7.061 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.015 * * * [progress]: [2/2] Setting up program. 0.017 * [progress]: [Phase 2 of 3] Improving. 0.017 * [simplify]: Simplifying using # : (sqrt (+ (* x x) y)) 0.017 * [simplify]: Sending expressions to egg_math: (sqrt (+ (* h0 h0) h1)) 0.020 * * [simplify]: iteration 0 : 7 enodes (cost 3 ) 0.021 * * [simplify]: iteration 1 : 7 enodes (cost 3 ) 0.021 * [simplify]: Simplified to: (sqrt (+ (* x x) y)) 0.021 * * [progress]: iteration 1 / 4 0.021 * * * [progress]: picking best candidate 0.023 * * * * [pick]: Picked # 0.023 * * * [progress]: localizing error 0.028 * * * [progress]: generating rewritten candidates 0.028 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.038 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.046 * * * [progress]: generating series expansions 0.046 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.046 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in (x y) around 0 0.047 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in y 0.047 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in y 0.047 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.047 * [taylor]: Taking taylor expansion of x in y 0.047 * [taylor]: Taking taylor expansion of y in y 0.047 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in x 0.047 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in x 0.047 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.047 * [taylor]: Taking taylor expansion of x in x 0.047 * [taylor]: Taking taylor expansion of y in x 0.048 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) y)) in x 0.048 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in x 0.048 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.048 * [taylor]: Taking taylor expansion of x in x 0.048 * [taylor]: Taking taylor expansion of y in x 0.048 * [taylor]: Taking taylor expansion of (sqrt y) in y 0.048 * [taylor]: Taking taylor expansion of y in y 0.050 * [taylor]: Taking taylor expansion of 0 in y 0.051 * [taylor]: Taking taylor expansion of (* 1/2 (sqrt (/ 1 y))) in y 0.051 * [taylor]: Taking taylor expansion of 1/2 in y 0.051 * [taylor]: Taking taylor expansion of (sqrt (/ 1 y)) in y 0.051 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.051 * [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 0.060 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in x 0.060 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in x 0.060 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.060 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.060 * [taylor]: Taking taylor expansion of x in x 0.061 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.061 * [taylor]: Taking taylor expansion of y in x 0.062 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 y))) in x 0.063 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in x 0.063 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.063 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.063 * [taylor]: Taking taylor expansion of x in x 0.063 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.063 * [taylor]: Taking taylor expansion of y in x 0.065 * [taylor]: Taking taylor expansion of 1 in y 0.065 * [taylor]: Taking taylor expansion of 0 in y 0.067 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.067 * [taylor]: Taking taylor expansion of 1/2 in y 0.067 * [taylor]: Taking taylor expansion of y in y 0.068 * [taylor]: Taking taylor expansion of 0 in y 0.071 * [taylor]: Taking taylor expansion of (/ -1/8 (pow y 2)) in y 0.071 * [taylor]: Taking taylor expansion of -1/8 in y 0.071 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.071 * [taylor]: Taking taylor expansion of y in y 0.073 * [approximate]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in (x y) around 0 0.073 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in y 0.073 