Details

analyze350.0ms (3.7%)

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)

sample3.3s (34.7%)

Results

1.4s	8256×	body	128	valid
1.1s	1374×	body	1024	invalid
426.0ms	713×	body	512	invalid
173.0ms	1139×	body	128	invalid
107.0ms	324×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-/l*_binary64`
625×	`associate-/r*_binary64`
461×	`div-sub_binary64`
445×	`distribute-frac-neg_binary64`
288×	`distribute-rgt-neg-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	65	22
3	129	22
4	280	22
5	634	20
6	1332	20
7	3121	20
8	4914	20
9	4550	20

prune4.0ms (0%)

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

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 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
✓	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) n)

series557.0ms (5.9%)

Counts

3 → 48

Calls

3 calls:

285.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
270.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`

Counts

3 → 108

Calls

3 calls:

6.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
5.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms	(.f64 (.f64 2 (PI.f64)) n)

simplify126.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

405×	`distribute-rgt-in_binary64`
399×	`distribute-lft-in_binary64`
243×	`fma-neg_binary64`
211×	`associate-/l*_binary64`
162×	`associate-l_binary64`

Counts

156 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	4057
1	428	3712
2	1390	3636
3	4506	3636
4	4960	3636

prune236.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	159	9	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	161	9	170

Error

Counts

170 → 9

Alt Table

Status	Error	Program
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 (cbrt.f64 k))))
	0.6b	(/.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))
	22.9b	(/.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))
	0.7b	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 (PI.f64)) (.f64 (cbrt.f64 n) (cbrt.f64 n))) (cbrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.5b	(.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) 1) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 k)))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
▶	0.5b	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))

Compiler

Compiled 4464 to 2822 computations (36.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series296.0ms (3.1%)

Counts

2 → 12

Calls

2 calls:

283.0ms	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
13.0ms	(/.f64 1 (sqrt.f64 k))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-exp-log_binary64`
50×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
32×	`prod-exp_binary64`

Counts

2 → 119

Calls

2 calls:

11.0ms	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
3.0ms	(/.f64 1 (sqrt.f64 k))

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-def_binary64`
657×	`times-frac_binary64`
385×	`associate-l_binary64`
297×	`distribute-rgt-in_binary64`
283×	`associate-r_binary64`

Counts

131 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	2775
1	248	2509
2	621	2509
3	1956	2470
4	4621	2470
5	4991	2470

prune315.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	215	3	218
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	219	8	227

Error

Counts

227 → 8

Alt Table

Status	Error	Program
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 (cbrt.f64 k))))
	22.9b	(/.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))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 k))) (sqrt.f64 (sqrt.f64 (/.f64 1 k)))))
	0.6b	(.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))) (/.f64 1 (sqrt.f64 k)))
▶	0.5b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))

Compiler

Compiled 5465 to 3682 computations (32.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series816.0ms (8.6%)

Counts

3 → 48

Calls

3 calls:

567.0ms

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

246.0ms

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

3.0ms

(*.f64 n (*.f64 2 (PI.f64)))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`sqrt-prod_binary64`
66×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
59×	`associate-r_binary64`
43×	`add-exp-log_binary64`

Counts

3 → 142

Calls

3 calls:

16.0ms

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

6.0ms

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

4.0ms

(*.f64 n (*.f64 2 (PI.f64)))

simplify167.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-def_binary64`
596×	`distribute-rgt-in_binary64`
338×	`times-frac_binary64`
293×	`associate-l_binary64`
266×	`associate-r_binary64`

Counts

190 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	271	7277
1	606	6772
2	2251	5070
3	4360	5062
4	5012	5062

prune391.0ms (4.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	228	7	235

Error

Counts

235 → 7

Alt Table

Status	Error	Program
	0.6b	(.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))) (/.f64 1 (sqrt.f64 k)))
▶	0.5b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 (cbrt.f64 k))))
	22.9b	(/.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))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))

Compiler

Compiled 9108 to 6238 computations (31.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 n) (.f64 2 (PI.f64)))
✓	0.4b	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (.f64 2 (PI.f64))))
✓	0.5b	(*.f64 (cbrt.f64 n) (cbrt.f64 n))
✓	0.6b	(cbrt.f64 n)

series125.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

41.0ms	(.f64 (cbrt.f64 n) (.f64 2 (PI.f64)))
38.0ms	(*.f64 (cbrt.f64 n) (cbrt.f64 n))
29.0ms	(cbrt.f64 n)
17.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (.f64 2 (PI.f64))))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 108

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (.f64 2 (PI.f64))))
6.0ms	(*.f64 (cbrt.f64 n) (cbrt.f64 n))
5.0ms	(.f64 (cbrt.f64 n) (.f64 2 (PI.f64)))
1.0ms	(cbrt.f64 n)

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

807×	`fma-def_binary64`
519×	`*-commutative_binary64`
326×	`sqr-pow_binary64`
310×	`log-prod_binary64`
268×	`exp-prod_binary64`

Counts

156 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	121	1587
1	248	1348
2	986	1310
3	1663	1296
4	3002	1202
5	4604	1202
6	4881	1202

prune285.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	181	7	188

Error

Counts

188 → 7

Alt Table

Status	Error	Program
	0.6b	(.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))) (/.f64 1 (sqrt.f64 k)))
✓	0.5b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 (cbrt.f64 k))))
	22.9b	(/.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))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))

Compiler

Compiled 7182 to 4309 computations (40% saved)

regimes1.9s (20.1%)

Accuracy

Total 0.4b remaining (91.4%)

Threshold costs 0.4b (91.4%)

Counts

350 → 1

Compiler

Compiled 42522 to 32670 computations (23.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	20
1	19	20
2	18	20

end180.0ms (1.9%)

Compiler: Compiled 275 to 197 computations (28.4% saved)

Details

analyze350.0ms (3.7%)

sample3.3s (34.7%)

simplify49.0ms (0.5%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series557.0ms (5.9%)

rewrite22.0ms (0.2%)

simplify126.0ms (1.3%)

prune236.0ms (2.5%)

localize13.0ms (0.1%)

series296.0ms (3.1%)

rewrite24.0ms (0.2%)

simplify117.0ms (1.2%)

prune315.0ms (3.3%)

localize17.0ms (0.2%)

series816.0ms (8.6%)

rewrite45.0ms (0.5%)

simplify167.0ms (1.8%)

prune391.0ms (4.1%)

localize20.0ms (0.2%)

series125.0ms (1.3%)

rewrite26.0ms (0.3%)

simplify103.0ms (1.1%)

prune285.0ms (3%)

regimes1.9s (20.1%)

simplify2.0ms (0%)

end180.0ms (1.9%)

Profiling