8.425 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.013 * * * [progress]: [2/2] Setting up program. 0.015 * [progress]: [Phase 2 of 3] Improving. 0.015 * [simplify]: Simplifying using # : (sqrt (+ (* x x) y)) 0.018 * * [simplify]: iteration 0 : 7 enodes (cost 3 ) 0.019 * * [simplify]: iteration 1 : 7 enodes (cost 3 ) 0.019 * [simplify]: Simplified to: (sqrt (+ (* x x) y)) 0.020 * * [progress]: iteration 1 / 4 0.020 * * * [progress]: picking best candidate 0.021 * * * * [pick]: Picked # 0.021 * * * [progress]: localizing error 0.026 * * * [progress]: generating rewritten candidates 0.026 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.031 * * * [progress]: generating series expansions 0.031 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.031 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in (x y) around 0 0.031 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in y 0.031 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in y 0.031 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.031 * [taylor]: Taking taylor expansion of x in y 0.031 * [taylor]: Taking taylor expansion of y in y 0.032 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in x 0.032 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in x 0.032 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.032 * [taylor]: Taking taylor expansion of x in x 0.032 * [taylor]: Taking taylor expansion of y in x 0.032 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in x 0.032 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in x 0.032 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.032 * [taylor]: Taking taylor expansion of x in x 0.032 * [taylor]: Taking taylor expansion of y in x 0.033 * [taylor]: Taking taylor expansion of (sqrt y) in y 0.033 * [taylor]: Taking taylor expansion of y in y 0.034 * [taylor]: Taking taylor expansion of 0 in y 0.035 * [taylor]: Taking taylor expansion of (* 1/2 (sqrt (/ 1 y))) in y 0.035 * [taylor]: Taking taylor expansion of 1/2 in y 0.035 * [taylor]: Taking taylor expansion of (sqrt (/ 1 y)) in y 0.035 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.035 * [taylor]: Taking taylor expansion of y in y 0.040 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in (x y) around 0 0.040 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in y 0.040 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in y 0.040 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.040 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.040 * [taylor]: Taking taylor expansion of x in y 0.041 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.041 * [taylor]: Taking taylor expansion of y in y 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 (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in x 0.045 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in x 0.045 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.045 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.045 * [taylor]: Taking taylor expansion of x in x 0.045 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.045 * [taylor]: Taking taylor expansion of y in x 0.047 * [taylor]: Taking taylor expansion of 1 in y 0.047 * [taylor]: Taking taylor expansion of 0 in y 0.052 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.052 * [taylor]: Taking taylor expansion of 1/2 in y 0.052 * [taylor]: Taking taylor expansion of y in y 0.054 * [taylor]: Taking taylor expansion of 0 in y 0.057 * [taylor]: Taking taylor expansion of (/ -1/8 (pow y 2)) in y 0.057 * [taylor]: Taking taylor expansion of -1/8 in y 0.057 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.057 * [taylor]: Taking taylor expansion of y in y 0.059 * [approximate]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in (x y) around 0 0.059 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in y 0.059 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in y 