diff --git a/src/cmd/go/internal/work/exec.go b/src/cmd/go/internal/work/exec.go
index 4564e32e65e18..626cacfe992d4 100644
--- a/src/cmd/go/internal/work/exec.go
+++ b/src/cmd/go/internal/work/exec.go
@@ -201,12 +201,12 @@ func (b *Builder) buildActionID(a *Action) cache.ActionID {
 	// same compiler settings and can reuse each other's results.
 	// If not, the reason is already recorded in buildGcflags.
 	fmt.Fprintf(h, "compile\n")
+	// Only include the package directory if it may affect the output.
+	// We trim workspace paths for all packages when -trimpath is set.
 	// The compiler hides the exact value of $GOROOT
-	// when building things in GOROOT,
-	// but it does not hide the exact value of $GOPATH.
-	// Include the full dir in that case.
+	// when building things in GOROOT.
 	// Assume b.WorkDir is being trimmed properly.
-	if !p.Goroot && !strings.HasPrefix(p.Dir, b.WorkDir) {
+	if !p.Goroot && !cfg.BuildTrimpath && !strings.HasPrefix(p.Dir, b.WorkDir) {
 		fmt.Fprintf(h, "dir %s\n", p.Dir)
 	}
 	fmt.Fprintf(h, "goos %s goarch %s\n", cfg.Goos, cfg.Goarch)
diff --git a/src/cmd/go/script_test.go b/src/cmd/go/script_test.go
index 4dcb4b4e0d5dc..5e50dd14c78be 100644
--- a/src/cmd/go/script_test.go
+++ b/src/cmd/go/script_test.go
@@ -441,10 +441,15 @@ func (ts *testScript) cmdCmp(neg bool, args []string) {
 		// It would be strange to say "this file can have any content except this precise byte sequence".
 		ts.fatalf("unsupported: ! cmp")
 	}
+	quiet := false
+	if len(args) > 0 && args[0] == "-q" {
+		quiet = true
+		args = args[1:]
+	}
 	if len(args) != 2 {
 		ts.fatalf("usage: cmp file1 file2")
 	}
-	ts.doCmdCmp(args, false)
+	ts.doCmdCmp(args, false, quiet)
 }
 
 // cmpenv compares two files with environment variable substitution.
@@ -452,13 +457,18 @@ func (ts *testScript) cmdCmpenv(neg bool, args []string) {
 	if neg {
 		ts.fatalf("unsupported: ! cmpenv")
 	}
+	quiet := false
+	if len(args) > 0 && args[0] == "-q" {
+		quiet = true
+		args = args[1:]
+	}
 	if len(args) != 2 {
 		ts.fatalf("usage: cmpenv file1 file2")
 	}
-	ts.doCmdCmp(args, true)
+	ts.doCmdCmp(args, true, quiet)
 }
 
-func (ts *testScript) doCmdCmp(args []string, env bool) {
+func (ts *testScript) doCmdCmp(args []string, env, quiet bool) {
 	name1, name2 := args[0], args[1]
 	var text1, text2 string
 	if name1 == "stdout" {
@@ -484,7 +494,9 @@ func (ts *testScript) doCmdCmp(args []string, env bool) {
 		return
 	}
 
-	fmt.Fprintf(&ts.log, "[diff -%s +%s]\n%s\n", name1, name2, diff(text1, text2))
+	if !quiet {
+		fmt.Fprintf(&ts.log, "[diff -%s +%s]\n%s\n", name1, name2, diff(text1, text2))
+	}
 	ts.fatalf("%s and %s differ", name1, name2)
 }
 
diff --git a/src/cmd/go/testdata/script/build_trimpath.txt b/src/cmd/go/testdata/script/build_trimpath.txt
index f785b0cb9ec9d..668f75599e77b 100644
--- a/src/cmd/go/testdata/script/build_trimpath.txt
+++ b/src/cmd/go/testdata/script/build_trimpath.txt
@@ -1,21 +1,44 @@
 [short] skip
 
 env -r GOROOT_REGEXP=$GOROOT
-env -r WORK_REGEXP=$WORK
+env -r WORK_REGEXP='$WORK'  # don't expand $WORK; grep replaces $WORK in text before matching.
 env GOROOT GOROOT_REGEXP WORK WORK_REGEXP
 
+# A binary built without -trimpath should contain the current workspace
+# and GOROOT for debugging and stack traces.
+cd a
+go build -o hello.exe hello.go
+grep -q $WORK_REGEXP hello.exe
+grep -q $GOROOT_REGEXP hello.exe
+
+# A binary built with -trimpath should not contain the current workspace
+# or GOROOT.
 go build -trimpath -o hello.exe hello.go
 ! grep -q $GOROOT_REGEXP hello.exe
 ! grep -q $WORK_REGEXP hello.exe
+cd ..
 
+# A binary from an external module built with -trimpath should not contain
+# the current workspace or GOROOT.
 env GO111MODULE=on
 go build -trimpath -o fortune.exe rsc.io/fortune
 ! grep -q $GOROOT_REGEXP fortune.exe
 ! grep -q $WORK_REGEXP fortune.exe
 
--- hello.go --
+# Two binaries built from identical packages in different directories
+# should be identical.
+mkdir b
+cp a/go.mod a/hello.go b
+cd a
+go build -trimpath -o ../a.exe .
+cd ../b
+go build -trimpath -o ../b.exe .
+cd ..
+cmp -q a.exe b.exe
+
+-- a/hello.go --
 package main
 func main() { println("hello") }
 
--- go.mod --
+-- a/go.mod --
 module m