Index: experimental/Intersection/CubicParameterizationCode.cpp |
diff --git a/experimental/Intersection/CubicParameterizationCode.cpp b/experimental/Intersection/CubicParameterizationCode.cpp |
deleted file mode 100644 |
index 7a7908e67f9a8fcc1a24613b0f6832a5d5bab3a0..0000000000000000000000000000000000000000 |
--- a/experimental/Intersection/CubicParameterizationCode.cpp |
+++ /dev/null |
@@ -1,405 +0,0 @@ |
-/* |
- * Copyright 2012 Google Inc. |
- * |
- * Use of this source code is governed by a BSD-style license that can be |
- * found in the LICENSE file. |
- */ |
-#include <vector> |
- |
-/* Given: |
- * Resultant[a*t^3 + b*t^2 + c*t + d - x, e*t^3 + f*t^2 + g*t + h - y, t] |
- */ |
- |
-const char result1[] = |
-"-d^3 e^3 + c d^2 e^2 f - b d^2 e f^2 + a d^2 f^3 - c^2 d e^2 g + " |
-" 2 b d^2 e^2 g + b c d e f g - 3 a d^2 e f g - a c d f^2 g - " |
-" b^2 d e g^2 + 2 a c d e g^2 + a b d f g^2 - a^2 d g^3 + c^3 e^2 h - " |
-" 3 b c d e^2 h + 3 a d^2 e^2 h - b c^2 e f h + 2 b^2 d e f h + " |
-" a c d e f h + a c^2 f^2 h - 2 a b d f^2 h + b^2 c e g h - " |
-" 2 a c^2 e g h - a b d e g h - a b c f g h + 3 a^2 d f g h + " |
-" a^2 c g^2 h - b^3 e h^2 + 3 a b c e h^2 - 3 a^2 d e h^2 + " |
-" a b^2 f h^2 - 2 a^2 c f h^2 - a^2 b g h^2 + a^3 h^3 + 3 d^2 e^3 x - " |
-" 2 c d e^2 f x + 2 b d e f^2 x - 2 a d f^3 x + c^2 e^2 g x - " |
-" 4 b d e^2 g x - b c e f g x + 6 a d e f g x + a c f^2 g x + " |
-" b^2 e g^2 x - 2 a c e g^2 x - a b f g^2 x + a^2 g^3 x + " |
-" 3 b c e^2 h x - 6 a d e^2 h x - 2 b^2 e f h x - a c e f h x + " |
-" 2 a b f^2 h x + a b e g h x - 3 a^2 f g h x + 3 a^2 e h^2 x - " |
-" 3 d e^3 x^2 + c e^2 f x^2 - b e f^2 x^2 + a f^3 x^2 + " |
-" 2 b e^2 g x^2 - 3 a e f g x^2 + 3 a e^2 h x^2 + e^3 x^3 - " |
-" c^3 e^2 y + 3 b c d e^2 y - 3 a d^2 e^2 y + b c^2 e f y - " |
-" 2 b^2 d e f y - a c d e f y - a c^2 f^2 y + 2 a b d f^2 y - " |
-" b^2 c e g y + 2 a c^2 e g y + a b d e g y + a b c f g y - " |
-" 3 a^2 d f g y - a^2 c g^2 y + 2 b^3 e h y - 6 a b c e h y + " |
-" 6 a^2 d e h y - 2 a b^2 f h y + 4 a^2 c f h y + 2 a^2 b g h y - " |
-" 3 a^3 h^2 y - 3 b c e^2 x y + 6 a d e^2 x y + 2 b^2 e f x y + " |
-" a c e f x y - 2 a b f^2 x y - a b e g x y + 3 a^2 f g x y - " |
-" 6 a^2 e h x y - 3 a e^2 x^2 y - b^3 e y^2 + 3 a b c e y^2 - " |
-" 3 a^2 d e y^2 + a b^2 f y^2 - 2 a^2 c f y^2 - a^2 b g y^2 + " |
-" 3 a^3 h y^2 + 3 a^2 e x y^2 - a^3 y^3"; |
- |
-const size_t len1 = sizeof(result1) - 1; |
- |
-/* Given: |
- * Expand[ |
- * Det[{{a, b, c, (d - x), 0, 0}, |
