26.040 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.015 * * * [progress]: [2/2] Setting up program. 0.017 * [progress]: [Phase 2 of 3] Improving. 0.018 * [simplify]: Simplifying using # : (sqrt (+ (+ (* x x) (* y y)) (* z z))) 0.020 * * [simplify]: iteration 0 : 14 enodes (cost 6 ) 0.022 * * [simplify]: iteration 1 : 25 enodes (cost 6 ) 0.024 * * [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 0.038 * * * [progress]: generating rewritten candidates 0.038 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.044 * * * [progress]: generating series expansions 0.044 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.044 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in (x y z) around 0 0.044 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in z 0.044 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in z 0.044 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.044 * [taylor]: Taking taylor expansion of x in z 0.044 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in z 0.044 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.044 * [taylor]: Taking taylor expansion of y in z 0.044 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.044 * [taylor]: Taking taylor expansion of z in z 0.046 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in y 0.046 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in y 0.046 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.046 * [taylor]: Taking taylor expansion of x in y 0.046 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.046 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.046 * [taylor]: Taking taylor expansion of y in y 0.046 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.046 * [taylor]: Taking taylor expansion of z in y 0.047 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in x 0.047 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in x 0.047 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.047 * [taylor]: Taking taylor expansion of x in x 0.047 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in x 0.047 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.047 * [taylor]: Taking taylor expansion of y in x 0.047 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.047 * [taylor]: Taking taylor expansion of z in x 0.048 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) in x 0.048 * [taylor]: Taking taylor expansion of (+ (pow x 2) (+ (pow y 2) (pow z 2))) in x 0.048 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.048 * [taylor]: Taking taylor expansion of x in x 0.048 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in x 0.048 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.048 * [taylor]: Taking taylor expansion of y in x 0.048 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.048 * [taylor]: Taking taylor expansion of z in x 0.050 * [taylor]: Taking taylor expansion of (sqrt (+ (pow y 2) (pow z 2))) in y 0.050 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.050 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.050 * [taylor]: Taking taylor expansion of y in y 0.050 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.050 * [taylor]: Taking taylor expansion of z in y 0.050 * [taylor]: Taking taylor expansion of z in z 0.050 * [taylor]: Taking taylor expansion of 0 in y 0.050 * [taylor]: Taking taylor expansion of 0 in z 0.050 * [taylor]: Taking taylor expansion of 0 in z 0.052 * [taylor]: Taking taylor expansion of (* 1/2 (sqrt (/ 1 (+ (pow y 2) (pow z 2))))) in y 0.053 * [taylor]: Taking taylor expansion of 1/2 in y 0.053 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (+ (pow y 2) (pow z 2)))) in y 0.053 * [taylor]: Taking taylor expansion of (/ 1 (+ (pow y 2) (pow z 2))) in y 0.053 * [taylor]: Taking taylor expansion of (+ (pow y 2) (pow z 2)) in y 0.053 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.053 * [taylor]: Taking taylor expansion of y in y 0.053 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.053 * [taylor]: Taking taylor expansion of z in y 0.053 * [taylor]: Taking taylor expansion of (/ 1/2 z) in z 0.053 * [taylor]: Taking taylor expansion of 1/2 in z 0.054 * [taylor]: Taking taylor expansion of z in z 0.054 * [taylor]: Taking taylor expansion of 0 in z 0.056 * [taylor]: Taking taylor expansion of (/ 1/2 z) in z 0.056 * [taylor]: Taking taylor expansion of 1/2 in z 0.056 * [taylor]: Taking taylor expansion of z in z 0.057 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in (x y z) around 0 0.057 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in z 0.057 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.057 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.057 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.057 * [taylor]: Taking taylor expansion of x in z 0.057 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.057 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.057 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.057 * [taylor]: Taking taylor expansion of z in z 0.058 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.058 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.058 * [taylor]: Taking taylor expansion of y in z 0.061 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in y 0.061 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.061 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.061 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.061 * [taylor]: Taking taylor expansion of x in y 0.061 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.061 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.061 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.061 * [taylor]: Taking taylor expansion of z in y 0.061 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.061 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.061 * [taylor]: Taking taylor expansion of y in y 0.064 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.064 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.064 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.064 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.064 * [taylor]: Taking taylor expansion of x in x 0.064 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.065 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.065 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.065 * [taylor]: Taking taylor expansion of z in x 0.065 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.065 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.065 * [taylor]: Taking taylor expansion of y in x 0.071 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.071 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.071 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.071 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.071 * [taylor]: Taking taylor expansion of x in x 0.072 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.072 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.072 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.072 * [taylor]: Taking taylor expansion of z in x 0.072 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.072 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.072 * [taylor]: Taking taylor expansion of y in x 0.074 * [taylor]: Taking taylor expansion of 1 in y 0.074 * [taylor]: Taking taylor expansion of 0 in y 0.074 * [taylor]: Taking taylor expansion of 1 in z 0.077 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.077 * [taylor]: Taking taylor expansion of 1/2 in y 0.077 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.077 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.077 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.077 * [taylor]: Taking taylor expansion of z in y 0.077 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.077 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.077 * [taylor]: Taking taylor expansion of y in y 0.079 * [taylor]: Taking taylor expansion of 0 in z 0.079 * [taylor]: Taking taylor expansion of 0 in z 0.079 * [taylor]: Taking taylor expansion of 0 in z 0.082 * [taylor]: Taking taylor expansion of 0 in y 0.083 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (pow z 2))) in z 0.083 * [taylor]: Taking taylor expansion of 1/2 in z 0.084 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.084 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.084 * [taylor]: Taking taylor expansion of z in z 0.085 * [taylor]: Taking taylor expansion of 0 in z 0.085 * [taylor]: Taking taylor expansion of 0 in z 0.089 * [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 0.089 * [taylor]: Taking taylor expansion of -1/2 in y 0.089 * [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 0.089 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow z 4))) in y 0.089 * [taylor]: Taking taylor expansion of 1/4 in y 0.089 * [taylor]: Taking taylor expansion of (/ 1 (pow z 4)) in y 0.089 * [taylor]: Taking taylor expansion of (pow z 4) in y 0.089 * [taylor]: Taking taylor expansion of z in y 0.089 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4)))) in y 0.089 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) in y 0.089 * [taylor]: Taking taylor expansion of 1/2 in y 0.090 * [taylor]: Taking taylor expansion of (/ 1 (* (pow z 2) (pow y 2))) in y 0.090 * [taylor]: Taking taylor expansion of (* (pow z 2) (pow y 2)) in y 0.090 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.090 * [taylor]: Taking taylor expansion of z in y 0.090 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.090 * [taylor]: Taking taylor expansion of y in y 0.090 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow y 4))) in y 0.090 * [taylor]: Taking taylor expansion of 1/4 in y 0.090 * [taylor]: Taking taylor expansion of (/ 1 (pow y 4)) in y 0.090 * [taylor]: Taking taylor expansion of (pow y 4) in y 0.090 * [taylor]: Taking taylor expansion of y in y 0.100 * [taylor]: Taking taylor expansion of 0 in z 0.101 * [taylor]: Taking taylor expansion of 0 in z 0.103 * [taylor]: Taking taylor expansion of 0 in z 0.103 * [taylor]: Taking taylor expansion of 0 in z 0.103 * [taylor]: Taking taylor expansion of 0 in z 0.105 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in (x y z) around 0 0.105 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in z 0.105 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in z 0.105 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in z 0.105 * [taylor]: Taking taylor expansion of (pow x 2) in z 0.105 * [taylor]: Taking taylor expansion of x in z 0.105 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in z 0.105 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.105 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.105 * [taylor]: Taking taylor expansion of z in z 0.106 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in z 0.106 * [taylor]: Taking taylor expansion of (pow y 2) in z 0.106 * [taylor]: Taking taylor expansion of y in z 0.108 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in y 0.109 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.109 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.109 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.109 * [taylor]: Taking taylor expansion of x in y 0.109 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.109 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.109 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.109 * [taylor]: Taking taylor expansion of z in y 0.109 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.109 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.109 * [taylor]: Taking taylor expansion of y in y 0.112 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.112 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.112 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.112 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.112 * [taylor]: Taking taylor expansion of x in x 0.112 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.112 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.112 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.112 * [taylor]: Taking taylor expansion of z in x 0.113 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.113 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.113 * [taylor]: Taking taylor expansion of y in x 0.115 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))))) in x 0.115 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in x 0.115 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.115 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.115 * [taylor]: Taking taylor expansion of x in x 0.115 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in x 0.115 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in x 0.115 * [taylor]: Taking taylor expansion of (pow z 2) in x 0.115 * [taylor]: Taking taylor expansion of z in x 0.116 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.116 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.116 * [taylor]: Taking taylor expansion of y in x 0.118 * [taylor]: Taking taylor expansion of 1 in y 0.118 * [taylor]: Taking taylor expansion of 0 in y 0.118 * [taylor]: Taking taylor expansion of 1 in z 0.120 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 (pow z 2)) (/ 1 (pow y 2)))) in y 0.120 * [taylor]: Taking taylor expansion of 1/2 in y 0.120 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow z 2)) (/ 1 (pow y 2))) in y 0.120 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in y 0.120 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.120 * [taylor]: Taking taylor expansion of z in y 0.120 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.120 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.120 * [taylor]: Taking taylor expansion of y in y 0.123 * [taylor]: Taking taylor expansion of 0 in z 0.123 * [taylor]: Taking taylor expansion of 0 in z 0.123 * [taylor]: Taking taylor expansion of 0 in z 0.125 * [taylor]: Taking taylor expansion of 0 in y 0.127 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (pow z 2))) in z 0.127 * [taylor]: Taking taylor expansion of 1/2 in z 0.127 * [taylor]: Taking taylor expansion of (/ 1 (pow z 2)) in z 0.127 * [taylor]: Taking taylor expansion of (pow z 2) in z 0.127 * [taylor]: Taking taylor expansion of z in z 0.129 * [taylor]: Taking taylor expansion of 0 in z 0.129 * [taylor]: Taking taylor expansion of 0 in z 0.133 * [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 0.133 * [taylor]: Taking taylor expansion of -1/2 in y 0.133 * [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 0.133 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow z 4))) in y 0.133 * [taylor]: Taking taylor expansion of 1/4 in y 0.133 * [taylor]: Taking taylor expansion of (/ 1 (pow z 4)) in y 0.133 * [taylor]: Taking taylor expansion of (pow z 4) in y 0.133 * [taylor]: Taking taylor expansion of z in y 0.133 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) (* 