Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze154.0ms (1.7%)

Memory

-12.5MiB live, 191.9MiB 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)

sample3.6s (41.3%)

Memory

-76.3MiB live, 3 399.5MiB allocated

Samples

1.1s	8 256×	0	valid
852.0ms	3 542×	1	invalid
415.0ms	1 863×	1	exit
351.0ms	511×	0	invalid
184.0ms	412×	2	invalid
35.0ms	226×	0	exit

Precisions

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

ival-pow: 475.0ms (23.6% of total)

ival-mult: 421.0ms (20.9% of total)

ival-div: 353.0ms (17.5% of total)

ival-sub: 294.0ms (14.6% of total)

ival-sqrt: 190.0ms (9.4% of total)

adjust: 162.0ms (8% of total)

ival-pi: 86.0ms (4.3% of total)

exact: 16.0ms (0.8% of total)

ival-true: 11.0ms (0.5% of total)

ival-assert: 6.0ms (0.3% of total)

Bogosity

explain200.0ms (2.3%)

Memory

-14.2MiB live, 224.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
3	77	(1.8094074298692307e-298 4.467136441961615e+269)	-	`(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	80	31

Confusion

	Predicted +	Predicted -
+	3	0
-	77	176

Precision

0.0375

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	0	0
-	77	31	145

Precision?

0.02702702702702703

Recall?

1.0

Freqs

test

number	freq
0	176
1	80

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

97.0ms

512×

valid

Compiler

Compiled 182 to 56 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-mult: 14.0ms (33.7% of total)

ival-pow: 10.0ms (24.1% of total)

ival-div: 7.0ms (16.8% of total)

ival-sqrt: 4.0ms (9.6% of total)

ival-sub: 3.0ms (7.2% of total)

ival-pi: 2.0ms (4.8% of total)

exact: 1.0ms (2.4% of total)

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

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

preprocess51.0ms (0.6%)

Memory

20.2MiB live, 57.4MiB 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	630	74
5	922	74
6	1089	74
7	1346	74
8	1405	74
9	1431	74
10	1449	74
11	1455	74
12	1455	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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(.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)

simplify6.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB 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)

localize42.0ms (0.5%)

Memory

-5.3MiB live, 67.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.13782507621494014	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.16015625	(.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	0.23046875	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.23828125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Samples

33.0ms

256×

valid

Compiler

Compiled 110 to 28 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 6.0ms (31.5% of total)

ival-pow: 5.0ms (26.3% of total)

ival-div: 3.0ms (15.8% of total)

ival-sqrt: 2.0ms (10.5% of total)

ival-pi: 1.0ms (5.3% of total)

ival-sub: 1.0ms (5.3% of total)

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

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

exact: 0.0ms (0% of total)

series112.0ms (1.3%)

Memory

-33.1MiB live, 67.3MiB 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
72.0ms	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)))
25.0ms	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)))

simplify155.0ms (1.8%)

Memory

9.1MiB live, 199.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	517
1	345	504
2	1021	460
3	3363	433
4	5589	421
0	8476	406

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 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 k (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (fma.f64 #s(literal 1/8 binary64) (.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))) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #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)))) (* 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)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 k (.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 (fma.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 #s(literal -1/2 binary64) k) #s(literal 1 binary64)) (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)))

rewrite182.0ms (2.1%)

Memory

25.6MiB live, 219.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4477	38
0	8503	37

Stop Event

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

Counts

6 → 413

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 (.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 (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 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))) (/.f64 #s(literal 1 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 #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)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) k #s(literal 2 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))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 k k k) #s(literal 2 binary64) #s(literal 2 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 #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 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (+.f64 #s(literal -1 binary64) (*.f64 k k)))) (-.f64 #s(literal 1 binary64) k))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -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 #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))
(/.f64 (fma.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 2 binary64) (*.f64 #s(literal -4 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) #s(literal -8 binary64))
(/.f64 (fma.f64 (-.f64 k #s(literal 1 binary64)) #s(literal 4 binary64) (*.f64 #s(literal -4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal -16 binary64))
(/.f64 (fma.f64 (-.f64 k #s(literal 1 binary64)) (/.f64 #s(literal -4 binary64) (-.f64 k #s(literal 1 binary64))) #s(literal -4 binary64)) (*.f64 #s(literal -4 binary64) (/.f64 #s(literal -4 binary64) (-.f64 k #s(literal 1 binary64)))))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)) #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 (.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal -2 binary64))
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(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 k k k) #s(literal 2 binary64) #s(literal 2 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))))

eval87.0ms (1%)

Memory: -18.7MiB live, 101.6MiB allocated
Compiler: Compiled 9 931 to 1 554 computations (84.4% saved)

prune17.0ms (0.2%)

