19.358 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.013 * * * [progress]: [2/2] Setting up program. 0.014 * [progress]: [Phase 2 of 3] Improving. 0.015 * [simplify]: Simplifying using # : (sqrt (+ (* x x) y)) 0.017 * * [simplify]: iteration 0 : 7 enodes (cost 3 ) 0.018 * * [simplify]: iteration 1 : 7 enodes (cost 3 ) 0.018 * [simplify]: Simplified to: (sqrt (+ (* x x) y)) 0.019 * * [progress]: iteration 1 / 4 0.019 * * * [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) 0.030 * * * [progress]: generating series expansions 0.030 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.030 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in (x y) around 0 0.030 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in y 0.030 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in y 0.030 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.030 * [taylor]: Taking taylor expansion of x in y 0.030 * [taylor]: Taking taylor expansion of y in y 0.031 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in x 0.031 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in x 0.031 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.031 * [taylor]: Taking taylor expansion of x in x 0.031 * [taylor]: Taking taylor expansion of y in x 0.031 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in x 0.031 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in x 0.031 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.031 * [taylor]: Taking taylor expansion of x in x 0.031 * [taylor]: Taking taylor expansion of y in x 0.032 * [taylor]: Taking taylor expansion of (sqrt y) in y 0.032 * [taylor]: Taking taylor expansion of y in y 0.033 * [taylor]: Taking taylor expansion of 0 in y 0.034 * [taylor]: Taking taylor expansion of (* 1/2 (sqrt (/ 1 y))) in y 0.034 * [taylor]: Taking taylor expansion of 1/2 in y 0.034 * [taylor]: Taking taylor expansion of (sqrt (/ 1 y)) in y 0.034 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.034 * [taylor]: Taking taylor expansion of y in y 0.039 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in (x y) around 0 0.039 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in y 0.039 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in y 0.039 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.039 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.039 * [taylor]: Taking taylor expansion of x in y 0.039 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.039 * [taylor]: Taking taylor expansion of y in y 0.041 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in x 0.041 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in x 0.041 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.041 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.041 * [taylor]: Taking taylor expansion of x in x 0.041 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.041 * [taylor]: Taking taylor expansion of y in x 0.043 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in x 0.043 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in x 0.043 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.043 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.043 * [taylor]: Taking taylor expansion of x in x 0.044 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.044 * [taylor]: Taking taylor expansion of y in x 0.046 * [taylor]: Taking taylor expansion of 1 in y 0.046 * [taylor]: Taking taylor expansion of 0 in y 0.047 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.047 * [taylor]: Taking taylor expansion of 1/2 in y 0.047 * [taylor]: Taking taylor expansion of y in y 0.049 * [taylor]: Taking taylor expansion of 0 in y 0.052 * [taylor]: Taking taylor expansion of (/ -1/8 (pow y 2)) in y 0.052 * [taylor]: Taking taylor expansion of -1/8 in y 0.052 