36 0.00 3.22 0.75
time (sec) N/A 0.023 0.141 0.083 0.362 0.469 0.000 0.163 1.045
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 120 120 87 0 87 250 0 759 73
normalized size 1 1.00 0.72 0.00 0.72 2.08 0.00 6.32 0.61
time (sec) N/A 0.048 0.303 0.428 0.353 0.618 0.000 0.218 1.088
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 197 292 0 138 584 0 3225 117
normalized size 1 0.97 1.44 0.00 0.68 2.88 0.00 15.89 0.58
time (sec) N/A 0.083 1.480 0.439 0.923 0.520 0.000 0.285 1.182
Problem 246 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 266 260 311 0 161 1123 0 6880 134
normalized size 1 0.98 1.17 0.00 0.61 4.22 0.00 25.86 0.50
time (sec) N/A 0.128 3.445 0.467 0.484 0.452 0.000 0.413 1.195
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 37 19 18 19 41 42 18
normalized size 1 1.00 2.06 1.06 1.00 1.06 2.28 2.33 1.00
time (sec) N/A 0.016 0.014 0.049 0.473 0.482 0.980 0.122 1.027
Problem 248 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 36 52 49 39 0 80 32
normalized size 1 1.00 0.92 1.33 1.26 1.00 0.00 2.05 0.82
time (sec) N/A 0.031 0.025 0.084 0.313 0.426 0.000 0.130 1.046
Problem 249 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 42 36 86 53 87 81 35
normalized size 1 1.00 1.00 0.86 2.05 1.26 2.07 1.93 0.83
time (sec) N/A 0.032 0.010 0.213 0.328 0.525 10.569 0.156 1.049
Problem 250 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 51 84 93 84 0 114 50
normalized size 1 1.00 0.70 1.15 1.27 1.15 0.00 1.56 0.68
time (sec) N/A 0.047 0.047 0.228 0.325 0.530 0.000 0.148 1.107
Problem 251 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 65 65 65 51 130 105 128 116 49
normalized size 1 1.00 1.00 0.78 2.00 1.62 1.97 1.78 0.75
time (sec) N/A 0.037 0.020 0.215 0.323 0.555 97.056 0.170 1.165
Problem 252 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 67 67 62 256 0 0 0 0 -1
normalized size 1 1.00 0.93 3.82 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.044 0.056 0.434 0.000 0.564 0.000 0.000 0.000
Problem 253 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 114 237 0 0 0 0 -1
normalized size 1 1.00 1.70 3.54 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.044 0.131 0.418 0.000 0.611 0.000 0.000 0.000
Problem 254 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 183 0 0 0 0 -1
normalized size 1 1.00 1.00 6.54 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.028 0.023 0.333 0.000 0.572 0.000 0.000 0.000
Problem 255 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 183 0 0 0 0 -1
normalized size 1 1.00 1.00 6.54 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.028 0.021 0.299 0.000 0.768 0.000 0.000 0.000
Problem 256 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 58 141 0 0 0 0 -1
normalized size 1 1.00 0.92 2.24 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.042 0.059 0.431 0.000 0.505 0.000 0.000 0.000
Problem 257 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 122 295 0 0 0 0 -1
normalized size 1 1.00 1.82 4.40 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.042 0.087 0.395 0.000 0.451 0.000 0.000 0.000
Problem 258 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F A F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 206 206 85 0 0 187 0 0 -1
normalized size 1 1.00 0.41 0.00 0.00 0.91 0.00 0.00 -0.00
time (sec) N/A 0.154 0.485 0.656 0.000 0.491 0.000 0.000 0.000
Problem 259 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 102 102 74 0 0 141 0 0 -1
normalized size 1 1.00 0.73 0.00 0.00 1.38 0.00 0.00 -0.01
time (sec) N/A 0.082 0.331 0.482 0.000 0.432 0.000 0.000 0.000