0.059 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.059 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.059 * [taylor]: Taking taylor expansion of x in y 0.059 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.059 * [taylor]: Taking taylor expansion of y in y 0.061 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in x 0.061 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in x 0.061 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.061 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.061 * [taylor]: Taking taylor expansion of x in x 0.062 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.062 * [taylor]: Taking taylor expansion of y in x 0.064 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in x 0.064 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in x 0.064 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.064 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.064 * [taylor]: Taking taylor expansion of x in x 0.064 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.064 * [taylor]: Taking taylor expansion of y in x 0.066 * [taylor]: Taking taylor expansion of 1 in y 0.066 * [taylor]: Taking taylor expansion of 0 in y 0.068 * [taylor]: Taking taylor expansion of (/ -1/2 y) in y 0.068 * [taylor]: Taking taylor expansion of -1/2 in y 0.068 * [taylor]: Taking taylor expansion of y in y 0.071 * [taylor]: Taking taylor expansion of 0 in y 0.074 * [taylor]: Taking taylor expansion of (/ -1/8 (pow y 2)) in y 0.074 * [taylor]: Taking taylor expansion of -1/8 in y 0.075 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.075 * [taylor]: Taking taylor expansion of y in y 0.076 * * * [progress]: simplifying candidates 0.077 * [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)))) 0.080 * * [simplify]: iteration 0 : 126 enodes (cost 102 ) 0.083 * * [simplify]: iteration 1 : 378 enodes (cost 95 ) 0.089 * * [simplify]: iteration 2 : 1147 enodes (cost 92 ) 0.114 * * [simplify]: iteration 3 : 4567 enodes (cost 90 ) 0.222 * * [simplify]: iteration 4 : 5001 enodes (cost 90 ) 0.222 * [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)))) 0.223 * * * [progress]: adding candidates to table 0.273 * * [progress]: iteration 2 / 4 0.273 * * * [progress]: picking best candidate 0.277 * * * * [pick]: Picked # 0.277 * * * [progress]: localizing error 0.286 * * * [progress]: generating rewritten candidates 0.286 * * * * [progress]: [ 1 / 1 ] rewriting at (2 2) 0.287 * * * [progress]: generating series expansions 0.287 * * * * [progress]: [ 1 / 1 ] generating series at (2 2) 0.287 * [approximate]: Taking taylor expansion of (hypot x (pow y 1/2)) in (x y) around 0 0.287 * [taylor]: Taking taylor expansion of (hypot x (pow y 1/2)) in y 0.287 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* (pow y 1/2) (pow y 1/2)))) 0.287 * [taylor]: Taking taylor expansion of (+ (* x x) (* (pow y 1/2) (pow y 1/2))) in y 0.287 * [taylor]: Taking taylor expansion of (* x x) in y 0.287 * [taylor]: Taking taylor expansion of x in y 0.287 * [taylor]: Taking taylor expansion of x in y 0.287 * [taylor]: Taking taylor expansion of (* (pow y 1/2) (pow y 1/2)) in y 0.287 * [taylor]: Taking taylor expansion of (pow y 1/2) in y 0.287 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log y))) in y 0.287 * [taylor]: Taking taylor expansion of (* 1/2 (log y)) in y 0.287 * [taylor]: Taking taylor expansion of 1/2 in y 0.287 * [taylor]: Taking taylor expansion of (log y) in y 0.287 * [taylor]: Taking taylor expansion of y in y 0.288 * [taylor]: Taking taylor expansion of (pow y 1/2) in y 0.288 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log y))) in y 0.288 * [taylor]: Taking taylor expansion of (* 1/2 (log y)) in y 0.288 * [taylor]: Taking taylor expansion of 1/2 in y 0.288 * [taylor]: Taking taylor expansion of (log y) in y 0.288 * [taylor]: Taking taylor expansion of y in y 0.293 * [taylor]: Taking taylor expansion of (hypot x (pow y 1/2)) in x 0.293 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* (pow y 1/2) (pow y 1/2)))) 0.293 * [taylor]: Taking taylor expansion of (+ (* x x) (* (pow y 1/2) (pow y 1/2))) in x 0.293 * [taylor]: Taking taylor expansion of (* x x) in x 0.293 * [taylor]: Taking taylor expansion of x in x 0.293 * [taylor]: Taking taylor expansion of x in x 0.293 * [taylor]: Taking taylor expansion of (* (pow y 1/2) (pow y 1/2)) in x 0.293 * [taylor]: Taking taylor expansion of (pow y 1/2) in x 0.294 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log y))) in x 0.294 * [taylor]: Taking taylor expansion of (* 1/2 (log y)) in x 0.294 * [taylor]: Taking taylor expansion of 1/2 in x 0.294 * [taylor]: Taking taylor expansion of (log y) in x 0.294 * [taylor]: Taking taylor expansion of y in x 0.294 * [taylor]: Taking taylor expansion of (pow y 1/2) in x 0.294 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log y))) in x 0.294 * [taylor]: Taking taylor expansion of (* 1/2 (log y)) in x 0.294 * [taylor]: Taking taylor expansion of 1/2 in x 0.294 * [taylor]: Taking taylor expansion of (log y) in x 0.294 * [taylor]: Taking taylor expansion of y in x 0.298 * [taylor]: Taking taylor expansion of (hypot x (pow y 1/2)) in x 0.298 * [taylor]: Rewrote expression to (sqrt (+ (* x x) (* (pow y 1/2) (pow y 1/2)))) 0.298 * [taylor]: Taking taylor expansion of (+ (* x x) (* (pow y 1/2) (pow y 1/2))) in x 0.298 * [taylor]: Taking taylor expansion of (* x x) in x 0.298 * [taylor]: Taking taylor expansion of x in x 0.298 * [taylor]: Taking taylor expansion of x in x 0.298 * [taylor]: Taking taylor expansion of (* (pow y 1/2) (pow y 1/2)) in x 0.298 * [taylor]: Taking taylor expansion of (pow y 1/2) in x 0.298 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log y))) in x 0.298 * [taylor]: Taking taylor expansion of (* 1/2 (log y)) in x 0.298 * [taylor]: Taking taylor expansion of 1/2 in x 0.298 * [taylor]: Taking taylor expansion of (log y) in x 0.298 * [taylor]: Taking taylor expansion of y in x 0.298 * [taylor]: Taking taylor expansion of (pow y 1/2) in x 0.298 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log y))) in x 0.298 * [taylor]: Taking taylor expansion of (* 1/2 (log y)) in x 0.298 * [taylor]: Taking taylor expansion of 1/2 in x 0.298 * [taylor]: Taking taylor expansion of (log y) in x 0.298 * [taylor]: Taking taylor expansion of y in x 0.302 * [taylor]: Taking taylor expansion of (sqrt y) in y 0.302 * [taylor]: Taking taylor expansion of y in y 0.303 * [taylor]: Taking taylor expansion of 0 in y 0.310 * [taylor]: Taking taylor expansion of (* 1/2 (sqrt (/ 1 y))) in y 0.310 * [taylor]: Taking taylor expansion of 1/2 in y 0.310 * [taylor]: Taking taylor expansion of (sqrt (/ 1 y)) in y 0.310 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.310 * [taylor]: Taking taylor expansion of y in y 0.315 * [approximate]: Taking taylor expansion of (hypot (/ 1 x) (pow (/ 1 y) 1/2)) in (x y) around 0 0.315 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (pow (/ 1 y) 1/2)) in y 0.315 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (pow (/ 1 y) 1/2) (pow (/ 1 y) 1/2)))) 0.315 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (pow (/ 1 y) 1/2) (pow (/ 1 y) 1/2))) in y 0.315 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in y 0.315 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.315 * [taylor]: Taking taylor expansion of x in y 0.315 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.315 * [taylor]: Taking taylor expansion of x in y 0.315 * [taylor]: Taking taylor expansion of (* (pow (/ 1 y) 1/2) (pow (/ 1 y) 1/2)) in y 0.315 * [taylor]: Taking taylor expansion of (pow (/ 1 y) 1/2) in y 0.315 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ 1 y)))) in y 0.315 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ 1 y))) in y 0.315 * [taylor]: Taking taylor