14.466 * [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) 0.029 * * * [progress]: generating series expansions 0.029 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.029 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in (x y) around 0 0.029 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in y 0.029 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in y 0.029 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.029 * [taylor]: Taking taylor expansion of x in y 0.029 * [taylor]: Taking taylor expansion of y in y 0.030 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in x 0.030 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in x 0.030 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.030 * [taylor]: Taking taylor expansion of x in x 0.030 * [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 0.031 * [taylor]: Taking taylor expansion of (sqrt y) in y 0.031 * [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 0.038 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in (x y) around 0 0.038 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in y 0.038 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in y 0.038 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.038 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.038 * [taylor]: Taking taylor expansion of x in y 0.038 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.038 * [taylor]: Taking taylor expansion of y in y 0.040 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in x 0.040 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in x 0.040 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.040 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.040 * [taylor]: Taking taylor expansion of x in x 0.040 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.040 * [taylor]: Taking taylor expansion of y in x 0.042 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in x 0.042 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in x 0.042 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.042 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.042 * [taylor]: Taking taylor expansion of x in x 0.043 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.043 * [taylor]: Taking taylor expansion of y in x 0.045 * [taylor]: Taking taylor expansion of 1 in y 0.045 * [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 0.051 * [taylor]: Taking taylor expansion of (/ -1/8 (pow y 2)) in y 0.051 * [taylor]: Taking taylor expansion of -1/8 in y 0.051 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.051 * [taylor]: Taking taylor expansion of y in y 0.053 * [approximate]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in (x y) around 0 0.053 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in y 0.053 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in y 0.053 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.053 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.053 * [taylor]: Taking taylor expansion of x in y 0.053 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.053 * [taylor]: Taking taylor expansion of y in y 0.055 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in x 0.055 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) 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 0.055 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.056 * [taylor]: Taking taylor expansion of y in x 0.057 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in x 0.057 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in x 0.057 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.057 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.057 * [taylor]: Taking taylor expansion of x in x 0.058 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.058 * [taylor]: Taking taylor expansion of y in x 0.060 * [taylor]: Taking taylor expansion of 1 in y 0.060 * [taylor]: Taking taylor expansion of 0 in y 0.062 * [taylor]: Taking taylor expansion of (/ -1/2 y) in y 0.062 * [taylor]: Taking taylor expansion of -1/2 in y 0.062 * [taylor]: Taking taylor expansion of y in y 0.064 * [taylor]: Taking taylor expansion of 0 in y 0.067 * [taylor]: Taking taylor expansion of (/ -1/8 (pow y 2)) in y 0.067 * [taylor]: Taking taylor expansion of -1/8 in y 0.067 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.067 * [taylor]: Taking taylor expansion of y in y 0.068 * * * [progress]: simplifying candidates 0.069 * [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)))) 0.072 * * [simplify]: iteration 0 : 126 enodes (cost 102 ) 0.075 * * [simplify]: iteration 1 : 378 enodes (cost 95 ) 0.081 * * [simplify]: iteration 2 : 1147 enodes (cost 92 ) 0.107 * * [simplify]: iteration 3 : 4567 enodes (cost 90 ) 0.214 * * [simplify]: iteration 4 : 5001 enodes (cost 90 ) 0.215 * [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)))) 0.215 * * * [progress]: adding candidates to table 0.264 * * [progress]: iteration 2 / 4 0.264 * * * [progress]: picking best candidate 0.266 * * * * [pick]: Picked # 0.266 * * * [progress]: localizing error 0.272 * * * [progress]: generating rewritten candidates 0.272 * * * * [progress]: [ 1 / 2 ] rewriting at (2 1) 0.274 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1 2) 0.285 * * * [progress]: generating series expansions 0.285 * * * * [progress]: [ 1 / 2 ] generating series at (2 1) 0.285 * [approximate]: Taking taylor expansion of (+ x (* 1/2 (/ y x))) in (x y) around 0 0.285 * [taylor]: Taking taylor expansion of (+ x (* 1/2 (/ y x))) in y 0.285 * [taylor]: Taking taylor expansion of x in y 0.285 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.285 * [taylor]: Taking taylor expansion of 1/2 in y 0.285 * [taylor]: Taking taylor expansion of (/ y x) in y 0.285 * [taylor]: Taking taylor expansion of y in y 0.285 * [taylor]: Taking taylor expansion of x in y 0.285 * [taylor]: Taking taylor expansion of (+ x (* 1/2 (/ y x))) in x 0.285 * [taylor]: Taking taylor expansion of x in x 0.285 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in x 0.285 * [taylor]: Taking taylor expansion of 1/2 in x 0.285 * [taylor]: Taking taylor expansion of (/ y x) in x 0.286 * [taylor]: Taking taylor expansion of y in x 0.286 * [taylor]: Taking taylor expansion of x in x 0.286 * [taylor]: Taking taylor expansion of (+ x (* 1/2 (/ y x))) in x 0.286 * [taylor]: Taking taylor expansion of x in x 0.286 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in x 0.286 * [taylor]: Taking taylor expansion of 1/2 in x 0.286 * [taylor]: Taking taylor expansion of (/ y x) in x 0.286 * [taylor]: Taking taylor expansion of y in x 0.286 * [taylor]: Taking taylor expansion of x in x 0.286 * [taylor]: Taking taylor expansion of (* 1/2 y) in y 0.286 * [taylor]: Taking taylor expansion of 1/2 in y 0.286 * [taylor]: Taking taylor expansion of y in y 0.287 * [taylor]: Taking taylor expansion of 0 in y 0.289 * [taylor]: Taking taylor expansion of 1 in y 0.292 * [taylor]: Taking taylor expansion of 0 in y 0.293 * [approximate]: Taking taylor expansion of (+ (* 1/2 (/ x y)) (/ 1 x)) in (x y) around 0 0.293 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ x y)) (/ 1 x)) in y 0.293 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.293 * [taylor]: Taking taylor expansion of 1/2 in y 0.293 * [taylor]: Taking taylor expansion of (/ x y) in y 0.293 * [taylor]: Taking taylor expansion of x in y 0.293 * [taylor]: Taking taylor expansion of y in y 0.293 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.293 * [taylor]: Taking taylor expansion of x in y 0.293 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ x y)) (/ 1 x)) in x 0.293 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.293 * [taylor]: Taking taylor expansion of 1/2 in x 0.293 * [taylor]: Taking taylor expansion of (/ x y) in x 0.293 * [taylor]: Taking taylor expansion of x in x 0.293 * [taylor]: Taking taylor expansion of y in x 0.293 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.293 * [taylor]: Taking taylor expansion of x in x 0.293 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ x y)) (/ 1 x)) in x 0.293 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.293 * [taylor]: Taking taylor expansion of 1/2 in x 0.294 * [taylor]: Taking taylor expansion of (/ x y) in x 0.294 * [taylor]: Taking taylor expansion of x in x 0.294 * [taylor]: Taking taylor expansion of y in x 0.294 