Details

analyze590.0ms (4.7%)

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%	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)

sample100.0ms (0.8%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
24.0ms	40×	body	1024	nan
16.0ms	71×	body	128	overflowed
9.0ms	21×	body	512	nan
3.0ms	39×	body	128	nan
1.0ms	6×	body	256	nan
0.0ms	4×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify49.0ms (0.4%)

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
▶	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.5b	(.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 (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)
✓	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series572.0ms (4.6%)

Counts

3 → 48

Calls

3 calls:

306.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
262.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite20.0ms (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:

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)

simplify130.0ms (1%)

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

prune220.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	161	7	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	7	170

Error

Counts

170 → 7

Alt Table

Status	Error	Program
	24.0b	(/.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 (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))))
	1.0b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
	0.6b	(/.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))
	0.4b	(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	1.0b	(.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)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
▶	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))))))

Compiler

Compiled 4391 to 2854 computations (35% 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))))))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.4b	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))

series136.0ms (1.1%)

Counts

3 → 12

Calls

3 calls:

94.0ms

(/.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))))))

38.0ms

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

3.0ms

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

rewrite57.0ms (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:

12.0ms

(/.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))))))

6.0ms

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

4.0ms

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

simplify394.0ms (3.2%)

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

prune587.0ms (4.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	409	2	411
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	411	7	418

Error

Counts

418 → 7

Alt Table

Status	Error	Program
	24.0b	(/.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 (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))))
	1.0b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
▶	0.3b	(/.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)))))))
	0.4b	(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	1.0b	(.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)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
✓	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))))))

Compiler

Compiled 14519 to 8899 computations (38.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series76.0ms (0.6%)

Counts

3 → 8

Calls

3 calls:

56.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))))
13.0ms	(.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))
7.0ms	(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`sqrt-prod_binary64`
24×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
24×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`

Counts

3 → 98

Calls

3 calls:

9.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))))
8.0ms	(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))
5.0ms	(.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

702×	`times-frac_binary64`
586×	`associate-/l*_binary64`
527×	`associate-/r*_binary64`
354×	`*-commutative_binary64`
293×	`associate-*l/_binary64`

Counts

106 → 134

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	138	2018
1	268	1867
2	783	1867
3	1582	1867
4	3464	1867
5	3876	1867
6	5125	1867

prune227.0ms (1.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	162	7	169

Error

Counts

169 → 7

Alt Table

Status	Error	Program
	24.0b	(/.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 (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))))
	1.0b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
✓	0.3b	(/.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)))))))
	0.4b	(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	1.0b	(.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)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
✓	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))))))

Compiler

Compiled 5300 to 3048 computations (42.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series653.0ms (5.3%)

Counts

3 → 28

Calls

3 calls:

508.0ms

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

91.0ms

(*.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))))

54.0ms

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

rewrite93.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

244×	`sqrt-prod_binary64`
207×	`times-frac_binary64`
192×	`add-sqr-sqrt_binary64`
103×	`*-un-lft-identity_binary64`
103×	`add-cube-cbrt_binary64`

Counts

3 → 288

Calls

3 calls:

36.0ms

(*.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))))

9.0ms

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

6.0ms

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

simplify334.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-def_binary64`
609×	`times-frac_binary64`
245×	`associate-*l/_binary64`
240×	`distribute-rgt-in_binary64`
235×	`distribute-lft-in_binary64`

Counts

316 → 385

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	332	13406
1	788	12515
2	2325	12303
3	4577	12301
4	5087	12301

prune686.0ms (5.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	445	0	445
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	445	7	452

Error

Counts

452 → 7

Alt Table

Status	Error	Program
	24.0b	(/.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 (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))))
	1.0b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
✓	0.3b	(/.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)))))))
	0.4b	(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	1.0b	(.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)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
✓	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))))))

Compiler

Compiled 16335 to 9126 computations (44.1% saved)

regimes4.2s (33.7%)

Accuracy

Total 0.3b remaining (83.9%)

Threshold costs 0.3b (83.9%)

Counts

664 → 1

Compiler

Compiled 98844 to 69840 computations (29.3% saved)

simplify2.0ms (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	18	31
1	25	31
2	22	31

end1.0ms (0%)

Compiler: Compiled 21 to 16 computations (23.8% saved)

sample3.1s (25.1%)

Algorithm

1×

intervals

Results

815.0ms	1297×	body	1024	nan
793.0ms	8000×	body	128	valid
429.0ms	2313×	body	128	overflowed
277.0ms	647×	body	512	nan
83.0ms	333×	body	256	nan
74.0ms	978×	body	128	nan
27.0ms	208×	body	128	invalid

Compiler

Compiled 289 to 210 computations (27.3% saved)

Details

analyze590.0ms (4.7%)

sample100.0ms (0.8%)

simplify49.0ms (0.4%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series572.0ms (4.6%)

rewrite20.0ms (0.2%)

simplify130.0ms (1%)

prune220.0ms (1.8%)

localize11.0ms (0.1%)

series136.0ms (1.1%)

rewrite57.0ms (0.5%)

simplify394.0ms (3.2%)

prune587.0ms (4.7%)

localize15.0ms (0.1%)

series76.0ms (0.6%)

rewrite31.0ms (0.2%)

simplify110.0ms (0.9%)

prune227.0ms (1.8%)

localize11.0ms (0.1%)

series653.0ms (5.3%)

rewrite93.0ms (0.7%)

simplify334.0ms (2.7%)

prune686.0ms (5.5%)

regimes4.2s (33.7%)

simplify2.0ms (0%)

end1.0ms (0%)

sample3.1s (25.1%)

Profiling