4.176 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.011 * * * [progress]: [2/2] Setting up program. 0.013 * [progress]: [Phase 2 of 3] Improving. 0.013 * [simplify]: Simplifying using # : (sqrt (+ (* x x) (* x x))) 0.015 * * [simplify]: iteration 0 : 8 enodes (cost 4 ) 0.016 * * [simplify]: iteration 1 : 11 enodes (cost 4 ) 0.017 * * [simplify]: iteration 2 : 14 enodes (cost 4 ) 0.018 * * [simplify]: iteration 3 : 14 enodes (cost 4 ) 0.018 * [simplify]: Simplified to: (sqrt (+ (* x x) (* x x))) 0.018 * * [progress]: iteration 1 / 4 0.018 * * * [progress]: picking best candidate 0.020 * * * * [pick]: Picked # 0.020 * * * [progress]: localizing error 0.024 * * * [progress]: generating rewritten candidates 0.024 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.028 * * * [progress]: generating series expansions 0.028 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.028 * [approximate]: Taking taylor expansion of (* x (sqrt 2)) in (x) around 0 0.028 * [taylor]: Taking taylor expansion of (* x (sqrt 2)) in x 0.028 * [taylor]: Taking taylor expansion of x in x 0.028 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.029 * [taylor]: Taking taylor expansion of 2 in x 0.029 * [taylor]: Taking taylor expansion of (* x (sqrt 2)) in x 0.029 * [taylor]: Taking taylor expansion of x in x 0.029 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.029 * [taylor]: Taking taylor expansion of 2 in x 0.030 * [approximate]: Taking taylor expansion of (/ (sqrt 2) x) in (x) around 0 0.030 * [taylor]: Taking taylor expansion of (/ (sqrt 2) x) in x 0.030 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.030 * [taylor]: Taking taylor expansion of 2 in x 0.030 * [taylor]: Taking taylor expansion of x in x 0.030 * [taylor]: Taking taylor expansion of (/ (sqrt 2) x) in x 0.030 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.030 * [taylor]: Taking taylor expansion of 2 in x 0.030 * [taylor]: Taking taylor expansion of x in x 0.031 * [approximate]: Taking taylor expansion of (/ (sqrt 2) x) in (x) around 0 0.031 * [taylor]: Taking taylor expansion of (/ (sqrt 2) x) in x 0.031 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.031 * [taylor]: Taking taylor expansion of 2 in x 0.031 * [taylor]: Taking taylor expansion of x in x 0.031 * [taylor]: Taking taylor expansion of (/ (sqrt 2) x) in x 0.031 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.031 * [taylor]: Taking taylor expansion of 2 in x 0.031 * [taylor]: Taking taylor expansion of x in x 0.032 * * * [progress]: simplifying candidates 0.033 * [simplify]: Simplifying using # : (log (sqrt (+ (* x x) (* x x)))) (exp (sqrt (+ (* x x) (* x x)))) (* (cbrt (sqrt (+ (* x x) (* x x)))) (cbrt (sqrt (+ (* x x) (* x x))))) (cbrt (sqrt (+ (* x x) (* x x)))) (* (* (sqrt (+ (* x x) (* x x))) (sqrt (+ (* x x) (* x x)))) (sqrt (+ (* x x) (* x x)))) (sqrt (* (cbrt (+ (* x x) (* x x))) (cbrt (+ (* x x) (* x x))))) (sqrt (cbrt (+ (* x x) (* x x)))) (sqrt (sqrt (+ (* x x) (* x x)))) (sqrt (sqrt (+ (* x x) (* x x)))) (sqrt 1) (sqrt (+ (* x x) (* x x))) (sqrt x) (sqrt (+ x x)) (sqrt x) (sqrt (+ x x)) (sqrt 2) (sqrt (* x x)) (sqrt (+ (pow (* x x) 3) (pow (* x x) 3))) (sqrt (+ (* (* x x) (* x x)) (- (* (* x x) (* x x)) (* (* x x) (* x x))))) (sqrt (- (* (* x x) (* x x)) (* (* x x) (* x x)))) (sqrt (- (* x x) (* x x))) (/ 1 2) (sqrt (sqrt (+ (* x x) (* x x)))) (sqrt (sqrt (+ (* x x) (* x x)))) (* x (sqrt 2)) (* x (sqrt 2)) (* -1 (* x (sqrt 2))) 0.035 * * [simplify]: iteration 0 : 75 enodes (cost 109 ) 0.037 * * [simplify]: iteration 1 : 237 enodes (cost 107 ) 0.046 * * [simplify]: iteration 2 : 2195 enodes (cost 97 ) 0.229 * * [simplify]: iteration 3 : 5002 enodes (cost 96 ) 0.230 * [simplify]: Simplified