2.661 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.026 * * * [progress]: [2/2] Setting up program. 0.028 * [progress]: [Phase 2 of 3] Improving. 0.028 * [simplify]: Simplifying using # : (sqrt (- 1.0 (* x x))) 0.030 * * [simplify]: iteration 0 : 7 enodes (cost 3 ) 0.031 * * [simplify]: iteration 1 : 11 enodes (cost 3 ) 0.032 * * [simplify]: iteration 2 : 11 enodes (cost 3 ) 0.032 * [simplify]: Simplified to: (sqrt (- 1.0 (* x x))) 0.032 * * [progress]: iteration 1 / 4 0.032 * * * [progress]: picking best candidate 0.034 * * * * [pick]: Picked # 0.034 * * * [progress]: localizing error 0.037 * * * [progress]: generating rewritten candidates 0.037 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.040 * * * [progress]: generating series expansions 0.040 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.040 * [approximate]: Taking taylor expansion of (sqrt (- 1.0 (pow x 2))) in (x) around 0 0.041 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (pow x 2))) in x 0.041 * [taylor]: Taking taylor expansion of (- 1.0 (pow x 2)) in x 0.041 * [taylor]: Taking taylor expansion of 1.0 in x 0.041 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.041 * [taylor]: Taking taylor expansion of x in x 0.042 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (pow x 2))) in x 0.042 * [taylor]: Taking taylor expansion of (- 1.0 (pow x 2)) in x 0.042 * [taylor]: Taking taylor expansion of 1.0 in x 0.042 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.042 * [taylor]: Taking taylor expansion of x in x 0.055 * [approximate]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in (x) around 0 0.055 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.055 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.055 * [taylor]: Taking taylor expansion of 1.0 in x 0.055 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.055 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.055 * [taylor]: Taking taylor expansion of x in x 0.058 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.058 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.058 * [taylor]: Taking taylor expansion of 1.0 in x 0.058 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.058 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.058 * [taylor]: Taking taylor expansion of x in x 0.078 * [approximate]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in (x) around 0 0.078 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.078 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.078 * [taylor]: Taking taylor expansion of 1.0 in x 0.079 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.079 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.079 * [taylor]: Taking taylor expansion of x in x 0.081 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.081 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.081 * [taylor]: Taking taylor expansion of 1.0 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 0.098 * * * [progress]: simplifying candidates 0.098 * [simplify]: Simplifying using # : (log (sqrt (- 1.0 (* x x)))) (exp (sqrt (- 1.0 (* x x)))) (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (cbrt (sqrt (- 1.0 (* x x)))) (* (* (sqrt (- 1.0 (* x x))) (sqrt (- 1.0 (* x x)))) (sqrt (- 1.0 (* x x)))) (sqrt (* (cbrt (- 1.0 (* x x))) (cbrt (- 1.0 (* x x))))) (sqrt (cbrt (- 1.0 (* x x)))) (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (- 1.0 (* x x)))) (sqrt 1) (sqrt (- 1.0 (* x x))) (sqrt (+ (sqrt 1.0) x)) (sqrt (- (sqrt 1.0) x)) (sqrt (- (pow 1.0 3) (pow (* x x) 3))) (sqrt (+ (* 1.0 1.0) (+ (* (* x x) (* x x)) (* 1.0 (* x x))))) (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x))) (/ 1 2) (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (- 1.0 (* x x)))) (- (sqrt 1.0) (+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))) (- (+ (* 0.5 (/ 1 (* x (sqrt -1)))) (* x (sqrt -1))) (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (- (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 0.5 (/ 1 (* x (sqrt -1)))) (* x (sqrt -1)))) 0.101 * * [simplify]: iteration 0 : 157 enodes (cost 124 ) 0.105 * * [simplify]: iteration 1 : 534 enodes (cost 121 ) 0.115 * * [simplify]: iteration 2 : 2617 enodes (cost 120 ) 0.174 * * [simplify]: iteration 3 : 5002 enodes (cost 119 ) 0.175 * [simplify]: Simplified to: (log (sqrt (- 1.0 (* x x)))) (exp (sqrt (- 1.0 (* x x)))) (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (cbrt (sqrt (- 1.0 (* x x)))) (pow (sqrt (- 1.0 (* x x))) 3) (fabs (cbrt (- 1.0 (* x x)))) (sqrt (cbrt (- 1.0 (* x x)))) (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (- 1.0 (* x x)))) 1 (sqrt (- 1.0 (* x x))) (sqrt (+ (sqrt 1.0) x)) (sqrt (- (sqrt 1.0) x)) (sqrt (- (pow 1.0 3) (pow (* x x) 3))) (sqrt (+ (* 1.0 1.0) (+ (* (* x x) (* x x)) (* 1.0 (* x x))))) (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x))) 1/2 (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (- 1.0 (* x x)))) (- (sqrt 1.0) (+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))) (+ (- (* x (sqrt -1)) (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (/ (/ 0.5 (sqrt -1)) x)) (- (/ (/ 0.125 (pow (sqrt -1) 3)) (pow x 3)) (- (/ (/ 0.5 (sqrt -1)) x) (- (* x (sqrt -1))))) 0.175 * * * [progress]: adding candidates to table 0.215 * * [progress]: iteration 2 / 4 0.215 * * * [progress]: picking best candidate 0.216 * * * * [pick]: Picked # 0.216 * * * [progress]: localizing error 0.222 * * * [progress]: generating rewritten candidates 0.222 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.226 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.229 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 0.249 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 0.257 * * * [progress]: generating series expansions 0.257 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.257 * [approximate]: Taking taylor expansion of (pow (- 1.0 (pow x 2)) 1/4) in (x) around 0 0.257 * [taylor]: Taking taylor expansion of (pow (- 1.0 (pow x 2)) 1/4) in x 0.257 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (pow x 2))))) in x 0.257 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (pow x 2)))) in x 0.257 * [taylor]: Taking taylor expansion of 1/4 in x 0.257 * [taylor]: Taking taylor expansion of (log (- 1.0 (pow x 2))) in x 0.257 * [taylor]: Taking taylor expansion of (- 1.0 (pow x 2)) in x 0.257 * [taylor]: Taking taylor expansion of 1.0 in x 0.257 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.257 * [taylor]: Taking taylor expansion of x in x 0.259 * [taylor]: Taking taylor expansion of (pow (- 1.0 (pow x 2)) 1/4) in x 0.259 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (pow x 2))))) in x 0.259 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (pow x 2)))) in x 0.259 * [taylor]: Taking taylor expansion of 1/4 in x 0.259 * [taylor]: Taking taylor expansion of (log (- 1.0 (pow x 2))) in x 0.259 * [taylor]: Taking taylor expansion of (- 1.0 (pow x 2)) in x 0.259 * [taylor]: Taking taylor expansion of 1.0 in x 0.259 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.259 * [taylor]: Taking taylor expansion of x in x 0.325 * [approximate]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in (x) around 0 0.325 * [taylor]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in x 0.325 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (/ 1 (pow x 2)))))) in x 0.325 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (/ 1 (pow x 2))))) in x 0.325 * [taylor]: Taking taylor expansion of 1/4 in x 0.325 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 (pow x 2)))) in x 0.325 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.325 * [taylor]: Taking taylor expansion of 1.0 in x 0.325 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.325 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.325 * [taylor]: Taking taylor expansion of x in x 0.328 * [taylor]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in x 0.328 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (/ 1 (pow x 2)))))) in x 0.328 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (/ 1 (pow x 2))))) in x 0.328 * [taylor]: Taking taylor expansion of 1/4 in x 0.328 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 (pow x 2)))) in x 0.328 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.328 * [taylor]: Taking taylor expansion of 1.0 in x 0.328 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.328 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.328 * [taylor]: Taking taylor expansion of x in x 0.384 * [approximate]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in (x) around 0 0.384 * [taylor]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in x 0.384 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (/ 1 (pow x 2)))))) in x 0.384 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (/ 1 (pow x 2))))) in x 0.384 * [taylor]: Taking taylor expansion of 1/4 in x 0.384 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 (pow x 2)))) in x 0.384 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.384 * [taylor]: Taking taylor expansion of 1.0 in x 0.384 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.384 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.384 * [taylor]: Taking taylor expansion of x in x 0.386 * [taylor]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in x 0.386 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (/ 1 (pow x 2)))))) in x 0.386 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (/ 1 (pow x 2))))) in x 0.386 * [taylor]: Taking taylor expansion of 1/4 in x 0.386 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 (pow x 2)))) in x 0.386 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.386 * [taylor]: Taking taylor expansion of 1.0 in x 0.386 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.386 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.386 * [taylor]: Taking taylor expansion of x in x 0.442 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.442 * [approximate]: Taking taylor expansion of (pow (- 1.0 (pow x 2)) 1/4) in (x) around 0 0.442 * [taylor]: Taking taylor expansion of (pow (- 1.0 (pow x 2)) 1/4) in x 0.442 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (pow x 2))))) in x 0.442 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (pow x 2)))) in x 0.442 * [taylor]: Taking taylor expansion of 1/4 in x 0.442 * [taylor]: Taking taylor expansion of (log (- 1.0 (pow x 2))) in x 0.442 * [taylor]: Taking taylor expansion of (- 1.0 (pow x 2)) in x 0.442 * [taylor]: Taking taylor expansion of 1.0 in x 0.442 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.442 * [taylor]: Taking taylor expansion of x in x 0.444 * [taylor]: Taking taylor expansion of (pow (- 1.0 (pow x 2)) 1/4) in x 0.444 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (pow x 2))))) in x 0.444 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (pow x 2)))) in x 0.444 * [taylor]: Taking taylor expansion of 1/4 in x 0.444 * [taylor]: Taking taylor expansion of (log (- 1.0 (pow x 2))) in x 0.444 * [taylor]: Taking taylor expansion of (- 1.0 (pow x 2)) in x 0.444 * [taylor]: Taking taylor expansion of 1.0 in x 0.444 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.444 * [taylor]: Taking taylor expansion of x in x 0.509 * [approximate]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in (x) around 0 0.510 * [taylor]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in x 0.510 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (/ 1 (pow x 2)))))) in x 0.510 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (/ 1 (pow x 2))))) in x 0.510 * [taylor]: Taking taylor expansion of 1/4 in x 0.510 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 (pow x 2)))) in x 0.510 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.510 * [taylor]: Taking taylor expansion of 1.0 in x 0.510 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.510 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.510 * [taylor]: Taking taylor expansion of x in x 0.512 * [taylor]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in x 0.512 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (/ 1 (pow x 2)))))) in x 0.512 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (/ 1 (pow x 2))))) in x 0.512 * [taylor]: Taking taylor expansion of 1/4 in x 0.512 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 (pow x 2)))) in x 0.512 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.512 * [taylor]: Taking taylor expansion of 1.0 in x 0.512 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.512 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.512 * [taylor]: Taking taylor expansion of x in x 0.564 * [approximate]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in (x) around 0 0.564 * [taylor]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in x 0.565 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (/ 1 (pow x 2)))))) in x 0.565 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (/ 1 (pow x 2))))) in x 0.565 * [taylor]: Taking taylor expansion of 1/4 in x 0.565 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 (pow x 2)))) in x 0.565 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.565 * [taylor]: Taking taylor expansion of 1.0 in x 0.565 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.565 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.565 * [taylor]: Taking taylor expansion of x in x 0.572 * [taylor]: Taking taylor expansion of (pow (- 1.0 (/ 1 (pow x 2))) 1/4) in x 0.573 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (- 1.0 (/ 1 (pow x 2)))))) in x 0.573 * [taylor]: Taking taylor expansion of (* 1/4 (log (- 1.0 (/ 1 (pow x 2))))) in x 0.573 * [taylor]: Taking taylor expansion of 1/4 in x 0.573 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 (pow x 2)))) in x 0.573 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.573 * [taylor]: Taking taylor expansion of 1.0 in x 0.573 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.573 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.573 * [taylor]: Taking taylor expansion of x in x 0.625 * * * * [progress]: [ 3 / 4 ] generating series at (2) 0.625 * [approximate]: Taking taylor expansion of (sqrt (- 1.0 (pow x 2))) in (x) around 0 0.626 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (pow x 2))) in x 0.626 * [taylor]: Taking taylor expansion of (- 1.0 (pow x 2)) in x 0.626 * [taylor]: Taking taylor expansion of 1.0 in x 0.626 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.626 * [taylor]: Taking taylor expansion of x in x 0.627 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (pow x 2))) in x 0.627 * [taylor]: Taking taylor expansion of (- 1.0 (pow x 2)) in x 0.627 * [taylor]: Taking taylor expansion of 1.0 in x 0.627 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.627 * [taylor]: Taking taylor expansion of x in x 0.641 * [approximate]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in (x) around 0 0.641 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.641 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.641 * [taylor]: Taking taylor expansion of 1.0 in x 0.641 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.641 