24.988 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.017 * * * [progress]: [2/2] Setting up program. 0.019 * [progress]: [Phase 2 of 3] Improving. 0.019 * [simplify]: Simplifying using # : (sqrt (+ (+ (* x x) (* y y)) (* z z))) 0.022 * * [simplify]: iteration 0 : 14 enodes (cost 6 ) 0.023 * * [simplify]: iteration 1 : 25 enodes (cost 6 ) 0.025 * * [simplify]: iteration 2 : 31 enodes (cost 6 ) 0.026 * * [simplify]: iteration 3 : 32 enodes (cost 6 ) 0.028 * * [simplify]: iteration 4 : 32 enodes (cost 6 ) 0.028 * [simplify]: Simplified to: (sqrt (+ (+ (* x x) (* y y)) (* z z))) 0.028 * * [progress]: iteration 1 / 4 0.028 * * * [progress]: picking best candidate 0.030 * * * * [pick]: Picked # 0.030 * * * [progress]: localizing error 0.039 * * * [progress]: generating rewritten candidates 0.039 * * * * [progress]: [ 1 / 3 ] rewriting at (2) 0.044 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1) 0.050 * * * * [progress]: [ 3 / 3 ] rewriting at (2 1 1) 0.055 * * * [progress]: generating series expansions 0.055 * * * * [progress]: [ 1 / 3 ] generating series at (2) 0.056 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in (x y z) around 0 0.056 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in z 0.056 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in z 0.056 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.056 * [taylor]: Taking taylor expansion of x in z 0.056 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in z 0.056 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.056 * [taylor]: Taking taylor expansion of y in z 0.056 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.056 * [taylor]: Taking taylor expansion of z in z 0.057 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in y 0.057 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in y 0.057 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.057 * [taylor]: Taking taylor expansion of x in y 0.057 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.058 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.058 * [taylor]: Taking taylor expansion of y in y 0.058 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.058 * [taylor]: Taking taylor expansion of z in y 0.059 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in x 0.059 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in x 0.059 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.059 * [taylor]: Taking taylor expansion of x in x 0.059 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in x 0.059 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.059 * [taylor]: Taking taylor expansion of y in x 0.059 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.059 * [taylor]: Taking taylor expansion of z in x 0.060 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in x 0.060 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in x 0.060 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.060 * [taylor]: Taking taylor expansion of x in x 0.060 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in x 0.060 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.060 * [taylor]: Taking taylor expansion of y in x 0.060 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.060 * [taylor]: Taking taylor expansion of z in x 0.062 * [taylor]: Taking taylor expansion of (sqrt (+ (pow y 2) (pow z 2))) in y 0.062 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.062 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.062 * [taylor]: Taking taylor expansion of y in y 0.062 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.062 * [taylor]: Taking taylor expansion of z in y 0.062 * [taylor]: Taking taylor expansion of z in z 0.063 * [taylor]: Taking taylor expansion of 0 in y 0.063 * [taylor]: Taking taylor expansion of 0 in z 0.063 * [taylor]: Taking taylor expansion of 0 in z 0.065 * [taylor]: Taking taylor expansion of (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) in y 0.065 * [taylor]: Taking taylor expansion of 1/2 in y 0.065 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (+ (pow y 2) (pow z 2)))) in y 0.065 * [taylor]: Taking taylor expansion of (/ 1 (+ (pow y 2) (pow z 2))) in y 0.066 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.066 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.066 * [taylor]: Taking taylor expansion of y in y 0.066 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.066 * [taylor]: Taking taylor expansion of z in y 0.067 * [taylor]: Taking taylor expansion of (/ 1/2 z) in z 0.067 * [taylor]: Taking taylor expansion of 1/2 in z 0.067 * [taylor]: Taking taylor expansion of z in z 0.068 * [taylor]: Taking taylor expansion of 0 in z 0.069 * [taylor]: Taking taylor expansion of (/ 1/2 z) in z 0.069 * [taylor]: Taking taylor expansion of 1/2 in z 0.069 * [taylor]: Taking taylor expansion of z in z 0.071 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in (x y z) around 0 0.071 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in z 0.071 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.071 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.071 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.071 * [taylor]: Taking taylor expansion of x in z 0.071 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.071 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.071 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.071 * [taylor]: Taking taylor expansion of z in z 0.072 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.072 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.072 * [taylor]: Taking taylor expansion of y in z 0.074 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in y 0.075 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.075 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.075 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.075 * [taylor]: Taking taylor expansion of x in y 0.075 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.075 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.075 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.075 * [taylor]: Taking taylor expansion of z in y 0.075 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.075 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.075 * [taylor]: Taking taylor expansion of y in y 0.078 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.078 