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.294 * [taylor]: Taking taylor expansion of x in x 0.294 * [taylor]: Taking taylor expansion of 1 in y 0.295 * [taylor]: Taking taylor expansion of 0 in y 0.295 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 y)) in y 0.295 * [taylor]: Taking taylor expansion of 1/2 in y 0.295 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.296 * [taylor]: Taking taylor expansion of y in y 0.297 * [taylor]: Taking taylor expansion of 0 in y 0.299 * [taylor]: Taking taylor expansion of 0 in y 0.300 * [approximate]: Taking taylor expansion of (- (* 1/2 (/ x y)) (/ 1 x)) in (x y) around 0 0.300 * [taylor]: Taking taylor expansion of (- (* 1/2 (/ x y)) (/ 1 x)) in y 0.300 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.300 * [taylor]: Taking taylor expansion of 1/2 in y 0.300 * [taylor]: Taking taylor expansion of (/ x y) in y 0.300 * [taylor]: Taking taylor expansion of x in y 0.300 * [taylor]: Taking taylor expansion of y in y 0.300 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.300 * [taylor]: Taking taylor expansion of x in y 0.300 * [taylor]: Taking taylor expansion of (- (* 1/2 (/ x y)) (/ 1 x)) in x 0.300 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.300 * [taylor]: Taking taylor expansion of 1/2 in x 0.300 * [taylor]: Taking taylor expansion of (/ x y) in x 0.300 * [taylor]: Taking taylor expansion of x in x 0.300 * [taylor]: Taking taylor expansion of y in x 0.300 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.300 * [taylor]: Taking taylor expansion of x in x 0.300 * [taylor]: Taking taylor expansion of (- (* 1/2 (/ x y)) (/ 1 x)) in x 0.300 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.300 * [taylor]: Taking taylor expansion of 1/2 in x 0.300 * [taylor]: Taking taylor expansion of (/ x y) in x 0.300 * [taylor]: Taking taylor expansion of x in x 0.300 * [taylor]: Taking taylor expansion of y in x 0.301 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.301 * [taylor]: Taking taylor expansion of x in x 0.301 * [taylor]: Taking taylor expansion of -1 in y 0.302 * [taylor]: Taking taylor expansion of 0 in y 0.303 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 y)) in y 0.303 * [taylor]: Taking taylor expansion of 1/2 in y 0.303 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.303 * [taylor]: Taking taylor expansion of y in y 0.305 * [taylor]: Taking taylor expansion of 0 in y 0.307 * [taylor]: Taking taylor expansion of 0 in y 0.307 * * * * [progress]: [ 2 / 2 ] generating series at (2 1 2) 0.307 * [approximate]: Taking taylor expansion of (* 1/2 (/ y x)) in (y x) around 0 0.308 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in x 0.308 * [taylor]: Taking taylor expansion of 1/2 in x 0.308 * [taylor]: Taking taylor expansion of (/ y x) in x 0.308 * [taylor]: Taking taylor expansion of y in x 0.308 * [taylor]: Taking taylor expansion of x in x 0.308 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.308 * [taylor]: Taking taylor expansion of 1/2 in y 0.308 * [taylor]: Taking taylor expansion of (/ y x) in y 0.308 * [taylor]: Taking taylor expansion of y in y 0.308 * [taylor]: Taking taylor expansion of x in y 0.308 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.308 * [taylor]: Taking taylor expansion of 1/2 in y 0.308 * [taylor]: Taking taylor expansion of (/ y x) in y 0.308 * [taylor]: Taking taylor expansion of y in y 0.308 * [taylor]: Taking taylor expansion of x in y 0.308 * [taylor]: Taking taylor expansion of (/ 1/2 x) in x 0.308 * [taylor]: Taking taylor expansion of 1/2 in x 0.308 * [taylor]: Taking taylor expansion of x in x 0.309 * [taylor]: Taking taylor expansion of 0 in x 0.310 * [taylor]: Taking taylor expansion of 0 in x 0.311 * [taylor]: Taking taylor expansion of 0 in x 0.312 * [approximate]: Taking taylor expansion of (* 1/2 (/ x y)) in (y x) around 0 0.312 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.312 * [taylor]: Taking taylor expansion of 1/2 in x 0.312 * [taylor]: Taking taylor expansion of (/ x y) in x 0.312 * [taylor]: Taking taylor expansion of x in x 0.312 * [taylor]: Taking taylor expansion of y in x 0.312 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.312 * [taylor]: Taking taylor expansion of 1/2 in y 0.312 * [taylor]: Taking taylor expansion of (/ x y) in y 0.312 * [taylor]: Taking taylor expansion of x in y 0.312 * [taylor]: Taking taylor expansion of y in y 0.312 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.312 * [taylor]: Taking taylor expansion of 1/2 in y 0.312 * [taylor]: Taking taylor expansion of (/ x y) in y 0.312 * [taylor]: Taking taylor expansion of x in y 0.312 * [taylor]: Taking taylor expansion of y in y 0.312 * [taylor]: Taking taylor expansion of (* 1/2 x) in x 0.312 * [taylor]: Taking taylor expansion of 1/2 in x 0.312 * [taylor]: Taking taylor expansion of x in x 0.313 * [taylor]: Taking taylor expansion of 0 in x 0.315 * [taylor]: Taking taylor expansion of 0 in x 0.318 * [taylor]: Taking taylor expansion of 0 in x 0.318 * [approximate]: Taking taylor expansion of (* 1/2 (/ x y)) in (y x) around 0 0.318 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.318 * [taylor]: Taking taylor expansion of 1/2 in x 0.318 * [taylor]: Taking taylor expansion of (/ x y) in x 0.318 * [taylor]: Taking taylor expansion of x in x 0.318 * [taylor]: Taking taylor expansion of y in x 0.318 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.318 * [taylor]: Taking taylor expansion of 1/2 in y 0.318 * [taylor]: Taking taylor expansion of (/ x y) in y 0.318 * [taylor]: Taking taylor expansion of x in y 0.318 * [taylor]: Taking taylor expansion of y in y 0.318 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.318 * [taylor]: Taking taylor expansion of 1/2 in y 0.318 * [taylor]: Taking taylor expansion of (/ x y) in y 0.318 * [taylor]: Taking taylor expansion of x in y 0.318 * [taylor]: Taking taylor expansion of y in y 0.318 * [taylor]: Taking taylor expansion of (* 1/2 x) in x 0.318 * [taylor]: Taking taylor expansion of 1/2 in x 0.318 * [taylor]: Taking taylor expansion of x in x 0.320 * [taylor]: Taking taylor expansion of 0 in x 0.321 * [taylor]: Taking taylor expansion of 0 in x 0.324 * [taylor]: Taking taylor expansion of 0 in x 0.324 * * * [progress]: simplifying candidates 0.325 * [simplify]: Simplifying using # : (expm1 (+ x (* 1/2 (/ y x)))) (log1p (+ x (* 1/2 (/ y x)))) (* (exp x) (exp (* 1/2 (/ y x)))) (log (+ x (* 1/2 (/ y x)))) (exp (+ x (* 1/2 (/ y x)))) (* (cbrt (+ x (* 1/2 (/ y x)))) (cbrt (+ x (* 1/2 (/ y x))))) (cbrt (+ x (* 1/2 (/ y x)))) (* (* (+ x (* 1/2 (/ y x))) (+ x (* 1/2 (/ y x)))) (+ x (* 1/2 (/ y x)))) (sqrt (+ x (* 1/2 (/ y x)))) (sqrt (+ x (* 1/2 (/ y x)))) (+ (pow x 3) (pow (* 1/2 (/ y x)) 3)) (+ (* x x) (- (* (* 1/2 (/ y x)) (* 1/2 (/ y x))) (* x (* 1/2 (/ y x))))) (- (* x x) (* (* 1/2 (/ y x)) (* 1/2 (/ y x)))) (- x (* 1/2 (/ y x))) (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) (+ x (* 1/2 (/ y x))) (+ x (* 1/2 (/ y x))) (+ x (* 1/2 (/ y x))) (* 1/2 (/ y x)) (* 1/2 (/ y x)) (* 1/2 (/ y x)) 0.329 * * [simplify]: iteration 0 : 230 enodes (cost 213 ) 0.334 * * [simplify]: iteration 1 : 988 enodes (cost 194 ) 0.357 * * [simplify]: iteration 2 : 4421 enodes (cost 194 ) 0.428 * * [simplify]: iteration 3 : 5001 enodes (cost 194 ) 0.429 * [simplify]: Simplified to: (expm1 (+ x (* 1/2 (/ y x)))) (log1p (+ x (* 1/2 (/ y x)))) (exp (+ x (* 1/2 (/ y x)))) (log (+ x (* 1/2 (/ y x)))) (exp (+ x (* 1/2 (/ y x)))) (* (cbrt (+ x (* 1/2 (/ y x)))) (cbrt (+ x (* 1/2 (/ y x))))) (cbrt (+ x (* 1/2 (/ y x)))) (pow (fma 1/2 (/ y x) x) 3) (sqrt (+ x (* 1/2 (/ y x)))) (sqrt (+ x (* 1/2 (/ y x)))) (fma 1/8 (pow (/ y x) 3) (pow x 3)) (fma (* 1/2 (/ y x)) (- (* 1/2 (/ y x)) x) (* x x)) (* (- x (* 1/2 (/ y x))) (fma 1/2 (/ y x) x)) (- x (* 1/2 (/ y x))) (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))) (pow (* 1/2 (/ y x)) 3) (pow (* 1/2 (/ y x)) 3) (* (cbrt (* 1/2 (/ y x))) (cbrt (* 1/2 (/ y x)))) (cbrt (* 1/2 (/ y x))) (pow (* 1/2 (/ 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) (fma 1/2 (/ y x) x) (fma 1/2 (/ y x) x) (fma 1/2 (/ y x) x) (* 1/2 (/ y x)) (* 1/2 (/ y x)) (* 1/2 (/ y x)) 0.429 * * * [progress]: adding candidates to table 0.523 * * [progress]: iteration 3 / 4 0.523 * * * [progress]: picking best candidate 0.525 * * * * [pick]: Picked # 0.525 * * * [progress]: localizing error 0.529 * * * [progress]: generating rewritten candidates 0.529 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.530 * * * [progress]: generating series expansions 0.530 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.530 * [approximate]: Taking taylor expansion of (fma 1/2 (/ y x) x) in (y x) around 0 0.530 * [taylor]: Taking taylor expansion of (fma 1/2 (/ y x) x) in x 0.530 * [taylor]: Rewrote expression to (+ (* 1/2 (/ y x)) x) 0.530 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in x 0.530 * [taylor]: Taking taylor expansion of 1/2 in x 0.530 * [taylor]: Taking taylor expansion of (/ y x) in x 0.530 * [taylor]: Taking taylor expansion of y in x 0.530 * [taylor]: Taking taylor expansion of x in x 0.530 * [taylor]: Taking taylor expansion of x in x 0.530 * [taylor]: Taking taylor expansion of (fma 1/2 (/ y x) x) in y 0.530 * [taylor]: Rewrote expression to (+ (* 1/2 (/ y x)) x) 0.530 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.530 * [taylor]: Taking taylor expansion of 1/2 in y 0.530 * [taylor]: Taking taylor expansion of (/ y x) in y 0.530 * [taylor]: Taking taylor expansion of y in y 0.530 * [taylor]: Taking taylor expansion of x in y 0.530 * [taylor]: Taking taylor expansion of x in y 0.530 * [taylor]: Taking taylor expansion of (fma 1/2 (/ y x) x) in y 0.531 * [taylor]: Rewrote expression to (+ (* 1/2 (/ y x)) x) 0.531 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.531 * [taylor]: Taking taylor expansion of 1/2 in y 0.531 * [taylor]: Taking taylor expansion of (/ y x) in y 0.531 * [taylor]: Taking taylor expansion of y in y 0.531 * [taylor]: Taking taylor expansion of x in y 0.531 * [taylor]: Taking taylor expansion of x in y 0.531 * [taylor]: Taking taylor expansion of x in x 0.531 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 x)) in x 0.531 * [taylor]: Taking taylor expansion of 1/2 in x 0.531 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.531 * [taylor]: Taking taylor expansion of x in x 0.532 * [taylor]: Taking taylor expansion of 0 in x 0.534 * [taylor]: Taking taylor expansion of 0 in x 0.536 * [taylor]: Taking taylor expansion of 0 in x 0.537 * [approximate]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in (y x) around 0 0.537 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in x 0.538 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ 1 x)) 0.538 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.538 * [taylor]: Taking taylor expansion of 1/2 in x 0.538 * [taylor]: Taking taylor expansion of (/ x y) in x 0.538 * [taylor]: Taking taylor expansion of x in x 0.538 * [taylor]: Taking taylor expansion of y in x 0.538 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.538 * [taylor]: Taking taylor expansion of x in x 0.538 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in y 0.538 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ 1 x)) 0.538 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.538 * [taylor]: Taking taylor expansion of 1/2 in y 0.538 * [taylor]: Taking taylor expansion of (/ x y) in y 0.538 * [taylor]: Taking taylor expansion of x in y 0.538 * [taylor]: Taking taylor expansion of y in y 0.538 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.538 * [taylor]: Taking taylor expansion of x in y 0.539 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in y 0.539 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ 1 x)) 0.539 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.539 * [taylor]: Taking taylor expansion of 1/2 in y 0.539 * [taylor]: Taking taylor expansion of (/ x y) in y 0.539 * [taylor]: Taking taylor expansion of x in y 0.539 * [taylor]: Taking taylor expansion of y in y 0.539 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.539 * [taylor]: Taking taylor expansion of x in y 0.539 * [taylor]: Taking taylor expansion of (* 1/2 x) in x 0.539 * [taylor]: Taking taylor expansion of 1/2 in x 0.539 * [taylor]: Taking taylor expansion of x in x 0.540 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.540 * [taylor]: Taking taylor expansion of x in x 0.542 * [taylor]: Taking taylor expansion of 0 in x 0.545 * [taylor]: Taking taylor expansion of 0 in x 0.549 * [taylor]: Taking taylor