- * {0, a, b, c, (d - x), 0}, |
- * {0, 0, a, b, c, (d - x)}, |
- * {e, f, g, (h - y), 0, 0}, |
- * {0, e, f, g, (h - y), 0}, |
- * {0, 0, e, f, g, (h - y)}}]] |
- */ |
- // result1 and result2 are the same. 102 factors: |
-const char result2[] = |
-"-d^3 e^3 + c d^2 e^2 f - b d^2 e f^2 + a d^2 f^3 - c^2 d e^2 g + " |
-" 2 b d^2 e^2 g + b c d e f g - 3 a d^2 e f g - a c d f^2 g - " |
-" b^2 d e g^2 + 2 a c d e g^2 + a b d f g^2 - a^2 d g^3 + c^3 e^2 h - " |
-" 3 b c d e^2 h + 3 a d^2 e^2 h - b c^2 e f h + 2 b^2 d e f h + " |
-" a c d e f h + a c^2 f^2 h - 2 a b d f^2 h + b^2 c e g h - " |
-" 2 a c^2 e g h - a b d e g h - a b c f g h + 3 a^2 d f g h + " |
-" a^2 c g^2 h - b^3 e h^2 + 3 a b c e h^2 - 3 a^2 d e h^2 + " |
-" a b^2 f h^2 - 2 a^2 c f h^2 - a^2 b g h^2 + a^3 h^3 + 3 d^2 e^3 x - " |
-" 2 c d e^2 f x + 2 b d e f^2 x - 2 a d f^3 x + c^2 e^2 g x - " |
-" 4 b d e^2 g x - b c e f g x + 6 a d e f g x + a c f^2 g x + " |
-" b^2 e g^2 x - 2 a c e g^2 x - a b f g^2 x + a^2 g^3 x + " |
-" 3 b c e^2 h x - 6 a d e^2 h x - 2 b^2 e f h x - a c e f h x + " |
-" 2 a b f^2 h x + a b e g h x - 3 a^2 f g h x + 3 a^2 e h^2 x - " |
-" 3 d e^3 x^2 + c e^2 f x^2 - b e f^2 x^2 + a f^3 x^2 + " |
-" 2 b e^2 g x^2 - 3 a e f g x^2 + 3 a e^2 h x^2 + e^3 x^3 - " |
-" c^3 e^2 y + 3 b c d e^2 y - 3 a d^2 e^2 y + b c^2 e f y - " |
-" 2 b^2 d e f y - a c d e f y - a c^2 f^2 y + 2 a b d f^2 y - " |
-" b^2 c e g y + 2 a c^2 e g y + a b d e g y + a b c f g y - " |
-" 3 a^2 d f g y - a^2 c g^2 y + 2 b^3 e h y - 6 a b c e h y + " |
-" 6 a^2 d e h y - 2 a b^2 f h y + 4 a^2 c f h y + 2 a^2 b g h y - " |
-" 3 a^3 h^2 y - 3 b c e^2 x y + 6 a d e^2 x y + 2 b^2 e f x y + " |
-" a c e f x y - 2 a b f^2 x y - a b e g x y + 3 a^2 f g x y - " |
-" 6 a^2 e h x y - 3 a e^2 x^2 y - b^3 e y^2 + 3 a b c e y^2 - " |
-" 3 a^2 d e y^2 + a b^2 f y^2 - 2 a^2 c f y^2 - a^2 b g y^2 + " |
-" 3 a^3 h y^2 + 3 a^2 e x y^2 - a^3 y^3"; |
- |
-const size_t len2 = sizeof(result2) - 1; |
- |
-/* Given: r1 = Resultant[ |
- * a*(1 - t)^3 + 3*b*(1 - t)^2*t + 3*c*(1 - t)*t^2 + d*t^3 - x, |
- * e*(1 - t)^3 + 3*f*(1 - t)^2*t + 3*g*(1 - t)*t^2 + h*t^3 - y, t] |
- * Collect[r1, {x, y}, Simplify] |
- * CForm[%] |
- * then use regex to replace Power\(([a-h]),3\) with \1*\1*\1 |
- * and Power\(([a-h]),2\) with \1*\1 |
- * yields: |
- |
-d*d*d*e*e*e - 3*d*d*(3*c*e*e*f + 3*b*e*(-3*f*f + 2*e*g) + a*(9*f*f*f - 9*e*f*g + e*e*h)) - |
- h*(27*c*c*c*e*e - 27*c*c*(3*b*e*f - 3*a*f*f + 2*a*e*g) + |
- h*(-27*b*b*b*e + 27*a*b*b*f - 9*a*a*b*g + a*a*a*h) + |