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.078 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.078 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.078 * [taylor]: Taking taylor expansion of x in x 0.079 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.079 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.079 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.079 * [taylor]: Taking taylor expansion of z in x 0.079 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.079 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.079 * [taylor]: Taking taylor expansion of y in x 0.081 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.081 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.081 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.081 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.081 * [taylor]: Taking taylor expansion of x in x 0.082 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.082 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.082 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.082 * [taylor]: Taking taylor expansion of z in x 0.082 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.082 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.082 * [taylor]: Taking taylor expansion of y in x 0.085 * [taylor]: Taking taylor expansion of 1 in y 0.085 * [taylor]: Taking taylor expansion of 0 in y 0.085 * [taylor]: Taking taylor expansion of 1 in z 0.087 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.087 * [taylor]: Taking taylor expansion of 1/2 in y 0.087 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.087 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.087 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.087 * [taylor]: Taking taylor expansion of z in y 0.088 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.088 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.088 * [taylor]: Taking taylor expansion of y in y 0.090 * [taylor]: Taking taylor expansion of 0 in z 0.090 * [taylor]: Taking taylor expansion of 0 in z 0.090 * [taylor]: Taking taylor expansion of 0 in z 0.093 * [taylor]: Taking taylor expansion of 0 in y 0.094 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (pow z 2))) in z 0.094 * [taylor]: Taking taylor expansion of 1/2 in z 0.095 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.095 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.095 * [taylor]: Taking taylor expansion of z in z 0.096 * [taylor]: Taking taylor expansion of 0 in z 0.096 * [taylor]: Taking taylor expansion of 0 in z 0.101 * [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 0.101 * [taylor]: Taking taylor expansion of -1/2 in y 0.101 * [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 0.101 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow z 4))) in y 0.101 * [taylor]: Taking taylor expansion of 1/4 in y 0.101 * [taylor]: Taking taylor expansion of (/ 1 (pow z 4)) in y 0.101 * [taylor]: Taking taylor expansion of (pow z 4) in y 0.101 * [taylor]: Taking taylor expansion of z in y 0.101 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4)))) in y 0.101 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) in y 0.101 * [taylor]: Taking taylor expansion of 1/2 in y 0.101 * [taylor]: Taking taylor expansion of (/ 1 (* (pow z 2) (pow y 2))) in y 0.101 * [taylor]: Taking taylor expansion of (* (pow z 2) (pow y 2)) in y 0.101 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.101 * [taylor]: Taking taylor expansion of z in y 0.101 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.101 * [taylor]: Taking taylor expansion of y in y 0.102 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow y 4))) in y 0.102 * [taylor]: Taking taylor expansion of 1/4 in y 0.102 * [taylor]: Taking taylor expansion of (/ 1 (pow y 4)) in y 0.102 * [taylor]: Taking taylor expansion of (pow y 4) in y 0.102 * [taylor]: Taking taylor expansion of y in y 0.116 * [taylor]: Taking taylor expansion of 0 in z 0.117 * [taylor]: Taking taylor expansion of 0 in z 0.119 * [taylor]: Taking taylor expansion of 0 in z 0.119 * [taylor]: Taking taylor expansion of 0 in z 0.119 * [taylor]: Taking taylor expansion of 0 in z 0.121 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in (x y z) around 0 0.121 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in z 0.121 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.121 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.121 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.121 * [taylor]: Taking taylor expansion of x in z 0.122 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.122 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.122 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.122 * [taylor]: Taking taylor expansion of z in z 0.122 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.122 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.122 * [taylor]: Taking taylor expansion of y in z 0.125 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in y 0.125 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.125 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.125 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.125 * [taylor]: Taking taylor expansion of x in y 0.125 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.125 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.125 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.126 * [taylor]: Taking taylor expansion of z in y 0.126 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.126 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.126 * [taylor]: Taking taylor expansion of y in y 0.129 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.129 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.129 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.129 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.129 * [taylor]: Taking taylor expansion of x in x 0.130 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.130 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.130 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.130 * [taylor]: Taking taylor expansion of z in x 0.130 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.130 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.130 * [taylor]: Taking taylor expansion of y in x 0.132 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.132 