Metrics for Migdal et al, Equation (51)

analyze159.0ms (1.2%)

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%	50%	1.6%	7
52.5%	25%	22.6%	0.1%	0%	50%	2.3%	8
53.8%	25%	21.5%	0.1%	0%	50%	3.5%	9
54.5%	25%	20.9%	0.1%	0%	50%	4.1%	10
55.3%	25%	20.2%	0.1%	0%	50%	4.8%	11
55.7%	25%	19.9%	0.1%	0%	50%	5.1%	12

Compiler

Compiled 19 to 14 computations (26.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-pow: 49.0ms (47.8% of total)

ival-mult: 24.0ms (23.4% of total)

ival-div: 13.0ms (12.7% of total)

ival-sqrt: 7.0ms (6.8% of total)

ival-sub: 5.0ms (4.9% of total)

ival-pi: 4.0ms (3.9% of total)

const: 2.0ms (2% of total)

backward-pass: 0.0ms (0% of total)

sample4.5s (33.8%)

Results

1.6s	3836×	5	exit
1.2s	8256×	0	valid
581.0ms	1950×	1	invalid
64.0ms	243×	0	unsamplable
35.0ms	415×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 2.5s

ival-pow: 805.0ms (31.8% of total)

ival-mult: 623.0ms (24.6% of total)

ival-div: 326.0ms (12.9% of total)

backward-pass: 274.0ms (10.8% of total)

ival-sqrt: 201.0ms (7.9% of total)

ival-sub: 131.0ms (5.2% of total)

ival-pi: 129.0ms (5.1% of total)

const: 41.0ms (1.6% of total)

Bogosity

preprocess83.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

1106×	`fnmadd-define`
930×	`fma-define`
846×	`fmsub-define`
760×	`fnmsub-define`
680×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	92
1	93	88
2	208	88
3	414	83
4	742	82
5	1486	82
6	2091	82
7	2661	82
8	3559	82
9	3711	82
10	3770	82
11	3814	82
12	3822	82
0	13	14
1	30	14
2	47	14
3	69	14
4	90	13
5	113	13
6	149	13
7	188	13
8	214	13
9	228	13
10	229	13
0	229	13

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

Outputs

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

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

Call 2

Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))

Outputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(* (rsqrt k) (pow (* 2 (* (PI) n)) (fnmsub k 1/2 -1/2)))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(* (rsqrt (neg k)) (pow (* 2 (* (PI) n)) (fnmsub k -1/2 -1/2)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(* (rsqrt k) (pow (* (PI) (* n -2)) (fnmsub k 1/2 -1/2)))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(fnmsub (rsqrt (neg k)) (pow (* 2 (* (PI) n)) (fnmsub k -1/2 -1/2)) 0)
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(* (pow (* (PI) (* n -2)) (fnmsub k 1/2 -1/2)) (neg (rsqrt k)))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))
(* (rsqrt n) (pow (* k (* 2 (PI))) (fnmsub n 1/2 -1/2)))

explain156.0ms (1.2%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
2	217	(3.033218529269442e+146 2.9771562410371315e-301)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
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)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`n`
0	0	-	-	`k`

Results

95.0ms

512×

valid

Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-pow: 19.0ms (34.7% of total)

ival-div: 11.0ms (20.1% of total)

ival-mult: 11.0ms (20.1% of total)

ival-sqrt: 8.0ms (14.6% of total)

ival-sub: 3.0ms (5.5% of total)

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

const: 1.0ms (1.8% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Status

Accuracy

Program

▶

99.6%

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

▶

99.5%

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

Compiler

Compiled 34 to 25 computations (26.5% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	cost-diff	0	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	128	(.f64 (/.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))))

Rules

64×	`sum3-define`
64×	`-lowering-.f32`
64×	`-lowering-.f64`
48×	`+-lowering-+.f64`
48×	`+-lowering-+.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	98
1	38	98
2	58	98
3	78	98
4	100	92
5	129	92
6	170	92
7	202	92
8	231	92
9	235	92
0	235	92

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/ 1 (sqrt k))
1
(sqrt k)
k
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(* (* 2 (PI)) n)
(* 2 (PI))
2
(PI)
n
(/ (- 1 k) 2)
(- 1 k)
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(- 1/2 (/ k 2))
1/2
(/ k 2)
k
(sqrt k)

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

localize100.0ms (0.8%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.8%	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓	accuracy	99.7%	(.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	99.6%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Results

69.0ms

256×

valid

Compiler

Compiled 105 to 21 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-pow: 20.0ms (46.8% of total)

ival-mult: 9.0ms (21.1% of total)

ival-div: 7.0ms (16.4% of total)

ival-sub: 3.0ms (7% of total)

ival-sqrt: 2.0ms (4.7% of total)

ival-pi: 1.0ms (2.3% of total)

const: 1.0ms (2.3% of total)

backward-pass: 0.0ms (0% of total)

series99.0ms (0.7%)

