Details

sample46.0ms

Algorithm

intervals

Results

12.0ms	527×	body	80	nan
11.0ms	231×	body	160	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	10	5
1	11	5
2	11	5

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 32.4b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
30.2b	(sqrt (- (* x x) 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`sqrt-prod`
9×	`*-un-lft-identity`
5×	`difference-of-squares`
4×	`add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out--`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-l` `sum-log` `*-commutative` `flip--` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 34

Calls

2 calls:

11.0ms	(+ x (sqrt (- (* x x) 1.0)))
12.0ms	(sqrt (- (* x x) 1.0))

series131.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(+ x (sqrt (- (* x x) 1.0)))
57.0ms	(sqrt (- (* x x) 1.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	228	257
1	748	245
2	2972	239
3	5002	236

prune75.0ms

Filtered

40 candidates to 30 candidates (25.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	1	41

Merged error: 0b

Counts

41 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- x (sqrt 1.0)))
0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`sqrt-prod`
18×	`*-un-lft-identity`
14×	`sqrt-div`
9×	`associate-r`
8×	`pow1` `add-cube-cbrt` `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×	`sqrt-pow1` `pow1/2` `pow-prod-down` `distribute-lft-out`
2×	`associate-r/` `associate-l/` `distribute-lft-out--`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

3 → 73

Calls

3 calls:

4.0ms	(sqrt (- x (sqrt 1.0)))
15.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series454.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(sqrt (- x (sqrt 1.0)))
159.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
217.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	407	833
1	1418	779
2	5002	761

prune181.0ms

Filtered

82 candidates to 59 candidates (28.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	1	83

Merged error: 0b

Counts

83 → 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

362.0ms	16048×	body	80	nan
357.0ms	7698×	body	160	nan
230.0ms	8000×	body	80	valid