Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze223.0ms (2.4%)

Memory

-23.2MiB live, 111.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.3s (35.6%)

Memory

51.2MiB live, 4 958.4MiB allocated

Samples

1.1s	8 256×	0	valid
771.0ms	3 554×	1	invalid
477.0ms	1 926×	1	exit
119.0ms	414×	2	invalid
69.0ms	213×	0	exit
49.0ms	495×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-pow: 475.0ms (25.6% of total)

ival-mult: 440.0ms (23.7% of total)

ival-div: 285.0ms (15.4% of total)

ival-pi: 171.0ms (9.2% of total)

adjust: 157.0ms (8.5% of total)

ival-sqrt: 154.0ms (8.3% of total)

ival-sub: 133.0ms (7.2% of total)

exact: 17.0ms (0.9% of total)

ival-true: 13.0ms (0.7% of total)

ival-assert: 7.0ms (0.4% of total)

Bogosity

explain143.0ms (1.6%)

Memory

24.1MiB live, 265.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
3	74	(1.5100035526161679e-242 3.8851844305496476e-151)	-	`(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	77	31

Confusion

	Predicted +	Predicted -
+	3	0
-	74	179

Precision

0.03896103896103896

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	0	0
-	74	31	148

Precision?

0.027777777777777776

Recall?

1.0

Freqs

test

number	freq
0	179
1	77

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

56.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-pow: 12.0ms (31.6% of total)

ival-mult: 9.0ms (23.7% of total)

ival-div: 8.0ms (21.1% of total)

ival-sqrt: 4.0ms (10.5% of total)

ival-sub: 3.0ms (7.9% of total)

ival-pi: 2.0ms (5.3% of total)

ival-true: 1.0ms (2.6% of total)

exact: 1.0ms (2.6% of total)

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

preprocess49.0ms (0.5%)

Memory

-9.7MiB live, 29.0MiB 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

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify6.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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)

localize40.0ms (0.4%)

Memory

-15.6MiB live, 65.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1652470815555653	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.19140625	(.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	0.25390625	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.2734375	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

32.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 5.0ms (24.1% of total)

ival-pow: 5.0ms (24.1% of total)

ival-sqrt: 4.0ms (19.3% of total)

ival-div: 3.0ms (14.5% of total)

ival-pi: 1.0ms (4.8% of total)

ival-sub: 1.0ms (4.8% of total)

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

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

exact: 0.0ms (0% of total)

series72.0ms (0.8%)

Memory

-5.2MiB live, 112.2MiB allocated

Counts

6 → 27

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 (-.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
(* (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)
1/2
(+ 1/2 (* -1/2 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 (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))
(* -1 (* k (- 1/2 (* 1/2 (/ 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
30.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
25.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
10.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
2.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (- 1 k) 2) (/ 1 (sqrt k)) (sqrt k) (* (* 2 (PI)) n) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

simplify146.0ms (1.6%)

Memory

18.4MiB live, 212.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	517
1	345	504
2	1022	460
3	3355	433
4	5591	421
0	8473	406

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

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

rewrite254.0ms (2.8%)

Memory

5.1MiB live, 176.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	22	43
1	89	40
2	497	38
3	4478	38
0	8506	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) (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) 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 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 (.f64 n (PI.f64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))
(.f64 (.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 k)) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))
(.f64 (.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))) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (.f64 (pow.f64 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)))) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (/.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))) (neg.f64 (sqrt.f64 k))) #s(literal -1 binary64))
(.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64))))
(.f64 (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))) (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (/.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(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.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 n (PI.f64)) (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 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 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 (PI.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 (.f64 (PI.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 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 (.f64 n (*.f64 (PI.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 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 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))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.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(literal 1 binary64)) (pow.f64 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 k)) (/.f64 (pow.f64 (.f64 (PI.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 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))
(.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 k)) (/.f64 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) #s(literal 1 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 k)) (pow.f64 n (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 k #s(literal -1/4 binary64)) (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/8 binary64))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(.f64 (neg.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)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (pow.f64 (sqrt.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 (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (.f64 (pow.f64 (.f64 n (PI.f64)) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))))
(.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal 1/2 binary64) k #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 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))) (/.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 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (/.f64 (pow.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))) (.f64 (pow.f64 (*.f64 n (PI.f64)) (fma.f64 #s(literal 1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(.f64 #s(literal -1 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))) (neg.f64 (sqrt.f64 k))))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 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 (pow.f64 n (fma.f64 #s(literal 1/2 binary64) 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))) (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 (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)) #s(literal 1 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))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (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(literal 1 binary64)))
(.f64 (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))))
(.f64 #s(literal 1 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)))
(pow.f64 (/.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)))) #s(literal -1 binary64))
(/.f64 (/.f64 (neg.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(literal -1 binary64)) (sqrt.f64 k))
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(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (*.f64 k k) (fma.f64 #s(literal 2 binary64) k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (/.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))))

eval103.0ms (1.1%)

Memory: 7.9MiB live, 84.7MiB allocated
Compiler: Compiled 9 931 to 1 555 computations (84.3% saved)

prune46.0ms (0.5%)

Memory

-7.2MiB live, 38.9MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	415	16	431
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	416	16	432

Accuracy

100.0%

Counts

432 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	45.2%	(/.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))
	99.7%	(/.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)))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
	45.1%	(/.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)))))
	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)))
▶	56.9%	(.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) (.f64 #s(literal -1/2 binary64) k))))
	45.8%	(.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))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
▶	80.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 k #s(literal 1/4 binary64)))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) k)))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (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))))))
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (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)))))
	45.8%	(.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)))))
	51.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.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 (.f64 #s(literal -1/2 binary64) k) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 1 binary64)) (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64))))) k))
	99.5%	#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))))
▶	36.0%	#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))))

Compiler

Compiled 796 to 602 computations (24.4% saved)

simplify210.0ms (2.3%)

Memory

-8.3MiB live, 102.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	374
0	83	369
1	129	355
2	202	355
3	500	349
4	1255	349
5	2047	349
6	2855	349
7	3016	349
8	3798	349
9	4435	349
10	5380	349
11	6299	349
12	7066	349
13	7471	349
14	7653	349
15	7689	349
0	8082	349

