An example of using Gorilla Repl and Clojure to plot some evolved approximations to the sine function. The evolution was done with the ECJ system (http://cs.gmu.edu/~eclab/projects/ecj/). I'd never used Gorilla Repl, and I was really impressed with how easy it was to get it up and running and generate some basic sketches with. If you want to see…

plotting_evolved_sine_functions_with_gorilla_repl.clj

;; gorilla-repl.fileformat = 1

;; **
;;; # Plotting some evolved sine results
;;; 
;;; I decided to play with [Gorilla Repl](http://gorilla-repl.org) to try to plot some of the evolved Sine results just to make sure we were solving the problem we thought we were solving.
;;; 
;;; The short version is that Gorilla Repl was quite excellent, and we are indeed solving the sine problem :-)
;;; 
;;; One of the nifty things is that Clojure allowed me to define the symbol % to be protected division, so we can paste in functions straight from ECJ and run them without having to do any annoying search/replace action to get things in a format that our graphing tool can process.
;;; 
;;; – Nic
;;; 
;;; If you have this loaded in a live Gorilla REPL, then Shift + enter evaluates code. Hit ctrl+g twice in quick succession or click the menu icon (upper-right corner) for more commands ...
;;; 
;;; None of that will work if you're seeing this in the web viewer, however.
;; **

;; @@
(ns plotting-sine-GP-results
  (:require [gorilla-plot.core :as plot]))

; Define protected division
(defn % [x y]
  (if (< (Math/abs y) 0.000001)
    1
    (/ x y)))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;plotting-sine-GP-results/%</span>","value":"#'plotting-sine-GP-results/%"}
;; <=

;; **
;;; Just to keep things from being too messy, I started with the shortest final program from one of the sets of 100 runs that I did:
;; **

;; @@
; The shortest final program in one of the set of runs that I did.
(defn f [x]
  (% (+ (+ (* (* x 0.08251808754236745) (+
     x x)) x) (* (* (+ (+ x x) (- x x)) (- (%
     x (- x x)) x)) 0.35368663199857253)) (+ (-
     (- (- x x) (% -0.24565992031690032 (+ (*
         (* x 0.08251808754236745) (% (+ (+ (+ x x)
         (* (+ x x) (- (% x (- x x)) x))) (* (* (+
         (* (* x 0.08251808754236745) (+ x x)) x)
         (- (% x (- x x)) x)) 0.35368663199857253))
         x)) x))) (* (* 0.08199740533475586 (- (*
     x x) (+ (- (% (+ (+ (* (* x 0.08251808754236745)
     (+ x x)) x) (* (* (+ (* (* x 0.08251808754236745)
     (+ (- -0.6543624729324293 x) (* x x))) x)
     (- (% x (* (* x 0.08251808754236745) (+ x
         x))) x)) 0.35368663199857253)) x) (* (* (+
     (- -0.6543624729324293 x) (* x x)) (- 0.660431470441156
     x)) 0.35368663199857253)) (+ 0.11129473428511871
     (+ x x))))) (* (* x 0.08251808754236745)
     (+ x x)))) (+ 0.11129473428511871 (% x (-
     x x))))))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;plotting-sine-GP-results/f</span>","value":"#'plotting-sine-GP-results/f"}
;; <=

;; @@
(plot/plot f [0 6.2])
;; @@
;; =>
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;; <=

;; **
;;; Hey Dee Ho! That looks like a sine curve, except for the bit on the right that is clearly kinda wonky. It's promising, though.
;;; 
;;; Now lets try the best program from that set of runs:
;; **

;; @@
; The best program in one of the sets of runs that I did.
(defn g [x]
  (% (- (- (+ (% x 0.1878165803028793) (* 0.4041295789960697
     x)) (+ (* x x) (+ (* (- x (- (* 0.7790185468006714
     x) (% (- (* 0.7790185468006714 x) x) (+ (-
     (* 0.9279115829235329 (* -0.7583897983492538
         (+ 0.4709715244797692 (% -0.7285016789959027
             x)))) (* 0.7790185468006714 x)) (* x x)))))
     0.2748897745619905) -0.3884188391842409)))
     (+ (- (* x x) (- x -0.15416253624891563))
         (- (- -0.5364803358639891 0.6322647851679684)
             (* -0.9343582711758056 x)))) (+ (* (% (-
     (- (% 0.9152797222383366 0.1710673978269237)
         (+ -0.8817943178743988 x)) (+ (* (- x (-
     (* 0.7790185468006714 x) (* (- (% x x) (*
     0.9361498173722331 -0.7607169969743153))
     0.2748897745619905))) 0.2748897745619905)
     (* x x))) (- (+ (* x 0.6663818683455585)
     (- (+ (% x 0.1878165803028793) (% (% (+ (-
         x (- (- x x) (% (- (* 0.7790185468006714
         x) x) x))) (+ (+ -0.8817943178743988 x) -0.3884188391842409))
         (+ 0.17631777678595362 x)) (- x x))) (+ (*
         x x) (+ (* (- (% x x) (* 0.9361498173722331
         -0.7607169969743153)) 0.2748897745619905)
         -0.3884188391842409)))) (% (+ x x) (% x -0.3035648741910095))))
     (- (* (- -0.5364803358639891 0.6322647851679684)
         (+ (+ x -0.6820812663709219) (* 0.9361498173722331
             -0.7607169969743153))) -0.22747467584270353))
     (% (- (% -0.8729232867227796 -0.9021282222161298)
         (* 0.9361498173722331 -0.7607169969743153))
         (% (* 0.31826212719083813 x) (+ 0.17631777678595362
             x))))))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;plotting-sine-GP-results/g</span>","value":"#'plotting-sine-GP-results/g"}
;; <=

;; @@
(plot/compose 
  (plot/plot g [0 6.2] :colour "blue")
  (plot/plot f [0 6.2])
  (plot/plot #(Math/sin %) [0 6.2] :color "green"))

; I had to do the crazy #(Math/sin %) thing because just putting Math/sin in didn't work.
; There are places where the interaction between Clojure and Java is odd, and this is an
; example of that. I could have alternatively defined a sine function here in this namespace
; that just called Math/sin, and then use that sine function here.
;; @@
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;; <=

;; **
;;; This plot shows that both of these were pretty close to the target, which is drawn in green, with the best (drawn in blue) being _really_ close over the test range. This provides some pretty good evidence that the evolutionary process is basically doing the "right" thing and solving the problem we think we're solving. Now we just need to figure out why including bias doesn't seem to change anything.
;; **

;; @@

;; @@