11.866 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.030 * * * [progress]: [2/2] Setting up program. 0.033 * [progress]: [Phase 2 of 3] Improving. 0.033 * [simplify]: Simplifying using # : (sqrt (+ (+ (* x x) (* y y)) (* z z))) 0.037 * * [simplify]: iteration 0 : 14 enodes (cost 6 ) 0.039 * * [simplify]: iteration 1 : 25 enodes (cost 6 ) 0.042 * * [simplify]: iteration 2 : 31 enodes (cost 6 ) 0.045 * * [simplify]: iteration 3 : 32 enodes (cost 6 ) 0.047 * * [simplify]: iteration 4 : 32 enodes (cost 6 ) 0.047 * [simplify]: Simplified to: (sqrt (+ (+ (* x x) (* y y)) (* z z))) 0.048 * * [progress]: iteration 1 / 4 0.048 * * * [progress]: picking best candidate 0.050 * * * * [pick]: Picked # 0.050 * * * [progress]: localizing error 0.059 * * * [progress]: generating rewritten candidates 0.059 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.075 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.088 * * * [progress]: generating series expansions 0.088 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.089 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in (x y z) around 0 0.089 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in z 0.089 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in z 0.089 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.089 * [taylor]: Taking taylor expansion of x in z 0.089 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in z 0.089 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.089 * [taylor]: Taking taylor expansion of y in z 0.089 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.089 * [taylor]: Taking taylor expansion of z in z 0.090 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in y 0.090 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in y 0.090 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.091 * [taylor]: Taking taylor expansion of x in y 0.091 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.091 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.091 * [taylor]: Taking taylor expansion of y in y 0.091 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.091 * [taylor]: Taking taylor expansion of z in y 0.092 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in x 0.092 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in x 0.092 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.092 * [taylor]: Taking taylor expansion of x in x 0.092 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in x 0.092 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.092 * [taylor]: Taking taylor expansion of y in x 0.092 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.092 * [taylor]: Taking taylor expansion of z in x 0.093 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in x 0.093 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in x 0.093 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.093 * [taylor]: Taking taylor expansion of x in x 0.093 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in x 0.093 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.093 * [taylor]: Taking taylor expansion of y in x 0.093 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.093 * [taylor]: Taking taylor expansion of z in x 0.095 * [taylor]: Taking taylor expansion of (sqrt (+ (pow y 2) (pow z 2))) in y 0.095 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.095 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.095 * [taylor]: Taking taylor expansion of y in y 0.095 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.095 * [taylor]: Taking taylor expansion of z in y 0.095 * [taylor]: Taking taylor expansion of z in z 0.096 * [taylor]: Taking taylor expansion of 0 in y 0.096 * [taylor]: Taking taylor expansion of 0 in z 0.096 * [taylor]: Taking taylor expansion of 0 in z 0.098 * [taylor]: Taking taylor expansion of (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) in y 0.098 * [taylor]: Taking taylor expansion of 1/2 in y 0.098 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (+ (pow y 2) (pow z 2)))) in y 0.098 * [taylor]: Taking taylor expansion of (/ 1 (+ (pow y 2) (pow z 2))) in y 0.098 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.098 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.098 * [taylor]: Taking taylor expansion of y in y 0.098 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.098 * [taylor]: Taking taylor expansion of z in y 0.099 * [taylor]: Taking taylor expansion of (/ 1/2 z) in z 0.099 * [taylor]: Taking taylor expansion of 1/2 in z 0.099 * [taylor]: Taking taylor expansion of z in z 0.100 * [taylor]: Taking taylor expansion of 0 in z 0.101 * [taylor]: Taking taylor expansion of (/ 1/2 z) in z 0.101 * [taylor]: Taking taylor expansion of 1/2 in z 0.101 * [taylor]: Taking taylor expansion of z in z 0.103 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in (x y z) around 0 0.103 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in z 0.103 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.103 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.103 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.103 * [taylor]: Taking taylor expansion of x in z 0.103 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.103 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.103 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.103 * [taylor]: Taking taylor expansion of z in z 0.104 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.104 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.104 * [taylor]: Taking taylor expansion of y in z 0.110 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in y 0.110 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.111 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.111 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.111 * [taylor]: Taking taylor expansion of x in y 0.111 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.111 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.111 