Metrics for Migdal et al, Equation (51)

analyze191.0ms (1.3%)

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: 87.0ms

ival-pow: 31.0ms (35.7% of total)

ival-sqrt: 18.0ms (20.7% of total)

ival-mult: 16.0ms (18.4% of total)

ival-div: 12.0ms (13.8% of total)

ival-sub: 4.0ms (4.6% of total)

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

const: 1.0ms (1.2% of total)

backward-pass: 1.0ms (1.2% of total)

sample4.3s (30.2%)

Results

2.0s	3917×	5	exit
995.0ms	8256×	0	valid
454.0ms	1969×	1	invalid
44.0ms	458×	0	invalid
23.0ms	185×	0	unsamplable

Precisions

Click to see histograms. Total time spent on operations: 2.3s

ival-pow: 675.0ms (29.1% of total)

ival-mult: 443.0ms (19.1% of total)

backward-pass: 336.0ms (14.5% of total)

ival-div: 326.0ms (14% of total)

ival-sqrt: 296.0ms (12.7% of total)

ival-sub: 118.0ms (5.1% of total)

ival-pi: 93.0ms (4% of total)

const: 37.0ms (1.6% of total)

Bogosity

preprocess99.0ms (0.7%)

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	102	88
2	217	88
3	425	83
4	751	82
5	1495	82
6	2098	82
7	2679	82
8	3577	82
9	3728	82
10	3787	82
11	3831	82
12	3839	82
0	13	14
1	33	14
2	50	14
3	72	14
4	93	13
5	116	13
6	152	13
7	191	13
8	217	13
9	231	13
10	232	13
0	232	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)))
(* (fast-isqrt k) (pow (* (PI) (* 2 n)) (fnmsub k 1/2 -1/2)))
(* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2)))
(* (fast-isqrt (neg k)) (pow (* (PI) (* 2 n)) (fnmsub k -1/2 -1/2)))
(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2)))
(* (fast-isqrt k) (pow (* (PI) (* n -2)) (fnmsub k 1/2 -1/2)))
(neg (* (/ 1 (sqrt (neg k))) (pow (* (* 2 (PI)) n) (/ (- 1 (neg k)) 2))))
(* (fast-isqrt (neg k)) (neg (pow (* (PI) (* 2 n)) (fnmsub k -1/2 -1/2))))
(neg (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) (neg n)) (/ (- 1 k) 2))))
(* (pow (* (PI) (* n -2)) (fnmsub k 1/2 -1/2)) (neg (fast-isqrt k)))
(* (/ 1 (sqrt n)) (pow (* (* 2 (PI)) k) (/ (- 1 n) 2)))
(* (fast-isqrt n) (pow (* k (* 2 (PI))) (fnmsub n 1/2 -1/2)))

explain182.0ms (1.3%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
6	220	(3.179453708321909e+95 1.8800970215346193e-114)	-	`(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

90.0ms

512×

valid

Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-mult: 10.0ms (25.8% of total)

ival-pow: 10.0ms (25.8% of total)

ival-div: 7.0ms (18.1% of total)

ival-sqrt: 5.0ms (12.9% of total)

ival-sub: 3.0ms (7.8% of total)

ival-pi: 2.0ms (5.2% of total)

const: 1.0ms (2.6% 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
▶	99.5%	(/.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

▶

99.5%

(/.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)

simplify13.0ms (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	41	98
2	61	98
3	81	98
4	103	92
5	132	92
6	173	92
7	205	92
8	234	92
9	238	92
0	238	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)

localize119.0ms (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	99.6%	(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%	(.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%	(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 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.6%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

91.0ms

256×

valid

Compiler

Compiled 105 to 21 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-pow: 10.0ms (31.7% of total)

ival-mult: 8.0ms (25.4% of total)

ival-div: 7.0ms (22.2% of total)

ival-sub: 3.0ms (9.5% of total)

ival-sqrt: 2.0ms (6.3% of total)

ival-pi: 1.0ms (3.2% of total)

const: 1.0ms (3.2% of total)

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

series81.0ms (0.6%)