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in y 0.073 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.073 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.073 * [taylor]: Taking taylor expansion of x in y 0.073 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.073 * [taylor]: Taking taylor expansion of y in y 0.075 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in x 0.075 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in x 0.075 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.075 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.075 * [taylor]: Taking taylor expansion of x in x 0.075 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.075 * [taylor]: Taking taylor expansion of y in x 0.077 * [taylor]: Taking taylor expansion of (sqrt (- (/ 1 (pow x 2)) (/ 1 y))) in x 0.077 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in x 0.077 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.077 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.077 * [taylor]: Taking taylor expansion of x in x 0.077 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.077 * [taylor]: Taking taylor expansion of y in x 0.079 * [taylor]: Taking taylor expansion of 1 in y 0.079 * [taylor]: Taking taylor expansion of 0 in y 0.081 * [taylor]: Taking taylor expansion of (/ -1/2 y) in y 0.081 * [taylor]: Taking taylor expansion of -1/2 in y 0.081 * [taylor]: Taking taylor expansion of y in y 0.083 * [taylor]: Taking taylor expansion of 0 in y 0.086 * [taylor]: Taking taylor expansion of (/ -1/8 (pow y 2)) in y 0.086 * [taylor]: Taking taylor expansion of -1/8 in y 0.086 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.086 * [taylor]: Taking taylor expansion of y in y 0.087 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.087 * [approximate]: Taking taylor expansion of (+ (pow x 2) y) in (x y) around 0 0.087 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in y 0.087 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.087 * [taylor]: Taking taylor expansion of x in y 0.087 * [taylor]: Taking taylor expansion of y in y 0.088 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in x 0.088 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.088 * [taylor]: Taking taylor expansion of x in x 0.088 * [taylor]: Taking taylor expansion of y in x 0.088 * [taylor]: Taking taylor expansion of (+ (pow x 2) y) in x 0.088 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.088 * [taylor]: Taking taylor expansion of x in x 0.088 * [taylor]: Taking taylor expansion of y in x 0.088 * [taylor]: Taking taylor expansion of y in y 0.088 * [taylor]: Taking taylor expansion of 0 in y 0.088 * [taylor]: Taking taylor expansion of 1 in y 0.089 * [taylor]: Taking taylor expansion of 0 in y 0.089 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in (x y) around 0 0.089 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in y 0.089 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.089 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.089 * [taylor]: Taking taylor expansion of x in y 0.090 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.090 * [taylor]: Taking taylor expansion of y in y 0.090 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in x 0.090 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.090 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.090 * [taylor]: Taking taylor expansion of x in x 0.090 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.090 * [taylor]: Taking taylor expansion of y in x 0.090 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 y)) in x 0.090 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.090 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.090 * [taylor]: Taking taylor expansion of x in x 0.091 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.091 * [taylor]: Taking taylor expansion of y in x 0.091 * [taylor]: Taking