Details

sample99.0ms

Algorithm

intervals

Results

27.0ms	249×	body	160	nan
26.0ms	533×	body	80	nan
16.0ms	256×	body	80	valid

simplify11.0ms

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: 32.9b

localize44.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
30.6b	(sqrt (- (* x x) 1.0))

rewrite24.0ms

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-cbrt-cube` `sqrt-div` `add-exp-log`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `flip-+` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

2 → 28

Calls

2 calls:

14.0ms	(+ x (sqrt (- (* x x) 1.0)))
9.0ms	(sqrt (- (* x x) 1.0))

series158.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(+ x (sqrt (- (* x x) 1.0)))
74.0ms	(sqrt (- (* x x) 1.0))

simplify1.6s

Counts

34 → 34

Iterations

Iter	Nodes
done	5025
3	2363
2	596
1	215
0	90

prune158.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 2 expressions with local error:

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))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
10×	`*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
6×	`pow1` `add-cube-cbrt`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 53

Calls

2 calls:

4.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
52.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series410.0ms

Counts

2 → 6

Calls

2 calls:

181.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
229.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify2.5s

Counts

59 → 59

Iterations

Iter	Nodes
done	5013
3	3719
2	1034
1	366
0	152

prune337.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify7.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample3.2s

Algorithm

intervals

Results

888.0ms	7707×	body	160	nan
887.0ms	8000×	body	80	valid
826.0ms	16160×	body	80	nan