Problem 260 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 61 0 0 68 0 0 -1
normalized size 1 1.00 1.45 0.00 0.00 1.62 0.00 0.00 -0.02
time (sec) N/A 0.050 0.156 0.474 0.000 0.492 0.000 0.000 0.000
Problem 261 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 121 0 0 128 0 0 -1
normalized size 1 1.00 1.20 0.00 0.00 1.27 0.00 0.00 -0.01
time (sec) N/A 0.075 0.267 0.472 0.000 0.585 0.000 0.000 0.000
Problem 262 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 373 347 0 171 0 764 -1
normalized size 1 1.00 3.69 3.44 0.00 1.69 0.00 7.56 -0.01
time (sec) N/A 0.177 0.369 0.125 0.000 0.521 0.000 5.288 0.000
Problem 263 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 111 358 0 366 0 749 -1
normalized size 1 1.00 1.04 3.35 0.00 3.42 0.00 7.00 -0.01
time (sec) N/A 0.194 0.309 0.419 0.000 0.641 0.000 15.289 0.000
Problem 264 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 83 83 62 45 68 113 139 60 58
normalized size 1 1.00 0.75 0.54 0.82 1.36 1.67 0.72 0.70
time (sec) N/A 0.039 0.047 0.217 0.320 0.519 54.778 0.122 0.502
Problem 265 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 47 49 53 95 207 57 42
normalized size 1 1.00 0.82 0.86 0.93 1.67 3.63 1.00 0.74
time (sec) N/A 0.037 0.041 0.227 0.316 0.478 15.947 0.140 0.262
Problem 266 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 39 35 40 54 78 34 34
normalized size 1 1.00 0.80 0.71 0.82 1.10 1.59 0.69 0.69
time (sec) N/A 0.029 0.023 0.213 0.306 0.935 4.342 0.137 0.965
Problem 267 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 37 24 50 63 22 18
normalized size 1 1.00 1.00 1.61 1.04 2.17 2.74 0.96 0.78
time (sec) N/A 0.015 0.013 0.043 0.313 0.630 1.020 0.115 0.921
Problem 268 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 19 16 30 0 16 16
normalized size 1 1.00 1.00 1.12 0.94 1.76 0.00 0.94 0.94
time (sec) N/A 0.017 0.015 0.029 0.419 0.427 0.000 0.115 0.922
Problem 269 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 36 27 37 105 0 35 48
normalized size 1 1.00 0.90 0.68 0.92 2.62 0.00 0.88 1.20
time (sec) N/A 0.029 0.067 0.075 0.411 0.519 0.000 0.140 0.079
Problem 270 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 29 22 68 86 0 31 31
normalized size 1 1.00 1.00 0.76 2.34 2.97 0.00 1.07 1.07
time (sec) N/A 0.027 0.019 0.213 0.312 0.685 0.000 0.118 0.927
Problem 271 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 64 43 83 513 0 60 130
normalized size 1 1.00 0.67 0.45 0.87 5.40 0.00 0.63 1.37
time (sec) N/A 0.047 0.091 0.218 0.406 0.647 0.000 0.117 0.956
Problem 272 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 44 35 172 233 0 42 42
normalized size 1 1.00 0.73 0.58 2.87 3.88 0.00 0.70 0.70
time (sec) N/A 0.048 0.037 0.224 0.333 0.478 0.000 0.125 0.955
Problem 273 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 26 34 17 47 42 17 17
normalized size 1 1.00 1.00 1.31 0.65 1.81 1.62 0.65 0.65
time (sec) N/A 0.020 0.015 0.096 0.306 0.435 0.651 0.138 0.076
Problem 274 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 19 19 16 22 13 26 20 13 12
normalized size 1 1.00 0.84 1.16 0.68 1.37 1.05 0.68 0.63
time (sec) N/A 0.011 0.010 0.070 0.307 0.564 0.255 0.117 0.052
Problem 275 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 24 25 76 113 0 76 77
normalized size 1 1.00 0.26 0.27 0.83 1.23 0.00 0.83 0.84
time (sec) N/A 0.064 0.011 0.141 0.416 0.585 0.000 0.115 1.114
Problem 276 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 106 36 88 162 0 88 85
normalized size 1 1.00 0.95 0.32 0.79 1.46 0.00 0.79 0.77
time (sec) N/A 0.075 0.093 0.151 0.424 0.540 0.000 0.123 1.088