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
34.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
27.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
7.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	k	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite413.0ms (2.9%)

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	135	68
2	873	64
0	8718	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 #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 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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (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)))) (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
(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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
(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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64))))))
(neg.f64 (/.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 (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 (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 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.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) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(/.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)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.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 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #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)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))))
(/.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 (.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 -1 binary64) (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 #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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.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 -1 binary64) (pow.f64 k #s(literal -1/2 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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
(/.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #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) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (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) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (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)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (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) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (.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) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (.f64 (/.f64 #s(literal -1 binary64) (pow.f64 k #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 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #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) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #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) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
(/.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 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (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 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #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)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (-.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 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (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) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (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 #s(literal 1/2 binary64) (/.f64 k #s(literal -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 #s(literal -1/2 binary64) (/.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)) (+.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 #s(literal -1/2 binary64) (/.f64 k #s(literal -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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
(.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 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.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 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.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))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal -2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
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(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
(.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) n))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (.f64 (PI.f64) n))))
(.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
(.f64 (exp.f64 (log.f64 (.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(.f64 (PI.f64) (.f64 #s(literal 1 binary64) n))
(*.f64 n (PI.f64))
(.f64 (.f64 (PI.f64) n) #s(literal 1 binary64))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) n))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n)))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.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 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)))
(.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)))
(.f64 (.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 #s(literal 1 binary64) n) (PI.f64))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(.f64 (.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 (PI.f64) (.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) n)))
(.f64 (PI.f64) (.f64 #s(literal 1 binary64) (*.f64 n #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))
(.f64 (.f64 (PI.f64) n) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1 binary64))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 2 binary64) n)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) n))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
(.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) n))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (exp.f64 (log.f64 n)))
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (.f64 (PI.f64) n))))
(.f64 (exp.f64 (log.f64 n)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))
(.f64 (exp.f64 (log.f64 (.f64 (PI.f64) n))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (*.f64 #s(literal 2 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 n (*.f64 #s(literal 2 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (PI.f64))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(+.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (.f64 (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))
(expm1.f64 (log1p.f64 (PI.f64)))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) (PI.f64))) #s(literal 1 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)))
(log1p.f64 (expm1.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1 binary64)))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.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 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 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))))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (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 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.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)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))

simplify277.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

5256×	`-lowering-.f32`
5256×	`-lowering-.f64`
2382×	`+-lowering-+.f64`
2382×	`+-lowering-+.f32`
1466×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	2132
1	409	2094
2	1221	1806
3	4209	1722
4	7799	1722
0	8149	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 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) (.f64 n (.f64 k (*.f64 k k))))))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* 1/8 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (.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 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) (.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)))) (sqrt.f64 #s(literal 2 binary64))))) k)
(/ (+ (* k (+ (* -1/2 (* (sqrt (* k (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/48 (* (sqrt (* (pow k 3) (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* 1/8 (* (sqrt (* k (* n (PI)))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (+.f64 (.f64 k (.f64 (.f64 k (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (+.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (.f64 k (.f64 k k))))) #s(literal -1/48 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) #s(literal 1/8 binary64)))))) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) (.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)))) (sqrt.f64 #s(literal 2 binary64))))) 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))
(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))
(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))
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(sqrt k)
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(* -1 (* (sqrt k) (pow (sqrt -1) 2)))
(sqrt.f64 k)
(exp (* 1/2 (* (+ (log n) (log (* 2 (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 n) (log (* 2 (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 n) (log (* 2 (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 n) (log (* 2 (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 (PI))) (* -1 (log (/ 1 n)))) (- 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 (PI))) (* -1 (log (/ 1 n)))) (- 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 (PI))) (* -1 (log (/ 1 n)))) (- 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 (PI))) (* -1 (log (/ 1 n)))) (- 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 (PI))) (* -1 (log (/ -1 n)))) (- 1 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))))
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(*.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)))

eval108.0ms (0.8%)

Compiler: Compiled 21456 to 2037 computations (90.5% saved)

prune107.0ms (0.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	974	15	989
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	975	16	991