taylor expansion of 1 in y 0.092 * [taylor]: Taking taylor expansion of 0 in y 0.093 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.093 * [taylor]: Taking taylor expansion of y in y 0.095 * [taylor]: Taking taylor expansion of 0 in y 0.097 * [taylor]: Taking taylor expansion of 0 in y 0.097 * [approximate]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in (x y) around 0 0.097 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in y 0.097 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.097 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.097 * [taylor]: Taking taylor expansion of x in y 0.098 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.098 * [taylor]: Taking taylor expansion of y in y 0.098 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in x 0.098 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.098 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.098 * [taylor]: Taking taylor expansion of x in x 0.098 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.098 * [taylor]: Taking taylor expansion of y in x 0.098 * [taylor]: Taking taylor expansion of (- (/ 1 (pow x 2)) (/ 1 y)) in x 0.098 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.098 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.098 * [taylor]: Taking taylor expansion of x in x 0.099 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.099 * [taylor]: Taking taylor expansion of y in x 0.099 * [taylor]: Taking taylor expansion of 1 in y 0.100 * [taylor]: Taking taylor expansion of 0 in y 0.101 * [taylor]: Taking taylor expansion of (- (/ 1 y)) in y 0.101 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.101 * [taylor]: Taking taylor expansion of y in y 0.103 * [taylor]: Taking taylor expansion of 0 in y 0.105 * [taylor]: Taking taylor expansion of 0 in y 0.106 * * * [progress]: simplifying candidates 0.106 * [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))) (expm1 (+ (* x x) y)) (log1p (+ (* x x) y)) (* (exp (* x x)) (exp y)) (log (+ (* x x) y)) (exp (+ (* x x) y)) (* (cbrt (+ (* x x) y)) (cbrt (+ (* x x) y))) (cbrt (+ (* x x) y)) (* (* (+ (* x x) y) (+ (* x x) y)) (+ (* x x) y)) (sqrt (+ (* x x) y)) (sqrt (+ (* x x) y)) (+ (pow (* x x) 3) (pow y 3)) (+ (* (* x x) (* x x)) (- (* y y) (* (* x x) y))) (- (* (* x x) (* x x)) (* y y)) (- (* 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)))) (+ (pow x 2) y) (+ (pow x 2) y) (+ (pow x 2) y) 0.106 * [simplify]: Sending expressions to egg_math: (expm1 (sqrt (+ (* h0 h0) h1))) (log1p (sqrt (+ (* h0 h0) h1))) (log (sqrt (+ (* h0 h0) h1))) (exp (sqrt (+ (* h0 h0) h1))) (* (cbrt (sqrt (+ (* h0 h0) h1))) (cbrt (sqrt (+ (* h0 h0) h1)))) (cbrt (sqrt (+ (* h0 h0) h1))) (* (* (sqrt (+ (* h0 h0) h1)) (sqrt (+ (* h0 h0) h1))) (sqrt (+ (* h0 h0) h1))) (sqrt (* (cbrt (+ (* h0 h0) h1)) (cbrt (+ (* h0 h0) h1)))) (sqrt (cbrt (+ (* h0 h0) h1))) (sqrt (sqrt (+ (* h0 h0) h1))) (sqrt (sqrt (+ (* h0 h0) h1))) (sqrt 1) (sqrt (+ (* h0 h0) h1)) (sqrt (+ (pow (* h0 h0) 3) (pow h1 3))) (sqrt (+ (* (* h0 h0) (* h0 h0)) (- (* h1 h1) (* (* h0 h0) h1)))) (sqrt (- (* (* h0 h0) (* h0 h0)) (* h1 h1))) (sqrt (- (* h0 h0) h1)) (/ 1 2) (sqrt (sqrt (+ (* h0 h0) h1))) (sqrt (sqrt (+ (* h0 h0) h1))) (expm1 (+ (* h0 h0) h1)) (log1p (+ (* h0 h0) h1)) (* (exp (* h0 h0)) (exp h1)) (log (+ (* h0 h0) h1)) (exp (+ (* h0 h0) h1)) (* (cbrt (+ (* h0 h0) h1)) (cbrt (+ (* h0 h0) h1))) (cbrt (+ (* h0 h0) h1)) (* (* (+ (* h0 h0) h1) (+ (* h0 h0) h1)) (+ (* h0 h0) h1)) (sqrt (+ (* h0 h0) h1)) (sqrt (+ (* h0 h0) h1)) (+ (pow (* h0 h0) 3) (pow h1 3)) (+ (* (* h0 h0) (* h0 h0)) (- (* h1 h1) (* (* h0 h0) h1))) (- (* (* h0 h0) (* h0 h0)) (* h1 h1)) (- (* h0 h0) h1) (- (+ (* h2 (pow h0 2)) (- (+ (* h2 (pow h1 2)) (- (* h2 h1)))))) (+ h0 (* 1/2 (/ h1 h0))) (- (+ h0 (* 1/2 (/ h1 h0)))) (+ (pow h0 2) h1) (+ (pow h0 2) h1) (+ (pow h0 2) h1) 0.110 * * [simplify]: iteration 0 : 153 enodes (cost 