diff --git a/src/compiler/nir/nir_opt_algebraic.py b/src/compiler/nir/nir_opt_algebraic.py
index cf7f85e8dc6..8c238c208da 100644
--- a/src/compiler/nir/nir_opt_algebraic.py
+++ b/src/compiler/nir/nir_opt_algebraic.py
@@ -804,6 +804,10 @@ optimizations.extend([
    (('ior', ('ior(is_used_once)', ('flt', a, c), d), ('flt(is_used_once)', b, c)), ('ior', ('flt', ('!fmin', a, b), c), d)),
    (('ior', ('ior(is_used_once)', ('flt(is_used_once)', a, b), d), ('flt', a, c)), ('ior', ('flt', a, ('!fmax', b, c)), d)),
    (('ior', ('ior(is_used_once)', ('flt', a, b), d), ('flt(is_used_once)', a, c)), ('ior', ('flt', a, ('!fmax', b, c)), d)),
+
+   # This is how SpvOpFOrdNotEqual might be implemented.  If both values are
+   # numbers, then it can be replaced with fneu.
+   (('ior', ('flt', 'a(is_a_number)', 'b(is_a_number)'), ('flt', b, a)), ('fneu', a, b)),
 ])
 
 # Float sizes
@@ -2414,6 +2418,16 @@ late_optimizations = [
    (('feq',  ('fadd(is_used_once)', 'a(is_finite)', b), 0.0), ('feq',  a, ('fneg', b))),
    (('fneu', ('fadd(is_used_once)', 'a(is_finite)', b), 0.0), ('fneu', a, ('fneg', b))),
 
+   # This is how SpvOpFOrdNotEqual might be implemented.  Replace it with
+   # SpvOpLessOrGreater.
+   (('iand', ('fneu', a, b),   ('iand', ('feq', a, a), ('feq', b, b))), ('ior', ('!flt', a, b), ('!flt', b, a))),
+   (('iand', ('fneu', a, 0.0),          ('feq', a, a)                ), ('!flt', 0.0, ('fabs', a))),
+
+   # This is how SpvOpFUnordEqual might be implemented.  Replace it with
+   # !SpvOpLessOrGreater.
+   (('ior', ('feq', a, b),   ('ior', ('fneu', a, a), ('fneu', b, b))), ('inot', ('ior', ('!flt', a, b), ('!flt', b, a)))),
+   (('ior', ('feq', a, 0.0),         ('fneu', a, a),                ), ('inot', ('!flt', 0.0, ('fabs', a)))),
+
    # nir_lower_to_source_mods will collapse this, but its existence during the
    # optimization loop can prevent other optimizations.
    (('fneg', ('fneg', a)), a),