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.111 * [taylor]: Taking taylor expansion of z in y 0.111 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.111 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.111 * [taylor]: Taking taylor expansion of y in y 0.114 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.114 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.114 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.114 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.114 * [taylor]: Taking taylor expansion of x in x 0.115 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.115 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.115 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.115 * [taylor]: Taking taylor expansion of z in x 0.115 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.115 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.115 * [taylor]: Taking taylor expansion of y in x 0.117 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.117 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.117 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.117 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.117 * [taylor]: Taking taylor expansion of x in x 0.118 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.118 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.118 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.118 * [taylor]: Taking taylor expansion of z in x 0.118 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.118 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.118 * [taylor]: Taking taylor expansion of y in x 0.120 * [taylor]: Taking taylor expansion of 1 in y 0.121 * [taylor]: Taking taylor expansion of 0 in y 0.121 * [taylor]: Taking taylor expansion of 1 in z 0.123 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.123 * [taylor]: Taking taylor expansion of 1/2 in y 0.123 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.123 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.123 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.123 * [taylor]: Taking taylor expansion of z in y 0.124 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.124 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.124 * [taylor]: Taking taylor expansion of y in y 0.126 * [taylor]: Taking taylor expansion of 0 in z 0.126 * [taylor]: Taking taylor expansion of 0 in z 0.126 * [taylor]: Taking taylor expansion of 0 in z 0.129 * [taylor]: Taking taylor expansion of 0 in y 0.131 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (pow z 2))) in z 0.131 * [taylor]: Taking taylor expansion of 1/2 in z 0.131 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.131 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.131 * [taylor]: Taking taylor expansion of z in z 0.133 * [taylor]: Taking taylor expansion of 0 in z 0.133 * [taylor]: Taking taylor expansion of 0 in z 0.137 * [taylor]: Taking taylor expansion of (* -1/2 (+ (* 1/4 (/ 1 (pow z 4))) (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4)))))) in y 0.137 * [taylor]: Taking taylor expansion of -1/2 in y 0.137 * [taylor]: Taking taylor expansion of (+ (* 1/4 (/ 1 (pow z 4))) (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4))))) in y 0.137 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow z 4))) in y 0.137 * [taylor]: Taking taylor expansion of 1/4 in y 0.137 * [taylor]: Taking taylor expansion of (/ 1 (pow z 4)) in y 0.137 * [taylor]: Taking taylor expansion of (pow z 4) in y 0.137 * [taylor]: Taking taylor expansion of z in y 0.137 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4)))) in y 0.138 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) in y 0.138 * [taylor]: Taking taylor expansion of 1/2 in y 0.138 * [taylor]: Taking taylor expansion of (/ 1 (* (pow z 2) (pow y 2))) in y 0.138 * [taylor]: Taking taylor expansion of (* (pow z 2) (pow y 2)) in y 0.138 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.138 * [taylor]: Taking taylor expansion of z in y 0.138 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.138 * [taylor]: Taking taylor expansion of y in y 0.138 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow y 4))) in y 0.138 * [taylor]: Taking taylor expansion of 1/4 in y 0.138 * [taylor]: Taking taylor expansion of (/ 1 (pow y 4)) in y 0.138 * [taylor]: Taking taylor expansion of (pow y 4) in y 0.138 * [taylor]: Taking taylor expansion of y in y 0.149 * [taylor]: Taking taylor expansion of 0 in z 0.149 * [taylor]: Taking taylor expansion of 0 in z 0.152 * [taylor]: Taking taylor expansion of 0 in z 0.152 * [taylor]: Taking taylor expansion of 0 in z 0.152 * [taylor]: Taking taylor expansion of 0 in z 0.154 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in (x y z) around 0 0.154 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in z 0.154 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.154 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.154 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.154 * [taylor]: Taking taylor expansion of x in z 0.154 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.154 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.154 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.154 * [taylor]: Taking taylor expansion of z in z 0.155 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.155 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.155 * [taylor]: Taking taylor expansion of y in z 0.158 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in y 0.158 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.158 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.158 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.158 * [taylor]: Taking taylor expansion of x in y 0.158 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.158 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.158 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.158 * [taylor]: Taking taylor expansion of z in y 0.158 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.158 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.158 * [taylor]: Taking taylor expansion of y in y 0.161 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.161 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.161 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.161 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.161 * [taylor]: Taking taylor expansion of x in x 0.162 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.162 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.162 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.162 * [taylor]: Taking taylor expansion of z in x 0.162 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.162 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.162 * [taylor]: Taking taylor expansion of y in x 0.164 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.164 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.164 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.164 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.164 * [taylor]: Taking taylor expansion of x in x 0.165 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.165 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.165 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.165 * [taylor]: Taking taylor expansion of z in x 0.165 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.165 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.165 * [taylor]: Taking taylor expansion of y in x 0.167 * [taylor]: Taking taylor expansion of 1 in y 0.168 * [taylor]: Taking taylor expansion of 0 in y 0.168 * [taylor]: Taking taylor expansion of 1 in z 0.170 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.170 * [taylor]: Taking taylor expansion of 1/2 in y 0.170 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.170 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.170 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.170 * [taylor]: Taking taylor expansion of z in y 0.171 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.171 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.171 * [taylor]: Taking taylor expansion of y in y 0.173 * [taylor]: Taking taylor expansion of 0 in z 0.173 * [taylor]: Taking taylor expansion of 0 in z 0.173 * [taylor]: Taking taylor expansion of 0 in z 0.176 * [taylor]: Taking taylor expansion of 0 in y 0.177 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (pow z 2))) in z 0.177 * [taylor]: Taking taylor expansion of 1/2 in z 0.178 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.178 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.178 * [taylor]: Taking taylor expansion of z in z 0.180 * [taylor]: Taking taylor expansion of 0 in z 0.180 * [taylor]: Taking taylor expansion of 0 in z 0.184 * [taylor]: Taking taylor expansion of (* -1/2 (+ (* 1/4 (/ 1 (pow z 4))) (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4)))))) in y 0.184 * [taylor]: Taking taylor expansion of -1/2 in y 0.184 * [taylor]: Taking taylor expansion of (+ (* 1/4 (/ 1 (pow z 4))) (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4))))) in y 0.184 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow z 4))) in y 0.184 * [taylor]: Taking taylor expansion of 1/4 in y 0.184 * [taylor]: Taking taylor expansion of (/ 1 (pow z 4)) in y 0.184 * [taylor]: Taking taylor expansion of (pow z 4) in y 0.184 * [taylor]: Taking taylor expansion of z in y 0.184 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4)))) in y 0.184 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) in y 0.184 * [taylor]: Taking taylor expansion of 1/2 in y 0.184 * [taylor]: Taking taylor expansion of (/ 1 (* (pow z 2) (pow y 2))) in y 0.184 * [taylor]: Taking taylor expansion of (* (pow z 2) (pow y 2)) in y 0.184 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.184 * [taylor]: Taking taylor expansion of z in y 0.184 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.184 * [taylor]: Taking taylor expansion of y in y 0.185 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow y 4))) in y 0.185 * [taylor]: Taking taylor expansion of 1/4 in y 0.185 * [taylor]: Taking taylor expansion of (/ 1 (pow y 4)) in y 0.185 * [taylor]: Taking taylor expansion of (pow y 4) in y 0.185 * [taylor]: Taking taylor expansion of y in y 0.196 * [taylor]: Taking taylor expansion of 0 in z 0.196 * [taylor]: Taking taylor expansion of 0 in z 0.198 * [taylor]: Taking taylor expansion of 0 in z 0.199 * [taylor]: Taking taylor expansion of 0 in z 0.199 * [taylor]: Taking taylor expansion of 0 in z 0.200 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.201 * [approximate]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in (x y z) around 0 0.201 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in z 0.201 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.201 * [taylor]: Taking taylor expansion of x in z 0.201 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in z 0.201 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.201 * [taylor]: Taking taylor expansion of y in z 0.201 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.201 * [taylor]: Taking taylor expansion of z in z 0.201 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in y 0.201 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.201 * [taylor]: Taking taylor expansion of x in y 0.201 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.201 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.201 * [taylor]: Taking taylor expansion of y in y 0.201 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.201 * [taylor]: Taking taylor expansion of z in y 0.201 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in x 0.201 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.201 * [taylor]: Taking taylor expansion of x in x 0.201 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in x 0.201 