1/4 (/ 1 (pow y 4)))) in y 0.133 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 (* (pow z 2) (pow y 2)))) in y 0.133 * [taylor]: Taking taylor expansion of 1/2 in y 0.133 * [taylor]: Taking taylor expansion of (/ 1 (* (pow z 2) (pow y 2))) in y 0.133 * [taylor]: Taking taylor expansion of (* (pow z 2) (pow y 2)) in y 0.133 * [taylor]: Taking taylor expansion of (pow z 2) in y 0.133 * [taylor]: Taking taylor expansion of z in y 0.133 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.133 * [taylor]: Taking taylor expansion of y in y 0.134 * [taylor]: Taking taylor expansion of (* 1/4 (/ 1 (pow y 4))) in y 0.134 * [taylor]: Taking taylor expansion of 1/4 in y 0.134 * [taylor]: Taking taylor expansion of (/ 1 (pow y 4)) in y 0.134 * [taylor]: Taking taylor expansion of (pow y 4) in y 0.134 * [taylor]: Taking taylor expansion of y in y 0.144 * [taylor]: Taking taylor expansion of 0 in z 0.144 * [taylor]: Taking taylor expansion of 0 in z 0.147 * [taylor]: Taking taylor expansion of 0 in z 0.147 * [taylor]: Taking taylor expansion of 0 in z 0.147 * [taylor]: Taking taylor expansion of 0 in z 0.148 * * * [progress]: simplifying candidates 0.149 * [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)))) z x (* -1 x) 0.153 * * [simplify]: iteration 0 : 96 enodes (cost 156 ) 0.156 * * [simplify]: iteration 1 : 305 enodes (cost 148 ) 0.163 * * [simplify]: iteration 2 : 1103 enodes (cost 148 ) 0.189 * * [simplify]: iteration 3 : 4548 enodes (cost 148 ) 0.266 * * [simplify]: iteration 4 : 5001 enodes (cost 148 ) 0.267 * [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)))) z x (* -1 x) 0.267 * * * [progress]: adding candidates to table 0.329 * * [progress]: iteration 2 / 4 0.329 * * * [progress]: picking best candidate 0.334 * * * * [pick]: Picked # 0.334 * * * [progress]: localizing error 0.341 * * * [progress]: generating rewritten candidates 0.341 * * * * [progress]: [ 1 / 1 ] rewriting at (2 1) 0.345 * * * [progress]: generating series expansions 0.345 * * * * [progress]: [ 1 / 1 ] generating series at (2 1) 0.345 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in (x y) around 0 0.345 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in y 0.345 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in y 0.345 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.345 * [taylor]: Taking taylor expansion of x in y 0.345 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.345 * [taylor]: Taking taylor expansion of y in y 0.346 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in x 0.346 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.346 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.346 * [taylor]: Taking taylor expansion of x in x 0.346 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.346 * [taylor]: Taking taylor expansion of y in x 0.347 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in x 0.347 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.347 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.347 * [taylor]: Taking taylor expansion of x in x 0.347 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.347 * [taylor]: Taking taylor expansion of y in x 0.348 * [taylor]: Taking taylor expansion of y in y 0.348 * [taylor]: Taking taylor expansion of 0 in y 0.349 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.349 * [taylor]: Taking taylor expansion of 1/2 in y 0.349 * [taylor]: Taking taylor expansion of y in y 0.351 * [taylor]: Taking taylor expansion of 0 in y 0.352 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in (x y) around 0 0.352 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in y 0.352 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.352 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.352 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.352 * [taylor]: Taking taylor expansion of x in y 0.352 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.352 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.352 * [taylor]: Taking taylor expansion of y in y 0.354 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.355 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.355 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.355 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.355 * [taylor]: Taking taylor expansion of x in x 0.355 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.355 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.355 * [taylor]: Taking taylor expansion of y in x 0.357 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.357 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.357 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.357 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.357 * [taylor]: Taking taylor expansion of x in x 0.358 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.358 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.358 * [taylor]: Taking taylor expansion of y in x 