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.132 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.132 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.132 * [taylor]: Taking taylor expansion of x in x 0.133 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.133 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.133 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.133 * [taylor]: Taking taylor expansion of z in x 0.133 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.133 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.133 * [taylor]: Taking taylor expansion of y in x 0.135 * [taylor]: Taking taylor expansion of 1 in y 0.135 * [taylor]: Taking taylor expansion of 0 in y 0.135 * [taylor]: Taking taylor expansion of 1 in z 0.138 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 (pow z 2)) (/ 1 (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)) (/ 1 (pow y 2))) in y 0.138 * [taylor]: Taking taylor expansion of (/ 1 (pow z 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 (/ 1 (pow y 2)) in y 0.138 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.138 * [taylor]: Taking taylor expansion of y in y 0.140 * [taylor]: Taking taylor expansion of 0 in z 0.140 * [taylor]: Taking taylor expansion of 0 in z 0.140 * [taylor]: Taking taylor expansion of 0 in z 0.143 * [taylor]: Taking taylor expansion of 0 in y 0.145 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (pow z 2))) in z 0.145 * [taylor]: Taking taylor expansion of 1/2 in z 0.145 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.145 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.145 * [taylor]: Taking taylor expansion of z in z 0.147 * [taylor]: Taking taylor expansion of 0 in z 0.147 * [taylor]: Taking taylor expansion of 0 in z 0.151 * [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 0.151 * [taylor]: Taking taylor expansion of -1/2 in y 0.151 * [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 0.151 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow z 4))) in y 0.151 * [taylor]: Taking taylor expansion of 1/4 in y 0.151 * [taylor]: Taking taylor expansion of (/ 1 (pow z 4)) in y 0.151 * [taylor]: Taking taylor expansion of (pow z 4) in y 0.151 * [taylor]: Taking taylor expansion of z in y 0.151 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4)))) in y 0.151 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) in y 0.151 * [taylor]: Taking taylor expansion of 1/2 in y 0.151 * [taylor]: Taking taylor expansion of (/ 1 (* (pow z 2) (pow y 2))) in y 0.151 * [taylor]: Taking taylor expansion of (* (pow z 2) (pow y 2)) in y 0.151 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.151 * [taylor]: Taking taylor expansion of z in y 0.151 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.151 * [taylor]: Taking taylor expansion of y in y 0.152 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow y 4))) in y 0.152 * [taylor]: Taking taylor expansion of 1/4 in y 0.152 * [taylor]: Taking taylor expansion of (/ 1 (pow y 4)) in y 0.152 * [taylor]: Taking taylor expansion of (pow y 4) in y 0.152 * [taylor]: Taking taylor expansion of y in y 0.163 * [taylor]: Taking taylor expansion of 0 in z 0.163 * [taylor]: Taking taylor expansion of 0 in z 0.165 * [taylor]: Taking taylor expansion of 0 in z 0.165 * [taylor]: Taking taylor expansion of 0 in z 0.165 * [taylor]: Taking taylor expansion of 0 in z 0.167 * * * * [progress]: [ 2 / 3 ] generating series at (2 1) 0.167 * [approximate]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in (x y z) around 0 0.168 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in z 0.168 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.168 * [taylor]: Taking taylor expansion of x in z 0.168 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in z 0.168 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.168 * [taylor]: Taking taylor expansion of y in z 0.168 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.168 * [taylor]: Taking taylor expansion of z in z 0.168 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 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) (pow z 2)) 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 z 2) in y 0.168 * [taylor]: Taking taylor expansion of z in y 0.168 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 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) (pow z 2)) 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 z 2) in x 0.168 * [taylor]: Taking taylor expansion of z in x 0.168 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 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) (pow z 2)) 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 z 2) in x 0.168 * [taylor]: Taking taylor expansion of z in x 0.169 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 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 (pow z 2) in y 0.169 * [taylor]: Taking taylor expansion of z in y 0.169 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.169 * [taylor]: Taking taylor expansion of z in z 0.169 * [taylor]: Taking taylor expansion of 0 in y 0.170 * [taylor]: Taking taylor expansion of 0 in z 0.170 * [taylor]: Taking taylor expansion of 0 in z 0.171 * [taylor]: Taking taylor expansion of 1 in y 0.171 * [taylor]: Taking taylor expansion of 1 in z 0.171 * [taylor]: Taking taylor expansion of 0 in z 0.172 * [taylor]: Taking taylor expansion of 1 in z 0.173 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in (x y z) around 0 0.173 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.173 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.173 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.173 * [taylor]: Taking taylor expansion of x in z 0.174 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.174 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.174 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.174 * [taylor]: Taking taylor expansion of z in z 0.174 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.174 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.174 * [taylor]: Taking taylor expansion of y in z 0.174 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.174 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.174 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.175 * [taylor]: Taking taylor expansion of x