Problem 277 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 26 34 17 67 42 17 17
normalized size 1 1.00 1.00 1.31 0.65 2.58 1.62 0.65 0.65
time (sec) N/A 0.019 0.017 0.098 0.311 0.470 0.638 0.133 0.076
Problem 278 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 16 26 13 38 20 13 12
normalized size 1 1.00 0.84 1.37 0.68 2.00 1.05 0.68 0.63
time (sec) N/A 0.012 0.011 0.096 0.314 0.628 0.248 0.113 0.926
Problem 279 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 24 79 71 83 0 44 65
normalized size 1 1.00 0.44 1.44 1.29 1.51 0.00 0.80 1.18
time (sec) N/A 0.058 0.012 0.137 0.426 0.528 0.000 0.113 1.039
Problem 280 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 34 59 79 154 0 79 84
normalized size 1 1.00 0.31 0.54 0.72 1.40 0.00 0.72 0.76
time (sec) N/A 0.205 0.022 0.240 0.416 0.767 0.000 0.124 0.309
Problem 281 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 26 34 17 87 42 17 17
normalized size 1 1.00 1.00 1.31 0.65 3.35 1.62 0.65 0.65
time (sec) N/A 0.019 0.017 0.095 0.330 0.506 0.627 0.130 0.961
Problem 282 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 26 13 46 20 13 14
normalized size 1 1.00 1.00 1.37 0.68 2.42 1.05 0.68 0.74
time (sec) N/A 0.011 0.011 0.092 0.319 1.414 0.249 0.136 0.049
Problem 283 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 371 371 24 25 0 1087 0 249 479
normalized size 1 1.00 0.06 0.07 0.00 2.93 0.00 0.67 1.29
time (sec) N/A 0.321 0.011 0.142 0.000 0.611 0.000 0.208 4.560
Problem 284 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 379 379 34 36 0 1367 0 261 473
normalized size 1 1.00 0.09 0.09 0.00 3.61 0.00 0.69 1.25
time (sec) N/A 0.319 0.022 0.164 0.000 0.536 0.000 0.145 3.467
Problem 285 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 202 202 159 326 134 2218 0 1239 154
normalized size 1 1.00 0.79 1.61 0.66 10.98 0.00 6.13 0.76
time (sec) N/A 0.078 0.702 0.293 0.354 0.653 0.000 0.272 1.811
Problem 286 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 85 143 94 699 604 903 100
normalized size 1 1.00 0.64 1.08 0.71 5.30 4.58 6.84 0.76
time (sec) N/A 0.053 0.236 0.167 0.351 1.135 30.568 0.237 1.249
Problem 287 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 50 74 63 246 316 611 74
normalized size 1 1.00 0.67 0.99 0.84 3.28 4.21 8.15 0.99
time (sec) N/A 0.018 0.117 0.070 0.344 0.549 6.474 0.206 1.007
Problem 288 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 68 68 70 0 0 0 0 0 -1
normalized size 1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.022 0.020 0.080 0.000 0.469 0.000 0.000 0.000
Problem 289 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 70 70 70 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.029 0.017 0.102 0.000 0.500 0.000 0.000 0.000
Problem 290 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 96 0 0 0 0 0 -1
normalized size 1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.052 0.255 0.112 0.000 0.598 0.000 0.000 0.000
Problem 291 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 133 133 101 0 0 0 0 0 -1
normalized size 1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.059 0.203 0.148 0.000 0.608 0.000 0.000 0.000
Problem 292 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 250 250 106 0 112 218 0 101 -1
normalized size 1 1.00 0.42 0.00 0.45 0.87 0.00 0.40 -0.00
time (sec) N/A 0.229 0.106 180.000 0.336 0.649 0.000 0.133 0.000
Problem 293 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 78 0 74 126 0 73 -1
normalized size 1 1.00 0.48 0.00 0.46 0.78 0.00 0.45 -0.01
