diff --git a/cranelift/codegen/src/opts/arithmetic.isle b/cranelift/codegen/src/opts/arithmetic.isle
index 2e0703ef6c53..a8aa42fdeeec 100644
--- a/cranelift/codegen/src/opts/arithmetic.isle
+++ b/cranelift/codegen/src/opts/arithmetic.isle
@@ -436,4 +436,140 @@
 (rule (simplify (uge ty x (umin ty x y))) (iconst_u ty 1))
 (rule (simplify (uge ty x (umin ty y x))) (iconst_u ty 1))
 (rule (simplify (ule ty (umin ty x y) x)) (iconst_u ty 1))
-(rule (simplify (ule ty (umin ty y x) x)) (iconst_u ty 1))
\ No newline at end of file
+(rule (simplify (ule ty (umin ty y x) x)) (iconst_u ty 1))
+
+;; min/max(x,x) --> x
+(rule (simplify (umin ty x x)) x)
+(rule (simplify (smin ty x x)) x)
+(rule (simplify (umax ty x x)) x)
+(rule (simplify (smax ty x x)) x)
+
+;; max(max(x, y), x) --> max(x, y)
+(rule (simplify (smax ty (smax ty x y) x)) (smax ty x y))
+(rule (simplify (smax ty (smax ty y x) x)) (smax ty x y))
+(rule (simplify (smax ty x (smax ty x y))) (smax ty x y))
+(rule (simplify (smax ty x (smax ty y x))) (smax ty x y))
+(rule (simplify (umax ty (umax ty x y) x)) (umax ty x y))
+(rule (simplify (umax ty (umax ty y x) x)) (umax ty x y))
+(rule (simplify (umax ty x (umax ty x y))) (umax ty x y))
+(rule (simplify (umax ty x (umax ty y x))) (umax ty x y))
+
+;; min(min(x, y), x) --> min(x, y)
+(rule (simplify (smin ty (smin ty x y) x)) (smin ty x y))
+(rule (simplify (smin ty (smin ty y x) x)) (smin ty x y))
+(rule (simplify (smin ty x (smin ty x y))) (smin ty x y))
+(rule (simplify (smin ty x (smin ty y x))) (smin ty x y))
+(rule (simplify (umin ty (umin ty x y) x)) (umin ty x y))
+(rule (simplify (umin ty (umin ty y x) x)) (umin ty x y))
+(rule (simplify (umin ty x (umin ty x y))) (umin ty x y))
+(rule (simplify (umin ty x (umin ty y x))) (umin ty x y))
+
+;; min(max(x, y), y) --> y ; max(min(x, y), y) --> y
+(rule (simplify (smin ty (smax ty x y) y)) y)
+(rule (simplify (smin ty (smax ty y x) y)) y)
+(rule (simplify (smin ty y (smax ty x y))) y)
+(rule (simplify (smin ty y (smax ty y x))) y)
+(rule (simplify (umin ty (umax ty x y) y)) y)
+(rule (simplify (umin ty (umax ty y x) y)) y)
+(rule (simplify (umin ty y (umax ty x y))) y)
+(rule (simplify (umin ty y (umax ty y x))) y)
+(rule (simplify (smax ty (smin ty x y) y)) y)
+(rule (simplify (smax ty (smin ty y x) y)) y)
+(rule (simplify (smax ty y (smin ty x y))) y)
+(rule (simplify (smax ty y (smin ty y x))) y)
+(rule (simplify (umax ty (umin ty x y) y)) y)
+(rule (simplify (umax ty (umin ty y x) y)) y)
+(rule (simplify (umax ty y (umin ty x y))) y)
+(rule (simplify (umax ty y (umin ty y x))) y)
+
+;; min(min(x, y), max(x, y)) --> min(x,y)
+(rule (simplify (smin ty (smax ty x y) (smin ty x y))) (smin ty x y))
+(rule (simplify (smin ty (smax ty x y) (smin ty y x))) (smin ty x y))
+(rule (simplify (smin ty (smax ty x y) (umin ty x y))) (umin ty x y))
+(rule (simplify (smin ty (smax ty x y) (umin ty y x))) (umin ty x y))
+
