Details

analyze442.0ms (2.1%)

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)

sample72.0ms (0.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
18.0ms	42×	body	1024	nan
10.0ms	78×	body	128	overflowed
4.0ms	12×	body	512	nan
3.0ms	15×	body	256	nan
1.0ms	23×	body	128	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify51.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

788×	`neg-mul-1_binary64`
672×	`associate-/l*_binary64`
625×	`associate-/r*_binary64`
480×	`div-sub_binary64`
445×	`distribute-frac-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	65	22
3	128	22
4	277	22
5	623	22
6	1296	22
7	3024	22
8	4691	22
9	4933	22

prune5.0ms (0%)

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

0.6b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
▶	0.7b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

Compiler

Compiled 84 to 69 computations (17.9% saved)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

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

rewrite206.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

48×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`
22×	`pow-unpow_binary64`

Counts

3 → 115

Calls

3 calls:

14.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2467 to 1670 computations (32.3% saved)

series101.0ms (0.5%)

Error

0.3b

Counts

3 → 18

Calls

3 calls:

43.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
36.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
8.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1081 to 812 computations (24.9% saved)

simplify138.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

517×	`distribute-rgt-in_binary64`
512×	`distribute-lft-in_binary64`
218×	`associate-/l*_binary64`
207×	`associate-/l/_binary64`
169×	`associate-l_binary64`

Counts

133 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3741
1	512	3560
2	1620	3374
3	4824	3370
4	5021	3370

prune131.0ms (0.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	10	122
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	114	10	124

Error

0.0b

Counts

124 → 10

Alt Table

Status	Error	Program
	23.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n PI.f64)) (-.f64 (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (.f64 k k) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 PI.f64))) 2))))) (+.f64 (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 PI.f64))) (.f64 k (sqrt.f64 2)))) (.f64 1/48 (.f64 (pow.f64 k 3) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 PI.f64))) 3))))))) (sqrt.f64 k))
	0.5b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)))) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))
	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))))
	0.6b	(.f64 (pow.f64 (.f64 2 PI.f64) (.f64 1/2 (-.f64 1 k))) (/.f64 (pow.f64 n (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
	1.1b	(.f64 (/.f64 (pow.f64 (.f64 2 PI.f64) (.f64 1/2 (-.f64 1 k))) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 n (*.f64 1/2 (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))
	0.8b	(.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 k))))
▶	0.5b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
	0.8b	(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4)))) (sqrt.f64 k))

Compiler

Compiled 2352 to 1634 computations (30.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
0.3b	(.f64 n (.f64 2 PI.f64))
0.3b	(.f64 n (.f64 2 PI.f64))
0.4b	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

rewrite526.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

284×	`times-frac_binary64`
126×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
111×	`sqrt-prod_binary64`
33×	`add-exp-log_binary64`
28×	`unpow-prod-down_binary64` `sqr-pow_binary64`

Counts

4 → 241

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
5.0ms	(.f64 n (.f64 2 PI.f64))
5.0ms	(.f64 n (.f64 2 PI.f64))
3.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 7593 to 4927 computations (35.1% saved)

series69.0ms (0.3%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

39.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
9.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
8.0ms	(.f64 n (.f64 2 PI.f64))
8.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 904 to 698 computations (22.8% saved)

simplify392.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

841×	`associate-/l*_binary64`
386×	`associate-/l/_binary64`
284×	`associate-*l/_binary64`
269×	`associate-/r/_binary64`
224×	`associate-/r*_binary64`

Counts

256 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	397	11938
1	856	11654
2	2335	11425
3	4521	11425
4	4994	11425
5	4961	11425

prune477.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	227	5	232
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	233	9	242

Error

Counts

242 → 9

Alt Table

Status	Error	Program
	23.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n PI.f64)) (-.f64 (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (.f64 k k) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 PI.f64))) 2))))) (+.f64 (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 PI.f64))) (.f64 k (sqrt.f64 2)))) (.f64 1/48 (.f64 (pow.f64 k 3) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 PI.f64))) 3))))))) (sqrt.f64 k))
▶	0.5b	(.f64 (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
	0.7b	(.f64 (/.f64 (/.f64 1 (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (pow.f64 (.f64 2 PI.f64) (.f64 1/2 (-.f64 1 k))) (/.f64 (pow.f64 n (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
	0.9b	(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (fabs.f64 (cbrt.f64 k))) (/.f64 (/.f64 1 (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 (cbrt.f64 k))))
	0.7b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2)))))
	0.8b	(.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 k))))
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4)))) (sqrt.f64 k))

Compiler

Compiled 5411 to 3192 computations (41% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
0.2b	(.f64 (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite4.0s (18.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

3158×	`times-frac_binary64`
2271×	`sqrt-prod_binary64`
2169×	`add-sqr-sqrt_binary64`
1135×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
478×	`unpow-prod-down_binary64`

Counts

4 → 1673

Calls

4 calls:

1.0s	(.f64 (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
28.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
15.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 51966 to 28460 computations (45.2% saved)

series158.0ms (0.7%)

Error

Counts

4 → 21

Calls

4 calls:

49.0ms	(.f64 (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
49.0ms	(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
34.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 2066 to 1588 computations (23.1% saved)

simplify1.6s (7.4%)

