Details

analyze543.0ms (6.1%)

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)

sample167.0ms (1.9%)

Algorithm

1×

intervals

Results

33.0ms	53×	body	1024	nan
25.0ms	256×	body	128	valid
15.0ms	29×	body	512	nan
14.0ms	82×	body	128	overflowed
4.0ms	19×	body	256	nan
3.0ms	37×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify48.0ms (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

prune7.0ms (0.1%)

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))
	0.4b	(.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)

localize20.0ms (0.2%)

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))

series636.0ms (7.1%)

Counts

3 → 48

Calls

3 calls:

350.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
283.0ms	(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×	`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:

7.0ms	(/.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)

simplify127.0ms (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

prune282.0ms (3.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	157	11	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Error

Counts

170 → 11

Alt Table

Status	Error	Program
	0.5b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	28.8b	(cbrt.f64 (/.f64 (.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) (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))
	0.8b	(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.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 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
	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))))))
	0.4b	(/.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))
	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))
	0.4b	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
▶	0.2b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.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))))

Compiler

Compiled 4447 to 2914 computations (34.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))
✓	0.1b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))

series158.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))
47.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
14.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
3.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`times-frac_binary64`
51×	`add-sqr-sqrt_binary64`
43×	`sqrt-prod_binary64`
40×	`add-exp-log_binary64`
38×	`*-un-lft-identity_binary64`

Counts

4 → 145

Calls

4 calls:

14.0ms	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))
5.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
4.0ms	(.f64 n (.f64 2 (PI.f64)))
3.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

simplify181.0ms (2%)

Algorithm

1×	egg-herbie

Rules

482×	`associate-/l*_binary64`
441×	`*-commutative_binary64`
366×	`fma-def_binary64`
350×	`associate-*r/_binary64`
319×	`associate-*l/_binary64`

Counts

157 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	4123
1	362	3862
2	1318	3834
3	3693	3834
4	4499	3834
5	4953	3834
6	4942	3834

prune388.0ms (4.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	240	10	250

Error

Counts

250 → 10

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
	0.4b	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
	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 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.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 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))))
	11.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)))
	0.4b	(/.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))
	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))
	0.6b	(.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))))

Compiler

Compiled 7128 to 4414 computations (38.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series82.0ms (0.9%)

Counts

2 → 0

Calls

2 calls:

45.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
37.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`times-frac_binary64`
108×	`*-un-lft-identity_binary64`
108×	`add-sqr-sqrt_binary64`
108×	`add-cube-cbrt_binary64`
94×	`sqrt-prod_binary64`

Counts

2 → 187

Calls

2 calls:

9.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
8.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))

simplify362.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-neg_binary64`
427×	`div-sub_binary64`
402×	`unswap-sqr_binary64`
360×	`*-commutative_binary64`
295×	`distribute-rgt-in_binary64`

Counts

187 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	5375
1	234	4957
2	578	4849
3	1697	4849
4	1832	4849
5	1921	4849
6	2409	4849
7	3236	4849
8	3882	4849
9	4991	4849
10	4651	4849

prune481.0ms (5.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	292	10	302

Error

Counts

302 → 10

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
	0.4b	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
	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 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.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 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
▶	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))))
	11.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)))
	0.4b	(/.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))
	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))
	0.6b	(.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))))

Compiler

Compiled 9409 to 6181 computations (34.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series253.0ms (2.8%)

Counts

3 → 8

Calls

3 calls:

203.0ms

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

47.0ms

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

2.0ms

(*.f64 n (PI.f64))

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`sqrt-prod_binary64`
99×	`add-sqr-sqrt_binary64`
92×	`times-frac_binary64`
64×	`*-un-lft-identity_binary64`
64×	`add-cube-cbrt_binary64`

Counts

3 → 172

Calls

3 calls:

21.0ms

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

7.0ms

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

3.0ms

(*.f64 n (PI.f64))

simplify253.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

436×	`associate-/l*_binary64`
413×	`fma-def_binary64`
298×	`*-commutative_binary64`
282×	`unswap-sqr_binary64`
276×	`associate-/l/_binary64`

Counts

180 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	4856
1	351	4657
2	1000	4503
3	2267	4503
4	2575	4503
5	3408	4503
6	4758	4503
7	4998	4503
8	4976	4503

prune428.0ms (4.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	289	10	299

Error

Counts

299 → 10

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
	0.4b	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
	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 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.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 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
✓	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))))
	11.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)))
	0.4b	(/.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))
	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))
	0.6b	(.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))))

Compiler

Compiled 10775 to 6406 computations (40.5% saved)

regimes835.0ms (9.4%)

Accuracy

Total 0.3b remaining (79%)

Threshold costs 0.3b (79%)

Counts

168 → 1

Compiler

Compiled 17952 to 13575 computations (24.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	24	43
2	24	43

end1.0ms (0%)

Compiler: Compiled 28 to 19 computations (32.1% saved)

sample3.5s (39%)

Algorithm

1×

intervals

Results

962.0ms	1350×	body	1024	nan
850.0ms	8000×	body	128	valid
446.0ms	2318×	body	128	overflowed
315.0ms	687×	body	512	nan
94.0ms	344×	body	256	nan
87.0ms	1000×	body	128	nan
27.0ms	242×	body	128	invalid

Compiler

Compiled 277 to 210 computations (24.2% saved)

Details

analyze543.0ms (6.1%)

sample167.0ms (1.9%)

simplify48.0ms (0.5%)

prune7.0ms (0.1%)

localize20.0ms (0.2%)

series636.0ms (7.1%)

rewrite22.0ms (0.2%)

simplify127.0ms (1.4%)

prune282.0ms (3.2%)

localize12.0ms (0.1%)

series158.0ms (1.8%)

rewrite36.0ms (0.4%)

simplify181.0ms (2%)

prune388.0ms (4.4%)

localize11.0ms (0.1%)

series82.0ms (0.9%)

rewrite36.0ms (0.4%)

simplify362.0ms (4.1%)

prune481.0ms (5.4%)

localize14.0ms (0.2%)

series253.0ms (2.8%)

rewrite51.0ms (0.6%)

simplify253.0ms (2.8%)

prune428.0ms (4.8%)

regimes835.0ms (9.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.5s (39%)

Profiling