0.360 * [taylor]: Taking taylor expansion of 1 in y 0.360 * [taylor]: Taking taylor expansion of 0 in y 0.362 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.362 * [taylor]: Taking taylor expansion of 1/2 in y 0.362 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.362 * [taylor]: Taking taylor expansion of y in y 0.365 * [taylor]: Taking taylor expansion of 0 in y 0.367 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in (x y) around 0 0.367 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in y 0.367 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.367 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.367 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.367 * [taylor]: Taking taylor expansion of x in y 0.367 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.367 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.367 * [taylor]: Taking taylor expansion of y in y 0.370 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.370 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.370 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.370 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.370 * [taylor]: Taking taylor expansion of x in x 0.370 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.370 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.370 * [taylor]: Taking taylor expansion of y in x 0.372 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.372 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.372 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.372 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.372 * [taylor]: Taking taylor expansion of x in x 0.373 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.373 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.373 * [taylor]: Taking taylor expansion of y in x 0.375 * [taylor]: Taking taylor expansion of 1 in y 0.375 * [taylor]: Taking taylor expansion of 0 in y 0.377 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.377 * [taylor]: Taking taylor expansion of 1/2 in y 0.377 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.377 * [taylor]: Taking taylor expansion of y in y 0.380 * [taylor]: Taking taylor expansion of 0 in y 0.382 * * * [progress]: simplifying candidates 0.382 * [simplify]: Simplifying using # : (expm1 (sqrt (+ (* x x) (* y y)))) (log1p (sqrt (+ (* x x) (* y y)))) (log (sqrt (+ (* x x) (* y y)))) (exp (sqrt (+ (* x x) (* y y)))) (* (cbrt (sqrt (+ (* x x) (* y y)))) (cbrt (sqrt (+ (* x x) (* y y))))) (cbrt (sqrt (+ (* x x) (* y y)))) (* (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y)))) (sqrt (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y))))) (sqrt (cbrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt 1) (sqrt (+ (* x x) (* y y))) (sqrt (+ (pow (* x x) 3) (pow (* y y) 3))) (sqrt (+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))) (sqrt (- (* (* x x) (* x x)) (* (* y y) (* y y)))) (sqrt (- (* x x) (* y y))) (/ 1 2) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) y x (* -1 x) 0.385 * * [simplify]: iteration 0 : 98 enodes (cost 103 ) 0.388 * * [simplify]: iteration 1 : 254 enodes (cost 98 ) 0.394 * * [simplify]: iteration 2 : 619 enodes (cost 98 ) 0.406 * * [simplify]: iteration 3 : 1573 enodes (cost 98 ) 0.442 * * [simplify]: iteration 4 : 5001 enodes (cost 98 ) 0.443 * [simplify]: Simplified to: (expm1 (sqrt (+ (* x x) (* y y)))) (log1p (sqrt (+ (* x x) (* y y)))) (log (sqrt (+ (* x x) (* y y)))) (exp (sqrt (+ (* x x) (* y y)))) (* (cbrt (sqrt (+ (* x x) (* y y)))) (cbrt (sqrt (+ (* x x) (* y y))))) (cbrt (sqrt (+ (* x x) (* y y)))) (pow (hypot x y) 3) (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (cbrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt 1) (hypot x y) (hypot (pow y 3) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))) (sqrt (- (* (* x x) (* x x)) (* (* y y) (* y y)))) (sqrt (- (* x x) (* y y))) 1/2 (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) y x (* -1 x) 0.443 * * * [progress]: adding candidates to table 0.503 * * [progress]: iteration 3 / 4 0.503 * * * [progress]: picking best candidate 0.505 * * * * [pick]: Picked # 0.505 * * * [progress]: localizing error 0.512 * * * [progress]: generating rewritten candidates 0.512 * * * [progress]: generating series expansions 0.512 * * * [progress]: simplifying candidates 0.512 * [simplify]: Simplifying using # : 0.517 * * [simplify]: iteration 0 : 0 enodes (cost 0 ) 0.517 * [simplify]: Simplified to: 0.517 * * * [progress]: adding candidates to table 0.517 * [progress]: [Phase 3 of 3] Extracting. 0.520 * [simplify]: Simplifying using # : (hypot (* (sqrt 1) (hypot x y)) z) 0.521 * * [simplify]: iteration 0 : 11 enodes (cost 4 ) 0.521 * * [simplify]: iteration 1 : 11 enodes (cost 4 ) 0.521 * [simplify]: Simplified to: (hypot (* (sqrt 1) (hypot x y)) z) 1.056 * [regime-testing]: End program error score: 0.004625578197274659 1.095 * [regime-testing]: Target error score: 25.201822345776588