Counts

10 → 156

Calls

Call 1

Inputs
#<alt (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))>
#<alt (/ 1 (sqrt k))>
#<alt (sqrt k)>
#<alt (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))>
#<alt (/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))>
#<alt (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))>
#<alt (* 2 (* (PI) n))>
#<alt (* (PI) n)>
#<alt (* (* 2 (PI)) n)>
#<alt (PI)>

Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k))))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k)))))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt (/ 1 k))>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (sqrt k)>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt k) (pow (sqrt -1) 2)))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log n) (log (* 2 (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (- 1 k))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (exp (* 1/2 (* (log (* 2 (* n (PI)))) (+ 1 (* -1 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* 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)>
#<alt (/ (+ (* 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)>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (* (sqrt (/ 1 k)) (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/2 (* 1/2 k))))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (+ (* -1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 2))) (sqrt (* n (PI))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (+ (* 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)))>
#<alt (+ (* 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)))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/2 (* 1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>

Calls

39 calls:

Time	Variable		Point	Expression
50.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
21.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
10.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
6.0ms	k	@	-inf	(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
1.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite302.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

5664×	`-lowering-.f32`
5664×	`-lowering-.f64`
3066×	`/-lowering-/.f32`
3066×	`/-lowering-/.f64`
1334×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	68
1	132	68
2	857	64
0	8649	64

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 740

Calls

Call 1

Inputs
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
(/ 1 (sqrt k))
(sqrt k)
(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))
(* 2 (* (PI) n))
(* (PI) n)
(* (* 2 (PI)) n)
(PI)

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

simplify308.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

5256×	`-lowering-.f32`
5256×	`-lowering-.f64`
2382×	`+-lowering-+.f64`
2382×	`+-lowering-+.f32`
1462×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	2132
1	385	2094
2	1192	1806
3	4167	1722
4	7737	1722
0	8108	1722

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

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

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

eval135.0ms (1%)

Compiler: Compiled 21585 to 2037 computations (90.6% saved)

prune110.0ms (0.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	977	12	989
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	978	13	991

Accuracy

100.0%

Counts

991 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
▶	99.6%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
▶	96.3%	(/.f64 (exp.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
	76.8%	(.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (*.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64))))
	99.6%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	78.3%	(.f64 (pow.f64 (sqrt.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #s(literal -1 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
▶	38.7%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	96.3%	(.f64 (exp.f64 (.f64 (log.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 2 binary64))))
	95.5%	(exp.f64 (-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal 1/2 binary64) (log.f64 k))))

Compiler

Compiled 464 to 340 computations (26.7% saved)

simplify179.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	cost-diff	0	(/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))
✓	cost-diff	6464	(exp.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))))
✓	cost-diff	6464	(/.f64 (exp.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
✓	cost-diff	0	(*.f64 (PI.f64) #s(literal -2 binary64))
✓	cost-diff	128	(/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n))
✓	cost-diff	128	(pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))))
✓	cost-diff	128	(/.f64 (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓	cost-diff	0	(pow.f64 k #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
✓	cost-diff	0	(*.f64 n (PI.f64))
✓	cost-diff	0	(/.f64 (*.f64 n (PI.f64)) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	cost-diff	0	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	64	(pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))
✓	cost-diff	64	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/2 binary64))
✓	cost-diff	128	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))

Rules

1764×	`-lowering-.f32`
1764×	`-lowering-.f64`
1592×	`sum3-define`
1404×	`fma-define`
1352×	`sum5-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	40	267
1	67	259
2	111	254
3	191	254
4	359	253
5	685	250
6	1378	250
7	2002	250
8	4791	250
9	5845	250
10	7104	250
11	7853	250
0	8001	250

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize363.0ms (2.7%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 (exp.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	96.4%	(exp.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.8%	(/.f64 (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	accuracy	99.8%	(pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))))
✓	accuracy	99.6%	(/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (*.f64 n (PI.f64)) k)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	90.3%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/2 binary64))
✓	accuracy	99.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	78.1%	(PI.f64)

Results

148.0ms	198×	0	valid
145.0ms	58×	5	exit

Compiler

Compiled 276 to 41 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 191.0ms

ival-pow: 70.0ms (36.6% of total)

ival-mult: 42.0ms (22% of total)

backward-pass: 36.0ms (18.8% of total)

ival-div: 21.0ms (11% of total)

ival-sqrt: 7.0ms (3.7% of total)

ival-log: 5.0ms (2.6% of total)

ival-sub: 3.0ms (1.6% of total)

ival-exp: 2.0ms (1% of total)

ival-pi: 2.0ms (1% of total)

ival-add: 2.0ms (1% of total)

const: 1.0ms (0.5% of total)

series80.0ms (0.6%)