+(rule (simplify (smin ty (smin ty x y) (smax ty x y))) (smin ty x y))
+(rule (simplify (smin ty (smin ty x y) (smax ty y x))) (smin ty x y))
+(rule (simplify (smin ty (smin ty x y) (umax ty x y))) (smin ty x y))
+(rule (simplify (smin ty (smin ty x y) (umax ty y x))) (smin ty x y))
+
+(rule (simplify (smin ty (umax ty x y) (smin ty x y))) (smin ty x y))
+(rule (simplify (smin ty (umax ty x y) (smin ty y x))) (smin ty x y))
+(rule (simplify (smin ty (umax ty x y) (umin ty x y))) (smin ty x y))
+(rule (simplify (smin ty (umax ty x y) (umin ty y x))) (smin ty x y))
+
+(rule (simplify (smin ty (umin ty x y) (smax ty x y))) (umin ty x y))
+(rule (simplify (smin ty (umin ty x y) (smax ty y x))) (umin ty x y))
+(rule (simplify (smin ty (umin ty x y) (umax ty x y))) (smin ty x y))
+(rule (simplify (smin ty (umin ty x y) (umax ty y x))) (smin ty x y))
+
+(rule (simplify (umin ty (smax ty x y) (smin ty x y))) (umin ty x y))
+(rule (simplify (umin ty (smax ty x y) (smin ty y x))) (umin ty x y))
+(rule (simplify (umin ty (smax ty x y) (umin ty x y))) (umin ty x y))
+(rule (simplify (umin ty (smax ty x y) (umin ty y x))) (umin ty x y))
+
+(rule (simplify (umin ty (smin ty x y) (smax ty x y))) (umin ty x y))
+(rule (simplify (umin ty (smin ty x y) (smax ty y x))) (umin ty x y))
+(rule (simplify (umin ty (smin ty x y) (umax ty x y))) (smin ty x y))
+(rule (simplify (umin ty (smin ty x y) (umax ty y x))) (smin ty x y))
+
+(rule (simplify (umin ty (umax ty x y) (smin ty x y))) (smin ty x y))
+(rule (simplify (umin ty (umax ty x y) (smin ty y x))) (smin ty x y))
+(rule (simplify (umin ty (umax ty x y) (umin ty x y))) (umin ty x y))
+(rule (simplify (umin ty (umax ty x y) (umin ty y x))) (umin ty x y))
+
+(rule (simplify (umin ty (umin ty x y) (smax ty x y))) (umin ty x y))
+(rule (simplify (umin ty (umin ty x y) (smax ty y x))) (umin ty x y))
+(rule (simplify (umin ty (umin ty x y) (umax ty x y))) (umin ty x y))
+(rule (simplify (umin ty (umin ty x y) (umax ty y x))) (umin ty x y))
+
+;; max(min(x, y), max(x, y)) --> max(x, y)
+(rule (simplify (smax ty (smax ty x y) (smin ty x y))) (smax ty x y))
+(rule (simplify (smax ty (smax ty x y) (smin ty y x))) (smax ty x y))
+(rule (simplify (smax ty (smax ty x y) (umin ty x y))) (smax ty x y))
+(rule (simplify (smax ty (smax ty x y) (umin ty y x))) (smax ty x y))
+
+(rule (simplify (smax ty (smin ty x y) (smax ty x y))) (smax ty x y))
+(rule (simplify (smax ty (smin ty x y) (smax ty y x))) (smax ty x y))
+(rule (simplify (smax ty (smin ty x y) (umax ty x y))) (umax ty x y))
+(rule (simplify (smax ty (smin ty x y) (umax ty y x))) (umax ty x y))
+
+(rule (simplify (smax ty (umax ty x y) (smin ty x y))) (umax ty x y))
+(rule (simplify (smax ty (umax ty x y) (smin ty y x))) (umax ty x y))
+(rule (simplify (smax ty (umax ty x y) (umin ty x y))) (smax ty x y))
+(rule (simplify (smax ty (umax ty x y) (umin ty y x))) (smax ty x y))
+
+(rule (simplify (smax ty (umin ty x y) (smax ty x y))) (smax ty x y))