Stop Event

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

Calls

Call 1

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

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

localize229.0ms (2.5%)

Memory

-5.7MiB live, 112.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.19140625	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.197597509768442	(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))
accuracy	12.616762770978257	(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 k #s(literal 1/4 binary64)))
accuracy	16.22616745782635	(PI.f64)
accuracy	0.18359375	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.19140625	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (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)))))
accuracy	0.234375	(/.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) n))
accuracy	16.22616745782635	(PI.f64)
accuracy	0.19140625	(.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))))
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	16.22616745782635	(PI.f64)
accuracy	29.61737032625547	#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
accuracy	0.34212875976844204	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	6.41788061712132	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	16.22616745782635	(PI.f64)
accuracy	18.09850570949981	#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	0.11328125	(sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))
accuracy	0.15234375	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/2 binary64))))
accuracy	0.19140625	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	16.22616745782635	(PI.f64)

Samples

88.0ms	189×	0	valid
22.0ms	67×	0	exit

Compiler

Compiled 330 to 43 computations (87% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-add: 28.0ms (32.6% of total)

ival-mult: 17.0ms (19.8% of total)

ival-pow: 16.0ms (18.6% of total)

ival-div: 10.0ms (11.7% of total)

ival-sqrt: 8.0ms (9.3% of total)

ival-pow2: 3.0ms (3.5% of total)

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

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

exact: 1.0ms (1.2% of total)

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

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

series170.0ms (1.9%)

Memory

20.1MiB live, 180.3MiB allocated

Counts

21 → 69

Calls

Call 1

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

Outputs
1
(+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2))))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/2 (* k (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/2 (* (log (* 2 (* n (PI)))) (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))) (* 1/2 (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt (/ (* n (PI)) k))
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(/ (+ (* -1/4 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2)))))) (* -1/4 (* (sqrt (* k (* n (PI)))) (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/4 (* (sqrt (* k (* n (PI)))) (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2)))))) (+ (* -1/128 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3) (sqrt 2))) (* 1/384 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(+ (* -1/4 (* (* k (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1 (* (* k (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/4 (* (sqrt (* n (PI))) (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/4 (* (sqrt (* n (PI))) (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2)))))) (+ (* -1/128 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3) (sqrt 2))) (* 1/384 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
1/2
(+ 1/2 (* -1/2 k))
(+ 1 (* 1/4 (* k (log (* 4 (* (pow n 2) (pow (PI) 2)))))))
(+ 1 (* k (+ (* 1/32 (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2))) (* 1/4 (log (* 4 (* (pow n 2) (pow (PI) 2))))))))
(+ 1 (* k (+ (* 1/4 (log (* 4 (* (pow n 2) (pow (PI) 2))))) (* k (+ (* 1/384 (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3))) (* 1/32 (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))))
(sqrt (pow (* 2 (* n (PI))) k))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/4 (* k (log (* 4 (* (pow n 2) (pow (PI) 2)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/4 (* k (log (* 4 (* (pow n 2) (pow (PI) 2)))))))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(exp (* 1/4 (* k (log (* 4 (* (pow n 2) (pow (PI) 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))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(sqrt (exp (* k (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* 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 (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))))))))
(exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))))))
(* 4 (* (pow n 2) (pow (PI) 2)))
(sqrt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))))))))
(exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))))))
(sqrt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n))))))))))
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n))))))))))
(exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))))))

Calls

6 calls:

Time	Variable		Point	Expression
60.0ms	n	@	0	((pow (pow (* n (* (PI) 2)) k) 1/2) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (sqrt (* n (* (PI) 2))) (* 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)) (* (/ 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))) (/ (* -2 (PI)) (/ -1 n)) (* (/ 1 (sqrt k)) (/ (sqrt (* n (* (PI) 2))) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4)))) (/ (sqrt (* n (* (PI) 2))) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4))) (PI) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4)) (pow (* n (* (PI) 2)) 2))
54.0ms	n	@	-inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (sqrt (* n (* (PI) 2))) (* 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)) (* (/ 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))) (/ (* -2 (PI)) (/ -1 n)) (* (/ 1 (sqrt k)) (/ (sqrt (* n (* (PI) 2))) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4)))) (/ (sqrt (* n (* (PI) 2))) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4))) (PI) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4)) (pow (* n (* (PI) 2)) 2))
36.0ms	n	@	inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (sqrt (* n (* (PI) 2))) (* 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)) (* (/ 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))) (/ (* -2 (PI)) (/ -1 n)) (* (/ 1 (sqrt k)) (/ (sqrt (* n (* (PI) 2))) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4)))) (/ (sqrt (* n (* (PI) 2))) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4))) (PI) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4)) (pow (* n (* (PI) 2)) 2))
8.0ms	k	@	0	((pow (pow (* n (* (PI) 2)) k) 1/2) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (sqrt (* n (* (PI) 2))) (* 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)) (* (/ 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))) (/ (* -2 (PI)) (/ -1 n)) (* (/ 1 (sqrt k)) (/ (sqrt (* n (* (PI) 2))) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4)))) (/ (sqrt (* n (* (PI) 2))) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4))) (PI) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4)) (pow (* n (* (PI) 2)) 2))
7.0ms	k	@	-inf	((pow (pow (* n (* (PI) 2)) k) 1/2) (/ (sqrt (* n (* (PI) 2))) (* (sqrt k) (pow (pow (* n (* (PI) 2)) k) 1/2))) (sqrt (* n (* (PI) 2))) (* 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)) (* (/ 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))) (/ (* -2 (PI)) (/ -1 n)) (* (/ 1 (sqrt k)) (/ (sqrt (* n (* (PI) 2))) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4)))) (/ (sqrt (* n (* (PI) 2))) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4))) (PI) (/ (- 1 k) 2) (* (* 2 (PI)) n) (pow (pow (* n (* (PI) 2)) 2) (* k 1/4)) (pow (* n (* (PI) 2)) 2))

simplify212.0ms (2.3%)

