13.209 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.015 * * * [progress]: [2/2] Setting up program. 0.018 * [progress]: [Phase 2 of 3] Improving. 0.019 * [simplify]: Simplifying using # : (/ (fabs (- x y)) (fabs y)) 0.020 * * [simplify]: iteration 0 : 8 enodes (cost 4 ) 0.021 * * [simplify]: iteration 1 : 9 enodes (cost 4 ) 0.023 * * [simplify]: iteration 2 : 9 enodes (cost 4 ) 0.023 * [simplify]: Simplified to: (/ (fabs (- x y)) (fabs y)) 0.023 * * [progress]: iteration 1 / 4 0.023 * * * [progress]: picking best candidate 0.026 * * * * [pick]: Picked # 0.026 * * * [progress]: localizing error 0.036 * * * [progress]: generating rewritten candidates 0.036 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.040 * * * [progress]: generating series expansions 0.040 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.040 * [approximate]: Approximating (/ (fabs (- x y)) (fabs y)) in (x y) around 0 0.042 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.042 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.042 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.043 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.043 * [approximate]: Approximating (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in (x y) around 0 0.043 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.044 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.044 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.045 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.045 * [approximate]: Approximating (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in (x y) around 0 0.045 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.046 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.046 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.047 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.047 * * * [progress]: simplifying candidates 0.047 * [simplify]: Simplifying using # : (- (log (fabs (- x y))) (log (fabs y))) (log (/ (fabs (- x y)) (fabs y))) (exp (/ (fabs (- x y)) (fabs y))) (/ (* (* (fabs (- x y)) (fabs (- x y))) (fabs (- x y))) (* (* (fabs y) (fabs y)) (fabs y))) (* (cbrt (/ (fabs (- x y)) (fabs y))) (cbrt (/ (fabs (- x y)) (fabs y)))) (cbrt (/ (fabs (- x y)) (fabs y))) (* (* (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y))) (/ (fabs (- x y)) (fabs y))) (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (/ (fabs (- x y)) (fabs y))) (neg (fabs (- x y))) (neg (fabs y)) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (cbrt (fabs (- x y))) (cbrt (fabs y))) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) (sqrt (fabs y))) (/ (cbrt (fabs (- x y))) (sqrt (fabs y))) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) 1) (/ (cbrt (fabs (- x y))) (fabs y)) (/ (sqrt (fabs (- x y))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (cbrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) 1) (/ (sqrt (fabs (- x y))) (fabs y)) (/ 1 (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (fabs (- x y)) (cbrt (fabs y))) (/ 1 (sqrt (fabs y))) (/ (fabs (- x y)) (sqrt (fabs y))) (/ 1 1) (/ (fabs (- x y)) (fabs y)) (/ 1 (fabs y)) (/ (fabs y) (fabs (- x y))) (/ (fabs (- x y)) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (fabs (- x y)) (sqrt (fabs y))) (/ (fabs (- x y)) 1) (/ (fabs y) (cbrt (fabs (- x y)))) (/ (fabs y) (sqrt (fabs (- x y)))) (/ (fabs y) (fabs (- x y))) (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y)) 0.050 * * [simplify]: iteration 0 : 86 enodes (cost 226 ) 0.052 * * [simplify]: iteration 1 : 235 enodes (cost 208 ) 0.055 * * [simplify]: iteration 2 : 584 enodes (cost 208 ) 0.064 * * [simplify]: iteration 3 : 1520 enodes (cost 208 ) 0.089 * * [simplify]: iteration 4 : 4363 enodes (cost 208 ) 0.130 * * [simplify]: iteration 5 : 5002 enodes (cost 208 ) 0.131 * [simplify]: Simplified to: (log (/ (fabs (- x y)) (fabs y))) (log (/ (fabs (- x y)) (fabs y))) (exp (/ (fabs (- x y)) (fabs y))) (pow (/ (fabs (- x y)) (fabs y)) 3) (* (cbrt (/ (fabs (- x y)) (fabs y))) (cbrt (/ (fabs (- x y)) (fabs y)))) (cbrt (/ (fabs (- x y)) (fabs y))) (pow (/ (fabs (- x y)) (fabs y)) 3) (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (/ (fabs (- x y)) (fabs y))) (neg (fabs (- x y))) (neg (fabs y)) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (cbrt (fabs (- x y))) (cbrt (fabs y))) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) (sqrt (fabs y))) (/ (cbrt (fabs (- x y))) (sqrt (fabs y))) (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) (/ (cbrt (fabs (- x y))) (fabs y)) (/ (sqrt (fabs (- x y))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (cbrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)) (/ 1 (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (fabs (- x y)) (cbrt (fabs y))) (/ 1 (sqrt (fabs y))) (/ (fabs (- x y)) (sqrt (fabs y))) 1 (/ (fabs (- x y)) (fabs y)) (/ 1 (fabs y)) (/ (fabs y) (fabs (- x y))) (/ (fabs (- x y)) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (fabs (- x y)) (sqrt (fabs y))) (fabs (- x y)) (/ (fabs y) (cbrt (fabs (- x y)))) (/ (fabs y) (sqrt (fabs (- x y)))) (/ (fabs y) (fabs (- x y))) (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y)) 0.132 * * * [progress]: adding candidates to table 0.173 * * [progress]: iteration 2 / 4 0.174 * * * [progress]: picking best candidate 0.184 * * * * [pick]: Picked # 0.184 * * * [progress]: localizing error 0.191 * * * [progress]: generating rewritten candidates 0.191 * * * * [progress]: [ 1 / 2 ] rewriting at (2 1) 0.195 * * * * [progress]: [ 2 / 2 ] rewriting at (2) 0.216 * * * [progress]: generating series expansions 0.216 * * * * [progress]: [ 1 / 2 ] generating series at (2 1) 0.216 * [approximate]: Approximating (* (fabs (- x y)) (sqrt (/ 1 (fabs y)))) in (x y) around 0 0.217 * [taylor]: Taking taylor expansion of (* (fabs (- x y)) (sqrt (/ 1 (fabs y)))) in y 0.217 * [taylor]: Taking taylor expansion of (* (fabs (- x y)) (sqrt (/ 1 (fabs y)))) in y 0.219 * [taylor]: Taking taylor expansion of (* (fabs (- x y)) (sqrt (/ 1 (fabs y)))) in y 0.221 * [taylor]: Taking taylor expansion of (* (fabs (- x y)) (sqrt (/ 1 (fabs y)))) in y 0.221 * [approximate]: Approximating (* (fabs (- (/ 1 x) (/ 1 y))) (sqrt (/ 1 (fabs (/ 1 y))))) in (x y) around 0 0.222 * [taylor]: Taking taylor expansion of (* (fabs (- (/ 1 x) (/ 1 y))) (sqrt (/ 1 (fabs (/ 1 y))))) in y 0.223 * [taylor]: Taking taylor expansion of (* (fabs (- (/ 1 x) (/ 1 y))) (sqrt (/ 1 (fabs (/ 1 y))))) in y 0.224 * [taylor]: Taking taylor expansion of (* (fabs (- (/ 1 x) (/ 1 y))) (sqrt (/ 1 (fabs (/ 1 y))))) in y 0.227 * [taylor]: Taking taylor expansion of (* (fabs (- (/ 1 x) (/ 1 y))) (sqrt (/ 1 (fabs (/ 1 y))))) in y 0.227 * [approximate]: Approximating (* (fabs (- (/ 1 y) (/ 1 x))) (sqrt (/ 1 (fabs (/ -1 y))))) in (x y) around 0 0.228 * [taylor]: Taking taylor expansion of (* (fabs (- (/ 1 y) (/ 1 x))) (sqrt (/ 1 (fabs (/ -1 y))))) in y 0.229 * [taylor]: Taking taylor expansion of (* (fabs (- (/ 1 y) (/ 