Details

sample77.0ms

Algorithm

intervals

Results

20.0ms	274×	body	160	nan
18.0ms	524×	body	80	nan
11.0ms	256×	body	80	valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize10.0ms

Local error

Found 1 expressions with local error:

31.7b

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp` `difference-of-squares`

Counts

1 → 18

Calls

1 calls:

15.0ms

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

series63.0ms

Counts

1 → 3

Calls

1 calls:

63.0ms

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

simplify1.4s

Counts

21 → 21

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	66	241
1	149	208
2	383	195
3	1204	181
done	5000	180

prune81.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 1 expressions with local error:

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

rewrite77.0ms

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×	`add-exp-log` `flip3--` `flip3-+` `pow-prod-down` `add-cbrt-cube` `flip--` `flip-+`
2×	`sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `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:

75.0ms

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

series277.0ms

Counts

1 → 3

Calls

1 calls:

277.0ms

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

simplify2.5s

Counts

47 → 47

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	128	857
1	290	720
2	781	699
3	2492	688
done	5001	681

prune148.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.2s	7880×	body	160	nan
905.0ms	16728×	body	80	nan
478.0ms	8000×	body	80	valid