15.457 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.016 * * * [progress]: [2/2] Setting up program. 0.018 * [progress]: [Phase 2 of 3] Improving. 0.018 * [simplify]: Simplifying using # : (sqrt (+ (+ (* x x) (* y y)) (* z z))) 0.021 * * [simplify]: iteration 0 : 14 enodes (cost 6 ) 0.022 * * [simplify]: iteration 1 : 25 enodes (cost 6 ) 0.023 * * [simplify]: iteration 2 : 31 enodes (cost 6 ) 0.025 * * [simplify]: iteration 3 : 32 enodes (cost 6 ) 0.026 * * [simplify]: iteration 4 : 32 enodes (cost 6 ) 0.026 * [simplify]: Simplified to: (sqrt (+ (+ (* x x) (* y y)) (* z z))) 0.027 * * [progress]: iteration 1 / 4 0.027 * * * [progress]: picking best candidate 0.028 * * * * [pick]: Picked # 0.028 * * * [progress]: localizing error 0.036 * * * [progress]: generating rewritten candidates 0.036 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.070 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1 1) 0.079 * * * [progress]: generating series expansions 0.079 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.079 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in (x y z) around 0 0.079 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in z 0.079 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in z 0.079 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.079 * [taylor]: Taking taylor expansion of x in z 0.079 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in z 0.079 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.079 * [taylor]: Taking taylor expansion of y in z 0.079 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.079 * [taylor]: Taking taylor expansion of z in z 0.080 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in y 0.080 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in y 0.080 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.080 * [taylor]: Taking taylor expansion of x in y 0.080 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.080 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.080 * [taylor]: Taking taylor expansion of y in y 0.080 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.080 * [taylor]: Taking taylor expansion of z in y 0.081 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in x 0.081 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 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 0.081 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in x 0.081 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.081 * [taylor]: Taking taylor expansion of y in x 0.081 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.081 * [taylor]: Taking taylor expansion of z in x 0.082 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in x 0.082 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in x 0.083 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.083 * [taylor]: Taking taylor expansion of x in x 0.083 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in x 0.083 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.083 * [taylor]: Taking taylor expansion of y in x 0.083 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.083 * [taylor]: Taking taylor expansion of z in x 0.084 * [taylor]: Taking taylor expansion of (sqrt (+ (pow y 2) (pow z 2))) in y 0.084 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.084 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.084 * [taylor]: Taking taylor expansion of y in y 0.084 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.084 * [taylor]: Taking taylor expansion of z in y 0.084 * [taylor]: Taking taylor expansion of z in z 0.084 * [taylor]: Taking taylor expansion of 0 in y 0.084 * [taylor]: Taking taylor expansion of 0 in z 0.084 * [taylor]: Taking taylor expansion of 0 in z 0.086 * [taylor]: Taking taylor expansion of (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) in y 0.086 * [taylor]: Taking taylor expansion of 1/2 in y 0.086 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (+ (pow y 2) (pow z 2)))) in y 0.086 * [taylor]: Taking taylor expansion of (/ 1 (+ (pow y 2) (pow z 2))) in y 0.086 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.086 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.086 * [taylor]: Taking taylor expansion of y in y 0.086 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.086 * [taylor]: Taking taylor expansion of z in y 0.087 * [taylor]: Taking taylor expansion of (/ 1/2 z) in z 0.087 * [taylor]: Taking taylor expansion of 1/2 in z 0.087 * [taylor]: Taking taylor expansion of z in z 0.088 * [taylor]: Taking taylor expansion of 0 in z 0.089 * [taylor]: Taking taylor expansion of (/ 1/2 z) in z 0.089 * [taylor]: Taking taylor expansion of 1/2 in z 0.089 * [taylor]: Taking taylor expansion of z in z 0.090 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in (x y z) around 0 0.090 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in z 0.090 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.090 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.090 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.090 * [taylor]: Taking taylor expansion of x in z 0.090 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.090 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.090 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.090 * [taylor]: Taking taylor expansion of z in z 