Counts

21 → 372

Calls

Call 1

Inputs
#<alt (/ (pow (* 2 (* (PI) n)) 1/2) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))>
#<alt (pow (* 2 (* (PI) n)) 1/2)>
#<alt (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)>
#<alt (* 2 (* (PI) n))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (/ (* n (PI)) k)>
#<alt (* n (PI))>
#<alt (/ (pow k -1/2) (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2)))>
#<alt (pow k -1/2)>
#<alt (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2))>
#<alt (/ (pow (/ (* (PI) -2) (/ -1 n)) (- 1/2 (* k 1/2))) (sqrt k))>
#<alt (pow (/ (* (PI) -2) (/ -1 n)) (- 1/2 (* k 1/2)))>
#<alt (/ (* (PI) -2) (/ -1 n))>
#<alt (* (PI) -2)>
#<alt (/ (exp (/ (log (* 2 (* (PI) n))) (/ 2 (- 1 k)))) (sqrt k))>
#<alt (exp (/ (log (* 2 (* (PI) n))) (/ 2 (- 1 k))))>
#<alt (/ (log (* 2 (* (PI) n))) (/ 2 (- 1 k)))>
#<alt (log (* 2 (* (PI) n)))>
#<alt (PI)>
#<alt (* (PI) n)>

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

Calls

93 calls:

Time	Variable		Point	Expression
31.0ms	n	@	-inf	(/ (pow (* 2 (* (PI) n)) 1/2) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
4.0ms	k	@	0	(/ (log (* 2 (* (PI) n))) (/ 2 (- 1 k)))
2.0ms	k	@	0	(/ (pow (* 2 (* (PI) n)) 1/2) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
2.0ms	n	@	-inf	(/ (pow k -1/2) (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2)))
2.0ms	n	@	inf	(/ (pow (* 2 (* (PI) n)) 1/2) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))

rewrite460.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4384×	`-lowering-.f32`
4384×	`-lowering-.f64`
2908×	`pow-lowering-pow.f64`
2908×	`pow-lowering-pow.f32`
2854×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	179
1	257	157
2	1774	156
0	8493	156

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 1018

Calls

Call 1

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

Outputs
(exp.f64 (-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) #s(literal 2 binary64))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 2 binary64)) (neg.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))))))
(exp.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (log.f64 k)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (+.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 #s(literal -1/2 binary64) (log.f64 k))))
(exp.f64 (+.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 2 binary64))))
(exp.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 2 binary64)))))
(exp.f64 (-.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k))) (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))))))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (sqrt.f64 k)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) #s(literal 1 binary64))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
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(.f64 (sqrt.f64 (cbrt.f64 (.f64 (.f64 (PI.f64) (PI.f64)) (.f64 (PI.f64) (PI.f64))))) (cbrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) n))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (.f64 n #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))

simplify325.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

6874×	`-lowering-.f32`
6874×	`-lowering-.f64`
2852×	`+-lowering-+.f64`
2852×	`+-lowering-+.f32`
1332×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	349	5201
1	1117	4921
2	4140	4619
0	8500	4619

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

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

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

eval287.0ms (2.2%)

Compiler: Compiled 38323 to 4198 computations (89% saved)

prune191.0ms (1.4%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	1832	11	1843
Fresh	7	0	7
Picked	3	2	5
Done	0	1	1
Total	1842	14	1856

Accuracy

100.0%

Counts

1856 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	99.6%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
	38.6%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
▶	48.3%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
▶	38.9%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
	48.3%	(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	38.7%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	38.7%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
▶	38.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	38.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
	48.2%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
▶	90.3%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
▶	38.8%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	36.3%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))

Compiler

Compiled 314 to 247 computations (21.3% saved)

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

256×	`-lowering-.f32`
256×	`-lowering-.f64`
174×	`/-lowering-/.f32`
174×	`/-lowering-/.f64`
78×	`associate-*r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	174
1	43	174
2	94	174
3	206	174
4	266	174
5	299	174
6	324	174
7	336	174
8	346	174
0	346	174

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k))))
(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(* k (pow (* 2 (* (PI) n)) k))
k
(pow (* 2 (* (PI) n)) k)
(sqrt (/ 2 (/ k (* (PI) n))))
(/ 2 (/ k (* (PI) n)))
2
(/ k (* (PI) n))
k
(* (PI) n)
(PI)
n
(* (sqrt (* (PI) (/ n k))) (sqrt 2))
(sqrt (* (PI) (/ n k)))
(* (PI) (/ n k))
(PI)
(/ n k)
n
k
(sqrt 2)
2
(/ (sqrt (* 2 (* (PI) n))) (sqrt k))
(sqrt (* 2 (* (PI) n)))
(* 2 (* (PI) n))
2
(* (PI) n)
(PI)
n
(sqrt k)
k
(/ (sqrt 2) (pow (/ k (* (PI) n)) 1/2))
(sqrt 2)
2
(pow (/ k (* (PI) n)) 1/2)
(/ k (* (PI) n))
k
(* (PI) n)
(PI)
n
1/2

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

localize277.0ms (2.1%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(/.f64 k (*.f64 (PI.f64) n))
✓	accuracy	99.4%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
✓	accuracy	90.5%	(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.8%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (PI.f64) (/.f64 n k))
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	90.3%	(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.7%	(/.f64 k (*.f64 (PI.f64) n))
✓	accuracy	99.7%	(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓	accuracy	90.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	accuracy	78.1%	(PI.f64)
✓	accuracy	99.8%	(/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	90.4%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
✓	accuracy	78.1%	(PI.f64)

