Details

analyze534.0ms (5%)

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%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample166.0ms (1.6%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
23.0ms	35×	body	1024	nan
15.0ms	59×	body	128	overflowed
9.0ms	21×	body	512	nan
2.0ms	25×	body	128	nan
2.0ms	7×	body	256	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify62.0ms (0.6%)

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

prune5.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.6b	(.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)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.3b	(/.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))

series598.0ms (5.6%)

Counts

3 → 48

Calls

3 calls:

310.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
285.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
4.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 108

Calls

3 calls:

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

simplify150.0ms (1.4%)

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

prune259.0ms (2.4%)

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

0.0b

Counts

170 → 9

Alt Table

Status	Error	Program
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
▶	0.5b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.8b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
	0.8b	(/.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))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
	0.8b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	22.8b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) k)))))) (sqrt.f64 k))
	1.1b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	0.9b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))

Compiler

Compiled 4353 to 2846 computations (34.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 k))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
✓	0.3b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))

series587.0ms (5.5%)

Counts

4 → 48

Calls

4 calls:

304.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
272.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
6.0ms	(sqrt.f64 (/.f64 1 k))
4.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
32×	`sqrt-prod_binary64`
27×	`add-exp-log_binary64`
25×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`

Counts

4 → 119

Calls

4 calls:

9.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
7.0ms	(sqrt.f64 (/.f64 1 k))
5.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
4.0ms	(.f64 n (.f64 2 (PI.f64)))

simplify211.0ms (2%)

Algorithm

1×	egg-herbie

Rules

498×	`*-commutative_binary64`
487×	`distribute-rgt-in_binary64`
481×	`distribute-lft-in_binary64`
259×	`times-frac_binary64`
231×	`fma-neg_binary64`

Counts

167 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	3470
1	391	3090
2	1278	3062
3	3634	3062
4	4927	3062
5	4999	3062
6	4930	3062

prune254.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	143	5	148
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	148	9	157

Error

0.0b

Counts

157 → 9

Alt Table

Status	Error	Program
	0.7b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 1 k))) (sqrt.f64 (cbrt.f64 (/.f64 1 k)))))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
	0.8b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
	22.8b	(.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 2))) -1/2))) (sqrt.f64 (/.f64 1 k)))
	0.8b	(.f64 (pow.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	22.8b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) k)))))) (sqrt.f64 k))
▶	0.7b	(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k))))
	0.8b	(.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
	0.9b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))

Compiler

Compiled 3924 to 2903 computations (26% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series439.0ms (4.1%)

Counts

4 → 32

Calls

4 calls:

370.0ms	(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k))))
38.0ms	(pow.f64 n (fma.f64 k -1/2 1/2))
25.0ms	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
6.0ms	(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-exp-log_binary64`
36×	`prod-exp_binary64`
32×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
19×	`sqrt-prod_binary64`

Counts

4 → 123

Calls

4 calls:

9.0ms	(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k))))
9.0ms	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
3.0ms	(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
2.0ms	(pow.f64 n (fma.f64 k -1/2 1/2))

simplify183.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

360×	`fma-neg_binary64`
326×	`fma-def_binary64`
245×	`associate-r_binary64`
236×	`distribute-rgt-in_binary64`
228×	`associate-l_binary64`

Counts

155 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	3894
1	499	3544
2	1674	3477
3	4281	3477
4	4941	3477
5	4957	3477

prune329.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	188	9	197

Error

0.0b

Counts

197 → 9

Alt Table

Status	Error	Program
▶	0.7b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 1 k))) (sqrt.f64 (cbrt.f64 (/.f64 1 k)))))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
	0.8b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
	22.8b	(.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 2))) -1/2))) (sqrt.f64 (/.f64 1 k)))
	0.8b	(.f64 (pow.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	22.8b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) k)))))) (sqrt.f64 k))
✓	0.7b	(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k))))
	0.8b	(.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
	0.9b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))

