diff --git a/nvm.sh b/nvm.sh
index 6ddac0a..d624be0 100644
--- a/nvm.sh
+++ b/nvm.sh
@@ -358,13 +358,13 @@ nvm_normalize_semver() {
         s/ ?- ?/ - /g;
 
         # ' 1 ' => ' 1.x.x '
-        # ' x ' => ' x.x.x '
-        s/ ([0-9]+|x) / \1.x.x /g;
+        # ' ~x ' => ' ~x.x.x '
+        s/ (~|\^)?([0-9]+|x) / \1\2.x.x /g;
 
         # ' 1.2 ' => ' 1.2.x '
-        # ' 1.x ' => ' 1.x.x '
-        # ' x.x ' => ' x.x.x '
-        s/ (([0-9]+|x)\.([0-9]+|x)) / \1.x /g;
+        # ' ~1.x ' => ' ~1.x.x '
+        # ' ^x.x ' => ' ^x.x.x '
+        s/ (~|\^)?(([0-9]+|x)\.([0-9]+|x)) / \1\2.x /g;
 
         # ' 1.2.3 - 1.2.4 ' => ' >=1.2.3 <=1.2.4 '
         s/ (([0-9]+|x)\.([0-9]+|x)\.([0-9]+|x)) ?\- ?(([0-9]+|x)\.([0-9]+|x)\.([0-9]+|x)) / >=\1 <=\5 /g;
@@ -387,9 +387,11 @@ nvm_normalize_semver() {
         # ` ^0.0.1 ` => ` >=0.0.1 <0.0.2 `
         # ` ^0.1.2 ` => ` >=0.1.2 <0.2.0 `
         # ` ^1.2.3 ` => ` >=1.2.3 <2.0.0 `
+        # ` ^1.0.0 ` => ` >=1.0.0 <2.0.0 `
         # ` ~0.0.1 ` => ` >=0.0.1 <0.1.0 `
         # ` ~0.1.2 ` => ` >=0.1.2 <0.2.0 `
         # ` ~1.2.3 ` => ` >=1.2.3 <1.3.0 `
+        # ` ~1.0.0 ` => ` >=1.0.0 <2.0.0 `
         # ` x.x.x ` => ` >0.0.0 `
         # ` x.x.1 ` => ` >0.0.0 `
         # ` x.1.x ` => ` >0.0.0 `
@@ -438,7 +440,11 @@ nvm_normalize_semver() {
               output=output ">=" version " <" a[1]+1 ".0.0 ";
             }
           } else if ( match(comparator, /^~/)  ) {
-            if ( match(comparator, /^~0.0.[0-9]+$/) ) {
+            if ( match(comparator, /^~[0-9]+.0.0$/) ) {
+              version=substr(comparator,2)
+              split(version, a, /\./)
+              output=output ">=" version " <" a[1]+1 ".0.0 "
+            } else if ( match(comparator, /^~0.0.[0-9]+$/) ) {
               version=substr(comparator,2)
               split(version, a, /\./)
               output=output ">=" version " <0." a[2]+1 ".0 "
@@ -472,9 +478,9 @@ nvm_normalize_semver() {
 
   if nvm_is_normalized_semver "$validated_semver"; then
     command printf '%s' "$validated_semver"
-  else
-    return 1
+    return 0
   fi
+  return 1
 }
 
 # Given a semver and version list, find the highest compatible version by doing the following:
@@ -490,9 +496,9 @@ nvm_interpret_complex_semver() {
   fi
 
   # For each comparator_set in the semver:
-  #   - Resolve the comparator_set to its newest compatible version.
-  #   - Add the discovered newest compatible version to highest_compatible_versions.
-  #   - Choose the highest version among all the versions collected in highest_compatible_versions.
+  #   - Try to resolve the comparator_set to its newest compatible version.
+  #   - But stop looking for a compatible version for a comparator_set if the current_version being iterated on is lower than an already found compatible version.
+  #   - If by the end of the algorithm, a version other than 0.0.0 is collected in highest_compatible_version, output that version.
   semver=$(command printf '%s' "$semver" | command tr '||' '\n')
   local version_list_copy
   local current_comparator_set
@@ -500,9 +506,8 @@ nvm_interpret_complex_semver() {
   local current_comparator_set_copy
   local current_comparator
   local stripped_version_from_comparator
-  local highest_compatible_versions
-  # TODO make this just always store the highest possible compatible version
-  highest_compatible_versions=''
+  local highest_compatible_version
+  highest_compatible_version='0.0.0'
 
   while [ -n "$semver" ]; do
     version_list_copy=$(command printf '%s' "$version_list")
@@ -511,13 +516,17 @@ nvm_interpret_complex_semver() {
     [ -n "$current_comparator_set" ] || continue
 