time (sec) N/A 0.124 0.116 180.000 0.345 0.524 0.000 0.144 0.000
Problem 294 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 48 0 29 66 204 23 76
normalized size 1 1.00 0.65 0.00 0.39 0.89 2.76 0.31 1.03
time (sec) N/A 0.099 0.042 180.000 0.340 0.518 16.611 0.112 0.121
Problem 295 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 42 0 21 42 0 20 -1
normalized size 1 1.00 0.95 0.00 0.48 0.95 0.00 0.45 -0.02
time (sec) N/A 0.113 0.056 180.000 0.434 0.560 0.000 0.122 0.000
Problem 296 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 46 0 84 120 0 38 76
normalized size 1 1.00 0.82 0.00 1.50 2.14 0.00 0.68 1.36
time (sec) N/A 0.129 0.076 180.000 0.338 0.485 0.000 0.119 0.944
Problem 297 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 72 0 209 315 0 51 89
normalized size 1 1.00 0.51 0.00 1.48 2.23 0.00 0.36 0.63
time (sec) N/A 0.197 0.073 180.000 0.334 0.596 0.000 0.137 0.104
Problem 298 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 191 191 84 0 386 589 0 64 345
normalized size 1 1.00 0.44 0.00 2.02 3.08 0.00 0.34 1.81
time (sec) N/A 0.259 0.086 180.000 0.332 0.592 0.000 0.119 0.111
Problem 299 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 28 62 0 45 99 32 45
normalized size 1 1.00 0.68 1.51 0.00 1.10 2.41 0.78 1.10
time (sec) N/A 0.013 0.049 0.091 0.000 0.605 0.649 0.134 0.087
Problem 300 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 79 72 65 104 0 73 -1
normalized size 1 1.00 0.93 0.85 0.76 1.22 0.00 0.86 -0.01
time (sec) N/A 0.081 0.082 0.230 0.311 0.585 0.000 0.141 0.000
Problem 301 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 91 97 81 130 0 91 -1
normalized size 1 1.00 0.90 0.96 0.80 1.29 0.00 0.90 -0.01
time (sec) N/A 0.125 0.154 0.453 0.322 0.529 0.000 0.142 0.000
Problem 302 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 51 52 45 44 0 45 -1
normalized size 1 1.00 0.78 0.80 0.69 0.68 0.00 0.69 -0.02
time (sec) N/A 0.064 0.070 0.256 0.323 0.534 0.000 0.125 0.000
Problem 303 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 71 48 47 76 0 49 -1
normalized size 1 1.00 1.09 0.74 0.72 1.17 0.00 0.75 -0.02
time (sec) N/A 0.079 0.102 0.740 0.316 0.631 0.000 0.139 0.000
Problem 304 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 122 105 89 165 0 101 -1
normalized size 1 1.00 1.06 0.91 0.77 1.43 0.00 0.88 -0.01
time (sec) N/A 0.159 0.370 0.753 0.328 0.554 0.000 0.126 0.000
Problem 305 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 102 100 90 211 0 106 -1
normalized size 1 1.00 0.93 0.91 0.82 1.92 0.00 0.96 -0.01
time (sec) N/A 0.148 0.128 0.158 0.324 0.469 0.000 0.148 0.000
Problem 306 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 148 148 149 126 127 278 0 355 -1
normalized size 1 1.00 1.01 0.85 0.86 1.88 0.00 2.40 -0.01
time (sec) N/A 0.191 0.700 0.286 0.416 0.621 0.000 0.185 0.000
Problem 307 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 239 239 286 207 200 443 0 223 -1
normalized size 1 1.00 1.20 0.87 0.84 1.85 0.00 0.93 -0.00
time (sec) N/A 0.286 0.429 0.415 0.431 0.453 0.000 0.166 0.000
Problem 308 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 123 126 102 251 0 134 -1
normalized size 1 1.00 1.07 1.10 0.89 2.18 0.00 1.17 -0.01
time (sec) N/A 0.220 0.276 0.156 0.333 0.640 0.000 0.152 0.000
Problem 309 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 220 158 143 334 0 389 -1
normalized size 1 1.00 1.37 0.98 0.89 2.07 0.00 2.42 -0.01
time (sec) N/A 0.273 0.649 0.283 0.435 0.643 0.000 0.201 0.000
Problem 310 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 257 257 353 265 228 539 0 285 -1