Memory

-17.4MiB live, 136.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	350	1818
1	1106	1725
2	4024	1654
0	8364	1600

Stop Event

1×	iter limit
1×	node limit

Counts

69 → 69

Calls

Call 1

Inputs
1
(+ 1 (* 1/2 (* k (log (* 2 (* n (PI)))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* 1/2 (* k (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2))))))))
(+ 1 (* k (+ (* 1/2 (log (* 2 (* n (PI))))) (* k (+ (* 1/2 (* k (- (* 1/6 (pow (log (* 2 (* n (PI)))) 3)) (* 1/2 (* (log (* 2 (* n (PI)))) (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))) (* 1/2 (- (* 1/2 (pow (log (* 2 (* n (PI)))) 2)) (* 1/4 (pow (log (* 2 (* n (PI)))) 2)))))))))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1/2 (* (sqrt (/ (* n (PI)) k)) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (* (sqrt 2) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (* (sqrt 2) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (+ (* -1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* 1/6 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (* 1/4 (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) k))))))))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(sqrt (/ (* n (PI)) k))
(sqrt (/ 1 k))
(sqrt k)
(* (sqrt (* n (PI))) (sqrt 2))
(+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (* k (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (sqrt (* n (PI))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (* k (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (sqrt (* n (PI))))) (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* n (PI))) (sqrt 2)))
(/ (+ (* -1/4 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2)))))) (* -1/4 (* (sqrt (* k (* n (PI)))) (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/ (+ (* k (+ (* -1/4 (* (sqrt (* k (* n (PI)))) (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* k (* n (PI)))) (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2)))))) (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (+ (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2)))))) (+ (* -1/128 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3) (sqrt 2))) (* 1/384 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3) (sqrt 2))))))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(+ (* -1/4 (* (* k (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1 (* (* k (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/4 (* (sqrt (* n (PI))) (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+ (* k (+ (* -1/4 (* (sqrt (* n (PI))) (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/4 (* (log (* 4 (* (pow n 2) (pow (PI) 2)))) (+ (* -1/16 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2))) (* 1/32 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2) (sqrt 2)))))) (+ (* -1/128 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3) (sqrt 2))) (* 1/384 (* (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3) (sqrt 2)))))) (sqrt (* n (PI))))))))) (* (sqrt (* n (PI))) (sqrt 2)))
1/2
(+ 1/2 (* -1/2 k))
(+ 1 (* 1/4 (* k (log (* 4 (* (pow n 2) (pow (PI) 2)))))))
(+ 1 (* k (+ (* 1/32 (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2))) (* 1/4 (log (* 4 (* (pow n 2) (pow (PI) 2))))))))
(+ 1 (* k (+ (* 1/4 (log (* 4 (* (pow n 2) (pow (PI) 2))))) (* k (+ (* 1/384 (* k (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 3))) (* 1/32 (pow (log (* 4 (* (pow n 2) (pow (PI) 2)))) 2)))))))
(sqrt (pow (* 2 (* n (PI))) k))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/4 (* k (log (* 4 (* (pow n 2) (pow (PI) 2)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/4 (* k (log (* 4 (* (pow n 2) (pow (PI) 2)))))))))
(* -1/2 k)
(* k (- (* 1/2 (/ 1 k)) 1/2))
(exp (* 1/4 (* k (log (* 4 (* (pow n 2) (pow (PI) 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))
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))
(* -1 (* k (- 1/2 (* 1/2 (/ 1 k)))))
(sqrt (exp (* k (+ (log n) (log (* 2 (PI)))))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(* 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 (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))))))))
(exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* 2 (log n))))))
(* 4 (* (pow n 2) (pow (PI) 2)))
(sqrt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))
(exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))))))))
(exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ 1 n)))))))
(sqrt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))
(* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n))))))))))
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n))))))))))
(exp (* 1/4 (* k (+ (log (* 4 (pow (PI) 2))) (* -2 (log (/ -1 n)))))))

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

rewrite169.0ms (1.9%)

Memory

18.8MiB live, 260.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	233
0	83	219
1	295	195
2	1747	187
0	8288	187