expansion of 0 in x 0.550 * [approximate]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in (y x) around 0 0.550 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in x 0.550 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ -1 x)) 0.550 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.550 * [taylor]: Taking taylor expansion of 1/2 in x 0.550 * [taylor]: Taking taylor expansion of (/ x y) in x 0.550 * [taylor]: Taking taylor expansion of x in x 0.550 * [taylor]: Taking taylor expansion of y in x 0.550 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.550 * [taylor]: Taking taylor expansion of -1 in x 0.550 * [taylor]: Taking taylor expansion of x in x 0.550 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in y 0.550 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ -1 x)) 0.550 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.550 * [taylor]: Taking taylor expansion of 1/2 in y 0.550 * [taylor]: Taking taylor expansion of (/ x y) in y 0.550 * [taylor]: Taking taylor expansion of x in y 0.550 * [taylor]: Taking taylor expansion of y in y 0.550 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.550 * [taylor]: Taking taylor expansion of -1 in y 0.550 * [taylor]: Taking taylor expansion of x in y 0.550 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in y 0.551 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ -1 x)) 0.551 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.551 * [taylor]: Taking taylor expansion of 1/2 in y 0.551 * [taylor]: Taking taylor expansion of (/ x y) in y 0.551 * [taylor]: Taking taylor expansion of x in y 0.551 * [taylor]: Taking taylor expansion of y in y 0.551 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.551 * [taylor]: Taking taylor expansion of -1 in y 0.551 * [taylor]: Taking taylor expansion of x in y 0.551 * [taylor]: Taking taylor expansion of (* 1/2 x) in x 0.551 * [taylor]: Taking taylor expansion of 1/2 in x 0.551 * [taylor]: Taking taylor expansion of x in x 0.552 * [taylor]: Taking taylor expansion of (- (/ 1 x)) in x 0.552 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.552 * [taylor]: Taking taylor expansion of x in x 0.554 * [taylor]: Taking taylor expansion of 0 in x 0.557 * [taylor]: Taking taylor expansion of 0 in x 0.561 * [taylor]: Taking taylor expansion of 0 in x 0.562 * * * [progress]: simplifying candidates 0.563 * [simplify]: Simplifying using # : (expm1 (fma 1/2 (/ y x) x)) (log1p (fma 1/2 (/ y x) x)) (* 1/2 (/ y x)) (log (fma 1/2 (/ y x) x)) (exp (fma 1/2 (/ y x) x)) (* (cbrt (fma 1/2 (/ y x) x)) (cbrt (fma 1/2 (/ y x) x))) (cbrt (fma 1/2 (/ y x) x)) (* (* (fma 1/2 (/ y x) x) (fma 1/2 (/ y x) x)) (fma 1/2 (/ y x) x)) (sqrt (fma 1/2 (/ y x) x)) (sqrt (fma 1/2 (/ y x) x)) (+ x (* 1/2 (/ y x))) (+ x (* 1/2 (/ y x))) (+ x (* 1/2 (/ y x))) 0.565 * * [simplify]: iteration 0 : 21 enodes (cost 44 ) 0.567 * * [simplify]: iteration 1 : 48 enodes (cost 39 ) 0.569 * * [simplify]: iteration 2 : 156 enodes (cost 39 ) 0.572 * * [simplify]: iteration 3 : 585 enodes (cost 39 ) 0.587 * * [simplify]: iteration 4 : 2784 enodes (cost 39 ) 0.638 * * [simplify]: iteration 5 : 5001 enodes (cost 39 ) 0.639 * [simplify]: Simplified to: (expm1 (fma 1/2 (/ y x) x)) (log1p (fma 1/2 (/ y x) x)) (* 1/2 (/ y x)) (log (fma 1/2 (/ y x) x)) (exp (fma 1/2 (/ y x) x)) (* (cbrt (fma 1/2 (/ y x) x)) (cbrt (fma 1/2 (/ y x) x))) (cbrt (fma 1/2 (/ y x) x)) (pow (fma 1/2 (/ y x) x) 3) (sqrt (fma 1/2 (/ y x) x)) (sqrt (fma 1/2 (/ y x) x)) (fma 1/2 (/ y x) x) (fma 1/2 (/ y x) x) (fma 1/2 (/ y x) x) 0.639 * * * [progress]: adding candidates to table 0.663 * [progress]: [Phase 3 of 3] Extracting. 0.663 * * [regime]: Finding splitpoints for: (# # #) 0.664 * * * [regime-changes]: Trying 5 branch expressions: ((* x x) (+ (* x x) y) (sqrt (+ (* x x) y)) y x) 0.664 * * * * [regimes]: Trying to branch on (* x x) from (# # #) 0.678 * * * * [regimes]: Trying to branch on (+ (* x x) y) from (# # #) 0.697 * * * * [regimes]: Trying to branch on (sqrt (+ (* x x) y)) from (# # #) 0.716 * * * * [regimes]: Trying to branch on y from (# # #) 0.738 * * * * [regimes]: Trying to branch on x from (# # #) 0.761 * * * [regime]: Found split indices: #