Memory

2.3MiB live, 40.0MiB allocated

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	417	14	431
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	418	14	432

Accuracy

100.0%

Counts

432 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.2%	(/.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))
	47.2%	(/.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)))))
	46.6%	(.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)))
▶	46.8%	(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
	46.8%	(.f64 (/.f64 (pow.f64 #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 (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) #s(literal 4 binary64)))
	99.5%	(.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))))
▶	99.6%	(.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))))
	55.4%	(.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))))
	47.9%	(.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 (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))))))
	47.8%	(.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))))
▶	35.6%	#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 556 to 450 computations (19.1% saved)

simplify12.0ms (0.1%)

Memory

16.8MiB live, 16.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	279
0	73	279
1	112	273
2	155	273
3	204	272
4	228	272
5	242	272
6	263	272
7	296	272
8	308	272
9	312	272
0	312	272

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize148.0ms (1.7%)

Memory

-2.0MiB live, 163.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.18600486869426486	(pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.19921875	(*.f64 n (PI.f64))
accuracy	0.46550614350769803	(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
accuracy	15.015259438585579	(PI.f64)
accuracy	0.16015625	(.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))))
accuracy	0.1875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.19921875	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	15.015259438585579	(PI.f64)
accuracy	0.15625	(/.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))
accuracy	0.18385201582150051	(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.19921875	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	15.015259438585579	(PI.f64)
accuracy	0.320976269536884	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	8.082576438485457	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	15.015259438585579	(PI.f64)
accuracy	18.02786541256277	#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	0.16015625	(.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))))))
accuracy	0.1875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.19921875	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	15.015259438585579	(PI.f64)

Samples

96.0ms	194×	0	valid
22.0ms	62×	0	exit

Compiler

Compiled 562 to 87 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-pow: 24.0ms (32.4% of total)

ival-mult: 20.0ms (27% of total)

ival-sqrt: 15.0ms (20.3% of total)

ival-div: 8.0ms (10.8% of total)

ival-add: 4.0ms (5.4% of total)

ival-pi: 1.0ms (1.4% of total)

ival-sub: 1.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series159.0ms (1.8%)