to: (log (sqrt (+ (* x x) (* x x)))) (exp (sqrt (+ (* x x) (* x x)))) (* (cbrt (sqrt (+ (* x x) (* x x)))) (cbrt (sqrt (+ (* x x) (* x x))))) (cbrt (sqrt (+ (* x x) (* x x)))) (pow (sqrt (+ (* x x) (* x x))) 3) (fabs (cbrt (+ (* x x) (* x x)))) (sqrt (cbrt (+ (* x x) (* x x)))) (sqrt (sqrt (+ (* x x) (* x x)))) (sqrt (sqrt (+ (* x x) (* x x)))) 1 (sqrt (+ (* x x) (* x x))) (sqrt x) (sqrt (+ x x)) (sqrt x) (sqrt (+ x x)) (sqrt 2) (fabs x) (sqrt (+ (pow (* x x) 3) (pow (* x x) 3))) (fabs (* x x)) (sqrt (- (* x x) (* x x))) (sqrt (- (* x x) (* x x))) 1/2 (sqrt (sqrt (+ (* x x) (* x x)))) (sqrt (sqrt (+ (* x x) (* x x)))) (* x (sqrt 2)) (* x (sqrt 2)) (* -1 (* x (sqrt 2))) 0.230 * * * [progress]: adding candidates to table 0.259 * * [progress]: iteration 2 / 4 0.259 * * * [progress]: picking best candidate 0.267 * * * * [pick]: Picked # 0.267 * * * [progress]: localizing error 0.271 * * * [progress]: generating rewritten candidates 0.271 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.276 * * * [progress]: generating series expansions 0.276 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.276 * [approximate]: Taking taylor expansion of (* (fabs x) (sqrt 2)) in (x) around 0 0.277 * [taylor]: Taking taylor expansion of (* (fabs x) (sqrt 2)) in x 0.277 * [taylor]: Taking taylor expansion of (fabs x) in x 0.277 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.277 * [taylor]: Taking taylor expansion of 2 in x 0.277 * [taylor]: Taking taylor expansion of (* (fabs x) (sqrt 2)) in x 0.277 * [taylor]: Taking taylor expansion of (fabs x) in x 0.277 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.277 * [taylor]: Taking taylor expansion of 2 in x 0.278 * [approximate]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt 2)) in (x) around 0 0.278 * [taylor]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt 2)) in x 0.278 * [taylor]: Taking taylor expansion of (fabs (/ 1 x)) in x 0.278 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.278 * [taylor]: Taking taylor expansion of 2 in x 0.278 * [taylor]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt 2)) in x 0.278 * [taylor]: Taking taylor expansion of (fabs (/ 1 x)) in x 0.278 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.278 * [taylor]: Taking taylor expansion of 2 in x 0.279 * [approximate]: Taking taylor expansion of (* (sqrt 2) (fabs (/ -1 x))) in (x) around 0 0.279 * [taylor]: Taking taylor expansion of (* (sqrt 2) (fabs (/ -1 x))) in x 0.279 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.279 * [taylor]: Taking taylor expansion of 2 in x 0.279 * [taylor]: Taking taylor expansion of (fabs (/ -1 x)) in x 0.279 * [taylor]: Taking taylor expansion of (* (sqrt 2) (fabs (/ -1 x))) in x 0.279 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.279 * [taylor]: Taking taylor expansion of 2 in x 0.279 * [taylor]: Taking taylor expansion of (fabs (/ -1 x)) in x 0.280 * * * [progress]: simplifying candidates 0.281 * [simplify]: Simplifying using # : (* (sqrt 2) (fabs x)) (+ (log (sqrt 2)) (log (fabs x))) (log (* (sqrt 2) (fabs x))) (exp (* (sqrt 2) (fabs x))) (* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* (fabs x) (fabs x)) (fabs x))) (* (cbrt (* (sqrt 2) (fabs x))) (cbrt (* (sqrt 2) (fabs x)))) (cbrt (* (sqrt 2) (fabs x))) (* (* (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x))) (* (sqrt 2) (fabs x))) (sqrt (* (sqrt 2) (fabs x))) (sqrt (* (sqrt 2) (fabs x))) (* (sqrt (sqrt 2)) (sqrt (fabs x))) (* (sqrt (sqrt 2)) (sqrt (fabs x))) (* (sqrt (sqrt 2)) (sqrt (fabs x))) (* (sqrt (sqrt 2)) (sqrt (fabs x))) (* (sqrt 2) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (sqrt 2) (sqrt (fabs x))) (* (sqrt 2) 1) (* (cbrt (sqrt 2)) (fabs x)) (* (sqrt (cbrt 