Details

sample55.0ms

Algorithm

intervals

Results

15.0ms	267×	body	160	nan
13.0ms	533×	body	80	nan
9.0ms	256×	body	80	valid

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: 30.6b

localize10.0ms

Local error

Found 1 expressions with local error:

28.5b

(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))

series107.0ms

Counts

1 → 3

Calls

1 calls:

107.0ms

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

simplify1.9s

Counts

21 → 21

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	66	5991
1	150	4694
2	419	4477
3	1633	4452
done	5002	4427

prune95.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
9×	`-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow1` `add-cube-cbrt`
4×	`frac-times` `unswap-sqr`
3×	`flip3-+` `flip3--` `add-cbrt-cube` `pow-prod-down` `add-exp-log` `flip-+` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `difference-of-squares`
1×	`expm1-log1p-u` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `add-log-exp`

Counts

1 → 44

Calls

1 calls:

70.0ms

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

series254.0ms

Counts

1 → 3

Calls

1 calls:

254.0ms

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

simplify3.6s

Counts

47 → 47

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	128	20640
1	297	16039
2	797	15818
3	2496	15648
done	5002	15573

prune263.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	16417×	body	80	nan
746.0ms	7563×	body	160	nan
614.0ms	8000×	body	80	valid