Memory

-6.9MiB live, 224.3MiB allocated

Counts

22 → 92

Calls

Call 1

Inputs
(.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 #s(literal 1 binary64) (sqrt.f64 k))
(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)))))
#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 (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))
(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 n (.f64 (PI.f64) #s(literal 2 binary64)))
(*.f64 (PI.f64) #s(literal 2 binary64))
(.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))))
(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 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))
(/.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
(PI.f64)
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 n (PI.f64))
(pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #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)
(/ (+ (* 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)))
(sqrt (/ (* n (PI)) k))
(/ (+ (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* 1/2 (* (sqrt (* k (* 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)))) (* 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)
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (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 (* k (* n (PI)))) (sqrt 2)) (* (sqrt (pow k 3)) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2))))))) k)
(/ (+ (* k (+ (* (sqrt k) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))) (* (sqrt (pow k 3)) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* k (+ (* (sqrt k) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n (PI))) (* (log 2) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (pow k 3)) (+ (* 1/48 (* (sqrt (* n (PI))) (* (pow (log 2) 3) (sqrt 2)))) (+ (* 1/48 (* (sqrt (* n (PI))) (* (pow (log (* n (PI))) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (* n (PI))) (* (log 2) (* (pow (log (* n (PI))) 2) (sqrt 2))))) (* 1/16 (* (sqrt (* n (PI))) (* (pow (log 2) 2) (* (log (* n (PI))) (sqrt 2))))))))))) (* (sqrt k) (+ (* 1/2 (* (sqrt (* n (PI))) (* (log 2) (sqrt 2)))) (* 1/2 (* (sqrt (* n (PI))) (* (log (* n (PI))) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (* k (* (log 2) (sqrt 2)))))
(+ (sqrt 2) (* k (+ (* 1/8 (* k (* (pow (log 2) 2) (sqrt 2)))) (* 1/2 (* (log 2) (sqrt 2))))))
(+ (sqrt 2) (* k (+ (* 1/2 (* (log 2) (sqrt 2))) (* k (+ (* 1/48 (* k (* (pow (log 2) 3) (sqrt 2)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2))))))))
1/2
(+ 1/2 (* 1/2 k))
(/ (+ (sqrt (* k (* n (PI)))) (* 1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (log (* n (PI)))))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 2))) (* 1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI)))))))) k)
(/ (+ (sqrt (* k (* n (PI)))) (* k (+ (* 1/2 (* (sqrt (* k (* n (PI)))) (log (* n (PI))))) (* k (+ (* 1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (pow (log (* n (PI))) 3))) (* 1/8 (* (sqrt (* k (* n (PI)))) (pow (log (* n (PI))) 2)))))))) k)
(sqrt (* n (PI)))
(+ (sqrt (* n (PI))) (* 1/2 (* (* k (log (* n (PI)))) (sqrt (* n (PI))))))
(+ (sqrt (* n (PI))) (* k (+ (* 1/8 (* (* k (pow (log (* n (PI))) 2)) (sqrt (* n (PI))))) (* 1/2 (* (sqrt (* n (PI))) (log (* n (PI))))))))
(+ (sqrt (* n (PI))) (* k (+ (* 1/2 (* (sqrt (* n (PI))) (log (* n (PI))))) (* k (+ (* 1/48 (* (* k (pow (log (* n (PI))) 3)) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (pow (log (* n (PI))) 2))))))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (log (* 2 (* n (PI))))))) (sqrt 2)))
(* (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 (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k))))))
(exp (* (log 2) (+ 1/2 (* 1/2 k))))
(* 1/2 k)
(* k (+ 1/2 (* 1/2 (/ 1 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k)))))
(exp (* (log (* n (PI))) (+ 1/2 (* 1/2 k))))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(* (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))
(* (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 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))
(exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (- 1/2 (* -1/2 k)))) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k))))))
(exp (* (log 2) (- 1/2 (* -1/2 k))))
(* (sqrt (/ 1 k)) (exp (* (log (* n (PI))) (- 1/2 (* -1/2 k)))))
(exp (* (log (* n (PI))) (- 1/2 (* -1/2 k))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 2)))
(* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log n) (log (* 2 (PI))))))) (sqrt 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 (/ 1 k)) (exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI)))))))
(exp (* (+ 1/2 (* -1/2 k)) (+ (log n) (log (* 2 (PI))))))
(* (sqrt (/ 1 k)) (* (exp (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI)))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI))))))
(* n (PI))
(exp (* (+ 1/2 (* 1/2 k)) (+ (log n) (log (PI)))))
(* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (sqrt 2)))
(* (sqrt (* n (PI))) (* (exp (* -1/2 (* 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)) (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 (* -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 (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n))))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n)))))))
(exp (* (+ 1/2 (* 1/2 k)) (+ (log (PI)) (* -1 (log (/ 1 n))))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (sqrt -2) (sqrt -1)))))
(* -1 (* (sqrt (* n (PI))) (* (exp (* -1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* (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)))
(* (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 (* -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 (* (log 2) (+ 1/2 (* 1/2 k)))) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n))))))))
(* (sqrt (/ 1 k)) (exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* (+ 1/2 (* 1/2 k)) (+ (log (* -1 (PI))) (* -1 (log (/ -1 n))))))

Calls

6 calls:

Time	Variable		Point	Expression
57.0ms	n	@	0	((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (pow (* n (* (PI) 2)) (+ (* 1/2 k) 1/2)) (sqrt k)) (pow (* n (* (PI) 2)) (+ (* 1/2 k) 1/2)) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2))) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (pow 2 (+ (* 1/2 k) 1/2)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) (sqrt k))) (pow 2 (+ (* 1/2 k) 1/2)) (+ (* 1/2 k) 1/2) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) (sqrt k)) (PI) (* (* 2 (PI)) n) (* n (PI)) (pow (* n (PI)) (+ (* 1/2 k) 1/2)))
47.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (pow (* n (* (PI) 2)) (+ (* 1/2 k) 1/2)) (sqrt k)) (pow (* n (* (PI) 2)) (+ (* 1/2 k) 1/2)) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2))) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (pow 2 (+ (* 1/2 k) 1/2)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) (sqrt k))) (pow 2 (+ (* 1/2 k) 1/2)) (+ (* 1/2 k) 1/2) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) (sqrt k)) (PI) (* (* 2 (PI)) n) (* n (PI)) (pow (* n (PI)) (+ (* 1/2 k) 1/2)))
29.0ms	n	@	inf	((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (pow (* n (* (PI) 2)) (+ (* 1/2 k) 1/2)) (sqrt k)) (pow (* n (* (PI) 2)) (+ (* 1/2 k) 1/2)) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2))) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (pow 2 (+ (* 1/2 k) 1/2)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) (sqrt k))) (pow 2 (+ (* 1/2 k) 1/2)) (+ (* 1/2 k) 1/2) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) (sqrt k)) (PI) (* (* 2 (PI)) n) (* n (PI)) (pow (* n (PI)) (+ (* 1/2 k) 1/2)))
9.0ms	k	@	inf	((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (pow (* n (* (PI) 2)) (+ (* 1/2 k) 1/2)) (sqrt k)) (pow (* n (* (PI) 2)) (+ (* 1/2 k) 1/2)) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2))) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (pow 2 (+ (* 1/2 k) 1/2)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) (sqrt k))) (pow 2 (+ (* 1/2 k) 1/2)) (+ (* 1/2 k) 1/2) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) (sqrt k)) (PI) (* (* 2 (PI)) n) (* n (PI)) (pow (* n (PI)) (+ (* 1/2 k) 1/2)))
8.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2))))) (/ 1 (sqrt k)) (sqrt k) (* (pow (* n (* (PI) 2)) (* k -1/2)) (sqrt (* n (* (PI) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (/ (pow (* n (* (PI) 2)) (+ (* 1/2 k) 1/2)) (sqrt k)) (pow (* n (* (PI) 2)) (+ (* 1/2 k) 1/2)) (* n (* (PI) 2)) (* (PI) 2) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2))) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (pow 2 (+ (* 1/2 k) 1/2)) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) (sqrt k))) (pow 2 (+ (* 1/2 k) 1/2)) (+ (* 1/2 k) 1/2) (/ (pow (* n (PI)) (+ (* 1/2 k) 1/2)) (sqrt k)) (PI) (* (* 2 (PI)) n) (* n (PI)) (pow (* n (PI)) (+ (* 1/2 k) 1/2)))