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.052 * [taylor]: Taking taylor expansion of y in y 0.054 * [approximate]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in (x y) around 0 0.054 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in y 0.054 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in y 0.054 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.054 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.054 * [taylor]: Taking taylor expansion of x in y 0.054 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.054 * [taylor]: Taking taylor expansion of y in y 0.056 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in x 0.056 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in x 0.056 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.056 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.056 * [taylor]: Taking taylor expansion of x in x 0.056 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.056 * [taylor]: Taking taylor expansion of y in x 0.058 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in x 0.058 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) 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 0.059 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.059 * [taylor]: Taking taylor expansion of y in x 0.061 * [taylor]: Taking taylor expansion of 1 in y 0.061 * [taylor]: Taking taylor expansion of 0 in y 0.062 * [taylor]: Taking taylor expansion of (/ -1/2 y) in y 0.063 * [taylor]: Taking taylor expansion of -1/2 in y 0.063 * [taylor]: Taking taylor expansion of y in y 0.065 * [taylor]: Taking taylor expansion of 0 in y 0.068 * [taylor]: Taking taylor expansion of (/ -1/8 (pow y 2)) in y 0.068 * [taylor]: Taking taylor expansion of -1/8 in y 0.068 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.068 * [taylor]: Taking taylor expansion of y in y 0.069 * * * [progress]: simplifying candidates 0.070 * [simplify]: Simplifying using # : (expm1 (sqrt (+ (* x x) y))) (log1p (sqrt (+ (* x x) y))) (log (sqrt (+ (* x x) y))) (exp (sqrt (+ (* x x) y))) (* (cbrt (sqrt (+ (* x x) y))) (cbrt (sqrt (+ (* x x) y)))) (cbrt (sqrt (+ (* x x) y))) (* (* (sqrt (+ (* x x) y)) (sqrt (+ (* x x) y))) (sqrt (+ (* x x) y))) (sqrt (* (cbrt (+ (* x x) y)) (cbrt (+ (* x x) y)))) (sqrt (cbrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))) (sqrt 1) (sqrt (+ (* x x) y)) (sqrt (+ (pow (* x x) 3) (pow y 3))) (sqrt (+ (* (* x x) (* x x)) (- (* y y) (* (* x x) y)))) (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)) (/ 1 2) (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))) (- (+ (* +nan.0 (pow x 2)) (- (+ (* +nan.0 (pow y 2)) (- (* +nan.0 y)))))) (+ x (* 1/2 (/ y x))) (- (+ x (* 1/2 (/ y x)))) 0.076 * * [simplify]: iteration 0 : 126 enodes (cost 102 ) 0.078 * * [simplify]: iteration 1 : 378 enodes (cost 95 ) 0.084 * * [simplify]: iteration 2 : 1147 enodes (cost 92 ) 0.109 * * [simplify]: iteration 3 : 4567 enodes (cost 90 ) 0.212 * * [simplify]: iteration 4 : 5001 enodes (cost 90 ) 0.213 * [simplify]: Simplified to: (expm1 (sqrt (+ (* x x) y))) (log1p (sqrt (+ (* x x) y))) (log (sqrt (+ (* x x) y))) (exp (sqrt (+ (* x x) y))) (* (cbrt (sqrt (+ (* x x) y))) (cbrt (sqrt (+ (* x x) y)))) (cbrt (sqrt (+ (* x x) y))) (pow (hypot x (pow y 1/2)) 3) (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))) 1 (hypot x (pow y 1/2)) (hypot (pow y 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* y y) (* (* x x) y)))) (sqrt (- (* (* x x) (* x x)) (* y y))) (sqrt (- (* x x) y)) 1/2 (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))) (* +nan.0 (fma (- x) x (fma y y (- y)))) (fma 1/2 (/ y x) x) (- (+ x (* 1/2 (/ y x)))) 0.213 * * * [progress]: adding candidates to table 0.257 * * [progress]: iteration 2 / 4 0.257 * * * [progress]: picking best candidate 