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.201 * [taylor]: Taking taylor expansion of y in x 0.201 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.201 * [taylor]: Taking taylor expansion of z in x 0.201 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in x 0.201 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.201 * [taylor]: Taking taylor expansion of x in x 0.201 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in x 0.201 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.205 * [taylor]: Taking taylor expansion of y in x 0.205 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.205 * [taylor]: Taking taylor expansion of z in x 0.205 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.205 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.206 * [taylor]: Taking taylor expansion of y in y 0.206 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.206 * [taylor]: Taking taylor expansion of z in y 0.206 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.206 * [taylor]: Taking taylor expansion of z in z 0.207 * [taylor]: Taking taylor expansion of 0 in y 0.207 * [taylor]: Taking taylor expansion of 0 in z 0.207 * [taylor]: Taking taylor expansion of 0 in z 0.209 * [taylor]: Taking taylor expansion of 1 in y 0.209 * [taylor]: Taking taylor expansion of 1 in z 0.209 * [taylor]: Taking taylor expansion of 0 in z 0.210 * [taylor]: Taking taylor expansion of 1 in z 0.211 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in (x y z) around 0 0.211 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.211 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.211 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.211 * [taylor]: Taking taylor expansion of x in z 0.211 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.211 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.211 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.211 * [taylor]: Taking taylor expansion of z in z 0.212 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.212 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.212 * [taylor]: Taking taylor expansion of y in z 0.212 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.212 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.212 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.212 * [taylor]: Taking taylor expansion of x in y 0.212 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.212 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.212 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.212 * [taylor]: Taking taylor expansion of z in y 0.212 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.213 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.213 * [taylor]: Taking taylor expansion of y in y 0.213 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.213 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.213 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.213 * [taylor]: Taking taylor expansion of x in x 0.214 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.214 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.214 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.214 * [taylor]: Taking taylor expansion of z in x 0.214 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.214 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.214 * [taylor]: Taking taylor expansion of y in x 0.214 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.214 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.214 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.214 * [taylor]: Taking taylor expansion of x in x 0.215 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.215 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.215 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.215 * [taylor]: Taking taylor expansion of z in x 0.215 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.215 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.215 * [taylor]: Taking taylor expansion of y in x 0.216 * [taylor]: Taking taylor expansion of 1 in y 0.217 * [taylor]: Taking taylor expansion of 0 in y 0.218 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.218 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.218 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.218 * [taylor]: Taking taylor expansion of z in y 0.219 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.219 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.219 * [taylor]: Taking taylor expansion of y in y 0.219 * [taylor]: Taking taylor expansion of 1 in z 0.220 * [taylor]: Taking taylor expansion of 1 in z 0.222 * [taylor]: Taking taylor expansion of 0 in y 0.223 * [taylor]: Taking taylor expansion of 0 in z 0.223 * [taylor]: Taking taylor expansion of 0 in z 0.223 * [taylor]: Taking taylor expansion of 0 in z 0.226 * [taylor]: Taking taylor expansion of 0 in y 0.227 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.227 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.227 * [taylor]: Taking taylor expansion of z in z 0.228 * [taylor]: Taking taylor expansion of 0 in z 0.228 * [taylor]: Taking taylor expansion of 0 in z 0.229 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in (x y z) around 0 0.229 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.229 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.229 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.229 * [taylor]: Taking taylor expansion of x in z 0.229 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.229 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.229 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.229 * [taylor]: Taking taylor expansion of z in z 0.230 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.230 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.230 * [taylor]: Taking taylor expansion of y in z 0.230 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.230 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.230 