diff --git a/src/closureps/cloenv.mbt b/src/closureps/cloenv.mbt
index f6fbc04..8261415 100644
--- a/src/closureps/cloenv.mbt
+++ b/src/closureps/cloenv.mbt
@@ -21,7 +21,7 @@ fn CloEnv::collect_named_fns(self : CloEnv, c : @cps.Cps) -> Unit {
       self.collect_named_fns(body)
       self.collect_named_fns(rest)
     }
-    If(_, _then, _else) => {
+    If(_, _then, _else) | IfEq(_, _, _then, _else) | IfLe(_, _, _then, _else) => {
       self.collect_named_fns(_then)
       self.collect_named_fns(_else)
     }
diff --git a/src/closureps/cps2closureps.mbt b/src/closureps/cps2closureps.mbt
index e6deeee..31aa0ea 100644
--- a/src/closureps/cps2closureps.mbt
+++ b/src/closureps/cps2closureps.mbt
@@ -52,7 +52,7 @@ fn CloEnv::collect_label_closure(
       self.collect_label_closure(rest, output)
       output.remove(fn_name)
     }
-    If(_, _then, _else) => {
+    If(_, _then, _else) | IfEq(_, _, _then, _else) | IfLe(_, _, _then, _else) => {
       self.collect_label_closure(_then, output)
       self.collect_label_closure(_else, output)
     }
@@ -125,6 +125,8 @@ fn CloEnv::collect_closure(
         self.add_rebind(bind, bind).collect_closure(rest, func_no_free_vars),
       )
     If(_cond, _then, _else) => If(_cond, rec(_then), rec(_else))
+    IfEq(lhs, rhs, _then, _else) => IfEq(lhs, rhs, rec(_then), rec(_else))
+    IfLe(lhs, rhs, _then, _else) => IfLe(lhs, rhs, rec(_then), rec(_else))
     Prim(op, args, bind, rest) =>
       Prim(
         op,
diff --git a/src/closureps_eval/interpreter.mbt b/src/closureps_eval/interpreter.mbt
index c0a5f61..4bb3101 100644
--- a/src/closureps_eval/interpreter.mbt
+++ b/src/closureps_eval/interpreter.mbt
@@ -172,6 +172,17 @@ pub fn CloPSInterpreter::eval(
         Bool(b) => continue if b { _then } else { _else }
         v => @util.die("unexpected condition \{v} for `if`")
       }
+    IfLe(lhs, rhs, _then, _else) =>
+      match (self.eval_v!(lhs), self.eval_v!(rhs)) {
+        (Double(a), Double(b)) => continue if a <= b { _then } else { _else }
+        (Int(a), Int(b)) => continue if a <= b { _then } else { _else }
+        (lhs, rhs) => @util.die("unexpected input \{lhs}, \{rhs} for `le`")
+      }
+    IfEq(lhs, rhs, _then, _else) => {
+      let lhs = self.eval_v!(lhs)
+      let rhs = self.eval_v!(rhs)
+      continue if lhs == rhs { _then } else { _else }
+    }
     Prim(Not, [v], bind, rest) => {
       match self.eval_v!(v) {
         Bool(b) => self.cur_env[bind] = Bool(not(b))
diff --git a/src/cps/cps_ir.mbt b/src/cps/cps_ir.mbt
index d2102d7..8c424be 100644
--- a/src/cps/cps_ir.mbt
+++ b/src/cps/cps_ir.mbt
@@ -62,6 +62,8 @@ pub enum Cps {
   KthTuple(Int, Value, Var, Cps)
   Fix(Var, Array[Var], Cps, Cps)
   If(Value, Cps, Cps)
+  IfLe(Value, Value, Cps, Cps)
+  IfEq(Value, Value, Cps, Cps)
   Prim(PrimOp, Array[Value], Var, Cps)
   // T marks the return type
   App(Value, Array[Value])
@@ -98,6 +100,10 @@ fn Cps::replace_var_bind(self : Cps, from : Var, to : Value) -> Cps {
       Fix(name, args, body_new, rest_new)
     }