expansion of 1/2 in y 0.315 * [taylor]: Taking taylor expansion of (log (/ 1 y)) in y 0.315 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.315 * [taylor]: Taking taylor expansion of y in y 0.316 * [taylor]: Taking taylor expansion of (pow (/ 1 y) 1/2) in y 0.316 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ 1 y)))) in y 0.316 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ 1 y))) in y 0.316 * [taylor]: Taking taylor expansion of 1/2 in y 0.316 * [taylor]: Taking taylor expansion of (log (/ 1 y)) in y 0.316 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.316 * [taylor]: Taking taylor expansion of y in y 0.322 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (pow (/ 1 y) 1/2)) in x 0.322 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (pow (/ 1 y) 1/2) (pow (/ 1 y) 1/2)))) 0.322 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (pow (/ 1 y) 1/2) (pow (/ 1 y) 1/2))) in x 0.322 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in x 0.323 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.323 * [taylor]: Taking taylor expansion of x in x 0.323 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.323 * [taylor]: Taking taylor expansion of x in x 0.323 * [taylor]: Taking taylor expansion of (* (pow (/ 1 y) 1/2) (pow (/ 1 y) 1/2)) in x 0.323 * [taylor]: Taking taylor expansion of (pow (/ 1 y) 1/2) in x 0.323 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ 1 y)))) in x 0.323 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ 1 y))) in x 0.323 * [taylor]: Taking taylor expansion of 1/2 in x 0.323 * [taylor]: Taking taylor expansion of (log (/ 1 y)) in x 0.323 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.323 * [taylor]: Taking taylor expansion of y in x 0.323 * [taylor]: Taking taylor expansion of (pow (/ 1 y) 1/2) in x 0.323 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ 1 y)))) in x 0.323 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ 1 y))) in x 0.323 * [taylor]: Taking taylor expansion of 1/2 in x 0.323 * [taylor]: Taking taylor expansion of (log (/ 1 y)) in x 0.323 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.323 * [taylor]: Taking taylor expansion of y in x 0.326 * [taylor]: Taking taylor expansion of (hypot (/ 1 x) (pow (/ 1 y) 1/2)) in x 0.326 * [taylor]: Rewrote expression to (sqrt (+ (* (/ 1 x) (/ 1 x)) (* (pow (/ 1 y) 1/2) (pow (/ 1 y) 1/2)))) 0.326 * [taylor]: Taking taylor expansion of (+ (* (/ 1 x) (/ 1 x)) (* (pow (/ 1 y) 1/2) (pow (/ 1 y) 1/2))) in x 0.327 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in x 0.327 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.327 * [taylor]: Taking taylor expansion of x in x 0.327 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.327 * [taylor]: Taking taylor expansion of x in x 0.327 * [taylor]: Taking taylor expansion of (* (pow (/ 1 y) 1/2) (pow (/ 1 y) 1/2)) in x 0.327 * [taylor]: Taking taylor expansion of (pow (/ 1 y) 1/2) in x 0.327 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ 1 y)))) in x 0.327 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ 1 y))) in x 0.327 * [taylor]: Taking taylor expansion of 1/2 in x 0.327 * [taylor]: Taking taylor expansion of (log (/ 1 y)) in x 0.327 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.327 * [taylor]: Taking taylor expansion of y in x 0.327 * [taylor]: Taking taylor expansion of (pow (/ 1 y) 1/2) in x 0.327 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ 1 y)))) in x 0.327 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ 1 y))) in x 0.328 * [taylor]: Taking taylor expansion of 1/2 in x 0.328 * [taylor]: Taking taylor expansion of (log (/ 1 y)) in x 0.328 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.328 * [taylor]: Taking taylor expansion of y in x 0.330 * [taylor]: Taking taylor expansion of 1 in y 0.330 * [taylor]: Taking taylor expansion of 0 in y 0.333 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.333 * [taylor]: Taking taylor expansion of 1/2 in y 0.333 * [taylor]: Taking taylor expansion of y in y 0.339 * [taylor]: Taking taylor expansion of 0 in y 0.339 * [approximate]: Taking taylor expansion of (hypot (/ -1 x) (pow (/ -1 y) 1/2)) in (x y) around 0 0.340 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (pow (/ -1 y) 1/2)) in y 0.340 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (pow (/ -1 y) 1/2) (pow (/ -1 y) 1/2)))) 0.340 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (pow (/ -1 y) 1/2) (pow (/ -1 y) 1/2))) in y 0.340 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in y 0.340 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.340 * [taylor]: Taking taylor expansion of -1 in y 0.340 * [taylor]: Taking taylor expansion of x in y 0.340 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.340 * [taylor]: Taking taylor expansion of -1 in y 0.340 * [taylor]: Taking taylor expansion of x in y 0.340 * [taylor]: Taking taylor expansion of (* (pow (/ -1 y) 1/2) (pow (/ -1 y) 1/2)) in y 0.340 * [taylor]: Taking taylor expansion of (pow (/ -1 y) 1/2) in y 0.340 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ -1 y)))) in y 0.340 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ -1 y))) in y 0.340 * [taylor]: Taking taylor expansion of 1/2 in y 0.340 * [taylor]: Taking taylor expansion of (log (/ -1 y)) in y 0.340 * [taylor]: Taking taylor expansion of (/ -1 y) in y 0.340 * [taylor]: Taking taylor expansion of -1 in y 0.340 * [taylor]: Taking taylor expansion of y in y 0.345 * [taylor]: Taking taylor expansion of (pow (/ -1 y) 1/2) in y 0.345 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ -1 y)))) in y 0.345 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ -1 y))) in y 0.345 * [taylor]: Taking taylor expansion of 1/2 in y 0.345 * [taylor]: Taking taylor expansion of (log (/ -1 y)) in y 0.345 * [taylor]: Taking taylor expansion of (/ -1 y) in y 0.345 * [taylor]: Taking taylor expansion of -1 in y 0.345 * [taylor]: Taking taylor expansion of y in y 0.356 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (pow (/ -1 y) 1/2)) in x 0.356 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (pow (/ -1 y) 1/2) (pow (/ -1 y) 1/2)))) 0.356 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (pow (/ -1 y) 1/2) (pow (/ -1 y) 1/2))) in x 0.356 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in x 0.356 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.356 * [taylor]: Taking taylor expansion of -1 in x 0.356 * [taylor]: Taking taylor expansion of x in x 0.357 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.357 * [taylor]: Taking taylor expansion of -1 in x 0.357 * [taylor]: Taking taylor expansion of x in x 0.357 * [taylor]: Taking taylor expansion of (* (pow (/ -1 y) 1/2) (pow (/ -1 y) 1/2)) in x 0.357 * [taylor]: Taking taylor expansion of (pow (/ -1 y) 1/2) in x 0.357 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ -1 y)))) in x 0.357 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ -1 y))) in x 0.357 * [taylor]: Taking taylor expansion of 1/2 in x 0.357 * [taylor]: Taking taylor expansion of (log (/ -1 y)) in x 0.357 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.357 * [taylor]: Taking taylor expansion of -1 in x 0.357 * [taylor]: Taking taylor expansion of y in x 0.357 * [taylor]: Taking taylor expansion of (pow (/ -1 y) 1/2) in x 0.357 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ -1 y)))) in x 0.357 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ -1 y))) in x 0.357 * [taylor]: Taking taylor expansion of 1/2 in x 0.357 * [taylor]: Taking taylor expansion of (log (/ -1 y)) in x 0.357 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.358 * [taylor]: Taking taylor expansion of -1 in x 0.358 * [taylor]: Taking taylor expansion of y in x 0.361 * [taylor]: Taking taylor expansion of (hypot (/ -1 x) (pow (/ -1 y) 