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.230 * [taylor]: Taking taylor expansion of x in y 0.230 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.230 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.230 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.230 * [taylor]: Taking taylor expansion of z in y 0.231 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.231 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.231 * [taylor]: Taking taylor expansion of y in y 0.231 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.231 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.231 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.231 * [taylor]: Taking taylor expansion of x in x 0.232 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.232 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.232 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.232 * [taylor]: Taking taylor expansion of z in x 0.232 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.232 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.232 * [taylor]: Taking taylor expansion of y in x 0.232 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.232 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.232 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.232 * [taylor]: Taking taylor expansion of x in x 0.233 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.233 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.233 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.233 * [taylor]: Taking taylor expansion of z in x 0.233 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.233 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.233 * [taylor]: Taking taylor expansion of y in x 0.234 * [taylor]: Taking taylor expansion of 1 in y 0.235 * [taylor]: Taking taylor expansion of 0 in y 0.236 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.236 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.236 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.236 * [taylor]: Taking taylor expansion of z in y 0.237 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.237 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.237 * [taylor]: Taking taylor expansion of y in y 0.237 * [taylor]: Taking taylor expansion of 1 in z 0.238 * [taylor]: Taking taylor expansion of 1 in z 0.240 * [taylor]: Taking taylor expansion of 0 in y 0.241 * [taylor]: Taking taylor expansion of 0 in z 0.241 * [taylor]: Taking taylor expansion of 0 in z 0.241 * [taylor]: Taking taylor expansion of 0 in z 0.244 * [taylor]: Taking taylor expansion of 0 in y 0.245 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.245 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.245 * [taylor]: Taking taylor expansion of z in z 0.246 * [taylor]: Taking taylor expansion of 0 in z 0.246 * [taylor]: Taking taylor expansion of 0 in z 0.247 * * * [progress]: simplifying candidates 0.247 * [simplify]: Simplifying using # : (expm1 (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (log1p (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (exp (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (* (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (* (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z))))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt 1) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (pow (+ (* x x) (* y y)) 3) (pow (* z z) 3))) (sqrt (+ (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (- (* (* z z) (* z z)) (* (+ (* x x) (* y y)) (* z z))))) (sqrt (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (* (* z z) (* z z)))) (sqrt (- (+ (* x x) (* y y)) (* z z))) (/ 1 2) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (expm1 (+ (+ (* x x) (* y y)) (* z z))) (log1p (+ (+ (* x x) (* y y)) (* z z))) (* (* (exp (* x x)) (exp (* y y))) (exp (* z z))) (* (exp (+ (* x x) (* y y))) (exp (* z z))) (log (+ (+ (* x x) (* y y)) (* z z))) (exp (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (+ (+ (* x x) (* y y)) (* z z))) (* (* (+ (+ (* x x) (* y y)) (* z z)) (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (pow (+ (* x x) (* y y)) 3) (pow (* z z) 3)) (+ (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (- (* (* z z) (* z z)) (* (+ (* x x) (* y y)) (* z z)))) (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (* (* z z) (* z z))) (- (+ (* x x) (* y y)) (* z z)) (+ (* y y) (* z z)) z x (* -1 x) (+ (pow x 2) (+ (pow y 2) (pow z 2))) (+ (pow x 2) (+ (pow y 2) (pow z 2))) (+ (pow x 2) (+ (pow y 2) (pow z 2))) 0.253 * * [simplify]: iteration 0 : 152 enodes (cost 287 ) 0.259 * * [simplify]: iteration 1 : 659 enodes (cost 259 ) 0.274 * * [simplify]: iteration 2 : 2778 enodes (cost 251 ) 0.335 * * [simplify]: iteration 3 : 5002 enodes (cost 248 ) 0.337 * [simplify]: Simplified to: (expm1 (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (log1p (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (exp (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (* (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (pow (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3) (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) 1 (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot (pow z 3) (pow (fma x x (* y y)) 3/2)) (sqrt (+ (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (- (* (* z z) (* z z)) (* (+ (* x x) (* y y)) (* z z))))) (sqrt (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (* (* z z) (* z z)))) (sqrt (- (+ (* x x) (* y y)) (* z z))) 1/2 (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (expm1 (+ (+ (* x x) (* y y)) (* z z))) (log1p (+ (+ (* x x) (* y y)) (* z z))) (exp (fma x x (fma y y (* z z)))) (exp (fma x x (fma y y (* z z)))) (log (+ (+ (* x x) (* y y)) (* z z))) (exp (fma x x (fma y y (* z z)))) (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (+ (+ (* x x) (* y y)) (* z z))) (pow (fma x x (fma y y (* z z))) 3) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (fma z (pow z 5) (pow (fma x x (* y y)) 3)) (fma (fma x x (* y y)) (fma x x (- (pow y 2) (pow z 2))) (pow z 4)) (* (fma x x (- (pow y 2) (pow z 2))) (fma x x (fma y y (* z z)))) (fma x x (- (pow y 2) (pow z 2))) (fma y y (* z z)) z x (* -1 x) (fma x x (fma y y (* z z))) (fma x x (fma y y (* z z))) (fma x x (fma y y (* z z))) 0.337 * * * [progress]: adding candidates to table 0.463 * * [progress]: iteration 2 / 4 0.463 * * * [progress]: picking best candidate 0.469 * * * * [pick]: Picked # 0.469 * * * [progress]: localizing error 0.477 * * * [progress]: generating rewritten candidates 0.477 * * * * [progress]: [ 1 / 1 ] rewriting at (2 1) 0.482 * * * [progress]: generating series expansions 0.482 * * * * [progress]: [ 1 / 1 ] generating series at (2 1) 0.482 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in (x y) around 0 0.482 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in y 0.482 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in y 0.482 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.482 * [taylor]: Taking taylor expansion of x in y 0.482 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.482 * [taylor]: Taking taylor expansion of y in y 0.483 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in x 0.483 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.483 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.483 * [taylor]: Taking taylor expansion of x in x 0.483 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.483 * [taylor]: Taking taylor expansion of y in x 0.484 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in x 0.484 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.484 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.484 * [taylor]: Taking taylor expansion of x in x 0.484 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.484 * [taylor]: Taking taylor expansion of y in x 0.485 * [taylor]: Taking taylor expansion of y in y 0.485 * [taylor]: Taking taylor expansion of 0 in y 0.486 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.486 * [taylor]: Taking taylor expansion of 1/2 in y 0.486 * [taylor]: Taking taylor expansion of y in y 0.488 * [taylor]: Taking taylor expansion of 0 in y 0.489 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in (x y) around 0 0.489 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in y 0.489 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.489 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.489 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.489 * [taylor]: Taking taylor expansion of x in y 0.489 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.490 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.490 * [taylor]: Taking taylor expansion of y in y 0.492 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.492 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.492 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.492 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.492 * [taylor]: Taking taylor expansion of x in x 0.493 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.493 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.493 * [taylor]: Taking taylor expansion of y in x 0.495 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.495 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.495 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.495 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.495 * [taylor]: Taking taylor expansion of x in x 0.496 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.496 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.496 * [taylor]: Taking taylor expansion of y in x 0.498 * [taylor]: Taking taylor expansion of 1 in y 0.498 * [taylor]: Taking taylor expansion of 0 in y 0.504 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.504 * [taylor]: Taking taylor expansion of 1/2 in y 0.504 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.504 * [taylor]: Taking taylor expansion of y in y 0.508 * [taylor]: Taking taylor expansion of 0 in y 0.510 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in (x y) around 0 0.510 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in y 0.510 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.510 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.510 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.510 * [taylor]: Taking taylor expansion of x in y 0.510 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.510 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.510 * [taylor]: Taking taylor expansion of y in y 0.513 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.513 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.513 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.513 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.513 * [taylor]: Taking taylor expansion of x in x 0.513 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.513 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.514 * [taylor]: Taking taylor expansion of y in x 0.516 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.516 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.516 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.516 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.516 * [taylor]: Taking taylor expansion of x in x 0.516 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.516 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.516 * [taylor]: Taking taylor expansion of y in x 0.519 * [taylor]: Taking taylor expansion of 1 in y 0.519 * [taylor]: Taking taylor expansion of 0 in y 0.521 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.521 * [taylor]: Taking taylor expansion of 1/2 in y 0.521 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.521 * [taylor]: Taking taylor expansion of y in y 0.525 * [taylor]: Taking taylor expansion of 0 in y 0.526 * * * [progress]: simplifying candidates 0.526 * [simplify]: Simplifying using # : (expm1 (sqrt (+ (* x x) (* y y)))) (log1p (sqrt (+ (* x x) (* y y)))) (log (sqrt (+ (* x x) (* y y)))) (exp (sqrt (+ (* x x) (* y y)))) (* (cbrt (sqrt (+ (* x x) (* y y)))) (cbrt (sqrt (+ (* x x) (* y y))))) (cbrt (sqrt (+ (* x x) (* y y)))) (* (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y)))) (sqrt (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y))))) (sqrt (cbrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt 1) (sqrt (+ (* x x) (* y y))) (sqrt (+ (pow (* x x) 3) (pow (* y y) 3))) (sqrt (+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))) (sqrt (- (* (* x x) (* x x)) (* (* y y) (* y y)))) (sqrt (- (* x x) (* y y))) (/ 1 2) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) y x (* -1 x) 0.531 * * [simplify]: iteration 0 : 98 enodes (cost 103 ) 0.535 * * [simplify]: iteration 1 : 254 enodes (cost 98 ) 0.542 * * [simplify]: iteration 2 : 619 enodes (cost 98 ) 0.557 * * [simplify]: iteration 3 : 1573 enodes (cost 98 ) 0.594 * * [simplify]: iteration 4 : 5001 enodes (cost 98 ) 0.596 * [simplify]: Simplified to: (expm1 (sqrt (+ (* x x) (* y y)))) (log1p (sqrt (+ (* x x) (* y y)))) (log (sqrt (+ (* x x) (* y y)))) (exp (sqrt (+ (* x x) (* y y)))) (* (cbrt (sqrt (+ (* x x) (* y y)))) (cbrt (sqrt (+ (* x x) (* y y))))) (cbrt (sqrt (+ (* x x) (* y y)))) (pow (hypot x y) 3) (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (cbrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt 1) (hypot x y) (hypot (pow y 3) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))) (sqrt (- (* (* x x) (* x x)) (* (* y y) (* y y)))) (sqrt (- (* x x) (* y y))) 1/2 (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) y x (* -1 x) 0.596 * * * [progress]: adding candidates to table 0.662 * * [progress]: iteration 3 / 4 0.662 * * * [progress]: picking best candidate 0.664 * * * * [pick]: Picked # 0.664 * * * [progress]: localizing error 0.669 * * * [progress]: generating rewritten candidates 0.669 * * * * [progress]: [ 1 / 1 ] rewriting at (2 1) 0.670 * * * [progress]: generating series expansions 0.670 * * * * [progress]: [ 1 / 1 ] generating series at (2 1) 0.670 * [approximate]: Taking taylor expansion of (hypot x y) in (x y) around 0 0.670 * [taylor]: Taking taylor expansion of (hypot x y) in y 0.670 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* y y))) 0.670 * [taylor]: Taking taylor expansion of (+ (* x x) (* y y)) in y 0.670 * [taylor]: Taking taylor expansion of (* x x) in y 0.670 * [taylor]: Taking taylor expansion of x in y 0.670 * [taylor]: Taking taylor expansion of x in y 0.670 * [taylor]: Taking taylor expansion of (* y y) in y 0.670 * [taylor]: Taking taylor expansion of y in y 0.670 * [taylor]: Taking taylor expansion of y in y 0.672 * [taylor]: Taking taylor expansion of (hypot x y) in x 0.672 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* y y))) 0.672 * [taylor]: Taking taylor expansion of (+ (* x x) (* y y)) in x 0.672 * [taylor]: Taking taylor expansion of (* x x) in x 0.672 * [taylor]: Taking taylor expansion of x in x 0.672 * [taylor]: Taking taylor expansion of x in x 0.672 * [taylor]: Taking taylor expansion of (* y y) in x 0.672 * [taylor]: Taking taylor expansion of y in x 0.672 * [taylor]: Taking taylor expansion of y in x 0.674 * [taylor]: Taking taylor expansion of (hypot x y) in x 0.674 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* y y))) 0.674 * [taylor]: Taking taylor expansion of (+ (* x x) (* y y)) in x 0.674 * [taylor]: Taking taylor expansion of (* x x) in x 0.674 * [taylor]: Taking taylor expansion of x in x 0.674 * [taylor]: Taking taylor expansion of x in x 0.674 * [taylor]: Taking taylor expansion of (* y y) in x 0.674 * [taylor]: Taking taylor expansion of y in x 0.674 * [taylor]: Taking taylor expansion of y in x 0.675 * [taylor]: Taking taylor expansion of y in y 0.675 * [taylor]: Taking taylor expansion of 0 in y 0.677 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.677 * [taylor]: Taking taylor expansion of 1/2 in y 0.677 * [taylor]: Taking taylor expansion of y in y 0.679 * [taylor]: Taking taylor expansion of 0 in y 0.680 * [approximate]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in (x y) around 0 0.680 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in y 0.680 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y)))) 0.680 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y))) in y 0.680 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in y 0.680 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.680 * [taylor]: Taking taylor expansion of x in y 0.680 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.680 * [taylor]: Taking taylor expansion of x in y 0.680 * [taylor]: Taking taylor expansion of (* (/ 1 y) (/ 1 y)) in y 0.680 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.680 * [taylor]: Taking taylor expansion of y in y 0.681 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.681 * [taylor]: Taking taylor expansion of y in y 0.684 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in x 0.684 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y)))) 0.684 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y))) in x 0.684 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in x 0.684 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.684 * [taylor]: Taking taylor expansion of x in x 0.684 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.684 * [taylor]: Taking taylor expansion of x in x 0.684 * [taylor]: Taking taylor expansion of (* (/ 1 y) (/ 1 y)) in x 0.685 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.685 * [taylor]: Taking taylor expansion of y in x 0.685 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.685 * [taylor]: Taking taylor expansion of y in x 0.687 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in x 0.687 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y)))) 0.687 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y))) in