Accuracy

100.0%

Counts

991 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (*.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (sqrt.f64 k))
	99.5%	(/.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))
✓	99.5%	(/.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 (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)))))
▶	99.7%	(/.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	99.5%	(/.f64 (/.f64 #s(literal 1 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))
▶	99.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
▶	99.5%	(/.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))))))
▶	99.4%	(/.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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
	72.5%	(.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))))
	99.5%	(.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)))
	74.6%	(.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))))
	72.4%	(.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.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)))) (sqrt.f64 k)))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/4 binary64) (.f64 k #s(literal 1/4 binary64)))) #s(literal 2 binary64)))
	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))))
▶	34.2%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))

Compiler

Compiled 594 to 424 computations (28.6% saved)

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	cost-diff	0	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 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 #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)))) (/.f64 #s(literal -1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
✓	cost-diff	256	(/.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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
✓	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	(sqrt.f64 k)
✓	cost-diff	0	(/.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)))))
✓	cost-diff	128	(/.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))))))
✓	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	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	cost-diff	0	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (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 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))

Rules

264×	`-lowering-.f32`
264×	`-lowering-.f64`
184×	`fma-define`
182×	`fma-lowering-fma.f32`
182×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	37	301
1	62	300
2	98	297
3	124	295
4	172	295
5	281	291
6	471	291
7	704	291
8	927	291
9	1154	291
10	1221	291
11	1232	291
0	1232	291

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize245.0ms (1.7%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.8%	(/.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	accuracy	47.0%	(PI.f64)
✓	accuracy	99.8%	(/.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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64)))))
✓	accuracy	99.7%	(.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 -1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
✓	accuracy	99.6%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))
✓	accuracy	47.0%	(PI.f64)
✓	accuracy	99.8%	(/.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)))))
✓	accuracy	99.8%	(/.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))))))
✓	accuracy	99.6%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
✓	accuracy	47.0%	(PI.f64)
✓	accuracy	99.8%	(*.f64 n (PI.f64))
✓	accuracy	99.7%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	90.4%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	47.0%	(PI.f64)
✓	accuracy	99.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
✓	accuracy	47.0%	(PI.f64)

Results

100.0ms	140×	0	unsamplable
72.0ms	116×	0	valid

Compiler

Compiled 307 to 38 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-pow: 44.0ms (53.7% of total)

ival-div: 16.0ms (19.5% of total)

ival-mult: 10.0ms (12.2% of total)

ival-sqrt: 7.0ms (8.5% of total)

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

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

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

const: 1.0ms (1.2% of total)

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

series70.0ms (0.5%)

Counts

19 → 372

Calls

Call 1

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

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

Calls

93 calls:

Time	Variable		Point	Expression
4.0ms	n	@	-inf	(/ (sqrt k) (pow (* 2 (* (PI) n)) (+ 1/2 (/ k -2))))
4.0ms	n	@	0	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
3.0ms	k	@	0	(/ (/ (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (/ k 2))) (sqrt k))
2.0ms	n	@	inf	(/ -1 (* (pow (* 2 (* (PI) n)) (- -1/2 (/ k -2))) (/ -1 (pow k -1/2))))
2.0ms	n	@	-inf	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))

rewrite413.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4022×	`-lowering-.f32`
4022×	`-lowering-.f64`
3066×	`/-lowering-/.f32`
3066×	`/-lowering-/.f64`
2358×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	181
1	235	160
2	1611	158
0	8262	158