Results

123.0ms	198×	0	valid
92.0ms	58×	5	exit

Compiler

Compiled 179 to 25 computations (86% saved)

Precisions

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

ival-sqrt: 27.0ms (30.8% of total)

ival-pow: 19.0ms (21.6% of total)

ival-mult: 15.0ms (17.1% of total)

ival-div: 12.0ms (13.7% of total)

backward-pass: 12.0ms (13.7% of total)

ival-pi: 2.0ms (2.3% of total)

const: 1.0ms (1.1% of total)

series67.0ms (0.5%)

Counts

16 → 300

Calls

Call 1

Inputs
#<alt (sqrt (/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k))))>
#<alt (/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))>
#<alt (* 2 (* (PI) n))>
#<alt (* (PI) n)>
#<alt (sqrt (/ 2 (/ k (* (PI) n))))>
#<alt (/ 2 (/ k (* (PI) n)))>
#<alt (/ k (* (PI) n))>
#<alt (* (sqrt (* (PI) (/ n k))) (sqrt 2))>
#<alt (sqrt (* (PI) (/ n k)))>
#<alt (* (PI) (/ n k))>
#<alt (PI)>
#<alt (/ (sqrt (* 2 (* (PI) n))) (sqrt k))>
#<alt (sqrt (* 2 (* (PI) n)))>
#<alt (/ (sqrt 2) (pow (/ k (* (PI) n)) 1/2))>
#<alt (sqrt 2)>
#<alt (pow (/ k (* (PI) n)) 1/2)>

Outputs
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
#<alt (/ (+ (* (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)>
#<alt (/ (+ (* (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)>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (/ (+ (* -2 (* k (* n (* (PI) (log (* 2 (* n (PI)))))))) (* 2 (* n (PI)))) k)>
#<alt (/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* k (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))) (* -2 (* n (* (PI) (log (* 2 (* n (PI)))))))))) k)>
#<alt (/ (+ (* 2 (* n (PI))) (* k (+ (* -2 (* n (* (PI) (log (* 2 (* n (PI))))))) (* k (+ (* -2 (* k (+ (* -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)))))))) (* -2 (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* 1/2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))))))))))) k)>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k))))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* 2 (* n (PI)))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (/ k (* n (PI)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* (sqrt (* n (PI))) (sqrt 2))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (* n (PI))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>

Calls

75 calls:

Time	Variable		Point	Expression
44.0ms	n	@	inf	(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))
5.0ms	n	@	-inf	(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))
2.0ms	k	@	-inf	(* (sqrt (* (PI) (/ n k))) (sqrt 2))
1.0ms	n	@	-inf	(pow (/ k (* (PI) n)) 1/2)
1.0ms	k	@	0	(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))

rewrite382.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

5548×	`-lowering-.f32`
5548×	`-lowering-.f64`
3484×	`/-lowering-/.f32`
3484×	`/-lowering-/.f64`
930×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	109
1	135	109
2	842	109
3	7623	109
0	8122	109

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 1275

Calls

Call 1

Inputs
(sqrt (/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k))))
(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))
(* 2 (* (PI) n))
(* (PI) n)
(sqrt (/ 2 (/ k (* (PI) n))))
(/ 2 (/ k (* (PI) n)))
(/ k (* (PI) n))
(* (sqrt (* (PI) (/ n k))) (sqrt 2))
(sqrt (* (PI) (/ n k)))
(* (PI) (/ n k))
(PI)
(/ (sqrt (* 2 (* (PI) n))) (sqrt k))
(sqrt (* 2 (* (PI) n)))
(/ (sqrt 2) (pow (/ k (* (PI) n)) 1/2))
(sqrt 2)
(pow (/ k (* (PI) n)) 1/2)

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

simplify307.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

4262×	`-lowering-.f32`
4262×	`-lowering-.f64`
2814×	`+-lowering-+.f64`
2814×	`+-lowering-+.f32`
2756×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	3014
1	508	2915
2	2082	2883
3	6970	2883
0	8459	2883

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

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

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

eval322.0ms (2.4%)

Compiler: Compiled 34141 to 4587 computations (86.6% saved)

prune289.0ms (2.2%)

Pruning

32 alts after pruning (26 fresh and 6 done)

	Pruned	Kept	Total
New	2231	23	2254
Fresh	3	3	6
Picked	2	3	5
Done	0	3	3
Total	2236	32	2268

Accuracy

100.0%

Counts

2268 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	39.0%	(pow.f64 (/.f64 k (.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
	26.6%	(pow.f64 (.f64 (/.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) k) (/.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k)) #s(literal 1/4 binary64))
	38.8%	(/.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
	48.2%	(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	38.7%	(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
✓	99.6%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
	38.6%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	48.3%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
▶	38.7%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64)))
	38.9%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
	38.7%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal -1/2 binary64)))
	38.6%	(.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)))
▶	48.3%	(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))
✓	38.7%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	38.7%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
	48.3%	(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) (sqrt.f64 n))
	38.6%	(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n))) (sqrt.f64 (PI.f64)))
▶	38.7%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
	38.9%	(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
	38.8%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
✓	90.3%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
	38.8%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) n)))
	38.8%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
	38.8%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
✓	38.8%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
▶	38.8%	(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64)))
	38.9%	(sqrt.f64 (.f64 (/.f64 n k) (.f64 #s(literal 2 binary64) (PI.f64))))
	38.8%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
▶	38.8%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
	36.3%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
	36.3%	(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))

