Details

sample75.0ms

Algorithm

intervals

Results

21.0ms	267×	body	160	nan
19.0ms	533×	body	80	nan
12.0ms	256×	body	80	valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	232
1	10	232
2	11	232
done	11	232

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize11.0ms

Local error

Found 1 expressions with local error:

28.5b

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip--` `add-log-exp` `difference-of-squares`

Counts

1 → 16

Calls

1 calls:

14.0ms

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

series99.0ms

Counts

1 → 3

Calls

1 calls:

99.0ms

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

simplify1.7s

Counts

19 → 19

Iterations

Useful iterations: 2 (133.0ms)

Iter	Nodes	Cost
0	64	5587
1	141	4390
2	371	4188
3	1546	4188
done	5000	4188

prune96.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite65.0ms

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×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `add-log-exp`

Counts

1 → 42

Calls

1 calls:

63.0ms

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

series257.0ms

Counts

1 → 3

Calls

1 calls:

257.0ms

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

simplify2.4s

Counts

45 → 45

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	126	19996
1	284	15480
2	768	15359
3	2381	15159
done	5006	15159

prune237.0ms

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

sample3.4s

Algorithm

intervals

Results

1.3s	7563×	body	160	nan
900.0ms	16417×	body	80	nan
569.0ms	8000×	body	80	valid