+(rule (simplify (smax ty (umin ty x y) (smax ty y x))) (smax ty x y))
+(rule (simplify (smax ty (umin ty x y) (umax ty x y))) (smax ty x y))
+(rule (simplify (smax ty (umin ty x y) (umax ty y x))) (smax ty x y))
+
+(rule (simplify (umax ty (smax ty x y) (smin ty x y))) (umax ty x y))
+(rule (simplify (umax ty (smax ty x y) (smin ty y x))) (umax ty x y))
+(rule (simplify (umax ty (smax ty x y) (umin ty x y))) (smax ty x y))
+(rule (simplify (umax ty (smax ty x y) (umin ty y x))) (smax ty x y))
+
+(rule (simplify (umax ty (smin ty x y) (smax ty x y))) (umax ty x y))
+(rule (simplify (umax ty (smin ty x y) (smax ty y x))) (umax ty x y))
+(rule (simplify (umax ty (smin ty x y) (umax ty x y))) (umax ty x y))
+(rule (simplify (umax ty (smin ty x y) (umax ty y x))) (umax ty x y))
+
+(rule (simplify (umax ty (umax ty x y) (smin ty x y))) (umax ty x y))
+(rule (simplify (umax ty (umax ty x y) (smin ty y x))) (umax ty x y))
+(rule (simplify (umax ty (umax ty x y) (umin ty x y))) (umax ty x y))
+(rule (simplify (umax ty (umax ty x y) (umin ty y x))) (umax ty x y))
+
+(rule (simplify (umax ty (umin ty x y) (smax ty x y))) (smax ty x y))
+(rule (simplify (umax ty (umin ty x y) (smax ty y x))) (smax ty x y))
+(rule (simplify (umax ty (umin ty x y) (umax ty x y))) (umax ty x y))
+(rule (simplify (umax ty (umin ty x y) (umax ty y x))) (umax ty x y))
+
+;; x > max(x, y) --> 0
+(rule (simplify (sgt ty x (smax ty x y))) (iconst_u ty 0))
+(rule (simplify (sgt ty x (smax ty y x))) (iconst_u ty 0))
+(rule (simplify (slt ty (smax ty x y) x)) (iconst_u ty 0))
+(rule (simplify (slt ty (smax ty y x) x)) (iconst_u ty 0))
+(rule (simplify (ugt ty x (umax ty x y))) (iconst_u ty 0))
+(rule (simplify (ugt ty x (umax ty y x))) (iconst_u ty 0))
+(rule (simplify (ult ty (umax ty x y) x)) (iconst_u ty 0))
+(rule (simplify (ult ty (umax ty y x) x)) (iconst_u ty 0))
\ No newline at end of file
diff --git a/cranelift/filetests/filetests/egraph/arithmetic-precise.clif b/cranelift/filetests/filetests/egraph/arithmetic-precise.clif
index 7249b7df8d2a..8ea8ec3c9cca 100644
--- a/cranelift/filetests/filetests/egraph/arithmetic-precise.clif
+++ b/cranelift/filetests/filetests/egraph/arithmetic-precise.clif
@@ -432,3 +432,163 @@ block0(v0: i32, v1: i32):
 ;     return v3
 ; }
 
+;; umin(x, x) --> x
+function %test_umin_same(i32) -> i32 fast {
+block0(v0: i32):
+    v1 = umin v0, v0
+    return v1
+}
+
+; function %test_umin_same(i32) -> i32 fast {
+; block0(v0: i32):
+;     return v0
+; }
+
+;; smin(x, x) --> x
+function %test_smin_same(i32) -> i32 fast {
+block0(v0: i32):
+    v1 = smin v0, v0
+    return v1
+}
+
+; function %test_smin_same(i32) -> i32 fast {
+; block0(v0: i32):
+;     return v0
+; }
+
+;; umax(x, x) --> x
+function %test_umax_same(i32) -> i32 fast {
+block0(v0: i32):
+    v1 = umax v0, v0
+    return v1
+}
+
+; function %test_umax_same(i32) -> i32 fast {
+; block0(v0: i32):