normalized size 1 1.00 1.37 1.03 0.89 2.10 0.00 1.11 -0.00
time (sec) N/A 0.466 0.798 0.434 0.444 0.525 0.000 0.164 0.000
Problem 311 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 133 133 104 117 105 216 0 132 -1
normalized size 1 1.00 0.78 0.88 0.79 1.62 0.00 0.99 -0.01
time (sec) N/A 0.194 0.153 0.161 0.324 0.621 0.000 0.149 0.000
Problem 312 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 131 139 131 242 0 150 -1
normalized size 1 1.00 0.81 0.86 0.81 1.50 0.00 0.93 -0.01
time (sec) N/A 0.220 0.230 0.252 0.333 0.604 0.000 0.156 0.000
Problem 313 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 271 271 214 234 211 426 0 264 -1
normalized size 1 1.00 0.79 0.86 0.78 1.57 0.00 0.97 -0.00
time (sec) N/A 0.338 0.468 0.446 0.337 0.495 0.000 0.168 0.000
Problem 314 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 75 70 69 145 0 75 -1
normalized size 1 1.00 0.93 0.86 0.85 1.79 0.00 0.93 -0.01
time (sec) N/A 0.158 0.333 0.138 0.326 0.434 0.000 0.130 0.000
Problem 315 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 128 128 179 101 100 254 0 107 -1
normalized size 1 1.00 1.40 0.79 0.78 1.98 0.00 0.84 -0.01
time (sec) N/A 0.203 0.564 0.267 0.335 0.496 0.000 0.141 0.000
Problem 316 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 171 171 270 144 143 491 0 155 -1
normalized size 1 1.00 1.58 0.84 0.84 2.87 0.00 0.91 -0.01
time (sec) N/A 0.297 1.235 0.370 0.333 0.689 0.000 0.157 0.000
Problem 317 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 165 147 127 321 0 172 -1
normalized size 1 1.00 1.18 1.05 0.91 2.29 0.00 1.23 -0.01
time (sec) N/A 0.311 0.673 0.175 0.342 0.431 0.000 0.146 0.000
Problem 318 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 258 177 161 420 0 198 -1
normalized size 1 1.00 1.41 0.97 0.88 2.30 0.00 1.08 -0.01
time (sec) N/A 0.332 1.489 0.291 0.336 0.643 0.000 0.159 0.000
Problem 319 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 300 300 478 302 263 847 0 352 -1
normalized size 1 1.00 1.59 1.01 0.88 2.82 0.00 1.17 -0.00
time (sec) N/A 0.581 5.998 0.420 0.344 0.529 0.000 0.193 0.000
Problem 320 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 134 156 129 262 0 169 -1
normalized size 1 1.00 0.88 1.02 0.84 1.71 0.00 1.10 -0.01
time (sec) N/A 0.291 0.321 0.167 0.345 0.590 0.000 0.154 0.000
Problem 321 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 219 219 183 211 185 341 0 225 -1
normalized size 1 1.00 0.84 0.96 0.84 1.56 0.00 1.03 -0.00
time (sec) N/A 0.369 0.564 0.283 0.340 0.513 0.000 0.147 0.000
Problem 322 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 315 315 262 316 263 526 0 343 -1
normalized size 1 1.00 0.83 1.00 0.83 1.67 0.00 1.09 -0.00
time (sec) N/A 0.457 1.023 0.387 0.340 0.635 0.000 0.163 0.000
Problem 323 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 185 160 139 324 0 181 -1
normalized size 1 1.00 1.20 1.04 0.90 2.10 0.00 1.18 -0.01
time (sec) N/A 0.321 0.679 0.183 0.334 0.542 0.000 0.158 0.000
Problem 324 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 257 217 199 466 0 239 -1
normalized size 1 1.00 1.14 0.96 0.88 2.07 0.00 1.06 -0.00
time (sec) N/A 0.350 2.279 0.365 0.341 0.480 0.000 0.156 0.000
Problem 325 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 323 323 2511 326 287 851 0 369 -1
normalized size 1 1.00 7.77 1.01 0.89 2.63 0.00 1.14 -0.00
time (sec) N/A 0.512 6.509 0.425 0.353 0.634 0.000 0.185 0.000
Problem 326 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 161 161 251 186 151 362 0 209 -1
normalized size 1 1.00 1.56 1.16 0.94 2.25 0.00 1.30 -0.01
