Details

analyze593.0ms (7.2%)

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)

sample90.0ms (1.1%)

Algorithm

1×

intervals

Results

31.0ms	40×	body	1024	nan
24.0ms	256×	body	128	valid
11.0ms	65×	body	128	overflowed
4.0ms	10×	body	512	nan
3.0ms	36×	body	128	nan
1.0ms	4×	body	256	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify52.0ms (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 → 1

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

prune9.0ms (0.1%)

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

Error

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.4b	(.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 81 to 66 computations (18.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))
0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.2b	(.f64 (.f64 2 PI.f64) n)

rewrite146.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

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

Compiler

Compiled 2163 to 1389 computations (35.8% saved)

series81.0ms (1%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

32.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
30.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))
6.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1028 to 765 computations (25.6% saved)

simplify149.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

418×	`distribute-rgt-in_binary64`
412×	`distribute-lft-in_binary64`
232×	`associate-/l*_binary64`
170×	`fma-def_binary64`
165×	`associate-l_binary64`

Counts

126 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	3436
1	441	3211
2	1419	3177
3	4590	3177
4	4987	3177
5	4978	3177

prune86.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	96	9	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Error

0.0b

Counts

107 → 9

Alt Table

Status	Error	Program
▶	0.2b	(/.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))
	1.1b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
	0.5b	(.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))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
	1.1b	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (sqrt.f64 (cbrt.f64 k))))
	0.6b	(.f64 (pow.f64 (.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	0.5b	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))

Compiler

Compiled 1947 to 1210 computations (37.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
0.2b	(/.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))
0.2b	(*.f64 n PI.f64)
0.2b	(*.f64 n PI.f64)

rewrite122.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

27×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64`

Counts

4 → 87

Calls

4 calls:

8.0ms	(/.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))
3.0ms	(*.f64 n PI.f64)
3.0ms	(*.f64 n PI.f64)
3.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

Compiler

Compiled 1988 to 1045 computations (47.4% saved)

series42.0ms (0.5%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

26.0ms	(/.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))
6.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
5.0ms	(*.f64 n PI.f64)
5.0ms	(*.f64 n PI.f64)

Compiler

Compiled 885 to 674 computations (23.8% saved)

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

732×	`associate-/l*_binary64`
664×	`times-frac_binary64`
284×	`associate-/r*_binary64`
248×	`fma-def_binary64`
219×	`associate-*l/_binary64`

Counts

102 → 58

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	167	2036
1	348	1772
2	1104	1772
3	4511	1772
4	4996	1772

prune64.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	58	9	67

Error

Counts

67 → 9

Alt Table

Status	Error	Program
	0.5b	(.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))))
▶	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
	0.6b	(.f64 (pow.f64 (.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2)))) (sqrt.f64 (sqrt.f64 (.f64 n (*.f64 PI.f64 2)))))) (sqrt.f64 k))
	1.1b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (sqrt.f64 (cbrt.f64 k))))
	0.5b	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	1.0b	(/.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 PI.f64 2)) (.f64 -1/2 k)) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (sqrt.f64 (.f64 n (*.f64 PI.f64 2)))) (cbrt.f64 (sqrt.f64 k)))

Compiler

Compiled 1385 to 887 computations (36% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite288.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

101×	`times-frac_binary64`
78×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`
50×	`add-exp-log_binary64`

Counts

4 → 187

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
11.0ms	(/.f64 (*.f64 PI.f64 -2) (/.f64 -1 n))
6.0ms	(pow.f64 (/.f64 (*.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
2.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 4666 to 3578 computations (23.3% saved)

series74.0ms (0.9%)

Error

Counts

4 → 21

Calls

4 calls:

29.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
27.0ms	(pow.f64 (/.f64 (*.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
5.0ms	(/.f64 (*.f64 PI.f64 -2) (/.f64 -1 n))
5.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 1161 to 894 computations (23% saved)

simplify169.0ms (2%)

Algorithm

1×	egg-herbie

Rules

566×	`fma-def_binary64`
541×	`times-frac_binary64`
355×	`distribute-rgt-in_binary64`
223×	`associate-l_binary64`
207×	`associate-r_binary64`

Counts

208 → 158

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	320	4722
1	709	4403
2	2261	4381
3	4589	4379
4	4953	4379

prune158.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	158	9	167

Error

Counts

167 → 9

Alt Table

Status	Error	Program
	0.5b	(.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))))
✓	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
	0.6b	(.f64 (pow.f64 (.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
▶	0.4b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2)))) (sqrt.f64 (sqrt.f64 (.f64 n (*.f64 PI.f64 2)))))) (sqrt.f64 k))
	0.5b	(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 PI.f64 (fma.f64 k -1/2 1/2))) (pow.f64 (/.f64 -2 (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
	1.0b	(/.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 PI.f64 2)) (.f64 -1/2 k)) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (sqrt.f64 (.f64 n (*.f64 PI.f64 2)))) (cbrt.f64 (sqrt.f64 k)))
	1.1b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (sqrt.f64 (cbrt.f64 k))))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))

