0.851 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.262 * * * [progress]: [2/2] Setting up program. 0.264 * [progress]: [Phase 2 of 3] Improving. 0.267 * [simplify]: Simplifying using # : (/ (- (+ f n)) (- f n)) 0.270 * * [simplify]: iteration 0 : 13 enodes (cost 4 ) 0.272 * * [simplify]: iteration 1 : 16 enodes (cost 4 ) 0.273 * * [simplify]: iteration 2 : 20 enodes (cost 4 ) 0.274 * * [simplify]: iteration 3 : 26 enodes (cost 4 ) 0.275 * * [simplify]: iteration 4 : 31 enodes (cost 4 ) 0.277 * * [simplify]: iteration 5 : 33 enodes (cost 4 ) 0.278 * * [simplify]: iteration 6 : 33 enodes (cost 4 ) 0.279 * [simplify]: Simplified to: (/ (- (+ f n)) (- f n)) 0.280 * * [progress]: iteration 1 / 4 0.280 * * * [progress]: picking best candidate 0.281 * * * * [pick]: Picked # 0.282 * * * [progress]: localizing error 0.289 * * * [progress]: generating rewritten candidates 0.289 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.327 * * * [progress]: generating series expansions 0.327 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.341 * [approximate]: Taking taylor expansion of (* -1 (/ (+ n f) (- f n))) in (f n) around 0 0.342 * [taylor]: Taking taylor expansion of (* -1 (/ (+ n f) (- f n))) in n 0.342 * [taylor]: Taking taylor expansion of -1 in n 0.342 * [taylor]: Taking taylor expansion of (/ (+ n f) (- f n)) in n 0.342 * [taylor]: Taking taylor expansion of (+ n f) in n 0.342 * [taylor]: Taking taylor expansion of n in n 0.342 * [taylor]: Taking taylor expansion of f in n 0.342 * [taylor]: Taking taylor expansion of (- f n) in n 0.342 * [taylor]: Taking taylor expansion of f in n 0.342 * [taylor]: Taking taylor expansion of n in n 0.343 * [taylor]: Taking taylor expansion of (* -1 (/ (+ n f) (- f n))) in f 0.343 * [taylor]: Taking taylor expansion of -1 in f 0.343 * [taylor]: Taking taylor expansion of (/ (+ n f) (- f n)) in f 0.343 * [taylor]: Taking taylor expansion of (+ n f) in f 0.343 * [taylor]: Taking taylor expansion of n in f 0.343 * [taylor]: Taking taylor expansion of f in f 0.343 * [taylor]: Taking taylor expansion of (- f n) in f 0.343 * [taylor]: Taking taylor expansion of f in f 0.343 * [taylor]: Taking taylor expansion of n in f 0.343 * [taylor]: Taking taylor expansion of (* -1 (/ (+ n f) (- f n))) in f 0.343 * [taylor]: Taking taylor expansion of -1 in f 0.343 * [taylor]: Taking taylor expansion of (/ (+ n f) (- f n)) in f 0.343 * [taylor]: Taking taylor expansion of (+ n f) in f 0.343 * [taylor]: Taking taylor expansion of n in f 0.343 * [taylor]: Taking taylor expansion of f in f 0.343 * [taylor]: Taking taylor expansion of (- f n) in f 0.343 * [taylor]: Taking taylor expansion of f in f 0.343 * [taylor]: Taking taylor expansion of n in f 0.344 * [taylor]: Taking taylor expansion of 1 in n 0.346 * [taylor]: Taking taylor expansion of (* 2 (/ 1 n)) in n 0.346 * [taylor]: Taking taylor expansion of 2 in n 0.346 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.346 * [taylor]: Taking taylor expansion of n in n 0.349 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 2))) in n 0.349 * [taylor]: Taking taylor expansion of 2 in n 0.349 * [taylor]: Taking taylor expansion of (/ 1 (pow n 2)) in n 0.349 * [taylor]: Taking taylor expansion of (pow n 2) in n 0.349 * [taylor]: Taking taylor expansion of n in n 0.354 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 3))) in n 0.354 * [taylor]: Taking taylor expansion of 2 in n 0.354 * [taylor]: Taking taylor expansion of (/ 1 (pow n 3)) in n 0.354 * [taylor]: Taking taylor expansion of (pow n 3) in n 0.354 * [taylor]: Taking taylor expansion of n in n 0.360 * [approximate]: Taking taylor expansion of (* -1 (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n)))) in (f n) around 0 0.360 * [taylor]: Taking taylor expansion of (* -1 (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n)))) in n 0.360 * [taylor]: Taking taylor expansion of -1 in n 0.360 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n))) in n 0.360 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in n 0.360 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.360 * [taylor]: Taking taylor expansion of f in n 0.360 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.360 * [taylor]: Taking taylor expansion of n in n 0.361 * [taylor]: Taking taylor expansion of (- (/ 1 f) (/ 1 n)) in n 0.361 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.361 * [taylor]: Taking taylor expansion of f in n 0.361 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.361 * [taylor]: Taking taylor expansion of n in n 0.362 * [taylor]: Taking taylor expansion of (* -1 (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n)))) in f 0.362 * [taylor]: Taking taylor expansion of -1 in f 0.362 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n))) in f 0.362 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.362 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.362 * [taylor]: Taking taylor expansion of f in f 0.362 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.362 * [taylor]: Taking taylor expansion of n in f 0.362 * [taylor]: Taking taylor expansion of (- (/ 1 f) (/ 1 n)) in f 0.362 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.362 * [taylor]: Taking taylor expansion of f in f 0.362 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.363 * [taylor]: Taking taylor expansion of n in f 0.363 * [taylor]: Taking taylor expansion of (* -1 (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n)))) in