0.091 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.091 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.091 * [taylor]: Taking taylor expansion of y in z 0.093 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in y 0.093 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.093 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.093 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.093 * [taylor]: Taking taylor expansion of x in y 0.093 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.093 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.093 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.093 * [taylor]: Taking taylor expansion of z in y 0.093 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.093 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.093 * [taylor]: Taking taylor expansion of y in y 0.096 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.096 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.096 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.096 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.096 * [taylor]: Taking taylor expansion of x in x 0.096 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.096 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.096 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.096 * [taylor]: Taking taylor expansion of z in x 0.097 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.097 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.097 * [taylor]: Taking taylor expansion of y in x 0.098 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.098 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.098 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.098 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.098 * [taylor]: Taking taylor expansion of x in x 0.099 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.099 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.099 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.099 * [taylor]: Taking taylor expansion of z in x 0.099 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.099 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.099 * [taylor]: Taking taylor expansion of y in x 0.101 * [taylor]: Taking taylor expansion of 1 in y 0.101 * [taylor]: Taking taylor expansion of 0 in y 0.101 * [taylor]: Taking taylor expansion of 1 in z 0.103 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.103 * [taylor]: Taking taylor expansion of 1/2 in y 0.103 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.103 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.103 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.103 * [taylor]: Taking taylor expansion of z in y 0.103 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.103 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.103 * [taylor]: Taking taylor expansion of y in y 0.105 * [taylor]: Taking taylor expansion of 0 in z 0.105 * [taylor]: Taking taylor expansion of 0 in z 0.105 * [taylor]: Taking taylor expansion of 0 in z 0.107 * [taylor]: Taking taylor expansion of 0 in y 0.109 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (pow z 2))) in z 0.109 * [taylor]: Taking taylor expansion of 1/2 in z 0.109 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.109 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.109 * [taylor]: Taking taylor expansion of z in z 0.110 * [taylor]: Taking taylor expansion of 0 in z 0.110 * [taylor]: Taking taylor expansion of 0 in z 0.114 * [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 0.114 * [taylor]: Taking taylor expansion of -1/2 in y 0.114 * [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 0.114 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow z 4))) in y 0.114 * [taylor]: Taking taylor expansion of 1/4 in y 0.114 * [taylor]: Taking taylor expansion of (/ 1 (pow z 4)) in y 0.114 * [taylor]: Taking taylor expansion of (pow z 4) in y 0.114 * [taylor]: Taking taylor expansion of z in y 0.114 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4)))) in y 0.114 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) in y 0.114 * [taylor]: Taking taylor expansion of 1/2 in y 0.114 * [taylor]: Taking taylor expansion of (/ 1 (* (pow z 2) (pow y 2))) in y 0.114 * [taylor]: Taking taylor expansion of (* (pow z 2) (pow y 2)) in y 0.114 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.114 * [taylor]: Taking taylor expansion of z in y 0.114 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.114 * [taylor]: Taking taylor expansion of y in y 0.115 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow y 4))) in y 0.115 * [taylor]: Taking taylor expansion of 1/4 in y 0.115 * [taylor]: Taking taylor expansion of (/ 1 (pow y 4)) in y 0.115 * [taylor]: Taking taylor expansion of (pow y 4) in y 0.115 * [taylor]: Taking taylor expansion of y in y 0.124 * [taylor]: Taking taylor expansion of 0 in z 0.124 * [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 0.126 * [taylor]: Taking taylor expansion of 0 in z 0.128 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in (x y z) around 0 0.128 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in z 0.128 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.128 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.128 