1 x))) (sqrt (/ 1 (fabs (/ -1 y))))) in y 0.230 * [taylor]: Taking taylor expansion of (* (fabs (- (/ 1 y) (/ 1 x))) (sqrt (/ 1 (fabs (/ -1 y))))) in y 0.233 * [taylor]: Taking taylor expansion of (* (fabs (- (/ 1 y) (/ 1 x))) (sqrt (/ 1 (fabs (/ -1 y))))) in y 0.233 * * * * [progress]: [ 2 / 2 ] generating series at (2) 0.233 * [approximate]: Approximating (/ (fabs (- x y)) (fabs y)) in (x y) around 0 0.233 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.234 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.234 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.234 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.234 * [approximate]: Approximating (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in (x y) around 0 0.235 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.235 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.236 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.236 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.237 * [approximate]: Approximating (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in (x y) around 0 0.237 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.237 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.238 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.238 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.239 * * * [progress]: simplifying candidates 0.242 * [simplify]: Simplifying using # : (- (log (fabs (- x y))) (log (sqrt (fabs y)))) (log (/ (fabs (- x y)) (sqrt (fabs y)))) (exp (/ (fabs (- x y)) (sqrt (fabs y)))) (/ (* (* (fabs (- x y)) (fabs (- x y))) (fabs (- x y))) (* (* (sqrt (fabs y)) (sqrt (fabs y))) (sqrt (fabs y)))) (* (cbrt (/ (fabs (- x y)) (sqrt (fabs y)))) (cbrt (/ (fabs (- x y)) (sqrt (fabs y))))) (cbrt (/ (fabs (- x y)) (sqrt (fabs y)))) (* (* (/ (fabs (- x y)) (sqrt (fabs y))) (/ (fabs (- x y)) (sqrt (fabs y)))) (/ (fabs (- x y)) (sqrt (fabs y)))) (sqrt (/ (fabs (- x y)) (sqrt (fabs y)))) (sqrt (/ (fabs (- x y)) (sqrt (fabs y)))) (neg (fabs (- x y))) (neg (sqrt (fabs y))) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) (* (cbrt (sqrt (fabs y))) (cbrt (sqrt (fabs y))))) (/ (cbrt (fabs (- x y))) (cbrt (sqrt (fabs y)))) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) (sqrt (* (cbrt (fabs y)) (cbrt (fabs y))))) (/ (cbrt (fabs (- x y))) (sqrt (cbrt (fabs y)))) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) (sqrt (sqrt (fabs y)))) (/ (cbrt (fabs (- x y))) (sqrt (sqrt (fabs y)))) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) (sqrt 1)) (/ (cbrt (fabs (- x y))) (sqrt (fabs y))) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) (sqrt (sqrt (fabs y)))) (/ (cbrt (fabs (- x y))) (sqrt (sqrt (fabs y)))) (/ (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y)))) 1) (/ (cbrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (* (cbrt (sqrt (fabs y))) (cbrt (sqrt (fabs y))))) (/ (sqrt (fabs (- x y))) (cbrt (sqrt (fabs y)))) (/ (sqrt (fabs (- x y))) (sqrt (* (cbrt (fabs y)) (cbrt (fabs y))))) (/ (sqrt (fabs (- x y))) (sqrt (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (sqrt (sqrt 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x y)) (sqrt (sqrt (fabs y)))) (/ (fabs (- x y)) 1) (/ (sqrt (fabs y)) (cbrt (fabs (- x y)))) (/ (sqrt (fabs y)) (sqrt (fabs (- x y)))) (/ (sqrt (fabs y)) (fabs (- x y))) (- (- (log (fabs (- x y))) (log (sqrt (fabs y)))) (log (sqrt (fabs y)))) (- (log (/ (fabs (- x y)) (sqrt (fabs y)))) (log (sqrt (fabs y)))) (log (/ (/ (fabs (- x