in y 0.175 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.175 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.175 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.175 * [taylor]: Taking taylor expansion of z in y 0.175 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.175 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.175 * [taylor]: Taking taylor expansion of y in y 0.175 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.175 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.175 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.175 * [taylor]: Taking taylor expansion of x in x 0.176 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.176 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.176 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.176 * [taylor]: Taking taylor expansion of z in x 0.177 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.177 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.177 * [taylor]: Taking taylor expansion of y in x 0.177 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.177 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.177 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.177 * [taylor]: Taking taylor expansion of x in x 0.177 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.177 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.177 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.177 * [taylor]: Taking taylor expansion of z in x 0.177 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.178 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.178 * [taylor]: Taking taylor expansion of y in x 0.178 * [taylor]: Taking taylor expansion of 1 in y 0.179 * [taylor]: Taking taylor expansion of 0 in y 0.181 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.181 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.181 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.181 * [taylor]: Taking taylor expansion of z in y 0.181 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.181 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.181 * [taylor]: Taking taylor expansion of y in y 0.182 * [taylor]: Taking taylor expansion of 1 in z 0.182 * [taylor]: Taking taylor expansion of 1 in z 0.184 * [taylor]: Taking taylor expansion of 0 in y 0.185 * [taylor]: Taking taylor expansion of 0 in z 0.185 * [taylor]: Taking taylor expansion of 0 in z 0.185 * [taylor]: Taking taylor expansion of 0 in z 0.188 * [taylor]: Taking taylor expansion of 0 in y 0.189 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.189 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.189 * [taylor]: Taking taylor expansion of z in z 0.190 * [taylor]: Taking taylor expansion of 0 in z 0.190 * [taylor]: Taking taylor expansion of 0 in z 0.191 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in (x y z) around 0 0.191 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.191 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.191 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.191 * [taylor]: Taking taylor expansion of x in z 0.191 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.191 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.191 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.191 * [taylor]: Taking taylor expansion of z in z 0.192 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.192 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.192 * [taylor]: Taking taylor expansion of y in z 0.192 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.192 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.192 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.192 * [taylor]: Taking taylor expansion of x in y 0.192 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.192 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.192 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.192 * [taylor]: Taking taylor expansion of z in y 0.192 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.192 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.192 * [taylor]: Taking taylor expansion of y in y 0.193 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.193 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.193 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.193 * [taylor]: Taking taylor expansion of x in x 0.194 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.194 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.194 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.194 * [taylor]: Taking taylor expansion of z in x 0.194 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.194 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.194 * [taylor]: Taking taylor expansion of y in x 0.194 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.194 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.194 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.194 * [taylor]: Taking taylor expansion of x in x 0.195 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.195 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.195 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.195 * [taylor]: Taking taylor expansion of z in x 0.195 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.195 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.195 * [taylor]: Taking taylor expansion of y in x 0.195 * [taylor]: Taking taylor expansion of 1 in y 0.196 * [taylor]: Taking taylor expansion of 0 in y 0.198 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.198 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.198 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.198 * [taylor]: Taking taylor expansion of z in y 0.198 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.198 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.198 * [taylor]: Taking taylor expansion of y in y 0.199 * [taylor]: Taking taylor expansion of 1 in z 0.199 * [taylor]: Taking taylor expansion of 1 in z 0.201 * [taylor]: Taking taylor expansion of 0 in y 0.202 * [taylor]: Taking taylor expansion of 0 in z 0.202 * [taylor]: Taking taylor expansion of 0 in z 0.202 * [taylor]: Taking taylor expansion of 0 in z 0.205 * [taylor]: Taking taylor expansion of 0 in y 0.207 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.207 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.207 * [taylor]: Taking