Compiler

Compiled 2955 to 2099 computations (29% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 n (.f64 PI.f64 2))
0.2b	(.f64 n (.f64 PI.f64 2))
0.2b	(*.f64 n PI.f64)
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2)))) (sqrt.f64 (sqrt.f64 (.f64 n (*.f64 PI.f64 2)))))

rewrite198.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

151×	`pow1_binary64`
140×	`sqrt-pow1_binary64`
80×	`pow-prod-down_binary64`
34×	`add-sqr-sqrt_binary64`
26×	`sqrt-prod_binary64`

Counts

4 → 152

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2)))) (sqrt.f64 (sqrt.f64 (.f64 n (*.f64 PI.f64 2)))))
4.0ms	(.f64 n (.f64 PI.f64 2))
4.0ms	(.f64 n (.f64 PI.f64 2))
3.0ms	(*.f64 n PI.f64)

Compiler

Compiled 3455 to 2279 computations (34% saved)

series30.0ms (0.4%)

Error

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 n PI.f64)
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2)))) (sqrt.f64 (sqrt.f64 (.f64 n (*.f64 PI.f64 2)))))
6.0ms	(.f64 n (.f64 PI.f64 2))
6.0ms	(.f64 n (.f64 PI.f64 2))

Compiler

Compiled 788 to 586 computations (25.6% saved)

simplify165.0ms (2%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-def_binary64`
327×	`*-commutative_binary64`
251×	`log-prod_binary64`
250×	`associate-+l+_binary64`
249×	`associate-*l/_binary64`

Counts

164 → 124

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	121	1800
1	218	1636
2	751	1594
3	1068	1499
4	1742	1499
5	3638	1436
6	4295	1432
7	4991	1432
8	4890	1432

prune87.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	124	9	133

Error

Counts

133 → 9

Alt Table

Status	Error	Program
	0.5b	(.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))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
	0.6b	(.f64 (pow.f64 (.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2)))) (sqrt.f64 (sqrt.f64 (.f64 n (*.f64 PI.f64 2)))))) (sqrt.f64 k))
	1.1b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (.f64 (sqrt.f64 (sqrt.f64 n)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64)))) (sqrt.f64 (sqrt.f64 (*.f64 PI.f64 2)))))) (sqrt.f64 k))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (sqrt.f64 (cbrt.f64 k))))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	1.0b	(/.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 PI.f64 2)) (.f64 -1/2 k)) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (sqrt.f64 (.f64 n (*.f64 PI.f64 2)))) (cbrt.f64 (sqrt.f64 k)))

Compiler

Compiled 1858 to 1167 computations (37.2% saved)

regimes2.1s (25.9%)

Accuracy

Total 0.3b remaining (91.3%)

Threshold costs 0.3b (91.3%)

Compiler

Compiled 38602 to 30162 computations (21.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	24	31
2	22	31

end1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

sample3.4s (40.9%)

Algorithm

1×

intervals

Results

920.0ms	8000×	body	128	valid
906.0ms	1452×	body	1024	nan
432.0ms	2320×	body	128	overflowed
282.0ms	656×	body	512	nan
86.0ms	1017×	body	128	nan
83.0ms	340×	body	256	nan
31.0ms	241×	body	128	invalid

Compiler

Compiled 308 to 221 computations (28.2% saved)

Details

analyze593.0ms (7.2%)

sample90.0ms (1.1%)

simplify52.0ms (0.6%)

prune9.0ms (0.1%)

localize9.0ms (0.1%)

rewrite146.0ms (1.8%)

series81.0ms (1%)

simplify149.0ms (1.8%)

prune86.0ms (1%)

localize10.0ms (0.1%)

rewrite122.0ms (1.5%)

series42.0ms (0.5%)

simplify98.0ms (1.2%)

prune64.0ms (0.8%)

localize12.0ms (0.1%)

rewrite288.0ms (3.5%)

series74.0ms (0.9%)

simplify169.0ms (2%)

prune158.0ms (1.9%)

localize17.0ms (0.2%)

rewrite198.0ms (2.4%)

series30.0ms (0.4%)

simplify165.0ms (2%)

prune87.0ms (1.1%)

regimes2.1s (25.9%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.4s (40.9%)

Profiling