diff --git a/singular_values.c b/singular_values.c
index bc06c61..3907c0f 100644
--- a/singular_values.c
+++ b/singular_values.c
@@ -9,7 +9,33 @@
 #define MAX_ELEMENTS 14000
 //#define DRAW_PICTURE 1
 
-void mpq_quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
+void continued_fraction_approximation(mpq_t out, double in, int level)
+{
+	mpq_t tmp;
+
+	if(in < 0) {
+		mpq_init(tmp);
+		mpq_set_ui(tmp, 0, 1);
+		continued_fraction_approximation(out, -in, level);
+		mpq_sub(out, tmp, out);
+		mpq_clear(tmp);
+		return;
+	}
+
+	if(level == 0) {
+		mpq_set_si(out, (signed long int)round(in), 1); // floor(in)
+	} else {
+		continued_fraction_approximation(out, 1/(in - floor(in)), level - 1);
+		mpq_init(tmp);
+		mpq_set_ui(tmp, 1, 1);
+		mpq_div(out, tmp, out); // out -> 1/out
+		mpq_set_si(tmp, (signed long int)in, 1); // floor(in)
+		mpq_add(out, out, tmp);
+		mpq_clear(tmp);
+	}
+}
+
+void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
 {
 	mpq_t tmp;
 	mpq_init(tmp);
@@ -46,12 +72,12 @@ void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t s, mpq_t
 	mpq_set_ui(*mat_ref(gen[1], 0, 0), 1, 1);
 	mpq_set_ui(*mat_ref(gen[1], 1, 0), 0, 1);
 	mpq_set_ui(*mat_ref(gen[1], 2, 0), 0, 1);
-	mpq_quartic(*mat_ref(gen[1], 0, 1), t, 0, 0, 1, -1, 2);
-	mpq_quartic(*mat_ref(gen[1], 1, 1), t, 0, 0, -1, 2, -2);
-	mpq_quartic(*mat_ref(gen[1], 2, 1), t, 0, 0, 1, -3, 3);
-	mpq_quartic(*mat_ref(gen[1], 0, 2), t, 0, 0, 1, 0, 3);
-	mpq_quartic(*mat_ref(gen[1], 1, 2), t, 0, 0, -1, 1, -1);
-	mpq_quartic(*mat_ref(gen[1], 2, 2), t, 0, 0, 1, -2, 1);
+	quartic(*mat_ref(gen[1], 0, 1), t, 0, 0, 1, -1, 2);
+	quartic(*mat_ref(gen[1], 1, 1), t, 0, 0, -1, 2, -2);
+	quartic(*mat_ref(gen[1], 2, 1), t, 0, 0, 1, -3, 3);
+	quartic(*mat_ref(gen[1], 0, 2), t, 0, 0, 1, 0, 3);
+	quartic(*mat_ref(gen[1], 1, 2), t, 0, 0, -1, 1, -1);
+	quartic(*mat_ref(gen[1], 2, 2), t, 0, 0, 1, -2, 1);
 
 	mat_pseudoinverse(ws, gen[3], gen[0]); // p^{-1}
 	mat_pseudoinverse(ws, gen[4], gen[1]); // q^{-1}
@@ -79,95 +105,152 @@ char *print_word(groupelement_t *g, char *str)
   return str;
 }
 
