4.942 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.015 * * * [progress]: [2/2] Setting up program. 0.016 * [progress]: [Phase 2 of 3] Improving. 0.017 * [simplify]: Simplifying using # : (+ (+ (* x x) y) y) 0.017 * [simplify]: Sending expressions to egg_math: (+ (+ (* h0 h0) h1) h1) 0.019 * * [simplify]: iteration 0 : 9 enodes (cost 3 ) 0.021 * * [simplify]: iteration 1 : 12 enodes (cost 3 ) 0.022 * * [simplify]: iteration 2 : 13 enodes (cost 3 ) 0.023 * * [simplify]: iteration 3 : 13 enodes (cost 3 ) 0.023 * [simplify]: Simplified to: (+ (+ (* x x) y) y) 0.024 * * [progress]: iteration 1 / 4 0.024 * * * [progress]: picking best candidate 0.025 * * * * [pick]: Picked # 0.025 * * * [progress]: localizing error 0.029 * * * [progress]: generating rewritten candidates 0.029 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.064 * * * [progress]: generating series expansions 0.064 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.065 * [approximate]: Taking taylor expansion of (+ (pow x 2) (* 2 y)) in (x y) around 0 0.065 * [taylor]: Taking taylor expansion of (+ (pow x 2) (* 2 y)) in y 0.065 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.065 * [taylor]: Taking taylor expansion of x in y 0.065 * [taylor]: Taking taylor expansion of (* 2 y) in y 0.065 * [taylor]: Taking taylor expansion of 2 in y 0.065 * [taylor]: Taking taylor expansion of y in y 0.065 * [taylor]: Taking taylor expansion of (+ (pow x 2) (* 2 y)) in x 0.065 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.065 * [taylor]: Taking taylor expansion of x in x 0.065 * [taylor]: Taking taylor expansion of (* 2 y) in x 0.065 * [taylor]: Taking taylor expansion of 2 in x 0.065 * [taylor]: Taking taylor expansion of y in x 0.065 * [taylor]: Taking taylor expansion of (+ (pow x 2) (* 2 y)) in x 0.065 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.065 * [taylor]: Taking taylor expansion of x in x 0.065 * [taylor]: Taking taylor expansion of (* 2 y) in x 0.065 * [taylor]: Taking taylor expansion of 2 in x 0.065 * [taylor]: Taking taylor expansion of y in x 0.065 * [taylor]: Taking taylor expansion of (* 2 y) in y 0.065 * [taylor]: Taking taylor expansion of 2 in y 0.065 * [taylor]: Taking taylor expansion of y in y 0.066 * [taylor]: Taking taylor expansion of 0 in y 0.068 * [taylor]: Taking taylor expansion of 1 in y 0.070 * [taylor]: Taking taylor expansion of 0 in y 0.071 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (* 2 (/ 1 y))) in (x y) around 0 0.071 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (* 2 (/ 1 y))) in y 0.071 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.071 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.071 * [taylor]: Taking taylor expansion of x in y 0.071 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in y 0.071 * [taylor]: Taking taylor expansion of 2 in y 0.071 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.071 * [taylor]: Taking taylor expansion of y in y 0.071 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (* 2 (/ 1 y))) in x 0.071 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.071 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.071 * [taylor]: Taking taylor expansion of x in x 0.072 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in x 0.072 * [taylor]: Taking taylor expansion of 2 in x 0.072 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.072 * [taylor]: Taking taylor expansion of y in x 0.072 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (* 2 (/ 1 y))) in x 0.072 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.072 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.072 * [taylor]: Taking taylor expansion of x in x 0.072 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in x 0.073 * [taylor]: Taking taylor expansion of 2 in x 0.073 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.073 * [taylor]: Taking taylor expansion of y in x 0.073 * [taylor]: Taking taylor expansion of 1 in y 0.074 * [taylor]: Taking taylor expansion of 0 in y 0.075 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in y 0.075 * [taylor]: Taking taylor expansion of 2 in y 0.075 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.075 * [taylor]: Taking taylor expansion of y in y 0.078 * [taylor]: Taking