160 ) 0.114 * * [simplify]: iteration 1 : 518 enodes (cost 146 ) 0.122 * * [simplify]: iteration 2 : 1716 enodes (cost 138 ) 0.157 * * [simplify]: iteration 3 : 5002 enodes (cost 136 ) 0.159 * [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))) (expm1 (+ (* x x) y)) (log1p (+ (* x x) y)) (exp (+ (* x x) y)) (log (+ (* x x) y)) (exp (+ (* x x) y)) (* (cbrt (+ (* x x) y)) (cbrt (+ (* x x) y))) (cbrt (+ (* x x) y)) (pow (fma x x y) 3) (hypot x (pow y 1/2)) (hypot x (pow y 1/2)) (fma (pow y 2) y (pow x 6)) (fma y (- y (pow x 2)) (pow x 4)) (- (pow x 4) (pow y 2)) (- (* x x) y) (* +nan.0 (fma (- x) x (fma y y (- y)))) (fma 1/2 (/ y x) x) (- (+ x (* 1/2 (/ y x)))) (fma x x y) (fma x x y) (fma x x y) 0.159 * * * [progress]: adding candidates to table 0.245 * * [progress]: iteration 2 / 4 0.245 * * * [progress]: picking best candidate 0.251 * * * * [pick]: Picked # 0.251 * * * [progress]: localizing error 0.255 * * * [progress]: generating rewritten candidates 0.256 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.257 * * * [progress]: generating series expansions 0.257 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.258 * [approximate]: Taking taylor expansion of (sqrt (fma x x y)) in (x y) around 0 0.258 * [taylor]: Taking taylor expansion of (sqrt (fma x x y)) in y 0.258 * [taylor]: Taking taylor expansion of (fma x x y) in y 0.258 * [taylor]: Rewrote expression to (+ (* x x) y) 0.258 * [taylor]: Taking taylor expansion of (* x x) in y 0.258 * [taylor]: Taking taylor expansion of x in y 0.258 * [taylor]: Taking taylor expansion of x in y 0.258 * [taylor]: Taking taylor expansion of y in y 0.259 * [taylor]: Taking taylor expansion of (sqrt (fma x x y)) in x 0.259 * [taylor]: Taking taylor expansion of (fma x x y) in x 0.259 * [taylor]: Rewrote expression to (+ (* x x) y) 0.259 * [taylor]: Taking taylor expansion of (* x x) in x 0.259 * [taylor]: Taking taylor expansion of x in x 0.259 * [taylor]: Taking taylor expansion of x in x 0.259 * [taylor]: Taking taylor expansion of y in x 0.260 * [taylor]: Taking taylor expansion of (sqrt (fma x x y)) in x 0.260 * [taylor]: Taking taylor expansion of (fma x x y) in x 0.260 * [taylor]: Rewrote expression to (+ (* x x) y) 0.260 * [taylor]: Taking taylor expansion of (* x x) in x 0.260 * [taylor]: Taking taylor expansion of x in x 0.260 * [taylor]: Taking taylor expansion of x in x 0.260 * [taylor]: Taking taylor expansion of y in x 0.261 * [taylor]: Taking taylor expansion of (sqrt y) in y 0.261 * [taylor]: Taking taylor expansion of y in y 0.262 * [taylor]: Taking taylor expansion of 0 in y 0.263 * [taylor]: Taking taylor expansion of (* 1/2 (sqrt (/ 1 y))) in y 0.263 * [taylor]: Taking taylor expansion of 1/2 in y 0.263 * [taylor]: Taking taylor expansion of (sqrt (/ 1 y)) in y 0.263 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.263 * [taylor]: Taking taylor expansion of y in y 0.268 * [approximate]: Taking taylor expansion of (sqrt (fma (/ 1 x) (/ 1 x) (/ 1 y))) in (x y) around 0 0.268 * [taylor]: Taking taylor expansion of (sqrt (fma (/ 1 x) (/ 1 x) (/ 1 y))) in y 0.268 * [taylor]: Taking taylor expansion of (fma (/ 1 x) (/ 1 x) (/ 1 y)) in y 0.268 * [taylor]: Rewrote expression to (+ (* (/ 1 x) (/ 1 x)) (/ 1 y)) 0.268 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in y 0.268 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.268 * [taylor]: Taking taylor expansion of x in y 0.268 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.268 * [taylor]: Taking taylor expansion of x in y 0.268 * [taylor]: Taking taylor expansion of (/ 1 y) in y 0.268 * [taylor]: Taking taylor expansion of y in y 0.270 * [taylor]: Taking taylor expansion of (sqrt (fma (/ 1 x) (/ 1 x) (/ 1 y))) in x 0.270 * [taylor]: Taking taylor expansion of (fma (/ 1 x) (/ 1 x) (/ 1 y)) in x 0.270 * [taylor]: Rewrote expression to (+ (* (/ 1 x) (/ 1 x)) (/ 1 y)) 0.270 