Compiler

Compiled 711 to 558 computations (21.5% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (PI.f64) (/.f64 k n))
✓	cost-diff	0	(pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64)))
✓	cost-diff	0	(/.f64 (PI.f64) k)
✓	cost-diff	0	(*.f64 (/.f64 (PI.f64) k) n)
✓	cost-diff	0	(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) k)
✓	cost-diff	128	(/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n))
✓	cost-diff	128	(*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64))
✓	cost-diff	128	(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64)))
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) k)
✓	cost-diff	0	(.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))
✓	cost-diff	0	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
✓	cost-diff	0	(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) k)
✓	cost-diff	0	(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))

Rules

96×	`-lowering-.f32`
96×	`-lowering-.f64`
64×	`/-lowering-/.f32`
64×	`/-lowering-/.f64`
50×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	145
1	49	144
2	83	144
3	132	144
4	172	144
5	174	144
0	174	144

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (pow (/ 2 k) 1/2) (pow (* (PI) n) 1/2))
(pow (/ 2 k) 1/2)
(/ 2 k)
2
k
1/2
(pow (* (PI) n) 1/2)
(* (PI) n)
(PI)
n
(sqrt (* (/ 2 k) (* (PI) n)))
(* (/ 2 k) (* (PI) n))
(/ 2 k)
2
k
(* (PI) n)
(PI)
n
(sqrt (* (/ (/ 2 k) (/ 1 n)) (PI)))
(* (/ (/ 2 k) (/ 1 n)) (PI))
(/ (/ 2 k) (/ 1 n))
(/ 2 k)
2
k
(/ 1 n)
1
n
(PI)
(* (sqrt (* (/ (PI) k) n)) (sqrt 2))
(sqrt (* (/ (PI) k) n))
(* (/ (PI) k) n)
(/ (PI) k)
(PI)
k
n
(sqrt 2)
2
(/ (sqrt 2) (pow (/ (PI) (/ k n)) -1/2))
(sqrt 2)
2
(pow (/ (PI) (/ k n)) -1/2)
(/ (PI) (/ k n))
(PI)
(/ k n)
k
n
-1/2

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

localize138.0ms (1%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.4%	(/.f64 (PI.f64) (/.f64 k n))
✓	accuracy	99.3%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64)))
✓	accuracy	79.3%	(pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64))
✓	accuracy	99.7%	(*.f64 (/.f64 (PI.f64) k) n)
✓	accuracy	99.6%	(/.f64 (PI.f64) k)
✓	accuracy	99.3%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	79.3%	(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.6%	(*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64))
✓	accuracy	99.5%	(/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n))
✓	accuracy	79.3%	(sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) n)) (PI.f64)))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))
✓	accuracy	79.3%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
✓	accuracy	99.8%	(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64))
✓	accuracy	99.8%	(pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))
✓	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.5%	(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))

Results

98.0ms

256×

valid

Compiler

Compiled 158 to 28 computations (82.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-pow: 20.0ms (35.8% of total)

ival-div: 15.0ms (26.8% of total)

ival-mult: 11.0ms (19.7% of total)

ival-sqrt: 7.0ms (12.5% of total)

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

const: 1.0ms (1.8% of total)

backward-pass: 0.0ms (0% of total)

series15.0ms (0.1%)

Counts

19 → 348

Calls

Call 1

Inputs
#<alt (* (pow (/ 2 k) 1/2) (pow (* (PI) n) 1/2))>
#<alt (pow (/ 2 k) 1/2)>
#<alt (/ 2 k)>
#<alt (pow (* (PI) n) 1/2)>
#<alt (sqrt (* (/ 2 k) (* (PI) n)))>
#<alt (* (/ 2 k) (* (PI) n))>
#<alt (* (PI) n)>
#<alt (sqrt (* (/ (/ 2 k) (/ 1 n)) (PI)))>
#<alt (* (/ (/ 2 k) (/ 1 n)) (PI))>
#<alt (/ (/ 2 k) (/ 1 n))>
#<alt (* (sqrt (* (/ (PI) k) n)) (sqrt 2))>
#<alt (sqrt (* (/ (PI) k) n))>
#<alt (* (/ (PI) k) n)>
#<alt (/ (PI) k)>
#<alt (/ (sqrt 2) (pow (/ (PI) (/ k n)) -1/2))>
#<alt (sqrt 2)>
#<alt (pow (/ (PI) (/ k n)) -1/2)>
#<alt (/ (PI) (/ k n))>
#<alt (PI)>

Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (/ 2 k)>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (sqrt (* n (PI)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* n (PI))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (sqrt (/ (* n (PI)) k))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (/ (PI) k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (sqrt (/ k (* n (PI))))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>
#<alt (/ (* n (PI)) k)>