+;     return v0
+; }
+
+;; smax(x, x) --> x
+function %test_smax_same(i32) -> i32 fast {
+block0(v0: i32):
+    v1 = smax v0, v0
+    return v1
+}
+
+; function %test_smax_same(i32) -> i32 fast {
+; block0(v0: i32):
+;     return v0
+; }
+
+;; smax(smax(x, y), x) --> smax(x, y)
+function %test_smax_nested_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = smax v0, v1
+    v3 = smax v2, v0
+    return v3
+}
+
+; function %test_smax_nested_absorb(i32, i32) -> i32 fast {
+; block0(v0: i32, v1: i32):
+;     v2 = smax v0, v1
+;     return v2
+; }
+
+;; umax(umax(x, y), x) --> umax(x, y)
+function %test_umax_nested_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = umax v0, v1
+    v3 = umax v2, v0
+    return v3
+}
+
+; function %test_umax_nested_absorb(i32, i32) -> i32 fast {
+; block0(v0: i32, v1: i32):
+;     v2 = umax v0, v1
+;     return v2
+; }
+
+;; smin(smin(x, y), x) --> smin(x, y)
+function %test_smin_nested_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = smin v0, v1
+    v3 = smin v2, v0
+    return v3
+}
+
+; function %test_smin_nested_absorb(i32, i32) -> i32 fast {
+; block0(v0: i32, v1: i32):
+;     v2 = smin v0, v1
+;     return v2
+; }
+
+;; umin(umin(x, y), x) --> umin(x, y)
+function %test_umin_nested_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = umin v0, v1
+    v3 = umin v2, v0
+    return v3
+}
+
+; function %test_umin_nested_absorb(i32, i32) -> i32 fast {
+; block0(v0: i32, v1: i32):
+;     v2 = umin v0, v1
+;     return v2
+; }
+
+;; smin(smax(x, y), y) --> y
+function %test_smin_smax_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = smax v0, v1
+    v3 = smin v2, v1
+    return v3
+}
+
+; function %test_smin_smax_absorb(i32, i32) -> i32 fast {
+; block0(v0: i32, v1: i32):
+;     return v1
+; }
+
+;; umax(umin(x, y), y) --> y
+function %test_umax_umin_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = umin v0, v1
+    v3 = umax v2, v1
+    return v3
+}
+
+; function %test_umax_umin_absorb(i32, i32) -> i32 fast {
+; block0(v0: i32, v1: i32):
+;     return v1
+; }
+
+;; x > smax(x, y) --> false
+function %test_sgt_x_smax(i32, i32) -> i8 fast {
+block0(v0: i32, v1: i32):
+    v2 = smax v0, v1
+    v3 = icmp sgt v0, v2
+    return v3
+}
+
+; function %test_sgt_x_smax(i32, i32) -> i8 fast {
+; block0(v0: i32, v1: i32):
+;     v2 = smax v0, v1
+;     v3 = icmp sgt v0, v2
+;     return v3
+; }
+
+;; x >_u umax(x, y) --> false
+function %test_ugt_x_umax(i32, i32) -> i8 fast {
+block0(v0: i32, v1: i32):
+    v2 = umax v0, v1
+    v3 = icmp ugt v0, v2
+    return v3
+}
+
+; function %test_ugt_x_umax(i32, i32) -> i8 fast {
+; block0(v0: i32, v1: i32):
+;     v2 = umax v0, v1
+;     v3 = icmp ugt v0, v2
+;     return v3
+; }
+
diff --git a/cranelift/filetests/filetests/runtests/arithmetic.clif b/cranelift/filetests/filetests/runtests/arithmetic.clif
index ac85426c0480..037d8bd4f0f5 100644
--- a/cranelift/filetests/filetests/runtests/arithmetic.clif