     # For each version in the version_list_copy (iterating from newest to oldest):
-    #   - If current_version satisfies all comparators in current_comparator_set, we've found the newest version compatible with all comparators in current current_comparator_set.
-    #   - Add discovered version to highest_compatible_versions and stop iterating through versions for current_comparator_set.
+    #   - If current_version satisfies all comparators in current_comparator_set, we've found the newest highest version compatible with all comparators in current current_comparator_set.
+    #   - Store the current_version in highest_compatible_version and stop iterating through versions for current_comparator_set.
     while [ -n "$version_list_copy" ]; do
       current_version=$(command printf '%s' "$version_list_copy" | command tail -n1 | command sed -E 's/^ +//;s/ +$//' | nvm_grep -o '^[0-9]\+\.[0-9]\+\.[0-9]\+$')
       version_list_copy=$(command printf '%s' "$version_list_copy" | command sed '$d')
       [ -n "$current_version" ] || continue
-      # TODO if current_version is less than the highest version in highest_compatile_versions, no need to continue
+      if [ "$highest_compatible_version" != '0.0.0' ] && nvm_version_greater "$highest_compatible_version" "$current_version"; then
+        # If we previously found a compatible version that is higher than the current_version, there is no need to continue checking versions.
+        version_list_copy=''
+        continue
+      fi
 
       # For each comparator in the current_comparator_set_copy:
       #   - If current_version is compatible with all comparators, we know current_version is the newest compatible version
@@ -537,7 +546,7 @@ nvm_interpret_complex_semver() {
             # current_comparator is looking for an exact match, and the current_version is the exact match, so this current_comparator is satisfied.
             if [ -z "$current_comparator_set_copy" ]; then
               # Also, this is the last comparator in the current_comparator_set_copy so we can assume we've found the newest compatible version of the current_comparator_set.
-              highest_compatible_versions="$highest_compatible_versions $current_version"
+              highest_compatible_version="$current_version"
               version_list_copy=''
             fi
           elif nvm_version_greater "$stripped_version_from_comparator" "$current_version"; then
@@ -554,7 +563,7 @@ nvm_interpret_complex_semver() {
             # current_version is less than or equal to the current_comparator version number so this current_comparator is satisfied.
             if [ -z "$current_comparator_set_copy" ]; then
               # Also, this is the last comparator in the current_comparator_set_copy so we can assume we've found the newest compatible version of the current_comparator_set.
-              highest_compatible_versions="$highest_compatible_versions $current_version"
+              highest_compatible_version="$current_version"
               version_list_copy=''
             fi
           else
@@ -567,7 +576,7 @@ nvm_interpret_complex_semver() {
             # current_version is greater than or equal to the current_comparator version number so this current_comparator is satisfied.
             if [ -z "$current_comparator_set_copy" ]; then
               # Also, this is the last comparator in the current_comparator_set_copy so we can assume we've found the newest compatible version of the current_comparator_set.
-              highest_compatible_versions="$highest_compatible_versions $current_version"
+              highest_compatible_version="$current_version"
               version_list_copy=''
             fi
           else
@@ -581,7 +590,7 @@ nvm_interpret_complex_semver() {
             # current_version is less than the current_comparator version number so this current_comparator is satisfied.
             if [ -z "$current_comparator_set_copy" ]; then
               # Also, this is the last comparator in the current_comparator_set_copy so we can assume we've found the newest compatible version of the current_comparator_set.
-              highest_compatible_versions="$highest_compatible_versions $current_version"
+              highest_compatible_version="$current_version"
               version_list_copy=''
             fi
           else
@@ -594,7 +603,7 @@ nvm_interpret_complex_semver() {
             # current_version is greater than the current_comparator version number so this current_comparator is satisfied.
             if [ -z "$current_comparator_set_copy" ];then
               # Also, this is the last comparator in the current_comparator_set_copy so we can assume we've found the newest compatible version of the current_comparator_set.
-              highest_compatible_versions="$highest_compatible_versions $current_version"
+              highest_compatible_version="$current_version"
               version_list_copy=''
             fi
           else
@@ -610,27 +619,11 @@ nvm_interpret_complex_semver() {
     done # while [ -n "$version_list_copy" ]; do
   done # while [ -n "$semver" ]; do
 
