Details

sample44.0ms

Algorithm

intervals

Results

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

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	5
done	12	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))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-cube-cbrt` `sqrt-prod` `add-log-exp`
3×	`pow1` `fma-def`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

19.0ms	(+ x (sqrt (- (* x x) 1.0)))
12.0ms	(sqrt (- (* x x) 1.0))

series110.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(+ x (sqrt (- (* x x) 1.0)))
47.0ms	(sqrt (- (* x x) 1.0))

simplify76.0ms

Counts

41 → 41

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	235	239
1	739	223
2	2858	218
3	5001	216
done	5001	216

prune106.0ms

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))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`sqrt-prod`
15×	`*-un-lft-identity`
14×	`sqrt-div`
9×	`add-cube-cbrt` `associate-r`
8×	`pow1`
7×	`associate-l`
5×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`expm1-log1p-u` `flip3--` `fma-def` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--` `log1p-expm1-u`
2×	`associate-r/` `associate-l/` `hypot-def` `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 → 80

Calls

3 calls:

5.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
10.0ms	(sqrt (+ x (sqrt 1.0)))
47.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series365.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
57.0ms	(sqrt (+ x (sqrt 1.0)))
176.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify42.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	439	856
1	1551	780
2	5001	760
done	5001	760

prune232.0ms

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

sample1.3s

Algorithm

intervals

Results

329.0ms	7463×	body	160	nan
318.0ms	15967×	body	80	nan
221.0ms	8000×	body	80	valid