Details

sample91.0ms

Algorithm

intervals

Results

26.0ms	552×	body	80	nan
20.0ms	249×	body	160	nan
14.0ms	256×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	11	9
2	12	9
done	12	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite69.0ms

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:

47.0ms	(+ x (sqrt (- (* x x) 1.0)))
21.0ms	(sqrt (- (* x x) 1.0))

series135.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(+ x (sqrt (- (* x x) 1.0)))
60.0ms	(sqrt (- (* x x) 1.0))

simplify701.0ms

Counts

41 → 41

Iterations

Useful iterations: done (700.0ms)

Iter	Nodes	Cost
0	95	483
1	244	425
2	969	392
done	5000	356

prune196.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize23.0ms

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))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`sqrt-prod`
15×	`*-un-lft-identity`
14×	`sqrt-div`
9×	`add-cube-cbrt` `associate-r`
8×	`pow1`
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×	`expm1-log1p-u` `fma-def` `sqrt-pow1` `pow1/2` `pow-prod-down` `log1p-expm1-u`
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 → 80

Calls

3 calls:

6.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
14.0ms	(sqrt (- x (sqrt 1.0)))
90.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series599.0ms

Counts

3 → 9

Calls

3 calls:

221.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
117.0ms	(sqrt (- x (sqrt 1.0)))
262.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.2s

Counts

89 → 89

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	180	1486
1	449	1274
2	1732	1188
done	5002	1175

prune443.0ms

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	14
1	13	14
done	13	14

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	16676×	body	80	nan
866.0ms	7760×	body	160	nan
465.0ms	8000×	body	80	valid