     If(cond, _then, _else) => If(recv(cond), rec(_then), rec(_else))
+    IfEq(lhs, rhs, _then, _else) =>
+      IfEq(recv(lhs), recv(rhs), rec(_then), rec(_else))
+    IfLe(lhs, rhs, _then, _else) =>
+      IfLe(recv(lhs), recv(rhs), rec(_then), rec(_else))
     Prim(op, args, bind, rest) => {
       let rest_new = if from != bind { rec(rest) } else { rest }
       Prim(op, args.map(recv), bind, rest_new)
@@ -140,6 +146,12 @@ pub fn Cps::free_variables(self : Cps) -> @hashset.T[Var] {
       .free_variables()
       .union(_then.free_variables())
       .union(_else.free_variables())
+    IfEq(lhs, rhs, _then, _else) | IfLe(lhs, rhs, _then, _else) =>
+      lhs
+      .free_variables()
+      .union(rhs.free_variables())
+      .union(_then.free_variables())
+      .union(_else.free_variables())
     Prim(_, args, bind, rest) => {
       let fv_rest = rest.free_variables()
       fv_rest.remove(bind)
diff --git a/src/cps/cps_ir_string.mbt b/src/cps/cps_ir_string.mbt
index 6bd8073..a7486f1 100644
--- a/src/cps/cps_ir_string.mbt
+++ b/src/cps/cps_ir_string.mbt
@@ -49,6 +49,28 @@ fn to_str(cps : Cps, ~ident : String = "") -> String {
       ident +
       "}\n" +
       rec(rest)
+    IfEq(lhs, rhs, _then, _else) =>
+      ident +
+      "if(\{lhs} == \{rhs}){\n" +
+      to_str(_then, ident=ident + "  ") +
+      "\n" +
+      ident +
+      "} else {\n" +
+      to_str(_else, ident=ident + "  ") +
+      "\n" +
+      ident +
+      "}"
+    IfLe(lhs, rhs, _then, _else) =>
+      ident +
+      "if(\{lhs} <= \{rhs}){\n" +
+      to_str(_then, ident=ident + "  ") +
+      "\n" +
+      ident +
+      "} else {\n" +
+      to_str(_else, ident=ident + "  ") +
+      "\n" +
+      ident +
+      "}"
     If(cond, _then, _else) =>
       ident +
       "if(\{cond}){\n" +
diff --git a/src/cps/precps2cps.mbt b/src/cps/precps2cps.mbt
index b2687ba..35675e2 100644
--- a/src/cps/precps2cps.mbt
+++ b/src/cps/precps2cps.mbt
@@ -144,6 +144,62 @@ pub fn CpsEnv::precps2cps(self : CpsEnv, s : P, c : Cont) -> Cps {
 
       self.precps2cps(tup, c1)
     }
+    If(ret_ty, Prim(Bool, Eq, [lhs, rhs]), _then, _else) => {
+      fn c1(lhs : Value) -> Cps {
+        // To avoid exponential growth in CPS ir, we abstract the outer `c` out.
+        fn c2(rhs : Value) -> Cps {
+          let k_ref = self.new_tmp(Fun([ret_ty], Unit))
+          let x_ref = self.new_tmp(ret_ty)
+          fn c3(branch : Value) -> Cps {
+            App(Var(k_ref), [branch].map(fix_label_to_var))
+          }
+
+          Fix(
+            k_ref,
+            [x_ref],
+            c(Var(x_ref)),
+            IfEq(
+              lhs,
+              rhs,
+              self.precps2cps(_then, c3),
+              self.precps2cps(_else, c3),
+            ),
+          )
+        }
+
+        self.precps2cps(rhs, c2)
+      }
+
+      self.precps2cps(lhs, c1)
+    }
+    If(ret_ty, Prim(Bool, Le, [lhs, rhs]), _then, _else) => {
+      fn c1(lhs : Value) -> Cps {
+        // To avoid exponential growth in CPS ir, we abstract the outer `c` out.