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in x 0.270 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.270 * [taylor]: Taking taylor expansion of x in x 0.270 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.270 * [taylor]: Taking taylor expansion of x in x 0.270 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.270 * [taylor]: Taking taylor expansion of y in x 0.273 * [taylor]: Taking taylor expansion of (sqrt (fma (/ 1 x) (/ 1 x) (/ 1 y))) in x 0.273 * [taylor]: Taking taylor expansion of (fma (/ 1 x) (/ 1 x) (/ 1 y)) in x 0.273 * [taylor]: Rewrote expression to (+ (* (/ 1 x) (/ 1 x)) (/ 1 y)) 0.273 * [taylor]: Taking taylor expansion of (* (/ 1 x) (/ 1 x)) in x 0.273 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.273 * [taylor]: Taking taylor expansion of x in x 0.273 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.273 * [taylor]: Taking taylor expansion of x in x 0.273 * [taylor]: Taking taylor expansion of (/ 1 y) in x 0.273 * [taylor]: Taking taylor expansion of y in x 0.276 * [taylor]: Taking taylor expansion of 1 in y 0.276 * [taylor]: Taking taylor expansion of 0 in y 0.278 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.278 * [taylor]: Taking taylor expansion of 1/2 in y 0.278 * [taylor]: Taking taylor expansion of y in y 0.280 * [taylor]: Taking taylor expansion of 0 in y 0.283 * [taylor]: Taking taylor expansion of (/ -1/8 (pow y 2)) in y 0.283 * [taylor]: Taking taylor expansion of -1/8 in y 0.283 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.283 * [taylor]: Taking taylor expansion of y in y 0.285 * [approximate]: Taking taylor expansion of (sqrt (fma (/ -1 x) (/ -1 x) (/ -1 y))) in (x y) around 0 0.285 * [taylor]: Taking taylor expansion of (sqrt (fma (/ -1 x) (/ -1 x) (/ -1 y))) in y 0.285 * [taylor]: Taking taylor expansion of (fma (/ -1 x) (/ -1 x) (/ -1 y)) in y 0.285 * [taylor]: Rewrote expression to (+ (* (/ -1 x) (/ -1 x)) (/ -1 y)) 0.285 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in y 0.285 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.285 * [taylor]: Taking taylor expansion of -1 in y 0.285 * [taylor]: Taking taylor expansion of x in y 0.285 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.285 * [taylor]: Taking taylor expansion of -1 in y 0.285 * [taylor]: Taking taylor expansion of x in y 0.285 * [taylor]: Taking taylor expansion of (/ -1 y) in y 0.285 * [taylor]: Taking taylor expansion of -1 in y 0.285 * [taylor]: Taking taylor expansion of y in y 0.287 * [taylor]: Taking taylor expansion of (sqrt (fma (/ -1 x) (/ -1 x) (/ -1 y))) in x 0.287 * [taylor]: Taking taylor expansion of (fma (/ -1 x) (/ -1 x) (/ -1 y)) in x 0.287 * [taylor]: Rewrote expression to (+ (* (/ -1 x) (/ -1 x)) (/ -1 y)) 0.287 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in x 0.287 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.287 * [taylor]: Taking taylor expansion of -1 in x 0.287 * [taylor]: Taking taylor expansion of x in x 0.287 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.287 * [taylor]: Taking taylor expansion of -1 in x 0.287 * [taylor]: Taking taylor expansion of x in x 0.287 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.287 * [taylor]: Taking taylor expansion of -1 in x 0.288 * [taylor]: Taking taylor expansion of y in x 0.290 * [taylor]: Taking taylor expansion of (sqrt (fma (/ -1 x) (/ -1 x) (/ -1 y))) in x 0.290 * [taylor]: Taking taylor expansion of (fma (/ -1 x) (/ -1 x) (/ -1 y)) in x 0.290 * [taylor]: Rewrote expression to (+ (* (/ -1 x) (/ -1 x)) (/ -1 y)) 0.290 * [taylor]: Taking taylor expansion of (* (/ -1 x) (/ -1 x)) in x 0.290 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.290 * [taylor]: Taking taylor expansion of -1 in x 0.290 * [taylor]: Taking taylor expansion of x in x 0.290 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.290 * [taylor]: Taking taylor expansion of -1 in x 0.290 * [taylor]: Taking taylor expansion of x in x 0.291 * [taylor]: Taking taylor expansion of (/ -1 y) in x 0.291 * [taylor]: Taking taylor expansion of -1 in x 0.291 * [taylor]: Taking taylor expansion of y in x 0.293 * [taylor]: Taking taylor expansion of 1 in y 0.293 * [taylor]: Taking taylor expansion of 0 in y 0.295 * [taylor]: Taking taylor expansion of (/ -1/2 y) in y 0.295 * [taylor]: Taking taylor expansion of -1/2 in y 0.295 * [taylor]: Taking taylor expansion of y in y 0.298 * [taylor]: Taking taylor expansion of 0 in y 0.301 * [taylor]: Taking taylor expansion of (/ -1/8 (pow y 2)) in y 0.301 * [taylor]: Taking taylor expansion of -1/8 in y 0.301 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.301 * [taylor]: Taking taylor expansion of y in y 0.302 * * * [progress]: simplifying candidates 0.303 * [simplify]: Simplifying using # : (expm1 (sqrt (fma x x y))) (log1p (sqrt (fma x x y))) (log (sqrt (fma x x y))) (exp (sqrt (fma x x y))) (* (cbrt (sqrt (fma x x y))) (cbrt (sqrt (fma x x y)))) (cbrt (sqrt (fma x x y))) (* (* (sqrt (fma x x y)) (sqrt (fma x x y))) (sqrt (fma x x y))) (sqrt (* (cbrt (fma x x y)) (cbrt (fma x x y)))) (sqrt (cbrt (fma x x y))) (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma x x y))) (sqrt 1) (sqrt (fma x x y)) (/ 1 2) (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma 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)))) 0.303 * [simplify]: Sending expressions to egg_math: (expm1 (sqrt (fma h0 h0 h1))) (log1p (sqrt (fma h0 h0 h1))) (log (sqrt (fma h0 h0 h1))) (exp (sqrt (fma h0 h0 h1))) (* (cbrt (sqrt (fma h0 h0 h1))) (cbrt (sqrt (fma h0 h0 h1)))) (cbrt (sqrt (fma h0 h0 h1))) (* (* (sqrt (fma h0 h0 h1)) (sqrt (fma h0 h0 h1))) (sqrt (fma h0 h0 h1))) (sqrt (* (cbrt (fma h0 h0 h1)) (cbrt (fma h0 h0 h1)))) (sqrt (cbrt (fma h0 h0 h1))) (sqrt (sqrt (fma h0 h0 h1))) (sqrt (sqrt (fma h0 h0 h1))) (sqrt 1) (sqrt (fma h0 h0 h1)) (/ 1 2) (sqrt (sqrt (fma h0 h0 h1))) (sqrt (sqrt (fma h0 h0 h1))) (- (+ (* h2 (pow h0 2)) (- (+ (* h2 (pow h1 2)) (- (* h2 h1)))))) (+ h0 (* 1/2 (/ h1 h0))) (- (+ h0 (* 1/2 (/ h1 h0)))) 0.306 * * [simplify]: iteration 0 : 76 enodes (cost 64 ) 0.308 * * [simplify]: iteration 1 : 185 enodes (cost 59 ) 0.312 * * [simplify]: iteration 2 : 616 enodes (cost 58 ) 0.326 * * [simplify]: iteration 3 : 2525 enodes (cost 56 ) 0.390 * * [simplify]: iteration 4 : 5001 enodes (cost 56 ) 0.391 * [simplify]: Simplified to: (expm1 (sqrt (fma x x y))) (log1p (sqrt (fma x x y))) (log (sqrt (fma x x y))) (exp (sqrt (fma x x y))) (* (cbrt (sqrt (fma x x y))) (cbrt (sqrt (fma x x y)))) (cbrt (sqrt (fma x x y))) (pow (sqrt (fma x x y)) 3) (fabs (cbrt (fma x x y))) (sqrt (cbrt (fma x x y))) (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma x x y))) 1 (sqrt (fma x x y)) 1/2 (sqrt (sqrt (fma x x y))) (sqrt (sqrt (fma x x y))) (* +nan.0 (fma (- x) x (- (pow y 2) y))) (fma 1/2 (/ y x) x) (- (+ x (* 1/2 (/ y x)))) 0.391 * * * [progress]: adding candidates to table 0.427 * * [progress]: iteration 3 / 4 0.427 * * * [progress]: picking best candidate 0.431 * * * * [pick]: Picked # 0.431 * * * [progress]: localizing error 0.441 * * * [progress]: generating rewritten candidates 0.441 * * * [progress]: generating series expansions 0.441 * * * [progress]: simplifying candidates 0.441 * [simplify]: Simplifying using # : 0.441 * [simplify]: Sending expressions to egg_math: 0.443 * * [simplify]: iteration 0 : 0 enodes (cost 0 ) 0.443 * [simplify]: Simplified to: 0.443 * * * [progress]: adding candidates to table 0.444 * * [progress]: iteration 4 / 4 0.444 * * * [progress]: picking best candidate 0.446 * * * * [pick]: Picked # 0.446 * * * [progress]: localizing error 0.451 * * * [progress]: generating rewritten candidates 0.451 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.451 * * * [progress]: generating series expansions 0.451 