f 0.363 * [taylor]: Taking taylor expansion of -1 in f 0.363 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n))) in f 0.363 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.363 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.363 * [taylor]: Taking taylor expansion of f in f 0.363 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.363 * [taylor]: Taking taylor expansion of n in f 0.364 * [taylor]: Taking taylor expansion of (- (/ 1 f) (/ 1 n)) in f 0.364 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.364 * [taylor]: Taking taylor expansion of f in f 0.364 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.364 * [taylor]: Taking taylor expansion of n in f 0.365 * [taylor]: Taking taylor expansion of -1 in n 0.366 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 n))) in n 0.366 * [taylor]: Taking taylor expansion of (* 2 (/ 1 n)) in n 0.366 * [taylor]: Taking taylor expansion of 2 in n 0.366 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.366 * [taylor]: Taking taylor expansion of n in n 0.370 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 2)))) in n 0.370 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 2))) in n 0.370 * [taylor]: Taking taylor expansion of 2 in n 0.370 * [taylor]: Taking taylor expansion of (/ 1 (pow n 2)) in n 0.370 * [taylor]: Taking taylor expansion of (pow n 2) in n 0.370 * [taylor]: Taking taylor expansion of n in n 0.377 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 3)))) in n 0.377 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 3))) in n 0.377 * [taylor]: Taking taylor expansion of 2 in n 0.377 * [taylor]: Taking taylor expansion of (/ 1 (pow n 3)) in n 0.377 * [taylor]: Taking taylor expansion of (pow n 3) in n 0.377 * [taylor]: Taking taylor expansion of n in n 0.382 * [approximate]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 n) (/ 1 f))) in (f n) around 0 0.382 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 n) (/ 1 f))) in n 0.382 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in n 0.382 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.382 * [taylor]: Taking taylor expansion of f in n 0.382 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.382 * [taylor]: Taking taylor expansion of n in n 0.382 * [taylor]: Taking taylor expansion of (- (/ 1 n) (/ 1 f)) in n 0.382 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.382 * [taylor]: Taking taylor expansion of n in n 0.383 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.383 * [taylor]: Taking taylor expansion of f in n 0.383 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 n) (/ 1 f))) in f 0.383 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.383 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.383 * [taylor]: Taking taylor expansion of f in f 0.384 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.384 * [taylor]: Taking taylor expansion of n in f 0.384 * [taylor]: Taking taylor expansion of (- (/ 1 n) (/ 1 f)) in f 0.384 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.384 * [taylor]: Taking taylor expansion of n in f 0.384 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.384 * [taylor]: Taking taylor expansion of f in f 0.385 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 n) (/ 1 f))) in f 0.385 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.385 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.385 * [taylor]: Taking taylor expansion of f in f 0.385 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.385 * [taylor]: Taking taylor expansion of n in f 0.385 * [taylor]: Taking taylor expansion of (- (/ 1 n) (/ 1 f)) in f 0.385 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.385 * [taylor]: Taking taylor expansion of n in f 0.385 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.385 * [taylor]: Taking taylor expansion of f in f 0.386 * [taylor]: Taking taylor expansion of -1 in n 0.387 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 n))) in n 0.387 * [taylor]: Taking taylor expansion of (* 2 (/ 1 n)) in n 0.387 * [taylor]: Taking taylor expansion of 2 in n 0.387 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.387 * [taylor]: Taking taylor expansion of n in n 0.391 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 2)))) in n 0.391 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 2))) in n 0.391 * [taylor]: Taking taylor expansion of 2 in n 0.391 * [taylor]: Taking taylor expansion of (/ 1 (pow n 2)) in n 0.391 * [taylor]: Taking taylor expansion of (pow n 2) in n 0.391 * [taylor]: Taking taylor expansion of n in n 0.397 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 3)))) in n 0.397 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 3))) in n 0.397 * [taylor]: Taking taylor expansion of 2 in n 0.397 * [taylor]: Taking taylor expansion of (/ 1 (pow n 3)) in n 0.397 * [taylor]: Taking taylor expansion of (pow n 3) in n 0.397 * [taylor]: Taking taylor expansion of n in n 0.402 * * * [progress]: simplifying candidates 0.404 * [simplify]: Simplifying using # : (expm1 (/ (- (+ f n)) (- f n))) (log1p (/ (- (+ f n)) (- f n))) (- (log (- (+ f n))) (log (- f n))) (log (/ (- (+ f n)) (- f n))) (exp (/ (- (+ f n)) (- f n))) (/ (* (* (- (+ f n)) (- (+ f n))) (- (+ f n))) (* (* (- f n) (- f n)) (- f n))) (* (cbrt (/ (- (+ f n)) (- f n))) (cbrt (/ (- (+ f n)) (- f n)))) (cbrt (/ (- (+ f n)) (- f n))) (* (* (/ (- (+ f n)) (- f n)) (/ (- (+ f n)) (- f n))) (/ (- (+ f n)) (- f