- 9*c*(9*b*b*e*g + a*b*(-9*f*g + 3*e*h) + a*a*(3*g*g - 2*f*h))) + |
- 3*d*(9*c*c*e*e*g + 9*b*b*e*(3*g*g - 2*f*h) + 3*a*b*(-9*f*g*g + 6*f*f*h + e*g*h) + |
- a*a*(9*g*g*g - 9*f*g*h + e*h*h) + 3*c*(3*b*e*(-3*f*g + e*h) + a*(9*f*f*g - 6*e*g*g - e*f*h))) |
- |
-- Power(e - 3*f + 3*g - h,3)*Power(x,3) |
- |
-+ 3*(6*b*d*d*e*e - d*d*d*e*e + 18*b*b*d*e*f - 18*b*d*d*e*f - |
- 9*b*d*d*f*f - 54*b*b*d*e*g + 12*b*d*d*e*g - 27*b*b*d*g*g - 18*b*b*b*e*h + 18*b*b*d*e*h + |
- 18*b*b*d*f*h + a*a*a*h*h - 9*b*b*b*h*h + 9*c*c*c*e*(e + 2*h) + |
- a*a*(-3*b*h*(2*g + h) + d*(-27*g*g + 9*g*h - h*(2*e + h) + 9*f*(g + h))) + |
- a*(9*b*b*h*(2*f + h) - 3*b*d*(6*f*f - 6*f*(3*g - 2*h) + g*(-9*g + h) + e*(g + h)) + |
- d*d*(e*e + 9*f*(3*f - g) + e*(-9*f - 9*g + 2*h))) - |
- 9*c*c*(d*e*(e + 2*g) + 3*b*(f*h + e*(f + h)) + a*(-3*f*f - 6*f*h + 2*(g*h + e*(g + h)))) + |
- 3*c*(d*d*e*(e + 2*f) + a*a*(3*g*g + 6*g*h - 2*h*(2*f + h)) + 9*b*b*(g*h + e*(g + h)) + |
- a*d*(-9*f*f - 18*f*g + 6*g*g + f*h + e*(f + 12*g + h)) + |
- b*(d*(-3*e*e + 9*f*g + e*(9*f + 9*g - 6*h)) + 3*a*(h*(2*e - 3*g + h) - 3*f*(g + h)))))*y |
- |
-- 3*(18*c*c*c*e - 18*c*c*d*e + 6*c*d*d*e - d*d*d*e + 3*c*d*d*f - 9*c*c*d*g + a*a*a*h + 9*c*c*c*h - |
- 9*b*b*b*(e + 2*h) - a*a*(d*(e - 9*f + 18*g - 7*h) + 3*c*(2*f - 6*g + h)) + |
- a*(-9*c*c*(2*e - 6*f + 2*g - h) + d*d*(-7*e + 18*f - 9*g + h) + 3*c*d*(7*e - 17*f + 3*g + h)) + |
- 9*b*b*(3*c*(e + g + h) + a*(f + 2*h) - d*(e - 2*(f - 3*g + h))) - |
- 3*b*(-(d*d*(e - 6*f + 2*g)) - 3*c*d*(e + 3*f + 3*g - h) + 9*c*c*(e + f + h) + a*a*(g + 2*h) + |
- a*(c*(-3*e + 9*f + 9*g + 3*h) + d*(e + 3*f - 17*g + 7*h))))*Power(y,2) |
- |
-+ Power(a - 3*b + 3*c - d,3)*Power(y,3) |
- |
-+ Power(x,2)*(-3*(-9*b*e*f*f + 9*a*f*f*f + 6*b*e*e*g - 9*a*e*f*g + 27*b*e*f*g - 27*a*f*f*g + 18*a*e*g*g - 54*b*e*g*g + |
- 27*a*f*g*g + 27*b*f*g*g - 18*a*g*g*g + a*e*e*h - 9*b*e*e*h + 3*a*e*f*h + 9*b*e*f*h + 9*a*f*f*h - |
- 18*b*f*f*h - 21*a*e*g*h + 51*b*e*g*h - 9*a*f*g*h - 27*b*f*g*h + 18*a*g*g*h + 7*a*e*h*h - 18*b*e*h*h - 3*a*f*h*h + |
- 18*b*f*h*h - 6*a*g*h*h - 3*b*g*h*h + a*h*h*h + |
- 3*c*(-9*f*f*(g - 2*h) + 3*g*g*h - f*h*(9*g + 2*h) + e*e*(f - 6*g + 6*h) + |
- e*(9*f*g + 6*g*g - 17*f*h - 3*g*h + 3*h*h)) - |
- d*(e*e*e + e*e*(-6*f - 3*g + 7*h) - 9*(2*f - g)*(f*f + g*g - f*(g + h)) + |
- e*(18*f*f + 9*g*g + 3*g*h + h*h - 3*f*(3*g + 7*h)))) ) |
- |
-+ Power(x,2)*(3*(a - 3*b + 3*c - d)*Power(e - 3*f + 3*g - h,2)*y) |
- |
-+ x*(-3*(27*b*b*e*g*g - 27*a*b*f*g*g + 9*a*a*g*g*g - 18*b*b*e*f*h + 18*a*b*f*f*h + 3*a*b*e*g*h - |