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 1028

Calls

Call 1

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

Outputs
(exp.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 (log.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 k) #s(literal 1/2 binary64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) k))))
(exp.f64 (+.f64 (neg.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) k))))
(exp.f64 (+.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) k)) (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) k)) (neg.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 k)))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) #s(literal 1/4 binary64)) (.f64 (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) #s(literal 1/4 binary64))))
(sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
(pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(.f64 (sqrt.f64 k) (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)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k))
(.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (pow.f64 (.f64 (pow.f64 (*.f64 (PI.f64) n) k) k) #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (.f64 (pow.f64 (*.f64 (PI.f64) n) k) k)))
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(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (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)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(.f64 (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 (.f64 n #s(literal 2 binary64)) (+.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 (.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (/.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)))) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 4 binary64)))) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 4 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 4 binary64)))) (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 (/.f64 k #s(literal 4 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 (PI.f64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(.f64 (pow.f64 (PI.f64) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 (.f64 n #s(literal 2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(.f64 (pow.f64 n (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 n (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 (PI.f64) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(.f64 (pow.f64 (PI.f64) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (.f64 n #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 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) n) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (PI.f64) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) n) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(.f64 (pow.f64 (PI.f64) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 (.f64 n #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(.f64 (pow.f64 n (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 n (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))) (pow.f64 (PI.f64) (.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64)))))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 4 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 4 binary64))) (sqrt.f64 (.f64 (PI.f64) n))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 n (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))) #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (exp.f64 (.f64 (/.f64 k #s(literal -2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(.f64 (exp.f64 (.f64 (/.f64 k #s(literal -2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (.f64 (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))
(expm1.f64 (log1p.f64 (PI.f64)))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)))))
(log1p.f64 (expm1.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(.f64 (pow.f64 (.f64 (*.f64 (PI.f64) (PI.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 (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 (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 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 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 (*.f64 (PI.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 (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)))

simplify360.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

6454×	`-lowering-.f32`
6454×	`-lowering-.f64`
1730×	`sum4-define`
1434×	`+-lowering-+.f64`
1434×	`+-lowering-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	458	6072
1	1647	5685
2	6620	5685
0	8008	5685

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

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

Outputs
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
(sqrt (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
(sqrt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(sqrt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))
(sqrt.f64 (.f64 k (exp.f64 (.f64 k (-.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))))))
(sqrt k)
(sqrt.f64 k)
(+ (sqrt k) (* 1/2 (* (sqrt (pow k 3)) (log (* 2 (* n (PI)))))))
(+.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 k (.f64 k k))) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))
(+ (sqrt k) (* (pow k 2) (+ (* 1/4 (* (sqrt k) (pow (log (* 2 (* n (PI)))) 2))) (* 1/2 (* (sqrt (/ 1 k)) (log (* 2 (* n (PI)))))))))
(+.f64 (sqrt.f64 k) (.f64 (.f64 k k) (+.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (.f64 (sqrt.f64 k) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(+ (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))))))))))
(+.f64 (sqrt.f64 k) (.f64 (.f64 k k) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))) (.f64 k (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))) (.f64 (-.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))) k)) (*.f64 (sqrt.f64 k) #s(literal 1/2 binary64))))))))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(sqrt (* k (pow (* 2 (* n (PI))) k)))
(sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k))))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k))))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k))))
(* -1 (* (sqrt (* k (pow (* 2 (* n (PI))) k))) (pow (sqrt -1) 2)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))) (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) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))) (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) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))) (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) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))) (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) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))) (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) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))) (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) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))) (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) (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))) (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) (exp.f64 (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (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) (exp.f64 (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (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) (exp.f64 (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (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) (exp.f64 (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 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 (.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 (.f64 (.f64 k (.f64 k k)) (PI.f64)) n))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (.f64 n (PI.f64)))))) 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)
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(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ (* n (PI)) k)) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log n) (log (* 2 (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (*.f64 k #s(literal 1/2 binary64)))))
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))) (exp.f64 (.f64 (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (.f64 k #s(literal 1/2 binary64)))))
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))) (exp.f64 (.f64 (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (.f64 k #s(literal 1/2 binary64)))))
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))) (exp.f64 (.f64 (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (.f64 k #s(literal 1/2 binary64)))))
(* -1 (* (sqrt (* n (PI))) (/ (* (sqrt -2) (sqrt -1)) (exp (* 1/2 (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))))
(/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (neg.f64 (sqrt.f64 (.f64 n (PI.f64))))) (exp.f64 (.f64 (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
(+ (* -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 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))
(+ (* k (+ (* -1 (* (* k (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))))) (sqrt (* n (PI))))) (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))))) (* (sqrt (* n (PI))) (sqrt 2)))
(+.f64 (.f64 k (.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal -1/8 binary64) k)) (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 k #s(literal -1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (* k (+ (* -1/2 (* (sqrt (* n (PI))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1 (* (sqrt (* n (PI))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (* -1 (* (* k (+ (* -1/2 (* (log (* 2 (* n (PI)))) (+ (* -1/4 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2))) (* 1/8 (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))))) (+ (* -1/16 (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2))) (* 1/48 (* (pow (log (* 2 (* n (PI)))) 3) (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 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))) (.f64 k (.f64 (.f64 k #s(literal -1 binary64)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/8 binary64))) (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/8 binary64))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/24 binary64))))))))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (* n (PI))) (/ (sqrt 2) (exp (* 1/2 (* k (log (* 2 (* n (PI)))))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 k #s(literal 1/2 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))