simplify260.0ms (3%)

Memory

34.0MiB live, 185.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	375	2197
1	1173	2090
2	3831	1984
3	7090	1953
0	8061	1899

Stop Event

1×	iter limit
1×	node limit

Counts

92 → 92

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

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

rewrite255.0ms (2.9%)

Memory

-2.0MiB live, 228.2MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	198
0	73	179
1	276	172
2	1508	171
0	8225	171

Stop Event

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

Counts

22 → 925

Calls

Call 1

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

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

eval191.0ms (2.2%)

Memory: -4.6MiB live, 306.1MiB allocated
Compiler: Compiled 28 688 to 3 721 computations (87% saved)

prune36.0ms (0.4%)

Memory

14.9MiB live, 96.4MiB allocated

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	1 140	17	1 157
Fresh	8	1	9
Picked	3	2	5
Done	0	0	0
Total	1 151	20	1 171

Accuracy

100.0%

Counts

1 171 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	75.1%	(.f64 (/.f64 (pow.f64 n (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 (.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1/2 binary64)) k) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))) #s(literal 1 binary64)))
✓	99.7%	(.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))))))
▶	47.8%	(.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%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))
	47.9%	#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)))
▶	37.0%	#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)))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
	47.8%	#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))))
	35.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	35.5%	#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))))
	47.8%	#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))))
	47.8%	#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)))))
▶	47.8%	#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)))))
	47.8%	#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)))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))))
✓	35.6%	#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))))
▶	35.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))

Compiler

Compiled 955 to 786 computations (17.7% saved)

simplify16.0ms (0.2%)

Memory

-18.0MiB live, 18.9MiB 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 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
cost-diff	0	#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)))))
cost-diff	704	(/.f64 (sqrt.f64 n) #s(literal 1 binary64))
cost-diff	0	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 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)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
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 k (*.f64 (PI.f64) n)))))
cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
cost-diff	0	(/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)
cost-diff	0	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
cost-diff	0	(/.f64 #s(literal 1 binary64) k)
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
cost-diff	0	#s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
cost-diff	0	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	317
0	74	309
1	109	301
2	164	301
3	236	296
4	312	296
5	339	296
6	365	296
7	400	296
8	428	296
9	434	296
0	434	296

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize150.0ms (1.7%)

Memory

-22.7MiB live, 194.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.33431625976844204	(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64)))
accuracy	0.4030075195368841	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
accuracy	1.0	(sqrt.f64 (PI.f64))
accuracy	33.18754842670258	#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)))))
accuracy	0.23046875	(*.f64 (PI.f64) n)
accuracy	0.23828125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.41244125976844204	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	33.21495970106844	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.23046875	(*.f64 (PI.f64) n)
accuracy	0.4296875	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
accuracy	14.932854015363949	(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
accuracy	33.18754842670258	#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)))))
accuracy	0.203125	(/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)
accuracy	0.23046875	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	15.360852718488072	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k))
accuracy	33.18754842670258	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
accuracy	0.09765625	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
accuracy	0.13782507621494014	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
accuracy	0.16015625	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))
accuracy	0.23046875	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