2)) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt 2) (fabs x)) (* (fabs x) (sqrt 2)) (* (fabs x) (sqrt 2)) (* (fabs x) (sqrt 2)) 0.283 * * [simplify]: iteration 0 : 65 enodes (cost 115 ) 0.285 * * [simplify]: iteration 1 : 224 enodes (cost 107 ) 0.288 * * [simplify]: iteration 2 : 526 enodes (cost 107 ) 0.294 * * [simplify]: iteration 3 : 884 enodes (cost 107 ) 0.307 * * [simplify]: iteration 4 : 2528 enodes (cost 107 ) 0.358 * * [simplify]: iteration 5 : 5001 enodes (cost 107 ) 0.359 * [simplify]: Simplified to: (* (sqrt 2) (fabs x)) (log (* (sqrt 2) (fabs x))) (log (* (sqrt 2) (fabs x))) (exp (* (sqrt 2) (fabs x))) (pow (* (sqrt 2) (fabs x)) 3) (* (cbrt (* (sqrt 2) (fabs x))) (cbrt (* (sqrt 2) (fabs x)))) (cbrt (* (sqrt 2) (fabs x))) (pow (* (sqrt 2) (fabs x)) 3) (sqrt (* (sqrt 2) (fabs x))) (sqrt (* (sqrt 2) (fabs x))) (* (sqrt (sqrt 2)) (sqrt (fabs x))) (* (sqrt (sqrt 2)) (sqrt (fabs x))) (* (sqrt (sqrt 2)) (sqrt (fabs x))) (* (sqrt (sqrt 2)) (sqrt (fabs x))) (* (sqrt 2) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (sqrt 2) (sqrt (fabs x))) (sqrt 2) (* (cbrt (sqrt 2)) (fabs x)) (* (sqrt (cbrt 2)) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) 0.359 * * * [progress]: adding candidates to table 0.389 * * [progress]: iteration 3 / 4 0.389 * * * [progress]: picking best candidate 0.401 * * * * [pick]: Picked # 0.401 * * * [progress]: localizing error 0.409 * * * [progress]: generating rewritten candidates 0.409 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.419 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2) 0.425 * * * [progress]: generating series expansions 0.425 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.426 * [approximate]: Taking taylor expansion of (* (fabs x) (sqrt 2)) in (x) around 0 0.426 * [taylor]: Taking taylor expansion of (* (fabs x) (sqrt 2)) in x 0.426 * [taylor]: Taking taylor expansion of (fabs x) in x 0.426 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.426 * [taylor]: Taking taylor expansion of 2 in x 0.426 * [taylor]: Taking taylor expansion of (* (fabs x) (sqrt 2)) in x 0.426 * [taylor]: Taking taylor expansion of (fabs x) in x 0.426 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.426 * [taylor]: Taking taylor expansion of 2 in x 0.427 * [approximate]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt 2)) in (x) around 0 0.427 * [taylor]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt 2)) in x 0.427 * [taylor]: Taking taylor expansion of (fabs (/ 1 x)) in x 0.427 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.427 * [taylor]: Taking taylor expansion of 2 in x 0.427 * [taylor]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt 2)) in x 0.427 * [taylor]: Taking taylor expansion of (fabs (/ 1 x)) in x 0.427 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.427 * [taylor]: Taking taylor expansion of 2 in x 0.428 * [approximate]: Taking taylor expansion of (* (sqrt 2) (fabs (/ -1 x))) in (x) around 0 0.428 * [taylor]: Taking taylor expansion of (* (sqrt 2) (fabs (/ -1 x))) in x 0.428 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.428 * [taylor]: Taking taylor expansion of 2 in x 0.428 * [taylor]: Taking taylor expansion of (fabs (/ -1 x)) in x 0.428 * [taylor]: Taking taylor expansion of (* (sqrt 2) (fabs (/ -1 x))) in x 0.428 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.428 * [taylor]: Taking taylor expansion of 2 in x 0.428 * [taylor]: Taking taylor expansion of (fabs (/ -1 x)) in x 0.429 * * * * [progress]: [ 2 / 2 ] generating series at (2 2) 0.429 * [approximate]: Taking taylor expansion of (* (fabs x) (pow (sqrt 2) 1/3)) in (x) around 0 0.429 * [taylor]: Taking taylor expansion of (* (fabs x) (pow (sqrt 2) 1/3)) in x 0.429 * [taylor]: Taking taylor expansion of (fabs x) in x 0.429 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 1/3) in x 0.429 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (sqrt 2)))) in x 0.430 * [taylor]: Taking taylor expansion of (* 1/3 (log (sqrt 2))) in x 0.430 * [taylor]: Taking taylor expansion of 1/3 in x 0.430 * [taylor]: Taking taylor expansion of (log (sqrt 2)) in x 0.430 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.430 * [taylor]: Taking taylor expansion of 2 in x 0.430 * [taylor]: Taking taylor expansion of (* (fabs x) (pow (sqrt 2) 1/3)) in x 0.430 * [taylor]: Taking taylor expansion of (fabs x) in x 0.430 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 1/3) in x 0.430 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (sqrt 2)))) in x 0.430 * [taylor]: Taking taylor expansion of (* 1/3 (log (sqrt 2))) in x 0.430 * [taylor]: Taking taylor expansion of 1/3 in x 0.430 * [taylor]: Taking taylor expansion of (log (sqrt 2)) in x 0.430 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.430 * [taylor]: Taking taylor expansion of 2 in x 0.437 * [approximate]: Taking taylor expansion of (* (fabs (/ 1 x)) (pow (sqrt 2) 1/3)) in (x) around 0 0.437 * [taylor]: Taking taylor expansion of (* (fabs (/ 1 x)) (pow (sqrt 2) 1/3)) in x 0.437 * [taylor]: Taking taylor expansion of (fabs (/ 1 x)) in x 0.437 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 1/3) in x 0.437 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (sqrt 2)))) in x 0.437 * [taylor]: Taking taylor expansion of (* 1/3 (log (sqrt 2))) in x 0.437 * [taylor]: Taking taylor expansion of 1/3 in x 0.437 * [taylor]: Taking taylor expansion of (log (sqrt 2)) in x 0.437 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.437 * [taylor]: Taking taylor expansion of 2 in x 0.437 * [taylor]: Taking taylor expansion of (* (fabs (/ 1 x)) (pow (sqrt 2) 1/3)) in x 0.437 * [taylor]: Taking taylor expansion of (fabs (/ 1 x)) in x 0.437 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 1/3) in x 0.437 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (sqrt 2)))) in x 0.437 * [taylor]: Taking taylor expansion of (* 1/3 (log (sqrt 2))) in x 0.437 * [taylor]: Taking taylor expansion of 1/3 in x 0.437 * [taylor]: Taking taylor expansion of (log (sqrt 2)) in x 0.437 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.437 * [taylor]: Taking taylor expansion of 2 in x 0.446 * [approximate]: Taking taylor expansion of (* (pow (sqrt 2) 1/3) (fabs (/ -1 x))) in (x) around 0 0.446 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 1/3) (fabs (/ -1 x))) in x 0.446 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 1/3) in x 0.446 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (sqrt 2)))) in x 0.446 * [taylor]: Taking taylor expansion of (* 1/3 (log (sqrt 2))) in x 0.446 * [taylor]: Taking taylor expansion of 1/3 in x 0.446 * [taylor]: Taking taylor expansion of (log (sqrt 2)) in x 0.446 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.446 * [taylor]: Taking taylor expansion of 2 in x 0.446 * [taylor]: Taking taylor expansion of (fabs (/ -1 x)) in x 0.447 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 1/3) (fabs (/ -1 x))) in x 0.447 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 1/3) in x 0.447 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (sqrt 2)))) in x 0.447 * [taylor]: Taking taylor expansion of (* 1/3 (log (sqrt 2))) in x 0.447 * [taylor]: Taking taylor expansion of 1/3 in x 0.447 * [taylor]: Taking taylor expansion of (log (sqrt 2)) in x 0.447 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.447 * [taylor]: Taking taylor expansion of 2 in x 0.447 * [taylor]: Taking taylor expansion of (fabs (/ -1 x)) in x 0.454 * * * [progress]: simplifying candidates 0.454 * [simplify]: Simplifying using # : (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x))) (+ (+ (log (cbrt (sqrt 2))) (log (cbrt (sqrt 2)))) (+ (log (cbrt (sqrt 2))) (log (fabs x)))) (+ (+ (log (cbrt (sqrt 2))) (log (cbrt (sqrt 2)))) (log (* (cbrt (sqrt 2)) (fabs x)))) (+ (log (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (+ (log (cbrt (sqrt 2))) (log (fabs x)))) (+ (log (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (log (* (cbrt (sqrt 2)) (fabs x)))) (log (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (exp (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (* (* (sqrt 2) (sqrt 2)) (* (sqrt 2) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) (fabs x)) (* (cbrt (sqrt 2)) (fabs x))) (* (cbrt (sqrt 2)) (fabs x)))) (* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (* (cbrt (sqrt 2)) (fabs x)) (* (cbrt (sqrt 2)) (fabs x))) (* (cbrt (sqrt 2)) (fabs x)))) (* (cbrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (cbrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x))))) (cbrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (sqrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (sqrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (fabs x))) (* (cbrt (sqrt 2)) (fabs x)) (+ (log (cbrt (sqrt 2))) (log (fabs x))) (log (* (cbrt (sqrt 2)) (fabs x))) (exp (* (cbrt (sqrt 2)) (fabs x))) (* (sqrt 2) (* (* (fabs x) (fabs x)) (fabs x))) (* (cbrt (* (cbrt (sqrt 2)) (fabs x))) (cbrt (* (cbrt (sqrt 2)) (fabs x)))) (cbrt (* (cbrt (sqrt 2)) (fabs x))) (* (* (* (cbrt (sqrt 2)) (fabs x)) (* (cbrt (sqrt 2)) (fabs x))) (* (cbrt (sqrt 2)) (fabs x))) (sqrt (* (cbrt (sqrt 2)) (fabs x))) (sqrt (* (cbrt (sqrt 2)) (fabs x))) (* (cbrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (cbrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (cbrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (cbrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (cbrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (cbrt (sqrt 2))) (sqrt (fabs x))) (* (cbrt (sqrt 2)) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (sqrt 2)) (sqrt (fabs x))) (* (cbrt (sqrt 2)) 1) (* (cbrt (cbrt (sqrt 2))) (fabs x)) (* (cbrt (sqrt (cbrt 2))) (fabs x)) (* (cbrt (sqrt (sqrt 2))) (fabs x)) (* (cbrt (sqrt 2)) (fabs x)) (* (cbrt (sqrt (sqrt 2))) (fabs x)) (* (cbrt (sqrt 2)) (fabs x)) (* (cbrt (cbrt (sqrt 2))) (fabs x)) (* (sqrt (cbrt (sqrt 2))) (fabs x)) (* (cbrt (sqrt 2)) (fabs x)) (* (fabs x) (sqrt 2)) (* (fabs x) (sqrt 2)) (* (fabs x) (sqrt 2)) (* (fabs x) (pow (sqrt 2) 1/3)) (* (fabs x) (pow (sqrt 2) 1/3)) (* (fabs x) (pow (sqrt 2) 1/3)) 0.458 * * [simplify]: iteration 0 : 155 enodes (cost 464 ) 0.461 * * [simplify]: iteration 1 : 674 enodes (cost 347 ) 0.481 * * [simplify]: iteration 2 : 4101 enodes (cost 308 ) 0.583 * * [simplify]: iteration 3 : 5001 enodes (cost 296 ) 0.585 * [simplify]: Simplified to: (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) (+ (log (sqrt 2)) (log (fabs x))) (+ (log (sqrt 2)) (log (fabs x))) (+ (log (sqrt 2)) (log (fabs x))) (+ (log (sqrt 2)) (log (fabs x))) (+ (log (sqrt 2)) (log (fabs x))) (pow (exp (fabs x)) (sqrt 2)) (* (* 2 (pow (fabs x) 3)) (sqrt 2)) (* (* 2 (pow (fabs x) 3)) (sqrt 2)) (* (* 2 (pow (fabs x) 3)) (sqrt 2)) (* (* 2 (pow (fabs x) 3)) (sqrt 2)) (* (cbrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (cbrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x))))) (cbrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (* (* 2 (pow (fabs x) 3)) (sqrt 2)) (sqrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (sqrt (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (fabs x)))) (sqrt 2) (* (fabs x) (pow (sqrt 2) 2/3)) (* (fabs x) (pow (sqrt 2) 