Calls

87 calls:

Time	Variable		Point	Expression
1.0ms	n	@	-inf	(pow (* (PI) n) 1/2)
1.0ms	k	@	0	(/ (/ 2 k) (/ 1 n))
0.0ms	n	@	0	(/ (/ 2 k) (/ 1 n))
0.0ms	k	@	inf	(pow (/ (PI) (/ k n)) -1/2)
0.0ms	n	@	-inf	(pow (/ (PI) (/ k n)) -1/2)

rewrite291.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

5278×	`-lowering-.f32`
5278×	`-lowering-.f64`
2764×	`/-lowering-/.f32`
2764×	`/-lowering-/.f64`
1034×	`frac-times`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	103
1	147	102
2	901	101
0	8128	101

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 1766

Calls

Call 1

Inputs
(* (pow (/ 2 k) 1/2) (pow (* (PI) n) 1/2))
(pow (/ 2 k) 1/2)
(/ 2 k)
(pow (* (PI) n) 1/2)
(sqrt (* (/ 2 k) (* (PI) n)))
(* (/ 2 k) (* (PI) n))
(* (PI) n)
(sqrt (* (/ (/ 2 k) (/ 1 n)) (PI)))
(* (/ (/ 2 k) (/ 1 n)) (PI))
(/ (/ 2 k) (/ 1 n))
(* (sqrt (* (/ (PI) k) n)) (sqrt 2))
(sqrt (* (/ (PI) k) n))
(* (/ (PI) k) n)
(/ (PI) k)
(/ (sqrt 2) (pow (/ (PI) (/ k n)) -1/2))
(sqrt 2)
(pow (/ (PI) (/ k n)) -1/2)
(/ (PI) (/ k n))
(PI)

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

simplify243.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

2752×	`fma-define`
2702×	`fnmadd-define`
2144×	`sum3-define`
1280×	`fma-lowering-fma.f32`
1280×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	2452
1	90	2388
2	231	2388
3	438	2388
4	883	2388
5	1603	2388
6	3136	2388
7	3669	2388
8	3853	2388
9	3908	2388
10	3990	2388
11	4231	2388
12	5791	2388
13	5791	2388
14	5867	2388
15	6332	2388
16	7192	2388
17	7196	2388
18	7260	2388
0	7260	2388

Stop Event

1×	iter limit
1×	saturated

Counts

348 → 348

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(/ 2 k)
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(sqrt (* n (PI)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (* n (PI))) (pow (sqrt -1) 2)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* n (PI))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (pow (sqrt -1) 2) (sqrt 2))))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(sqrt (/ (* n (PI)) k))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (pow (sqrt -1) 2)))
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(/ (PI) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2)))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(sqrt (/ k (* n (PI))))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(* (sqrt (/ k (* n (PI)))) (pow (sqrt -1) 2))
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)
(/ (* n (PI)) k)

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

eval345.0ms (2.6%)

Compiler: Compiled 34712 to 4162 computations (88% saved)

prune272.0ms (2%)

Pruning

39 alts after pruning (30 fresh and 9 done)

	Pruned	Kept	Total
New	2541	13	2554
Fresh	4	17	21
Picked	2	3	5
Done	0	6	6
Total	2547	39	2586

Accuracy

100.0%

Counts

2586 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	39.0%	(pow.f64 (/.f64 k (.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
	19.1%	(pow.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) (.f64 (PI.f64) (.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
	38.6%	(/.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
	48.2%	(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	99.6%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
	38.6%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	48.2%	(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) (pow.f64 n #s(literal -1/2 binary64)))
✓	48.3%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	38.7%	(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
	38.8%	(/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n)) #s(literal 1/2 binary64)))
✓	38.7%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal -1/2 binary64)))
	38.9%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 (PI.f64) n))))
	38.7%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) k) #s(literal -1/2 binary64)))
	38.7%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
	48.2%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 n #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))))
	38.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
	38.6%	(.f64 (pow.f64 (/.f64 n k) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)))
	37.7%	(.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
	48.3%	(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))
✓	38.7%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	38.7%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
	48.3%	(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) (sqrt.f64 n))
	38.6%	(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n))) (sqrt.f64 (PI.f64)))
✓	38.7%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
	38.9%	(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
	38.8%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
✓	90.3%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
	38.8%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) k)) n)))
	38.8%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
	38.8%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
✓	38.8%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	38.2%	(sqrt.f64 (-.f64 (/.f64 (+.f64 (PI.f64) #s(literal 1 binary64)) (/.f64 k (*.f64 #s(literal 2 binary64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
	38.9%	(sqrt.f64 (*.f64 (/.f64 (/.f64 n k) #s(literal 1/2 binary64)) (PI.f64)))
	38.8%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
	38.8%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n))))
✓	38.8%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
	36.3%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
	36.3%	(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) k))))

Compiler

Compiled 1213 to 602 computations (50.4% saved)

regimes78.0ms (0.6%)

