Details

analyze523.0ms (5.9%)

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)

sample173.0ms (2%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
29.0ms	50×	body	1024	nan
17.0ms	97×	body	128	overflowed
12.0ms	31×	body	512	nan
2.0ms	32×	body	128	nan
2.0ms	8×	body	256	nan
1.0ms	5×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify47.0ms (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

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)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series556.0ms (6.3%)

Counts

3 → 48

Calls

3 calls:

287.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
266.0ms	(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 (0.3%)

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:

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)

simplify129.0ms (1.5%)

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

prune239.0ms (2.7%)

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

0.0b

Counts

170 → 10

Alt Table

Status	Error	Program
	1.2b	(.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))))
	0.5b	(.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))))
	0.5b	(.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))))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	0.5b	(/.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))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
	19.8b	(cbrt.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (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))))
▶	0.3b	(.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)))
	0.7b	(.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))))

Compiler

Compiled 4509 to 2948 computations (34.6% saved)

localize10.0ms (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)))
✓	0.2b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
✓	0.3b	(.f64 n (.f64 2 (PI.f64)))
✓	0.4b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))

series162.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(.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)))
56.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
15.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
3.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite35.0ms (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:

11.0ms	(.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))))

simplify184.0ms (2.1%)

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

prune383.0ms (4.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	234	5	239
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	240	9	249

Error

Counts

249 → 9

Alt Table

Status	Error	Program
✓	0.3b	(.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)))
	0.4b	(.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))))
	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)))
	0.5b	(.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 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))) (sqrt.f64 k)))
	35.9b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (cbrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) (sqrt.f64 k)))))
	0.9b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))))
	1.0b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (/.f64 (sqrt.f64 n) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (cbrt.f64 (sqrt.f64 k)))))
	0.7b	(.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))))

Compiler

Compiled 7189 to 4440 computations (38.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series64.0ms (0.7%)

Counts

3 → 8

Calls

3 calls:

48.0ms	(/.f64 (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))) (sqrt.f64 k))
10.0ms	(.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))
6.0ms	(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))

rewrite27.0ms (0.3%)

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:

8.0ms	(/.f64 (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))) (sqrt.f64 k))
7.0ms	(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))
5.0ms	(.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))

simplify109.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

531×	`associate-/r*_binary64`
509×	`associate-*l/_binary64`
455×	`associate-/r/_binary64`
392×	`*-commutative_binary64`
311×	`associate-*r/_binary64`

Counts

106 → 133

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	138	2007
1	268	1856
2	786	1856
3	1646	1856
4	3790	1856
5	4377	1856
6	4977	1856

prune240.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	163	9	172

Error

Counts

172 → 9

Alt Table

Status	Error	Program
	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))))))
	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)))
	1.0b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (/.f64 (sqrt.f64 n) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (cbrt.f64 (sqrt.f64 k)))))
	11.0b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64)))) k)))
✓	0.3b	(.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)))
▶	0.4b	(.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))))
✓	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))) (sqrt.f64 k)))
	35.9b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (cbrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k)) (sqrt.f64 k)))))
	0.7b	(.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))))

Compiler

Compiled 5333 to 3054 computations (42.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series270.0ms (3.1%)

Counts

3 → 8

Calls

3 calls:

217.0ms

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

51.0ms

(*.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:

22.0ms

(*.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))

simplify265.0ms (3%)

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	5324
1	351	4657
2	1000	4503
3	2267	4503
4	2575	4503
5	3408	4503
6	4758	4503
7	4998	4503
8	4976	4503

prune424.0ms (4.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	287	2	289
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	290	8	298

Error

Counts

298 → 8

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))) (sqrt.f64 k)))
	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 (pow.f64 (*.f64 (PI.f64) n) 1/4) (sqrt.f64 (/.f64 (sqrt.f64 2) k)))))
	1.0b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (/.f64 (sqrt.f64 n) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (cbrt.f64 (sqrt.f64 k)))))
	11.0b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64)))) k)))
	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (PI.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)))
✓	0.3b	(.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)))
	0.7b	(.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))))

Compiler

Compiled 10756 to 6389 computations (40.6% saved)

regimes1.7s (19.2%)

Accuracy

Total 0.4b remaining (84.9%)

Threshold costs 0.4b (84.9%)

Counts

268 → 1

Compiler

Compiled 31737 to 23465 computations (26.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	23	37
2	23	37

end1.0ms (0%)

Compiler: Compiled 25 to 19 computations (24% saved)

sample3.1s (35.8%)

Algorithm

1×

intervals

Results

882.0ms	1323×	body	1024	nan
781.0ms	8000×	body	128	valid
421.0ms	2323×	body	128	overflowed
291.0ms	700×	body	512	nan
82.0ms	336×	body	256	nan
76.0ms	1035×	body	128	nan
27.0ms	236×	body	128	invalid

Compiler

Compiled 255 to 192 computations (24.7% saved)

Details

analyze523.0ms (5.9%)

sample173.0ms (2%)

simplify47.0ms (0.5%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series556.0ms (6.3%)

rewrite22.0ms (0.3%)

simplify129.0ms (1.5%)

prune239.0ms (2.7%)

localize10.0ms (0.1%)

series162.0ms (1.8%)

rewrite35.0ms (0.4%)

simplify184.0ms (2.1%)

prune383.0ms (4.4%)

localize13.0ms (0.1%)

series64.0ms (0.7%)

rewrite27.0ms (0.3%)

simplify109.0ms (1.2%)

prune240.0ms (2.7%)

localize15.0ms (0.2%)

series270.0ms (3.1%)

rewrite51.0ms (0.6%)

simplify265.0ms (3%)

prune424.0ms (4.8%)

regimes1.7s (19.2%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.1s (35.8%)

Profiling