+void enumerate(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t)
+{
+	mat_workspace *ws;
+	mat tmp;
+	mat gen[6];
+	char buf[100], buf2[100], buf3[100];
+
+	// allocate stuff
+	ws = mat_workspace_init(3);
+	for(int i = 0; i < 6; i++)
+		mat_init(gen[i], 3);
+	mat_init(tmp, 3);
+
+	initialize_triangle_generators(ws, gen, s, t);
+
+	mat_identity(matrices[0]);
+	for(int i = 1; i < MAX_ELEMENTS; i++) {
+		if(group[i].length % 2 != 0)
+			continue;
+		if(!group[i].inverse)
+			continue;
+
+		int parent = group[i].parent->id;
+		int grandparent = group[i].parent->parent->id;
+		int letter;
+
+		if(group[parent].letter == 1 && group[i].letter == 2)
+			letter = 0; // p = bc
+		else if(group[parent].letter == 2 && group[i].letter == 0)
+			letter = 1; // q = ca
+		else if(group[parent].letter == 0 && group[i].letter == 1)
+			letter = 2; // r = ab
+		if(group[parent].letter == 2 && group[i].letter == 1)
+			letter = 3; // p^{-1} = cb
+		else if(group[parent].letter == 0 && group[i].letter == 2)
+			letter = 4; // q^{-1} = ac
+		else if(group[parent].letter == 1 && group[i].letter == 0)
+			letter = 5; // r^{-1} = ba
+
+		mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
+	}
+
+	// free stuff
+	for(int i = 0; i < 6; i++)
+		mat_clear(gen[i]);
+	mat_clear(tmp);
+	mat_workspace_clear(ws);
+}
+
+void output_invariants(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t)
+{
+	mpq_t tr, trinv;
+	char buf[100];
+
+	mpq_inits(tr, trinv, NULL);
+
+	for(int i = 0; i < MAX_ELEMENTS; i++) {
+		if(group[i].length % 2 != 0 || !group[i].inverse)
+			continue;
+
+		mat_trace(tr, matrices[i]);
+		mat_trace(trinv, matrices[group[i].inverse->id]);
+
+		gmp_printf("%d %d %s %Qd %Qd %f %f\n", i, group[i].length, print_word(&group[i], buf), tr, trinv, log(mpq_get_d(tr)), log(mpq_get_d(trinv)));
+	}
+
+	mpq_clears(tr, trinv, NULL);
+}
+
+double max_slope(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t, int *index)
+{
+	double max = 0;
+	double slope;
+
+	mpq_t tr, trinv;
+	char buf[100];
+
+	mpq_inits(tr, trinv, NULL);
+
+	for(int i = 0; i < MAX_ELEMENTS; i++) {
+		if(group[i].length % 2 != 0 || !group[i].inverse)
+			continue;
+
+		mat_trace(tr, matrices[i]);
+		mat_trace(trinv, matrices[group[i].inverse->id]);
+
+		slope = log(mpq_get_d(trinv))/log(mpq_get_d(tr));
+		if(slope > max)
+		{
+			*index = i;
+			max = slope;
+		}
+	}
+
+	mpq_clears(tr, trinv, NULL);
+
+	return max;
+}
+
 int main(int argc, char *argv[])
 {
-  groupelement_t *group;
-  mat_workspace *ws;
-  mat *matrices;
-  mat tmp;
-  mat gen[6];
-  char buf[100], buf2[100], buf3[100];
-  mpq_t s,t;
-  mpq_t det, tr, trinv;
+	mpq_t s, t, tmp;
+	mpz_t accuracy;
+	double t_;
+	mat *matrices;
+	groupelement_t *group;
+	int index;
 
-  // allocate stuff
-  group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
-  ws = mat_workspace_init(3);
-  matrices = malloc(MAX_ELEMENTS*sizeof(mat));
-  for(int i = 0; i < MAX_ELEMENTS; i++)
-	  mat_init(matrices[i], 3);
-  for(int i = 0; i < 6; i++)
-	  mat_init(gen[i], 3);
-  mat_init(tmp, 3);
+	mpq_inits(s, t, tmp, NULL);
+	mpz_init(accuracy);
+	group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
+	matrices = malloc(MAX_ELEMENTS*sizeof(mat));
+	for(int i = 0; i < MAX_ELEMENTS; i++)
+		mat_init(matrices[i], 3);
 
-  mpq_inits(s, t, det, tr, trinv, NULL);
+	// mpq_set_str(t, argv[1], 10);
+	mpz_set_ui(accuracy, 100);
+	for(int i = 0; ; i++) {
+		mpq_set(t, tmp);
+		continued_fraction_approximation(tmp, atof(argv[1]), i);
+		if(mpz_cmp(mpq_numref(tmp),accuracy) > 0 && mpz_cmp(mpq_denref(tmp),accuracy) > 0)
+			break;
+	}
+	mpq_canonicalize(t);
+	gmp_fprintf(stdout, "\"t = %Qd = %.3f\"\n", mpq_get_d(t), t);
 
-  mpq_set_ui(s,1,1);
-  double t_ = atof(argv[1]);
-  mpq_set_ui(t,(int)(t_*100),100);
-  mpq_canonicalize(s);
-  mpq_canonicalize(t);
+	if(argc > 2 && strcmp(argv[2],"p") == 0) {
+		gmp_fprintf(stdout, "%Qd\n", t);
+		return 0;
+	}
 
-  // the real action
-  generate_triangle_group(group, MAX_ELEMENTS, 3, 3, 4);
-  initialize_triangle_generators(ws, gen, s, t);
+	generate_triangle_group(group, MAX_ELEMENTS, 3, 3, 4);
 