- 27*b*b*e*g*h - 9*a*a*f*g*h + 27*a*b*f*g*h - 9*a*a*g*g*h + a*a*e*h*h - 9*a*b*e*h*h + |
- 27*b*b*e*h*h + 6*a*a*f*h*h - 18*a*b*f*h*h - 9*b*b*f*h*h + 3*a*a*g*h*h + |
- 6*a*b*g*h*h - a*a*h*h*h + 9*c*c*(e*e*(g - 3*h) - 3*f*f*h + e*(3*f + 2*g)*h) + |
- d*d*(e*e*e - 9*f*f*f + 9*e*f*(f + g) - e*e*(3*f + 6*g + h)) + |
- d*(-3*c*(-9*f*f*g + e*e*(2*f - 6*g - 3*h) + e*(9*f*g + 6*g*g + f*h)) + |
- a*(-18*f*f*f - 18*e*g*g + 18*g*g*g - 2*e*e*h + 3*e*g*h + 2*e*h*h + 9*f*f*(3*g + 2*h) + |
- 3*f*(6*e*g - 9*g*g - e*h - 6*g*h)) - 3*b*(9*f*g*g + e*e*(4*g - 3*h) - 6*f*f*h - |
- e*(6*f*f + g*(18*g + h) - 3*f*(3*g + 4*h)))) + |
- 3*c*(3*b*(e*e*h + 3*f*g*h - e*(3*f*g - 6*f*h + 6*g*h + h*h)) + |
- a*(9*f*f*(g - 2*h) + f*h*(-e + 9*g + 4*h) - 3*(2*g*g*h + e*(2*g*g - 4*g*h + h*h))))) ) |
- |
-+ x*3*(-2*a*d*e*e - 7*d*d*e*e + 15*a*d*e*f + 21*d*d*e*f - 9*a*d*f*f - 18*d*d*f*f - 15*a*d*e*g - |
- 3*d*d*e*g - 9*a*a*f*g + 9*d*d*f*g + 18*a*a*g*g + 9*a*d*g*g + 2*a*a*e*h - 2*d*d*e*h + |
- 3*a*a*f*h + 15*a*d*f*h - 21*a*a*g*h - 15*a*d*g*h + 7*a*a*h*h + 2*a*d*h*h - |
- 9*c*c*(2*e*e + 3*f*f + 3*f*h - 2*g*h + e*(-3*f - 4*g + h)) + |
- 9*b*b*(3*g*g - 3*g*h + 2*h*(-2*f + h) + e*(-2*f + 3*g + h)) + |
- 3*b*(3*c*(e*e + 3*e*(f - 3*g) + (9*f - 3*g - h)*h) + a*(6*f*f + e*g - 9*f*g - 9*g*g - 5*e*h + 9*f*h + 14*g*h - 7*h*h) + |
- d*(-e*e + 12*f*f - 27*f*g + e*(-9*f + 20*g - 5*h) + g*(9*g + h))) + |
- 3*c*(a*(-(e*f) - 9*f*f + 27*f*g - 12*g*g + 5*e*h - 20*f*h + 9*g*h + h*h) + |
- d*(7*e*e + 9*f*f + 9*f*g - 6*g*g - f*h + e*(-14*f - 9*g + 5*h))))*y |
- |
-- x*3*Power(a - 3*b + 3*c - d,2)*(e - 3*f + 3*g - h)*Power(y,2) |
- |
-*/ |
- |
-const int factors = 8; |
- |
-struct coeff { |
- int s; // constant and coefficient sign |
- int n[factors]; // 0 or power of a (1, 2, or 3) for a through h |
-}; |
- |
-enum { |
- xxx_coeff, |
- xxy_coeff, |
- xyy_coeff, |
- yyy_coeff, |
- xx_coeff, |
- xy_coeff, |
- yy_coeff, |
- x_coeff, |
- y_coeff, |
- c_coeff, |
- coeff_count |
-}; |
- |
-typedef std::vector<coeff> coeffs; |
-typedef std::vector<coeffs> n_coeffs; |
- |
-static char skipSpace(const char* str, size_t& index) { |
- do { |
- ++index; |
- } while (str[index] == ' '); |
- return str[index]; |
-} |
- |
-static char backSkipSpace(const char* str, size_t& end) { |
- while (str[end - 1] == ' ') { |
- --end; |
- } |
- return str[end - 1]; |
-} |
- |
-static void match(const char* str, size_t len, coeffs& co, const char pattern[]) { |
- size_t patternLen = strlen(pattern); |
- size_t index = 0; |
- while (index < len) { |
- char ch = str[index]; |
- if (ch != '-' && ch != '+') { |