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.641 * [taylor]: Taking taylor expansion of x in x 0.644 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.644 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.644 * [taylor]: Taking taylor expansion of 1.0 in x 0.644 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.644 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.644 * [taylor]: Taking taylor expansion of x in x 0.667 * [approximate]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in (x) around 0 0.667 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.667 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.667 * [taylor]: Taking taylor expansion of 1.0 in x 0.667 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.667 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.667 * [taylor]: Taking taylor expansion of x in x 0.670 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.670 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.670 * [taylor]: Taking taylor expansion of 1.0 in x 0.670 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.670 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.670 * [taylor]: Taking taylor expansion of x in x 0.687 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 0.687 * [approximate]: Taking taylor expansion of (sqrt (- 1.0 (pow x 2))) in (x) around 0 0.687 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (pow x 2))) in x 0.687 * [taylor]: Taking taylor expansion of (- 1.0 (pow x 2)) in x 0.687 * [taylor]: Taking taylor expansion of 1.0 in x 0.687 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.687 * [taylor]: Taking taylor expansion of x in x 0.689 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (pow x 2))) in x 0.689 * [taylor]: Taking taylor expansion of (- 1.0 (pow x 2)) in x 0.689 * [taylor]: Taking taylor expansion of 1.0 in x 0.689 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.689 * [taylor]: Taking taylor expansion of x in x 0.702 * [approximate]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in (x) around 0 0.702 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.702 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.702 * [taylor]: Taking taylor expansion of 1.0 in x 0.702 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.702 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.702 * [taylor]: Taking taylor expansion of x in x 0.704 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.705 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.705 * [taylor]: Taking taylor expansion of 1.0 in x 0.705 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.705 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.705 * [taylor]: Taking taylor expansion of x in x 0.722 * [approximate]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in (x) around 0 0.722 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.722 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.722 * [taylor]: Taking taylor expansion of 1.0 in x 0.722 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.722 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.722 * [taylor]: Taking taylor expansion of x in x 0.725 * [taylor]: Taking taylor expansion of (sqrt (- 1.0 (/ 1 (pow x 2)))) in x 0.725 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 (pow x 2))) in x 0.725 * [taylor]: Taking taylor expansion of 1.0 in x 0.725 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.725 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.725 * [taylor]: Taking taylor expansion of x in x 0.748 * * * [progress]: simplifying candidates 0.750 * [simplify]: Simplifying using # : (log (sqrt (sqrt (- 1.0 (* x x))))) (exp (sqrt (sqrt (- 1.0 (* x x))))) (* (cbrt (sqrt (sqrt (- 1.0 (* x x))))) (cbrt (sqrt (sqrt (- 1.0 (* x x)))))) (cbrt (sqrt (sqrt (- 1.0 (* x x))))) (* (* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x)))))) (sqrt (cbrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt (* (cbrt (- 1.0 (* x x))) (cbrt (- 1.0 (* x x)))))) (sqrt (sqrt (cbrt (- 1.0 (* x x))))) (sqrt (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt 1)) (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (+ (sqrt 1.0) x))) (sqrt (sqrt (- (sqrt 1.0) x))) (sqrt (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt (sqrt (- 1.0 (* x x))))) (sqrt 1) (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (- (pow 1.0 3) (pow (* x x) 3)))) (sqrt (sqrt (+ (* 1.0 1.0) (+ (* (* x x) (* x x)) (* 1.0 (* x x)))))) (sqrt (sqrt (- (* 1.0 1.0) (* (* x x) (* x x))))) (sqrt (sqrt (+ 1.0 (* x x)))) (/ 1/2 2) (/ 1 2) (/ (/ 1 2) 2) (sqrt (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt (sqrt (- 1.0 (* x x))))) (log (sqrt (sqrt (- 1.0 (* x x))))) (exp (sqrt (sqrt (- 1.0 (* x x))))) (* (cbrt (sqrt (sqrt (- 1.0 (* x x))))) (cbrt (sqrt (sqrt (- 1.0 (* x x)))))) (cbrt (sqrt (sqrt (- 1.0 (* x x))))) (* (* (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x)))))) (sqrt (cbrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt (* (cbrt (- 1.0 (* x