eval290.0ms (2%)

Compiler: Compiled 41265 to 3850 computations (90.7% saved)

prune218.0ms (1.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	1911	16	1927
Fresh	8	2	10
Picked	5	0	5
Done	0	1	1
Total	1924	19	1943

Accuracy

100.0%

Counts

1943 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.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 (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)))))
	34.2%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
▶	43.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	34.2%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
	34.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
	90.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
	34.2%	(/.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))))
	34.2%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶	99.5%	(.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)))
	34.2%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
	34.2%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	43.8%	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	43.8%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	77.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k))))
	74.7%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
	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))))
▶	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
▶	32.4%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))

Compiler

Compiled 520 to 392 computations (24.6% saved)

simplify23.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 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)))) (pow.f64 k #s(literal -1/2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	cost-diff	0	(.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64))
✓	cost-diff	6528	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	cost-diff	0	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(/.f64 k (*.f64 (PI.f64) n))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.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	(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 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64)))))

Rules

96×	`-lowering-.f32`
96×	`-lowering-.f64`
52×	`sum3-define`
48×	`/-lowering-/.f32`
48×	`/-lowering-/.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	26	205
1	45	205
2	75	205
3	105	205
4	132	205
5	162	202
6	189	202
7	211	202
8	237	202
9	260	202
10	266	202
11	269	202
0	269	202

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize223.0ms (1.6%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	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)))) (pow.f64 k #s(literal -1/2 binary64)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))
✓	accuracy	74.6%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	94.8%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
✓	accuracy	90.1%	(log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	accuracy	74.6%	(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	74.6%	(PI.f64)
✓	accuracy	99.7%	(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	90.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	accuracy	74.6%	(PI.f64)
✓	accuracy	99.8%	(/.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)))))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal -2 binary64))))
✓	accuracy	74.6%	(PI.f64)

Results

127.0ms	189×	0	valid
31.0ms	67×	0	unsamplable

Compiler

Compiled 211 to 27 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-pow: 16.0ms (34.5% of total)

ival-div: 8.0ms (17.2% of total)

ival-mult: 7.0ms (15.1% of total)

ival-sqrt: 5.0ms (10.8% of total)

ival-exp: 3.0ms (6.5% of total)

ival-log: 3.0ms (6.5% of total)

ival-pi: 1.0ms (2.2% of total)

ival-add: 1.0ms (2.2% of total)

ival-sub: 1.0ms (2.2% of total)

const: 1.0ms (2.2% of total)

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

series206.0ms (1.4%)

Counts

16 → 312

Calls

Call 1

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

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

Calls

78 calls:

Time	Variable		Point	Expression
43.0ms	n	@	inf	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
40.0ms	k	@	0	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
37.0ms	k	@	-inf	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
35.0ms	k	@	inf	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)
17.0ms	n	@	-inf	(* (log (/ 2 (/ k (* (PI) n)))) 1/2)

rewrite410.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4504×	`-lowering-.f32`
4504×	`-lowering-.f64`
4294×	`/-lowering-/.f32`
4294×	`/-lowering-/.f64`
1636×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	124
1	164	120
2	1156	117
0	8192	117

