C++ Mathematical Expression Library (ExprTk) https://www.partow.net/programming/exprtk/index.html
diff --git a/readme.txt b/readme.txt
index 1a5d67a..49d6fc8 100644
--- a/readme.txt
+++ b/readme.txt
@@ -3558,9 +3558,28 @@
[*] Total Single Eval Time: 0.000ms
-From the results above we can see that the third expression (e^(3y))
-consumes the largest amount of time and should perhaps be replaced
-with the 'exp' function for more efficient evaluation.
+From the results above we conclude that the third expression (e^(3y))
+consumes the largest amount of time. The variable 'e', as used in both
+the benchmark and in the expression, is an approximation of the
+transcendental mathematical constant e (2.71828182845904...) hence the
+sub-expression should perhaps be modified to use the generally more
+efficient built-in 'exp' function.
+
+ ./exprtk_benchmark test.txt 1000000
+ Expr 1 of 5 86.563 ns 8656300ns (296417859.6) '1/sqrt(2x)*e^(3y)'
+ Expr 2 of 5 40.506 ns 4050600ns (296417859.6) '1/sqrt(2x)*exp(3y)'
+ Expr 3 of 5 14.248 ns 1424799ns ( 44267.2) '1/sqrt(2x)'
+ Expr 4 of 5 88.840 ns 8884000ns (615985286.9) 'e^(3y)'
+ Expr 5 of 5 29.267 ns 2926699ns (615985286.9) 'exp(3y)'
+ [*] Number Of Evals: 5000000
+ [*] Total Time: 0.260sec
+ [*] Total Single Eval Time: 0.000ms
+
+
+The above output demonstrates the results from making the previously
+mentioned modification to the expression. As can be seen the new form
+of the expression using the 'exp' function reduces the evaluation time
+by over 50%, in other words increases the evaluation rate by two fold.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