1/3)) (log (* (cbrt (sqrt 2)) (fabs x))) (log (* (cbrt (sqrt 2)) (fabs x))) (exp (* (cbrt (sqrt 2)) (fabs x))) (pow (* (fabs x) (pow (sqrt 2) 1/3)) 3) (* (cbrt (* (cbrt (sqrt 2)) (fabs x))) (cbrt (* (cbrt (sqrt 2)) (fabs x)))) (cbrt (* (cbrt (sqrt 2)) (fabs x))) (pow (* (fabs x) (pow (sqrt 2) 1/3)) 3) (sqrt (* (cbrt (sqrt 2)) (fabs x))) (sqrt (* (cbrt (sqrt 2)) (fabs x))) (* (cbrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (cbrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (cbrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (cbrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (cbrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (cbrt (sqrt 2))) (sqrt (fabs x))) (* (cbrt (sqrt 2)) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (sqrt 2)) (sqrt (fabs x))) (pow (sqrt 2) 1/3) (* (cbrt (cbrt (sqrt 2))) (fabs x)) (* (cbrt (sqrt (cbrt 2))) (fabs x)) (* (cbrt (sqrt (sqrt 2))) (fabs x)) (* (fabs x) (pow (sqrt 2) 1/3)) (* (cbrt (sqrt (sqrt 2))) (fabs x)) (* (fabs x) (pow (sqrt 2) 1/3)) (* (cbrt (cbrt (sqrt 2))) (fabs x)) (* (sqrt (cbrt (sqrt 2))) (fabs x)) (* (fabs x) (pow (sqrt 2) 1/3)) (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) (* (fabs x) (pow (sqrt 2) 1/3)) (* (fabs x) (pow (sqrt 2) 1/3)) (* (fabs x) (pow (sqrt 2) 1/3)) 0.585 * * * [progress]: adding candidates to table 0.673 * * [progress]: iteration 4 / 4 0.674 * * * [progress]: picking best candidate 0.683 * * * * [pick]: Picked # 0.683 * * * [progress]: localizing error 0.691 * * * [progress]: generating rewritten candidates 0.691 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.700 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2) 0.707 * * * [progress]: generating series expansions 0.707 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.707 * [approximate]: Taking taylor expansion of (* (fabs x) (sqrt 2)) in (x) around 0 0.707 * [taylor]: Taking taylor expansion of (* (fabs x) (sqrt 2)) in x 0.707 * [taylor]: Taking taylor expansion of (fabs x) in x 0.707 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.707 * [taylor]: Taking taylor expansion of 2 in x 0.707 * [taylor]: Taking taylor expansion of (* (fabs x) (sqrt 2)) in x 0.707 * [taylor]: Taking taylor expansion of (fabs x) in x 0.707 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.707 * [taylor]: Taking taylor expansion of 2 in x 0.708 * [approximate]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt 2)) in (x) around 0 0.708 * [taylor]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt 2)) in x 0.708 * [taylor]: Taking taylor expansion of (fabs (/ 1 x)) in x 0.708 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.708 * [taylor]: Taking taylor expansion of 2 in x 0.708 * [taylor]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt 2)) in x 0.708 * [taylor]: Taking taylor expansion of (fabs (/ 1 x)) in x 0.708 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.708 * [taylor]: Taking taylor expansion of 2 in x 0.709 * [approximate]: Taking taylor expansion of (* (sqrt 2) (fabs (/ -1 x))) in (x) around 0 0.709 * [taylor]: Taking taylor expansion of (* (sqrt 2) (fabs (/ -1 x))) in x 0.709 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.709 * [taylor]: Taking taylor expansion of 2 in x 0.710 * [taylor]: Taking taylor expansion of (fabs (/ -1 x)) in x 0.710 * [taylor]: Taking taylor expansion of (* (sqrt 2) (fabs (/ -1 x))) in x 0.710 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.710 * [taylor]: Taking taylor expansion of 2 in x 0.710 * [taylor]: Taking taylor expansion of (fabs (/ -1 x)) in x 0.711 * * * * [progress]: [ 2 / 2 ] generating series at (2 2) 0.711 * [approximate]: Taking taylor expansion of (* (fabs x) (sqrt (sqrt 2))) in (x) around 0 