-  # Iterate through each of the versions in highest_compatible_versions, which are the highest versions that satisfy each of the comparator sets.
-  # Since comparator sets are separated by '||', choosing any of the highest versions compatible with any of the comparator_sets would be compatible with the whole semver.
-  # Therefore, we should resolve to the highest version in highest_compatible_versions.
-  local highest_compatible_version
-  local compatible_node_version
-  highest_compatible_version='0.0.0'
-  highest_compatible_versions=$(command printf '%s' "$highest_compatible_versions" | command tr ' ' '\n')
-  while [ -n "$highest_compatible_versions" ]; do
-    compatible_node_version=$(command printf '%s' "$highest_compatible_versions" | command head -n1 | command sed -E 's/^ +//;s/ +$//')
-    highest_compatible_versions=$(command printf '%s' "$highest_compatible_versions" | command tail -n +2)
-    [ -n "$compatible_node_version" ] || continue
-
-    if nvm_version_greater "$compatible_node_version" "$highest_compatible_version"; then
-      highest_compatible_version="$compatible_node_version"
-    fi
-  done
-  if [ "$highest_compatible_version" != '0.0.0' ]; then
+  if [ -n "$highest_compatible_version" ] && [ "$highest_compatible_version" != '0.0.0' ]; then
     command printf '%s' "$highest_compatible_version"
-  else
-    return 1
+    return 0
   fi
+  return 1
 }
 
 # Given a semver and version list, optimize discovery of highest compatible version with this function which quickly interprets some common semvers.
@@ -677,7 +670,7 @@ nvm_interpret_simple_semver() {
       command printf '%s' "$newest_version_from_list"
       return 0
     else
-      # TODO we know it's not worth doing the complex semver interpretation at this point
+      command printf '%s' 'STOP' # we have determined no node version will be compatible with the semver
       return 1
     fi
 
diff --git a/test/fast/Unit tests/nvm_get_node_from_pkg_json b/test/fast/Unit tests/nvm_get_node_from_pkg_json
index 5f1f3eb..1bef708 100755
--- a/test/fast/Unit tests/nvm_get_node_from_pkg_json	
+++ b/test/fast/Unit tests/nvm_get_node_from_pkg_json	
@@ -3,14 +3,14 @@
 \. ../../../nvm.sh
 \. ../../generated_semvers.sh
 
+# This test suite validates the behavior of extracting the semver from a package.json's engine.node value given valid/invalid semvers and valid/invalid json structures.
 
-# POSITIVE TEST CASES
-
-
-# (TEST SET #1) uses valid TEST_SEMVER's and valid package.json templates
+# (TEST 1 POSITIVE TEST CASES)
+# SEMVERS: valid
+# PACKAGE.JSON TEMPLATES: invalid
 test_cases="$VALID_SEMVERS_FOR_PKG_JSON"
 if [ -z "$test_cases" ]; then
-  die 'TEST SET 1 for nvm_get_node_from_pkg_json given an empty set of test cases'
+  die 'TEST 1 for nvm_get_node_from_pkg_json given an empty set of test cases'
 fi
 prev_semver=''
 for template_file_name in package_json_templates/_valid_*; do
@@ -21,26 +21,24 @@ for template_file_name in package_json_templates/_valid_*; do
     expectedOutput=$(nvm_trim_and_reduce_whitespace_to_one_space "$semver")
 
     if [ "$prev_semver" = "$semver" ]; then
-      die "Problem iterating through test_cases (TEST SET #1). Encountered the same value twice in a row. prev_semver='$prev_semver' semver='$semver'.\n"
+      die "Problem iterating through test_cases (TEST 1). Encountered the same value twice in a row. prev_semver='$prev_semver' semver='$semver'.\n"
     fi
     prev_semver="$semver"
 
     pkg_json_contents=$(sed "s/NODE_SEMVER/$semver/g" "$template_file_name" | tail -n +3)
     actual_output=$(nvm_get_node_from_pkg_json "$pkg_json_contents")
     if [ "$actual_output" != "$expectedOutput" ] || [ -z "$actual_output" ] || [ -z "$pkg_json_contents" ]; then
-      die "'nvm_get_node_from_pkg_json' POSITIVE test case failed (TEST SET #1). Expected '$expectedOutput' but got '$actual_output' when given input '$semver' and template '$template_file_name':\n$pkg_json_contents"
+      die "'nvm_get_node_from_pkg_json' POSITIVE test case failed (TEST 1). Expected '$expectedOutput' but got '$actual_output' when given input '$semver' and template '$template_file_name':\n$pkg_json_contents"
     fi
   done
 done
 
