Details

sample47.0ms

Algorithm

intervals

Results

13.0ms	279×	body	160	nan
11.0ms	505×	body	80	nan
7.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.9b

Counts

2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

30.6b

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

rewrite5.0ms

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:

5.0ms

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

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

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

simplify59.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	152	121
1	479	117
2	1970	116
3	5001	115

prune48.0ms

Filtered

21 candidates to 18 candidates (85.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	1	22

Merged error: 0b

Counts

22 → 1

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

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:

13.0ms

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

series195.0ms

Counts

1 → 3

Calls

1 calls:

195.0ms

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

simplify127.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	292	512
1	1019	480
2	4968	468
3	5001	468

prune102.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	1	48

Merged error: 0b

Counts

48 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

372.0ms	16247×	body	80	nan
365.0ms	7672×	body	160	nan
229.0ms	8000×	body	80	valid