Counts

61 → 1

Calls

Call 1

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

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

Calls

4 calls:

21.0ms	k
19.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
17.0ms	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
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 31 to 23 computations (25.8% saved)

regimes74.0ms (0.6%)

Counts

58 → 1

Calls

Call 1

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

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

Calls

4 calls:

18.0ms	k
17.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
17.0ms	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
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 31 to 23 computations (25.8% saved)

regimes33.0ms (0.2%)

Counts

47 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

16.0ms	k
13.0ms	n

Results

Accuracy	Segments	Branch
59.2%	2	`k`
48.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes19.0ms (0.1%)

Counts

46 → 2

Calls

Call 1

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

Outputs

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

(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (PI.f64) (*.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))

Calls

1 calls:

16.0ms

Results

Accuracy	Segments	Branch
53.3%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts

27 → 2

Calls

Call 1

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

Outputs

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

(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (PI.f64) (*.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
53.3%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes15.0ms (0.1%)

Counts

23 → 2

Calls

Call 1

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

Outputs

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

(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (PI.f64) (*.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))

Calls

1 calls:

13.0ms

Results

Accuracy	Segments	Branch
53.3%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes13.0ms (0.1%)

Counts

19 → 2

Calls

Call 1

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

Outputs

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

(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (*.f64 k k)) (*.f64 (PI.f64) (*.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))

Calls

2 calls:

6.0ms	k
6.0ms	n

Results

Accuracy	Segments	Branch
39.0%	1	`n`
44.0%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes14.0ms (0.1%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	k
5.0ms	n

Results

Accuracy	Segments	Branch
39.0%	1	`n`
39.0%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	n
3.0ms	k

Results

Accuracy	Segments	Branch
38.9%	1	`k`
38.9%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	k
2.0ms	n

Results

Accuracy	Segments	Branch
38.8%	1	`k`
38.8%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))

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

Calls

2 calls:

1.0ms	n
1.0ms	k

Results

Accuracy	Segments	Branch
38.8%	1	`k`
38.8%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch3.0ms (0%)

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
2.0ms	4.454537288694067e-46	1.0925631702117585e-40

Results

2.0ms

16×

valid

Compiler

Compiled 51 to 40 computations (21.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

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

bsearch23.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
21.0ms	2.2022514880208335e+154	4.154848720000434e+156

Results

17.0ms

112×

valid

Compiler

Compiled 233 to 178 computations (23.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 5.0ms (36.6% of total)

ival-pow: 4.0ms (29.3% of total)

ival-div: 2.0ms (14.6% of total)

ival-sub: 1.0ms (7.3% of total)

ival-sqrt: 1.0ms (7.3% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch29.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
27.0ms	2.2022514880208335e+154	4.154848720000434e+156

Results

23.0ms

112×

valid

Compiler

Compiled 233 to 178 computations (23.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-pow: 4.0ms (36.9% of total)

ival-div: 2.0ms (18.4% of total)

ival-mult: 2.0ms (18.4% of total)

ival-sub: 1.0ms (9.2% of total)

ival-sqrt: 1.0ms (9.2% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch21.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	2.2022514880208335e+154	4.154848720000434e+156

Results

16.0ms

112×

valid

Compiler

Compiled 233 to 178 computations (23.6% saved)

Precisions

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

ival-pow: 6.0ms (49.1% of total)

ival-div: 2.0ms (16.4% of total)

ival-mult: 2.0ms (16.4% of total)

ival-sub: 1.0ms (8.2% of total)

ival-sqrt: 1.0ms (8.2% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch15.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	8.883359455166143e+153	2.2022514880208335e+154

Results

11.0ms

80×

valid

Compiler

Compiled 173 to 132 computations (23.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-pow: 3.0ms (34.3% of total)

ival-div: 2.0ms (22.9% of total)

ival-mult: 2.0ms (22.9% of total)

ival-sqrt: 1.0ms (11.4% of total)

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	204
1	80	204
2	89	204
3	95	204
4	100	204
5	102	204

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 6427752177035961/12855504354071922204335696738729300820177623950262342682411008 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
(if (<=.f64 k #s(literal 22500000000000000459178351141959369210816864978487727427761875070431876369408262113249838982777431993744833480349327934346847195128257057415137899157913600 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) (.f64 (PI.f64) (.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 22500000000000000459178351141959369210816864978487727427761875070431876369408262113249838982777431993744833480349327934346847195128257057415137899157913600 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) (sqrt.f64 n)) (pow.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 22500000000000000459178351141959369210816864978487727427761875070431876369408262113249838982777431993744833480349327934346847195128257057415137899157913600 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) (.f64 (PI.f64) (.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 13500000000000000275507010685175621526490118987092636456657125042259125821644957267949903389666459196246900088209596760608108317076954234449082739494748160 binary64)) (pow.f64 (/.f64 k (.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) (.f64 (PI.f64) (.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 k (.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 #s(literal 2 binary64) (PI.f64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))