-
-# NEGATIVE TEST CASES
-
-
-# (TEST SET #2) uses valid TEST_SEMVER's but invalid package.json templates
+# (TEST 2 NEGATIVE TEST CASES)
+# SEMVERS: valid
+# PACKAGE.JSON TEMPLATES: invalid
 test_cases="$VALID_SEMVERS_FOR_PKG_JSON"
 if [ -z "$test_cases" ]; then
-  die 'TEST SET 2 for nvm_get_node_from_pkg_json given an empty set of test cases'
+  die 'TEST 2 for nvm_get_node_from_pkg_json given an empty set of test cases'
 fi
 prev_semver=''
 for template_file_name in package_json_templates/_invalid_*; do
@@ -50,23 +48,25 @@ for template_file_name in package_json_templates/_invalid_*; do
     [ -n "$semver" ] || continue
 
     if [ "$prev_semver" = "$semver" ]; then
-      die "Problem iterating through test_cases (TEST SET #2). Encountered the same value twice in a row. prev_semver='$prev_semver' semver='$semver'.\n"
+      die "Problem iterating through test_cases (TEST 2). Encountered the same value twice in a row. prev_semver='$prev_semver' semver='$semver'.\n"
     fi
     prev_semver="$semver"
 
     pkg_json_contents=$(sed "s/NODE_SEMVER/$semver/g" "$template_file_name" | tail -n +3)
     actual_output=$(nvm_get_node_from_pkg_json "$pkg_json_contents")
     if [ "$actual_output" != "" ] || [ -z "$semver" ] || [ -z "$pkg_json_contents" ]; then
-      die "'nvm_get_node_from_pkg_json' NEGATIVE test case failed (TEST SET #2). Expected to get empty string but got '$actual_output' when given input template '$template_file_name':\n$pkg_json_contents"
+      die "'nvm_get_node_from_pkg_json' NEGATIVE test case failed (TEST 2). Expected to get empty string but got '$actual_output' when given input template '$template_file_name':\n$pkg_json_contents"
     fi
   done
 done
 
 
-# (TEST SET #3) uses invalid TEST_SEMVER's but valid package.json templates
+# (TEST 3 NEGATIVE TEST CASES)
+# SEMVERS: invalid
+# PACKAGE.JSON TEMPLATES: valid
 test_cases="$INVALID_SEMVERS_FOR_PKG_JSON"
 if [ -z "$test_cases" ]; then
-  die 'TEST SET 3 for nvm_get_node_from_pkg_json given an empty set of test cases'
+  die 'TEST 3 for nvm_get_node_from_pkg_json given an empty set of test cases'
 fi
 prev_semver=''
 for template_file_name in package_json_templates/_valid_*; do
@@ -76,22 +76,24 @@ for template_file_name in package_json_templates/_valid_*; do
     test_cases=$(echo "$test_cases" | tail -n +2)
 
     if [ "$prev_semver" = "$semver" ]; then
-      die "Problem iterating through test_cases (TEST SET #3). Encountered the same value twice in a row. prev_semver='$prev_semver' semver='$semver'.\n"
+      die "Problem iterating through test_cases (TEST 3). Encountered the same value twice in a row. prev_semver='$prev_semver' semver='$semver'.\n"
     fi
-    prev_semver=$(printf "%s" "$semver")
+    prev_semver="$semver"
 
     pkg_json_contents=$(sed "s/NODE_SEMVER/$semver/g" "$template_file_name" | tail -n +3)
     actual_output=$(nvm_get_node_from_pkg_json "$pkg_json_contents")
     if [ "$actual_output" != "" ] || [ -z "$semver" ] || [ -z "$pkg_json_contents" ]; then
-      die "'nvm_get_node_from_pkg_json' NEGATIVE test case failed (TEST SET #3). Expected to get empty string but got '$actual_output' when given input template '$template_file_name':\n$pkg_json_contents"
+      die "'nvm_get_node_from_pkg_json' NEGATIVE test case failed (TEST 3). Expected to get empty string but got '$actual_output' when given input template '$template_file_name':\n$pkg_json_contents"
     fi
   done
 done
 