time (sec) N/A 0.426 1.514 0.187 0.335 0.536 0.000 0.168 0.000
Problem 327 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 239 239 339 249 215 516 0 273 -1
normalized size 1 1.00 1.42 1.04 0.90 2.16 0.00 1.14 -0.00
time (sec) N/A 0.506 6.167 0.327 0.331 0.473 0.000 0.185 0.000
Problem 328 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 344 344 2991 384 315 939 0 431 -1
normalized size 1 1.00 8.69 1.12 0.92 2.73 0.00 1.25 -0.00
time (sec) N/A 0.734 6.649 0.440 0.347 0.478 0.000 0.211 0.000
Problem 329 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F(-2) F F(-2) F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 20 20 46 0 0 0 0 0 39
normalized size 1 1.00 2.30 0.00 0.00 0.00 0.00 0.00 1.95
time (sec) N/A 0.050 0.362 180.000 0.000 0.000 0.000 0.000 0.148
Problem 330 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 16 0 0 109 0 0 42
normalized size 1 1.00 0.67 0.00 0.00 4.54 0.00 0.00 1.75
time (sec) N/A 0.051 0.082 0.005 0.000 0.499 0.000 0.000 0.967
Problem 331 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F(-1) F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 47 47 64 0 0 0 0 0 110
normalized size 1 1.00 1.36 0.00 0.00 0.00 0.00 0.00 2.34
time (sec) N/A 0.071 0.610 180.000 0.000 0.000 0.000 0.000 1.106
Problem 332 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-2) F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 76 0 0 0 0 0 -1
normalized size 1 1.00 2.11 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.094 0.189 180.000 0.000 0.000 0.000 0.000 0.000
Problem 333 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 26 25 36 23 41 36 24
normalized size 1 1.00 0.87 0.83 1.20 0.77 1.37 1.20 0.80
time (sec) N/A 0.038 0.066 0.031 0.306 0.665 0.189 0.131 0.049
Problem 334 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 56 56 51 52 81 54 85 75 48
normalized size 1 1.00 0.91 0.93 1.45 0.96 1.52 1.34 0.86
time (sec) N/A 0.075 0.093 0.220 0.318 0.568 0.315 0.117 0.069
Problem 335 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 213 213 180 212 0 316 0 0 -1
normalized size 1 1.00 0.85 1.00 0.00 1.48 0.00 0.00 -0.00
time (sec) N/A 0.523 0.299 0.118 0.000 0.517 0.000 0.000 0.000
Problem 336 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) B F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 271 271 248 376 0 671 0 0 -1
normalized size 1 1.00 0.92 1.39 0.00 2.48 0.00 0.00 -0.00
time (sec) N/A 0.751 0.499 0.105 0.000 0.533 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 [279] had the largest ratio of [1.125]

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 1 1 1.00 6 0.167
2 A 2 2 1.00 8 0.250
3 A 2 1 1.00 8 0.125
4 A 3 2 1.00 8 0.250
5 A 2 1 1.00 8 0.125
6 A 4 2 1.00 8 0.250
7 A 3 2 1.00 10 0.200
8 A 2 2 1.00 10 0.200
9 A 2 2 1.00 10 0.200
10 A 1 1 1.00 10 0.100
11 A 1 1 1.00 10 0.100
12 A 2 2 1.00 10 0.200
13 A 2 2 1.00 10 0.200
14 A 3 2 1.00 10 0.200
15 A 4 3 1.00 8 0.375
16 A 3 3 1.00 8 0.375
17 A 3 3 1.00 8 0.375
18 A 2 2 1.00 8 0.250
19 A 2 2 1.00 8 0.250
20 A 3 3 1.00 8 0.375
21 A 3 3 1.00 8 0.375
22 A 4 3 1.00 8 0.375
23 A 1 1 1.00 10 0.100
24 A 6 5 1.00 13 0.385
25 A 2 2 1.00 13 0.154
26 A 4 4 1.00 13 0.308
27 A 2 2 1.00 11 0.182
28 A 3 3 1.00 11 0.273
29 A 5 5 1.00 13 0.385
30 A 6 6 1.00 13 0.462
31 A 6 5 1.00 13 0.385
32 A 1 1 1.00 10 0.100
33 A 2 2 1.00 10 0.200
34 A 3 2 1.00 10 0.200
35 A 4 2 1.00 10 0.200
36 A 1 1 1.00 12 0.083
37 A 2 2 1.00 12 0.167
38 A 3 2 1.00 12 0.167
39 A 4 2 1.00 12 0.167
40 A 3 3 1.00 13 0.231
41 A 3 3 1.00 14 0.214
42 A 3 2 1.00 14 0.143