x 0.688 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in x 0.688 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.688 * [taylor]: Taking taylor expansion of x in x 0.688 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.688 * [taylor]: Taking taylor expansion of x in x 0.688 * [taylor]: Taking taylor expansion of (* (/ 1 y) (/ 1 y)) in x 0.688 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.688 * [taylor]: Taking taylor expansion of y in x 0.688 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.688 * [taylor]: Taking taylor expansion of y in x 0.691 * [taylor]: Taking taylor expansion of 1 in y 0.691 * [taylor]: Taking taylor expansion of 0 in y 0.694 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.694 * [taylor]: Taking taylor expansion of 1/2 in y 0.694 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.694 * [taylor]: Taking taylor expansion of y in y 0.698 * [taylor]: Taking taylor expansion of 0 in y 0.699 * [approximate]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in (x y) around 0 0.699 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in y 0.699 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y)))) 0.699 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y))) in y 0.699 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in y 0.699 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.699 * [taylor]: Taking taylor expansion of -1 in y 0.699 * [taylor]: Taking taylor expansion of x in y 0.699 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.699 * [taylor]: Taking taylor expansion of -1 in y 0.699 * [taylor]: Taking taylor expansion of x in y 0.699 * [taylor]: Taking taylor expansion of (* (/ -1 y) (/ -1 y)) in y 0.699 * [taylor]: Taking taylor expansion of (/ -1 y) in y 0.699 * [taylor]: Taking taylor expansion of -1 in y 0.699 * [taylor]: Taking taylor expansion of y in y 0.700 * [taylor]: Taking taylor expansion of (/ -1 y) in y 0.700 * [taylor]: Taking taylor expansion of -1 in y 0.700 * [taylor]: Taking taylor expansion of y in y 0.703 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in x 0.703 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y)))) 0.703 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y))) in x 0.703 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in x 0.703 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.703 * [taylor]: Taking taylor expansion of -1 in x 0.703 * [taylor]: Taking taylor expansion of x in x 0.703 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.704 * [taylor]: Taking taylor expansion of -1 in x 0.704 * [taylor]: Taking taylor expansion of x in x 0.704 * [taylor]: Taking taylor expansion of (* (/ -1 y) (/ -1 y)) in x 0.704 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.704 * [taylor]: Taking taylor expansion of -1 in x 0.704 * [taylor]: Taking taylor expansion of y in x 0.704 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.704 * [taylor]: Taking taylor expansion of -1 in x 0.704 * [taylor]: Taking taylor expansion of y in x 0.707 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in x 0.707 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y)))) 0.707 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y))) in x 0.707 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in x 0.707 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.707 * [taylor]: Taking taylor expansion of -1 in x 0.707 * [taylor]: Taking taylor expansion of x in x 0.707 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.707 * [taylor]: Taking taylor expansion of -1 in x 0.708 * [taylor]: Taking taylor expansion of x in x 0.708 * [taylor]: Taking taylor expansion of (* (/ -1 y) (/ -1 y)) in x 0.708 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.708 * [taylor]: Taking taylor expansion of -1 in x 0.708 * [taylor]: Taking taylor expansion of y in x 0.708 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.708 * [taylor]: Taking taylor expansion of -1 in x 0.708 * [taylor]: Taking taylor expansion of y in x 0.711 * [taylor]: Taking taylor expansion of 1 in y 0.711 * [taylor]: Taking taylor expansion of 0 in y 0.714 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.714 * [taylor]: Taking taylor expansion of 1/2 in y 0.714 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.714 * [taylor]: Taking taylor expansion of y in y 0.718 * [taylor]: Taking taylor expansion of 0 in y 0.719 * * * [progress]: simplifying candidates 0.720 * [simplify]: Simplifying using # : (expm1 (hypot x y)) (log1p (hypot x y)) (+ (* x x) (* y y)) (log (hypot x y)) (exp (hypot x y)) (* (cbrt (hypot x y)) (cbrt (hypot x y))) (cbrt (hypot x y)) (* (* (hypot x y) (hypot x y)) (hypot x y)) (sqrt (hypot x y)) (sqrt (hypot x y)) y x (* -1 x) 0.728 * * [simplify]: iteration 0 : 22 enodes (cost 27 ) 0.731 * * [simplify]: iteration 1 : 25 enodes (cost 24 ) 0.734 * * [simplify]: iteration 2 : 29 enodes (cost 24 ) 0.736 * * [simplify]: iteration 3 : 34 enodes (cost 24 ) 0.739 * * [simplify]: iteration 4 : 53 enodes (cost 24 ) 0.742 * * [simplify]: iteration 5 : 107 enodes (cost 24 ) 0.749 * * [simplify]: iteration 6 : 513 enodes (cost 24 ) 0.769 * * [simplify]: iteration 7 : 1687 enodes (cost 24 ) 0.845 * * [simplify]: iteration 8 : 5001 enodes (cost 24 ) 0.846 * [simplify]: Simplified to: (expm1 (hypot x y)) (log1p (hypot x y)) (fma x x (* y y)) (log (hypot x y)) (exp (hypot x y)) (* (cbrt (hypot x y)) (cbrt (hypot x y))) (cbrt (hypot x y)) (pow (hypot x y) 3) (sqrt (hypot x y)) (sqrt (hypot x y)) y x (* -1 x) 0.846 * * * [progress]: adding candidates to table 0.884 * [progress]: [Phase 3 of 3] Extracting. 0.886 * [simplify]: Simplifying using # : (hypot (hypot x y) z) 0.887 * * [simplify]: iteration 0 : 5 enodes (cost 2 ) 0.887 * [simplify]: Simplified to: (hypot (hypot x y) z) 1.883 * [regime-testing]: End program error score: 0.004000500062507814 1.919 * [regime-testing]: Target error score: 25.005687732287804