Details

analyze513.0ms (3.1%)

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)

sample147.0ms (0.9%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
16.0ms	29×	body	1024	nan
14.0ms	78×	body	128	overflowed
8.0ms	21×	body	512	nan
5.0ms	10×	body	256	nan
3.0ms	11×	body	128	invalid
2.0ms	33×	body	128	nan

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify47.0ms (0.3%)

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

series547.0ms (3.3%)

Counts

3 → 48

Calls

3 calls:

293.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
250.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
4.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite21.0ms (0.1%)

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)

simplify124.0ms (0.8%)

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

prune245.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	158	10	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	160	10	170

Error

Counts

170 → 10

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))) (sqrt.f64 k))
	1.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) (fabs.f64 (cbrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 (cbrt.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))
	3.2b	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.5b	(.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))))
	21.9b	(/.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 (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))))
	0.6b	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))

Compiler

Compiled 4527 to 2958 computations (34.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
✓	0.3b	(.f64 n (.f64 2 (PI.f64)))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.4b	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))

series130.0ms (0.8%)

Counts

3 → 12

Calls

3 calls:

83.0ms

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

43.0ms

(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

3.0ms

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

rewrite86.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

308×	`times-frac_binary64`
140×	`*-un-lft-identity_binary64`
140×	`add-sqr-sqrt_binary64`
140×	`add-cube-cbrt_binary64`
130×	`sqrt-prod_binary64`

Counts

3 → 267

Calls

3 calls:

11.0ms

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

5.0ms

(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

4.0ms

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

simplify375.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

725×	`associate-/r*_binary64`
365×	`fma-neg_binary64`
297×	`associate-/r/_binary64`
237×	`associate-/l/_binary64`
218×	`*-commutative_binary64`

Counts

279 → 383

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	365	12747
1	735	12412
2	2603	12184
3	3405	12184
4	4878	12184
5	5156	12184

prune695.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	407	4	411
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	413	8	421

Error

Counts

421 → 8

Alt Table

Status	Error	Program
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))))))
	0.5b	(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	9.6b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 n (*.f64 2 (PI.f64))))))
	21.9b	(/.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 (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))))
	1.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) (fabs.f64 (cbrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 (cbrt.f64 k))))
▶	0.3b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))

Compiler

Compiled 14562 to 8935 computations (38.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series98.0ms (0.6%)

Counts

2 → 0

Calls

2 calls:

82.0ms	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
16.0ms	(/.f64 1 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))

rewrite183.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

1486×	`times-frac_binary64`
580×	`*-un-lft-identity_binary64`
580×	`add-sqr-sqrt_binary64`
580×	`add-cube-cbrt_binary64`
364×	`sqrt-prod_binary64`

Counts

2 → 677

Calls

2 calls:

20.0ms	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
6.0ms	(/.f64 1 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))

simplify1.1s (6.7%)

Algorithm

1×	egg-herbie

Rules

594×	`associate-/l/_binary64`
478×	`fma-neg_binary64`
339×	`associate-/r/_binary64`
298×	`associate-/r*_binary64`
292×	`associate-*l/_binary64`

Counts

677 → 727

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	461	40876
1	1145	39211
2	3582	38371
3	3326	38367
4	4874	38367
5	5229	38367

prune1.3s (7.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	782	3	785
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	787	6	793

Error

Counts

793 → 6

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) -1/2))
	21.9b	(/.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))
	0.4b	(/.f64 (.f64 (sqrt.f64 n) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 -1/2 k)) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 (*.f64 2 (PI.f64)))))
	0.7b	(/.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)) (sqrt.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (/.f64 (pow.f64 n (.f64 k -1/2)) (sqrt.f64 (cbrt.f64 k)))))
	9.6b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 n (*.f64 2 (PI.f64))))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))

Compiler

Compiled 33521 to 22875 computations (31.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series343.0ms (2.1%)

Counts

2 → 12

Calls

2 calls:

267.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 k))
75.0ms	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) -1/2))

rewrite67.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

380×	`times-frac_binary64`
158×	`*-un-lft-identity_binary64`
158×	`add-sqr-sqrt_binary64`
158×	`add-cube-cbrt_binary64`
121×	`add-exp-log_binary64`

Counts

2 → 313

Calls

2 calls:

11.0ms	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) -1/2))
5.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (sqrt.f64 k))

simplify378.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-/r/_binary64`
493×	`associate-/l/_binary64`
421×	`associate-*l/_binary64`
350×	`associate-/r*_binary64`
320×	`associate-*r/_binary64`

Counts

325 → 408

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	433	16777
1	863	16472
2	2651	15880
3	4153	15880
4	4974	15880

prune730.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	466	0	466
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	466	6	472

Error

Counts

472 → 6

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) -1/2))
	21.9b	(/.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))
	0.4b	(/.f64 (.f64 (sqrt.f64 n) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 -1/2 k)) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 (*.f64 2 (PI.f64)))))
	0.7b	(/.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)) (sqrt.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (/.f64 (pow.f64 n (.f64 k -1/2)) (sqrt.f64 (cbrt.f64 k)))))
	9.6b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 n (*.f64 2 (PI.f64))))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))

Compiler

Compiled 17277 to 11379 computations (34.1% saved)

regimes6.1s (37.2%)

Accuracy

Total 0.4b remaining (83.9%)

Threshold costs 0.4b (83.9%)

Counts

892 → 1

Compiler

Compiled 135336 to 100946 computations (25.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	44
1	30	44
2	34	44
3	36	44
4	37	44
5	36	44

end1.0ms (0%)

Compiler: Compiled 29 to 24 computations (17.2% saved)

sample3.2s (19.5%)

Algorithm

1×

intervals

Results

881.0ms	1347×	body	1024	nan
791.0ms	8000×	body	128	valid
412.0ms	2340×	body	128	overflowed
307.0ms	645×	body	512	nan
84.0ms	313×	body	256	nan
69.0ms	988×	body	128	nan
31.0ms	250×	body	128	invalid

Compiler

Compiled 245 to 183 computations (25.3% saved)

Details

analyze513.0ms (3.1%)

sample147.0ms (0.9%)

simplify47.0ms (0.3%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series547.0ms (3.3%)

rewrite21.0ms (0.1%)

simplify124.0ms (0.8%)

prune245.0ms (1.5%)

localize11.0ms (0.1%)

series130.0ms (0.8%)

rewrite86.0ms (0.5%)

simplify375.0ms (2.3%)

prune695.0ms (4.2%)

localize12.0ms (0.1%)

series98.0ms (0.6%)

rewrite183.0ms (1.1%)

simplify1.1s (6.7%)

prune1.3s (7.7%)

localize14.0ms (0.1%)

series343.0ms (2.1%)

rewrite67.0ms (0.4%)

simplify378.0ms (2.3%)

prune730.0ms (4.4%)

regimes6.1s (37.2%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.2s (19.5%)

Profiling