+        fn c2(rhs : Value) -> Cps {
+          let k_ref = self.new_tmp(Fun([ret_ty], Unit))
+          let x_ref = self.new_tmp(ret_ty)
+          fn c3(branch : Value) -> Cps {
+            App(Var(k_ref), [branch].map(fix_label_to_var))
+          }
+
+          Fix(
+            k_ref,
+            [x_ref],
+            c(Var(x_ref)),
+            IfLe(
+              lhs,
+              rhs,
+              self.precps2cps(_then, c3),
+              self.precps2cps(_else, c3),
+            ),
+          )
+        }
+
+        self.precps2cps(rhs, c2)
+      }
+
+      self.precps2cps(lhs, c1)
+    }
     If(ret_ty, cond, _then, _else) => {
       fn c1(cond : Value) -> Cps {
         // To avoid exponential growth in CPS ir, we abstract the outer `c` out.
diff --git a/src/js/clops2js.mbt b/src/js/clops2js.mbt
index 8549c80..28e11d9 100644
--- a/src/js/clops2js.mbt
+++ b/src/js/clops2js.mbt
@@ -73,6 +73,24 @@ pub fn JsEmitter::emit_cps(self : JsEmitter, cps : @cps.Cps) -> String {
       output += self.indent().emit_cps(_else)
       output += line_start + "}"
     }
+    IfEq(lhs, rhs, _then, _else) => {
+      let lhs_emit = self.emit_val(lhs)
+      let rhs_emit = self.emit_val(rhs)
+      output += line_start + "if (\{lhs_emit} === \{rhs_emit}) {"
+      output += self.indent().emit_cps(_then)
+      output += line_start + "} else { "
+      output += self.indent().emit_cps(_else)
+      output += line_start + "}"
+    }
+    IfLe(lhs, rhs, _then, _else) => {
+      let lhs_emit = self.emit_val(lhs)
+      let rhs_emit = self.emit_val(rhs)
+      output += line_start + "if (\{lhs_emit} <= \{rhs_emit}) {"
+      output += self.indent().emit_cps(_then)
+      output += line_start + "} else { "
+      output += self.indent().emit_cps(_else)
+      output += line_start + "}"
+    }
     Prim(Not, [b], bind, rest) => {
       let bool_emit = self.emit_val(b)
       output += line_start + "const \{emit_var(bind)} = !\{bool_emit};"
diff --git a/src/riscv/before_alloc.mbt b/src/riscv/before_alloc.mbt
index b32f416..c796ab5 100644
--- a/src/riscv/before_alloc.mbt
+++ b/src/riscv/before_alloc.mbt
@@ -28,6 +28,39 @@ fn reserve_fregs(cfg : @ssacfg.SsaCfg, block : @ssacfg.Block) -> Unit {
       inst => insts.push(inst)
     }
   }
+  match block.last_inst.val {
+    BranchEq(lhs, rhs, _then, _else) => {
+      let lhs_is_imm = match lhs {
+        Var(_) => false
+        _ => true
+      }
+      let rhs_is_imm = match rhs {
+        Var(_) => false
+        _ => true
+      }
+      if lhs_is_imm && rhs_is_imm {
+        let tmp = cfg.new_named("tmp", ty=lhs.get_type())
+        insts.push(@ssacfg.Inst::Copy(tmp, lhs))
+        block.last_inst.val = BranchEq(Var(tmp), rhs, _then, _else)
+      }
+    }
+    BranchLe(lhs, rhs, _then, _else) => {
+      let lhs_is_imm = match lhs {
+        Var(_) => false
+        _ => true
+      }
+      let rhs_is_imm = match rhs {
+        Var(_) => false
+        _ => true
+      }
+      if lhs_is_imm && rhs_is_imm {
+        let tmp = cfg.new_named("tmp", ty=lhs.get_type())
+        insts.push(@ssacfg.Inst::Copy(tmp, lhs))
+        block.last_inst.val = BranchLe(Var(tmp), rhs, _then, _else)
+      }
+    }
+    _ => ()
+  }
   block.insts = insts
 }
 
@@ -63,10 +96,11 @@ fn freeze_closure(
   }
   block.insts = insts
   block.last_inst.val = match block.last_inst.val {
-    Branch(cond, _then, _else) => Branch(fix_val(cond), _then, _else)