Compiler

Compiled 5912 to 4461 computations (24.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 1 k))) (sqrt.f64 (cbrt.f64 (/.f64 1 k)))))
	0.3b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
✓	0.4b	(*.f64 (fabs.f64 (cbrt.f64 (/.f64 1 k))) (sqrt.f64 (cbrt.f64 (/.f64 1 k))))
✓	0.5b	(cbrt.f64 (/.f64 1 k))

series696.0ms (6.6%)

Counts

3 → 48

Calls

3 calls:

601.0ms

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

59.0ms

(*.f64 (fabs.f64 (cbrt.f64 (/.f64 1 k))) (sqrt.f64 (cbrt.f64 (/.f64 1 k))))

36.0ms

(cbrt.f64 (/.f64 1 k))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64`
102×	`cbrt-prod_binary64`
69×	`times-frac_binary64`
52×	`sqrt-prod_binary64`
50×	`*-un-lft-identity_binary64`

Counts

3 → 164

Calls

3 calls:

18.0ms

(*.f64 (fabs.f64 (cbrt.f64 (/.f64 1 k))) (sqrt.f64 (cbrt.f64 (/.f64 1 k))))

14.0ms

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

2.0ms

(cbrt.f64 (/.f64 1 k))

simplify176.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

537×	`unswap-sqr_binary64`
318×	`associate-r_binary64`
270×	`associate-l_binary64`
254×	`fma-neg_binary64`
223×	`distribute-rgt-in_binary64`

Counts

212 → 240

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	5916
1	539	5099
2	1498	4343
3	3494	4289
4	5078	4289

prune508.0ms (4.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	301	1	302
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	302	9	311

Error

0.0b

Counts

311 → 9

Alt Table

Status	Error	Program
	0.7b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (.f64 (fabs.f64 (cbrt.f64 1)) (sqrt.f64 (cbrt.f64 (/.f64 1 k))))) (fabs.f64 (cbrt.f64 k)))
✓	0.7b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (.f64 (fabs.f64 (cbrt.f64 (/.f64 1 k))) (sqrt.f64 (cbrt.f64 (/.f64 1 k)))))
	0.8b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
	22.8b	(.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k (sqrt.f64 2))) -1/2))) (sqrt.f64 (/.f64 1 k)))
	0.8b	(.f64 (pow.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	22.8b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) k)))))) (sqrt.f64 k))
✓	0.7b	(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k))))
	0.8b	(.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 (/.f64 1 k)))
	0.9b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))

Compiler

Compiled 9556 to 7287 computations (23.7% saved)

regimes1.8s (16.8%)

Accuracy

Total 0.4b remaining (96.4%)

Threshold costs 0.4b (96.4%)

Counts

250 → 1

Compiler

Compiled 23842 to 19117 computations (19.8% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	23
1	21	23
2	20	23

end1.0ms (0%)

Compiler: Compiled 17 to 14 computations (17.6% saved)

sample3.5s (32.6%)

Algorithm

1×

intervals

Results

901.0ms	1361×	body	1024	nan
850.0ms	8000×	body	128	valid
481.0ms	2333×	body	128	overflowed
310.0ms	700×	body	512	nan
79.0ms	970×	body	128	nan
74.0ms	310×	body	256	nan
26.0ms	231×	body	128	invalid

Compiler

Compiled 278 to 222 computations (20.1% saved)

Details

analyze534.0ms (5%)

sample166.0ms (1.6%)

simplify62.0ms (0.6%)

prune5.0ms (0%)

localize10.0ms (0.1%)

series598.0ms (5.6%)

rewrite24.0ms (0.2%)

simplify150.0ms (1.4%)

prune259.0ms (2.4%)

localize13.0ms (0.1%)

series587.0ms (5.5%)

rewrite34.0ms (0.3%)

simplify211.0ms (2%)

prune254.0ms (2.4%)

localize18.0ms (0.2%)

series439.0ms (4.1%)

rewrite36.0ms (0.3%)

simplify183.0ms (1.7%)

prune329.0ms (3.1%)

localize23.0ms (0.2%)

series696.0ms (6.6%)

rewrite56.0ms (0.5%)

simplify176.0ms (1.7%)

prune508.0ms (4.8%)

regimes1.8s (16.8%)

simplify5.0ms (0%)

end1.0ms (0%)

sample3.5s (32.6%)

Profiling