- printf("missing sign\n"); |
- } |
- size_t end = index + 1; |
- while (str[end] != '+' && str[end] != '-' && ++end < len) { |
- ; |
- } |
- backSkipSpace(str, end); |
- size_t idx = index; |
- index = end; |
- skipSpace(str, index); |
- if (!strncmp(&str[end - patternLen], pattern, patternLen) == 0) { |
- continue; |
- } |
- size_t endCoeff = end - patternLen; |
- char last = backSkipSpace(str, endCoeff); |
- if (last == '2' || last == '3') { |
- last = str[endCoeff - 3]; // skip ^2 |
- } |
- if (last == 'x' || last == 'y') { |
- continue; |
- } |
- coeff c; |
- c.s = str[idx] == '-' ? -1 : 1; |
- bzero(c.n, sizeof(c.n)); |
- ch = skipSpace(str, idx); |
- if (ch >= '2' && ch <= '6') { |
- c.s *= ch - '0'; |
- ch = skipSpace(str, idx); |
- } |
- while (idx < endCoeff) { |
- char x = str[idx]; |
- if (x < 'a' || x > 'a' + factors) { |
- printf("expected factor\n"); |
- } |
- idx++; |
- int pow = 1; |
- if (str[idx] == '^') { |
- idx++; |
- char exp = str[idx]; |
- if (exp < '2' || exp > '3') { |
- printf("expected exponent\n"); |
- } |
- pow = exp - '0'; |
- } |
- skipSpace(str, idx); |
- c.n[x - 'a'] = pow; |
- } |
- co.push_back(c); |
- } |
-} |
- |
-void cubecode_test(int test); |
- |
-void cubecode_test(int test) { |
- const char* str = test ? result2 : result1; |
- size_t len = strlen(str); |
- n_coeffs c(coeff_count); |
- match(str, len, c[xxx_coeff], "x^3"); // 1 factor |
- match(str, len, c[xxy_coeff], "x^2 y"); // 1 factor |
- match(str, len, c[xyy_coeff], "x y^2"); // 1 factor |
- match(str, len, c[yyy_coeff], "y^3"); // 1 factor |
- match(str, len, c[xx_coeff], "x^2"); // 7 factors |
- match(str, len, c[xy_coeff], "x y"); // 8 factors |
- match(str, len, c[yy_coeff], "y^2"); // 7 factors |
- match(str, len, c[x_coeff], "x"); // 21 factors |
- match(str, len, c[y_coeff], "y"); // 21 factors |
- match(str, len, c[c_coeff], ""); // 34 factors : total 102 |
-#define COMPUTE_MOST_FREQUENT_EXPRESSION_TRIPLETS 0 |
-#define WRITE_AS_NONOPTIMIZED_C_CODE 0 |
-#if COMPUTE_MOST_FREQUENT_EXPRESSION_TRIPLETS |
- int count[factors][factors][factors]; |
- bzero(count, sizeof(count)); |
-#endif |
-#if WRITE_AS_NONOPTIMIZED_C_CODE |
- printf("// start of generated code"); |
-#endif |
- for (n_coeffs::iterator it = c.begin(); it < c.end(); ++it) { |
- coeffs& co = *it; |
-#if WRITE_AS_NONOPTIMIZED_C_CODE |
- printf("\nstatic double calc_%c(double a, double b, double c, double d," |
- "\n double e, double f, double g, double h) {" |
- "\n return" |
- "\n ", 'A' + (it - c.begin())); |