y)) (sqrt (fabs y))) (sqrt (fabs y)))) (exp (/ (/ (fabs (- x y)) (sqrt (fabs y))) (sqrt (fabs y)))) (/ (/ (* (* (fabs (- x y)) (fabs (- x y))) (fabs (- x y))) (* (* (sqrt (fabs y)) (sqrt (fabs y))) (sqrt (fabs y)))) (* (* (sqrt (fabs y)) (sqrt (fabs y))) (sqrt (fabs y)))) (/ (* (* (/ (fabs (- x y)) (sqrt (fabs y))) (/ (fabs (- x y)) (sqrt (fabs y)))) (/ (fabs (- x y)) (sqrt (fabs y)))) (* (* (sqrt (fabs y)) (sqrt (fabs y))) (sqrt (fabs y)))) (* (cbrt (/ (/ (fabs (- x y)) (sqrt (fabs y))) (sqrt (fabs y)))) (cbrt (/ (/ (fabs (- x y)) (sqrt (fabs y))) (sqrt (fabs y))))) (cbrt (/ (/ (fabs (- x y)) (sqrt (fabs y))) (sqrt (fabs y)))) (* (* (/ (/ (fabs (- x y)) (sqrt 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(cbrt (sqrt (fabs y))))) (/ (/ (fabs (- x y)) (sqrt (fabs y))) (cbrt (sqrt (fabs y)))) (/ 1 (* 1 (fabs (cbrt (fabs y))))) (/ (/ (fabs (- x y)) (sqrt (fabs y))) (sqrt (cbrt (fabs y)))) (/ 1 (sqrt (sqrt (fabs y)))) (/ (fabs (- x y)) (/ (pow (sqrt (sqrt (fabs y))) 3) 1)) 1 (/ (fabs (- x y)) (fabs y)) (/ 1 (sqrt (sqrt (fabs y)))) (/ (fabs (- x y)) (/ (pow (sqrt (sqrt (fabs y))) 3) 1)) 1 (/ (fabs (- x y)) (fabs y)) (/ 1 (* (cbrt (sqrt (fabs y))) (cbrt (sqrt (fabs y))))) (/ (/ (fabs (- x y)) (sqrt (fabs y))) (cbrt (sqrt (fabs y)))) (/ 1 (* 1 (fabs (cbrt (fabs y))))) (/ (/ (fabs (- x y)) (sqrt (fabs y))) (sqrt (cbrt (fabs y)))) (/ 1 (sqrt (sqrt (fabs y)))) (/ (fabs (- x y)) (/ (pow (sqrt (sqrt (fabs y))) 3) 1)) 1 (/ (fabs (- x y)) (fabs y)) (/ 1 (sqrt (sqrt (fabs y)))) (/ (fabs (- x y)) (/ (pow (sqrt (sqrt (fabs y))) 3) 1)) 1 (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (* (cbrt (sqrt (fabs y))) (cbrt (sqrt (fabs y))))) (/ (/ 1 (sqrt (fabs y))) (cbrt (sqrt (fabs y)))) (/ (fabs (- x y)) (fabs 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(/ (fabs y) (cbrt (fabs (- x y)))) (/ (sqrt (fabs y)) (/ (cbrt (fabs (- x y))) (sqrt (sqrt (fabs y))))) (/ (fabs y) (cbrt (fabs (- x y)))) (/ (sqrt (fabs y)) (/ (sqrt (fabs (- x y))) (cbrt (sqrt (fabs y))))) (/ (sqrt (fabs y)) (/ (sqrt (fabs (- x y))) (sqrt (cbrt (fabs y))))) (/ (pow (sqrt (sqrt (fabs y))) 3) (sqrt (fabs (- x y)))) (/ (fabs y) (sqrt (fabs (- x y)))) (/ (pow (sqrt (sqrt (fabs y))) 3) (sqrt (fabs (- x y)))) (/ (fabs y) (sqrt (fabs (- x y)))) (/ (sqrt (fabs y)) (/ (fabs (- x y)) (cbrt (sqrt (fabs y))))) (/ (sqrt (fabs y)) (/ (fabs (- x y)) (sqrt (cbrt (fabs y))))) (/ (sqrt (fabs y)) (/ (fabs (- x y)) (sqrt (sqrt (fabs y))))) (/ (fabs y) (fabs (- x y))) (/ (sqrt (fabs y)) (/ (fabs (- x y)) (sqrt (sqrt (fabs y))))) (/ (fabs y) (fabs (- x y))) (/ (fabs y) (fabs (- x y))) (fabs y) (fabs y) (* (fabs (- x y)) (sqrt (/ 1 (fabs y)))) (* (fabs (- x y)) (sqrt (/ 1 (fabs y)))) (* (fabs (- x y)) (sqrt (/ 1 (fabs y)))) (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y)) 0.313 * * * [progress]: adding candidates to table 0.759 * * [progress]: iteration 3 / 4 0.759 * * * [progress]: picking best candidate 0.762 * * * * [pick]: Picked # 0.762 * * * [progress]: localizing error 0.769 * * * [progress]: generating rewritten candidates 0.769 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.779 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2) 0.786 * * * [progress]: generating series expansions 0.786 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.786 * [approximate]: Approximating (/ (fabs (- x y)) (fabs y)) in (x y) around 0 0.787 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.787 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.787 