simplify sqrtnint in formulas

Author: ckrause

CHANGELOG.md

@@ -5,6 +5,7 @@ To install or update LODA, please follow the [installation instructions](https:/
 ### Enhancements
 
 * Improve negativity check in formula generation
+* Simplify formulas generated from `nrt` operations
 
 ## v24.12.8
 

src/form/formula_gen.cpp

@@ -141,8 +141,13 @@ bool FormulaGenerator::update(const Operation& op) {
       break;
     }
     case Operation::Type::NRT: {
-      res = Expression(Expression::Type::FUNCTION, "sqrtnint",
-                       {prevTarget, source});
+      if (source.type == Expression::Type::CONSTANT &&
+          source.value == Number(2)) {
+        res = Expression(Expression::Type::FUNCTION, "sqrtint", {prevTarget});
+      } else {
+        res = Expression(Expression::Type::FUNCTION, "sqrtnint",
+                         {prevTarget, source});
+      }
       break;
     }
     case Operation::Type::GCD: {

tests/formula/formula.txt

@@ -79,6 +79,7 @@ A110158: a(n) = b(max(n-2,0)), b(n) = b(n-2)+A077847(max(n-2,0)), b(1) = 0, b(0)
 A112032: a(n) = 2*a(n-2), a(1) = 1, a(0) = 4
 A123111: a(n) = ((n+1)^5+(n+1)^3+n+2)*(n+1)^2+1
 A134271: a(n) = b(max(n-2,0))+min(n-2,0), b(n) = 2*b(n-3)+b(n-2), b(2) = 4, b(1) = 0, b(0) = 2
+A135668: a(n) = sqrtint(n-1)+n+1
 A154118: a(n) = 2*a(n-1)+5, a(1) = 2, a(0) = 1
 A157823: a(n) = (min(n-1,0)-1)*(b(max(n-1,0))+3)+3, b(n) = 2*b(n-1), b(0) = 1
 A173673: a(n) = truncate((b(n)+min(n,n%2))/2), b(n) = b(n-2)+b(n-4), b(4) = 1, b(3) = 1, b(2) = 1, b(1) = 0, b(0) = 0

tests/programs/oeis/135/A135668.asm

@@ -0,0 +1,11 @@
+; A135668: a(n) = ceiling(n + sqrt(n)).
+; 2,4,5,6,8,9,10,11,12,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,32,33,34,35,36,37,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89
+
+#offset 1
+
+sub $0,1
+mov $1,$0
+nrt $1,2
+add $1,$0
+mov $0,$1
+add $0,2