Details

sample94.0ms

Algorithm

intervals

Results

22.0ms	253×	body	80	nan
21.0ms	42×	body	1280	valid
20.0ms	56×	body	640	valid
13.0ms	131×	body	80	valid
6.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify19.0ms

Calls

1 calls:

Slowest

19.0ms

(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize53.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b	(/ 1 (sqrt x))
0.2b	(/ 1 (sqrt (+ x 1)))
0.0b	(sqrt (+ x 1))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

1063×	`times-frac`
1001×	`*-un-lft-identity`
863×	`add-sqr-sqrt`
789×	`add-cube-cbrt`
667×	`sqrt-prod`
594×	`prod-diff`
175×	`associate-/r*`
156×	`frac-sub`
86×	`distribute-lft-out`
81×	`associate-/l*`
56×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
27×	`clear-num` `frac-2neg`
25×	`difference-of-squares`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `1-exp` `hypot-def` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `flip--`

Calls

4 calls:

Slowest

55.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
13.0ms	(/ 1 (sqrt (+ x 1)))
6.0ms	(sqrt (+ x 1))
5.0ms	(/ 1 (sqrt x))

series222.0ms

Calls

4 calls:

Slowest

103.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
47.0ms	(/ 1 (sqrt x))
36.0ms	(/ 1 (sqrt (+ x 1)))
35.0ms	(sqrt (+ x 1))

simplify2.6m

Calls

1724 calls:

Slowest

658.0ms	(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (cbrt 1) (cbrt (sqrt x))) (- (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
483.0ms	(fma (- (sqrt (+ (* x x) (- (* 1 1) (* x 1))))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))) (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3))))))
438.0ms	(fma (- (/ (sqrt 1) (sqrt (sqrt (+ x 1))))) (/ (sqrt 1) (sqrt (sqrt (+ x 1)))) (* (/ (sqrt 1) (sqrt (sqrt (+ x 1)))) (/ (sqrt 1) (sqrt (sqrt (+ x 1))))))
429.0ms	(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt x) (cbrt x)))) (/ (cbrt 1) (sqrt (cbrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
413.0ms	(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (cbrt 1) (cbrt (sqrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))

prune5.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.1b

localize28.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))
0.3b	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))
0.2b	(/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
0.2b	(/ (- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

58184×	`sqrt-prod`
28660×	`times-frac`
28080×	`add-sqr-sqrt`
19060×	`*-un-lft-identity`
12584×	`add-cube-cbrt`
9024×	`prod-diff`
3500×	`difference-of-squares`
2223×	`distribute-lft-out`
1220×	`associate-r`
1098×	`associate-l` `unswap-sqr`
1056×	`frac-sub`
1002×	`associate-/l*`
918×	`associate-/r*`
620×	`associate-/l/`
595×	`distribute-lft-out--`
564×	`sqrt-div`
193×	`div-inv`
190×	`associate-/r/`
141×	`flip3-+` `flip-+`
122×	`*-commutative`
94×	`clear-num` `frac-2neg` `fma-neg`
13×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
8×	`sqrt-pow1`
6×	`add-log-exp`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `pow1/2` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp`
2×	`flip3--` `prod-exp` `cbrt-unprod` `flip--`
1×	`sqrt-undiv` `sub-neg` `sqrt-unprod` `diff-log` `div-sub`

Calls

4 calls:

Slowest

292.0ms	(/ (- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))
103.0ms	(- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))
20.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))
12.0ms	(/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))

series604.0ms

Calls

4 calls:

Slowest

277.0ms	(/ (- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))
182.0ms	(- (/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))) (/ (sqrt (sqrt x)) (sqrt (sqrt (+ x 1)))))
76.0ms	(/ (sqrt (sqrt (+ x 1))) (sqrt (sqrt x)))
68.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1))))