n))) (sqrt (/ (- (+ f n)) (- f n))) (sqrt (/ (- (+ f n)) (- f n))) (- (- (+ f n))) (- (- f n)) (/ 0 (- f n)) (/ (+ f n) (- f n)) (/ (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (cbrt (- (+ f n))) (cbrt (- f n))) (/ (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) (sqrt (- f n))) (/ (cbrt (- (+ f n))) (sqrt (- f n))) (/ (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) 1) (/ (cbrt (- (+ f n))) (- f n)) (/ (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) (+ (sqrt f) (sqrt n))) (/ (cbrt (- (+ f n))) (- (sqrt f) (sqrt n))) (/ (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) 1) (/ (cbrt (- (+ f n))) (- f n)) (/ (sqrt (- (+ f n))) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (sqrt (- (+ f n))) (cbrt (- f n))) (/ (sqrt (- (+ f n))) (sqrt (- f n))) (/ (sqrt (- (+ f n))) (sqrt (- f n))) (/ (sqrt (- (+ f n))) 1) (/ (sqrt (- (+ f n))) (- f n)) (/ (sqrt (- (+ f n))) (+ (sqrt f) (sqrt n))) (/ (sqrt (- (+ f n))) (- (sqrt f) (sqrt n))) (/ (sqrt (- (+ f n))) 1) (/ (sqrt (- (+ f n))) (- f n)) (/ 1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (+ f n)) (cbrt (- f n))) (/ 1 (sqrt (- f n))) (/ (- (+ f n)) (sqrt (- f n))) (/ 1 1) (/ (- (+ f n)) (- f n)) (/ 1 (+ (sqrt f) (sqrt n))) (/ (- (+ f n)) (- (sqrt f) (sqrt n))) (/ 1 1) (/ (- (+ f n)) (- f n)) (/ -1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ (+ f n) (cbrt (- f n))) (/ -1 (sqrt (- f n))) (/ (+ f n) (sqrt (- f n))) (/ -1 1) (/ (+ f n) (- f n)) (/ -1 (+ (sqrt f) (sqrt n))) (/ (+ f n) (- (sqrt f) (sqrt n))) (/ -1 1) (/ (+ f n) (- f n)) (/ (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (cbrt (+ f n)) (cbrt (- f n))) (/ (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (sqrt (- f n))) (/ (cbrt (+ f n)) (sqrt (- f n))) (/ (- (* (cbrt (+ f n)) (cbrt (+ f n)))) 1) (/ (cbrt (+ f n)) (- f n)) (/ (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (+ (sqrt f) (sqrt n))) (/ (cbrt (+ f n)) (- (sqrt f) (sqrt n))) (/ (- (* (cbrt (+ f n)) (cbrt (+ f n)))) 1) (/ (cbrt (+ f n)) (- f n)) (/ (- (sqrt (+ f n))) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (sqrt (+ f n)) (cbrt (- f n))) (/ (- (sqrt (+ f n))) (sqrt (- f n))) (/ (sqrt (+ f n)) (sqrt (- f n))) (/ (- (sqrt (+ f n))) 1) (/ (sqrt (+ f n)) (- f n)) (/ (- (sqrt (+ f n))) (+ (sqrt f) (sqrt n))) (/ (sqrt (+ f n)) (- (sqrt f) (sqrt n))) (/ (- (sqrt (+ f n))) 1) (/ (sqrt (+ f n)) (- f n)) (/ (- 1) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (+ f n) (cbrt (- f n))) (/ (- 1) (sqrt (- f n))) (/ (+ f n) (sqrt (- f n))) (/ (- 1) 1) (/ (+ f n) (- f n)) (/ (- 1) (+ (sqrt f) (sqrt n))) (/ (+ f n) (- (sqrt f) (sqrt n))) (/ (- 1) 1) (/ (+ f n) (- f n)) (/ (- 1) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (+ f n) (cbrt (- f n))) (/ (- 1) (sqrt (- f n))) (/ (+ f n) (sqrt (- f n))) (/ (- 1) 1) (/ (+ f n) (- f n)) (/ (- 1) (+ (sqrt f) (sqrt n))) (/ (+ f n) (- (sqrt f) (sqrt n))) (/ (- 1) 1) (/ (+ f n) (- f n)) (/ (* (cbrt (+ f n)) (cbrt (+ f n))) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (cbrt (+ f n))) (cbrt (- f n))) (/ (* (cbrt (+ f n)) (cbrt (+ f n))) (sqrt (- f n))) (/ (- (cbrt (+ f n))) (sqrt (- f n))) (/ (* (cbrt (+ f n)) (cbrt (+ f n))) 1) (/ (- (cbrt (+ f n))) (- f n)) (/ (* (cbrt (+ f n)) (cbrt (+ f n))) (+ (sqrt f) (sqrt n))) (/ (- (cbrt (+ f n))) (- (sqrt f) (sqrt n))) (/ (* (cbrt (+ f n)) (cbrt (+ f n))) 1) (/ (- (cbrt (+ f n))) (- f n)) (/ (sqrt (+ f n)) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (sqrt (+ f n))) (cbrt (- f n))) (/ (sqrt (+ f n)) (sqrt (- f n))) (/ (- (sqrt (+ f n))) (sqrt (- f n))) (/ (sqrt (+ f n)) 1) (/ (- (sqrt (+ f n))) (- f n)) (/ (sqrt (+ f n)) (+ (sqrt f) (sqrt n))) (/ (- (sqrt (+ f n))) (- (sqrt f) (sqrt n))) (/ (sqrt (+ f n)) 1) (/ (- (sqrt (+ f n))) (- f n)) (/ 1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (+ f n)) (cbrt (- f n))) (/ 1 (sqrt (- f n))) (/ (- (+ f n)) (sqrt (- f n))) (/ 1 1) (/ (- (+ f n)) (- f n)) (/ 1 (+ (sqrt f) (sqrt n))) (/ (- (+ f n)) (- (sqrt f) (sqrt n))) (/ 1 1) (/ (- (+ f n)) (- f n)) (/ 1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (+ f n)) (cbrt (- f n))) (/ 1 (sqrt (- f n))) (/ (- (+ f n)) (sqrt (- f n))) (/ 1 1) (/ (- (+ f n)) (- f n)) (/ 1 (+ (sqrt f) (sqrt n))) (/ (- (+ f n)) (- (sqrt f) (sqrt n))) (/ 1 1) (/ (- (+ f n)) (- f n)) (/ 1 (- f n)) (/ (- f n) (- (+ f n))) (/ (+ f n) (- f n)) (/ (- (+ f n)) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (+ f n)) (sqrt (- f n))) (/ (- (+ f n)) 1) (/ (- (+ f n)) (+ (sqrt f) (sqrt n))) (/ (- (+ f n)) 1) (/ (- f n) (cbrt (- (+ f n)))) (/ (- f n) (sqrt (- (+ f n)))) (/ (- f n) (- (+ f n))) (/ (- f n) (+ f n)) (/ (- f n) (cbrt (+ f n))) (/ (- f n) (sqrt (+ f n))) (/ (- f n) (+ f n)) (/ (- f n) (+ f n)) (/ (- f n) (- (cbrt (+ f n)))) (/ (- f n) (- (sqrt (+ f n)))) (/ (- f n) (- (+ f n))) (/ (- f n) (- (+ f n))) (/ (- (+ f n)) (- (pow f 3) (pow n 3))) (/ (- (+ f n)) (- (* f f) (* n n))) (* (- f n) (+ (* f f) (- (* n n) (* f n)))) (* (- f n) (- f n)) 1 -1 -1 0.409 * * [simplify]: iteration 0 : 293 enodes (cost 774 ) 0.413 * * [simplify]: iteration 1 : 927 enodes (cost 758 ) 0.427 * * [simplify]: iteration 2 : 3021 enodes (cost 743 ) 0.465 * * [simplify]: iteration 3 : 5001 enodes (cost 743 ) 0.468 * [simplify]: Simplified to: (expm1 (/ (- (+ f n)) (- f n))) (log1p (/ (- (+ f n)) (- f n))) (log (/ (- (+ f n)) (- f n))) (log (/ (- (+ f n)) (- f n))) (exp (/ (- (+ f n)) (- f n))) (pow (/ (- (+ f n)) (- f n)) 3) (* (cbrt (/ (- (+ f n)) (- f n))) (cbrt (/ (- (+ f n)) (- f n)))) (cbrt (/ (- (+ f n)) (- f n))) (pow (/ (- (+ f n)) (- f n)) 3) (sqrt (/ (- (+ f n)) (- f n))) (sqrt (/ (- (+ f n)) (- f n))) (+ f n) (- n f) 0 (/ (+ f n) (- f n)) (/ (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (cbrt (- (+ f n))) (cbrt (- f n))) (/ (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) (sqrt (- f n))) (/ (cbrt (- (+ f n))) (sqrt (- f n))) (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) (/ (cbrt (- (+ f n))) (- f n)) (/ (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) (+ (sqrt f) (sqrt n))) (/ (cbrt (- (+ f n))) (- (sqrt f) (sqrt n))) (* (cbrt (- (+ f n))) (cbrt (- (+ f n)))) (/ (cbrt (- (+ f n))) (- f n)) (/ (sqrt (- (+ f n))) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (sqrt (- (+ f n))) (cbrt (- f n))) (/ (sqrt (- (+ f n))) (sqrt (- f n))) (/ (sqrt (- (+ f n))) (sqrt (- f n))) (sqrt (- (+ f n))) (/ (sqrt (- (+ f n))) (- f n)) (/ (sqrt (- (+ f n))) (+ (sqrt f) (sqrt n))) (/ (sqrt (- (+ f n))) (- (sqrt f) (sqrt n))) (sqrt (- (+ f n))) (/ (sqrt (- (+ f n))) (- f n)) (/ 1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (+ f n)) (cbrt (- f n))) (/ 1 (sqrt (- f n))) (/ (- (+ f n)) (sqrt (- f n))) 1 (/ (- (+ f n)) (- f n)) (/ 1 (+ (sqrt f) (sqrt n))) (/ (- (+ f n)) (- (sqrt f) (sqrt n))) 1 (/ (- (+ f n)) (- f n)) (/ -1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ (+ f n) (cbrt (- f n))) (/ -1 (sqrt (- f n))) (/ (+ f n) (sqrt (- f n))) -1 (/ (+ f n) (- f n)) (/ -1 (+ (sqrt f) (sqrt n))) (/ (+ f n) (- (sqrt f) (sqrt n))) -1 (/ (+ f n) (- f n)) (/ (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (cbrt (+ f n)) (cbrt (- f n))) (/ (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (sqrt (- f n))) (/ (cbrt (+ f n)) (sqrt (- f n))) (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (/ (cbrt (+ f n)) (- f n)) (/ (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (+ (sqrt f) (sqrt n))) (/ (cbrt (+ f n)) (- (sqrt f) (sqrt n))) (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (/ (cbrt (+ f n)) (- f n)) (/ (- (sqrt (+ f n))) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (sqrt (+ f n)) (cbrt (- f n))) (/ (- (sqrt (+ f n))) (sqrt (- f n))) (/ (sqrt (+ f n)) (sqrt (- f n))) (- (sqrt (+ f n))) (/ (sqrt (+ f n)) (- f n)) (/ (- (sqrt (+ f n))) (+ (sqrt f) (sqrt n))) (/ (sqrt (+ f n)) (- (sqrt f) (sqrt n))) (- (sqrt (+ f n))) (/ (sqrt (+ f n)) (- f n)) (/ -1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ (+ f n) (cbrt (- f n))) (/ -1 (sqrt (- f n))) (/ (+ f n) (sqrt (- f n))) -1 (/ (+ f n) (- f n)) (/ -1 (+ (sqrt f) (sqrt n))) (/ (+ f n) (- (sqrt f) (sqrt n))) -1 (/ (+ f n) (- f n)) (/ -1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ (+ f n) (cbrt (- f n))) (/ -1 (sqrt (- f n))) (/ (+ f n) (sqrt (- f n))) -1 (/ (+ f n) (- f n)) (/ -1 (+ (sqrt f) (sqrt n))) (/ (+ f n) (- (sqrt f) (sqrt n))) -1 (/ (+ f n) (- f n)) (/ (* (cbrt (+ f n)) (cbrt (+ f n))) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (cbrt (+ f n))) (cbrt (- f n))) (/ (* (cbrt (+ f n)) (cbrt (+ f n))) (sqrt (- f n))) (/ (- (cbrt (+ f n))) (sqrt (- f n))) (* (cbrt (+ f n)) (cbrt (+ f n))) (/ (- (cbrt (+ f n))) (- f n)) (/ (* (cbrt (+ f n)) (cbrt (+ f n))) (+ (sqrt f) (sqrt n))) (/ (- (cbrt (+ f n))) (- (sqrt f) (sqrt n))) (* (cbrt (+ f n)) (cbrt (+ f n))) (/ (- (cbrt (+ f n))) (- f n)) (/ (sqrt (+ f n)) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (sqrt (+ f n))) (cbrt (- f n))) (/ (sqrt (+ f n)) (sqrt (- f n))) (/ (- (sqrt (+ f n))) (sqrt (- f n))) (sqrt (+ f n)) (/ (- (sqrt (+ f n))) (- f n)) (/ (sqrt (+ f n)) (+ (sqrt f) (sqrt n))) (/ (- (sqrt (+ f n))) (- (sqrt f) (sqrt n))) (sqrt (+ f n)) (/ (- (sqrt (+ f n))) (- f n)) (/ 1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (+ f n)) (cbrt (- f n))) (/ 1 (sqrt (- f n))) (/ (- (+ f n)) (sqrt (- f n))) 1 (/ (- (+ f n)) (- f n)) (/ 1 (+ (sqrt f) (sqrt n))) (/ (- (+ f n)) (- (sqrt f) (sqrt n))) 1 (/ (- (+ f n)) (- f n)) (/ 1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (+ f n)) (cbrt (- f n))) (/ 1 (sqrt (- f n))) (/ (- (+ f n)) (sqrt (- f n))) 1 (/ (- (+ f n)) (- f n)) (/ 1 (+ (sqrt f) (sqrt n))) (/ (- (+ f n)) (- (sqrt f) (sqrt n))) 1 (/ (- (+ f n)) (- f n)) (/ 1 (- f n)) (/ (- f n) (- (+ f n))) (/ (+ f n) (- f n)) (/ (- (+ f n)) (* (cbrt (- f n)) (cbrt (- f n)))) (/ (- (+ f n)) (sqrt (- f n))) (- (+ f n)) (/ (- (+ f n)) (+ (sqrt f) (sqrt n))) (- (+ f n)) (/ (- f n) (cbrt (- (+ f n)))) (/ (- f n) (sqrt (- (+ f n)))) (/ (- f n) (- (+ f n))) (/ (- f n) (+ f n)) (/ (- f n) (cbrt (+ f n))) (/ (- f n) (sqrt (+ f n))) (/ (- f n) (+ f n)) (/ (- f n) (+ f n)) (/ (- f n) (- (cbrt (+ f n)))) (/ (- f n) (- (sqrt (+ f n)))) (/ (- f n) (- (+ f n))) (/ (- f n) (- (+ f n))) (/ (- (+ f n)) (- (pow f 3) (pow n 3))) (/ -1 (- f n)) (* (fma f f (- (* n n) (* f n))) (- f n)) (* (- f n) (- f n)) 1 -1 -1 0.469 * * * [progress]: adding candidates to table 0.612 * * [progress]: iteration 2 / 4 0.612 * * * [progress]: picking best candidate 0.613 * * * * [pick]: Picked # 0.613 * * * [progress]: localizing error 0.620 * * * [progress]: generating rewritten candidates 0.620 * * * * [progress]: [ 1 / 2 ] rewriting at (2 2) 0.644 * * * * [progress]: [ 2 / 2 ] rewriting at (2) 0.699 * * * [progress]: generating series expansions 0.699 * * * * [progress]: [ 1 / 2 ] generating series at (2 2) 0.699 * [approximate]: Taking taylor expansion of (/ (- f n) (+ n f)) in (f n) around 0 0.699 * [taylor]: Taking taylor expansion of (/ (- f n) (+ n f)) in n 0.699 * [taylor]: Taking taylor expansion of (- f n) in n 0.699 * [taylor]: Taking taylor expansion of f in n 0.699 * [taylor]: Taking taylor expansion of n in n 0.699 * [taylor]: Taking taylor expansion of (+ n f) in n 0.699 * [taylor]: Taking taylor expansion of n in n 0.699 * [taylor]: Taking taylor expansion of f in n 0.700 * [taylor]: Taking taylor expansion of (/ (- f n) (+ n f)) in f 0.700 * [taylor]: Taking taylor expansion of (- f n) in f 0.700 * [taylor]: Taking taylor expansion of f in f 0.700 * [taylor]: Taking taylor expansion of n in f 0.700 * [taylor]: Taking taylor expansion of (+ n f) in f 0.700 * [taylor]: Taking taylor expansion of n in f 0.700 * [taylor]: Taking taylor expansion of f in f 0.700 * [taylor]: Taking taylor expansion of (/ (- f n) (+ n f)) in f 0.700 * [taylor]: Taking taylor expansion of (- f n) in f 0.700 * [taylor]: Taking taylor expansion of f in f 0.700 * [taylor]: Taking taylor expansion of n in f 0.700 * [taylor]: Taking taylor expansion of (+ n f) in f 0.700 * [taylor]: Taking taylor expansion of n in f 0.700 * [taylor]: Taking taylor expansion of f in f 0.700 * [taylor]: Taking taylor expansion of -1 in n 0.701 * [taylor]: Taking taylor expansion of (* 2 (/ 1 n)) in n 0.701 * [taylor]: Taking taylor expansion of 2 in n 0.701 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.701 * [taylor]: Taking taylor expansion of n in n 0.703 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 2)))) in n 0.703 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 2))) in n 0.703 * [taylor]: Taking taylor expansion of 2 in n 0.703 * [taylor]: Taking taylor expansion of (/ 1 (pow n 2)) in n 0.703 * [taylor]: Taking taylor expansion of (pow n 2) in n 0.703 * [taylor]: Taking taylor expansion of n in n 0.708 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 3))) in n 0.708 * [taylor]: Taking taylor expansion of 2 in n 0.708 * [taylor]: Taking taylor expansion of (/ 1 (pow n 3)) in n 0.708 * [taylor]: Taking taylor expansion of (pow n 3) in n 0.708 * [taylor]: Taking taylor expansion of n in n 0.713 * [approximate]: Taking taylor expansion of (/ (- (/ 1 f) (/ 1 n)) (+ (/ 1 f) (/ 1 n))) in (f n) around 0 0.713 * [taylor]: Taking taylor expansion of (/ (- (/ 1 f) (/ 1 n)) (+ (/ 1 f) (/ 1 n))) in n 0.713 * [taylor]: Taking taylor expansion of (- (/ 1 f) (/ 1 n)) in n 0.713 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.713 * [taylor]: Taking taylor expansion of f in n 0.713 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.713 * [taylor]: Taking taylor expansion of n in n 0.713 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in n 0.713 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.713 * [taylor]: Taking taylor expansion of f in n 0.713 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.713 * [taylor]: Taking taylor expansion of n in n 0.714 * [taylor]: Taking taylor expansion of (/ (- (/ 1 f) (/ 1 n)) (+ (/ 1 f) (/ 1 n))) in f 0.714 * [taylor]: Taking taylor expansion of (- (/ 1 f) (/ 1 n)) in f 0.714 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.714 * [taylor]: Taking taylor expansion of f in f 0.715 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.715 * [taylor]: Taking taylor expansion of n in f 0.715 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.715 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.715 * [taylor]: Taking taylor expansion of f in f 0.715 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.715 * [taylor]: Taking taylor expansion of n in f 0.716 * [taylor]: Taking taylor expansion of (/ (- (/ 1 f) (/ 1 n)) (+ (/ 1 f) (/ 1 n))) in f 0.716 * [taylor]: Taking taylor expansion of (- (/ 1 f) (/ 1 n)) in f 0.716 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.716 * [taylor]: Taking taylor expansion of f in f 0.716 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.716 * [taylor]: Taking taylor expansion of n in f 0.716 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.716 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.716 * [taylor]: Taking taylor expansion of f in f 0.717 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.717 * [taylor]: Taking taylor expansion of n in f 0.717 * [taylor]: Taking taylor expansion of 1 in n 0.718 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 n))) in n 0.718 * [taylor]: Taking taylor expansion of (* 2 (/ 1 n)) in n 0.718 * [taylor]: Taking taylor expansion of 2 in n 0.718 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.718 * [taylor]: Taking taylor expansion of n in n 0.722 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 2))) in n 0.722 * [taylor]: Taking taylor expansion of 2 in n 0.722 * [taylor]: Taking taylor expansion of (/ 1 (pow n 2)) in n 0.722 * [taylor]: Taking taylor expansion of (pow n 2) in n 0.722 * [taylor]: Taking taylor expansion of n in n 0.728 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 3)))) in n 0.728 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 3))) in n 0.728 * [taylor]: Taking taylor expansion of 2 in n 0.728 * [taylor]: Taking taylor expansion of (/ 1 (pow n 3)) in n 0.728 * [taylor]: Taking taylor expansion of (pow n 3) in n 0.728 * [taylor]: Taking taylor expansion of n in n 0.733 * [approximate]: Taking taylor expansion of (* -1 (/ (- (/ 1 n) (/ 1 f)) (+ (/ 1 f) (/ 1 n)))) in (f n) around 0 0.733 * [taylor]: Taking taylor expansion of (* -1 (/ (- (/ 1 n) (/ 1 f)) (+ (/ 1 f) (/ 1 n)))) in n 0.733 * [taylor]: Taking taylor expansion of -1 