0.262 * * * * [pick]: Picked # 0.262 * * * [progress]: localizing error 0.267 * * * [progress]: generating rewritten candidates 0.268 * * * * [progress]: [ 1 / 1 ] rewriting at (2 1 2) 0.277 * * * [progress]: generating series expansions 0.277 * * * * [progress]: [ 1 / 1 ] generating series at (2 1 2) 0.277 * [approximate]: Taking taylor expansion of (* 1/2 (/ y x)) in (y x) around 0 0.277 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in x 0.277 * [taylor]: Taking taylor expansion of 1/2 in x 0.277 * [taylor]: Taking taylor expansion of (/ y x) in x 0.277 * [taylor]: Taking taylor expansion of y in x 0.277 * [taylor]: Taking taylor expansion of x in x 0.277 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.277 * [taylor]: Taking taylor expansion of 1/2 in y 0.277 * [taylor]: Taking taylor expansion of (/ y x) in y 0.277 * [taylor]: Taking taylor expansion of y in y 0.277 * [taylor]: Taking taylor expansion of x in y 0.277 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.277 * [taylor]: Taking taylor expansion of 1/2 in y 0.277 * [taylor]: Taking taylor expansion of (/ y x) in y 0.277 * [taylor]: Taking taylor expansion of y in y 0.277 * [taylor]: Taking taylor expansion of x in y 0.277 * [taylor]: Taking taylor expansion of (/ 1/2 x) in x 0.277 * [taylor]: Taking taylor expansion of 1/2 in x 0.277 * [taylor]: Taking taylor expansion of x in x 0.278 * [taylor]: Taking taylor expansion of 0 in x 0.279 * [taylor]: Taking taylor expansion of 0 in x 0.281 * [taylor]: Taking taylor expansion of 0 in x 0.281 * [approximate]: Taking taylor expansion of (* 1/2 (/ x y)) in (y x) around 0 0.281 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.281 * [taylor]: Taking taylor expansion of 1/2 in x 0.281 * [taylor]: Taking taylor expansion of (/ x y) in x 0.281 * [taylor]: Taking taylor expansion of x in x 0.281 * [taylor]: Taking taylor expansion of y in x 0.281 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.281 * [taylor]: Taking taylor expansion of 1/2 in y 0.281 * [taylor]: Taking taylor expansion of (/ x y) in y 0.281 * [taylor]: Taking taylor expansion of x in y 0.281 * [taylor]: Taking taylor expansion of y in y 0.282 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.282 * [taylor]: Taking taylor expansion of 1/2 in y 0.282 * [taylor]: Taking taylor expansion of (/ x y) in y 0.282 * [taylor]: Taking taylor expansion of x in y 0.282 * [taylor]: Taking taylor expansion of y in y 0.282 * [taylor]: Taking taylor expansion of (* 1/2 x) in x 0.282 * [taylor]: Taking taylor expansion of 1/2 in x 0.282 * [taylor]: Taking taylor expansion of x in x 0.283 * [taylor]: Taking taylor expansion of 0 in x 0.285 * [taylor]: Taking taylor expansion of 0 in x 0.287 * [taylor]: Taking taylor expansion of 0 in x 0.287 * [approximate]: Taking taylor expansion of (* 1/2 (/ x y)) in (y x) around 0 0.287 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.287 * [taylor]: Taking taylor expansion of 1/2 in x 0.287 * [taylor]: Taking taylor expansion of (/ x y) in x 0.287 * [taylor]: Taking taylor expansion of x in x 0.287 * [taylor]: Taking taylor expansion of y in x 0.288 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.288 * [taylor]: Taking taylor expansion of 1/2 in y 0.288 * [taylor]: Taking taylor expansion of (/ x y) in y 0.288 * [taylor]: Taking taylor expansion of x in y 0.288 * [taylor]: Taking taylor expansion of y in y 0.288 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.288 * [taylor]: Taking taylor expansion of 1/2 in y 0.288 * [taylor]: Taking taylor expansion of (/ x y) in y 0.288 * [taylor]: Taking taylor expansion of x in y 0.288 * [taylor]: Taking taylor expansion of y in y 0.288 * [taylor]: Taking taylor expansion of (* 1/2 x) in x 0.288 * [taylor]: Taking taylor expansion