Stop Event

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

Counts

21 → 865

Calls

Call 1

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

Outputs
(.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 (.f64 k #s(literal 1/8 binary64)) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/8 binary64))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 (.f64 k #s(literal 1/8 binary64)) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/8 binary64))))
(.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 (.f64 k #s(literal 1/8 binary64)) #s(literal 1/2 binary64)))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 (*.f64 k #s(literal 1/8 binary64)) #s(literal 1/2 binary64)))))
(.f64 (fabs.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k)) (fabs.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
(.f64 (fabs.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k)) (fabs.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 (pow.f64 #s(literal 2 binary64) k)))
(.f64 (sqrt.f64 (pow.f64 #s(literal 2 binary64) k)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) n) k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k))
(.f64 (pow.f64 (sqrt.f64 #s(literal 2 binary64)) k) (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))
(.f64 (pow.f64 (sqrt.f64 n) k) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) k))
(.f64 (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) k) (pow.f64 (sqrt.f64 n) k))
(.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) k) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) k)) (log.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
(pow.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) k) (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) k)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 4 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) k))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 4 binary64)) k) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) #s(literal 1 binary64)) k)
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 4 binary64)) (*.f64 k #s(literal 1/8 binary64)))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)) (neg.f64 (*.f64 #s(literal 1/2 binary64) k)))
(pow.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) k) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k) #s(literal 1 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (fma.f64 k #s(literal 1/8 binary64) (.f64 k #s(literal 1/8 binary64)))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) k)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 (.f64 k #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/8 binary64)))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/8 binary64) (*.f64 k #s(literal 1/8 binary64))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 k #s(literal 1/8 binary64))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) k))
(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal 2 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (fma.f64 #s(literal 1/2 binary64) k (*.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal 2 binary64) (.f64 k #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/8 binary64)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal 1/4 binary64) k (*.f64 #s(literal 1/4 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/8 binary64) (.f64 k #s(literal 1/8 binary64)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/8 binary64)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) k)) #s(literal 1/2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (fma.f64 #s(literal 1/2 binary64) k (.f64 #s(literal 1/2 binary64) k)) #s(literal 1/2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/8 binary64))) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(/.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)) #s(literal -1 binary64))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal -1/2 binary64)))
(neg.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k))
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(fabs.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(fabs.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k))
(exp.f64 (fma.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (.f64 k #s(literal 1/8 binary64)) (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (*.f64 k #s(literal 1/8 binary64)))))
(exp.f64 (fma.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal 1/4 binary64) (.f64 (log.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (*.f64 k #s(literal 1/8 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 4 binary64))) (.f64 k #s(literal 1/8 binary64))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))) k))
(exp.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/8 binary64) (.f64 k #s(literal 1/8 binary64)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/8 binary64)))))
(exp.f64 (log.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(.f64 (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))) (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))))
(.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(.f64 (pow.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))) (sqrt.f64 k)) #s(literal -1/2 binary64)) (pow.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))) (sqrt.f64 k)) #s(literal -1/2 binary64)))
(.f64 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))) (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/4 binary64))) (pow.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 (neg.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))) (sqrt.f64 k)) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (neg.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))) (/.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (+.f64 #s(literal -1 binary64) k) #s(literal -1/4 binary64))))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 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 n (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
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(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 k #s(literal 1/8 binary64))))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) k))
(pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal 2 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (fma.f64 #s(literal 1/2 binary64) k (*.f64 #s(literal 1/2 binary64) k)) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 (.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) k) #s(literal 1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal 2 binary64) (.f64 k #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/8 binary64)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (fma.f64 #s(literal 1/4 binary64) k (*.f64 #s(literal 1/4 binary64) k)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal 2 binary64) (fma.f64 k #s(literal 1/8 binary64) (.f64 k #s(literal 1/8 binary64)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/8 binary64)))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) k)) #s(literal 1/2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (fma.f64 #s(literal 1/2 binary64) k (.f64 #s(literal 1/2 binary64) k)) #s(literal 1/2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/8 binary64))) #s(literal 2 binary64)))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal 1/2 binary64) k))
(/.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)) #s(literal -1 binary64))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal -1/2 binary64)))
(neg.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(sqrt.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k))
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(fabs.f64 (neg.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(fabs.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k))
(exp.f64 (fma.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (.f64 k #s(literal 1/8 binary64)) (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (*.f64 k #s(literal 1/8 binary64)))))
(exp.f64 (fma.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal 1/4 binary64) (.f64 (log.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (*.f64 k #s(literal 1/8 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 4 binary64))) (.f64 k #s(literal 1/8 binary64))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))) k))
(exp.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (fma.f64 k #s(literal 1/8 binary64) (.f64 k #s(literal 1/8 binary64)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (*.f64 k #s(literal 1/8 binary64)))))
(exp.f64 (log.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) k)))
(.f64 (.f64 (.f64 (PI.f64) #s(literal -1 binary64)) (.f64 (PI.f64) #s(literal -1 binary64))) (.f64 (.f64 #s(literal -2 binary64) n) (*.f64 #s(literal -2 binary64) n)))
(.f64 (.f64 (neg.f64 n) (neg.f64 n)) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 (.f64 (neg.f64 n) (PI.f64)) (.f64 (neg.f64 n) (PI.f64))) #s(literal 4 binary64))
(.f64 (.f64 (.f64 #s(literal 2 binary64) n) (.f64 #s(literal 2 binary64) n)) (*.f64 (PI.f64) (PI.f64)))
(.f64 (.f64 (.f64 n #s(literal 2 binary64)) (.f64 n #s(literal 2 binary64))) (*.f64 (PI.f64) (PI.f64)))
(.f64 (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) n) (.f64 (*.f64 #s(literal -2 binary64) (PI.f64)) n))
(.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 (PI.f64) n)) #s(literal 2 binary64))
(.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal 2 binary64) (PI.f64))) n)
(.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) (*.f64 (PI.f64) n))
(.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) n) (*.f64 #s(literal 2 binary64) (PI.f64)))
(.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (.f64 #s(literal -2 binary64) (neg.f64 n)) (*.f64 #s(literal -2 binary64) (neg.f64 n))))
(.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (.f64 #s(literal 2 binary64) n) (*.f64 #s(literal 2 binary64) n)))
(.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (.f64 n #s(literal 2 binary64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 4 binary64))
(.f64 #s(literal 4 binary64) (.f64 (.f64 (neg.f64 n) (PI.f64)) (.f64 (neg.f64 n) (PI.f64))))
(.f64 #s(literal 4 binary64) (pow.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64)) (*.f64 (neg.f64 n) (neg.f64 n)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64)) (*.f64 n n))
(.f64 (.f64 n n) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 (PI.f64) n) (.f64 #s(literal 2 binary64) (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)))
(.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 n (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)))
(.f64 #s(literal 2 binary64) (.f64 (.f64 (PI.f64) n) (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n)))
(.f64 n (.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (*.f64 #s(literal 2 binary64) (PI.f64))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))
(pow.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) n) (.f64 #s(literal -2 binary64) (PI.f64))) (pow.f64 n #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) n) #s(literal 1 binary64)) (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))))
(/.f64 (.f64 (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) n) (.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 #s(literal -1 binary64) n))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) n)) (*.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 (/.f64 #s(literal -1 binary64) n) (pow.f64 n #s(literal -1 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) n)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)) #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (.f64 #s(literal -2 binary64) (PI.f64)) n)) (/.f64 #s(literal -1 binary64) n))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1 binary64)) (.f64 (pow.f64 n #s(literal -1 binary64)) (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 (pow.f64 n #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) n)))
(/.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) n) (/.f64 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) (PI.f64))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal -1 binary64) n) (/.f64 #s(literal -1 binary64) n)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 2 binary64)) (.f64 (pow.f64 n #s(literal -1 binary64)) (pow.f64 n #s(literal -1 binary64))))
(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (.f64 (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)) (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))))
(/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (.f64 (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) (pow.f64 n #s(literal -1 binary64))))
(/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (.f64 (/.f64 #s(literal -1 binary64) n) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))))
(/.f64 (.f64 #s(literal -2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) n)))
(/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (neg.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) n)))
(/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (/.f64 #s(literal -1 binary64) n) (neg.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)))))
(/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64)) (pow.f64 n #s(literal -1 binary64))))
(/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 (pow.f64 n #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal -1 binary64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(literal 2 binary64))))

eval163.0ms (1.8%)