-# (TEST SET #4) uses invalid TEST_SEMVER's and invalid package.json templates
+# (TEST 4 NEGATIVE TEST CASES)
+# SEMVERS: invalid
+# PACKAGE.JSON TEMPLATES: invalid
 test_cases="$INVALID_SEMVERS_FOR_PKG_JSON"
 if [ -z "$test_cases" ]; then
-  die 'TEST SET 4 for nvm_get_node_from_pkg_json given an empty set of test cases'
+  die 'TEST 4 for nvm_get_node_from_pkg_json given an empty set of test cases'
 fi
 prev_semver=''
 for template_file_name in package_json_templates/_invalid_*; do
@@ -101,14 +103,14 @@ for template_file_name in package_json_templates/_invalid_*; do
     test_cases=$(echo "$test_cases" | tail -n +2)
 
     if [ "$prev_semver" = "$semver" ]; then
-      die "Problem iterating through test_cases (TEST SET #4). Encountered the same value twice in a row. prev_semver='$prev_semver' semver='$semver'.\n"
+      die "Problem iterating through test_cases (TEST 4). Encountered the same value twice in a row. prev_semver='$prev_semver' semver='$semver'.\n"
     fi
-    prev_semver=$(printf "%s" "$semver")
+    prev_semver="$semver"
 
     pkg_json_contents=$(sed "s/NODE_SEMVER/$semver/g" "$template_file_name" | tail -n +3)
     actual_output=$(nvm_get_node_from_pkg_json "$pkg_json_contents")
     if [ "$actual_output" != "" ] || [ -z "$semver" ] || [ -z "$pkg_json_contents" ]; then
-      die "'nvm_get_node_from_pkg_json' NEGATIVE test case failed (TEST SET #4). Expected to get empty string but got '$actual_output' when given input template '$template_file_name':\n$pkg_json_contents"
+      die "'nvm_get_node_from_pkg_json' NEGATIVE test case failed (TEST 4). Expected to get empty string but got '$actual_output' when given input template '$template_file_name':\n$pkg_json_contents"
     fi
   done
 done
diff --git a/test/fast/Unit tests/nvm_is_normalized_semver b/test/fast/Unit tests/nvm_is_normalized_semver
index 9e7d0fa..2be8cff 100755
--- a/test/fast/Unit tests/nvm_is_normalized_semver	
+++ b/test/fast/Unit tests/nvm_is_normalized_semver	
@@ -3,19 +3,13 @@
 \. ../../../nvm.sh
 \. ../../generated_semvers.sh
 
-# nvm_is_normalized_semver validates that given semvers adhere to the following grammer
-#
-# semver         ::= comparator_set ( ' || '  comparator_set )*
-# comparator_set ::= comparator ( ' ' comparator )*
-# comparator     ::= ( '<' | '<=' | '>' | '>=' | '' ) [0-9]+ '.' [0-9]+ '.' [0-9]+
+# nvm_is_normalized_semver validates that a given semver adheres to a particular grammar. See grammar with definition of function nvm_is_normalized_semver() in nvm.sh.
 
 # POSITIVE TEST CASES
-
 positive_test_cases="$VALID_NORMALIZED_SEMVERS"
 if [ -z "$positive_test_cases" ]; then
   die 'positive test cases are empty'
 fi
-
 prev_semver=''
 while [ -n "$positive_test_cases" ]; do
   semver=$(echo "$positive_test_cases" | head -n1)
@@ -30,12 +24,10 @@ while [ -n "$positive_test_cases" ]; do
 done
 
 # NEGATIVE TEST CASES
-
 negative_test_cases=$(printf "%s\n%s" "$VALID_NON_NORMALIZED_SEMVERS" "$INVALID_SEMVERS_FOR_PKG_JSON")
 if [ -z "$negative_test_cases" ]; then
   die 'negative test cases are empty'
 fi
-
 prev_semver='initialized to non empty string'
 while [ -n "$negative_test_cases" ]; do
   semver=$(echo "$negative_test_cases" | head -n1)
diff --git a/test/fast/Unit tests/nvm_normalize_semver b/test/fast/Unit tests/nvm_normalize_semver
index e48b74a..b68da17 100755
--- a/test/fast/Unit tests/nvm_normalize_semver	
+++ b/test/fast/Unit tests/nvm_normalize_semver	
@@ -3,6 +3,8 @@
 \. ../../../nvm.sh
 \. ../../generated_semvers.sh
 