taylor expansion of z in z 0.207 * [taylor]: Taking taylor expansion of 0 in z 0.207 * [taylor]: Taking taylor expansion of 0 in z 0.208 * * * * [progress]: [ 3 / 3 ] generating series at (2 1 1) 0.208 * [approximate]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in (x y) around 0 0.208 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in y 0.208 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.208 * [taylor]: Taking taylor expansion of x in y 0.208 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.208 * [taylor]: Taking taylor expansion of y in y 0.208 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.208 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.208 * [taylor]: Taking taylor expansion of x in x 0.208 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.208 * [taylor]: Taking taylor expansion of y in x 0.208 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.209 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.209 * [taylor]: Taking taylor expansion of x in x 0.209 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.209 * [taylor]: Taking taylor expansion of y in x 0.209 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.209 * [taylor]: Taking taylor expansion of y in y 0.209 * [taylor]: Taking taylor expansion of 0 in y 0.210 * [taylor]: Taking taylor expansion of 1 in y 0.215 * [taylor]: Taking taylor expansion of 0 in y 0.217 * [taylor]: Taking taylor expansion of 0 in y 0.217 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in (x y) around 0 0.217 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.217 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.218 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.218 * [taylor]: Taking taylor expansion of x in y 0.218 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.218 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.218 * [taylor]: Taking taylor expansion of y in y 0.218 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.218 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.218 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.218 * [taylor]: Taking taylor expansion of x in x 0.219 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.219 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.219 * [taylor]: Taking taylor expansion of y in x 0.219 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.219 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.219 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.219 * [taylor]: Taking taylor expansion of x in x 0.220 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.220 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.220 * [taylor]: Taking taylor expansion of y in x 0.220 * [taylor]: Taking taylor expansion of 1 in y 0.221 * [taylor]: Taking taylor expansion of 0 in y 0.222 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.223 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.223 * [taylor]: Taking taylor expansion of y in y 0.225 * [taylor]: Taking taylor expansion of 0 in y 0.228 * [taylor]: Taking taylor expansion of 0 in y 0.230 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in (x y) around 0 0.230 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 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 y 2)) in y 0.230 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.230 * [taylor]: Taking taylor expansion of y in y 0.231 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 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 0.231 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.231 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.231 * [taylor]: Taking taylor expansion of y in x 0.231 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 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 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 in y 0.234 * [taylor]: Taking taylor expansion of 0 in y 0.235 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.235 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.235 * [taylor]: Taking taylor expansion of y in y 0.237 * [taylor]: Taking taylor expansion of 0 in y 0.240 * [taylor]: Taking taylor expansion of 0 in y 0.242 * * * [progress]: simplifying candidates 0.242 * [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)) (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 z 2))) (+ (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 x 2) (pow y 2)) (+ (pow x 2) (pow y 2)) 0.247 * * [simplify]: iteration 0 : 225 enodes (cost 355 ) 0.254 * * [simplify]: iteration 1 : 1043 enodes (cost 323 ) 0.272 * * [simplify]: iteration 2 : 3749 enodes (cost 312 ) 0.341 * * [simplify]: iteration 3 : 5001 enodes (cost 309 ) 0.344 * [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)))) (sqrt 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)) (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 (fma y y (* z z))) (fma x x (fma y y (* z z))) (fma x x (fma y y (* z z))) (fma x x (* y y)) (fma x x (* y y)) (fma x x (* y y)) 0.344 * * * [progress]: adding candidates to table 0.516 * * [progress]: iteration 2 / 4 0.516 * * * [progress]: picking best candidate 0.521 * * * * [pick]: Picked # 0.521 * * * [progress]: localizing error 0.529 * * * [progress]: generating rewritten candidates 0.529 * * * * [progress]: [ 1 / 2 ] rewriting at (2 1) 0.533 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1 1) 0.538 * * * [progress]: generating series expansions 0.538 * * * * [progress]: [ 1 / 2 ] generating series at (2 1) 0.538 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in (x y) around 0 0.538 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in y 0.538 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in y 0.538 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.538 * [taylor]: Taking taylor expansion of x in y 0.538 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.538 * [taylor]: Taking taylor expansion of y in y 0.539 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in x 0.539 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.539 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.539 * [taylor]: Taking taylor expansion of x in x 0.539 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.539 * [taylor]: Taking taylor expansion of y in x 0.540 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in x 0.540 