Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze246.0ms (2.6%)

Memory

-1.5MiB live, 152.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
50%	25%	25%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
50%	25%	25%	0.1%	0%	50%	0%	6
51.6%	25%	23.4%	0.1%	0%	51.5%	0%	7
52.5%	25%	22.6%	0.1%	0%	52.3%	0%	8
53.8%	25%	21.5%	0.1%	0%	53.5%	0%	9
54.5%	25%	20.9%	0.1%	0%	54%	0%	10
55.3%	25%	20.2%	0.1%	0%	54.7%	0%	11
55.7%	25%	19.9%	0.1%	0%	55.1%	0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.3s (35.4%)

Memory

51.7MiB live, 3 553.3MiB allocated

Samples

1.2s	8 256×	0	valid
748.0ms	3 466×	1	invalid
469.0ms	1 835×	1	exit
206.0ms	402×	2	invalid
42.0ms	444×	0	invalid
28.0ms	241×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 2.0s

ival-pow: 578.0ms (28.9% of total)

ival-mult: 417.0ms (20.8% of total)

ival-sqrt: 281.0ms (14% of total)

ival-div: 269.0ms (13.4% of total)

ival-sub: 169.0ms (8.4% of total)

adjust: 158.0ms (7.9% of total)

ival-pi: 94.0ms (4.7% of total)

exact: 17.0ms (0.8% of total)

ival-true: 12.0ms (0.6% of total)

ival-assert: 7.0ms (0.3% of total)

Bogosity

explain361.0ms (3.8%)

Memory

-11.6MiB live, 466.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
3	87	(1.360082097065034e-178 2.259419131699051e-128)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	-	`k`
0	0	-	-	`n`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	90	26

Confusion

	Predicted +	Predicted -
+	3	0
-	87	166

Precision

0.03333333333333333

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	0	0
-	87	26	140

Precision?

0.02586206896551724

Recall?

1.0

Freqs

test

number	freq
0	166
1	90

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

73.0ms

512×

valid

Compiler

Compiled 236 to 98 computations (58.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-sub: 17.0ms (31.4% of total)

ival-pow: 11.0ms (20.3% of total)

ival-div: 10.0ms (18.5% of total)

ival-mult: 9.0ms (16.6% of total)

ival-sqrt: 4.0ms (7.4% of total)

ival-pi: 2.0ms (3.7% of total)

ival-true: 1.0ms (1.8% of total)

exact: 1.0ms (1.8% of total)

ival-assert: 0.0ms (0% of total)

preprocess57.0ms (0.6%)

Memory

32.6MiB live, 68.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	82	74
2	193	74
3	383	74
4	607	74
5	878	74
6	1047	74
7	1230	74
8	1285	74
9	1309	74
10	1327	74
11	1331	74
12	1331	74
0	13	16
0	22	16
1	37	14
2	54	14
3	75	14
4	93	14
5	108	14
6	129	14
7	156	14
8	165	14
9	168	14
0	168	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Outputs

(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

(/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify43.0ms (0.5%)

Memory

-43.9MiB live, 7.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	512	(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)

Outputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)

localize51.0ms (0.5%)

Memory

23.8MiB live, 62.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1640625	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.17112110413510145	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.25	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.26953125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Samples

41.0ms

256×

valid

Compiler

Compiled 110 to 28 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 15.0ms (48.9% of total)

ival-pow: 6.0ms (19.6% of total)

ival-div: 4.0ms (13.1% of total)

ival-sqrt: 2.0ms (6.5% of total)

ival-pi: 1.0ms (3.3% of total)

ival-sub: 1.0ms (3.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series89.0ms (0.9%)

Memory

10.7MiB live, 166.7MiB allocated

Counts

6 → 27

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))

Outputs
1/2
(+ 1/2 (* -1/2 k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* 2 (* n (PI)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))

Calls

6 calls:

Time	Variable		Point	Expression
51.0ms	n	@	0	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
22.0ms	n	@	-inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
8.0ms	n	@	inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	-inf	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	0	((/ (- 1 k) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

simplify138.0ms (1.5%)

Memory

-27.7MiB live, 167.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	517
1	345	504
2	1013	460
3	3349	433
4	5543	427
0	8350	412

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/2 k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* 2 (* n (PI)))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 k))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) k) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (.f64 k k) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))))) (.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))) k)
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 k (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) k) (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 k (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/48 binary64) k) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1/8 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))) k (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
(* -1/2 k)
(*.f64 #s(literal -1/2 binary64) k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* 2 (* n (PI)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))

rewrite141.0ms (1.5%)

Memory

10.4MiB live, 206.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4474	38
0	8599	37

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

6 → 419

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))

Outputs
(.f64 (/.f64 (.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (neg.f64 k) k #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) k))
(.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 k k k) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 k k k)))
(.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (fma.f64 k k k) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 k k k) (-.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 #s(literal -1 binary64) (.f64 k k))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -1/2 binary64))
(*.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)) #s(literal 1/4 binary64))
(.f64 (.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 k k) #s(literal 1/4 binary64))) (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal 1/4 binary64) (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k)))
(*.f64 #s(literal -1/2 binary64) (-.f64 k #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64))
(*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 k k k) #s(literal 2 binary64) #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (-.f64 k #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(.f64 #s(literal -1 binary64) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 2 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) k) (*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 k k) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 #s(literal -1 binary64) (*.f64 k k))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) k))
(/.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64)))) #s(literal -1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 k k)) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal -1/2 binary64)) (-.f64 k #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal -1/2 binary64)) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 k k)) #s(literal 1/2 binary64)) (-.f64 k #s(literal 1 binary64)))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1 binary64) (.f64 k k))) (-.f64 k #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 k #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) k))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 k k) #s(literal 1/4 binary64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 k) k #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (fma.f64 (fma.f64 k k k) #s(literal 2 binary64) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 k #s(literal -1/2 binary64)) (.f64 k #s(literal -1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)))
(/.f64 (/.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 k #s(literal -1/2 binary64)) (.f64 k #s(literal -1/2 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) (-.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))
(/.f64 (+.f64 (pow.f64 (/.f64 #s(literal -4 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -3 binary64)) (pow.f64 (/.f64 #s(literal -4 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -3 binary64))) (fma.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 k k) #s(literal 1/4 binary64)) (.f64 k #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (neg.f64 k) k #s(literal 1 binary64)) #s(literal 1/2 binary64))) (-.f64 k #s(literal 1 binary64)))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 k k) #s(literal 1/4 binary64)))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(/.f64 (neg.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64) (.f64 #s(literal -2 binary64) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal -4 binary64) (.f64 #s(literal -2 binary64) (-.f64 k #s(literal 1 binary64)))) #s(literal 8 binary64))
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal 2 binary64) (.f64 #s(literal -2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -4 binary64))
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal 4 binary64) (.f64 #s(literal -2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal -8 binary64))
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal -4 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -2 binary64)) (.f64 #s(literal -2 binary64) (/.f64 #s(literal -4 binary64) (-.f64 k #s(literal 1 binary64)))))
(/.f64 (fma.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -2 binary64) (.f64 #s(literal -4 binary64) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))) #s(literal 8 binary64))
(/.f64 (fma.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -4 binary64) (*.f64 #s(literal -4 binary64) (-.f64 k #s(literal 1 binary64)))) #s(literal 16 binary64))
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(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/4 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (.f64 (.f64 k k) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) k) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)) #s(literal -1 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 k k) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (fma.f64 (fma.f64 k k k) #s(literal 2 binary64) #s(literal 2 binary64)) #s(literal -1 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (pow.f64 k #s(literal 3 binary64)) (fma.f64 (fma.f64 k k k) #s(literal 2 binary64) #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 k (/.f64 k (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (/.f64 (pow.f64 k #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) k #s(literal 1 binary64))) #s(literal 2 binary64))))
(/.f64 (.f64 (sqrt.f64 n) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 1/2 binary64)))
(/.f64 (.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 1/2 binary64)))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 n)) (pow.f64 n (*.f64 #s(literal 1/2 binary64) k)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (neg.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 (.f64 k #s(literal 1/4 binary64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 k #s(literal 1/4 binary64))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -4 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 k #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (.f64 (log.f64 (exp.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 k #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) k)))
(exp.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(exp.f64 (.f64 (.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)) (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))