+# This test suite validates the behavior of normalizing a semver from its raw form to a specific grammar. See the grammar defined with nvm_is_normalized_semver() in nvm.sh.
+
 # TEST 1: Validate that for already normalized semvers, nvm_normalize_semver outputs the same semver.
 test_cases="$VALID_NORMALIZED_SEMVERS"
 if [ -z "$test_cases" ]; then
diff --git a/test/fast/Unit tests/nvm_string_contains_regexp b/test/fast/Unit tests/nvm_string_contains_regexp
index 495b860..b3116cf 100755
--- a/test/fast/Unit tests/nvm_string_contains_regexp	
+++ b/test/fast/Unit tests/nvm_string_contains_regexp	
@@ -2,11 +2,11 @@
 
 \. ../../../nvm.sh
 \. ../../generated_semvers.sh
-
 normalized_semver_regexp='^( ?(<|<=|>|>=)?[0-9]+\.[0-9]+\.[0-9]+)+( \|\| ( ?(<|<=|>|>=)?[0-9]+\.[0-9]+\.[0-9]+)+)*$'
 
-# POSITIVE TEST CASES
+# Validates the behavior of nvm_string_contains_regexp() which returns 0 if the given string contains the given regular expression.
 
+# POSITIVE TEST CASES
 test_cases="$VALID_NORMALIZED_SEMVERS"
 while [ -n "$test_cases" ]; do
   string=$(echo "$test_cases" | head -n1)
@@ -17,10 +17,8 @@ while [ -n "$test_cases" ]; do
 done
 
 # NEGATIVE TEST CASES
-
 # string:regexp
 test_cases=$(printf "%s\n%s" "$VALID_NON_NORMALIZED_SEMVERS" "$INVALID_SEMVERS_FOR_PKG_JSON")
-
 while [ -n "$test_cases" ]; do
   string=$(echo "$test_cases" | head -n1)
   if [ -z "$normalized_semver_regexp" ] || nvm_string_contains_regexp "$string" "$normalized_semver_regexp"; then
diff --git a/test/fast/Unit tests/nvm_trim_and_reduce_whitespace_to_one_space b/test/fast/Unit tests/nvm_trim_and_reduce_whitespace_to_one_space
index 0e5da6f..358a5f6 100755
--- a/test/fast/Unit tests/nvm_trim_and_reduce_whitespace_to_one_space	
+++ b/test/fast/Unit tests/nvm_trim_and_reduce_whitespace_to_one_space	
@@ -1,8 +1,9 @@
 #!/bin/sh
 
+\. ../../../nvm.sh
 die () { printf "$@" ; exit 1; }
 
-\. ../../../nvm.sh
+# Validates the behavior of nvm_trim_and_reduce_whitespace_to_one_space() which consolidates all consecutive white space to one space, and then trims any spaces from the ends.
 
 # Test cases that have no new lines
 # input:expected_output
@@ -26,27 +27,27 @@ done
 
 # Test cases that have new lines
 expected_output='1 2 3'
-new_line_1=' 1
+test_case_with_new_line_1=' 1
  2 	3 '
-actual_output=$(nvm_trim_and_reduce_whitespace_to_one_space "$new_line_1")
+actual_output=$(nvm_trim_and_reduce_whitespace_to_one_space "$test_case_with_new_line_1")
 if [ "$actual_output" != "$expected_output" ]; then
-  die "nvm_trim_and_reduce_whitespace_to_one_space test with new_line_1 failed. Actual output: '$actual_output' Expected output: '$expected_output'"
+  die "nvm_trim_and_reduce_whitespace_to_one_space test with test_case_with_new_line_1 failed. Actual output: '$actual_output' Expected output: '$expected_output'"
 fi
 
-new_line_2=' 1	 2
+test_case_with_new_line_2=' 1	 2
 3	 '
-actual_output=$(nvm_trim_and_reduce_whitespace_to_one_space "$new_line_2")
+actual_output=$(nvm_trim_and_reduce_whitespace_to_one_space "$test_case_with_new_line_2")
 if [ "$actual_output" != "$expected_output" ]; then
-  die "nvm_trim_and_reduce_whitespace_to_one_space test with new_line_2 failed. Actual output: '$actual_output' Expected output: '$expected_output'"
+  die "nvm_trim_and_reduce_whitespace_to_one_space test with test_case_with_new_line_2 failed. Actual output: '$actual_output' Expected output: '$expected_output'"
 fi
 