taylor expansion of 0 in y 0.080 * [taylor]: Taking taylor expansion of 0 in y 0.081 * [approximate]: Taking taylor expansion of (- (/ 1 (pow x 2)) (* 2 (/ 1 y))) in (x y) around 0 0.081 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (* 2 (/ 1 y))) in y 0.081 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.081 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.081 * [taylor]: Taking taylor expansion of x in y 0.081 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in y 0.081 * [taylor]: Taking taylor expansion of 2 in y 0.081 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.081 * [taylor]: Taking taylor expansion of y in y 0.081 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (* 2 (/ 1 y))) in x 0.081 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.081 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.081 * [taylor]: Taking taylor expansion of x in x 0.082 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in x 0.082 * [taylor]: Taking taylor expansion of 2 in x 0.082 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.082 * [taylor]: Taking taylor expansion of y in x 0.082 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (* 2 (/ 1 y))) in x 0.082 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.082 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.082 * [taylor]: Taking taylor expansion of x in x 0.082 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in x 0.082 * [taylor]: Taking taylor expansion of 2 in x 0.082 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.082 * [taylor]: Taking taylor expansion of y in x 0.083 * [taylor]: Taking taylor expansion of 1 in y 0.084 * [taylor]: Taking taylor expansion of 0 in y 0.085 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 y))) in y 0.085 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in y 0.085 * [taylor]: Taking taylor expansion of 2 in y 0.085 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.085 * [taylor]: Taking taylor expansion of y in y 0.087 * [taylor]: Taking taylor expansion of 0 in y 0.090 * [taylor]: Taking taylor expansion of 0 in y 0.091 * * * [progress]: simplifying candidates 0.091 * [simplify]: Simplifying using # : (* (* (exp (* x x)) (exp y)) (exp y)) (* (exp (+ (* x x) y)) (exp y)) (log (+ (+ (* x x) y) y)) (exp (+ (+ (* x x) y) y)) (* (cbrt (+ (+ (* x x) y) y)) (cbrt (+ (+ (* x x) y) y))) (cbrt (+ (+ (* x x) y) y)) (* (* (+ (+ (* x x) y) y) (+ (+ (* x x) y) y)) (+ (+ (* x x) y) y)) (sqrt (+ (+ (* x x) y) y)) (sqrt (+ (+ (* x x) y) y)) (+ (pow (+ (* x x) y) 3) (pow y 3)) (+ (* (+ (* x x) y) (+ (* x x) y)) (- (* y y) (* (+ (* x x) y) y))) (- (* (+ (* x x) y) (+ (* x x) y)) (* y y)) (- (+ (* x x) y) y) (+ (+ (* x x) y) y) (+ y y) (+ (pow x 2) (* 2 y)) (+ (pow x 2) (* 2 y)) (+ (pow x 2) (* 2 y)) 0.091 * [simplify]: Sending expressions to egg_math: (* (* (exp (* h0 h0)) (exp h1)) (exp h1)) (* (exp (+ (* h0 h0) h1)) (exp h1)) (log (+ (+ (* h0 h0) h1) h1)) (exp (+ (+ (* h0 h0) h1) h1)) (* (cbrt (+ (+ (* h0 h0) h1) h1)) (cbrt (+ (+ (* h0 h0) h1) h1))) (cbrt (+ (+ (* h0 h0) h1) h1)) (* (* (+ (+ (* h0 h0) h1) h1) (+ (+ (* h0 h0) h1) h1)) (+ (+ (* h0 h0) h1) h1)) (sqrt (+ (+ (* h0 h0) h1) h1)) (sqrt (+ (+ (* h0 h0) h1) h1)) (+ (pow (+ (* h0 h0) h1) 3) (pow h1 3)) (+ (* (+ (* h0 h0) h1) (+ (* h0 h0) h1)) (- (* h1 h1) (* (+ (* h0 h0) h1) h1))) (- (* (+ (* h0 h0) h1) (+ (* h0 h0) h1)) (* h1 h1)) (- (+ (* h0 h0) h1) h1) (+ (+ (* h0 h0) h1) h1) (+ h1 h1) (+ (pow h0 2) (* 2 h1)) (+ (pow h0 2) (* 2 h1)) (+ (pow h0 2) (* 2 h1)) 0.094 * * [simplify]: iteration 0 : 91 enodes (cost 86 ) 0.098 * * [simplify]: iteration 1 : 310 enodes (cost 77 ) 0.104 * * [simplify]: iteration 2 : 1307 enodes (cost 71 ) 0.131 * * [simplify]: iteration 3 : 5002 enodes (cost 70 ) 0.131 * [simplify]: Simplified to: (exp (+ (+ (* x x) y) y)) (exp (+ (+ (* x x) y) y)) (log (+ (+ (* x x) y) y)) (exp (+ (+ (* x x) y) y)) (* (cbrt (+ (+ (* x x) y) y)) (cbrt (+ (+ (* x x) y) y))) (cbrt (+ (+ (* x x) y) y)) (pow (+ (+ (* x x) y) y) 3) (sqrt (+ (+ (* x x) y) y)) (sqrt (+ (+ (* x x) y) y)) (+ (pow (+ (* x x) y) 3) (pow y 3)) (+ (pow x 4) (* (+ (* x x) y) y)) (* (pow x 2) (+ (+ (* x x) y) y)) (pow x 2) (+ (+ (* x x) y) y) (+ y y) (+ (+ (* x x) y) y) (+ (+ (* x x) y) y) (+ (+ (* x x) y) y) 0.132 * * * [progress]: adding candidates to table 0.154 * * [progress]: iteration 2 / 4 0.154 * * * [progress]: picking best candidate 0.155 * * * * [pick]: Picked # 0.155 * * * [progress]: localizing error 0.159 * * * [progress]: generating rewritten candidates 0.159 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.183 * * * [progress]: generating series expansions 0.183 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.183 * [approximate]: Taking taylor expansion of (+ (pow x 2) (* 2 y)) in (x y) around 0 0.183 * [taylor]: Taking taylor expansion of (+ (pow x 2) (* 2 y)) in y 0.183 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.183 * [taylor]: Taking taylor expansion of x in y 0.183 * [taylor]: Taking taylor expansion of (* 2 y) in y 0.183 * [taylor]: Taking taylor expansion of 2 in y 0.183 * [taylor]: Taking taylor expansion of y in y 0.183 * [taylor]: Taking taylor expansion of (+ (pow x 2) (* 2 y)) in x 0.183 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.183 * [taylor]: Taking taylor expansion of x in x 0.183 * [taylor]: Taking taylor expansion of (* 2 y) in x 0.183 * [taylor]: Taking taylor expansion of 2 in x 0.183 * [taylor]: Taking taylor expansion of y in x 0.183 * [taylor]: Taking taylor expansion of (+ (pow x 2) (* 2 y)) in x 0.183 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.183 * [taylor]: Taking taylor expansion of x in x 0.183 * [taylor]: Taking taylor expansion of (* 2 y) in x 0.183 * [taylor]: Taking taylor expansion of 2 in x 0.183 * [taylor]: Taking taylor expansion of y in x 0.183 * [taylor]: Taking taylor expansion of (* 2 y) in y 0.183 * [taylor]: Taking taylor expansion of 2 in y 0.183 * [taylor]: Taking taylor expansion of y in y 0.185 * [taylor]: Taking taylor expansion of 0 in y 0.186 * [taylor]: Taking taylor expansion of 1 in y 0.188 * [taylor]: Taking taylor expansion of 0 in y 0.189 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (* 2 (/ 1 y))) in (x y) around 0 0.189 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (* 2 (/ 1 y))) in y 0.189 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.189 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.189 * [taylor]: Taking taylor expansion of x in y 0.189 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in y 0.189 * [taylor]: Taking taylor expansion of 2 in y 0.189 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.189 * [taylor]: Taking taylor expansion of y in y 0.189 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (* 2 (/ 1 y))) in x 0.189 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.189 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.189 * [taylor]: Taking taylor expansion of x in x 0.190 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in x 0.190 * [taylor]: Taking taylor expansion of 2 in x 0.190 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.190 * [taylor]: Taking taylor expansion of y in x 0.190 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (* 2 (/ 1 y))) in x 0.190 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.190 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.190 * [taylor]: Taking taylor expansion of x in x 0.190 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in x 0.190 * [taylor]: Taking taylor expansion of 2 in x 0.190 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.190 * [taylor]: Taking taylor expansion of y in x 0.191 * [taylor]: Taking taylor expansion of 1 in y 0.191 * [taylor]: Taking taylor expansion of 0 in y 0.193 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in y 0.193 * [taylor]: Taking taylor expansion of 2 in y 0.193 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.193 * [taylor]: Taking taylor expansion of y in y 0.195 * [taylor]: Taking taylor expansion of 0 in y 0.197 * [taylor]: Taking taylor expansion of 0 in y 0.198 * [approximate]: Taking taylor expansion of (- (/ 1 (pow x 2)) (* 2 (/ 1 y))) in (x y) around 0 0.198 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (* 2 (/ 1 y))) in y 0.198 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.198 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.198 * [taylor]: Taking taylor expansion of x in y 0.198 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in y 0.198 * [taylor]: Taking taylor