x))) (cbrt (- 1.0 (* x x)))))) (sqrt (sqrt (cbrt (- 1.0 (* x x))))) (sqrt (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt 1)) (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (+ (sqrt 1.0) x))) (sqrt (sqrt (- (sqrt 1.0) x))) (sqrt (sqrt (sqrt (- 1.0 (* x x))))) (sqrt (sqrt (sqrt (- 1.0 (* x x))))) (sqrt 1) (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (- (pow 1.0 3) (pow (* x x) 3)))) (sqrt 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x 4) (pow (/ 1 (pow 1.0 7)) 1/4))))) (- (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (+ (* 0.09375 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (pow x 4))) (* 0.25 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (pow x 2))))) (- (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (+ (* 0.25 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 2))) (* 0.09375 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 4))))) (- (+ (pow 1.0 1/4) (* 0.03125 (* (pow x 4) (pow 1.0 1/4)))) (+ (* 0.25 (* (pow x 2) (pow 1.0 1/4))) (* 1/8 (* (pow x 4) (pow (/ 1 (pow 1.0 7)) 1/4))))) (- (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (+ (* 0.09375 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (pow x 4))) (* 0.25 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (pow x 2))))) (- (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (+ (* 0.25 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 2))) (* 0.09375 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 4))))) (- (sqrt 1.0) (+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))) (- (+ (* 0.5 (/ 1 (* x (sqrt -1)))) (* x (sqrt -1))) (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (- (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 0.5 (/ 1 (* x (sqrt -1)))) (* x (sqrt -1)))) (- (sqrt 1.0) (+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))) (- (+ (* 0.5 (/ 1 (* x (sqrt -1)))) (* x (sqrt -1))) (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (- (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 0.5 (/ 1 (* x (sqrt -1)))) (* x (sqrt -1)))) 0.758 * * [simplify]: iteration 0 : 386 enodes (cost 1164 ) 0.766 * * [simplify]: iteration 1 : 1660 enodes (cost 1100 ) 0.800 * * [simplify]: iteration 2 : 5002 enodes (cost 1088 ) 0.805 * [simplify]: Simplified to: (log (sqrt (sqrt (- 1.0 (* x x))))) (exp (sqrt (sqrt (- 1.0 (* x x))))) (* (cbrt (sqrt (sqrt (- 1.0 (* x x))))) (cbrt (sqrt (sqrt (- 1.0 (* x x)))))) (cbrt (sqrt (sqrt (- 1.0 (* x x))))) (pow (sqrt 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(pow (* x x) 3))) (sqrt (+ (* 1.0 1.0) (+ (* (* x x) (* x x)) (* 1.0 (* x x))))) (sqrt (- (* 1.0 1.0) (* (* x x) (* x x)))) (sqrt (+ 1.0 (* x x))) 1/2 (sqrt (sqrt (- 1.0 (* x x)))) (sqrt (sqrt (- 1.0 (* x x)))) (- (- (* (+ (* 0.03125 (pow x 4)) 1) (pow 1.0 1/4)) (* 1/8 (* (pow x 4) (pow (/ 1 (pow 1.0 7)) 1/4)))) (* 0.25 (* (pow x 2) (pow 1.0 1/4)))) (- (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (+ (* 0.09375 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (pow x 4))) (* 0.25 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (pow x 2))))) (- (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (+ (* 0.25 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 2))) (* 0.09375 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 4))))) (- (- (* (+ (* 0.03125 (pow x 4)) 1) (pow 1.0 1/4)) (* 1/8 (* (pow x 4) (pow (/ 1 (pow 1.0 7)) 1/4)))) (* 0.25 (* (pow x 2) (pow 1.0 1/4)))) (- (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (+ (* 0.09375 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (pow x 4))) (* 0.25 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ 1 x)))))) (pow x 2))))) (- (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (+ (* 0.25 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 2))) (* 0.09375 (/ (exp (* 1/4 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 4))))) (- (sqrt 1.0) (+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))) (+ (- (* x (sqrt -1)) (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (/ (/ 0.5 (sqrt -1)) x)) (- (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 0.5 (/ 1 (* x (sqrt -1)))) (* x (sqrt -1)))) (- (sqrt 1.0) (+ (* 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3))) (* 1/2 (/ (pow x 2) (sqrt 1.0))))) (+ (- (* x (sqrt -1)) (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (/ (/ 0.5 (sqrt -1)) x)) (- (* 0.125 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 0.5 (/ 1 (* x (sqrt -1)))) (* x (sqrt -1)))) 0.806 * * * [progress]: adding candidates to table 1.122 * [progress]: [Phase 3 of 3] Extracting. 1.122 * * [regime]: Finding splitpoints for: (# #) 1.122 * * * [regime-changes]: Trying 4 branch expressions: ((* x x) (- 1.0 (* x x)) (sqrt (- 1.0 (* x x))) x) 1.122 * * * * [regimes]: Trying to branch on (* x x) from (# #) 1.130 * * * * [regimes]: Trying to branch on (- 1.0 (* x x)) from (# #) 1.138 * * * * [regimes]: Trying to branch on (sqrt (- 1.0 (* x x))) from (# #) 1.148 * * * * [regimes]: Trying to branch on x from (# #) 1.160 * * * [regime]: Found split indices: #