110.0ms

256×

valid

Compiler

Compiled 580 to 86 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-mult: 44.0ms (50.1% of total)

ival-div: 16.0ms (18.2% of total)

ival-sqrt: 14.0ms (15.9% of total)

ival-pow: 10.0ms (11.4% of total)

ival-pi: 1.0ms (1.1% of total)

ival-add: 1.0ms (1.1% of total)

ival-sub: 1.0ms (1.1% of total)

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

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

exact: 0.0ms (0% of total)

series51.0ms (0.6%)

Memory

22.6MiB live, 66.8MiB allocated

Counts

24 → 48

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* 2 (PI)) n) k)) (/ (* (* 2 (PI)) n) k) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt n) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (/ (sqrt (PI)) (sqrt k)) (/ (sqrt n) 1))) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (PI) n) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (PI)) (* (/ (sqrt (PI)) (sqrt k)) (/ (sqrt n) 1)))
12.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* 2 (PI)) n) k)) (/ (* (* 2 (PI)) n) k) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt n) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (/ (sqrt (PI)) (sqrt k)) (/ (sqrt n) 1))) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (PI) n) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (PI)) (* (/ (sqrt (PI)) (sqrt k)) (/ (sqrt n) 1)))
10.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* 2 (PI)) n) k)) (/ (* (* 2 (PI)) n) k) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt n) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (/ (sqrt (PI)) (sqrt k)) (/ (sqrt n) 1))) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (PI) n) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (PI)) (* (/ (sqrt (PI)) (sqrt k)) (/ (sqrt n) 1)))
5.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* 2 (PI)) n) k)) (/ (* (* 2 (PI)) n) k) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt n) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (/ (sqrt (PI)) (sqrt k)) (/ (sqrt n) 1))) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (PI) n) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (PI)) (* (/ (sqrt (PI)) (sqrt k)) (/ (sqrt n) 1)))
3.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2))) (/ 1 (sqrt k)) (sqrt (/ 1 k)) (/ 1 k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ (* (* 2 (PI)) n) k)) (/ (* (* 2 (PI)) n) k) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (sqrt (/ k (* (PI) n)))) (sqrt 2) (sqrt (/ k (* (PI) n))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (/ (sqrt n) 1) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (/ (sqrt (PI)) (sqrt k)) (/ (sqrt n) 1))) (pow (* (* 2 (PI)) n) (+ (* k -1/2) 1/2)) (* (PI) n) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (PI)) (* (/ (sqrt (PI)) (sqrt k)) (/ (sqrt n) 1)))

simplify138.0ms (1.6%)

Memory

-11.7MiB live, 144.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	741
1	449	719
2	1416	680
3	2732	662
4	5012	662
0	8511	650

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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

rewrite170.0ms (1.9%)

Memory

29.9MiB live, 181.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	252
0	74	232
1	240	217
2	1286	212
0	8497	212

Stop Event

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

Counts

24 → 899

Calls

Call 1

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

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

eval135.0ms (1.5%)

Memory: -33.7MiB live, 170.6MiB allocated
Compiler: Compiled 22 016 to 2 798 computations (87.3% saved)

prune75.0ms (0.9%)

Memory

-4.5MiB live, 158.9MiB allocated

Pruning

47 alts after pruning (41 fresh and 6 done)

	Pruned	Kept	Total
New	738	34	772
Fresh	6	7	13
Picked	1	4	5
Done	0	2	2
Total	745	47	792

Accuracy

100.0%

Counts

792 → 47

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	47.9%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	47.8%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))
	75.1%	(.f64 (/.f64 (pow.f64 n (.f64 #s(literal -1/2 binary64) k)) (sqrt.f64 k)) (/.f64 (.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1/2 binary64)) k) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))) #s(literal 1 binary64)))
✓	99.7%	(.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))))))
✓	47.8%	(.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)))))
▶	47.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
	47.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))))
	47.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
✓	99.6%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)) (*.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 k (PI.f64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 n))) (sqrt.f64 k)))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (neg.f64 (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 k) (sqrt.f64 n))))
	47.9%	#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)))))
▶	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64)))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64))))))
	35.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))))))
✓	37.0%	#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 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) #s(literal 1 binary64))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n))) (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) #s(literal -1 binary64))))
▶	47.9%	#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)))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
	47.9%	#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)))))
	47.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n)))
	35.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
	47.8%	#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))))
	47.8%	#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))))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (neg.f64 (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))
	47.8%	#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))))))
	47.8%	#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))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))))))
✓	35.6%	#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))))
✓	35.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
	35.7%	#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))))
	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))))
	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) (/.f64 (PI.f64) #s(literal 1 binary64)))))
	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64)))))
	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64)))))
▶	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))

Compiler

Compiled 2 302 to 1 890 computations (17.9% saved)

simplify11.0ms (0.1%)