+    Branch(cond, _then, _else) => Branch(cond, _then, _else)
+    BranchEq(lhs, rhs, _then, _else) => BranchEq(lhs, rhs, _then, _else)
+    BranchLe(lhs, rhs, _then, _else) => BranchLe(lhs, rhs, _then, _else)
     Call(f, args) => Call(fix_val(f), args.map(fix_val))
-    MakeArray(len, elem, kont) =>
-      MakeArray(fix_val(len), fix_val(elem), fix_val(kont))
+    MakeArray(len, elem, kont) => MakeArray(len, fix_val(elem), fix_val(kont))
     Exit => Exit
   }
 }
diff --git a/src/riscv/codegen.mbt b/src/riscv/codegen.mbt
index b6ef1f3..33c9d42 100644
--- a/src/riscv/codegen.mbt
+++ b/src/riscv/codegen.mbt
@@ -854,6 +854,88 @@ fn CodegenBlock::codegen(self : CodegenBlock) -> Unit {
       )
       self.branch_to(blk_else).codegen()
     }
+    BranchEq(lhs, rhs, blk_then, blk_else) =>
+      match get_reg_ty(lhs) {
+        // TODO: just like Eq & Le, we need to ensure the 2 regs doesn't crash
+        F64 => {
+          let reg_lhs = self.pull_val_f(lhs)
+          let reg_rhs = self.pull_val_f(rhs)
+          // NOTE: since we've reserve freg first, this won't happen
+          if reg_lhs == reg_rhs {
+            @util.die("pulling same reg for comparing floats")
+          }
+          self.insert_asms(
+            [
+              FeqD(reg_swap, reg_lhs, reg_rhs),
+              Beq(reg_swap, Zero, blk_else.to_string()),
+            ],
+          )
+          self.branch_to(blk_then).codegen()
+          self.insert_asm(
+            Comment(
+              "we have tail call so no point generating a jump to skip the else branch",
+            ),
+          )
+          self.branch_to(blk_else).codegen()
+        }
+        _ => {
+          let reg_lhs = self.pull_val_i(lhs)
+          let reg_rhs = self.pull_val_i(rhs)
+          // NOTE: since we've reserve freg first, this won't happen
+          if reg_lhs == reg_rhs {
+            @util.die("pulling same reg for comparing floats")
+          }
+          self.insert_asm(Bne(reg_lhs, reg_rhs, blk_else.to_string()))
+          self.branch_to(blk_then).codegen()
+          self.insert_asm(
+            Comment(
+              "we have tail call so no point generating a jump to skip the else branch",
+            ),
+          )
+          self.branch_to(blk_else).codegen()
+        }
+      }
+    BranchLe(lhs, rhs, blk_then, blk_else) =>
+      match get_reg_ty(lhs) {
+        // TODO: just like Eq & Le, we need to ensure the 2 regs doesn't crash
+        F64 => {
+          let reg_lhs = self.pull_val_f(lhs)
+          let reg_rhs = self.pull_val_f(rhs)
+          // NOTE: since we've reserve freg first, this won't happen
+          if reg_lhs == reg_rhs {
+            @util.die("pulling same reg for comparing floats")
+          }
+          self.insert_asms(
+            [
+              FleD(reg_swap, reg_lhs, reg_rhs),
+              Beq(reg_swap, Zero, blk_else.to_string()),
+            ],
+          )
+          self.branch_to(blk_then).codegen()
+          self.insert_asm(
+            Comment(
+              "we have tail call so no point generating a jump to skip the else branch",
+            ),
+          )
+          self.branch_to(blk_else).codegen()
+        }
+        _ => {
+          let reg_lhs = self.pull_val_i(lhs)
+          let reg_rhs = self.pull_val_i(rhs)
+          // NOTE: since we've reserve freg first, this won't happen
+          if reg_lhs == reg_rhs {