Memory: -6.0MiB live, 308.0MiB allocated
Compiler: Compiled 32 173 to 4 094 computations (87.3% saved)

prune32.0ms (0.3%)

Memory

10.1MiB live, 88.8MiB allocated

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	1 193	16	1 209
Fresh	9	2	11
Picked	4	1	5
Done	0	0	0
Total	1 206	19	1 225

Accuracy

100.0%

Counts

1 225 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.9%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
	99.5%	(/.f64 #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)))
	45.8%	(.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)))))
	99.7%	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
	89.9%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
	45.9%	#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)))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
▶	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
	99.5%	#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))))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
	35.8%	#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))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))))
▶	45.8%	#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))))
	45.8%	#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)))))
	45.7%	#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)))))
✓	36.0%	#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))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
▶	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))

Compiler

Compiled 898 to 725 computations (19.3% saved)

simplify13.0ms (0.1%)

Memory

-20.4MiB live, 18.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	297
0	64	297
1	91	291
2	124	291
3	179	291
4	208	291
5	222	291
6	243	291
7	286	291
8	348	291
9	357	291
0	357	285

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize158.0ms (1.7%)

Memory

26.3MiB live, 148.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1652470815555653	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)))
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	16.22616745782635	(PI.f64)
accuracy	29.61737032625547	#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))
accuracy	0.30306625976844204	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
accuracy	0.34212875976844204	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
accuracy	16.22616745782635	(PI.f64)
accuracy	18.09850570949981	#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))))
accuracy	0.1953125	(/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
accuracy	6.194140431045018	(sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))
accuracy	16.22616745782635	(PI.f64)
accuracy	18.09850570949981	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)))))
accuracy	0.19140625	(*.f64 (PI.f64) n)
accuracy	6.444969798206227	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
accuracy	16.22616745782635	(PI.f64)
accuracy	18.09850570949981	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
accuracy	0.11328125	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n))
accuracy	0.15234375	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	16.22616745782635	(PI.f64)

Samples

119.0ms	189×	0	valid
17.0ms	67×	0	exit

Compiler

Compiled 256 to 34 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-sqrt: 40.0ms (40.3% of total)

ival-pow: 33.0ms (33.2% of total)

ival-div: 11.0ms (11.1% of total)

ival-mult: 11.0ms (11.1% of total)

ival-pi: 1.0ms (1% of total)

ival-sub: 1.0ms (1% of total)

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

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

exact: 0.0ms (0% of total)

series54.0ms (0.6%)

Memory

-28.0MiB live, 91.3MiB allocated

Counts

21 → 46

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	n	@	-inf	((/ (sqrt (* (* 2 (PI)) n)) (sqrt (* k (pow (* (* 2 (PI)) n) k)))) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (sqrt (/ k (* (* 2 (PI)) n))) (/ k (* (* 2 (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (PI) n) (/ (- 1 k) 2))
13.0ms	n	@	inf	((/ (sqrt (* (* 2 (PI)) n)) (sqrt (* k (pow (* (* 2 (PI)) n) k)))) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (sqrt (/ k (* (* 2 (PI)) n))) (/ k (* (* 2 (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (PI) n) (/ (- 1 k) 2))
11.0ms	n	@	0	((/ (sqrt (* (* 2 (PI)) n)) (sqrt (* k (pow (* (* 2 (PI)) n) k)))) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (sqrt (/ k (* (* 2 (PI)) n))) (/ k (* (* 2 (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (PI) n) (/ (- 1 k) 2))
6.0ms	k	@	0	((/ (sqrt (* (* 2 (PI)) n)) (sqrt (* k (pow (* (* 2 (PI)) n) k)))) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (sqrt (/ k (* (* 2 (PI)) n))) (/ k (* (* 2 (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (PI) n) (/ (- 1 k) 2))
5.0ms	k	@	-inf	((/ (sqrt (* (* 2 (PI)) n)) (sqrt (* k (pow (* (* 2 (PI)) n) k)))) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* 2 (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* (PI) n) k) 2)) (* (/ (* (PI) n) k) 2) (/ (* (PI) n) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (sqrt (/ k (* (* 2 (PI)) n))) (/ k (* (* 2 (PI)) n)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (/ (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* (PI) n) (/ (- 1 k) 2))

simplify434.0ms (4.8%)

Memory

-140.6MiB live, 234.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	216	944
1	646	906
2	2229	853
3	5038	824
0	8589	805

Stop Event

1×	iter limit
1×	node limit

Counts

46 → 46

Calls

Call 1

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

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

rewrite146.0ms (1.6%)

Memory

-5.0MiB live, 192.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	220
0	64	210
1	210	204
2	1096	198
0	8447	195