eval90.0ms (1%)

Memory: -14.4MiB live, 140.6MiB allocated
Compiler: Compiled 10 078 to 1 565 computations (84.5% saved)

prune18.0ms (0.2%)

Memory

5.0MiB live, 43.7MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	421	16	437
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	422	16	438

Accuracy

100.0%

Counts

438 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	47.1%	(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
	47.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
	46.5%	(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
▶	55.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
	47.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
	47.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Compiler

Compiled 642 to 514 computations (19.9% saved)

simplify58.0ms (0.6%)

Memory

-19.4MiB live, 24.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	128	(*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
cost-diff	6464	(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	128	(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
cost-diff	0	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
cost-diff	0	(*.f64 (PI.f64) #s(literal 2 binary64))
cost-diff	0	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
cost-diff	5824	(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	330
0	76	327
1	118	319
2	175	315
3	236	315
4	315	315
5	460	315
6	612	315
7	745	315
8	858	315
9	1014	315
10	1194	315
11	1461	315
12	1644	315
13	1669	315
14	1683	315
15	1695	315
16	1695	315
0	1695	303

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))
(sqrt.f64 k)
k
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))
#s(literal -1/2 binary64)
(-.f64 #s(literal 1 binary64) k)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
(*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) k)

Outputs
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) (sqrt.f64 k))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(PI.f64)
#s(literal 2 binary64)
(.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) k)) (sqrt.f64 k))
(sqrt.f64 k)
k
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))
(sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(*.f64 #s(literal -1/2 binary64) k)
#s(literal -1/2 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))))
(/.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64)))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(PI.f64)
#s(literal 2 binary64)
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(fma.f64 #s(literal 1/2 binary64) k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(-.f64 #s(literal 1 binary64) k)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
n
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(PI.f64)
#s(literal 2 binary64)
(*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))
(fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(-.f64 #s(literal 1 binary64) k)

localize121.0ms (1.3%)

Memory

5.4MiB live, 200.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.19140625	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.19921875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.2265625	(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))
accuracy	15.257441042433733	(PI.f64)
accuracy	0.19140625	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.19218304673804268	(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
accuracy	0.19921875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	15.257441042433733	(PI.f64)
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.19921875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	15.257441042433733	(PI.f64)
accuracy	31.182109754090284	#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
accuracy	0.3405075195368841	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	6.4156169539332035	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	15.257441042433733	(PI.f64)
accuracy	17.901000441024806	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
accuracy	0.08203125	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
accuracy	0.140625	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
accuracy	0.19140625	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	15.257441042433733	(PI.f64)

Samples

69.0ms	193×	0	valid
20.0ms	63×	0	exit

Compiler

Compiled 640 to 88 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 20.0ms (32% of total)

ival-pow: 19.0ms (30.4% of total)

ival-sqrt: 9.0ms (14.4% of total)

ival-div: 7.0ms (11.2% of total)

ival-pow2: 3.0ms (4.8% of total)

ival-pi: 1.0ms (1.6% of total)

ival-sub: 1.0ms (1.6% of total)

exact: 1.0ms (1.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series73.0ms (0.8%)

Memory

10.6MiB live, 129.9MiB allocated

Counts

22 → 87

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))
(PI.f64)
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))

Outputs
1
(+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2))))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/2 (* k (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/2 (* (log (* 2 (* n (PI)))) (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))) (* 1/2 (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt (/ (* n (PI)) k))
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
-1/2
(- (* 1/2 k) 1/2)
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* k (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* (sqrt (pow k 3)) (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
1/4
(+ 1/4 (* -1/4 k))
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
1/2
(+ 1/2 (* -1/2 k))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(sqrt (pow (* 2 (* n (PI))) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
(* 1/2 k)
(* k (- 1/2 (* 1/2 (/ 1 k))))
(pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2)
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2))
(* -1/4 k)
(* k (- (* 1/4 (/ 1 k)) 1/4))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
(* -1 (* k (- (* 1/2 (/ 1 k)) 1/2)))
(pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2)
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2))
(* -1 (* k (- 1/4 (* 1/4 (/ 1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(sqrt (exp (* k (+ (log n) (log (* 2 (PI)))))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
(pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(sqrt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
(pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(sqrt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	n	@	-inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (* -1/2 (- 1 k)) (pow (pow (* n (* (PI) 2)) (* 1/4 (- 1 k))) 2) (* (/ 1 (sqrt k)) (pow (pow (* n (* (PI) 2)) (* 1/4 (- 1 k))) 2)) (* 1/4 (- 1 k)) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))
16.0ms	n	@	inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (* -1/2 (- 1 k)) (pow (pow (* n (* (PI) 2)) (* 1/4 (- 1 k))) 2) (* (/ 1 (sqrt k)) (pow (pow (* n (* (PI) 2)) (* 1/4 (- 1 k))) 2)) (* 1/4 (- 1 k)) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))
13.0ms	n	@	0	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (* -1/2 (- 1 k)) (pow (pow (* n (* (PI) 2)) (* 1/4 (- 1 k))) 2) (* (/ 1 (sqrt k)) (pow (pow (* n (* (PI) 2)) (* 1/4 (- 1 k))) 2)) (* 1/4 (- 1 k)) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))
10.0ms	k	@	-inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (* -1/2 (- 1 k)) (pow (pow (* n (* (PI) 2)) (* 1/4 (- 1 k))) 2) (* (/ 1 (sqrt k)) (pow (pow (* n (* (PI) 2)) (* 1/4 (- 1 k))) 2)) (* 1/4 (- 1 k)) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))
8.0ms	k	@	0	((pow (pow (* n (* (PI) 2)) k) 1/2) (sqrt (* n (* (PI) 2))) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (* -1/2 (- 1 k)) (pow (pow (* n (* (PI) 2)) (* 1/4 (- 1 k))) 2) (* (/ 1 (sqrt k)) (pow (pow (* n (* (PI) 2)) (* 1/4 (- 1 k))) 2)) (* 1/4 (- 1 k)) (PI) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))

simplify161.0ms (1.7%)

Memory

1.7MiB live, 160.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	374	1925
1	1152	1839
2	4092	1784
0	8123	1737