Algorithm

1×	egg-herbie

Rules

877×	`associate-/l*_binary64`
460×	`associate-/l/_binary64`
353×	`*-commutative_binary64`
295×	`associate-*r/_binary64`
283×	`associate-*l/_binary64`

Counts

1694 → 1464

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1217	95888
1	3464	94628
2	5249	94628

prune1.5s (7.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1462	2	1464
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	1464	9	1473

Error

Counts

1473 → 9

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (.f64 (pow.f64 (/.f64 1 k) 1/4) (.f64 (sqrt.f64 PI.f64) (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 PI.f64 2)))))))))
▶	0.5b	(.f64 (.f64 (sqrt.f64 PI.f64) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
✓	0.5b	(.f64 (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
	0.7b	(.f64 (/.f64 (/.f64 1 (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (pow.f64 (.f64 2 PI.f64) (.f64 1/2 (-.f64 1 k))) (/.f64 (pow.f64 n (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
	0.9b	(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (fabs.f64 (cbrt.f64 k))) (/.f64 (/.f64 1 (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 (cbrt.f64 k))))
	0.7b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2)))))
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4)))) (sqrt.f64 k))

Compiler

Compiled 32354 to 17376 computations (46.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sqrt.f64 PI.f64) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
0.2b	(*.f64 (sqrt.f64 PI.f64) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
0.3b	(/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
1.0b	(sqrt.f64 PI.f64)

rewrite2.5s (11.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

2052×	`times-frac_binary64`
1597×	`sqrt-prod_binary64`
1075×	`add-sqr-sqrt_binary64`
920×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
728×	`associate-r_binary64`

Counts

4 → 1238

Calls

4 calls:

118.0ms	(*.f64 (sqrt.f64 PI.f64) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
99.0ms	(.f64 (.f64 (sqrt.f64 PI.f64) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
17.0ms	(/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 40771 to 22789 computations (44.1% saved)

series159.0ms (0.8%)

Error

Counts

4 → 21

Calls

4 calls:

53.0ms	(*.f64 (sqrt.f64 PI.f64) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
51.0ms	(.f64 (.f64 (sqrt.f64 PI.f64) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
29.0ms	(/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2073 to 1588 computations (23.4% saved)

simplify1.2s (5.5%)

Algorithm

1×	egg-herbie

Rules

845×	`associate-/l*_binary64`
349×	`*-commutative_binary64`
335×	`associate-/l/_binary64`
325×	`times-frac_binary64`
311×	`associate-*r/_binary64`

Counts

1259 → 1096

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1073	53360
1	2807	52041
2	4856	52000
3	4990	52000

prune1.2s (5.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1095	1	1096
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	1097	8	1105

Error

Counts

1105 → 8

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 (.f64 2 PI.f64) (/.f64 k 2))) (*.f64 (sqrt.f64 PI.f64) (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))))) (sqrt.f64 k))
	0.5b	(.f64 (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (.f64 (pow.f64 (/.f64 1 k) 1/4) (.f64 (sqrt.f64 PI.f64) (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 PI.f64 2)))))))))
	0.5b	(.f64 (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (*.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
	0.7b	(.f64 (/.f64 (/.f64 1 (pow.f64 n (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 PI.f64 2) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (pow.f64 (.f64 2 PI.f64) (.f64 1/2 (-.f64 1 k))) (/.f64 (pow.f64 n (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)))
	0.9b	(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (fabs.f64 (cbrt.f64 k))) (/.f64 (/.f64 1 (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 (cbrt.f64 k))))
	0.7b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2)))))

Compiler

Compiled 19757 to 11044 computations (44.1% saved)

regimes3.7s (17.4%)

Accuracy

Total 0.4b remaining (94.2%)

Threshold costs 0.4b (94.2%)

Compiler

Compiled 70557 to 52318 computations (25.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	21	41
2	21	41

end1.0ms (0%)

Compiler: Compiled 27 to 21 computations (22.2% saved)

sample2.6s (12.3%)

Algorithm

1×

intervals

Results

615.0ms	8000×	body	128	valid
610.0ms	1321×	body	1024	nan
319.0ms	2328×	body	128	overflowed
210.0ms	677×	body	512	nan
60.0ms	345×	body	256	nan
52.0ms	964×	body	128	nan
21.0ms	240×	body	128	invalid

Compiler

Compiled 273 to 206 computations (24.5% saved)

Details

analyze442.0ms (2.1%)

sample72.0ms (0.3%)

simplify51.0ms (0.2%)

prune5.0ms (0%)

localize10.0ms (0%)

rewrite206.0ms (1%)

series101.0ms (0.5%)

simplify138.0ms (0.7%)

prune131.0ms (0.6%)

localize11.0ms (0.1%)

rewrite526.0ms (2.5%)

series69.0ms (0.3%)

simplify392.0ms (1.9%)

prune477.0ms (2.3%)

localize17.0ms (0.1%)

rewrite4.0s (18.8%)

series158.0ms (0.7%)

simplify1.6s (7.4%)

prune1.5s (7.1%)

localize21.0ms (0.1%)

rewrite2.5s (11.8%)

series159.0ms (0.8%)

simplify1.2s (5.5%)

prune1.2s (5.7%)

regimes3.7s (17.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.6s (12.3%)

Profiling