Stop Event

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

Counts

21 → 1 005

Calls

Call 1

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

Outputs
(.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64)) (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))) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n))
(.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))) (sqrt.f64 (/.f64 n (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k))))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k))))
(.f64 (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64)))) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))))
(.f64 (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64)))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64)))) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))
(.f64 (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64)))) (pow.f64 #s(literal 2 binary64) (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64)))) (pow.f64 (.f64 n (PI.f64)) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))))
(.f64 (.f64 (.f64 (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 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64))) (pow.f64 (pow.f64 n (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k)) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (.f64 (pow.f64 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)))) (pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 n (fma.f64 #s(literal -1/2 binary64) 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))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (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 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 k #s(literal 1 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))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(.f64 (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64)))) (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (-.f64 k #s(literal 1 binary64)) #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) n) (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k)) n) (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)))
(.f64 (/.f64 (pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 (*.f64 n (PI.f64)) k) #s(literal 1/2 binary64))))
(.f64 (/.f64 (pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))) (/.f64 (pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 n k))))
(.f64 (/.f64 (pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 n k))) (/.f64 (pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal -1/4 binary64)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(.f64 (/.f64 (pow.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (*.f64 n (PI.f64)) k) #s(literal 1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))) (/.f64 (pow.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 n k))))
(.f64 (/.f64 (pow.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 n k))) (/.f64 (pow.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (pow.f64 #s(literal 2 binary64) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 (.f64 n (PI.f64)) k) #s(literal 1/2 binary64))))
(.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 (pow.f64 n k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))))
(.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 n k))))
(.f64 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (.f64 k #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (*.f64 n (PI.f64)) k) #s(literal 1/2 binary64))))
(.f64 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 n k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(.f64 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 n k))))
(.f64 (/.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 1/4 binary64))) (/.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 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (*.f64 n (PI.f64)) k) #s(literal 1/2 binary64))))
(.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (pow.f64 n k))))
(.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 n k))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) 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 (.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) k) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k) 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 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) (/.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))) (neg.f64 (sqrt.f64 k))) (/.f64 (neg.f64 (sqrt.f64 n)) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
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(exp.f64 (.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k)) #s(literal 1/2 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(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k)) #s(literal 1 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(approx (/ (- 1 k) 2) (.f64 #s(literal -1/2 binary64) k))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (sqrt.f64 (PI.f64)))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))))
(.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (PI.f64))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (PI.f64)) (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (exp.f64 (log.f64 (sqrt.f64 (PI.f64)))) (exp.f64 (log.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (exp.f64 (log.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (exp.f64 (log.f64 (cbrt.f64 (PI.f64)))))
(.f64 (.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (pow.f64 (pow.f64 (.f64 (cbrt.f64 (PI.f64)) (PI.f64)) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (PI.f64))))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(fabs.f64 (PI.f64))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (log.f64 (PI.f64)))
(log.f64 (exp.f64 (PI.f64)))
(PI.f64)
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(.f64 (.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 1 binary64) n) (PI.f64))
(.f64 (.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(*.f64 (neg.f64 (neg.f64 (PI.f64))) n)
(*.f64 (neg.f64 (neg.f64 n)) (PI.f64))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (neg.f64 (PI.f64)) (neg.f64 n))
(*.f64 (neg.f64 n) (neg.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (.f64 (cbrt.f64 (PI.f64)) n))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 (PI.f64)) n))
(.f64 (.f64 n (PI.f64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))
(*.f64 n (neg.f64 (neg.f64 (PI.f64))))
(*.f64 n (PI.f64))
(*.f64 (PI.f64) (neg.f64 (neg.f64 n)))
(*.f64 (PI.f64) n)
(neg.f64 (*.f64 (neg.f64 (PI.f64)) n))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (PI.f64)) n))
#s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))

eval212.0ms (2.3%)

Memory: -1.8MiB live, 300.0MiB allocated
Compiler: Compiled 35 312 to 4 657 computations (86.8% saved)

prune86.0ms (0.9%)

Memory

9.2MiB live, 137.5MiB allocated

Pruning

48 alts after pruning (43 fresh and 5 done)

	Pruned	Kept	Total
New	1 267	34	1 301
Fresh	4	9	13
Picked	1	4	5
Done	0	1	1
Total	1 272	48	1 320

Accuracy

100.0%

Counts

1 320 → 48

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) #s(approx (/ (- 1 k) 2) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	56.9%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
✓	99.7%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
	45.8%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
	99.5%	(/.f64 #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)))
	45.8%	(.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)))))
▶	99.7%	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
	89.9%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
	89.9%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) n) (/.f64 (PI.f64) k)))
▶	45.9%	#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)))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n)))))
▶	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 k))))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))))
	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))))
▶	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ k (* (* 2 (PI)) n))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))))
	99.5%	#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))))
	45.7%	#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 (neg.f64 (sqrt.f64 n)) (sqrt.f64 k))))
	45.8%	#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 n (PI.f64))) #s(literal 1 binary64))))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n)))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 n)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 n (PI.f64)))))
	35.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
	45.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))))
✓	45.8%	#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))))
	45.8%	#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)))))
✓	36.0%	#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))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
	36.1%	#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))))
	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 n (/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64)))))
	36.1%	#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))))))
	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal -2 binary64) (/.f64 (/.f64 k (PI.f64)) (neg.f64 n)))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k) #s(literal 2 binary64))))
✓	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	36.1%	#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)))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (*.f64 n (sqrt.f64 (PI.f64))) k) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))) #s(literal 2 binary64))))
	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))))
▶	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 2 393 to 1 916 computations (19.9% saved)

simplify18.0ms (0.2%)

Memory

-22.6MiB live, 15.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	365
0	80	365
1	123	351
2	176	347
3	247	347
4	286	347
5	305	347
6	327	347
7	372	347
8	434	347
9	443	347
0	443	343

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize132.0ms (1.4%)

Memory

-4.2MiB live, 201.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.73828125	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	6.133856483342426	(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
accuracy	16.22616745782635	(PI.f64)
accuracy	18.09850570949981	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
accuracy	0.32650375976844204	(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n))))
accuracy	6.133856483342426	(sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))
accuracy	16.22616745782635	(PI.f64)
accuracy	18.09850570949981	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ k (* (* 2 (PI)) n))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))))
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.23046875	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 k))
accuracy	16.22616745782635	(PI.f64)
accuracy	18.09850570949981	#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)))
accuracy	0.19140625	(/.f64 (PI.f64) k)
accuracy	6.444969798206227	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
accuracy	16.22616745782635	(PI.f64)
accuracy	18.09850570949981	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
accuracy	0.13671875	(/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)))
accuracy	0.17578125	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
accuracy	0.19140625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	16.22616745782635	(PI.f64)

Samples

60.0ms	189×	0	valid
35.0ms	67×	0	exit

Compiler

Compiled 293 to 43 computations (85.3% saved)

Precisions

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

ival-mult: 29.0ms (39.4% of total)

ival-div: 17.0ms (23.1% of total)

ival-sqrt: 16.0ms (21.7% of total)

ival-pow: 9.0ms (12.2% 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)

series61.0ms (0.7%)