in n 0.733 * [taylor]: Taking taylor expansion of (/ (- (/ 1 n) (/ 1 f)) (+ (/ 1 f) (/ 1 n))) in n 0.733 * [taylor]: Taking taylor expansion of (- (/ 1 n) (/ 1 f)) in n 0.733 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.733 * [taylor]: Taking taylor expansion of n in n 0.733 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.733 * [taylor]: Taking taylor expansion of f in n 0.733 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in n 0.733 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.733 * [taylor]: Taking taylor expansion of f in n 0.733 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.734 * [taylor]: Taking taylor expansion of n in n 0.734 * [taylor]: Taking taylor expansion of (* -1 (/ (- (/ 1 n) (/ 1 f)) (+ (/ 1 f) (/ 1 n)))) in f 0.734 * [taylor]: Taking taylor expansion of -1 in f 0.734 * [taylor]: Taking taylor expansion of (/ (- (/ 1 n) (/ 1 f)) (+ (/ 1 f) (/ 1 n))) in f 0.734 * [taylor]: Taking taylor expansion of (- (/ 1 n) (/ 1 f)) in f 0.734 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.734 * [taylor]: Taking taylor expansion of n in f 0.734 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.734 * [taylor]: Taking taylor expansion of f in f 0.735 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.735 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.735 * [taylor]: Taking taylor expansion of f in f 0.735 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.735 * [taylor]: Taking taylor expansion of n in f 0.736 * [taylor]: Taking taylor expansion of (* -1 (/ (- (/ 1 n) (/ 1 f)) (+ (/ 1 f) (/ 1 n)))) in f 0.736 * [taylor]: Taking taylor expansion of -1 in f 0.736 * [taylor]: Taking taylor expansion of (/ (- (/ 1 n) (/ 1 f)) (+ (/ 1 f) (/ 1 n))) in f 0.736 * [taylor]: Taking taylor expansion of (- (/ 1 n) (/ 1 f)) in f 0.736 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.736 * [taylor]: Taking taylor expansion of n in f 0.736 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.736 * [taylor]: Taking taylor expansion of f in f 0.736 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.736 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.736 * [taylor]: Taking taylor expansion of f in f 0.736 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.736 * [taylor]: Taking taylor expansion of n in f 0.738 * [taylor]: Taking taylor expansion of 1 in n 0.739 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 n))) in n 0.739 * [taylor]: Taking taylor expansion of (* 2 (/ 1 n)) in n 0.739 * [taylor]: Taking taylor expansion of 2 in n 0.739 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.739 * [taylor]: Taking taylor expansion of n in n 0.743 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 2))) in n 0.743 * [taylor]: Taking taylor expansion of 2 in n 0.743 * [taylor]: Taking taylor expansion of (/ 1 (pow n 2)) in n 0.743 * [taylor]: Taking taylor expansion of (pow n 2) in n 0.743 * [taylor]: Taking taylor expansion of n in n 0.749 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 3)))) in n 0.749 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 3))) in n 0.750 * [taylor]: Taking taylor expansion of 2 in n 0.750 * [taylor]: Taking taylor expansion of (/ 1 (pow n 3)) in n 0.750 * [taylor]: Taking taylor expansion of (pow n 3) in n 0.750 * [taylor]: Taking taylor expansion of n in n 0.755 * * * * [progress]: [ 2 / 2 ] generating series at (2) 0.755 * [approximate]: Taking taylor expansion of (* -1 (/ (+ n f) (- f n))) in (f n) around 0 0.755 * [taylor]: Taking taylor expansion of (* -1 (/ (+ n f) (- f n))) in n 0.755 * [taylor]: Taking taylor expansion of -1 in n 0.755 * [taylor]: Taking taylor expansion of (/ (+ n f) (- f n)) in n 0.755 * [taylor]: Taking taylor expansion of (+ n f) in n 0.755 * [taylor]: Taking taylor expansion of n in n 0.755 * [taylor]: Taking taylor expansion of f in n 0.755 * [taylor]: Taking taylor expansion of (- f n) in n 0.755 * [taylor]: Taking taylor expansion of f in n 0.755 * [taylor]: Taking taylor expansion of n in n 0.755 * [taylor]: Taking taylor expansion of (* -1 (/ (+ n f) (- f n))) in f 0.755 * [taylor]: Taking taylor expansion of -1 in f 0.755 * [taylor]: Taking taylor expansion of (/ (+ n f) (- f n)) in f 0.755 * [taylor]: Taking taylor expansion of (+ n f) in f 0.756 * [taylor]: Taking taylor expansion of n in f 0.756 * [taylor]: Taking taylor expansion of f in f 0.756 * [taylor]: Taking taylor expansion of (- f n) in f 0.756 * [taylor]: Taking taylor expansion of f in f 0.756 * [taylor]: Taking taylor expansion of n in f 0.756 * [taylor]: Taking taylor expansion of (* -1 (/ (+ n f) (- f n))) in f 0.756 * [taylor]: Taking taylor expansion of -1 in f 0.756 * [taylor]: Taking taylor expansion of (/ (+ n f) (- f n)) in f 0.756 * [taylor]: Taking taylor expansion of (+ n f) in f 0.756 * [taylor]: Taking taylor expansion of n in f 0.756 * [taylor]: Taking taylor expansion of f in f 0.756 * [taylor]: Taking taylor expansion of (- f n) in f 0.756 * [taylor]: Taking taylor expansion of f in f 0.756 * [taylor]: Taking taylor expansion of n in f 0.756 * [taylor]: Taking taylor expansion of 1 in n 0.757 * [taylor]: Taking taylor expansion of (* 2 (/ 1 n)) in n 0.757 * [taylor]: Taking taylor expansion of 2 in n 0.757 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.757 * [taylor]: Taking taylor expansion of n in n 0.759 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 2))) in n 0.759 * [taylor]: Taking taylor expansion of 