Stop Event

1×	iter limit
1×	node limit

Counts

87 → 87

Calls

Call 1

Inputs
1
(+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2))))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/2 (* k (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/2 (* (log (* 2 (* n (PI)))) (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))) (* 1/2 (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt (/ (* n (PI)) k))
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
-1/2
(- (* 1/2 k) 1/2)
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* k (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* (sqrt (pow k 3)) (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
1/4
(+ 1/4 (* -1/4 k))
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
1/2
(+ 1/2 (* -1/2 k))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(sqrt (pow (* 2 (* n (PI))) k))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
(* 1/2 k)
(* k (- 1/2 (* 1/2 (/ 1 k))))
(pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2)
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (- 1 k)))) 2))
(* -1/4 k)
(* k (- (* 1/4 (/ 1 k)) 1/4))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
(* -1 (* k (- (* 1/2 (/ 1 k)) 1/2)))
(pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2)
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))) 2))
(* -1 (* k (- 1/4 (* 1/4 (/ 1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(sqrt (exp (* k (+ (log n) (log (* 2 (PI)))))))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
(pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2)
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))) 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(sqrt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
(pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(sqrt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) k) (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1 binary64))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2))))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 (.f64 k #s(literal 1/4 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) #s(literal 1 binary64))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/2 (* k (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/2 (* (log (* 2 (* n (PI)))) (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))) (* 1/2 (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) k) (fma.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal 1/6 binary64))) k (.f64 #s(literal 1/4 binary64) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)))) (.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1/2 binary64))) k #s(literal 1 binary64))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) k (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64))) (sqrt.f64 #s(literal 2 binary64)))) k (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) k (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt k)
(sqrt.f64 k)
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 #s(literal -1/2 binary64) k) (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) k) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)))) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) k)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
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(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (.f64 (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k)))
(sqrt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 n k)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2)
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n))))
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))) 2))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (.f64 (/.f64 n k) (PI.f64)) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 n k)))) (sqrt.f64 #s(literal 2 binary64)))
(exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (.f64 (+.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (log.f64 n)) (-.f64 #s(literal 1 binary64) k)))
(sqrt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(sqrt.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k)) (pow.f64 (.f64 #s(literal -2 binary64) (PI.f64)) k)))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2)
(sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (*.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))
(* (sqrt (/ 1 k)) (pow (exp (* 1/4 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))) 2))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 #s(literal 1 binary64) k)) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (.f64 (/.f64 (PI.f64) (pow.f64 (.f64 #s(literal -2 binary64) (PI.f64)) k)) (/.f64 (/.f64 n k) (pow.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 k))))))
(exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(pow.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (-.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))

rewrite184.0ms (1.9%)

Memory

11.8MiB live, 205.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	211
0	76	198
1	260	183
2	1459	183
0	8132	183

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

22 → 1 399

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))
(PI.f64)
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))

Outputs
(.f64 (fabs.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k)) (fabs.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
(.f64 (fabs.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (fabs.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 (pow.f64 #s(literal 2 binary64) k)))
(.f64 (sqrt.f64 (pow.f64 #s(literal 2 binary64) k)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) n) k)))
(.f64 (pow.f64 (pow.f64 (pow.f64 n k) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) (.f64 #s(literal 1/2 binary64) k)) (pow.f64 (PI.f64) (.f64 #s(literal 1/2 binary64) k)))
(.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) k)) (pow.f64 (PI.f64) (.f64 #s(literal 1/2 binary64) k)))
(.f64 (pow.f64 (PI.f64) (.f64 #s(literal 1/2 binary64) k)) (pow.f64 (.f64 #s(literal 2 binary64) n) (.f64 #s(literal 1/2 binary64) k)))
(.f64 (pow.f64 (PI.f64) (.f64 #s(literal 1/2 binary64) k)) (pow.f64 (.f64 n #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k))
(.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k) (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))
(.f64 (pow.f64 (sqrt.f64 n) k) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) k))
(.f64 (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (sqrt.f64 n) k))
(.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) k) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (*.f64 k #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k) #s(literal 1 binary64))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (fma.f64 #s(literal 1/2 binary64) k (*.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal 2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) k)) #s(literal 1/2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (fma.f64 #s(literal 1/2 binary64) k (.f64 #s(literal 1/2 binary64) k)) #s(literal 1/2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k))
(fabs.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(fabs.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k))
(exp.f64 (fma.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal 1/4 binary64) (.f64 (log.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 n))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) n)))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
(exp.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) #s(literal 1/4 binary64) (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) #s(literal 1/2 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (.f64 (PI.f64) n))))
(.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))
(exp.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (PI.f64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(.f64 (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (neg.f64 (sqrt.f64 n)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)))
(.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))
(.f64 (sqrt.f64 (/.f64 n k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) #s(literal 1 binary64)))
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
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(.f64 (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64))
(pow.f64 (exp.f64 (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) (log.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)))
(pow.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 k k))) (pow.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3 binary64)))) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) k)) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (neg.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)) (neg.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)) (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) k) (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1 binary64))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) k))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k))
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) k)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (neg.f64 (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (neg.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)) #s(literal -1 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) k)))
(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) k) #s(literal -1 binary64))) (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (/.f64 (*.f64 k k) (+.f64 #s(literal 1 binary64) k))))
(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (fma.f64 k k k) #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (/.f64 (pow.f64 k #s(literal 3 binary64)) (+.f64 (fma.f64 k k k) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64))
(/.f64 (neg.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) k))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k))))
(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (neg.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64))) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (neg.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64))))
(exp.f64 (neg.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64))))
(exp.f64 (neg.f64 (/.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)) (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)))))
(exp.f64 (fma.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)) (.f64 (log.f64 n) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))))
(exp.f64 (fma.f64 (log.f64 n) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/2 binary64)))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (fma.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1/2 binary64))) (-.f64 #s(literal 1 binary64) k)))

eval330.0ms (3.5%)

Memory: 14.9MiB live, 322.5MiB allocated
Compiler: Compiled 33 634 to 4 360 computations (87% saved)

prune220.0ms (2.3%)

Memory

-40.3MiB live, 134.5MiB allocated

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	1 331	19	1 350
Fresh	8	3	11
Picked	4	1	5
Done	0	0	0
Total	1 343	23	1 366

Accuracy

100.0%

Counts

1 366 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	55.0%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
▶	47.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
	47.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	89.9%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)))
	38.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	38.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
▶	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
▶	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
▶	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))

Compiler

Compiled 1 146 to 935 computations (18.4% saved)

simplify144.0ms (1.5%)

Memory

16.5MiB live, 54.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
cost-diff	320	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))
cost-diff	0	(/.f64 (*.f64 (PI.f64) n) k)
cost-diff	0	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
cost-diff	0	(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
cost-diff	0	(/.f64 (*.f64 (PI.f64) n) k)
cost-diff	0	(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
cost-diff	0	(*.f64 #s(literal 2 binary64) (PI.f64))
cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
cost-diff	0	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	346
0	81	346
1	122	334
2	175	334
3	233	334
4	271	334
5	316	334
6	392	334
7	582	334
8	1085	334
9	2078	334
10	2561	334
11	3156	334
12	3304	334
13	3348	334
14	3362	334
15	3384	334
16	3384	334
17	3400	334
18	3421	334
19	3421	334
20	3525	334
21	4126	334
0	4126	328