Memory

23.0MiB live, 98.1MiB allocated

Counts

24 → 58

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	n	@	-inf	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* 2 (PI)) n)) (sqrt k)) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (sqrt (/ k (* (* 2 (PI)) n))) (* (sqrt 1/2) (sqrt (/ k (* (PI) n)))) (/ 1 (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ k (* n (PI)))) (PI) (/ (PI) k) (sqrt (/ k (* (PI) n))) (/ 1 (sqrt 2)))
13.0ms	n	@	0	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* 2 (PI)) n)) (sqrt k)) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (sqrt (/ k (* (* 2 (PI)) n))) (* (sqrt 1/2) (sqrt (/ k (* (PI) n)))) (/ 1 (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ k (* n (PI)))) (PI) (/ (PI) k) (sqrt (/ k (* (PI) n))) (/ 1 (sqrt 2)))
12.0ms	n	@	inf	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* 2 (PI)) n)) (sqrt k)) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (sqrt (/ k (* (* 2 (PI)) n))) (* (sqrt 1/2) (sqrt (/ k (* (PI) n)))) (/ 1 (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ k (* n (PI)))) (PI) (/ (PI) k) (sqrt (/ k (* (PI) n))) (/ 1 (sqrt 2)))
7.0ms	k	@	-inf	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* 2 (PI)) n)) (sqrt k)) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (sqrt (/ k (* (* 2 (PI)) n))) (* (sqrt 1/2) (sqrt (/ k (* (PI) n)))) (/ 1 (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ k (* n (PI)))) (PI) (/ (PI) k) (sqrt (/ k (* (PI) n))) (/ 1 (sqrt 2)))
5.0ms	k	@	0	((* (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))))) (sqrt n) (sqrt (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (/ (* 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* n (/ (PI) k)) 2)) (* (* n (/ (PI) k)) 2) (* n (/ (PI) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (sqrt (* (* 2 (PI)) n)) (sqrt k)) (sqrt (* (* 2 (PI)) n)) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (sqrt (/ k (* (* 2 (PI)) n))) (* (sqrt 1/2) (sqrt (/ k (* (PI) n)))) (/ 1 (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2)))) (* (sqrt (/ k (* n (PI)))) (/ 1 (sqrt 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (/ k (* n (PI)))) (PI) (/ (PI) k) (sqrt (/ k (* (PI) n))) (/ 1 (sqrt 2)))

simplify178.0ms (1.9%)

Memory

14.5MiB live, 201.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	285	1290
1	847	1226
2	3162	1146
0	8464	1120

Stop Event

1×	iter limit
1×	node limit

Counts

58 → 58

Calls

Call 1

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

rewrite181.0ms (2%)

Memory

-23.6MiB live, 230.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	295
0	80	275
1	259	266
2	1340	259
0	8944	259

Stop Event

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

Counts

24 → 1 237

Calls

Call 1

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

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

eval207.0ms (2.3%)

Memory: 26.6MiB live, 292.6MiB allocated
Compiler: Compiled 37 813 to 5 660 computations (85% saved)

prune148.0ms (1.6%)

Memory

-8.3MiB live, 189.7MiB allocated

Pruning

63 alts after pruning (53 fresh and 10 done)

	Pruned	Kept	Total
New	1 242	27	1 269
Fresh	12	26	38
Picked	0	5	5
Done	0	5	5
Total	1 254	63	1 317

Accuracy

100.0%

Counts

1 317 → 63

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 k))
✓	56.9%	(/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) #s(approx (/ (- 1 k) 2) (*.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 k))
✓	99.7%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k))))
	45.8%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 k))
	99.5%	(/.f64 #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)))
	45.8%	(.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)))))
✓	99.7%	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k)))))
	45.9%	(.f64 (sqrt.f64 n) (sqrt.f64 #s(approx (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k))) (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
	45.8%	(.f64 (sqrt.f64 n) #s(approx (sqrt (/ ( 2 (PI)) (* k (pow (* (* 2 (PI)) n) k)))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))))
	89.9%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) k) k)))
	89.9%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) n) (/.f64 (PI.f64) k)))
	45.7%	#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 n)) (sqrt.f64 k)))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 k)))
✓	45.9%	#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)))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 k) (sqrt.f64 #s(literal 2 binary64)))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n)))))
	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))
	36.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 n (PI.f64))))))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	36.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 (/.f64 k n)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (neg.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 n)))))
✓	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 k))))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))))))
	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))))
	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) k))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ k (* (* 2 (PI)) n))) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)))))))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ k (* (* 2 (PI)) n))) (/.f64 (.f64 (sqrt.f64 (/.f64 k (PI.f64))) #s(literal 1 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64)))))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ k (* (* 2 (PI)) n))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))))
	36.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ k (* (* 2 (PI)) n))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n)))))))
✓	36.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (/ k (* (* 2 (PI)) n))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k (.f64 (PI.f64) n)))))))
	99.5%	#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))))
	45.7%	#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 (neg.f64 (sqrt.f64 n)) (sqrt.f64 k))))
	45.8%	#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 n (PI.f64))) #s(literal 1 binary64))))
	45.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 n)))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (PI.f64) n))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 (PI.f64) k))))
	45.9%	#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)))))
	35.9%	#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))))
	45.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (neg.f64 (sqrt.f64 n)) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))))
	35.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 n k) #s(literal 2 binary64)))))
✓	45.8%	#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))))
	45.8%	#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)))))
✓	36.0%	#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))))
	45.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) n))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
	36.1%	#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))))
	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 k (PI.f64)))))
	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))))
✓	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64))))
	36.1%	#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)))))
	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
	36.1%	#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)))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) n)) #s(literal 2 binary64))))
✓	36.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 n (.f64 (sqrt.f64 (PI.f64)) (.f64 (neg.f64 (sqrt.f64 (PI.f64))) (/.f64 #s(literal -1 binary64) k)))) #s(literal 2 binary64))))
	35.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) #s(approx (/ 1 (sqrt (/ k (* (* 2 (PI)) n)))) (/.f64 (sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 4 247 to 1 807 computations (57.5% saved)

regimes141.0ms (1.5%)