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.540 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.540 * [taylor]: Taking taylor expansion of x in x 0.540 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.540 * [taylor]: Taking taylor expansion of y in x 0.541 * [taylor]: Taking taylor expansion of y in y 0.541 * [taylor]: Taking taylor expansion of 0 in y 0.542 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.542 * [taylor]: Taking taylor expansion of 1/2 in y 0.543 * [taylor]: Taking taylor expansion of y in y 0.545 * [taylor]: Taking taylor expansion of 0 in y 0.546 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in (x y) around 0 0.546 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in y 0.546 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.546 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.546 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.546 * [taylor]: Taking taylor expansion of x in y 0.546 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.546 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.546 * [taylor]: Taking taylor expansion of y in y 0.549 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.549 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.549 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.549 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.549 * [taylor]: Taking taylor expansion of x in x 0.549 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.549 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.549 * [taylor]: Taking taylor expansion of y in x 0.552 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.552 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.552 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.552 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.552 * [taylor]: Taking taylor expansion of x in x 0.553 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.553 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.553 * [taylor]: Taking taylor expansion of y in x 0.555 * [taylor]: Taking taylor expansion of 1 in y 0.555 * [taylor]: Taking taylor expansion of 0 in y 0.557 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.558 * [taylor]: Taking taylor expansion of 1/2 in y 0.558 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.558 * [taylor]: Taking taylor expansion of y in y 0.561 * [taylor]: Taking taylor expansion of 0 in y 0.563 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in (x y) around 0 0.563 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in y 0.563 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.563 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.563 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.563 * [taylor]: Taking taylor expansion of x in y 0.563 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.563 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.563 * [taylor]: Taking taylor expansion of y in y 0.566 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.566 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.566 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.566 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.566 * [taylor]: Taking taylor expansion of x in x 0.567 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.567 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.567 * [taylor]: Taking taylor expansion of y in x 0.569 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.569 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.569 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.569 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.569 * [taylor]: Taking taylor expansion of x in x 0.570 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.570 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.570 * [taylor]: Taking taylor expansion of y in x 0.572 * [taylor]: Taking taylor expansion of 1 in y 0.572 * [taylor]: Taking taylor expansion of 0 in y 0.579 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.579 * [taylor]: Taking taylor expansion of 1/2 in y 0.579 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.579 * [taylor]: Taking taylor expansion of y in y 0.583 * [taylor]: Taking taylor expansion of 0 in y 0.585 * * * * [progress]: [ 2 / 2 ] generating series at (2 1 1) 0.585 * [approximate]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in (x y) around 0 0.585 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in y 0.585 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.585 * [taylor]: Taking taylor expansion of x in y 0.585 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.585 * [taylor]: Taking taylor expansion of y in y 0.585 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.585 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.585 * [taylor]: Taking taylor expansion of x in x 0.585 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.585 * [taylor]: Taking taylor expansion of y in x 0.585 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.585 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.585 * [taylor]: Taking taylor expansion of x in x 0.585 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.585 * [taylor]: Taking taylor expansion of y in x 0.586 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.586 * [taylor]: Taking taylor expansion of y in y 0.586 * [taylor]: Taking taylor expansion of 0 in y 0.587 * [taylor]: Taking taylor expansion of 1 in y 0.589 * [taylor]: Taking taylor expansion of 0 in y 0.591 * [taylor]: Taking taylor expansion of 0 in y 0.592 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in (x y) around 0 0.592 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.592 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.592 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.592 * [taylor]: Taking taylor expansion of x in y 0.592 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.592 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.592 * [taylor]: Taking taylor expansion of y in y 0.593 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.593 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.593 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.593 * [taylor]: Taking taylor expansion of x in x 0.593 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.593 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.593 * [taylor]: Taking taylor expansion of y in x 0.594 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.594 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.594 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.594 * [taylor]: Taking taylor expansion of x in x 0.594 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.594 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.594 * [taylor]: Taking taylor expansion of y in x 0.595 * [taylor]: Taking taylor expansion of 1 in y 0.596 * [taylor]: Taking taylor expansion of 0 in y 0.598 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.598 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.598 * [taylor]: Taking taylor expansion of y in y 0.600 * [taylor]: Taking taylor expansion of 0 in y 0.604 * [taylor]: Taking taylor expansion of 0 in y 0.606 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in (x y) around 0 0.606 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.606 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.606 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.606 * [taylor]: Taking taylor expansion of x in y 0.606 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.606 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.606 * [taylor]: Taking taylor expansion of y in y 0.607 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.607 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.607 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.607 * [taylor]: Taking taylor expansion of x in x 0.607 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.607 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.607 * [taylor]: Taking taylor expansion of y in x 0.607 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.607 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.607 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.607 * [taylor]: Taking taylor expansion of x in x 0.608 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.608 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.608 * [taylor]: Taking taylor expansion of y in x 0.609 * [taylor]: Taking taylor expansion of 1 in y 0.610 * [taylor]: Taking taylor expansion of 0 in y 0.611 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.611 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.611 * [taylor]: Taking taylor expansion of y in y 0.614 * [taylor]: Taking taylor expansion of 0 in y 0.617 * [taylor]: Taking taylor expansion of 0 in y 0.618 * * * [progress]: simplifying candidates 0.619 * [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)) 0.623 * * [simplify]: iteration 0 : 136 enodes (cost 177 ) 0.628 * * [simplify]: iteration 1 : 589 enodes (cost 162 ) 0.639 * * [simplify]: iteration 2 : 1761 enodes (cost 158 ) 0.683 * * [simplify]: iteration 3 : 5002 enodes (cost 156 ) 0.685 * [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)) 0.685 * * * [progress]: adding candidates to table 0.790 * * [progress]: iteration 3 / 4 0.790 * * * [progress]: picking best candidate 0.792 * * * * [pick]: Picked # 0.792 * * * [progress]: localizing error 0.797 * * * [progress]: generating rewritten candidates 0.797 * * * * [progress]: [ 1 / 1 ] rewriting at (2 1) 0.798 * * * [progress]: generating series expansions 0.798 * * * * [progress]: [ 1 / 1 ] generating series at (2 1) 0.798 * [approximate]: Taking taylor expansion of (hypot x y) in (x y) around 0 0.798 * [taylor]: Taking taylor expansion of (hypot x y) in y 0.798 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* y y))) 0.798 * [taylor]: Taking taylor expansion of (+ (* x x) (* y y)) in y 0.798 * [taylor]: Taking taylor expansion of (* x x) in y 0.798 * [taylor]: Taking taylor expansion of x in y 0.798 * [taylor]: Taking taylor expansion of x in y 0.798 * [taylor]: Taking taylor expansion of (* y y) in y 0.798 * [taylor]: Taking taylor expansion of y in y 0.798 * [taylor]: Taking taylor expansion of y in y 0.800 * [taylor]: Taking taylor expansion of (hypot x y) in x 0.800 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* y y))) 0.800 * [taylor]: Taking taylor expansion of (+ (* x x) (* y y)) in x 0.800 * [taylor]: Taking taylor expansion of (* x x) in x 0.800 * [taylor]: Taking taylor expansion of x in x 0.800 * [taylor]: Taking taylor expansion of x in x 0.800 * [taylor]: Taking taylor expansion of (* y y) in x 0.800 * [taylor]: Taking taylor expansion of y in x 0.800 * [taylor]: Taking taylor expansion of y in x 0.801 * [taylor]: Taking taylor expansion of (hypot x y) in x 0.801 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* y y))) 0.801 * [taylor]: Taking taylor expansion of (+ (* x x) (* y y)) in x 0.801 * [taylor]: Taking taylor expansion of (* x x) in x 0.801 * [taylor]: Taking taylor expansion of x in x 0.801 * [taylor]: Taking taylor expansion of x in x 0.801 * [taylor]: Taking taylor expansion of (* y y) in x 0.801 * [taylor]: Taking taylor expansion of y in x 0.801 * [taylor]: Taking taylor expansion of y in x 0.803 * [taylor]: Taking taylor expansion of y in y 0.803 * [taylor]: Taking taylor expansion of 0 in y 0.804 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.804 * [taylor]: Taking taylor expansion of 1/2 in y 0.804 * [taylor]: Taking taylor expansion of y in y 0.806 * [taylor]: Taking taylor expansion of 0 in y 0.807 * [approximate]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in (x y) around 0 0.807 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in y 0.807 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y)))) 0.807 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y))) in y 0.807 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in y 0.807 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.807 * [taylor]: Taking taylor expansion of x in y 0.808 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.808 * [taylor]: Taking taylor expansion of x in y 0.808 * [taylor]: Taking taylor expansion of (* (/ 1 y) (/ 1 y)) in y 0.808 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.808 * [taylor]: Taking taylor expansion of y in y 0.808 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.808 * [taylor]: Taking taylor expansion of y in y 0.811 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in x 0.811 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y)))) 0.811 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y))) in