+            @util.die("pulling same reg for comparing floats")
+          }
+          self.insert_asm(Bgt(reg_lhs, reg_rhs, blk_else.to_string()))
+          self.branch_to(blk_then).codegen()
+          self.insert_asm(
+            Comment(
+              "we have tail call so no point generating a jump to skip the else branch",
+            ),
+          )
+          self.branch_to(blk_else).codegen()
+        }
+      }
     Exit => self.insert_asms([Li(A0, "0"), Li(A7, "93"), Ecall])
     MakeArray(len, elem, continuation) => {
       // 1. call to generate an array
diff --git a/src/riscv/collect_labels.mbt b/src/riscv/collect_labels.mbt
index 057b055..508f4f8 100644
--- a/src/riscv/collect_labels.mbt
+++ b/src/riscv/collect_labels.mbt
@@ -46,6 +46,12 @@ fn collect_externals(cfg : @ssacfg.SsaCfg) -> ExternalLabels {
         collect_label_var(_then)
         collect_label_var(_else)
       }
+      BranchEq(lhs, rhs, _then, _else) | BranchLe(lhs, rhs, _then, _else) => {
+        collect_label_val(lhs)
+        collect_label_val(rhs)
+        collect_label_var(_then)
+        collect_label_var(_else)
+      }
       Call(f, args) => {
         collect_label_val(f)
         args.each(collect_label_val)
diff --git a/src/riscv/interference_graph_build.mbt b/src/riscv/interference_graph_build.mbt
index 8138172..bfd45a4 100644
--- a/src/riscv/interference_graph_build.mbt
+++ b/src/riscv/interference_graph_build.mbt
@@ -79,6 +79,10 @@ fn LiveVarAnalysis::collect_pc_inst(
 ) -> Unit {
   match inst {
     Branch(cond, _then, _else) => self.collect_val(cond)
+    BranchEq(lhs, rhs, _then, _else) | BranchLe(lhs, rhs, _then, _else) => {
+      self.collect_val(lhs)
+      self.collect_val(rhs)
+    }
     Call(f, args) => {
       self.collect_val(f)
       args.each(fn(arg) { self.collect_val(arg) })
@@ -127,7 +131,9 @@ fn collect_blocks_of_fn(cfg : @ssacfg.SsaCfg, fn_name : Var) -> Array[Var] {
       let cur_blk = cfg.blocks[label].unwrap()
       stack_process.push(label)
       match cur_blk.last_inst.val {
-        Branch(_, blk_then, blk_else) => {
+        Branch(_, blk_then, blk_else)
+        | BranchEq(_, _, blk_then, blk_else)
+        | BranchLe(_, _, blk_then, blk_else) => {
           q_collect.push(blk_then)
           q_collect.push(blk_else)
         }
diff --git a/src/riscv/reg_spill.mbt b/src/riscv/reg_spill.mbt
index c59572e..3c477c9 100644
--- a/src/riscv/reg_spill.mbt
+++ b/src/riscv/reg_spill.mbt
@@ -77,6 +77,8 @@ fn reg_spill_block(blk : @ssacfg.Block, spilled_var : Var) -> @ssacfg.Block {
   }
   let load_before_exit = match blk.last_inst.val {
     Branch(cond, _, _) => val_spilled(cond)
+    BranchEq(lhs, rhs, _, _) | BranchLe(lhs, rhs, _, _) =>
+      val_spilled(lhs) || val_spilled(rhs)
     Call(f, args) => val_spilled(f) || vals_spilled(args)
     MakeArray(len, elem, kont) =>
       val_spilled(len) || val_spilled(elem) || val_spilled(kont)
diff --git a/src/ssacfg/clops2ssacfg.mbt b/src/ssacfg/clops2ssacfg.mbt
index b41ce7f..1bb0c79 100644
--- a/src/ssacfg/clops2ssacfg.mbt
+++ b/src/ssacfg/clops2ssacfg.mbt
@@ -52,6 +52,44 @@ fn SsaCfg::cps2block(
     }
     Prim(Put, args, _, _) => @util.die("unexpect args \{args} for put")
     Fix(_) => @util.die("unexpected nested function")
+    IfLe(lhs, rhs, _then, _else) => {
+      // NOTE: for control flow connection points there's no reason for us to 
+      // generate a type for it.