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.788 * [taylor]: Taking taylor expansion of (/ (fabs (- x y)) (fabs y)) in y 0.788 * [approximate]: Approximating (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in (x y) around 0 0.789 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.789 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.790 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.790 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 x) (/ 1 y))) (fabs (/ 1 y))) in y 0.790 * [approximate]: Approximating (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in (x y) around 0 0.791 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.791 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.792 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.792 * [taylor]: Taking taylor expansion of (/ (fabs (- (/ 1 y) (/ 1 x))) (fabs (/ -1 y))) in y 0.792 * * * * [progress]: [ 2 / 2 ] generating series at (2 2) 0.793 * [approximate]: Approximating (* (sqrt (fabs (- x y))) (/ 1 (fabs y))) in (x y) around 0 0.793 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- x y))) (/ 1 (fabs y))) in y 0.793 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- x y))) (/ 1 (fabs y))) in y 0.795 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- x y))) (/ 1 (fabs y))) in y 0.797 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- x y))) (/ 1 (fabs y))) in y 0.798 * [approximate]: Approximating (* (sqrt (fabs (- (/ 1 x) (/ 1 y)))) (/ 1 (fabs (/ 1 y)))) in (x y) around 0 0.799 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- (/ 1 x) (/ 1 y)))) (/ 1 (fabs (/ 1 y)))) in y 0.799 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- (/ 1 x) (/ 1 y)))) (/ 1 (fabs (/ 1 y)))) in y 0.801 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- (/ 1 x) (/ 1 y)))) (/ 1 (fabs (/ 1 y)))) in y 0.803 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- (/ 1 x) (/ 1 y)))) (/ 1 (fabs (/ 1 y)))) in y 0.804 * [approximate]: Approximating (* (sqrt (fabs (- (/ 1 y) (/ 1 x)))) (/ 1 (fabs (/ -1 y)))) in (x y) around 0 0.805 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- (/ 1 y) (/ 1 x)))) (/ 1 (fabs (/ -1 y)))) in y 0.805 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- (/ 1 y) (/ 1 x)))) (/ 1 (fabs (/ -1 y)))) in y 0.807 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- (/ 1 y) (/ 1 x)))) (/ 1 (fabs (/ -1 y)))) in y 0.813 * [taylor]: Taking taylor expansion of (* (sqrt (fabs (- (/ 1 y) (/ 1 x)))) (/ 1 (fabs (/ -1 y)))) in y 0.813 * * * [progress]: simplifying candidates 0.814 * [simplify]: Simplifying using # : (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y))) (+ (log (sqrt (fabs (- x y)))) (- (log (sqrt (fabs (- x y)))) (log (fabs y)))) (+ (log (sqrt (fabs (- x y)))) (log (/ (sqrt (fabs (- x y))) (fabs y)))) (log (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (exp (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (* (* (* (sqrt (fabs (- x y))) (sqrt (fabs (- x y)))) (sqrt (fabs (- x y)))) (/ (* (* (sqrt (fabs (- x y))) (sqrt (fabs (- x y)))) (sqrt (fabs (- x y)))) (* (* (fabs y) (fabs y)) (fabs y)))) (* (* (* (sqrt (fabs (- x y))) (sqrt (fabs (- x y)))) (sqrt (fabs (- x y)))) (* (* (/ (sqrt (fabs (- x y))) (fabs y)) (/ (sqrt (fabs (- x y))) (fabs y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (* (cbrt (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (cbrt (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y))))) (cbrt (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (* (* (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y))) (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (sqrt (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (sqrt (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y)))) (* (sqrt (fabs (- x y))) (* (cbrt (/ (sqrt (fabs (- x y))) (fabs y))) (cbrt (/ (sqrt (fabs (- x y))) (fabs y))))) (* (sqrt (fabs (- x y))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (fabs (- x y))) (/ (* (cbrt (sqrt (fabs (- x y)))) (cbrt (sqrt (fabs (- x y))))) (* (cbrt (fabs y)) (cbrt (fabs y))))) (* (sqrt (fabs (- x y))) (/ (* (cbrt (sqrt (fabs (- x y)))) (cbrt (sqrt (fabs (- x y))))) (sqrt (fabs y)))) (* (sqrt (fabs (- x y))) (/ (* (cbrt (sqrt (fabs (- x y)))) (cbrt (sqrt (fabs (- x y))))) 1)) (* (sqrt (fabs (- x y))) (/ (sqrt (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y))))) (* (cbrt (fabs y)) (cbrt (fabs y))))) (* (sqrt (fabs (- x y))) (/ (sqrt (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y))))) (sqrt (fabs y)))) (* (sqrt (fabs (- x y))) (/ (sqrt (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y))))) 1)) (* (sqrt (fabs (- x y))) (/ (sqrt (sqrt (fabs (- x y)))) (* (cbrt (fabs y)) (cbrt (fabs y))))) (* (sqrt (fabs (- x y))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y)))) (* (sqrt (fabs (- x y))) (/ (sqrt (sqrt (fabs (- x y)))) 1)) (* (sqrt (fabs (- x y))) (/ (sqrt 1) (* (cbrt (fabs y)) (cbrt (fabs y))))) (* (sqrt (fabs (- x y))) (/ (sqrt 1) (sqrt (fabs y)))) (* (sqrt (fabs (- x y))) (/ (sqrt 1) 1)) (* (sqrt (fabs (- x y))) (/ (sqrt (sqrt (fabs (- x y)))) (* (cbrt (fabs y)) (cbrt (fabs y))))) (* (sqrt (fabs (- x y))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y)))) (* (sqrt (fabs (- x y))) (/ (sqrt (sqrt (fabs (- x y)))) 1)) (* (sqrt (fabs (- x y))) (/ 1 (* (cbrt (fabs y)) (cbrt (fabs y))))) (* (sqrt (fabs (- x y))) (/ 1 (sqrt (fabs y)))) (* (sqrt (fabs (- x y))) (/ 1 1)) (* (sqrt (fabs (- x y))) 1) (* (sqrt (fabs (- x y))) (sqrt (fabs (- x y)))) (* (cbrt (sqrt (fabs (- x y)))) (/ (sqrt (fabs (- x y))) (fabs y))) (* (sqrt (cbrt (fabs (- x y)))) (/ (sqrt (fabs (- x y))) (fabs y))) (* (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (fabs (- x y))) (fabs y))) (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y))) (* (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (fabs (- x y))) (fabs y))) (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y))) (* (sqrt (fabs (- x y))) (sqrt (fabs (- x y)))) (- (log (sqrt (fabs (- x y)))) (log (fabs y))) (log (/ (sqrt 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(* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (cbrt (fabs (- x y)))) (cbrt (fabs y))) (/ (sqrt (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y))))) (sqrt (fabs y))) (/ (sqrt (cbrt (fabs (- x y)))) (sqrt (fabs y))) (/ (sqrt (* (cbrt (fabs (- x y))) (cbrt (fabs (- x y))))) 1) (/ (sqrt (cbrt (fabs (- x y)))) (fabs y)) (/ (sqrt (sqrt (fabs (- x y)))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (sqrt (fabs (- x y)))) (cbrt (fabs y))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y))) (/ (sqrt (sqrt (fabs (- x y)))) 1) (/ (sqrt (sqrt (fabs (- x y)))) (fabs y)) (/ (sqrt 1) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (cbrt (fabs y))) (/ (sqrt 1) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt 1) 1) (/ (sqrt (fabs (- x y))) (fabs y)) (/ (sqrt (sqrt (fabs (- x y)))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (sqrt (fabs (- x y)))) (cbrt (fabs y))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y))) (/ (sqrt (sqrt (fabs (- x y)))) 1) (/ (sqrt (sqrt (fabs (- x y)))) (fabs y)) (/ 1 (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (cbrt (fabs y))) (/ 1 (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ 1 1) (/ (sqrt (fabs (- x y))) (fabs y)) (/ 1 (fabs y)) (/ (fabs y) (sqrt (fabs (- x y)))) (/ (sqrt (fabs (- x y))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) 1) (/ (fabs y) (cbrt (sqrt (fabs (- x y))))) (/ (fabs y) (sqrt (cbrt (fabs (- x y))))) (/ (fabs y) (sqrt (sqrt (fabs (- x y))))) (/ (fabs y) (sqrt (fabs (- x y)))) (/ (fabs y) (sqrt (sqrt (fabs (- x y))))) (/ (fabs y) (sqrt (fabs (- x y)))) (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y)) (* (sqrt (fabs (- x y))) (/ 1 (fabs y))) (* (sqrt (fabs (- x y))) (/ 1 (fabs y))) (* (sqrt (fabs (- x y))) (/ 1 (fabs y))) 0.819 * * [simplify]: iteration 0 : 222 enodes (cost 981 ) 0.823 * * [simplify]: iteration 1 : 1015 enodes (cost 849 ) 0.844 * * [simplify]: iteration 2 : 4514 enodes (cost 812 ) 0.897 * * [simplify]: iteration 3 : 5002 enodes (cost 812 ) 0.902 * [simplify]: Simplified to: (/ (fabs (- x y)) (fabs y)) (- (log (fabs (- x y))) (log (fabs y))) (- (log (fabs (- x y))) (log (fabs y))) (- (log (fabs (- x y))) (log (fabs y))) (pow (exp (fabs (- x y))) (/ 1 (fabs y))) (pow (/ (fabs (- x y)) (fabs y)) 3) (pow (/ (fabs (- x y)) (fabs y)) 3) (* (cbrt (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (cbrt (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y))))) (cbrt (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (pow (/ (fabs (- x y)) (fabs y)) 3) (sqrt (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (sqrt (* (sqrt (fabs (- x y))) (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y)))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (* (sqrt (sqrt (fabs (- x y)))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (sqrt (fabs (- x y)))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y)))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (* (sqrt (fabs (- x y))) (* (cbrt (/ (sqrt (fabs (- x y))) (fabs y))) (cbrt (/ (sqrt (fabs (- x y))) (fabs y))))) (* (sqrt (fabs (- x y))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y)))) (* (sqrt (fabs (- x y))) (/ (* (cbrt (sqrt (fabs (- x y)))) (cbrt (sqrt (fabs (- x y))))) (* (cbrt (fabs y)) (cbrt (fabs y))))) (* (sqrt (fabs (- x y))) (/ (* (cbrt (sqrt (fabs (- x y)))) (cbrt (sqrt (fabs (- x y))))) (sqrt (fabs y)))) (* (* (cbrt (sqrt (fabs (- x y)))) (cbrt (sqrt (fabs (- x y))))) (sqrt (fabs (- x y)))) (/ (* (sqrt (fabs (- x y))) (fabs (cbrt (fabs (- x y))))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (* (sqrt (fabs (- x y))) (fabs (cbrt (fabs (- x y))))) (sqrt (fabs y))) (* (fabs (cbrt (fabs (- x y)))) (sqrt (fabs (- x y)))) (/ (pow (sqrt (sqrt (fabs (- x y)))) 3) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (pow (sqrt (sqrt (fabs (- x y)))) 3) (sqrt (fabs y))) (pow (sqrt (sqrt (fabs (- x y)))) 3) (/ (sqrt (fabs (- x y))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (sqrt (fabs (- x y))) (/ (pow (sqrt (sqrt (fabs (- x y)))) 3) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (pow (sqrt (sqrt (fabs (- x y)))) 3) (sqrt (fabs y))) (pow (sqrt (sqrt (fabs (- x y)))) 3) (/ (sqrt (fabs (- x y))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (sqrt (fabs (- x y))) (sqrt (fabs (- x y))) (fabs (- x y)) (* (cbrt (sqrt (fabs (- x