Memory

-11.0MiB live, 152.3MiB allocated

Counts

94 → 1

Calls

Call 1

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

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

Calls

4 calls:

42.0ms	k
38.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
32.0ms	n
24.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes101.0ms (1.1%)

Memory

-1.3MiB live, 193.5MiB allocated

Counts

85 → 1

Calls

Call 1

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

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

Calls

4 calls:

26.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	k
24.0ms	n
20.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.7%	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	`k`
99.7%	1	`n`
99.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes113.0ms (1.2%)

Memory

7.0MiB live, 126.4MiB allocated

Counts

84 → 1

Calls

Call 1

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

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

Calls

4 calls:

41.0ms	(.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))))
24.0ms	n
23.0ms	k
21.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

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)

regimes112.0ms (1.2%)

Memory

14.5MiB live, 90.0MiB allocated

Counts

74 → 2

Calls

Call 1

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

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

Calls

4 calls:

53.0ms	k
19.0ms	n
18.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
97.9%	2	`k`
56.9%	1	`n`
97.9%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
56.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes83.0ms (0.9%)

Memory

-0.0MiB live, 116.7MiB allocated

Counts

72 → 1

Calls

Call 1

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

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

Calls

4 calls:

23.0ms	k
21.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
19.0ms	n
16.0ms	(.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
45.9%	1	`n`
45.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
45.9%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
45.9%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes15.0ms (0.2%)

Memory

17.6MiB live, 17.6MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	n
3.0ms	k
3.0ms	(.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
36.1%	1	`n`
36.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
36.1%	1	`k`
36.1%	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))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes34.0ms (0.4%)

Memory

-29.6MiB live, 9.4MiB allocated

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

Counts

2 → 1

Calls

Call 1

Inputs

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

Calls

4 calls:

30.0ms	(.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	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	k
1.0ms	n

Results

Accuracy	Segments	Branch
36.1%	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))))`
36.1%	1	`n`
36.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
36.1%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch17.0ms (0.2%)

Memory

25.2MiB live, 25.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.3822702276747195	7.645038699050749

Samples

11.0ms

112×

valid

Compiler

Compiled 327 to 291 computations (11% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 2.0ms (25.4% of total)

ival-pow: 2.0ms (25.4% of total)

ival-div: 1.0ms (12.7% of total)

ival-sub: 1.0ms (12.7% of total)

ival-sqrt: 1.0ms (12.7% of total)

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

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

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

exact: 0.0ms (0% of total)

simplify74.0ms (0.8%)

Memory

-27.6MiB live, 20.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	177
1	66	169
2	83	169
3	107	169
4	134	169
5	163	169
6	236	169
7	531	169
8	4981	169

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness807.0ms (8.8%)

Memory

9.5MiB live, 595.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	216	944
1	646	906
2	2229	853
3	5038	824
0	8589	805
0	52	233
0	83	219
1	295	195
2	1747	187
0	8288	187
0	13	43
0	22	43
1	89	40
2	497	38
3	4478	38
0	8506	37
0	128	517
1	345	504
2	1022	460
3	3355	433
4	5591	421
0	8473	406
0	41	220
0	64	210
1	210	204
2	1096	198
0	8447	195

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

Compiler

Compiled 643 to 360 computations (44% saved)

preprocess93.0ms (1%)

Memory: -21.4MiB live, 128.6MiB allocated
Compiler: Compiled 386 to 134 computations (65.3% 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	41	297
0	64	297
1	91	291
2	124	291
3	179	291
4	208	291
5	222	291
6	243	291
7	286	291
8	348	291
9	357	291
0	357	285

Iter	Nodes	Cost
0	50	365
0	80	365
1	123	351
2	176	347
3	247	347
4	286	347
5	305	347
6	327	347
7	372	347
8	434	347
9	443	347
0	443	343

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	41	297
0	64	297
1	91	291
2	124	291
3	179	291
4	208	291
5	222	291
6	243	291
7	286	291
8	348	291
9	357	291
0	357	285

Iter	Nodes	Cost
0	50	365
0	80	365
1	123	351
2	176	347
3	247	347
4	286	347
5	305	347
6	327	347
7	372	347
8	434	347
9	443	347
0	443	343

start0.0ms (0%)

analyze223.0ms (2.4%)

sample3.3s (35.6%)

explain143.0ms (1.6%)

preprocess49.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize40.0ms (0.4%)

series72.0ms (0.8%)

simplify146.0ms (1.6%)

rewrite254.0ms (2.8%)

eval103.0ms (1.1%)

prune46.0ms (0.5%)

simplify210.0ms (2.3%)

localize229.0ms (2.5%)

series170.0ms (1.9%)

simplify212.0ms (2.3%)

rewrite169.0ms (1.9%)

eval163.0ms (1.8%)

prune32.0ms (0.3%)

simplify13.0ms (0.1%)

localize158.0ms (1.7%)

series54.0ms (0.6%)

simplify434.0ms (4.8%)

rewrite146.0ms (1.6%)

eval212.0ms (2.3%)

prune86.0ms (0.9%)

simplify18.0ms (0.2%)

localize132.0ms (1.4%)

series61.0ms (0.7%)

simplify178.0ms (1.9%)

rewrite181.0ms (2%)

eval207.0ms (2.3%)

prune148.0ms (1.6%)

regimes141.0ms (1.5%)

regimes101.0ms (1.1%)

regimes113.0ms (1.2%)

regimes112.0ms (1.2%)

regimes83.0ms (0.9%)

regimes15.0ms (0.2%)

regimes34.0ms (0.4%)

bsearch17.0ms (0.2%)

simplify74.0ms (0.8%)

soundness807.0ms (8.8%)

preprocess93.0ms (1%)

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	41	297
0	64	297
1	91	291
2	124	291
3	179	291
4	208	291
5	222	291
6	243	291
7	286	291
8	348	291
9	357	291
0	357	285

Iter	Nodes	Cost
0	50	365
0	80	365
1	123	351
2	176	347
3	247	347
4	286	347
5	305	347
6	327	347
7	372	347
8	434	347
9	443	347
0	443	343