43 A 2 2 1.00 14 0.143
44 A 1 1 1.00 14 0.071
45 A 2 2 1.00 14 0.143
46 A 3 3 1.00 14 0.214
47 A 4 3 1.00 14 0.214
48 A 3 2 1.00 15 0.133
49 A 2 2 1.00 15 0.133
50 A 1 1 1.00 15 0.067
51 A 2 2 1.00 15 0.133
52 A 3 3 1.00 15 0.200
53 A 4 3 1.00 15 0.200
54 A 6 6 1.00 13 0.462
55 A 5 5 1.00 13 0.385
56 A 5 5 1.00 13 0.385
57 A 3 3 1.00 11 0.273
58 A 4 4 1.00 11 0.364
59 A 6 6 1.00 13 0.462
60 A 6 6 1.00 13 0.462
61 A 7 6 1.00 13 0.462
62 A 4 3 1.00 12 0.250
63 A 3 3 1.00 12 0.250
64 A 2 2 1.00 12 0.167
65 A 1 1 1.00 12 0.083
66 A 2 1 1.00 10 0.100
67 A 2 2 1.00 12 0.167
68 A 4 4 1.00 12 0.333
69 A 5 5 1.00 12 0.417
70 A 6 5 1.00 12 0.417
71 A 2 2 1.00 12 0.167
72 A 4 4 1.00 12 0.333
73 A 5 5 1.00 12 0.417
74 A 6 5 1.00 12 0.417
75 A 1 1 1.00 12 0.083
76 A 3 3 1.00 12 0.250
77 A 4 4 1.00 12 0.333
78 A 5 4 1.00 12 0.333
79 A 7 7 1.00 10 0.700
80 A 6 6 1.00 10 0.600
81 A 2 2 1.00 14 0.143
82 A 2 2 1.00 10 0.200
83 A 4 4 1.00 10 0.400
84 A 7 7 1.00 10 0.700
85 A 8 7 1.00 10 0.700
86 A 5 5 1.00 13 0.385
87 A 4 3 1.00 17 0.176
88 A 3 3 1.00 17 0.176
89 A 2 2 1.00 17 0.118
90 A 4 3 1.00 18 0.167
91 A 3 3 1.00 18 0.167
92 A 2 2 1.00 18 0.111
93 A 2 2 1.00 13 0.154
94 A 2 2 1.00 13 0.154
95 A 3 3 1.00 13 0.231
96 A 4 3 1.00 13 0.231
97 A 2 2 1.00 15 0.133
98 A 2 2 1.00 15 0.133
99 A 3 3 1.00 15 0.200
100 A 4 3 1.00 15 0.200
101 A 3 3 1.00 17 0.176
102 A 3 3 1.00 17 0.176
103 A 4 4 1.00 17 0.235
104 A 3 3 1.00 18 0.167
105 A 3 3 1.00 18 0.167
106 A 4 4 1.00 18 0.222
107 A 8 6 1.00 17 0.353
108 A 7 6 1.00 17 0.353
109 A 6 6 1.00 17 0.353
110 A 3 3 1.00 15 0.200
111 A 4 4 1.00 15 0.267
112 A 5 4 1.00 15 0.267
113 A 6 4 1.00 15 0.267
114 A 3 3 1.00 20 0.150
115 A 2 2 1.00 20 0.100
116 A 2 2 1.00 15 0.133
117 A 2 2 1.00 13 0.154
118 A 5 5 1.00 17 0.294
119 A 6 6 1.00 17 0.353
120 A 7 6 1.00 17 0.353
121 A 5 3 1.00 10 0.300
122 A 4 3 1.00 10 0.300
123 A 3 3 1.00 10 0.300
124 A 2 2 1.00 10 0.200
125 A 2 2 1.00 10 0.200
126 A 3 3 1.00 10 0.300
127 A 4 3 1.00 10 0.300
128 A 6 3 1.00 10 0.300
129 A 4 3 1.00 10 0.300
130 A 3 3 1.00 10 0.300
131 A 3 3 1.00 10 0.300
132 A 4 3 1.00 10 0.300
133 A 6 3 1.00 10 0.300
134 A 7 3 1.00 10 0.300
135 A 5 3 1.00 10 0.300
136 A 3 3 1.00 10 0.300
137 A 3 3 1.00 10 0.300
138 A 3 2 1.00 10 0.200
139 A 3 2 1.00 10 0.200
140 A 2 2 1.00 9 0.222
141 A 2 2 1.00 11 0.182
142 A 2 2 1.00 11 0.182
143 A 2 2 1.00 13 0.154
144 A 3 2 1.00 11 0.182
145 A 3 2 1.00 13 0.154
146 A 2 2 1.00 9 0.222
147 A 2 2 1.00 11 0.182
148 A 1 1 1.00 11 0.091
149 A 1 1 1.00 13 0.077
150 A 3 2 1.00 11 0.182
151 A 3 2 1.00 13 0.154
152 A 5 3 1.00 13 0.231
153 A 3 2 1.00 13 0.154
154 A 4 3 1.00 13 0.231
155 A 3 2 1.00 13 0.154
156 A 3 3 1.00 13 0.231
157 A 2 1 1.00 13 0.077
158 A 2 2 1.00 13 0.154
159 A 2 2 1.00 11 0.182
160 A 4 3 1.00 11 0.273
161 A 3 3 1.00 13 0.231
162 A 4 3 1.00 13 0.231
163 A 3 2 1.00 13 0.154
164 A 4 3 1.00 13 0.231
165 A 3 2 1.00 13 0.154
166 A 6 5 1.00 13 0.385
167 A 3 2 1.00 13 0.154
168 A 5 5 1.00 13 0.385
169 A 3 2 1.00 13 0.154
170 A 4 4 1.00 13 0.308
171 A 2 2 1.00 11 0.182
172 A 6 4 1.00 11 0.364
173 A 4 4 1.00 13 0.308
174 A 4 3 1.00 13 0.231
175 A 5 5 1.00 13 0.385
176 A 5 4 1.00 13 0.308
177 A 6 5 1.00 13 0.385
178 A 4 4 1.00 13 0.308
179 A 6 6 1.00 13 0.462
180 A 3 2 1.00 13 0.154
181 A 6 6 1.00 13 0.462
182 A 4 4 1.00 11 0.364
183 A 3 2 1.00 11 0.182
184 A 7 6 1.00 13 0.462
185 A 4 3 1.00 13 0.231
186 A 12 8 1.00 13 0.615
187 A 6 5 1.00 13 0.385
188 A 5 4 1.00 13 0.308
189 A 5 5 1.00 13 0.385
190 A 5 4 1.00 13 0.308
191 A 4 4 1.00 13 0.308
192 A 4 4 1.00 11 0.364