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.128 * [taylor]: Taking taylor expansion of x in z 0.128 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.128 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.128 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.128 * [taylor]: Taking taylor expansion of z in z 0.128 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.128 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.128 * [taylor]: Taking taylor expansion of y in z 0.131 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in y 0.131 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.131 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.131 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.131 * [taylor]: Taking taylor expansion of x in y 0.131 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.131 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.131 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.131 * [taylor]: Taking taylor expansion of z in y 0.131 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.131 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.131 * [taylor]: Taking taylor expansion of y in y 0.134 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.134 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.134 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.134 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.134 * [taylor]: Taking taylor expansion of x in x 0.134 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.134 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.134 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.134 * [taylor]: Taking taylor expansion of z in x 0.134 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.134 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.134 * [taylor]: Taking taylor expansion of y in x 0.136 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.136 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.136 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.136 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.136 * [taylor]: Taking taylor expansion of x in x 0.137 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.137 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.137 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.137 * [taylor]: Taking taylor expansion of z in x 0.137 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.137 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.137 * [taylor]: Taking taylor expansion of y in x 0.139 * [taylor]: Taking taylor expansion of 1 in y 0.139 * [taylor]: Taking taylor expansion of 0 in y 0.139 * [taylor]: Taking taylor expansion of 1 in z 0.141 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.141 * [taylor]: Taking taylor expansion of 1/2 in y 0.141 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.141 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.141 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.141 * [taylor]: Taking taylor expansion of z in y 0.141 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.141 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.141 * [taylor]: Taking taylor expansion of y in y 0.143 * [taylor]: Taking taylor expansion of 0 in z 0.143 * [taylor]: Taking taylor expansion of 0 in z 0.143 * [taylor]: Taking taylor expansion of 0 in z 0.148 * [taylor]: Taking taylor expansion of 0 in y 0.149 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (pow z 2))) in z 0.149 * [taylor]: Taking taylor expansion of 1/2 in z 0.149 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.149 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.149 * [taylor]: Taking taylor expansion of z in z 0.151 * [taylor]: Taking taylor expansion of 0 in z 0.151 * [taylor]: Taking taylor expansion of 0 in z 0.154 * [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 0.154 * [taylor]: Taking taylor expansion of -1/2 in y 0.154 * [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 0.154 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow z 4))) in y 0.154 * [taylor]: Taking taylor expansion of 1/4 in y 0.154 * [taylor]: Taking taylor expansion of (/ 1 (pow z 4)) in y 0.154 * [taylor]: Taking taylor expansion of (pow z 4) in y 0.154 * [taylor]: Taking taylor expansion of z in y 0.155 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4)))) in y 0.155 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) in y 0.155 * [taylor]: Taking taylor expansion of 1/2 in y 0.155 * [taylor]: Taking taylor expansion of (/ 1 (* (pow z 2) (pow y 2))) in y 0.155 * [taylor]: Taking taylor expansion of (* (pow z 2) (pow y 2)) in y 0.155 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.155 * [taylor]: Taking taylor expansion of z in y 0.155 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.155 * [taylor]: Taking taylor expansion of y in y 0.155 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow y 4))) in y 0.155 * [taylor]: Taking taylor expansion of 1/4 in y 0.155 * [taylor]: Taking taylor expansion of (/ 1 (pow y 4)) in y 0.155 * [taylor]: Taking taylor expansion of (pow y 4) in y 0.155 * [taylor]: Taking taylor expansion of y in y 0.164 * [taylor]: Taking taylor expansion of 0 in z 0.164 * [taylor]: Taking taylor expansion of 0 in z 0.166 * [taylor]: Taking taylor expansion