+++ b/cranelift/filetests/filetests/runtests/arithmetic.clif
@@ -947,4 +947,122 @@ block0(v0: i32, v1: i32):
 
 ; run: %test_ule_umin_x(0, 0) == 1
 ; run: %test_ule_umin_x(1, 2) == 1
-; run: %test_ule_umin_x(2, 1) == 1
\ No newline at end of file
+; run: %test_ule_umin_x(2, 1) == 1
+
+function %test_umin_same(i32) -> i32 fast {
+block0(v0: i32):
+    v1 = umin v0, v0
+    return v1
+}
+
+; run: %test_umin_same(0) == 0
+; run: %test_umin_same(1) == 1
+
+function %test_smin_same(i32) -> i32 fast {
+block0(v0: i32):
+    v1 = smin v0, v0
+    return v1
+}
+
+; run: %test_smin_same(0) == 0
+; run: %test_smin_same(1) == 1
+
+function %test_umax_same(i32) -> i32 fast {
+block0(v0: i32):
+    v1 = umax v0, v0
+    return v1
+}
+
+; run: %test_umax_same(0) == 0
+; run: %test_umax_same(1) == 1
+
+function %test_smax_same(i32) -> i32 fast {
+block0(v0: i32):
+    v1 = smax v0, v0
+    return v1
+}
+
+; run: %test_smax_same(0) == 0
+; run: %test_smax_same(1) == 1
+
+function %test_smax_nested_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = smax v0, v1
+    v3 = smax v2, v0
+    return v3
+}
+
+; run: %test_smax_nested_absorb(0, 0) == 0
+; run: %test_smax_nested_absorb(1, 2) == 2
+; run: %test_smax_nested_absorb(2, 1) == 2
+
+function %test_umax_nested_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = umax v0, v1
+    v3 = umax v2, v0
+    return v3
+}
+
+; run: %test_umax_nested_absorb(0, 0) == 0
+; run: %test_umax_nested_absorb(1, 2) == 2
+
+function %test_smin_nested_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = smin v0, v1
+    v3 = smin v2, v0
+    return v3
+}
+
+; run: %test_smin_nested_absorb(0, 0) == 0
+; run: %test_smin_nested_absorb(1, 2) == 1
+; run: %test_smin_nested_absorb(2, 1) == 1
+
+function %test_umin_nested_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = umin v0, v1
+    v3 = umin v2, v0
+    return v3
+}
+
+; run: %test_umin_nested_absorb(0, 0) == 0
+; run: %test_umin_nested_absorb(1, 2) == 1
+; run: %test_umin_nested_absorb(2, 1) == 1
+
+function %test_smin_smax_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = smax v0, v1
+    v3 = smin v2, v1
+    return v3
+}
+
+; run: %test_smin_smax_absorb(0, 0) == 0
+; run: %test_smin_smax_absorb(1, 2) == 2
+
+function %test_umax_umin_absorb(i32, i32) -> i32 fast {
+block0(v0: i32, v1: i32):
+    v2 = umin v0, v1
+    v3 = umax v2, v1
+    return v3
+}
+
+; run: %test_umax_umin_absorb(0, 0) == 0
+; run: %test_umax_umin_absorb(1, 2) == 2
+
+function %test_sgt_x_smax(i32, i32) -> i8 fast {
+block0(v0: i32, v1: i32):
+    v2 = smax v0, v1
+    v3 = icmp sgt v0, v2
+    return v3
+}
+
+; run: %test_sgt_x_smax(0, 0) == 0
+; run: %test_sgt_x_smax(1, 2) == 0
+function %test_ugt_x_umax(i32, i32) -> i8 fast {
+block0(v0: i32, v1: i32):
+    v2 = umax v0, v1
+    v3 = icmp ugt v0, v2
+    return v3
+}
+
+; run: %test_ugt_x_umax(0, 0) == 0
+; run: %test_ugt_x_umax(1, 2) == 0
\ No newline at end of file