x 0.811 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in x 0.811 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.811 * [taylor]: Taking taylor expansion of x in x 0.811 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.811 * [taylor]: Taking taylor expansion of x in x 0.812 * [taylor]: Taking taylor expansion of (* (/ 1 y) (/ 1 y)) in x 0.812 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.812 * [taylor]: Taking taylor expansion of y in x 0.812 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.812 * [taylor]: Taking taylor expansion of y in x 0.814 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (/ 1 y)) in x 0.814 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y)))) 0.814 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (/ 1 y) (/ 1 y))) in x 0.814 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in x 0.814 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.815 * [taylor]: Taking taylor expansion of x in x 0.815 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.815 * [taylor]: Taking taylor expansion of x in x 0.815 * [taylor]: Taking taylor expansion of (* (/ 1 y) (/ 1 y)) in x 0.815 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.815 * [taylor]: Taking taylor expansion of y in x 0.815 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.815 * [taylor]: Taking taylor expansion of y in x 0.818 * [taylor]: Taking taylor expansion of 1 in y 0.818 * [taylor]: Taking taylor expansion of 0 in y 0.821 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.821 * [taylor]: Taking taylor expansion of 1/2 in y 0.821 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.821 * [taylor]: Taking taylor expansion of y in y 0.825 * [taylor]: Taking taylor expansion of 0 in y 0.826 * [approximate]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in (x y) around 0 0.826 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in y 0.826 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y)))) 0.826 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y))) in y 0.826 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in y 0.826 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.826 * [taylor]: Taking taylor expansion of -1 in y 0.826 * [taylor]: Taking taylor expansion of x in y 0.826 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.826 * [taylor]: Taking taylor expansion of -1 in y 0.826 * [taylor]: Taking taylor expansion of x in y 0.826 * [taylor]: Taking taylor expansion of (* (/ -1 y) (/ -1 y)) in y 0.826 * [taylor]: Taking taylor expansion of (/ -1 y) in y 0.826 * [taylor]: Taking taylor expansion of -1 in y 0.826 * [taylor]: Taking taylor expansion of y in y 0.827 * [taylor]: Taking taylor expansion of (/ -1 y) in y 0.827 * [taylor]: Taking taylor expansion of -1 in y 0.827 * [taylor]: Taking taylor expansion of y in y 0.830 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in x 0.830 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y)))) 0.830 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y))) in x 0.830 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in x 0.830 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.830 * [taylor]: Taking taylor expansion of -1 in x 0.830 * [taylor]: Taking taylor expansion of x in x 0.831 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.831 * [taylor]: Taking taylor expansion of -1 in x 0.831 * [taylor]: Taking taylor expansion of x in x 0.831 * [taylor]: Taking taylor expansion of (* (/ -1 y) (/ -1 y)) in x 0.831 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.831 * [taylor]: Taking taylor expansion of -1 in x 0.831 * [taylor]: Taking taylor expansion of y in x 0.831 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.831 * [taylor]: Taking taylor expansion of -1 in x 0.831 * [taylor]: Taking taylor expansion of y in x 0.834 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (/ -1 y)) in x 0.834 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y)))) 0.834 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (/ -1 y) (/ -1 y))) in x 0.834 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in x 0.834 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.834 * [taylor]: Taking taylor expansion of -1 in x 0.834 * [taylor]: Taking taylor expansion of x in x 0.835 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.835 * [taylor]: Taking taylor expansion of -1 in x 0.835 * [taylor]: Taking taylor expansion of x in x 0.835 * [taylor]: Taking taylor expansion of (* (/ -1 y) (/ -1 y)) in x 0.835 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.835 * [taylor]: Taking taylor expansion of -1 in x 0.835 * [taylor]: Taking taylor expansion of y in x 0.835 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.835 * [taylor]: Taking taylor expansion of -1 in x 0.835 * [taylor]: Taking taylor expansion of y in x 0.838 * [taylor]: Taking taylor expansion of 1 in y 0.838 * [taylor]: Taking taylor expansion of 0 in y 0.841 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.841 * [taylor]: Taking taylor expansion of 1/2 in y 0.841 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.841 * [taylor]: Taking taylor expansion of y in y 0.845 * [taylor]: Taking taylor expansion of 0 in y 0.846 * * * [progress]: simplifying candidates 0.847 * [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) 0.850 * * [simplify]: iteration 0 : 22 enodes (cost 27 ) 0.852 * * [simplify]: iteration 1 : 25 enodes (cost 24 ) 0.854 * * [simplify]: iteration 2 : 29 enodes (cost 24 ) 0.856 * * [simplify]: iteration 3 : 34 enodes (cost 24 ) 0.858 * * [simplify]: iteration 4 : 53 enodes (cost 24 ) 0.861 * * [simplify]: iteration 5 : 107 enodes (cost 24 ) 0.867 * * [simplify]: iteration 6 : 513 enodes (cost 24 ) 0.883 * * [simplify]: iteration 7 : 1687 enodes (cost 24 ) 0.953 * * [simplify]: iteration 8 : 5001 enodes (cost 24 ) 0.954 * [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) 0.954 * * * [progress]: adding candidates to table 0.994 * [progress]: [Phase 3 of 3] Extracting. 0.996 * [simplify]: Simplifying using # : (hypot (hypot x y) z) 0.996 * * [simplify]: iteration 0 : 5 enodes (cost 2 ) 0.996 * [simplify]: Simplified to: (hypot (hypot x y) z) 1.500 * [regime-testing]: End program error score: 0.004125515689461182 1.536 * [regime-testing]: Target error score: 25.454020301869672