of 0 in z 0.166 * [taylor]: Taking taylor expansion of 0 in z 0.167 * [taylor]: Taking taylor expansion of 0 in z 0.168 * * * * [progress]: [ 2 / 2 ] generating series at (2 1 1) 0.168 * [approximate]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in (x y) around 0 0.168 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in y 0.168 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.168 * [taylor]: Taking taylor expansion of x in y 0.168 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.168 * [taylor]: Taking taylor expansion of y in y 0.168 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.168 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.168 * [taylor]: Taking taylor expansion of x in x 0.168 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.168 * [taylor]: Taking taylor expansion of y in x 0.168 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.168 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.168 * [taylor]: Taking taylor expansion of x in x 0.168 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.168 * [taylor]: Taking taylor expansion of y in x 0.169 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.169 * [taylor]: Taking taylor expansion of y in y 0.169 * [taylor]: Taking taylor expansion of 0 in y 0.170 * [taylor]: Taking taylor expansion of 1 in y 0.171 * [taylor]: Taking taylor expansion of 0 in y 0.172 * [taylor]: Taking taylor expansion of 0 in y 0.173 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in (x y) around 0 0.173 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.173 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.173 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.173 * [taylor]: Taking taylor expansion of x in y 0.173 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.173 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.173 * [taylor]: Taking taylor expansion of y in y 0.173 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.173 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.173 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.173 * [taylor]: Taking taylor expansion of x in x 0.174 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.174 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.174 * [taylor]: Taking taylor expansion of y in x 0.174 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.174 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.174 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.174 * [taylor]: Taking taylor expansion of x in x 0.174 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.174 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.175 * [taylor]: Taking taylor expansion of y in x 0.175 * [taylor]: Taking taylor expansion of 1 in y 0.176 * [taylor]: Taking taylor expansion of 0 in y 0.177 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.177 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.177 * [taylor]: Taking taylor expansion of y in y 0.179 * [taylor]: Taking taylor expansion of 0 in y 0.181 * [taylor]: Taking taylor expansion of 0 in y 0.182 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in (x y) around 0 0.182 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.182 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.182 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.182 * [taylor]: Taking taylor expansion of x in y 0.183 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.183 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.183 * [taylor]: Taking taylor expansion of y in y 0.183 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.183 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.183 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.183 * [taylor]: Taking taylor expansion of x in x 0.184 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.184 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.184 * [taylor]: Taking taylor expansion of y in x 0.184 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.184 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.184 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.184 * [taylor]: Taking taylor expansion of x in x 0.184 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.184 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.184 * [taylor]: Taking taylor expansion of y in x 0.185 * [taylor]: Taking taylor expansion of 1 in y 0.186 * [taylor]: Taking taylor expansion of 0 in y 0.187 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.187 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.187 * [taylor]: Taking taylor expansion of y in y 0.189 * [taylor]: Taking taylor expansion of 0 in y 0.191 * [taylor]: Taking taylor expansion of 0 in y 0.192 * * * [progress]: simplifying candidates 0.193 * [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))) (log1p (+ (* x x) (* y 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)) z x (* -1 x) (+ (pow x 2) (pow y 2)) (+ (pow x 2) (pow y 2)) (+ (pow x 2) (pow y 2)) 0.197 * * [simplify]: iteration 0 : 186 enodes (cost 224 ) 0.201 * * [simplify]: iteration 1 : 767 enodes (cost 212 ) 0.212 * * [simplify]: iteration 2 : 2319 enodes (cost 209 ) 0.255 * * [simplify]: iteration 3 : 5001 enodes (cost 207 ) 0.256 * [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))) (log1p (+ (* 