Memory

20.3MiB live, 20.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	277
0	72	277
1	101	269
2	134	269
3	171	264
4	199	264
5	219	264
6	240	264
7	269	264
8	283	264
9	287	264
0	287	264

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize165.0ms (1.9%)

Memory

21.4MiB live, 213.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.21484375	(/.f64 k (PI.f64))
accuracy	0.34994125976844204	(/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))
accuracy	0.4296875	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)))
accuracy	33.18754842670258	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
accuracy	0.23828125	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.45607377930532605	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))
accuracy	1.0	(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	33.21495970106844	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n)))
accuracy	0.1171875	(sqrt.f64 (/.f64 (PI.f64) k))
accuracy	0.2421875	(/.f64 (PI.f64) k)
accuracy	0.33203125	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
accuracy	33.18754842670258	#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)))))
accuracy	0.203125	(*.f64 (/.f64 (PI.f64) k) n)
accuracy	0.2421875	(/.f64 (PI.f64) k)
accuracy	15.360852718488072	(sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64)))
accuracy	33.18754842670258	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
accuracy	0.0	(PI.f64)
accuracy	0.13782507621494014	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.15625	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
accuracy	0.23046875	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

136.0ms

256×

valid

Compiler

Compiled 513 to 85 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-pow: 40.0ms (48.3% of total)

ival-mult: 14.0ms (16.9% of total)

ival-sqrt: 13.0ms (15.7% of total)

ival-div: 10.0ms (12.1% of total)

ival-add: 3.0ms (3.6% of total)

ival-pi: 1.0ms (1.2% of total)

ival-sub: 1.0ms (1.2% of total)

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

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

exact: 0.0ms (0% of total)

series93.0ms (1.1%)

Memory

-29.1MiB live, 90.4MiB allocated

Counts

24 → 45

Calls

Call 1

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

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))
(/ (* n (PI)) k)
(sqrt (/ (PI) k))
(/ (PI) k)
(sqrt (/ 1 k))
(sqrt k)
(sqrt (/ k (* n (PI))))
(/ k (PI))
(* (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 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 (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (PI) k)) (pow (sqrt -1) 2))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* (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 (/ 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)) (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)))))
(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)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(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))) (* (pow (sqrt -1) 2) (sqrt 2))))

Calls

6 calls:

Time	Variable		Point	Expression
41.0ms	n	@	0	((/ (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (/ (PI) k) n) 2)) (* (* (/ (PI) k) n) 2) (* (/ (PI) k) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* n 2))) (sqrt (/ (PI) k)) (/ (PI) 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)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (/ (sqrt (/ k (PI))) (sqrt n))) (sqrt 2) (/ (sqrt (/ k (PI))) (sqrt n)) (PI) (sqrt (* (PI) 2)) (* (sqrt (* (PI) 2)) (sqrt n)) (/ k (PI)))
25.0ms	n	@	-inf	((/ (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (/ (PI) k) n) 2)) (* (* (/ (PI) k) n) 2) (* (/ (PI) k) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* n 2))) (sqrt (/ (PI) k)) (/ (PI) 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)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (/ (sqrt (/ k (PI))) (sqrt n))) (sqrt 2) (/ (sqrt (/ k (PI))) (sqrt n)) (PI) (sqrt (* (PI) 2)) (* (sqrt (* (PI) 2)) (sqrt n)) (/ k (PI)))
10.0ms	n	@	inf	((/ (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (/ (PI) k) n) 2)) (* (* (/ (PI) k) n) 2) (* (/ (PI) k) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* n 2))) (sqrt (/ (PI) k)) (/ (PI) 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)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (/ (sqrt (/ k (PI))) (sqrt n))) (sqrt 2) (/ (sqrt (/ k (PI))) (sqrt n)) (PI) (sqrt (* (PI) 2)) (* (sqrt (* (PI) 2)) (sqrt n)) (/ k (PI)))
7.0ms	k	@	0	((/ (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (/ (PI) k) n) 2)) (* (* (/ (PI) k) n) 2) (* (/ (PI) k) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* n 2))) (sqrt (/ (PI) k)) (/ (PI) 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)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (/ (sqrt (/ k (PI))) (sqrt n))) (sqrt 2) (/ (sqrt (/ k (PI))) (sqrt n)) (PI) (sqrt (* (PI) 2)) (* (sqrt (* (PI) 2)) (sqrt n)) (/ k (PI)))
5.0ms	k	@	-inf	((/ (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (sqrt k)) (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* (/ (PI) k) n) 2)) (* (* (/ (PI) k) n) 2) (* (/ (PI) k) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* n 2))) (sqrt (/ (PI) k)) (/ (PI) 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)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt 2) (/ (sqrt (/ k (PI))) (sqrt n))) (sqrt 2) (/ (sqrt (/ k (PI))) (sqrt n)) (PI) (sqrt (* (PI) 2)) (* (sqrt (* (PI) 2)) (sqrt n)) (/ k (PI)))

simplify163.0ms (1.9%)