expansion of 2 in y 0.198 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.198 * [taylor]: Taking taylor expansion of y in y 0.198 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (* 2 (/ 1 y))) in x 0.198 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.198 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.198 * [taylor]: Taking taylor expansion of x in x 0.199 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in x 0.199 * [taylor]: Taking taylor expansion of 2 in x 0.199 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.199 * [taylor]: Taking taylor expansion of y in x 0.199 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (* 2 (/ 1 y))) in x 0.199 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.199 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.199 * [taylor]: Taking taylor expansion of x in x 0.199 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in x 0.199 * [taylor]: Taking taylor expansion of 2 in x 0.199 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.199 * [taylor]: Taking taylor expansion of y in x 0.200 * [taylor]: Taking taylor expansion of 1 in y 0.201 * [taylor]: Taking taylor expansion of 0 in y 0.202 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 y))) in y 0.202 * [taylor]: Taking taylor expansion of (* 2 (/ 1 y)) in y 0.202 * [taylor]: Taking taylor expansion of 2 in y 0.202 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.202 * [taylor]: Taking taylor expansion of y in y 0.204 * [taylor]: Taking taylor expansion of 0 in y 0.207 * [taylor]: Taking taylor expansion of 0 in y 0.207 * * * [progress]: simplifying candidates 0.208 * [simplify]: Simplifying using # : (* (exp (* x x)) (* (exp y) (exp y))) (* (exp (* x x)) (exp (+ y y))) (log (+ (* x x) (+ y y))) (exp (+ (* x x) (+ y y))) (* (cbrt (+ (* x x) (+ y y))) (cbrt (+ (* x x) (+ y y)))) (cbrt (+ (* x x) (+ y y))) (* (* (+ (* x x) (+ y y)) (+ (* x x) (+ y y))) (+ (* x x) (+ y y))) (sqrt (+ (* x x) (+ y y))) (sqrt (+ (* x x) (+ y y))) (+ (pow (* x x) 3) (pow (+ y y) 3)) (+ (* (* x x) (* x x)) (- (* (+ y y) (+ y y)) (* (* x x) (+ y y)))) (- (* (* x x) (* x x)) (* (+ y y) (+ y y))) (- (* x x) (+ y y)) (+ (* x x) y) (+ (pow x 2) (* 2 y)) (+ (pow x 2) (* 2 y)) (+ (pow x 2) (* 2 y)) 0.208 * [simplify]: Sending expressions to egg_math: (* (exp (* h0 h0)) (* (exp h1) (exp h1))) (* (exp (* h0 h0)) (exp (+ h1 h1))) (log (+ (* h0 h0) (+ h1 h1))) (exp (+ (* h0 h0) (+ h1 h1))) (* (cbrt (+ (* h0 h0) (+ h1 h1))) (cbrt (+ (* h0 h0) (+ h1 h1)))) (cbrt (+ (* h0 h0) (+ h1 h1))) (* (* (+ (* h0 h0) (+ h1 h1)) (+ (* h0 h0) (+ h1 h1))) (+ (* h0 h0) (+ h1 h1))) (sqrt (+ (* h0 h0) (+ h1 h1))) (sqrt (+ (* h0 h0) (+ h1 h1))) (+ (pow (* h0 h0) 3) (pow (+ h1 h1) 3)) (+ (* (* h0 h0) (* h0 h0)) (- (* (+ h1 h1) (+ h1 h1)) (* (* h0 h0) (+ h1 h1)))) (- (* (* h0 h0) (* h0 h0)) (* (+ h1 h1) (+ h1 h1))) (- (* h0 h0) (+ h1 h1)) (+ (* h0 h0) h1) (+ (pow h0 2) (* 2 h1)) (+ (pow h0 2) (* 2 h1)) (+ (pow h0 2) (* 2 h1)) 0.211 * * [simplify]: iteration 0 : 103 enodes (cost 83 ) 0.214 * * [simplify]: iteration 1 : 468 enodes (cost 74 ) 0.224 * * [simplify]: iteration 2 : 1756 enodes (cost 74 ) 0.265 * * [simplify]: iteration 3 : 5002 enodes (cost 74 ) 0.266 * [simplify]: Simplified to: (exp (+ (* x x) (+ y y))) (exp (+ (* x x) (+ y y))) (log (+ (* x x) (+ y y))) (exp (+ (* x x) (+ y y))) (* (cbrt (+ (* x x) (+ y y))) (cbrt (+ (* x x) (+ y y)))) (cbrt (+ (* x x) (+ y y))) (pow (+ (* x x) (+ y y)) 3) (sqrt (+ (* x x) (+ y y))) (sqrt (+ (* x x) (+ y y))) (+ (pow (* x x) 3) (pow (+ y y) 3)) (- (* 4 (* y y)) (- (* (* x x) (+ y y)) (pow x 4))) (+ (- (* (+ y y) (+ y y))) (pow x 4)) (- (* x x) (+ y y)) (+ (* x x) y) (+ (* x x) (+ y y)) (+ (* x x) (+ y y)) (+ (* x x) (+ y y)) 0.266 * * * [progress]: adding candidates to table 0.291 * [progress]: [Phase 3 of 3] Extracting. 0.292 * [simplify]: Simplifying using # : (+ (* x x) (+ y y)) 0.292 * [simplify]: Sending expressions to egg_math: (+ (* h0 h0) (+ h1 h1)) 0.292 * * [simplify]: iteration 0 : 6 enodes (cost 3 ) 0.293 * * [simplify]: iteration 1 : 6 enodes (cost 3 ) 0.293 * [simplify]: Simplified to: (+ (* x x) (+ y y)) 0.732 * [regime-testing]: End program error score: 0.005089916929324431 0.751 * [regime-testing]: Target error score: 0.005089916929324431