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 (fma x x (* y y)) 3) (hypot x y) (hypot x y) (fma y (pow y 5) (pow x 6)) (fma y (- (pow y 3) (* (pow x 2) y)) (pow x 4)) (fma (- (pow y 3)) y (pow x 4)) (- (* x x) (* y y)) z x (* -1 x) (fma x x (* y y)) (fma x x (* y y)) (fma x x (* y y)) 0.257 * * * [progress]: adding candidates to table 0.345 * * [progress]: iteration 2 / 4 0.345 * * * [progress]: picking best candidate 0.351 * * * * [pick]: Picked # 0.351 * * * [progress]: localizing error 0.358 * * * [progress]: generating rewritten candidates 0.358 * * * * [progress]: [ 1 / 2 ] rewriting at (2 1) 0.366 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1 1) 0.374 * * * [progress]: generating series expansions 0.374 * * * * [progress]: [ 1 / 2 ] generating series at (2 1) 0.374 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in (x y) around 0 0.374 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in y 0.374 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in y 0.374 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.374 * [taylor]: Taking taylor expansion of x in y 0.374 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.374 * [taylor]: Taking taylor expansion of y in y 0.375 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in x 0.375 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.375 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.375 * [taylor]: Taking taylor expansion of x in x 0.375 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.375 * [taylor]: Taking taylor expansion of y in x 0.375 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in x 0.375 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.375 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.375 * [taylor]: Taking taylor expansion of x in x 0.375 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.375 * [taylor]: Taking taylor expansion of y in x 0.376 * [taylor]: Taking taylor expansion of y in y 0.376 * [taylor]: Taking taylor expansion of 0 in y 0.377 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.377 * [taylor]: Taking taylor expansion of 1/2 in y 0.377 * [taylor]: Taking taylor expansion of y in y 0.379 * [taylor]: Taking taylor expansion of 0 in y 0.382 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in (x y) around 0 0.382 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in y 0.382 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.382 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.382 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.382 * [taylor]: Taking taylor expansion of x in y 0.382 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.382 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.382 * [taylor]: Taking taylor expansion of y in y 0.384 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.384 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.384 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.384 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.384 * [taylor]: Taking taylor expansion of x in x 0.385 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.385 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.385 * [taylor]: Taking taylor expansion of y in x 0.387 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.387 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.387 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.387 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.387 * [taylor]: Taking taylor expansion of x in x 0.387 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.387 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.387 * [taylor]: Taking taylor expansion of y in x 0.389 * [taylor]: Taking taylor expansion of 1 in y 0.389 * [taylor]: Taking taylor expansion of 0 in y 0.391 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.391 * [taylor]: Taking taylor expansion of 1/2 in y 0.391 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.391 * [taylor]: Taking taylor expansion of y in y 0.393 * [taylor]: Taking taylor expansion of 0 in y 0.395 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in (x y) around 0 0.395 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in y 0.395 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.395 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.395 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.395 * [taylor]: Taking taylor expansion of x in y 0.395 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.395 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.395 * [taylor]: Taking taylor expansion of y in y 0.397 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.397 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.397 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.397 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.397 * [taylor]: Taking taylor expansion of x in x 0.398 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.398 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.398 * [taylor]: Taking taylor expansion of y in x 0.399 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.399 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.399 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.399 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.399 * [taylor]: Taking taylor