+      // NOTE: complete cur block; phis need to be fixed, but we'll deal with it in a later pass 
+      let label_then = self.new_named("then")
+      let label_else = self.new_named("else")
+      cur_block.last_inst.val = BranchLe(lhs, rhs, label_then, label_else)
+      // NOTE: convert then block to ssa block 
+      let block_then = Block::new_from(cur_block.fn_name, cur_label)
+      self.blocks[label_then] = block_then
+      self.cps2block(_then, block_then, label_then)
+      // NOTE: convert else block to ssa block 
+      let block_else = Block::new_from(cur_block.fn_name, cur_label)
+      self.blocks[label_else] = block_else
+      cur_block = block_else
+      cur_label = label_else
+      continue _else
+      // no need to add merge point after if statements as we always have a tail call
+    }
+    IfEq(lhs, rhs, _then, _else) => {
+      // NOTE: for control flow connection points there's no reason for us to 
+      // generate a type for it.
+      // NOTE: complete cur block; phis need to be fixed, but we'll deal with it in a later pass 
+      let label_then = self.new_named("then")
+      let label_else = self.new_named("else")
+      cur_block.last_inst.val = BranchEq(lhs, rhs, label_then, label_else)
+      // NOTE: convert then block to ssa block 
+      let block_then = Block::new_from(cur_block.fn_name, cur_label)
+      self.blocks[label_then] = block_then
+      self.cps2block(_then, block_then, label_then)
+      // NOTE: convert else block to ssa block 
+      let block_else = Block::new_from(cur_block.fn_name, cur_label)
+      self.blocks[label_else] = block_else
+      cur_block = block_else
+      cur_label = label_else
+      continue _else
+      // no need to add merge point after if statements as we always have a tail call
+    }
     If(cond, _then, _else) => {
       // NOTE: for control flow connection points there's no reason for us to 
       // generate a type for it.
diff --git a/src/ssacfg/ssa_ir.mbt b/src/ssacfg/ssa_ir.mbt
index 862c8c2..e3fab27 100644
--- a/src/ssacfg/ssa_ir.mbt
+++ b/src/ssacfg/ssa_ir.mbt
@@ -25,6 +25,8 @@ pub enum Inst {
 pub enum PCInst {
   // join points (val, block ref)
   Branch(Value, Var, Var)
+  BranchEq(Value, Value, Var, Var)
+  BranchLe(Value, Value, Var, Var)
   Call(Value, Array[Value])
   // len, elem, continuation
   MakeArray(Value, Value, Value)
diff --git a/test/build_all b/test/build_all
index c6f4c24..ff74a4b 100755
--- a/test/build_all
+++ b/test/build_all
@@ -1,11 +1,16 @@
 #!/usr/bin/env bash
 
+echo "building CPS IR"
 moon run ../src/bin/main.mbt -- --end-stage cps ./test_src/$1.mbt -o $1.cps
+echo "building CLOPS IR"
 moon run ../src/bin/main.mbt -- --end-stage clops ./test_src/$1.mbt -o $1.clops
+echo "building ASM"
 moon run ../src/bin/main.mbt -- ./test_src/$1.mbt -o $1.s
+echo "building JS"
 moon run ../src/bin/main.mbt -- ./test_src/$1.mbt -o $1.js --js
 
 
+echo "building Binary"
 zig build-exe -target riscv64-linux -femit-bin=$1 \
   $1.s ../riscv_rt/zig-out/lib/libmincaml.a \
   -O Debug -fno-strip -mcpu=baseline_rv64