Outputs
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 6427752177035961/12855504354071922204335696738729300820177623950262342682411008 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)) (.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
(if (<=.f64 k #s(literal 22500000000000000459178351141959369210816864978487727427761875070431876369408262113249838982777431993744833480349327934346847195128257057415137899157913600 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) (.f64 (PI.f64) (.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 22500000000000000459178351141959369210816864978487727427761875070431876369408262113249838982777431993744833480349327934346847195128257057415137899157913600 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) (sqrt.f64 n)) (pow.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) (.f64 (PI.f64) (.f64 n (.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 22500000000000000459178351141959369210816864978487727427761875070431876369408262113249838982777431993744833480349327934346847195128257057415137899157913600 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) (.f64 (PI.f64) (.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 22500000000000000459178351141959369210816864978487727427761875070431876369408262113249838982777431993744833480349327934346847195128257057415137899157913600 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) (.f64 (PI.f64) (.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 13500000000000000275507010685175621526490118987092636456657125042259125821644957267949903389666459196246900088209596760608108317076954234449082739494748160 binary64)) (pow.f64 (/.f64 k (.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 4 binary64) (.f64 k k)) (.f64 (PI.f64) (.f64 n (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 k (.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 #s(literal 2 binary64) (PI.f64))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
(sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k)))

soundness2.0s (15.1%)

Rules

5664×	`-lowering-.f32`
5664×	`-lowering-.f64`
5548×	`-lowering-.f32`
5548×	`-lowering-.f64`
5278×	`-lowering-.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	179
1	257	157
2	1774	156
0	8493	156
0	13	14
1	30	14
2	47	14
3	69	14
4	90	13
5	113	13
6	149	13
7	188	13
8	214	13
9	228	13
10	229	13
0	229	13
0	27	103
1	147	102
2	901	101
0	8128	101
0	24	109
1	135	109
2	842	109
3	7623	109
0	8122	109
0	20	68
1	132	68
2	857	64
0	8649	64
0	139	2132
1	385	2094
2	1192	1806
3	4167	1722
4	7737	1722
0	8108	1722

Stop Event

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

Compiler

Compiled 732 to 479 computations (34.6% saved)

preprocess87.0ms (0.7%)

Compiler: Compiled 448 to 152 computations (66.1% saved)

Iter	Nodes	Cost
0	20	98
1	38	98
2	58	98
3	78	98
4	100	92
5	129	92
6	170	92
7	202	92
8	231	92
9	235	92
0	235	92

Iter	Nodes	Cost
0	24	174
1	43	174
2	94	174
3	206	174
4	266	174
5	299	174
6	324	174
7	336	174
8	346	174
0	346	174

Iter	Nodes	Cost
0	20	98
1	38	98
2	58	98
3	78	98
4	100	92
5	129	92
6	170	92
7	202	92
8	231	92
9	235	92
0	235	92

Iter	Nodes	Cost
0	24	174
1	43	174
2	94	174
3	206	174
4	266	174
5	299	174
6	324	174
7	336	174
8	346	174
0	346	174

analyze159.0ms (1.2%)

sample4.5s (33.8%)

preprocess83.0ms (0.6%)

explain156.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify17.0ms (0.1%)

localize100.0ms (0.8%)

series99.0ms (0.7%)

rewrite302.0ms (2.3%)

simplify308.0ms (2.3%)

eval135.0ms (1%)

prune110.0ms (0.8%)

simplify179.0ms (1.3%)

localize363.0ms (2.7%)

series80.0ms (0.6%)

rewrite460.0ms (3.5%)

simplify325.0ms (2.4%)

eval287.0ms (2.2%)

prune191.0ms (1.4%)

simplify31.0ms (0.2%)

localize277.0ms (2.1%)

series67.0ms (0.5%)

rewrite382.0ms (2.9%)

simplify307.0ms (2.3%)

eval322.0ms (2.4%)

prune289.0ms (2.2%)

simplify11.0ms (0.1%)

localize138.0ms (1%)

series15.0ms (0.1%)

rewrite291.0ms (2.2%)

simplify243.0ms (1.8%)

eval345.0ms (2.6%)

prune272.0ms (2%)

regimes78.0ms (0.6%)

regimes74.0ms (0.6%)

regimes33.0ms (0.2%)

regimes19.0ms (0.1%)

regimes10.0ms (0.1%)

regimes15.0ms (0.1%)

regimes13.0ms (0.1%)

regimes14.0ms (0.1%)

regimes6.0ms (0%)

regimes6.0ms (0%)

regimes3.0ms (0%)

bsearch3.0ms (0%)

bsearch23.0ms (0.2%)

bsearch29.0ms (0.2%)

bsearch21.0ms (0.2%)

bsearch15.0ms (0.1%)

simplify11.0ms (0.1%)

soundness2.0s (15.1%)

preprocess87.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	20	98
1	38	98
2	58	98
3	78	98
4	100	92
5	129	92
6	170	92
7	202	92
8	231	92
9	235	92
0	235	92

Iter	Nodes	Cost
0	24	174
1	43	174
2	94	174
3	206	174
4	266	174
5	299	174
6	324	174
7	336	174
8	346	174
0	346	174