expansion of x in x 0.400 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.400 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.400 * [taylor]: Taking taylor expansion of y in x 0.402 * [taylor]: Taking taylor expansion of 1 in y 0.402 * [taylor]: Taking taylor expansion of 0 in y 0.403 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.403 * [taylor]: Taking taylor expansion of 1/2 in y 0.403 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.403 * [taylor]: Taking taylor expansion of y in y 0.407 * [taylor]: Taking taylor expansion of 0 in y 0.408 * * * * [progress]: [ 2 / 2 ] generating series at (2 1 1) 0.408 * [approximate]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in (x y) around 0 0.408 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in y 0.408 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.408 * [taylor]: Taking taylor expansion of x in y 0.408 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.408 * [taylor]: Taking taylor expansion of y in y 0.408 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.408 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.408 * [taylor]: Taking taylor expansion of x in x 0.408 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.408 * [taylor]: Taking taylor expansion of y in x 0.408 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.408 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.408 * [taylor]: Taking taylor expansion of x in x 0.408 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.408 * [taylor]: Taking taylor expansion of y in x 0.408 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.408 * [taylor]: Taking taylor expansion of y in y 0.408 * [taylor]: Taking taylor expansion of 0 in y 0.409 * [taylor]: Taking taylor expansion of 1 in y 0.410 * [taylor]: Taking taylor expansion of 0 in y 0.412 * [taylor]: Taking taylor expansion of 0 in y 0.412 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in (x y) around 0 0.412 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.412 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.412 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.412 * [taylor]: Taking taylor expansion of x in y 0.412 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.413 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.413 * [taylor]: Taking taylor expansion of y in y 0.413 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.413 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.413 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.413 * [taylor]: Taking taylor expansion of x in x 0.413 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.413 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.413 * [taylor]: Taking taylor expansion of y in x 0.414 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.414 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.414 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.414 * [taylor]: Taking taylor expansion of x in x 0.414 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.414 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.414 * [taylor]: Taking taylor expansion of y in x 0.414 * [taylor]: Taking taylor expansion of 1 in y 0.415 * [taylor]: Taking taylor expansion of 0 in y 0.416 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.416 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.416 * [taylor]: Taking taylor expansion of y in y 0.418 * [taylor]: Taking taylor expansion of 0 in y 0.421 * [taylor]: Taking taylor expansion of 0 in y 0.422 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in (x y) around 0 0.422 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.422 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.422 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.422 * [taylor]: Taking taylor expansion of x in y 0.422 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.422 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.422 * [taylor]: Taking taylor expansion of y in y 0.422 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.423 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.423 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.423 * [taylor]: Taking taylor expansion of x in x 0.423 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.423 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.423 * [taylor]: Taking taylor expansion of y in x 0.423 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.423 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.423 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.423 * [taylor]: Taking taylor expansion of x in x 0.424 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.424 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.424 * [taylor]: Taking taylor expansion of y in x 0.424 * [taylor]: Taking taylor expansion of 1 in y 0.425 * [taylor]: Taking taylor expansion of 0 in y 0.426 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.426 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.426 * [taylor]: Taking taylor expansion of y in y 0.428 * [taylor]: Taking taylor expansion of 0 in y 0.430 * [taylor]: Taking taylor expansion of 0 in y 0.431 * * * [progress]: simplifying candidates 0.432 * [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)))) (expm1 (+ (* x x) (* y