Memory

25.4MiB live, 149.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	727
1	434	705
2	1376	666
3	2673	648
4	4881	648
0	8228	636

Stop Event

1×	iter limit
1×	node limit

Counts

45 → 45

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

rewrite190.0ms (2.2%)

Memory

-8.7MiB live, 217.7MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	228
0	72	218
1	226	209
2	1189	204
0	8728	204

Stop Event

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

Counts

24 → 989

Calls

Call 1

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

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

eval190.0ms (2.2%)

Memory: 10.0MiB live, 284.1MiB allocated
Compiler: Compiled 30 737 to 4 327 computations (85.9% saved)

prune120.0ms (1.4%)

Memory

-11.8MiB live, 204.4MiB allocated

Pruning

59 alts after pruning (49 fresh and 10 done)

	Pruned	Kept	Total
New	1 098	23	1 121
Fresh	10	26	36
Picked	1	4	5
Done	0	6	6
Total	1 109	59	1 168

Accuracy

100.0%

Counts

1 168 → 59

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
	47.9%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (sqrt.f64 k))
	48.3%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (.f64 (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 k))
	47.8%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (+ (* -1/2 k) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	47.8%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))))
✓	99.7%	(.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))))))
	47.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n))))
✓	47.8%	(.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)))))
	47.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64)))))
	47.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))
✓	99.6%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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))))
	47.7%	(.f64 #s(approx (/ 1 (sqrt k)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 n))))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1 binary64)) (*.f64 (sqrt.f64 k) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 n))) (sqrt.f64 k)))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (neg.f64 (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (/.f64 k (PI.f64))))))
	47.9%	#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)))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) k))) (sqrt.f64 n))))
✓	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (PI.f64)))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64))))))
	35.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 k) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 n (PI.f64)))))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (/.f64 k (PI.f64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))
	37.0%	#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))))
✓	37.0%	#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 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 n)))
	47.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))))
	47.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 n)))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 (PI.f64))))
	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n k))) (sqrt.f64 (PI.f64))))
✓	47.9%	#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)))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
	47.9%	#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)))))
	47.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n)))
	35.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	48.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n)))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal -1 binary64) k) (neg.f64 (PI.f64)))) (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 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
	35.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)))))
	47.8%	#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))))
	47.8%	#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))))))
	47.8%	#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))))))
	47.8%	#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))))
	47.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))))))
✓	35.6%	#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))))
	47.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (neg.f64 (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 n)))))
✓	35.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
	35.7%	#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))))
	35.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64)))))
	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))))
	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) (PI.f64))))
	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64)))))
	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64)))))
	35.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (/.f64 (*.f64 (sqrt.f64 (PI.f64)) n) k)) #s(literal 2 binary64))))
✓	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
	35.7%	#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)))
	35.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 n (/.f64 #s(literal -1 binary64) k)) (neg.f64 (PI.f64))) #s(literal 2 binary64))))

Compiler

Compiled 3 825 to 1 636 computations (57.2% saved)

regimes127.0ms (1.4%)

Memory

8.6MiB live, 163.3MiB allocated

Counts

89 → 1

Calls

Call 1

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

Outputs

(*.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))))))

Calls

4 calls:

42.0ms	(.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))))
28.0ms	k
27.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	n

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)

regimes99.0ms (1.1%)

Memory

-1.8MiB live, 157.0MiB allocated

Counts

81 → 1

Calls

Call 1

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

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:

25.0ms	n
24.0ms	k
24.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
22.0ms	(.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)

regimes89.0ms (1%)

Memory

13.3MiB live, 133.0MiB allocated

Counts

75 → 1

Calls

Call 1

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

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

Calls

4 calls:

23.0ms	n
22.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
21.0ms	(.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))))
20.0ms	k

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)

regimes135.0ms (1.5%)

Memory

-4.8MiB live, 161.6MiB allocated

Counts

73 → 1

Calls

Call 1

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

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

Calls

4 calls:

51.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
36.0ms	n
23.0ms	k
21.0ms	(.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
48.0%	1	`k`
48.0%	1	`n`
48.0%	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))))`
48.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes19.0ms (0.2%)

Memory

-7.2MiB live, 31.0MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	(.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
35.8%	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))))`
35.8%	1	`k`
35.8%	1	`n`
35.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes38.0ms (0.4%)