- if (co[0].s > 0) { |
- printf(" "); |
- } |
- if (abs(co[0].s) == 1) { |
- printf(" "); |
- } |
-#endif |
- for (coeffs::iterator ct = co.begin(); ct < co.end(); ++ct) { |
- const coeff& cf = *ct; |
-#if WRITE_AS_NONOPTIMIZED_C_CODE |
- printf(" "); |
- bool firstFactor = false; |
- if (ct - co.begin() > 0 || cf.s < 0) { |
- printf("%c", cf.s < 0 ? '-' : '+'); |
- } |
- if (ct - co.begin() > 0) { |
- printf(" "); |
- } |
- if (abs(cf.s) > 1) { |
- printf("%d * ", abs(cf.s)); |
- } else { |
- if (ct - co.begin() > 0) { |
- printf(" "); |
- } |
- } |
-#endif |
- for (int x = 0; x < factors; ++x) { |
- if (cf.n[x] == 0) { |
- continue; |
- } |
-#if WRITE_AS_NONOPTIMIZED_C_CODE |
- for (int y = 0 ; y < cf.n[x]; ++y) { |
- if (y > 0 || firstFactor) { |
- printf(" * "); |
- } |
- printf("%c", 'a' + x); |
- } |
- firstFactor = true; |
-#endif |
-#if COMPUTE_MOST_FREQUENT_EXPRESSION_TRIPLETS |
- for (int y = x; y < factors; ++y) { |
- if (cf.n[y] == 0) { |
- continue; |
- } |
- if (x == y && cf.n[y] == 1) { |
- continue; |
- } |
- for (int z = y; z < factors; ++z) { |
- if (cf.n[z] == 0) { |
- continue; |
- } |
- if ((x == z || y == z) && cf.n[z] == 1) { |
- continue; |
- } |
- if (x == y && y == z && cf.n[z] == 2) { |
- continue; |
- } |
- count[x][y][z]++; |
- } |
- } |
-#endif |
- } |
-#if WRITE_AS_NONOPTIMIZED_C_CODE |
- if (ct + 1 < co.end()) { |
- printf("\n"); |
- } |
-#endif |
- } |
-#if WRITE_AS_NONOPTIMIZED_C_CODE |
- printf(";\n}\n"); |
-#endif |
- } |
-#if WRITE_AS_NONOPTIMIZED_C_CODE |
- printf("// end of generated code\n"); |
-#endif |
-#if COMPUTE_MOST_FREQUENT_EXPRESSION_TRIPLETS |
- const int bestCount = 20; |
- int best[bestCount][4]; |
- bzero(best, sizeof(best)); |
- for (int x = 0; x < factors; ++x) { |
- for (int y = x; y < factors; ++y) { |
- for (int z = y; z < factors; ++z) { |
- if (!count[x][y][z]) { |
- continue; |
- } |
- for (int w = 0; w < bestCount; ++w) { |
- if (best[w][0] < count[x][y][z]) { |
- best[w][0] = count[x][y][z]; |
- best[w][1] = x; |
- best[w][2] = y; |
- best[w][3] = z; |
- break; |
- } |
- } |
- } |
- } |
- } |
- for (int w = 0; w < bestCount; ++w) { |
- printf("%c%c%c=%d\n", 'a' + best[w][1], 'a' + best[w][2], |
- 'a' + best[w][3], best[w][0]); |
- } |
-#endif |
-#if WRITE_AS_NONOPTIMIZED_C_CODE |
- printf("\n"); |
-#endif |
-} |
- |
-/* results: variable triplets used 10 or more times: |
-aah=14 |
-ade=14 |
-aeh=14 |
-dee=14 |
-bce=13 |
-beg=13 |
-beh=12 |
-bbe=11 |
-bef=11 |
-cee=11 |
-cef=11 |
-def=11 |
-ceh=10 |
-deg=10 |
-*/ |