y))) (log1p (+ (* x x) (* y 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)) y x (* -1 x) (+ (pow x 2) (pow y 2)) (+ (pow x 2) (pow y 2)) (+ (pow x 2) (pow y 2)) 0.436 * * [simplify]: iteration 0 : 136 enodes (cost 177 ) 0.439 * * [simplify]: iteration 1 : 589 enodes (cost 162 ) 0.447 * * [simplify]: iteration 2 : 1761 enodes (cost 158 ) 0.483 * * [simplify]: iteration 3 : 5002 enodes (cost 156 ) 0.484 * [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)))) 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)))) (expm1 (+ (* x x) (* y y))) (log1p (+ (* 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 (hypot x y) 6) (hypot x y) (hypot x y) (fma y (pow y 5) (pow x 6)) (fma y (- (pow y 3) (* (pow x 2) y)) (pow x 4)) (fma (- (pow y 3)) y (pow x 4)) (- (* x x) (* y y)) y x (* -1 x) (fma x x (* y y)) (fma x x (* y y)) (fma x x (* y y)) 0.484 * * * [progress]: adding candidates to table 0.576 * * [progress]: iteration 3 / 4 0.576 * * * [progress]: picking best candidate 0.577 * * * * [pick]: Picked # 0.577 * * * [progress]: localizing error 0.582 * * * [progress]: generating rewritten candidates 0.582 * * * * [progress]: [ 1 / 1 ] rewriting at (2 1) 0.582 * * * [progress]: generating series expansions 0.582 * * * * [progress]: [ 1 / 1 ] generating series at (2 1) 0.582 * [approximate]: Taking taylor expansion of (hypot x y) in (x y) around 0 0.583 * [taylor]: Taking taylor expansion of (hypot x y) in y 0.583 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* y y))) 0.583 * [taylor]: Taking taylor expansion of (+ (* x x) (* y y)) in y 0.583 * [taylor]: Taking taylor expansion of (* x x) in y 0.583 * [taylor]: Taking taylor expansion of x in y 0.583 * [taylor]: Taking taylor expansion of x in y 0.583 * [taylor]: Taking taylor expansion of (* y y) in y 0.583 * [taylor]: Taking taylor expansion of y in y 0.583 * [taylor]: Taking taylor expansion of y in y 0.584 * [taylor]: Taking taylor expansion of (hypot x y) in x 0.584 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* y y))) 0.584 * [taylor]: Taking taylor expansion of (+ (* x x) (* y y)) in x 0.584 * [taylor]: Taking taylor expansion of (* x x) in x 0.584 * [taylor]: Taking taylor expansion of x in x 0.584 * [taylor]: Taking taylor expansion of x in x 0.584 * [taylor]: Taking taylor expansion of (* y y) in x 0.584 * [taylor]: Taking taylor expansion of y in x 0.584 * [taylor]: Taking taylor expansion of y in x 0.585 * [taylor]: Taking taylor expansion of (hypot x y) in x 0.586 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* y y))) 0.586 * [taylor]: Taking taylor expansion of (+ (* x x) (* y y)) in x 0.586 * [taylor]: Taking taylor expansion of (* x x) in x 0.586 * [taylor]: Taking taylor expansion of x in x 0.586 * [taylor]: Taking taylor expansion of x in x 0.586 * [taylor]: Taking taylor expansion of (* y y) in x 0.586 * [taylor]: Taking taylor expansion of y in x 0.586 * [taylor]: Taking taylor expansion of y in x 0.587 * [taylor]: Taking taylor expansion of y in y 0.587 * [taylor]: Taking taylor expansion of 0 in y 0.588 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.588 * [taylor]: Taking taylor expansion of 1/2 in y 0.588 * [taylor]: Taking taylor expansion of y in y 0.590 * [taylor]: Taking taylor expansion of 0 in y 0.591 * [approximate]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in (x y) around 0 0.591 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in y 0.591 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y)))) 0.591 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y))) in y 0.591 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in y 0.591 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.591 * [taylor]: Taking taylor expansion of x in y 0.591 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.591 * [taylor]: Taking taylor expansion of x in y 0.591 * [taylor]: Taking taylor expansion of (* (/ 1 y) (/ 1 y)) in y 0.591 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.591 * [taylor]: Taking taylor expansion of y in y 0.592 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.592 * [taylor]: Taking taylor expansion of y in y 0.594 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in x 0.594 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y)))) 0.594 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y))) in x 0.594 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in x 0.594 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.594 * [taylor]: Taking taylor expansion of x in x 0.595 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.595 * [taylor]: Taking taylor expansion of x in x 0.595 * [taylor]: Taking taylor expansion of (* (/ 1 y) (/ 1 y)) in x 0.595 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.595 * [taylor]: Taking taylor expansion of y in x 0.595 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.595 * [taylor]: Taking taylor expansion of y in x 0.597 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in x 0.597 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y)))) 0.597 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y))) in x 0.597 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in x 0.597 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.597 * [taylor]: Taking taylor expansion of x in x 0.598 