diff --git a/src/compiler/spirv/vtn_alu.c b/src/compiler/spirv/vtn_alu.c
index 54019c37396..a9bdb4c3cf1 100644
--- a/src/compiler/spirv/vtn_alu.c
+++ b/src/compiler/spirv/vtn_alu.c
@@ -600,7 +600,29 @@ vtn_handle_alu(struct vtn_builder *b, SpvOp opcode,
       break;
    }
 
-   case SpvOpFUnordEqual:
+   case SpvOpFUnordEqual: {
+      const bool save_exact = b->nb.exact;
+
+      b->nb.exact = true;
+
+      /* This could also be implemented as !(a < b || b < a).  If one or both
+       * of the source are numbers, later optimization passes can easily
+       * eliminate the isnan() checks.  This may trim the sequence down to a
+       * single (a == b) operation.  Otherwise, the optimizer can transform
+       * whatever is left to !(a < b || b < a).  Since some applications will
+       * open-code this sequence, these optimizations are needed anyway.
+       */
+      dest->def =
+         nir_ior(&b->nb,
+                 nir_feq(&b->nb, src[0], src[1]),
+                 nir_ior(&b->nb,
+                         nir_fneu(&b->nb, src[0], src[0]),
+                         nir_fneu(&b->nb, src[1], src[1])));
+
+      b->nb.exact = save_exact;
+      break;
+   }
+
    case SpvOpFUnordLessThan:
    case SpvOpFUnordGreaterThan:
    case SpvOpFUnordLessThanEqual:
@@ -623,12 +645,16 @@ vtn_handle_alu(struct vtn_builder *b, SpvOp opcode,
 
       b->nb.exact = true;
 
+      /* Use the property FUnordLessThan(a, b) ≡ !FOrdGreaterThanEqual(a, b). */
+      switch (op) {
+      case nir_op_fge: op = nir_op_flt; break;
+      case nir_op_flt: op = nir_op_fge; break;
+      default: unreachable("Impossible opcode.");
+      }
+
       dest->def =
-         nir_ior(&b->nb,
-                 nir_build_alu(&b->nb, op, src[0], src[1], NULL, NULL),
-                 nir_ior(&b->nb,
-                         nir_fneu(&b->nb, src[0], src[0]),
-                         nir_fneu(&b->nb, src[1], src[1])));
+         nir_inot(&b->nb,
+                  nir_build_alu(&b->nb, op, src[0], src[1], NULL, NULL));
 
       b->nb.exact = save_exact;
       break;