2 in n 0.759 * [taylor]: Taking taylor expansion of (/ 1 (pow n 2)) in n 0.759 * [taylor]: Taking taylor expansion of (pow n 2) in n 0.759 * [taylor]: Taking taylor expansion of n in n 0.764 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 3))) in n 0.765 * [taylor]: Taking taylor expansion of 2 in n 0.765 * [taylor]: Taking taylor expansion of (/ 1 (pow n 3)) in n 0.765 * [taylor]: Taking taylor expansion of (pow n 3) in n 0.765 * [taylor]: Taking taylor expansion of n in n 0.770 * [approximate]: Taking taylor expansion of (* -1 (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n)))) in (f n) around 0 0.770 * [taylor]: Taking taylor expansion of (* -1 (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n)))) in n 0.770 * [taylor]: Taking taylor expansion of -1 in n 0.770 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n))) in n 0.770 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in n 0.770 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.770 * [taylor]: Taking taylor expansion of f in n 0.770 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.770 * [taylor]: Taking taylor expansion of n in n 0.770 * [taylor]: Taking taylor expansion of (- (/ 1 f) (/ 1 n)) in n 0.770 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.771 * [taylor]: Taking taylor expansion of f in n 0.771 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.771 * [taylor]: Taking taylor expansion of n in n 0.772 * [taylor]: Taking taylor expansion of (* -1 (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n)))) in f 0.774 * [taylor]: Taking taylor expansion of -1 in f 0.774 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n))) in f 0.774 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.774 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.774 * [taylor]: Taking taylor expansion of f in f 0.775 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.775 * [taylor]: Taking taylor expansion of n in f 0.775 * [taylor]: Taking taylor expansion of (- (/ 1 f) (/ 1 n)) in f 0.775 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.775 * [taylor]: Taking taylor expansion of f in f 0.775 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.775 * [taylor]: Taking taylor expansion of n in f 0.776 * [taylor]: Taking taylor expansion of (* -1 (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n)))) in f 0.776 * [taylor]: Taking taylor expansion of -1 in f 0.776 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 f) (/ 1 n))) in f 0.776 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.776 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.776 * [taylor]: Taking taylor expansion of f in f 0.776 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.776 * [taylor]: Taking taylor expansion of n in f 0.776 * [taylor]: Taking taylor expansion of (- (/ 1 f) (/ 1 n)) in f 0.776 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.776 * [taylor]: Taking taylor expansion of f in f 0.776 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.776 * [taylor]: Taking taylor expansion of n in f 0.777 * [taylor]: Taking taylor expansion of -1 in n 0.779 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 n))) in n 0.779 * [taylor]: Taking taylor expansion of (* 2 (/ 1 n)) in n 0.779 * [taylor]: Taking taylor expansion of 2 in n 0.779 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.779 * [taylor]: Taking taylor expansion of n in n 0.782 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 2)))) in n 0.782 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 2))) in n 0.782 * [taylor]: Taking taylor expansion of 2 in n 0.782 * [taylor]: Taking taylor expansion of (/ 1 (pow n 2)) in n 0.782 * [taylor]: Taking taylor expansion of (pow n 2) in n 0.782 * [taylor]: Taking taylor expansion of n in n 0.789 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 3)))) in n 0.789 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 3))) in n 0.789 * [taylor]: Taking taylor expansion of 2 in n 0.789 * [taylor]: Taking taylor expansion of (/ 1 (pow n 3)) in n 0.789 * [taylor]: Taking taylor expansion of (pow n 3) in n 0.789 * [taylor]: Taking taylor expansion of n in n 0.795 * [approximate]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 n) (/ 1 f))) in (f n) around 0 0.795 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 n) (/ 1 f))) in n 0.795 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in n 0.795 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.795 * [taylor]: Taking taylor expansion of f in n 0.795 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.795 * [taylor]: Taking taylor expansion of n in n 0.795 * [taylor]: Taking taylor expansion of (- (/ 1 n) (/ 1 f)) in n 0.795 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.795 * [taylor]: Taking taylor expansion of n in n 0.796 * [taylor]: Taking taylor expansion of (/ 1 f) in n 0.796 * [taylor]: Taking taylor expansion of f in n 0.796 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 n) (/ 1 f))) in f 0.796 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.796 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.796 * [taylor]: Taking taylor expansion of f in f 0.797 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.797 * [taylor]: Taking taylor expansion of n in f 0.797 * [taylor]: Taking taylor expansion of (- (/ 1 n) (/ 1 f)) in f 0.797 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.797 * [taylor]: Taking taylor expansion of n in f 0.797 