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.598 * [taylor]: Taking taylor expansion of x in x 0.598 * [taylor]: Taking taylor expansion of (* (/ 1 y) (/ 1 y)) in x 0.598 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.598 * [taylor]: Taking taylor expansion of y in x 0.598 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.598 * [taylor]: Taking taylor expansion of y in x 0.600 * [taylor]: Taking taylor expansion of 1 in y 0.600 * [taylor]: Taking taylor expansion of 0 in y 0.603 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.603 * [taylor]: Taking taylor expansion of 1/2 in y 0.603 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.603 * [taylor]: Taking taylor expansion of y in y 0.606 * [taylor]: Taking taylor expansion of 0 in y 0.607 * [approximate]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in (x y) around 0 0.607 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in y 0.607 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y)))) 0.607 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y))) in y 0.607 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in y 0.607 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.607 * [taylor]: Taking taylor expansion of -1 in y 0.607 * [taylor]: Taking taylor expansion of x in y 0.607 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.607 * [taylor]: Taking taylor expansion of -1 in y 0.608 * [taylor]: Taking taylor expansion of x in y 0.608 * [taylor]: Taking taylor expansion of (* (/ -1 y) (/ -1 y)) in y 0.608 * [taylor]: Taking taylor expansion of (/ -1 y) in y 0.608 * [taylor]: Taking taylor expansion of -1 in y 0.608 * [taylor]: Taking taylor expansion of y in y 0.608 * [taylor]: Taking taylor expansion of (/ -1 y) in y 0.608 * [taylor]: Taking taylor expansion of -1 in y 0.608 * [taylor]: Taking taylor expansion of y in y 0.611 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in x 0.611 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y)))) 0.611 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y))) in x 0.611 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in x 0.611 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.611 * [taylor]: Taking taylor expansion of -1 in x 0.611 * [taylor]: Taking taylor expansion of x in x 0.611 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.611 * [taylor]: Taking taylor expansion of -1 in x 0.611 * [taylor]: Taking taylor expansion of x in x 0.611 * [taylor]: Taking taylor expansion of (* (/ -1 y) (/ -1 y)) in x 0.611 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.611 * [taylor]: Taking taylor expansion of -1 in x 0.611 * [taylor]: Taking taylor expansion of y in x 0.611 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.611 * [taylor]: Taking taylor expansion of -1 in x 0.612 * [taylor]: Taking taylor expansion of y in x 0.614 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in x 0.614 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y)))) 0.614 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y))) in x 0.614 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in x 0.614 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.614 * [taylor]: Taking taylor expansion of -1 in x 0.614 * [taylor]: Taking taylor expansion of x in x 0.614 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.614 * [taylor]: Taking taylor expansion of -1 in x 0.614 * [taylor]: Taking taylor expansion of x in x 0.615 * [taylor]: Taking taylor expansion of (* (/ -1 y) (/ -1 y)) in x 0.615 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.615 * [taylor]: Taking taylor expansion of -1 in x 0.615 * [taylor]: Taking taylor expansion of y in x 0.615 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.615 * [taylor]: Taking taylor expansion of -1 in x 0.615 * [taylor]: Taking taylor expansion of y in x 0.617 * [taylor]: Taking taylor expansion of 1 in y 0.617 * [taylor]: Taking taylor expansion of 0 in y 0.620 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.620 * [taylor]: Taking taylor expansion of 1/2 in y 0.620 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.620 * [taylor]: Taking taylor expansion of y in y 0.623 * [taylor]: Taking taylor expansion of 0 in y 0.624 * * * [progress]: simplifying candidates 0.627 * [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) 0.630 * * [simplify]: iteration 0 : 22 enodes (cost 27 ) 0.632 * * [simplify]: iteration 1 : 25 enodes (cost 24 ) 0.633 * * [simplify]: iteration 2 : 29 enodes (cost 24 ) 0.635 * * [simplify]: iteration 3 : 34 enodes (cost 24 ) 0.636 * * [simplify]: iteration 4 : 53 enodes (cost 24 ) 0.638 * * [simplify]: iteration 5 : 107 enodes (cost 24 ) 0.642 * * [simplify]: iteration 6 : 513 enodes (cost 24 ) 0.657 * * [simplify]: iteration 7 : 1687 enodes (cost 24 ) 0.722 * * [simplify]: iteration 8 : 5001 enodes (cost 24 ) 0.722 * [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) 0.723 * * * [progress]: adding candidates to table 0.753 * [progress]: [Phase 3 of 3] Extracting. 0.754 * [simplify]: Simplifying using # : (hypot (hypot x y) z) 0.755 * * [simplify]: iteration 0 : 5 enodes (cost 2 ) 0.755 * [simplify]: Simplified to: (hypot (hypot x y) z) 1.299 * [regime-testing]: End program error score: 0.006000750093761721 1.335 * [regime-testing]: Target error score: 26.04533298167017