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
(.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
(/.f64 k (*.f64 (PI.f64) n))
k
(*.f64 (PI.f64) n)
(PI.f64)
n
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
n
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)

Outputs
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k)))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 2 binary64))
#s(literal 2 binary64)
(PI.f64)
n
(sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
(sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k))
(.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(PI.f64)
n
k
#s(literal 2 binary64)
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(/.f64 (*.f64 (PI.f64) n) k)
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(PI.f64)
n
k
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(/.f64 k (*.f64 (PI.f64) n))
(/.f64 k (*.f64 n (PI.f64)))
k
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(PI.f64)
n
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(/.f64 #s(literal 1 binary64) #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))
(/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(PI.f64)
n
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)

localize203.0ms (2.1%)

Memory

16.0MiB live, 133.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.19921875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.35775375976844204	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	15.257441042433733	(PI.f64)
accuracy	17.991362967449437	#s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.3405075195368841	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))
accuracy	6.019760441742942	(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
accuracy	15.257441042433733	(PI.f64)
accuracy	17.901000441024806	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
accuracy	0.3522262695368841	(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	6.4156169539332035	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	15.257441042433733	(PI.f64)
accuracy	17.901000441024806	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.203125	(/.f64 (*.f64 (PI.f64) n) k)
accuracy	6.462247786637709	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
accuracy	15.257441042433733	(PI.f64)
accuracy	17.901000441024806	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
accuracy	0.08203125	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
accuracy	0.140625	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	15.257441042433733	(PI.f64)

Samples

103.0ms	193×	0	valid
38.0ms	63×	0	exit

Compiler

Compiled 633 to 97 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-div: 47.0ms (39.1% of total)

ival-mult: 39.0ms (32.4% of total)

ival-sqrt: 17.0ms (14.1% of total)

ival-pow: 13.0ms (10.8% of total)

ival-pi: 1.0ms (0.8% of total)

ival-sub: 1.0ms (0.8% of total)

exact: 1.0ms (0.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series114.0ms (1.2%)

Memory

-5.6MiB live, 70.8MiB allocated

Counts

23 → 63

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))))
(PI.f64)
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
#s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))

Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* 2 (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(sqrt (/ (* n (PI)) k))
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))
(+ (* -1/2 (* (/ (* k (log (* 2 (* n (PI))))) (sqrt 1/2)) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(+ (* k (- (* -1 (* k (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(sqrt (/ k (* n (PI))))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(* -1 (sqrt (/ (* n (PI)) k)))
(/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (/ 1 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))

Calls

6 calls:

Time	Variable		Point	Expression
39.0ms	n	@	inf	((/ (sqrt (* (* 2 (PI)) n)) (sqrt (* k (pow (* (* 2 (PI)) n) k)))) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/ (sqrt (/ (* (PI) n) k)) (sqrt 1/2)) (sqrt (/ (* (PI) n) k)) (* (sqrt 2) (/ 1 (sqrt (/ k (* (PI) n))))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt 2) (/ 1 (sqrt (/ k (* (PI) n)))) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k)))) (PI) (sqrt (/ k (* (PI) n))) (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (* (sqrt (/ 1 (* (PI) n))) (sqrt 1/2)))
36.0ms	k	@	0	((/ (sqrt (* (* 2 (PI)) n)) (sqrt (* k (pow (* (* 2 (PI)) n) k)))) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/ (sqrt (/ (* (PI) n) k)) (sqrt 1/2)) (sqrt (/ (* (PI) n) k)) (* (sqrt 2) (/ 1 (sqrt (/ k (* (PI) n))))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt 2) (/ 1 (sqrt (/ k (* (PI) n)))) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k)))) (PI) (sqrt (/ k (* (PI) n))) (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (* (sqrt (/ 1 (* (PI) n))) (sqrt 1/2)))
14.0ms	n	@	-inf	((/ (sqrt (* (* 2 (PI)) n)) (sqrt (* k (pow (* (* 2 (PI)) n) k)))) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/ (sqrt (/ (* (PI) n) k)) (sqrt 1/2)) (sqrt (/ (* (PI) n) k)) (* (sqrt 2) (/ 1 (sqrt (/ k (* (PI) n))))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt 2) (/ 1 (sqrt (/ k (* (PI) n)))) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k)))) (PI) (sqrt (/ k (* (PI) n))) (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (* (sqrt (/ 1 (* (PI) n))) (sqrt 1/2)))
13.0ms	n	@	0	((/ (sqrt (* (* 2 (PI)) n)) (sqrt (* k (pow (* (* 2 (PI)) n) k)))) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/ (sqrt (/ (* (PI) n) k)) (sqrt 1/2)) (sqrt (/ (* (PI) n) k)) (* (sqrt 2) (/ 1 (sqrt (/ k (* (PI) n))))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt 2) (/ 1 (sqrt (/ k (* (PI) n)))) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k)))) (PI) (sqrt (/ k (* (PI) n))) (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (* (sqrt (/ 1 (* (PI) n))) (sqrt 1/2)))
6.0ms	k	@	-inf	((/ (sqrt (* (* 2 (PI)) n)) (sqrt (* k (pow (* (* 2 (PI)) n) k)))) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/ (sqrt (/ (* (PI) n) k)) (sqrt 1/2)) (sqrt (/ (* (PI) n) k)) (* (sqrt 2) (/ 1 (sqrt (/ k (* (PI) n))))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt 2) (/ 1 (sqrt (/ k (* (PI) n)))) (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/ 1 (sqrt k)) (sqrt k) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k)))) (PI) (sqrt (/ k (* (PI) n))) (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (* (sqrt (/ 1 (* (PI) n))) (sqrt 1/2)))

simplify198.0ms (2.1%)

Memory

-5.8MiB live, 227.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	295	1545
1	914	1452
2	3339	1375
0	8134	1344

Stop Event

1×	iter limit
1×	node limit

Counts

63 → 63

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* 2 (/ (* n (PI)) k))
(/ (* n (PI)) k)
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (pow k 3)) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* -1 (* (sqrt k) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* -1 (* (sqrt (pow k 3)) (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))))))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(sqrt (/ (* n (PI)) k))
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (/ 1 (sqrt 1/2)))
(+ (* -1/2 (* (/ (* k (log (* 2 (* n (PI))))) (sqrt 1/2)) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(+ (* k (- (* -1 (* k (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(+ (* k (- (* k (- (* -1 (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (+ (* -1/16 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))) (* 1/48 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2)))))))) (+ (* -1/4 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))) (* 1/8 (* (sqrt (* n (PI))) (/ (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))))))) (* 1/2 (* (sqrt (* n (PI))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (* n (PI))) (/ 1 (sqrt 1/2))))
(sqrt (/ k (* n (PI))))
(* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(+ (* k (+ (* 1/2 (* (sqrt (/ 1 (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* k (+ (* 1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* 1/8 (* (sqrt (/ 1 (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 1/2)))))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))))
(* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2)))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(/ 1 (exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(exp (* -1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* (sqrt (* n (PI))) (sqrt 2))
(* 2 (* n (PI)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(exp (* -1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))))
(/ 1 (exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* -1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(* -1 (sqrt (/ (* n (PI)) k)))
(/ 1 (exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(exp (* -1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* (sqrt (/ 1 (* n (PI)))) (* (pow (sqrt -1) 2) (sqrt 1/2)))

Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 k k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (.f64 (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (PI.f64) n)) #s(literal -1/2 binary64))))) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))) (fma.f64 (.f64 #s(literal 1/2 binary64) n) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (PI.f64)) (fma.f64 (.f64 #s(literal 1/4 binary64) n) (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (PI.f64) k)) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (PI.f64) n)) #s(literal -1/3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (PI.f64) n) k))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (PI.f64) n)) #s(literal -1/2 binary64))))) k (.f64 (.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))) (.f64 k k) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))))) k (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
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rewrite188.0ms (2%)

Memory

11.1MiB live, 205.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	262
0	81	243
1	274	227
2	1496	221
0	8291	218

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

23 → 844

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))
(/.f64 (*.f64 (PI.f64) n) k)
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(/.f64 #s(literal 1 binary64) #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))))
(PI.f64)
(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
#s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64)))

Outputs
(.f64 (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))) (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))))
(.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(.f64 (pow.f64 (.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(.f64 (pow.f64 (sqrt.f64 (/.f64 k (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) n)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) #s(literal 1/2 binary64)) (pow.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (.f64 n (PI.f64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(.f64 (pow.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)))) #s(literal -1 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))))
(.f64 (pow.f64 (.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) #s(literal -1 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))))
(.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(.f64 (sqrt.f64 (/.f64 n k)) (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k))))
(.f64 (sqrt.f64 n) (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 n (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k))))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))
(.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (pow.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))))
(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (neg.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))))) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)))))
(/.f64 (.f64 #s(literal -1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))) (.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)))))
(/.f64 (.f64 #s(literal -1 binary64) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) #s(literal -1 binary64)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64))) (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64))) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k))))
(/.f64 (sqrt.f64 (.f64 #s(literal -2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 (neg.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(/.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64))))
(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k))))
(/.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
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(exp.f64 (fma.f64 (neg.f64 (log.f64 (.f64 n (PI.f64)))) #s(literal 1/2 binary64) (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 (neg.f64 (log.f64 (.f64 n (PI.f64)))) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal 1/2 binary64)))

eval149.0ms (1.6%)

Memory: 18.5MiB live, 254.3MiB allocated
Compiler: Compiled 26 541 to 3 589 computations (86.5% saved)

prune76.0ms (0.8%)

Memory

-12.4MiB live, 181.7MiB allocated

Pruning

54 alts after pruning (49 fresh and 5 done)

	Pruned	Kept	Total
New	900	36	936
Fresh	4	13	17
Picked	1	4	5
Done	0	1	1
Total	905	54	959

Accuracy

100.0%

Counts

959 → 54

Alt Table

Click to see full alt table

Status	Accuracy	Program
	55.0%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	47.7%	(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
	47.6%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
	47.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))))
	47.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
✓	47.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
	47.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	47.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (/ 1 (pow ( n (* (PI) 2)) (* -1/2 (- 1 k)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 1/2 binary64)))))
	89.9%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
	90.0%	(sqrt.f64 (.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 k)))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)))
▶	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
	38.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
	38.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
▶	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
▶	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
	38.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64))))))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (PI.f64)))))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n))))))
✓	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
▶	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
✓	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
▶	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 1/2 binary64))))
	37.4%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) k) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))

Compiler

Compiled 2 723 to 2 239 computations (17.8% saved)

simplify74.0ms (0.8%)

Memory

12.7MiB live, 52.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))
cost-diff	0	(sqrt.f64 (*.f64 n (PI.f64)))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
cost-diff	256	(*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
cost-diff	0	(/.f64 (/.f64 k n) (neg.f64 (PI.f64)))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64)))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
cost-diff	896	(/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))
cost-diff	0	(/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)
cost-diff	0	(.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
cost-diff	0	(sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
cost-diff	0	(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	335
0	86	332
1	137	318
2	235	310
3	464	305
4	832	305
5	1327	305
6	1916	305
7	2170	305
8	2289	305
9	2388	305
10	2455	305
11	2465	305
12	2467	305
13	2471	305
0	2471	305

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
(.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
n
(/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64)))))
(/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))
#s(literal -2 binary64)
(/.f64 (/.f64 k n) (neg.f64 (PI.f64)))
(/.f64 k n)
k
n
(neg.f64 (PI.f64))
(PI.f64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
n
(PI.f64)
(*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(neg.f64 (sqrt.f64 k))
(sqrt.f64 k)
k
(neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))
(sqrt.f64 (/.f64 k (PI.f64)))
(/.f64 k (PI.f64))
k
(PI.f64)
(sqrt.f64 n)
n

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) n)
(*.f64 n #s(literal 2 binary64))
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
k
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(/.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)))
(sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
n
(/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)
(*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
k
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)))
(sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64)))))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
#s(literal -2 binary64)
(/.f64 (/.f64 k n) (neg.f64 (PI.f64)))
(/.f64 (/.f64 (neg.f64 k) (PI.f64)) n)
(/.f64 k n)
k
n
(neg.f64 (PI.f64))
(PI.f64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
n
(PI.f64)
(*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 k))
(neg.f64 (sqrt.f64 k))
(sqrt.f64 k)
k
(neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))
(/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))
(sqrt.f64 (/.f64 k (PI.f64)))
(/.f64 k (PI.f64))
k
(PI.f64)
(sqrt.f64 n)
n

localize211.0ms (2.2%)

Memory

-29.6MiB live, 220.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.2890625	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))
accuracy	0.31087875976844204	(/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))
accuracy	0.4342575195368841	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
accuracy	33.302710890406786	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
accuracy	0.25	(*.f64 n (PI.f64))
accuracy	0.3125	(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
accuracy	0.4271087890737681	(*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	33.302710890406786	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
accuracy	0.2660489236592897	(/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))
accuracy	0.27734375	(/.f64 (/.f64 k n) (neg.f64 (PI.f64)))
accuracy	14.095464034057082	(sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64)))))
accuracy	33.302710890406786	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
accuracy	0.234375	(.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
accuracy	0.3203125	(/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)
accuracy	14.095464034057082	(sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
accuracy	33.302710890406786	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
accuracy	0.12890625	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
accuracy	0.1640625	(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
accuracy	0.17112110413510145	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.25	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))

Samples

130.0ms

256×

valid

Compiler

Compiled 614 to 104 computations (83.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 106.0ms

ival-mult: 50.0ms (47.3% of total)

ival-sqrt: 21.0ms (19.9% of total)

ival-div: 17.0ms (16.1% of total)

ival-pow: 10.0ms (9.5% of total)

ival-neg: 3.0ms (2.8% of total)

ival-pi: 1.0ms (0.9% of total)

ival-add: 1.0ms (0.9% of total)

ival-sub: 1.0ms (0.9% of total)

exact: 1.0ms (0.9% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series51.0ms (0.5%)

