Details

sample71.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
16.0ms	273×	body	160	nan
15.0ms	575×	body	80	nan

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	232
1	11	232
2	12	232
done	12	232

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize10.0ms

Local error

Found 1 expressions with local error:

28.7b

(sqrt (- (* x x) 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
1×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `log1p-expm1-u` `flip--` `add-log-exp` `difference-of-squares`

Counts

1 → 18

Calls

1 calls:

10.0ms

(sqrt (- (* x x) 1.0))

series76.0ms

Counts

1 → 3

Calls

1 calls:

76.0ms

(sqrt (- (* x x) 1.0))

simplify803.0ms

Counts

21 → 21

Iterations

Useful iterations: done (801.0ms)

Iter	Nodes	Cost
0	66	5991
1	158	4694
2	638	4477
done	5000	4452

prune123.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`sqrt-prod`
14×	`sqrt-div`
13×	`*-un-lft-identity`
9×	`associate-r`
7×	`pow1` `associate-l` `add-cube-cbrt`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `unswap-sqr`
3×	`sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `flip--`
2×	`expm1-log1p-u` `associate-l/` `associate-r/` `hypot-def` `log1p-expm1-u` `distribute-lft-out` `add-log-exp` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

2 → 64

Calls

2 calls:

8.0ms	(sqrt (+ x (sqrt 1.0)))
68.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series335.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(sqrt (+ x (sqrt 1.0)))
246.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.0s

Counts

70 → 70

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	154	27460
1	361	21183
2	1350	20750
done	5001	20340

prune350.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	352
1	13	352
done	13	352

end0.0ms

sample3.3s

Algorithm

intervals

Results

960.0ms	8000×	body	80	valid
913.0ms	7642×	body	160	nan
814.0ms	15820×	body	80	nan