-  mat_identity(matrices[0]);
-  for(int i = 1; i < MAX_ELEMENTS; i++) {
-	  if(group[i].length % 2 != 0)
-		  continue;
-	  if(!group[i].inverse)
-		  continue;
+//	for(int i = 0; i < 10; i++) {
+//		mpq_set_ui(t,100+i,100);
+//		mpq_canonicalize(t);
 
-	  int parent = group[i].parent->id;
-	  int grandparent = group[i].parent->parent->id;
-	  int letter;
+		enumerate(group, matrices, s, t);
+		//printf("%f %f\n", mpq_get_d(t), max_slope(group, matrices, s, t, &index));
+		output_invariants(group, matrices, s, t);
+//	}
 
-	  if(group[parent].letter == 1 && group[i].letter == 2)
-		  letter = 0; // p = bc
-	  else if(group[parent].letter == 2 && group[i].letter == 0)
-		  letter = 1; // q = ca
-	  else if(group[parent].letter == 0 && group[i].letter == 1)
-		  letter = 2; // r = ab
-	  if(group[parent].letter == 2 && group[i].letter == 1)
-		  letter = 3; // p^{-1} = cb
-	  else if(group[parent].letter == 0 && group[i].letter == 2)
-		  letter = 4; // q^{-1} = ac
-	  else if(group[parent].letter == 1 && group[i].letter == 0)
-		  letter = 5; // r^{-1} = ba
-
-	  mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
-  }
-
-  for(int i = 0; i < MAX_ELEMENTS; i++) {
-	  if(group[i].length % 2 != 0)
-		  continue;
-	  if(!group[i].inverse)
-		  continue;
-
-	  mat_trace(tr, matrices[i]);
-	  mat_trace(trinv, matrices[group[i].inverse->id]);
-
-	  double lambda1, lambda2, lambda3;
-//	  int realevs = gsl_poly_solve_cubic(-mpq_get_d(tr), mpq_get_d(trinv), -1, &lambda3, &lambda2, &lambda1);
-//	  if(realevs != 3)
-//		  continue;
-//	  if(lambda1 < 0 || lambda2 < 0 || lambda3 < 0)
-//		  continue;
-
-//	  gmp_printf("%d %d %s %Qd %Qd\n", i, group[i].length, print_word(&group[i], buf), tr, trinv);
-	  printf("%d %d %s %f %f %f\n", i, group[i].length, print_word(&group[i], buf), log(mpq_get_d(tr)), log(mpq_get_d(trinv)));
-
-  }
-
-  // free stuff
-  for(int i = 0; i < MAX_ELEMENTS; i++)
-    mat_clear(matrices[i]);
-  for(int i = 0; i < 6; i++)
-    mat_clear(gen[i]);
-  mat_clear(tmp);
-  mpq_clears(s, t, det, tr, trinv, NULL);
-  mat_workspace_clear(ws);
-
-  return 0;
+	for(int i = 0; i < MAX_ELEMENTS; i++)
+		mat_clear(matrices[i]);
+	free(matrices);
+	free(group);
+	mpq_clears(s, t, tmp, NULL);
+	mpz_clear(accuracy);
 }
diff --git a/singular_values.plt b/singular_values.plt
index ce251a7..cd4894e 100644
--- a/singular_values.plt
+++ b/singular_values.plt
@@ -3,7 +3,7 @@ if(!exists("logs")) logs = log(1.0)
 
 file = sprintf("< ./singular_values %f", exp(logt))
 #title = sprintf("s = %f, t = %f", exp(logs), exp(logt))
-title = sprintf("t = %.3f", floor(exp(logt)*100)/100.0)
+title = sprintf("t = %.3f", exp(logt))
 # print title
 
 set zeroaxis
@@ -23,7 +23,7 @@ set parametric
 tr(a,b) = exp(a) + exp(b-a) + exp(-b)
 trinv(a,b) = exp(-a) + exp(a-b) + exp(b)
 
-plot file using 4:5 w p pt 7 ps 0.5 lc 1 t title, \
+plot file using 6:7 w p pt 7 ps 0.5 lc 1 t columnheader, \
 	 log(tr(t,t*2)),log(trinv(t,2*t)) w l lw 2 t "", \
 	 log(tr(t,t/2)),log(trinv(t,t/2)) w l lw 2 t ""