Memory

18.8MiB live, 96.1MiB allocated

Counts

23 → 43

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
(.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
(/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)
(/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64)))))
(/.f64 (/.f64 k n) (neg.f64 (PI.f64)))
(*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(sqrt.f64 (*.f64 n (PI.f64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(*.f64 n (PI.f64))
(/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))

Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (PI) k))
(* -1 (/ k (* n (PI))))
(* (sqrt k) (sqrt 1/2))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ 1 k))
(sqrt (/ k (* n (PI))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* -1 (* (sqrt k) (* (pow (sqrt -1) 2) (sqrt 1/2))))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* 2 (* n (PI)))
(sqrt (* n (PI)))
(* n (PI))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (* (PI) 2) k))) (* n (/ (* (PI) 2) k)) (/ (* (PI) 2) k) (/ -2 (/ (/ k n) (neg (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ -2 (/ (/ k n) (neg (PI))))) (/ (/ k n) (neg (PI))) (* (neg (sqrt k)) (neg (sqrt 1/2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* n (PI))) (* (neg (sqrt k)) (neg (sqrt 1/2)))) (sqrt (* n (PI))) (/ 1 (/ (sqrt (/ k (PI))) (sqrt n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ 1 (/ (sqrt (/ k (PI))) (sqrt n)))) (sqrt 2) (sqrt (/ 1 k)) (* n (PI)) (/ (sqrt (/ k (PI))) (sqrt n)))
13.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (* (PI) 2) k))) (* n (/ (* (PI) 2) k)) (/ (* (PI) 2) k) (/ -2 (/ (/ k n) (neg (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ -2 (/ (/ k n) (neg (PI))))) (/ (/ k n) (neg (PI))) (* (neg (sqrt k)) (neg (sqrt 1/2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* n (PI))) (* (neg (sqrt k)) (neg (sqrt 1/2)))) (sqrt (* n (PI))) (/ 1 (/ (sqrt (/ k (PI))) (sqrt n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ 1 (/ (sqrt (/ k (PI))) (sqrt n)))) (sqrt 2) (sqrt (/ 1 k)) (* n (PI)) (/ (sqrt (/ k (PI))) (sqrt n)))
11.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (* (PI) 2) k))) (* n (/ (* (PI) 2) k)) (/ (* (PI) 2) k) (/ -2 (/ (/ k n) (neg (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ -2 (/ (/ k n) (neg (PI))))) (/ (/ k n) (neg (PI))) (* (neg (sqrt k)) (neg (sqrt 1/2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* n (PI))) (* (neg (sqrt k)) (neg (sqrt 1/2)))) (sqrt (* n (PI))) (/ 1 (/ (sqrt (/ k (PI))) (sqrt n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ 1 (/ (sqrt (/ k (PI))) (sqrt n)))) (sqrt 2) (sqrt (/ 1 k)) (* n (PI)) (/ (sqrt (/ k (PI))) (sqrt n)))
6.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (* (PI) 2) k))) (* n (/ (* (PI) 2) k)) (/ (* (PI) 2) k) (/ -2 (/ (/ k n) (neg (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ -2 (/ (/ k n) (neg (PI))))) (/ (/ k n) (neg (PI))) (* (neg (sqrt k)) (neg (sqrt 1/2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* n (PI))) (* (neg (sqrt k)) (neg (sqrt 1/2)))) (sqrt (* n (PI))) (/ 1 (/ (sqrt (/ k (PI))) (sqrt n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ 1 (/ (sqrt (/ k (PI))) (sqrt n)))) (sqrt 2) (sqrt (/ 1 k)) (* n (PI)) (/ (sqrt (/ k (PI))) (sqrt n)))
4.0ms	k	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (/ 1 k))) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (* (* 2 n) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* n (/ (* (PI) 2) k))) (* n (/ (* (PI) 2) k)) (/ (* (PI) 2) k) (/ -2 (/ (/ k n) (neg (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ -2 (/ (/ k n) (neg (PI))))) (/ (/ k n) (neg (PI))) (* (neg (sqrt k)) (neg (sqrt 1/2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* n (PI))) (* (neg (sqrt k)) (neg (sqrt 1/2)))) (sqrt (* n (PI))) (/ 1 (/ (sqrt (/ k (PI))) (sqrt n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ 1 (/ (sqrt (/ k (PI))) (sqrt n)))) (sqrt 2) (sqrt (/ 1 k)) (* n (PI)) (/ (sqrt (/ k (PI))) (sqrt n)))

simplify122.0ms (1.3%)

Memory

-3.1MiB live, 152.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	168	711
1	467	687
2	1446	638
3	2844	623
4	5287	623
0	8862	611

Stop Event

1×	iter limit
1×	node limit

Counts

43 → 43

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (PI) k))
(* -1 (/ k (* n (PI))))
(* (sqrt k) (sqrt 1/2))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(sqrt (/ (* n (PI)) k))
(sqrt (/ 1 k))
(sqrt (/ k (* n (PI))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* -1 (* (sqrt k) (* (pow (sqrt -1) 2) (sqrt 1/2))))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* 2 (* n (PI)))
(sqrt (* n (PI)))
(* n (PI))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))

Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64))))) k (.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) #s(literal 1/8 binary64) (.f64 (.f64 #s(literal -1/48 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64))))) k (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))) k (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))) k)
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(.f64 (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 k (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) k) #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(fma.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 k (fma.f64 (.f64 #s(literal -1/48 binary64) k) (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) (.f64 (.f64 (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(* 2 (/ (* n (PI)) k))
(.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))
(* 2 (/ (PI) k))
(*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))
(* -1 (/ k (* n (PI))))
(/.f64 (/.f64 (neg.f64 k) (PI.f64)) n)
(* (sqrt k) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 k))
(* (sqrt (/ (* n (PI)) k)) (/ 1 (sqrt 1/2)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt (/ (* n (PI)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt (/ 1 k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt (/ k (* n (PI))))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (* (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))) (pow (sqrt -1) 2)))
(.f64 (neg.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))) (sqrt.f64 #s(literal -2 binary64)))
(* -1 (* (sqrt k) (* (pow (sqrt -1) 2) (sqrt 1/2))))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 k))
(* (sqrt (/ 1 k)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* 2 (* n (PI)))
(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
(sqrt (* n (PI)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* n (PI))
(*.f64 n (PI.f64))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(pow.f64 (/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (pow (sqrt -1) 2) (sqrt 1/2))))
(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(sqrt.f64 (*.f64 n (PI.f64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))

rewrite190.0ms (2%)

Memory

-6.1MiB live, 272.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	274
0	86	253
1	290	236
2	1683	228
0	8277	228