1/2)) in x 0.361 * [taylor]: Rewrote expression to (sqrt (+ (* (/ -1 x) (/ -1 x)) (* (pow (/ -1 y) 1/2) (pow (/ -1 y) 1/2)))) 0.361 * [taylor]: Taking taylor expansion of (+ (* (/ -1 x) (/ -1 x)) (* (pow (/ -1 y) 1/2) (pow (/ -1 y) 1/2))) in x 0.361 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in x 0.361 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.361 * [taylor]: Taking taylor expansion of -1 in x 0.361 * [taylor]: Taking taylor expansion of x in x 0.361 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.361 * [taylor]: Taking taylor expansion of -1 in x 0.361 * [taylor]: Taking taylor expansion of x in x 0.361 * [taylor]: Taking taylor expansion of (* (pow (/ -1 y) 1/2) (pow (/ -1 y) 1/2)) in x 0.361 * [taylor]: Taking taylor expansion of (pow (/ -1 y) 1/2) in x 0.361 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ -1 y)))) in x 0.361 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ -1 y))) in x 0.362 * [taylor]: Taking taylor expansion of 1/2 in x 0.362 * [taylor]: Taking taylor expansion of (log (/ -1 y)) in x 0.362 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.362 * [taylor]: Taking taylor expansion of -1 in x 0.362 * [taylor]: Taking taylor expansion of y in x 0.362 * [taylor]: Taking taylor expansion of (pow (/ -1 y) 1/2) in x 0.362 * [taylor]: Taking taylor expansion of (exp (* 1/2 (log (/ -1 y)))) in x 0.362 * [taylor]: Taking taylor expansion of (* 1/2 (log (/ -1 y))) in x 0.362 * [taylor]: Taking taylor expansion of 1/2 in x 0.362 * [taylor]: Taking taylor expansion of (log (/ -1 y)) in x 0.362 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.362 * [taylor]: Taking taylor expansion of -1 in x 0.362 * [taylor]: Taking taylor expansion of y in x 0.365 * [taylor]: Taking taylor expansion of 1 in y 0.365 * [taylor]: Taking taylor expansion of 0 in y 0.367 * [taylor]: Taking taylor expansion of (/ -1/2 y) in y 0.367 * [taylor]: Taking taylor expansion of -1/2 in y 0.367 * [taylor]: Taking taylor expansion of y in y 0.374 * [taylor]: Taking taylor expansion of 0 in y 0.374 * * * [progress]: simplifying candidates 0.374 * [simplify]: Simplifying using # : (expm1 (hypot x (pow y 1/2))) (log1p (hypot x (pow y 1/2))) (+ (* x x) (* (pow y 1/2) (pow y 1/2))) (log (hypot x (pow y 1/2))) (exp (hypot x (pow y 1/2))) (* (cbrt (hypot x (pow y 1/2))) (cbrt (hypot x (pow y 1/2)))) (cbrt (hypot x (pow y 1/2))) (* (* (hypot x (pow y 1/2)) (hypot x (pow y 1/2))) (hypot x (pow y 1/2))) (sqrt (hypot x (pow y 1/2))) (sqrt (hypot x (pow y 1/2))) (- (+ (* +nan.0 (pow x 2)) (- (+ (* +nan.0 (pow y 2)) (- (* +nan.0 y)))))) x (* -1 x) 0.377 * * [simplify]: iteration 0 : 67 enodes (cost 50 ) 0.379 * * [simplify]: iteration 1 : 162 enodes (cost 41 ) 0.384 * * [simplify]: iteration 2 : 598 enodes (cost 40 ) 0.400 * * [simplify]: iteration 3 : 2964 enodes (cost 39 ) 0.499 * * [simplify]: iteration 4 : 5001 enodes (cost 39 ) 0.499 * [simplify]: Simplified to: (expm1 (hypot x (pow y 1/2))) (log1p (hypot x (pow y 1/2))) (+ y (pow x 2)) (log (hypot x (pow y 1/2))) (exp (hypot x (pow y 1/2))) (* (cbrt (hypot x (pow y 1/2))) (cbrt (hypot x (pow y 1/2)))) (cbrt (hypot x (pow y 1/2))) (pow (hypot x (pow y 1/2)) 3) (sqrt (hypot x (pow y 1/2))) (sqrt (hypot x (pow y 1/2))) (* +nan.0 (fma (* -1 x) x (- (pow y 2) y))) x (* -1 x) 0.499 * * * [progress]: adding candidates to table 0.530 * * [progress]: iteration 3 / 4 0.530 * * * [progress]: picking best candidate 0.536 * * * * [pick]: Picked # 0.536 * * * [progress]: localizing error 0.539 * * * [progress]: generating rewritten candidates 0.539 * * * [progress]: generating series expansions 0.539 * * * [progress]: simplifying candidates 0.539 * [simplify]: Simplifying using # : 0.542 * * [simplify]: iteration 0 : 0 enodes (cost 0 ) 0.542 * [simplify]: Simplified to: 0.542 * * * [progress]: adding candidates to table 0.542 * * [progress]: iteration 4 / 4 0.542 * * * [progress]: picking best candidate 0.543 * * * * [pick]: Picked # 0.543 * * * [progress]: localizing error 0.547 * * * [progress]: generating rewritten candidates 0.547 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.548 * * * [progress]: generating series expansions 0.548 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.548 * [approximate]: Taking taylor expansion of (fma 1/2 (/ y x) x) in (y x) around 0 0.548 * [taylor]: Taking taylor expansion of (fma 1/2 (/ y x) x) in x 0.548 * [taylor]: Rewrote expression to (+ (* 1/2 (/ y x)) x) 0.548 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in x 0.548 * [taylor]: Taking taylor expansion of 1/2 in x 0.548 * [taylor]: Taking taylor expansion of (/ y x) in x 0.548 * [taylor]: Taking taylor expansion of y in x 0.548 * [taylor]: Taking taylor expansion of x in x 0.548 * [taylor]: Taking taylor expansion of x in x 0.548 * [taylor]: Taking taylor expansion of (fma 1/2 (/ y x) x) in y 0.548 * [taylor]: Rewrote expression to (+ (* 1/2 (/ y x)) x) 0.548 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.548 * [taylor]: Taking taylor expansion of 1/2 in y 0.548 * [taylor]: Taking taylor expansion of (/ y x) in y 0.548 * [taylor]: Taking taylor expansion of y in y 0.548 * [taylor]: Taking taylor expansion of x in y 0.549 * [taylor]: Taking taylor expansion of x in y 0.549 * [taylor]: Taking taylor expansion of (fma 1/2 (/ y x) x) in y 0.549 * [taylor]: Rewrote expression to (+ (* 1/2 (/ y x)) x) 0.549 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.549 * [taylor]: Taking taylor expansion of 1/2 in y 0.549 * [taylor]: Taking taylor expansion of (/ y x) in y 0.549 * [taylor]: Taking taylor expansion of y in y 0.549 * [taylor]: Taking taylor expansion of x in y 0.549 * [taylor]: Taking taylor expansion of x in y 0.549 * [taylor]: Taking taylor expansion of x in x 0.549 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 x)) in x 0.549 * [taylor]: Taking taylor expansion of 1/2 in x 0.549 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.549 * [taylor]: Taking taylor expansion of x in x 0.551 * [taylor]: Taking taylor expansion of 0 in x 0.553 * [taylor]: Taking taylor expansion of 0 in x 0.555 * [taylor]: Taking taylor expansion of 0 in x 0.556 * [approximate]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in (y x) around 0 0.556 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in x 0.556 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ 1 x)) 0.557 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.557 * [taylor]: Taking taylor expansion of 1/2 in x 0.557 * [taylor]: Taking taylor expansion of (/ x y) in x 0.557 * [taylor]: Taking taylor expansion of x in x 0.557 * [taylor]: Taking taylor expansion of y in x 0.557 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.557 * [taylor]: Taking taylor expansion of x in x 0.557 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in y 0.557 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ 1 x)) 0.557 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.557 * [taylor]: Taking taylor expansion of 1/2 in y 0.557 * [taylor]: Taking taylor expansion of (/ x y) in y 0.557 * [taylor]: Taking taylor expansion of x in y 0.557 * [taylor]: Taking taylor expansion of y in y 0.557 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.557 * [taylor]: Taking taylor expansion of x in y 0.557 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in y 0.557 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ 1 x)) 0.557 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.557 * [taylor]: Taking taylor expansion of 1/2 in y 0.557 * [taylor]: Taking taylor expansion of (/ x y) in y 0.557 * [taylor]: Taking taylor expansion of x in y 0.557 * [taylor]: Taking taylor expansion of y in y 0.557 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.558 * [taylor]: Taking taylor expansion of x in y 0.558 * [taylor]: Taking taylor expansion of (* 1/2 x) in x 0.558 * [taylor]: Taking taylor expansion of 1/2 in x 0.558 * [taylor]: Taking taylor expansion of x in x 0.559 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.559 * [taylor]: Taking taylor expansion of x in x 0.561 * [taylor]: Taking taylor expansion of 0 in x 0.564 * [taylor]: Taking taylor expansion of 0 in x 0.568 * [taylor]: Taking taylor expansion of 0 in x 0.569 * [approximate]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in (y x) around 0 0.569 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in x 0.569 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ -1 x)) 0.569 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.569 * [taylor]: Taking taylor expansion of 1/2 in x 0.569 * [taylor]: Taking taylor expansion of (/ x y) in x 0.570 * [taylor]: Taking taylor expansion of x in x 0.570 * [taylor]: Taking taylor expansion of y in x 0.570 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.570 * [taylor]: Taking taylor expansion of -1 in x 0.570 * [taylor]: Taking taylor expansion of x in x 0.570 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in y 0.570 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ -1 x)) 0.570 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.570 * [taylor]: Taking taylor expansion of 1/2 in y 0.570 * [taylor]: Taking taylor expansion of (/ x y) in y 0.570 * [taylor]: Taking taylor expansion of x in y 0.570 * [taylor]: Taking taylor expansion of y in y 0.570 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.570 * [taylor]: Taking taylor expansion of -1 in y 0.570 * [taylor]: Taking taylor expansion of x in y 0.570 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in y 0.570 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ -1 x)) 0.570 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.570 * [taylor]: Taking taylor expansion of 1/2 in y 0.570 * [taylor]: Taking taylor expansion of (/ x y) in y 0.570 * [taylor]: Taking taylor expansion of x in y 0.570 * [taylor]: Taking taylor expansion of y in y 0.570 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.570 * [taylor]: Taking taylor expansion of -1 in y 0.570 * [taylor]: Taking taylor expansion of x in y 0.571 * [taylor]: Taking taylor expansion of (* 1/2 x) in x 0.571 * [taylor]: Taking taylor expansion of 1/2 in x 0.571 * [taylor]: Taking taylor expansion of x in x 0.572 * [taylor]: Taking taylor expansion of (- (/ 1 x)) in x 0.572 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.572 * [taylor]: Taking taylor expansion of x in x 0.574 * [taylor]: Taking taylor expansion of 0 in x 0.577 * [taylor]: Taking taylor expansion of 0 in x 0.582 * [taylor]: Taking taylor expansion of 0 in x 0.583 * * * [progress]: simplifying candidates 0.583 * [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))) 0.586 * * [simplify]: iteration 0 : 21 enodes (cost 44 ) 0.587 * * [simplify]: iteration 1 : 48 enodes (cost 39 ) 0.589 * * [simplify]: iteration 2 : 156 enodes (cost 39 ) 0.592 * * [simplify]: iteration 3 : 585 enodes (cost 39 ) 0.607 * * [simplify]: iteration 4 : 2784 enodes (cost 39 ) 0.658 * * [simplify]: iteration 5 : 5001 enodes (cost 39 ) 0.659 * [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) 0.659 * * * [progress]: adding candidates to table 0.682 * [progress]: [Phase 3 of 3] Extracting. 0.682 * * [regime]: Finding splitpoints for: (# # # #) 0.682 * * * [regime-changes]: Trying 5 branch expressions: ((* x x) (+ (* x x) y) (sqrt (+ (* x x) y)) y x) 0.682 * * * * [regimes]: Trying to branch on (* x x) from (# # # #) 0.700 * * * * [regimes]: Trying to branch on (+ (* x x) y) from (# # # #) 0.721 * * * * [regimes]: Trying to branch on (sqrt (+ (* x x) y)) from (# # # #) 0.743 * * * * [regimes]: Trying to branch on y from (# # # #) 0.782 * * * * [regimes]: Trying to branch on x from (# # # #) 0.808 * * * [regime]: Found split indices: #