C++ Mathematical Expression Library (ExprTk)  https://www.partow.net/programming/exprtk/index.html

exprtk_simple_example_10.cpp

diff --git a/exprtk_simple_example_10.cpp b/exprtk_simple_example_10.cpp
index 48f2078..3e1dbe8 100644
--- a/exprtk_simple_example_10.cpp
+++ b/exprtk_simple_example_10.cpp
@@ -44,22 +44,22 @@
       .add(
       function_t( // define function: newton_sqrt(x)
            "newton_sqrt",
-           " switch                               "
-           " {                                    "
-           "   case x < 0  : -inf;                "
-           "   case x == 0 : 0;                   "
-           "   case x == 1 : 1;                   "
-           "   default:                           "
-           "   ~{                                 "
-           "      var z := 100;                   "
-           "      var y := x / 2;                 "
-           "      repeat                          "
-           "        y := (1 / 2) * (y + (x / y)); "
-           "        if (equal(y * y, x))          "
-           "          break[y];                   "
-           "      until ((z -= 1) <= 0);          "
-           "    };                                "
-           " }                                    ",
+           " switch                                              "
+           " {                                                   "
+           "   case x < 0  : -inf;                               "
+           "   case x == 0 : 0;                                  "
+           "   case x == 1 : 1;                                  "
+           "   default:                                          "
+           "   ~{                                                "
+           "      var z := 100;                                  "
+           "      var sqrt_x := x / 2;                           "
+           "      repeat                                         "
+           "        sqrt_x := (1 / 2) * (sqrt_x + (x / sqrt_x)); "
+           "        if (equal(sqrt_x^2, x))                      "
+           "          break[sqrt_x];                             "
+           "      until ((z -= 1) <= 0);                         "
+           "    };                                               "
+           " }                                                   ",
            "x"));
 
    std::string expression_str = "newton_sqrt(x)";

readme.txt

diff --git a/readme.txt b/readme.txt
index 3686f5d..6133c44 100644
--- a/readme.txt
+++ b/readme.txt
@@ -877,8 +877,8 @@
 muli-threading et al.
 
 The prescribed method for cloning an expression is to compile it  from
-its string form. Doing so will allow the one to properly consider  the
-exact source of user defined variables and functions.
+its string  form. Doing so will allow the 'user' to  properly consider
+the exact source of user defined variables and functions.
 
 Note:  The  exprtk::parser  is  a  non-copyable  and  non-thread  safe
 component, and should only be shared via either a reference, a  shared
@@ -893,19 +893,19 @@
 inserting  the  newly  minted  exprtk::expression  instances  into   a
 std::vector.
 
-
-                        +--[exprtk::parser]--+
-                        | expression factory |
-                     +---->- compile(....) ->---+
-                     |  +--------------------+  |
-  Expressions        |                          |   Expressions as
-  in string form     A                          V   exprtk::expression
-                     |                          |   instances
-  [s0:'x+1']------+  |                          |   +-[e0: x+1]
-                  |  |                          |   |
-  [s1:'2z+y']-----+--+                          +-->+-[e1: 2z+y]
-                  |                                 |
-  [s2:'sin(k+w)']-+                                 +-[e2: sin(k+w)]
+                      +----[exprtk::parser]---+
+                      |   Expression Factory  |
+                      | parser_t::compile(...)|
+                    +--> ~.~.~.~.~.~.~.~.~.~ ->--+
+                    | +-----------------------+  |
+ Expressions in     |                            |  Expressions as
+ string form        A                            V  exprtk::expression
+                    |                            |  instances
+ [s0:'x+1']--->--+  |                            |  +-[e0: x+1]
+                 |  |                            |  |
+ [s1:'2z+y']-->--+--+                            +->+-[e1: 2z+y]
+                 |                                  |
+ [s2:'sin(k+w)']-+                                  +-[e2: sin(k+w)]
 
 
    const std::string expression_str[3]