Details

sample73.0ms

Algorithm

intervals

Results

15.0ms	306×	body	80	nan
9.0ms	159×	body	80	valid
6.0ms	24×	body	1280	valid
5.0ms	26×	body	640	valid
4.0ms	27×	body	320	valid
4.0ms	16×	body	1280	nan
3.0ms	17×	body	640	nan
2.0ms	20×	body	160	valid
1.0ms	8×	body	320	nan
1.0ms	11×	body	160	nan

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	18	27
1	39	27
2	86	27
3	179	27
4	353	27
5	583	27
6	936	27
7	1824	27
8	3618	27
done	5001	27

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
12.4b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

24.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

424.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
44.0ms	(* (sqrt 2.0) t)
215.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify565.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (133.0ms)

Iter	Nodes	Cost
0	168	2472
1	425	2287
2	1791	2075
done	5000	2075

prune308.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.0b

localize23.0ms

Local error

Found 4 expressions with local error:

3.4b	(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
5.9b	(/ (pow l 2) x)
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+l+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

13.0ms	(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
4.0ms	(/ (pow l 2) x)
4.0ms	(/ (pow t 2) x)
23.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
19.0ms	(/ (pow l 2) x)
25.0ms	(/ (pow t 2) x)
270.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

simplify152.0ms

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	254	2312
1	538	2086