Details

sample50.0ms

Algorithm

intervals

Results

13.0ms	231×	body	160	nan
10.0ms	504×	body	80	nan
7.0ms	256×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5
done	11	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
30.8b	(sqrt (- (* x x) 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 28

Calls

2 calls:

17.0ms	(+ x (sqrt (- (* x x) 1.0)))
11.0ms	(sqrt (- (* x x) 1.0))

series122.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(+ x (sqrt (- (* x x) 1.0)))
54.0ms	(sqrt (- (* x x) 1.0))

simplify70.0ms

Counts

34 → 34

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	217	222
1	651	211
2	2521	205
3	5001	204
done	5001	204

prune79.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.0b	(sqrt (+ x (sqrt 1.0)))
0.4b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`sqrt-prod`
14×	`*-un-lft-identity` `sqrt-div`
9×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
5×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`flip3--` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--`
2×	`associate-r/` `associate-l/` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 69

Calls

3 calls:

5.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
10.0ms	(sqrt (+ x (sqrt 1.0)))
54.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series410.0ms

Counts

3 → 9

Calls

3 calls:

150.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
59.0ms	(sqrt (+ x (sqrt 1.0)))
201.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify41.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	411	796
1	1435	742
2	5002	724
done	5002	724

prune214.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9
done	13	9

end0.0ms

sample1.4s

Algorithm

intervals

Results

333.0ms	7463×	body	160	nan
324.0ms	15967×	body	80	nan
226.0ms	8000×	body	80	valid