Details

analyze346.0ms (4.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	25%	57.9%	7
18%	20.3%	61.8%	8
18.3%	16.4%	65.3%	9
18.5%	13.7%	67.8%	10
18.6%	11.5%	69.9%	11
18.7%	10%	71.3%	12
18.7%	8.9%	72.4%	13
18.7%	8.2%	73.1%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.1s (41.5%)

Results

1.3s	8256×	body	128	valid
1.1s	1371×	body	1024	invalid
350.0ms	672×	body	512	invalid
182.0ms	1164×	body	128	invalid
121.0ms	337×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-/l*_binary64`
544×	`associate-/r*_binary64`
257×	`associate-*l/_binary64`
214×	`unswap-sqr_binary64`
214×	`div-sub_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	140	22
4	354	22
5	958	20
6	2187	20

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.9b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
✓	0.3b	(*.f64 (PI.f64) n)
✓	0.7b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))

series426.0ms (5.7%)

Counts

3 → 48

Calls

3 calls:

217.0ms	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
207.0ms	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
2.0ms	(*.f64 (PI.f64) n)

rewrite54.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`log-prod_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
222×	`log-pow_binary64`
132×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	274	40
2	3319	40

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

52.0ms	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
52.0ms	(*.f64 (PI.f64) n)
52.0ms	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
433×	`associate-r_binary64`
373×	`associate-l_binary64`
176×	`distribute-rgt-in_binary64`
172×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1144
1	183	984
2	587	828
3	3443	826

Stop Event

1×	node limit

Counts

130 → 99

prune129.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	89	10	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	91	10	101

Error

0.0b

Counts

101 → 10

Alt Table

Status	Error	Program
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.9b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	1.0b	(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	11.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
	1.0b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	24.1b	(/.f64 (-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
	24.2b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (fma.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 k k)) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 k -1/2)))))) (sqrt.f64 k))
	1.4b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))
	1.1b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
▶	0.7b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))

Compiler

Compiled 2703 to 1868 computations (30.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))
✓	0.3b	(.f64 n (.f64 2 (PI.f64)))
✓	0.5b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 k -1/2))
✓	0.6b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

series259.0ms (3.5%)

Counts

4 → 36

Calls

4 calls:

193.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 k -1/2))
55.0ms	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))
8.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
3.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite60.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

263×	`log-pow_binary64`
256×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`
144×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	63
1	298	54
2	3841	52

Stop Event

1×	node limit

Counts

4 → 107

Calls

4 calls:

58.0ms	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))
58.0ms	(.f64 n (.f64 2 (PI.f64)))
58.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 k -1/2))
58.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

711×	`cancel-sign-sub-inv_binary64`
282×	`fma-neg_binary64`
184×	`associate-r_binary64`
182×	`associate-l_binary64`
179×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	632
1	148	600
2	456	532
3	2587	528

Stop Event

1×	node limit

Counts

143 → 122

prune188.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	141	9	150

Error

0.0b

Counts

150 → 9

Alt Table

Status	Error	Program
	1.0b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) -1)
	11.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
	1.0b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	1.0b	(/.f64 (.f64 (.f64 (pow.f64 (.f64 n 2) (.f64 k -1/2)) (pow.f64 (PI.f64) (.f64 k -1/2))) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
▶	0.8b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.9b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	1.0b	(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	24.1b	(/.f64 (-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
	0.9b	(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (pow.f64 k 1/4)))

Compiler

Compiled 3650 to 2380 computations (34.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 n (fma.f64 k -1/2 1/2))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
✓	0.3b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
✓	0.6b	(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

series529.0ms (7.1%)

Counts

4 → 56

Calls

4 calls:

268.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
229.0ms	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
28.0ms	(pow.f64 n (fma.f64 k -1/2 1/2))
4.0ms	(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

rewrite58.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`log-pow_binary64`
253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
144×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	299	55
2	3734	55

Stop Event

1×	node limit

Counts

4 → 100

Calls

4 calls:

56.0ms	(pow.f64 n (fma.f64 k -1/2 1/2))
56.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
56.0ms	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
56.0ms	(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-def_binary64`
392×	`cancel-sign-sub-inv_binary64`
225×	`associate-l_binary64`
207×	`associate-r_binary64`
201×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	1829
1	451	1629
2	1834	1497

Stop Event

1×	node limit

Counts

156 → 135

prune166.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	135	9	144

Error

Counts

144 → 9

Alt Table

Status	Error	Program
	1.0b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) -1)
	11.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
	1.0b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	1.0b	(/.f64 (.f64 (.f64 (pow.f64 (.f64 n 2) (.f64 k -1/2)) (pow.f64 (PI.f64) (.f64 k -1/2))) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
✓	0.8b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
▶	0.9b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	24.1b	(/.f64 (-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
	0.9b	(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (pow.f64 k 1/4)))
	1.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))

Compiler

Compiled 3945 to 2681 computations (32% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
✓	0.3b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	0.3b	(*.f64 (PI.f64) n)
✓	0.7b	(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))

series635.0ms (8.5%)

Counts

3 → 48

Calls

3 calls:

253.0ms

(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))

202.0ms

(/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

179.0ms

(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))

rewrite61.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
150×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`
144×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	56
1	343	49
2	3910	49

Stop Event

1×	node limit

Counts

3 → 102

Calls

3 calls:

59.0ms

(/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

59.0ms

(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))

59.0ms

(pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2))

simplify42.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

484×	`fma-neg_binary64`
311×	`associate-r_binary64`
283×	`associate-l_binary64`
229×	`unswap-sqr_binary64`
167×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	1312
1	216	997
2	594	975
3	3106	975

Stop Event

1×	node limit

Counts

150 → 123

prune182.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	142	9	151

Error

Counts

151 → 9

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	1.0b	(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	1.0b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) -1)
	11.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
	1.0b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	1.0b	(/.f64 (.f64 (.f64 (pow.f64 (.f64 n 2) (.f64 k -1/2)) (pow.f64 (PI.f64) (.f64 k -1/2))) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
✓	0.9b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	24.1b	(/.f64 (-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
	1.5b	(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))

Compiler

Compiled 3673 to 2448 computations (33.4% saved)

regimes848.0ms (11.4%)

Accuracy

Total 0.5b remaining (96.4%)

Threshold costs 0.5b (96.4%)

Counts

179 → 1

Compiler

Compiled 17086 to 13438 computations (21.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	21	31

Stop Event

1×

saturated

end179.0ms (2.4%)

Compiler: Compiled 277 to 211 computations (23.8% saved)

Details

analyze346.0ms (4.6%)

sample3.1s (41.5%)

simplify18.0ms (0.2%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series426.0ms (5.7%)

rewrite54.0ms (0.7%)

simplify49.0ms (0.7%)

prune129.0ms (1.7%)

localize9.0ms (0.1%)

series259.0ms (3.5%)

rewrite60.0ms (0.8%)

simplify34.0ms (0.5%)

prune188.0ms (2.5%)

localize12.0ms (0.2%)

series529.0ms (7.1%)

rewrite58.0ms (0.8%)

simplify43.0ms (0.6%)

prune166.0ms (2.2%)

localize12.0ms (0.2%)

series635.0ms (8.5%)

rewrite61.0ms (0.8%)

simplify42.0ms (0.6%)

prune182.0ms (2.4%)

regimes848.0ms (11.4%)

simplify2.0ms (0%)

end179.0ms (2.4%)

Profiling