Memory

-20.5MiB live, 17.8MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

31.0ms	k
2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
2.0ms	(.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
35.7%	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))))`
35.7%	1	`k`
35.7%	1	`n`
35.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes5.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB 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 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n)))

Outputs
#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)))

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	k
1.0ms	n

Results

Accuracy	Segments	Branch
35.7%	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))))`
35.7%	1	`k`
35.7%	1	`n`
35.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

simplify71.0ms (0.8%)

Memory

-13.6MiB live, 32.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	167
1	71	157
2	87	157
3	111	157
4	138	157
5	167	157
6	240	157
7	529	157
8	5003	157

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness722.0ms (8.2%)

Memory

28.4MiB live, 661.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	228
0	72	218
1	226	209
2	1189	204
0	8728	204
0	46	252
0	74	232
1	240	217
2	1286	212
0	8497	212
0	44	198
0	73	179
1	276	172
2	1508	171
0	8225	171
0	128	517
1	345	504
2	1021	460
3	3363	433
4	5589	421
0	8476	406
0	13	43
0	22	43
1	89	40
2	497	38
3	4477	38
0	8503	37

Stop Event

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

Compiler

Compiled 504 to 320 computations (36.5% saved)

preprocess125.0ms (1.4%)

Memory: 8.7MiB live, 79.9MiB allocated
Compiler: Compiled 366 to 138 computations (62.3% 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	44	279
0	73	279
1	112	273
2	155	273
3	204	272
4	228	272
5	242	272
6	263	272
7	296	272
8	308	272
9	312	272
0	312	272

Iter	Nodes	Cost
0	46	317
0	74	309
1	109	301
2	164	301
3	236	296
4	312	296
5	339	296
6	365	296
7	400	296
8	428	296
9	434	296
0	434	296

Iter	Nodes	Cost
0	45	277
0	72	277
1	101	269
2	134	269
3	171	264
4	199	264
5	219	264
6	240	264
7	269	264
8	283	264
9	287	264
0	287	264

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	44	279
0	73	279
1	112	273
2	155	273
3	204	272
4	228	272
5	242	272
6	263	272
7	296	272
8	308	272
9	312	272
0	312	272

Iter	Nodes	Cost
0	46	317
0	74	309
1	109	301
2	164	301
3	236	296
4	312	296
5	339	296
6	365	296
7	400	296
8	428	296
9	434	296
0	434	296

Iter	Nodes	Cost
0	45	277
0	72	277
1	101	269
2	134	269
3	171	264
4	199	264
5	219	264
6	240	264
7	269	264
8	283	264
9	287	264
0	287	264

start0.0ms (0%)

analyze154.0ms (1.7%)

sample3.6s (41.3%)

explain200.0ms (2.3%)

preprocess51.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize42.0ms (0.5%)

series112.0ms (1.3%)

simplify155.0ms (1.8%)

rewrite182.0ms (2.1%)

eval87.0ms (1%)

prune17.0ms (0.2%)

simplify12.0ms (0.1%)

localize148.0ms (1.7%)

series159.0ms (1.8%)

simplify260.0ms (3%)

rewrite255.0ms (2.9%)

eval191.0ms (2.2%)

prune36.0ms (0.4%)

simplify16.0ms (0.2%)

localize150.0ms (1.7%)

series51.0ms (0.6%)

simplify138.0ms (1.6%)

rewrite170.0ms (1.9%)

eval135.0ms (1.5%)

prune75.0ms (0.9%)

simplify11.0ms (0.1%)

localize165.0ms (1.9%)

series93.0ms (1.1%)

simplify163.0ms (1.9%)

rewrite190.0ms (2.2%)

eval190.0ms (2.2%)

prune120.0ms (1.4%)

regimes127.0ms (1.4%)

regimes99.0ms (1.1%)

regimes89.0ms (1%)

regimes135.0ms (1.5%)

regimes19.0ms (0.2%)

regimes38.0ms (0.4%)

regimes5.0ms (0.1%)

simplify71.0ms (0.8%)

soundness722.0ms (8.2%)

preprocess125.0ms (1.4%)

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

Iter	Nodes	Cost
0	44	279
0	73	279
1	112	273
2	155	273
3	204	272
4	228	272
5	242	272
6	263	272
7	296	272
8	308	272
9	312	272
0	312	272

Iter	Nodes	Cost
0	46	317
0	74	309
1	109	301
2	164	301
3	236	296
4	312	296
5	339	296
6	365	296
7	400	296
8	428	296
9	434	296
0	434	296

Iter	Nodes	Cost
0	45	277
0	72	277
1	101	269
2	134	269
3	171	264
4	199	264
5	219	264
6	240	264
7	269	264
8	283	264
9	287	264
0	287	264