0.711 * [taylor]: Taking taylor expansion of (* (fabs x) (sqrt (sqrt 2))) in x 0.711 * [taylor]: Taking taylor expansion of (fabs x) in x 0.711 * [taylor]: Taking taylor expansion of (sqrt (sqrt 2)) in x 0.711 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.711 * [taylor]: Taking taylor expansion of 2 in x 0.711 * [taylor]: Taking taylor expansion of (* (fabs x) (sqrt (sqrt 2))) in x 0.711 * [taylor]: Taking taylor expansion of (fabs x) in x 0.711 * [taylor]: Taking taylor expansion of (sqrt (sqrt 2)) in x 0.711 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.711 * [taylor]: Taking taylor expansion of 2 in x 0.712 * [approximate]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt (sqrt 2))) in (x) around 0 0.712 * [taylor]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt (sqrt 2))) in x 0.712 * [taylor]: Taking taylor expansion of (fabs (/ 1 x)) in x 0.712 * [taylor]: Taking taylor expansion of (sqrt (sqrt 2)) in x 0.712 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.712 * [taylor]: Taking taylor expansion of 2 in x 0.712 * [taylor]: Taking taylor expansion of (* (fabs (/ 1 x)) (sqrt (sqrt 2))) in x 0.713 * [taylor]: Taking taylor expansion of (fabs (/ 1 x)) in x 0.713 * [taylor]: Taking taylor expansion of (sqrt (sqrt 2)) in x 0.713 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.713 * [taylor]: Taking taylor expansion of 2 in x 0.714 * [approximate]: Taking taylor expansion of (* (sqrt (sqrt 2)) (fabs (/ -1 x))) in (x) around 0 0.714 * [taylor]: Taking taylor expansion of (* (sqrt (sqrt 2)) (fabs (/ -1 x))) in x 0.714 * [taylor]: Taking taylor expansion of (sqrt (sqrt 2)) in x 0.714 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.714 * [taylor]: Taking taylor expansion of 2 in x 0.714 * [taylor]: Taking taylor expansion of (fabs (/ -1 x)) in x 0.714 * [taylor]: Taking taylor expansion of (* (sqrt (sqrt 2)) (fabs (/ -1 x))) in x 0.714 * [taylor]: Taking taylor expansion of (sqrt (sqrt 2)) in x 0.714 * [taylor]: Taking taylor expansion of (sqrt 2) in x 0.714 * [taylor]: Taking taylor expansion of 2 in x 0.714 * [taylor]: Taking taylor expansion of (fabs (/ -1 x)) in x 0.716 * * * [progress]: simplifying candidates 0.716 * [simplify]: Simplifying using # : (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x))) (+ (log (sqrt (sqrt 2))) (+ (log (sqrt (sqrt 2))) (log (fabs x)))) (+ (log (sqrt (sqrt 2))) (log (* (sqrt (sqrt 2)) (fabs x)))) (log (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (exp (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt 2)) (fabs x)))) (* (cbrt (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (cbrt (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x))))) (cbrt (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (* (* (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (sqrt (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (sqrt (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (* (cbrt (sqrt (sqrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (cbrt (sqrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt (cbrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt (sqrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt (sqrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt (sqrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt 2)) (fabs x)) (+ (log (sqrt (sqrt 2))) (log (fabs x))) (log (* (sqrt (sqrt 2)) (fabs x))) (exp (* (sqrt (sqrt 2)) (fabs x))) (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (fabs x) (fabs x)) (fabs x))) (* (cbrt (* (sqrt (sqrt 2)) (fabs x))) (cbrt (* (sqrt (sqrt 2)) (fabs x)))) (cbrt (* (sqrt (sqrt 2)) (fabs x))) (* (* (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt 2)) (fabs x))) (sqrt (* (sqrt (sqrt 2)) (fabs x))) (sqrt (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt 2)) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (sqrt (sqrt 2)) (sqrt (fabs x))) (* (sqrt (sqrt 2)) 1) (* (cbrt (sqrt (sqrt 2))) (fabs x)) (* (sqrt (cbrt (sqrt 2))) (fabs x)) (* (sqrt (sqrt (cbrt 2))) (fabs x)) (* (sqrt (sqrt (sqrt 2))) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt (sqrt (sqrt 2))) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt (sqrt (sqrt 2))) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (fabs x) (sqrt 2)) (* (fabs x) (sqrt 2)) (* (fabs x) (sqrt 2)) (* (fabs x) (sqrt (sqrt 2))) (* (fabs x) (sqrt (sqrt 2))) (* (fabs x) (sqrt (sqrt 2))) 0.719 * * [simplify]: iteration 0 : 125 enodes (cost 357 ) 0.722 * * [simplify]: iteration 1 : 514 enodes (cost 305 ) 0.732 * * [simplify]: iteration 2 : 1466 enodes (cost 305 ) 0.750 * * [simplify]: iteration 3 : 2518 enodes (cost 305 ) 0.789 * * [simplify]: iteration 4 : 5001 enodes (cost 305 ) 0.791 * [simplify]: Simplified to: (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) (+ (log (sqrt 2)) (log (fabs x))) (+ (log (sqrt 2)) (log (fabs x))) (+ (log (sqrt 2)) (log (fabs x))) (pow (exp (sqrt 2)) (fabs x)) (pow (* (sqrt 2) (fabs x)) 3) (pow (* (sqrt 2) (fabs x)) 3) (* (cbrt (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (cbrt (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x))))) (cbrt (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (pow (* (sqrt 2) (fabs x)) 3) (sqrt (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (sqrt (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) (fabs x)))) (sqrt 2) (* (cbrt (sqrt (sqrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (cbrt (sqrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt (cbrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt (sqrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt 2) (fabs x)) (* (sqrt (sqrt (sqrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt 2) (fabs x)) (* (sqrt (sqrt (sqrt 2))) (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt 2) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (log (* (sqrt (sqrt 2)) (fabs x))) (log (* (sqrt (sqrt 2)) (fabs x))) (exp (* (sqrt (sqrt 2)) (fabs x))) (pow (* (sqrt (sqrt 2)) (fabs x)) 3) (* (cbrt (* (sqrt (sqrt 2)) (fabs x))) (cbrt (* (sqrt (sqrt 2)) (fabs x)))) (cbrt (* (sqrt (sqrt 2)) (fabs x))) (pow (* (sqrt (sqrt 2)) (fabs x)) 3) (sqrt (* (sqrt (sqrt 2)) (fabs x))) (sqrt (* (sqrt (sqrt 2)) (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt (sqrt 2))) (sqrt (fabs x))) (* (sqrt (sqrt 2)) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (sqrt (sqrt 2)) (sqrt (fabs x))) (sqrt (sqrt 2)) (* (cbrt (sqrt (sqrt 2))) (fabs x)) (* (sqrt (cbrt (sqrt 2))) (fabs x)) (* (sqrt (sqrt (cbrt 2))) (fabs x)) (* (sqrt (sqrt (sqrt 2))) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt (sqrt (sqrt 2))) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt (sqrt (sqrt 2))) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt 2) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) (* (sqrt (sqrt 2)) (fabs x)) 0.791 * * * [progress]: adding candidates to table 0.866 * [progress]: [Phase 3 of 3] Extracting. 0.866 * * [regime]: Finding splitpoints for: (# # # # # #) 0.867 * * * [regime-changes]: Trying 4 branch expressions: ((* x x) (+ (* x x) (* x x)) (sqrt (+ (* x x) (* x x))) x) 0.867 * * * * [regimes]: Trying to branch on (* x x) from (# # # # # #) 0.900 * * * * [regimes]: Trying to branch on (+ (* x x) (* x x)) from (# # # # # #) 0.934 * * * * [regimes]: Trying to branch on (sqrt (+ (* x x) (* x x))) from (# # # # # #) 0.970 * * * * [regimes]: Trying to branch on x from (# # # # # #) 1.005 * * * [regime]: Found split indices: #