193 A 5 5 1.00 11 0.454
194 A 5 4 1.00 13 0.308
195 A 6 5 1.00 13 0.385
196 A 6 5 1.00 13 0.385
197 A 4 4 1.00 13 0.308
198 A 3 3 1.00 13 0.231
199 A 6 5 1.00 15 0.333
200 A 5 4 1.00 13 0.308
201 A 5 4 1.00 15 0.267
202 A 8 7 1.00 15 0.467
203 A 7 5 1.00 15 0.333
204 A 5 5 1.00 15 0.333
205 A 11 8 1.00 15 0.533
206 A 6 6 1.00 31 0.194
207 A 7 7 1.00 31 0.226
208 A 8 7 1.00 31 0.226
209 A 9 7 1.00 31 0.226
210 A 9 6 1.00 12 0.500
211 A 11 7 1.00 14 0.500
212 A 13 8 1.00 14 0.571
213 A 5 3 1.00 36 0.083
214 A 4 3 1.00 36 0.083
215 A 2 2 1.00 34 0.059
216 A 0 0 0.00 0 0.000
217 A 0 0 0.00 0 0.000
218 A 3 3 1.00 12 0.250
219 A 5 5 1.00 12 0.417
220 A 13 5 1.00 20 0.250
221 A 0 0 0.00 0 0.000
222 A 11 6 1.00 22 0.273
223 A 9 5 1.00 22 0.227
224 A 7 4 1.00 20 0.200
225 A 2 2 1.00 19 0.105
226 A 0 0 0.00 0 0.000
227 A 0 0 0.00 0 0.000
228 A 18 11 1.00 24 0.458
229 A 15 10 1.00 24 0.417
230 A 12 9 1.00 22 0.409
231 A 4 4 1.00 21 0.190
232 A 0 0 0.00 0 0.000
233 A 0 0 0.00 0 0.000
234 A 21 14 1.00 24 0.583
235 A 16 11 1.00 24 0.458
236 A 13 10 1.00 22 0.454
237 A 3 2 1.00 21 0.095
238 A 0 0 0.00 0 0.000
239 A 1 1 1.00 11 0.091
240 A 2 2 1.00 13 0.154
241 A 2 2 1.00 13 0.154
242 A 3 2 1.00 13 0.154
243 A 1 1 1.00 15 0.067
244 A 2 2 1.00 17 0.118
245 A 2 2 0.97 17 0.118
246 A 3 2 0.98 17 0.118
247 A 2 1 1.00 15 0.067
248 A 3 2 1.00 17 0.118
249 A 3 1 1.00 17 0.059
250 A 4 2 1.00 17 0.118
251 A 3 1 1.00 17 0.059
252 A 3 2 1.00 19 0.105
253 A 3 2 1.00 19 0.105
254 A 2 1 1.00 19 0.053
255 A 2 1 1.00 19 0.053
256 A 3 2 1.00 19 0.105
257 A 3 2 1.00 19 0.105
258 A 8 8 1.00 18 0.444
259 A 6 6 1.00 18 0.333
260 A 3 3 1.00 18 0.167
261 A 4 4 1.00 18 0.222
262 A 5 5 1.00 14 0.357
263 A 6 6 1.00 16 0.375
264 A 4 3 1.00 16 0.188
265 A 5 4 1.00 16 0.250
266 A 4 3 1.00 16 0.188
267 A 4 3 1.00 14 0.214
268 A 3 3 1.00 14 0.214
269 A 4 4 1.00 16 0.250
270 A 3 3 1.00 16 0.188
271 A 6 5 1.00 16 0.312
272 A 5 4 1.00 16 0.250
273 A 4 3 1.00 10 0.300
274 A 4 3 1.00 8 0.375
275 A 11 8 1.00 8 1.000
276 A 12 9 1.00 10 0.900
277 A 4 3 1.00 10 0.300
278 A 4 3 1.00 8 0.375
279 A 9 9 1.00 8 1.125
280 A 13 9 1.00 10 0.900
281 A 4 3 1.00 10 0.300
282 A 4 3 1.00 8 0.375
283 A 21 9 1.00 8 1.125
284 A 22 9 1.00 10 0.900
285 A 2 2 1.00 18 0.111
286 A 2 2 1.00 18 0.111
287 A 1 1 1.00 16 0.062
288 A 1 1 1.00 16 0.062
289 A 1 1 1.00 18 0.056
290 A 2 2 1.00 18 0.111
291 A 2 2 1.00 18 0.111
292 A 6 5 1.00 25 0.200
293 A 6 5 1.00 25 0.200
294 A 5 4 1.00 25 0.160
295 A 4 4 1.00 25 0.160
296 A 4 4 1.00 25 0.160
297 A 6 5 1.00 25 0.200
298 A 6 5 1.00 25 0.200
299 A 1 1 1.00 10 0.100
300 A 6 4 1.00 12 0.333
301 A 6 4 1.00 15 0.267
302 A 6 3 1.00 12 0.250
303 A 4 2 1.00 14 0.143
304 A 6 3 1.00 17 0.176
305 A 8 5 1.00 16 0.312
306 A 9 6 1.00 18 0.333
307 A 14 5 1.00 18 0.278
308 A 8 5 1.00 19 0.263
309 A 9 6 1.00 21 0.286
310 A 14 5 1.00 21 0.238
311 A 8 4 1.00 16 0.250
312 A 9 4 1.00 18 0.222
313 A 14 4 1.00 18 0.222
314 A 6 4 1.00 18 0.222
315 A 7 4 1.00 20 0.200
316 A 10 4 1.00 20 0.200
317 A 8 5 1.00 21 0.238
318 A 9 5 1.00 23 0.217
319 A 14 5 1.00 23 0.217
320 A 8 4 1.00 19 0.210
321 A 10 4 1.00 21 0.190
322 A 14 4 1.00 21 0.190
323 A 8 5 1.00 21 0.238
324 A 10 5 1.00 23 0.217
325 A 14 5 1.00 23 0.217
326 A 8 5 1.00 24 0.208
327 A 10 5 1.00 26 0.192
328 A 14 5 1.00 26 0.192
329 A 2 1 1.00 17 0.059
330 A 2 1 1.00 20 0.050
331 A 3 1 1.00 20 0.050
332 A 3 2 1.00 21 0.095
333 A 6 5 1.00 6 0.833
334 A 9 6 1.00 6 1.000
335 A 8 4 1.00 16 0.250
336 A 8 4 1.00 19 0.210

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