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

23 → 1 074

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
(.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
(/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)
(/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64)))))
(/.f64 (/.f64 k n) (neg.f64 (PI.f64)))
(*.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(sqrt.f64 (*.f64 n (PI.f64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(*.f64 n (PI.f64))
(/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (.f64 #s(literal -1 binary64) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (*.f64 n #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (*.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
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(exp.f64 (*.f64 (neg.f64 (log.f64 k)) #s(literal 1/2 binary64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 n #s(literal 1 binary64)) (PI.f64))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (cbrt.f64 (PI.f64)) n))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))
(*.f64 (sqrt.f64 (/.f64 k (sqrt.f64 (PI.f64)))) (sqrt.f64 (/.f64 (pow.f64 n #s(literal -1 binary64)) (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (/.f64 k (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 n #s(literal -1 binary64)) (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (/.f64 k (sqrt.f64 (PI.f64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (pow.f64 n #s(literal -1 binary64)) (sqrt.f64 (PI.f64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 k (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (pow.f64 n #s(literal -1 binary64)) (cbrt.f64 (PI.f64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 n k)) #s(literal -1 binary64)) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 n)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (/.f64 (neg.f64 k) n)) (pow.f64 (neg.f64 (PI.f64)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (/.f64 (neg.f64 k) (PI.f64)) n)))
(*.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (neg.f64 (/.f64 #s(literal -1 binary64) (PI.f64)))))
(*.f64 (sqrt.f64 (/.f64 k n)) (pow.f64 (neg.f64 (/.f64 #s(literal -1 binary64) (PI.f64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 k n)) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))) (pow.f64 n #s(literal -1/2 binary64)))
(*.f64 (pow.f64 n #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 k (PI.f64))))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) #s(literal -1 binary64))
(.f64 (neg.f64 (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 n)))))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 k (PI.f64)))) (pow.f64 (neg.f64 (sqrt.f64 n)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (pow.f64 n #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (pow.f64 (pow.f64 n #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 k (PI.f64))) (pow.f64 n #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (pow.f64 (PI.f64) #s(literal -1 binary64)) n)))
(*.f64 (sqrt.f64 k) (sqrt.f64 (/.f64 (pow.f64 n #s(literal -1 binary64)) (PI.f64))))
(*.f64 (sqrt.f64 k) (pow.f64 (/.f64 (pow.f64 (PI.f64) #s(literal -1 binary64)) n) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 k) (pow.f64 (/.f64 (pow.f64 n #s(literal -1 binary64)) (PI.f64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) n) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)))
(pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) n) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1 binary64))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 k (PI.f64)))))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 n)))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 k n))) (neg.f64 (sqrt.f64 (PI.f64))))
(/.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 k))) (.f64 (neg.f64 (sqrt.f64 n)) (sqrt.f64 (neg.f64 (PI.f64)))))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 k))) (.f64 (neg.f64 (sqrt.f64 n)) (neg.f64 (sqrt.f64 (PI.f64)))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (sqrt.f64 (.f64 (neg.f64 (PI.f64)) n)))
(/.f64 (.f64 (sqrt.f64 (neg.f64 k)) (pow.f64 n #s(literal -1/2 binary64))) (.f64 (sqrt.f64 (neg.f64 (PI.f64))) #s(literal 1 binary64)))
(/.f64 (.f64 (sqrt.f64 (neg.f64 k)) #s(literal -1 binary64)) (.f64 (sqrt.f64 (neg.f64 (PI.f64))) (neg.f64 (sqrt.f64 n))))
(/.f64 (.f64 (sqrt.f64 (neg.f64 k)) #s(literal 1 binary64)) (sqrt.f64 (.f64 (neg.f64 (PI.f64)) n)))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 (PI.f64) n))))
(/.f64 (.f64 (neg.f64 (sqrt.f64 k)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 n))))
(/.f64 (.f64 (neg.f64 (sqrt.f64 k)) #s(literal 1 binary64)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 n)))
(/.f64 (sqrt.f64 (/.f64 (/.f64 k n) (sqrt.f64 (PI.f64)))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 (*.f64 (/.f64 k n) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal -2 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (neg.f64 n)))
(/.f64 (sqrt.f64 (/.f64 (neg.f64 k) n)) (sqrt.f64 (neg.f64 (PI.f64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 (/.f64 (neg.f64 (PI.f64)) k) n)))
(/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 n)) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))) (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 n)))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))) (neg.f64 (neg.f64 (sqrt.f64 n))))
(/.f64 (sqrt.f64 (neg.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (neg.f64 n))))
(/.f64 (sqrt.f64 (neg.f64 k)) (sqrt.f64 (*.f64 (neg.f64 (PI.f64)) n)))
(/.f64 (pow.f64 n #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) #s(literal -1 binary64))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 k (PI.f64)))) (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 n))))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 k (PI.f64)))) (neg.f64 (sqrt.f64 n)))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k))))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (neg.f64 (sqrt.f64 n))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(/.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))
(/.f64 (neg.f64 (sqrt.f64 k)) (*.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 n))))
(/.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (sqrt.f64 k) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 n))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (neg.f64 (*.f64 (neg.f64 (PI.f64)) n))))
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (PI.f64) n)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 n))) (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (*.f64 (/.f64 (neg.f64 (PI.f64)) k) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(neg.f64 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 n)))) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 n)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 n))) (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
(-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal -1 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 (/.f64 k (PI.f64))) #s(literal 1/2 binary64)) (.f64 (log.f64 n) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (log.f64 (sqrt.f64 k)) (.f64 (log.f64 (.f64 (PI.f64) n)) #s(literal 1/2 binary64))))
(exp.f64 (neg.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) #s(literal -1 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 k (PI.f64)) n)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))) #s(literal -1 binary64)))

eval179.0ms (1.9%)

Memory: 21.0MiB live, 173.2MiB allocated
Compiler: Compiled 21 893 to 2 865 computations (86.9% saved)

prune378.0ms (4%)

Memory

-153.3MiB live, 163.0MiB allocated

Pruning

61 alts after pruning (55 fresh and 6 done)

	Pruned	Kept	Total
New	648	28	676
Fresh	17	27	44
Picked	3	2	5
Done	1	4	5
Total	669	61	730

Accuracy

100.0%

Counts

730 → 61

Alt Table

Click to see full alt table

Status	Accuracy	Program
	55.0%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
	47.6%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))
	47.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))))
	47.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
✓	47.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
	47.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	47.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (/ 1 (pow ( n (* (PI) 2)) (* -1/2 (- 1 k)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 1/2 binary64)))))
	89.9%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
	90.0%	(sqrt.f64 (.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 k)))
	47.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (.f64 k #s(literal 1/2 binary64)) (*.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 k)) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 k) (sqrt.f64 #s(literal 1/2 binary64)))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal -2 binary64) (neg.f64 (PI.f64)))) (sqrt.f64 (/.f64 k n))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
	38.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
	38.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
✓	99.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	47.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 n) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 k)))))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))) (neg.f64 (sqrt.f64 n))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))))))
	38.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64))))))
	47.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n))))))
✓	38.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
	37.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 n (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
✓	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))
	37.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))))
✓	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
	37.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 1/2 binary64))))
	37.4%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) k) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
	37.5%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
✓	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
	37.7%	#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64))))

Compiler

Compiled 4 241 to 1 789 computations (57.8% saved)

regimes140.0ms (1.5%)

Memory

7.4MiB live, 241.7MiB allocated

Counts

100 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 n (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal -2 binary64) (neg.f64 (PI.f64)))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 k) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))) (neg.f64 (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (/ 1 (pow ( n (* (PI) 2)) (* -1/2 (- 1 k)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) k) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 n) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (.f64 k #s(literal 1/2 binary64)) (*.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 k)) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))

Outputs
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))

Calls

4 calls:

49.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
32.0ms	n
28.0ms	k
28.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.7%	1	`k`
99.7%	1	`n`
99.7%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes117.0ms (1.2%)

Memory

-24.7MiB live, 223.1MiB allocated

Counts

92 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 n (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal -2 binary64) (neg.f64 (PI.f64)))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 k) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))) (neg.f64 (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (/ 1 (pow ( n (* (PI) 2)) (* -1/2 (- 1 k)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) k) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 n) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (.f64 k #s(literal 1/2 binary64)) (*.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 k)) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal -1/2 binary64)))))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 n (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))

Outputs

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))

Calls

4 calls:

37.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
26.0ms	k
26.0ms	n
23.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.6%	1	`k`
99.6%	1	`n`
99.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes92.0ms (1%)

Memory

2.8MiB live, 162.1MiB allocated

Counts

84 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 n (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal -2 binary64) (neg.f64 (PI.f64)))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 k) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))) (neg.f64 (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (/ 1 (pow ( n (* (PI) 2)) (* -1/2 (- 1 k)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) k) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 n) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (.f64 k #s(literal 1/2 binary64)) (*.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 k)) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))

Outputs

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))

Calls

4 calls:

23.0ms	n
23.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms	k
20.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.6%	1	`k`
99.6%	1	`n`
99.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes88.0ms (0.9%)

Memory

29.9MiB live, 149.4MiB allocated

Counts

81 → 2

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 n (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal -2 binary64) (neg.f64 (PI.f64)))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 k) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))) (neg.f64 (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (/ 1 (pow ( n (* (PI) 2)) (* -1/2 (- 1 k)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) k) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 n) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (.f64 k #s(literal 1/2 binary64)) (*.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 k)) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))

Outputs

#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))

(/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))

Calls

4 calls:

22.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms	n
21.0ms	k
19.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
97.9%	2	`k`
59.4%	3	`n`
97.9%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
59.4%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes102.0ms (1.1%)

Memory

-32.1MiB live, 129.3MiB allocated

Counts

80 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 n (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal -2 binary64) (neg.f64 (PI.f64)))) (sqrt.f64 (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 k) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 #s(approx (pow ( (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (neg.f64 #s(approx (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))) (neg.f64 (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (PI.f64)))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (/ 1 (pow ( n (* (PI) 2)) (* -1/2 (- 1 k)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 n) #s(literal -1 binary64)) (/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 k)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 k n) (neg.f64 (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) k) (/.f64 #s(literal -1 binary64) (*.f64 n (PI.f64))))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 n) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (PI.f64)) (neg.f64 (sqrt.f64 k)))))
#s(approx (* (/ 1 (sqrt k)) (/ 1 (pow (* n (* (PI) 2)) (* -1/2 (- 1 k))))) (/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (.f64 k #s(literal 1/2 binary64)) (*.f64 (+.f64 #s(literal 0 binary64) (sqrt.f64 k)) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 k (PI.f64))))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (neg.f64 (sqrt.f64 k)) (sqrt.f64 n)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) #s(approx (pow ( n (* (PI) 2)) (* -1/2 (- 1 k))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) #s(literal 1/2 binary64))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))

Calls

4 calls:

34.0ms	n
22.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
20.0ms	k
20.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
47.7%	1	`n`
47.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
47.7%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
47.7%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes30.0ms (0.3%)

Memory

-4.5MiB live, 34.5MiB allocated

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 n (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 (PI.f64) n))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))

Calls

4 calls:

6.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
6.0ms	k
6.0ms	n
6.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
47.7%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
47.7%	1	`k`
47.7%	1	`n`
47.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes17.0ms (0.2%)

Memory

20.8MiB live, 20.8MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n (/.f64 k (PI.f64))) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 n (*.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))

Calls

4 calls:

4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	n
4.0ms	k
4.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
37.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
37.9%	1	`n`
37.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
37.9%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes6.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))

Outputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))

Calls

4 calls:

1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
1.0ms	n
1.0ms	k

Results

Accuracy	Segments	Branch
37.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
37.9%	1	`k`
37.9%	1	`n`
37.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch22.0ms (0.2%)

Memory

-10.7MiB live, 28.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.416078312993463	25.30090972850638

Samples

15.0ms

112×

valid

Compiler

Compiled 327 to 291 computations (11% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sub: 4.0ms (34.1% of total)

ival-mult: 2.0ms (17.1% of total)

ival-pow: 2.0ms (17.1% of total)

ival-div: 1.0ms (8.5% of total)

ival-sqrt: 1.0ms (8.5% of total)

ival-pi: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

simplify27.0ms (0.3%)

Memory

12.6MiB live, 49.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	229
1	78	229

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(if (<=.f64 k #s(literal 1 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))

Outputs
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(if (<=.f64 k #s(literal 1 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
(if (<=.f64 k #s(literal 1 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)) (sqrt.f64 n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))

soundness762.0ms (8.1%)

Memory

-9.0MiB live, 546.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	211
0	76	198
1	260	183
2	1459	183
0	8132	183
0	13	43
0	22	43
1	89	40
2	497	38
3	4474	38
0	8599	37
0	128	517
1	345	504
2	1013	460
3	3349	433
4	5543	427
0	8350	412
0	53	274
0	86	253
1	290	236
2	1683	228
0	8277	228
0	52	262
0	81	243
1	274	227
2	1496	221
0	8291	218

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 697 to 440 computations (36.9% saved)

preprocess47.0ms (0.5%)

Memory: 26.6MiB live, 100.5MiB allocated
Compiler: Compiled 490 to 146 computations (70.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49

start0.0ms (0%)

analyze246.0ms (2.6%)

sample3.3s (35.4%)

explain361.0ms (3.8%)

preprocess57.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify43.0ms (0.5%)

localize51.0ms (0.5%)

series89.0ms (0.9%)

simplify138.0ms (1.5%)

rewrite141.0ms (1.5%)

eval90.0ms (1%)

prune18.0ms (0.2%)

simplify58.0ms (0.6%)

localize121.0ms (1.3%)

series73.0ms (0.8%)

simplify161.0ms (1.7%)

rewrite184.0ms (1.9%)

eval330.0ms (3.5%)

prune220.0ms (2.3%)

simplify144.0ms (1.5%)

localize203.0ms (2.1%)

series114.0ms (1.2%)

simplify198.0ms (2.1%)

rewrite188.0ms (2%)

eval149.0ms (1.6%)

prune76.0ms (0.8%)

simplify74.0ms (0.8%)

localize211.0ms (2.2%)

series51.0ms (0.5%)

simplify122.0ms (1.3%)

rewrite190.0ms (2%)

eval179.0ms (1.9%)

prune378.0ms (4%)

regimes140.0ms (1.5%)

regimes117.0ms (1.2%)

regimes92.0ms (1%)

regimes88.0ms (0.9%)

regimes102.0ms (1.1%)

regimes30.0ms (0.3%)

regimes17.0ms (0.2%)

regimes6.0ms (0.1%)

bsearch22.0ms (0.2%)

simplify27.0ms (0.3%)

soundness762.0ms (8.1%)

preprocess47.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	54	52
3	75	52
4	93	52
5	108	52
6	129	52
7	156	52
8	165	52
9	168	52
0	168	49