Details

sample98.0ms

Algorithm

intervals

Results

29.0ms	270×	body	160	nan
21.0ms	433×	body	80	nan
16.0ms	256×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	7

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize63.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
24.8b	(sqrt (- (* x x) 1.0))

rewrite62.0ms

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:

36.0ms	(+ x (sqrt (- (* x x) 1.0)))
25.0ms	(sqrt (- (* x x) 1.0))

series227.0ms

Counts

2 → 6

Calls

2 calls:

121.0ms	(+ x (sqrt (- (* x x) 1.0)))
106.0ms	(sqrt (- (* x x) 1.0))

simplify2.9s

Counts

34 → 34

Iterations

Iter	Nodes
done	5001
3	1770
2	580
1	217
0	91

prune269.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x (sqrt 1.0)))
0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite140.0ms

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:

19.0ms	(sqrt (+ x (sqrt 1.0)))
11.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
104.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series847.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(sqrt (+ x (sqrt 1.0)))
256.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
450.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify5.1s

Counts

78 → 78

Iterations

Iter	Nodes
done	5026
3	4123
2	1160
1	414
0	175

prune651.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify5.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.3s	16520×	body	80	nan
996.0ms	7734×	body	160	nan