Details

sample88.0ms

Algorithm

intervals

Results

30.0ms	249×	body	160	nan
19.0ms	552×	body	80	nan
12.0ms	256×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	11	9
done	11	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
31.7b	(sqrt (- (* x x) 1.0))

rewrite45.0ms

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:

23.0ms	(+ x (sqrt (- (* x x) 1.0)))
21.0ms	(sqrt (- (* x x) 1.0))

series166.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(+ x (sqrt (- (* x x) 1.0)))
82.0ms	(sqrt (- (* x x) 1.0))

simplify511.0ms

Counts

34 → 34

Iterations

Useful iterations: done (510.0ms)

Iter	Nodes	Cost
0	91	451
1	225	402
2	885	366
done	5001	358

prune109.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize19.0ms

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

10.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
18.0ms	(sqrt (- x (sqrt 1.0)))
75.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series541.0ms

Counts

3 → 9

Calls

3 calls:

162.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
117.0ms	(sqrt (- x (sqrt 1.0)))
261.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.0s

Counts

80 → 80

Iterations

Useful iterations: 2 (391.0ms)

Iter	Nodes	Cost
0	174	1422
1	421	1220
2	1617	1152
done	5001	1152

prune383.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
done	13	14

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	16676×	body	80	nan
860.0ms	7760×	body	160	nan
580.0ms	8000×	body	80	valid