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.797 * [taylor]: Taking taylor expansion of f in f 0.798 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 f) (/ 1 n)) (- (/ 1 n) (/ 1 f))) in f 0.798 * [taylor]: Taking taylor expansion of (+ (/ 1 f) (/ 1 n)) in f 0.798 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.798 * [taylor]: Taking taylor expansion of f in f 0.798 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.798 * [taylor]: Taking taylor expansion of n in f 0.798 * [taylor]: Taking taylor expansion of (- (/ 1 n) (/ 1 f)) in f 0.798 * [taylor]: Taking taylor expansion of (/ 1 n) in f 0.798 * [taylor]: Taking taylor expansion of n in f 0.798 * [taylor]: Taking taylor expansion of (/ 1 f) in f 0.798 * [taylor]: Taking taylor expansion of f in f 0.799 * [taylor]: Taking taylor expansion of -1 in n 0.800 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 n))) in n 0.800 * [taylor]: Taking taylor expansion of (* 2 (/ 1 n)) in n 0.800 * [taylor]: Taking taylor expansion of 2 in n 0.801 * [taylor]: Taking taylor expansion of (/ 1 n) in n 0.801 * [taylor]: Taking taylor expansion of n in n 0.804 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 2)))) in n 0.804 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 2))) in n 0.804 * [taylor]: Taking taylor expansion of 2 in n 0.804 * [taylor]: Taking taylor expansion of (/ 1 (pow n 2)) in n 0.804 * [taylor]: Taking taylor expansion of (pow n 2) in n 0.804 * [taylor]: Taking taylor expansion of n in n 0.811 * [taylor]: Taking taylor expansion of (- (* 2 (/ 1 (pow n 3)))) in n 0.811 * [taylor]: Taking taylor expansion of (* 2 (/ 1 (pow n 3))) in n 0.811 * [taylor]: Taking taylor expansion of 2 in n 0.811 * [taylor]: Taking taylor expansion of (/ 1 (pow n 3)) in n 0.811 * [taylor]: Taking taylor expansion of (pow n 3) in n 0.811 * [taylor]: Taking taylor expansion of n in n 0.816 * * * [progress]: simplifying candidates 0.822 * [simplify]: Simplifying using # : (expm1 (/ (- f n) (+ f n))) (log1p (/ (- f n) (+ f n))) (- (log (- f n)) (log (+ f n))) (log (/ (- f n) (+ f n))) (exp (/ (- f n) (+ f n))) (/ (* (* (- f n) (- f n)) (- f n)) (* (* (+ f n) (+ f n)) (+ f n))) (* (cbrt (/ (- f n) (+ f n))) (cbrt (/ (- f n) (+ f n)))) (cbrt (/ (- f n) (+ f n))) (* (* (/ (- f n) (+ f n)) (/ (- f n) (+ f n))) (/ (- f n) (+ f n))) (sqrt (/ (- f n) (+ f n))) (sqrt (/ (- f n) (+ f n))) (- (- f n)) (- (+ f n)) (/ f (+ f n)) (/ n (+ f n)) (/ (* (cbrt (- f n)) (cbrt (- f n))) (* (cbrt (+ f n)) (cbrt (+ f n)))) (/ (cbrt (- f n)) (cbrt (+ f n))) (/ (* (cbrt (- f n)) (cbrt (- f n))) (sqrt (+ f n))) (/ (cbrt (- f n)) (sqrt (+ f n))) (/ (* (cbrt (- f n)) (cbrt (- f n))) 1) (/ (cbrt (- f n)) (+ f n)) (/ (* (cbrt (- f n)) (cbrt (- f n))) 1) (/ (cbrt (- f n)) (+ f n)) (/ (sqrt (- f n)) (* (cbrt (+ f n)) (cbrt (+ f n)))) (/ (sqrt (- f n)) (cbrt (+ f n))) (/ (sqrt (- f n)) (sqrt (+ f n))) (/ (sqrt (- f n)) (sqrt (+ f n))) (/ (sqrt (- f n)) 1) (/ (sqrt (- f n)) (+ f n)) (/ (sqrt (- f n)) 1) (/ (sqrt (- f n)) (+ f n)) (/ 1 (* (cbrt (+ f n)) (cbrt (+ f n)))) (/ (- f n) (cbrt (+ f n))) (/ 1 (sqrt (+ f n))) (/ (- f n) (sqrt (+ f n))) (/ 1 1) (/ (- f n) (+ f n)) (/ 1 1) (/ (- f n) (+ f n)) (/ (+ (sqrt f) (sqrt n)) (* (cbrt (+ f n)) (cbrt (+ f n)))) (/ (- (sqrt f) (sqrt n)) (cbrt (+ f n))) (/ (+ (sqrt f) (sqrt n)) (sqrt (+ f n))) (/ (- (sqrt f) (sqrt n)) (sqrt (+ f n))) (/ (+ (sqrt f) (sqrt n)) 1) (/ (- (sqrt f) (sqrt n)) (+ f n)) (/ (+ (sqrt f) (sqrt n)) 1) (/ (- (sqrt f) (sqrt n)) (+ f n)) (/ 1 (* (cbrt (+ f n)) (cbrt (+ f n)))) (/ (- f n) (cbrt (+ f n))) (/ 1 (sqrt (+ f n))) (/ (- f n) (sqrt (+ f n))) (/ 1 1) (/ (- f n) (+ f n)) (/ 1 1) (/ (- f n) (+ f n)) (/ 1 (+ f n)) (/ (+ f n) (- f n)) (/ (- f n) (* (cbrt (+ f n)) (cbrt (+ f n)))) (/ (- f n) (sqrt (+ f n))) (/ (- f n) 1) (/ (- f n) 1) 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(+ f n)))) (/ -1 (/ (* (cbrt (- f n)) (cbrt (- f n))) (* (cbrt (+ f n)) (cbrt (+ f n))))) (/ -1 (/ (* (cbrt (- f n)) (cbrt (- f n))) (sqrt (+ f n)))) (/ -1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ -1 (* (cbrt (- f n)) (cbrt (- f n)))) (/ -1 (/ (sqrt (- f n)) (* (cbrt (+ f n)) (cbrt (+ f n))))) (/ -1 (/ (sqrt (- f n)) (sqrt (+ f n)))) (/ -1 (sqrt (- f n))) (/ -1 (sqrt (- f n))) (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (- (sqrt (+ f n))) -1 -1 (/ -1 (/ (+ (sqrt f) (sqrt n)) (* (cbrt (+ f n)) (cbrt (+ f n))))) (/ -1 (/ (+ (sqrt f) (sqrt n)) (sqrt (+ f n)))) (/ -1 (+ (sqrt f) (sqrt n))) (/ -1 (+ (sqrt f) (sqrt n))) (- (* (cbrt (+ f n)) (cbrt (+ f n)))) (- (sqrt (+ f n))) -1 -1 -1 (/ -1 (- f n)) (/ -1 (/ (- f n) (+ (pow f 3) (pow n 3)))) (/ -1 (/ (- f n) (- (* f f) (* n n)))) (/ (/ (- f n) (+ f n)) (cbrt (- 1))) (/ (/ (- f n) (+ f n)) (sqrt (- 1))) (/ (/ (- f n) -1) (+ f n)) (/ (- f n) (+ f n)) (/ (/ (- f n) (+ f n)) (cbrt 1)) (/ (- f n) (+ f n)) (/ (- f n) (+ f n)) (/ (/ (- f n) (+ f n)) (- (cbrt 1))) (/ (/ (- f n) -1) (+ f n)) (/ (/ (- f n) -1) (+ f n)) (/ -1 (- f n)) -1 1 1 1 -1 -1 0.878 * * * [progress]: adding candidates to table 1.310 * [progress]: [Phase 3 of 3] Extracting. 1.310 * * [regime]: Finding splitpoints for: (# #) 1.311 * * * [regime-changes]: Trying 3 branch expressions: ((/ (- (+ f n)) (- f n)) n f) 1.312 * * * * [regimes]: Trying to branch on (/ (- (+ f n)) (- f n)) from (# #) 1.322 * * * * [regimes]: Trying to branch on n from (# #) 1.335 * * * * [regimes]: Trying to branch on f from (# #) 1.345 * * * [regime]: Found split indices: #