of 1/2 in x 0.288 * [taylor]: Taking taylor expansion of x in x 0.289 * [taylor]: Taking taylor expansion of 0 in x 0.291 * [taylor]: Taking taylor expansion of 0 in x 0.293 * [taylor]: Taking taylor expansion of 0 in x 0.294 * * * [progress]: simplifying candidates 0.294 * [simplify]: Simplifying using # : (expm1 (* 1/2 (/ y x))) (log1p (* 1/2 (/ y x))) (* 1/2 (/ y x)) (+ (log 1/2) (- (log y) (log x))) (+ (log 1/2) (log (/ y x))) (log (* 1/2 (/ y x))) (exp (* 1/2 (/ y x))) (* (* (* 1/2 1/2) 1/2) (/ (* (* y y) y) (* (* x x) x))) (* (* (* 1/2 1/2) 1/2) (* (* (/ y x) (/ y x)) (/ y x))) (* (cbrt (* 1/2 (/ y x))) (cbrt (* 1/2 (/ y x)))) (cbrt (* 1/2 (/ y x))) (* (* (* 1/2 (/ y x)) (* 1/2 (/ y x))) (* 1/2 (/ y x))) (sqrt (* 1/2 (/ y x))) (sqrt (* 1/2 (/ y x))) (* (sqrt 1/2) (sqrt (/ y x))) (* (sqrt 1/2) (sqrt (/ y x))) (* (sqrt 1/2) (/ (sqrt y) (sqrt x))) (* (sqrt 1/2) (/ (sqrt y) (sqrt x))) (* 1/2 (* (cbrt (/ y x)) (cbrt (/ y x)))) (* 1/2 (sqrt (/ y x))) (* 1/2 (/ (* (cbrt y) (cbrt y)) (* (cbrt x) (cbrt x)))) (* 1/2 (/ (* (cbrt y) (cbrt y)) (sqrt x))) (* 1/2 (/ (* (cbrt y) (cbrt y)) 1)) (* 1/2 (/ (sqrt y) (* (cbrt x) (cbrt x)))) (* 1/2 (/ (sqrt y) (sqrt x))) (* 1/2 (/ (sqrt y) 1)) (* 1/2 (/ 1 (* (cbrt x) (cbrt x)))) (* 1/2 (/ 1 (sqrt x))) (* 1/2 (/ 1 1)) (* 1/2 1) (* 1/2 y) (* (cbrt 1/2) (/ y x)) (* (sqrt 1/2) (/ y x)) (* 1/2 (/ y x)) (* 1/2 y) (* 1/2 (/ y x)) (* 1/2 (/ y x)) (* 1/2 (/ y x)) 0.298 * * [simplify]: iteration 0 : 166 enodes (cost 134 ) 0.302 * * [simplify]: iteration 1 : 729 enodes (cost 124 ) 0.316 * * [simplify]: iteration 2 : 2968 enodes (cost 124 ) 0.356 * * [simplify]: iteration 3 : 5001 enodes (cost 124 ) 0.357 * [simplify]: Simplified to: (expm1 (* 1/2 (/ y x))) (log1p (* 1/2 (/ y x))) (* 1/2 (/ y x)) (log (* 1/2 (/ y x))) (log (* 1/2 (/ y x))) (log (* 1/2 (/ y x))) (exp (* 1/2 (/ y x))) (* 1/8 (pow (/ y x) 3)) (* 1/8 (pow (/ y x) 3)) (* (cbrt (* 1/2 (/ y x))) (cbrt (* 1/2 (/ y x)))) (cbrt (* 1/2 (/ y x))) (* 1/8 (pow (/ y x) 3)) (sqrt (* 1/2 (/ y x))) (sqrt (* 1/2 (/ y x))) (* (sqrt 1/2) (sqrt (/ y x))) (* (sqrt 1/2) (sqrt (/ y x))) (* (sqrt 1/2) (/ (sqrt y) (sqrt x))) (* (sqrt 1/2) (/ (sqrt y) (sqrt x))) (* 1/2 (* (cbrt (/ y x)) (cbrt (/ y x)))) (* 1/2 (sqrt (/ y x))) (* 1/2 (/ (* (cbrt y) (cbrt y)) (* (cbrt x) (cbrt x)))) (* 1/2 (/ (* (cbrt y) (cbrt y)) (sqrt x))) (* (* (cbrt y) (cbrt y)) 1/2) (* 1/2 (/ (sqrt y) (* (cbrt x) (cbrt x)))) (* 1/2 (/ (sqrt y) (sqrt x))) (* (sqrt y) 1/2) (/ 1/2 (* (cbrt x) (cbrt x))) (/ 1/2 (sqrt x)) 1/2 1/2 (* 1/2 y) (* (cbrt 1/2) (/ y x)) (* (sqrt 1/2) (/ y x)) (* 1/2 (/ y x)) (* 1/2 y) (* 1/2 (/ y x)) (* 1/2 (/ y x)) (* 1/2 (/ y x)) 0.357 * * * [progress]: adding candidates to table 0.414 * * [progress]: iteration 3 / 4 0.414 * * * [progress]: picking best candidate 0.415 * * * * [pick]: Picked # 0.415 * * * [progress]: localizing error 0.419 * * * [progress]: generating rewritten candidates 0.419 * * * [progress]: generating series expansions 0.419 * * * [progress]: simplifying candidates 0.419 * [simplify]: Simplifying using # : 0.421 * * [simplify]: iteration 0 : 0 enodes (cost 0 ) 0.421 * [simplify]: Simplified to: 0.421 * * * [progress]: adding candidates to table 0.422 * [progress]: [Phase 3 of 3] Extracting. 0.422 * * [regime]: Finding splitpoints for: (# # #) 0.422 * * * [regime-changes]: Trying 5 branch expressions: ((* x x) (+ (* x x) y) (sqrt (+ (* x x) y)) y x) 0.422 * * * * [regimes]: Trying to branch on (* x x) from (# # #) 0.440 * * * * [regimes]: Trying to branch on (+ (* x x) y) from (# # #) 0.457 * * * * [regimes]: Trying to branch on (sqrt (+ (* x x) y)) from (# # #) 0.478 * * * * [regimes]: Trying to branch on y from (# # #) 0.517 * * * * [regimes]: Trying to branch on x from (# # #) 0.540 * * * [regime]: Found split indices: #