-new_line_3='	1
+test_case_with_new_line_3='	1
 
 2
 3'
-actual_output=$(nvm_trim_and_reduce_whitespace_to_one_space "$new_line_3")
+actual_output=$(nvm_trim_and_reduce_whitespace_to_one_space "$test_case_with_new_line_3")
 if [ "$actual_output" != "$expected_output" ]; then
-  die "nvm_trim_and_reduce_whitespace_to_one_space test with new_line_3 failed. Actual output: '$actual_output' Expected output: '$expected_output'"
+  die "nvm_trim_and_reduce_whitespace_to_one_space test with test_case_with_new_line_3 failed. Actual output: '$actual_output' Expected output: '$expected_output'"
 fi
 exit 0
 
diff --git a/test/generated_semvers.sh b/test/generated_semvers.sh
index 7ea9384..422f11b 100755
--- a/test/generated_semvers.sh
+++ b/test/generated_semvers.sh
@@ -18,7 +18,7 @@ VALID_NON_NORMALIZED_SEMVER_OPERATORS='v
 # Versions (stripped of any operators) that are considered valid inputs to the semver interpretation logic.
 VALID_NORMALIZED_VERSIONS='4.1.0
 0.12.18
-0.11.16
+8.0.0
 6.11.4
 10.0.0'
 
@@ -62,8 +62,6 @@ asdf
 1111
 1  1
 1.
-1.1
-1.*
 1.2
 11.222
 1.2.a
@@ -71,8 +69,6 @@ asdf
 1.x.x
 11.22.a
 =1.2.3
-~1.2.3
-^1.2.3
 1.1.1 2.2.2
 >1.1.1 <1.1.0
 1.2 - 1.3
@@ -81,9 +77,7 @@ asdf
 1.2.3 - 1.2.4
 1.2.3-1.2.4
 1.2 1.3
-1 2
-1.2.3||1.2.4
-1.2||1.3
+10 20
 1||2
 >1000
 <0"
@@ -97,12 +91,23 @@ VALID_NORMALIZED_COMPLEX_SEMVERS='10.3.0 || 8.1.1 || 4.1.0
 
 # Valid semvers that should resolve to a node version but need to be validated/normalized before interpretting.
 VALID_NON_NORMALIZED_COMPLEX_SEMVERS='x
+10
+~10
+^10
 X
 *
 x.x
 X.X
 *.*
+10.x
+~10.x
+^10.x
+10.X.X
+~10.X.X
+^10.X.X
 x.x.x
+~X.X.X
+^X.X.X
 X.X.X
 x.X.*
 *.x.X
diff --git a/test/slow/nvm_interpret_node_semver b/test/slow/nvm_interpret_node_semver
index 379d923..95a9284 100755
--- a/test/slow/nvm_interpret_node_semver
+++ b/test/slow/nvm_interpret_node_semver
@@ -29,14 +29,23 @@ while [ -n "$test_cases" ]; do
   fi
 done
 
-# TODO add more test cases here
-# TODO get the following semvers working: ^7 ^7.x ^7.0 ~8 ~8.0
 # Verify actual outputs given some inputs
 # input:expected_output
 test_cases="*:$NEWEST_NODE_VERSION
+^5:$NEWEST_NODE_VERSION_5
+^5.0:$NEWEST_NODE_VERSION_5
+^5.x:$NEWEST_NODE_VERSION_5
+^5.X:$NEWEST_NODE_VERSION_5
+^5.*:$NEWEST_NODE_VERSION_5
+~5:$NEWEST_NODE_VERSION_5
+~5.0:$NEWEST_NODE_VERSION_5
+~5.x:$NEWEST_NODE_VERSION_5
+~5.X:$NEWEST_NODE_VERSION_5
+~5.*:$NEWEST_NODE_VERSION_5
 5:$NEWEST_NODE_VERSION_5
 x:$NEWEST_NODE_VERSION
 X:$NEWEST_NODE_VERSION
+x.x.x:$NEWEST_NODE_VERSION
 0.12.18:0.12.18
 0.11.16:0.11.16
 7.0.0||7.2.1:7.2.1