y)))) (/ (sqrt (fabs (- x y))) (fabs y))) (* (sqrt (cbrt (fabs (- x y)))) (/ (sqrt (fabs (- x y))) (fabs y))) (/ (pow (sqrt (sqrt (fabs (- x y)))) 3) (fabs y)) (/ (fabs (- x y)) (fabs y)) (/ (pow (sqrt (sqrt (fabs (- x y)))) 3) (fabs y)) (/ (fabs (- x y)) (fabs y)) (fabs (- x y)) (log (/ (sqrt (fabs (- x y))) (fabs y))) (log (/ (sqrt (fabs (- x y))) (fabs y))) (exp (/ (sqrt (fabs (- x y))) (fabs y))) (pow (/ (sqrt (fabs (- x y))) (fabs y)) 3) (* (cbrt (/ (sqrt (fabs (- x y))) (fabs y))) (cbrt (/ (sqrt (fabs (- x y))) (fabs y)))) (cbrt (/ (sqrt (fabs (- x y))) (fabs y))) (pow (/ (sqrt (fabs (- x y))) (fabs y)) 3) (sqrt (/ (sqrt (fabs (- x y))) (fabs y))) (sqrt (/ (sqrt (fabs (- x y))) (fabs y))) (neg (sqrt (fabs (- x y)))) (neg (fabs y)) (/ (* (cbrt (sqrt (fabs (- x y)))) (cbrt (sqrt (fabs (- x y))))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (cbrt (sqrt (fabs (- x y)))) (cbrt (fabs y))) (/ (* (cbrt (sqrt (fabs (- x y)))) (cbrt (sqrt (fabs (- x y))))) (sqrt (fabs y))) (/ (cbrt (sqrt (fabs (- x y)))) (sqrt (fabs y))) (* (cbrt (sqrt (fabs (- x y)))) (cbrt (sqrt (fabs (- x y))))) (/ (cbrt (sqrt (fabs (- x y)))) (fabs y)) (/ (/ (fabs (cbrt (fabs (- x y)))) (cbrt (fabs y))) (cbrt (fabs y))) (/ (sqrt (cbrt (fabs (- x y)))) (cbrt (fabs y))) (/ (fabs (cbrt (fabs (- x y)))) (* (sqrt (fabs y)) 1)) (/ (sqrt (cbrt (fabs (- x y)))) (sqrt (fabs y))) (fabs (cbrt (fabs (- x y)))) (/ (sqrt (cbrt (fabs (- x y)))) (fabs y)) (/ (sqrt (sqrt (fabs (- x y)))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (sqrt (fabs (- x y)))) (cbrt (fabs y))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y))) (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (sqrt (fabs (- x y)))) (fabs y)) (/ 1 (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (cbrt (fabs y))) (/ 1 (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) 1 (/ (sqrt (fabs (- x y))) (fabs y)) (/ (sqrt (sqrt (fabs (- x y)))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (sqrt (fabs (- x y)))) (cbrt (fabs y))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y))) (/ (sqrt (sqrt (fabs (- x y)))) (sqrt (fabs y))) (sqrt (sqrt (fabs (- x y)))) (/ (sqrt (sqrt (fabs (- x y)))) (fabs y)) (/ 1 (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (cbrt (fabs y))) (/ 1 (sqrt (fabs y))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) 1 (/ (sqrt (fabs (- x y))) (fabs y)) (/ 1 (fabs y)) (/ (fabs y) (sqrt (fabs (- x y)))) (/ (sqrt (fabs (- x y))) (* (cbrt (fabs y)) (cbrt (fabs y)))) (/ (sqrt (fabs (- x y))) (sqrt (fabs y))) (sqrt (fabs (- x y))) (/ (fabs y) (cbrt (sqrt (fabs (- x y))))) (/ (fabs y) (sqrt (cbrt (fabs (- x y))))) (/ (fabs y) (sqrt (sqrt (fabs (- x y))))) (/ (fabs y) (sqrt (fabs (- x y)))) (/ (fabs y) (sqrt (sqrt (fabs (- x y))))) (/ (fabs y) (sqrt (fabs (- x y)))) (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y)) (/ (fabs (- x y)) (fabs y)) (/ (sqrt (fabs (- x y))) (fabs y)) (/ (sqrt (fabs (- x y))) (fabs y)) (/ (sqrt (fabs (- x y))) (fabs y)) 0.902 * * * [progress]: adding candidates to table 1.070 * [progress]: [Phase 3 of 3] Extracting. 1.070 * * [regime]: Finding splitpoints for: (# # #) 1.071 * * * [regime-changes]: Trying 3 branch expressions: ((/ (fabs (- x y)) (fabs y)) y x) 1.071 * * * * [regimes]: Trying to branch on (/ (fabs (- x y)) (fabs y)) from (# # #) 1.113 * * * * [regimes]: Trying to branch on y from (# # #) 1.150 * * * * [regimes]: Trying to branch on x from (# # #) 1.186 * * * [regime]: Found split indices: #