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.451 * [approximate]: Taking taylor expansion of (fma 1/2 (/ y x) x) in (y x) around 0 0.451 * [taylor]: Taking taylor expansion of (fma 1/2 (/ y x) x) in x 0.452 * [taylor]: Rewrote expression to (+ (* 1/2 (/ y x)) x) 0.452 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in x 0.452 * [taylor]: Taking taylor expansion of 1/2 in x 0.452 * [taylor]: Taking taylor expansion of (/ y x) in x 0.452 * [taylor]: Taking taylor expansion of y in x 0.452 * [taylor]: Taking taylor expansion of x in x 0.452 * [taylor]: Taking taylor expansion of x in x 0.452 * [taylor]: Taking taylor expansion of (fma 1/2 (/ y x) x) in y 0.452 * [taylor]: Rewrote expression to (+ (* 1/2 (/ y x)) x) 0.452 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.452 * [taylor]: Taking taylor expansion of 1/2 in y 0.452 * [taylor]: Taking taylor expansion of (/ y x) in y 0.452 * [taylor]: Taking taylor expansion of y in y 0.452 * [taylor]: Taking taylor expansion of x in y 0.452 * [taylor]: Taking taylor expansion of x in y 0.452 * [taylor]: Taking taylor expansion of (fma 1/2 (/ y x) x) in y 0.452 * [taylor]: Rewrote expression to (+ (* 1/2 (/ y x)) x) 0.452 * [taylor]: Taking taylor expansion of (* 1/2 (/ y x)) in y 0.452 * [taylor]: Taking taylor expansion of 1/2 in y 0.452 * [taylor]: Taking taylor expansion of (/ y x) in y 0.452 * [taylor]: Taking taylor expansion of y in y 0.452 * [taylor]: Taking taylor expansion of x in y 0.452 * [taylor]: Taking taylor expansion of x in y 0.452 * [taylor]: Taking taylor expansion of x in x 0.452 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 x)) in x 0.452 * [taylor]: Taking taylor expansion of 1/2 in x 0.452 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.452 * [taylor]: Taking taylor expansion of x in x 0.454 * [taylor]: Taking taylor expansion of 0 in x 0.455 * [taylor]: Taking taylor expansion of 0 in x 0.457 * [taylor]: Taking taylor expansion of 0 in x 0.458 * [approximate]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in (y x) around 0 0.458 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in x 0.458 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ 1 x)) 0.459 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.459 * [taylor]: Taking taylor expansion of 1/2 in x 0.459 * [taylor]: Taking taylor expansion of (/ x y) in x 0.459 * [taylor]: Taking taylor expansion of x in x 0.459 * [taylor]: Taking taylor expansion of y in x 0.459 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.459 * [taylor]: Taking taylor expansion of x in x 0.459 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in y 0.459 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ 1 x)) 0.459 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.459 * [taylor]: Taking taylor expansion of 1/2 in y 0.459 * [taylor]: Taking taylor expansion of (/ x y) in y 0.459 * [taylor]: Taking taylor expansion of x in y 0.459 * [taylor]: Taking taylor expansion of y in y 0.459 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.459 * [taylor]: Taking taylor expansion of x in y 0.459 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ 1 x)) in y 0.459 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ 1 x)) 0.459 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.459 * [taylor]: Taking taylor expansion of 1/2 in y 0.459 * [taylor]: Taking taylor expansion of (/ x y) in y 0.459 * [taylor]: Taking taylor expansion of x in y 0.459 * [taylor]: Taking taylor expansion of y in y 0.459 * [taylor]: Taking taylor expansion of (/ 1 x) in y 0.459 * [taylor]: Taking taylor expansion of x in y 0.460 * [taylor]: Taking taylor expansion of (* 1/2 x) in x 0.460 * [taylor]: Taking taylor expansion of 1/2 in x 0.460 * [taylor]: Taking taylor expansion of x in x 0.460 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.460 * [taylor]: Taking taylor expansion of x in x 0.462 * [taylor]: Taking taylor expansion of 0 in x 0.465 * [taylor]: Taking taylor expansion of 0 in x 0.472 * [taylor]: Taking taylor expansion of 0 in x 0.473 * [approximate]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in (y x) around 0 0.473 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in x 0.473 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ -1 x)) 0.473 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in x 0.473 * [taylor]: Taking taylor expansion of 1/2 in x 0.473 * [taylor]: Taking taylor expansion of (/ x y) in x 0.473 * [taylor]: Taking taylor expansion of x in x 0.473 * [taylor]: Taking taylor expansion of y in x 0.473 * [taylor]: Taking taylor expansion of (/ -1 x) in x 0.473 * [taylor]: Taking taylor expansion of -1 in x 0.473 * [taylor]: Taking taylor expansion of x in x 0.474 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in y 0.474 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ -1 x)) 0.474 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.474 * [taylor]: Taking taylor expansion of 1/2 in y 0.474 * [taylor]: Taking taylor expansion of (/ x y) in y 0.474 * [taylor]: Taking taylor expansion of x in y 0.474 * [taylor]: Taking taylor expansion of y in y 0.474 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.474 * [taylor]: Taking taylor expansion of -1 in y 0.474 * [taylor]: Taking taylor expansion of x in y 0.474 * [taylor]: Taking taylor expansion of (fma 1/2 (/ x y) (/ -1 x)) in y 0.474 * [taylor]: Rewrote expression to (+ (* 1/2 (/ x y)) (/ -1 x)) 0.474 * [taylor]: Taking taylor expansion of (* 1/2 (/ x y)) in y 0.474 * [taylor]: Taking taylor expansion of 1/2 in y 0.474 * [taylor]: Taking taylor expansion of (/ x y) in y 0.474 * [taylor]: Taking taylor expansion of x in y 0.474 * [taylor]: Taking taylor expansion of y in y 0.474 * [taylor]: Taking taylor expansion of (/ -1 x) in y 0.474 * [taylor]: Taking taylor expansion of -1 in y 0.474 * [taylor]: Taking taylor expansion of x in y 0.474 * [taylor]: Taking taylor expansion of (* 1/2 x) in x 0.474 * [taylor]: Taking taylor expansion of 1/2 in x 0.474 * [taylor]: Taking taylor expansion of x in x 0.475 * [taylor]: Taking taylor expansion of (- (/ 1 x)) in x 0.475 * [taylor]: Taking taylor expansion of (/ 1 x) in x 0.475 * [taylor]: Taking taylor expansion of x in x 0.477 * [taylor]: Taking taylor expansion of 0 in x 0.481 * [taylor]: Taking taylor expansion of 0 in x 0.484 * [taylor]: Taking taylor expansion of 0 in x 0.485 * * * [progress]: simplifying candidates 0.486 * [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))) 0.486 * [simplify]: Sending expressions to egg_math: (expm1 (fma 1/2 (/ h0 h1) h1)) (log1p (fma 1/2 (/ h0 h1) h1)) (* 1/2 (/ h0 h1)) (log (fma 1/2 (/ h0 h1) h1)) (exp (fma 1/2 (/ h0 h1) h1)) (* (cbrt (fma 1/2 (/ h0 h1) h1)) (cbrt (fma 1/2 (/ h0 h1) h1))) (cbrt (fma 1/2 (/ h0 h1) h1)) (* (* (fma 1/2 (/ h0 h1) h1) (fma 1/2 (/ h0 h1) h1)) (fma 1/2 (/ h0 h1) h1)) (sqrt (fma 1/2 (/ h0 h1) h1)) (sqrt (fma 1/2 (/ h0 h1) h1)) (+ h1 (* 1/2 (/ h0 h1))) (+ h1 (* 1/2 (/ h0 h1))) (+ h1 (* 1/2 (/ h0 h1))) 0.489 * * [simplify]: iteration 0 : 21 enodes (cost 44 ) 0.490 * * [simplify]: iteration 1 : 48 enodes (cost 39 ) 0.492 * * [simplify]: iteration 2 : 156 enodes (cost 39 ) 0.496 * * [simplify]: iteration 3 : 585 enodes (cost 39 ) 0.511 * * [simplify]: iteration 4 : 2784 enodes (cost 39 ) 0.562 * * [simplify]: iteration 5 : 5001 enodes (cost 39 ) 0.563 * [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) 0.563 * * * [progress]: adding candidates to table 0.585 * [progress]: [Phase 3 of 3] Extracting. 0.586 * * [regime]: Finding splitpoints for: (# # # #) 0.586 * * * [regime-changes]: Trying 2 branch expressions: (y x) 0.586 * * * * [regimes]: Trying to branch on y from (# # # #) 0.623 * * * * [regimes]: Trying to branch on x from (# # # #) 0.650 * * * [regime]: Found split indices: #