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 853

Calls

Call 1

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

Outputs
(exp.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (log.f64 k)) (.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
(exp.f64 (+.f64 (.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (.f64 #s(literal -1/2 binary64) (log.f64 k))))
(exp.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (log.f64 k)) (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
(exp.f64 (.f64 (log.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)))) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (-.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (*.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 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal -2 binary64) k))))
(exp.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (.f64 #s(literal -1/2 binary64) (log.f64 k))))
(exp.f64 (neg.f64 (-.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (.f64 #s(literal -1/2 binary64) (log.f64 k)))))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (-.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) (.f64 (-.f64 #s(literal 0 binary64) (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 (/.f64 #s(literal 0 binary64) (-.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 (pow.f64 k #s(literal -1/2 binary64)) (-.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)))))))
(neg.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (-.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)))))))
(neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (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 #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 #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 #s(literal 0 binary64) (sqrt.f64 k)) (-.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 1 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))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.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)))) (pow.f64 k #s(literal -1/2 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 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.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)) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -2 binary64) k)))) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -2 binary64) k)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64))) (-.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 -1 binary64) (-.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)))) (pow.f64 k #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (-.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 -1 binary64) (.f64 (-.f64 #s(literal 0 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 #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 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)))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 k #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) (-.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 (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 (.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 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 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
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(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))) (pow.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64))))))
(.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal -1/2 binary64) (/.f64 k #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (pow.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) n) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (PI.f64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (PI.f64) (+.f64 (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 (.f64 n #s(literal 2 binary64)) (+.f64 (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 n (+.f64 (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 n (+.f64 (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) (+.f64 (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (pow.f64 (PI.f64) (+.f64 (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))) (pow.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))) (pow.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))) (pow.f64 (.f64 n #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))))
(.f64 (pow.f64 n (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))) (pow.f64 n (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) n) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))) (pow.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (pow.f64 n (/.f64 (+.f64 (/.f64 k #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (exp.f64 (.f64 (/.f64 k #s(literal -2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))) (exp.f64 (.f64 (/.f64 k #s(literal -2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))) (pow.f64 (.f64 (PI.f64) n) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64))) (pow.f64 n #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/4 binary64))) (/.f64 (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/4 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/4 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/4 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) n) (/.f64 k #s(literal -2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1/2 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal -2 binary64))) (pow.f64 n #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal -2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))) (/.f64 (pow.f64 n (/.f64 k #s(literal -2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal -2 binary64))) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64))) (/.f64 (pow.f64 n (/.f64 k #s(literal -2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal -2 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1/2 binary64))) (/.f64 (pow.f64 n (/.f64 k #s(literal -2 binary64))) (pow.f64 n #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal -2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/4 binary64))) (/.f64 (pow.f64 n (/.f64 k #s(literal -2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/4 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -2 binary64) k))) (pow.f64 #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 #s(literal -2 binary64) k))) (pow.f64 (.f64 (PI.f64) n) #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -2 binary64) k))) (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 #s(literal -2 binary64) k))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -2 binary64) k))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -2 binary64) k))) (pow.f64 n #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -2 binary64) k))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/4 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -2 binary64) k))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/4 binary64))))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(+.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (.f64 (.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))))
(expm1.f64 (log1p.f64 (PI.f64)))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)))))
(log1p.f64 (expm1.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(.f64 (pow.f64 (.f64 (*.f64 (PI.f64) (PI.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 (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 (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 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 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 (*.f64 (PI.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 (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)))

simplify375.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

5040×	`-lowering-.f32`
5040×	`-lowering-.f64`
2342×	`+-lowering-+.f64`
2342×	`+-lowering-+.f32`
1358×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	3825
1	812	3583
2	2752	3515
3	6157	3515
0	8245	3515

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

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

eval284.0ms (2%)

Compiler: Compiled 27746 to 2986 computations (89.2% saved)

prune176.0ms (1.2%)

Pruning

39 alts after pruning (33 fresh and 6 done)

	Pruned	Kept	Total
New	1617	23	1640
Fresh	3	10	13
Picked	0	5	5
Done	0	1	1
Total	1620	39	1659

Accuracy

100.0%

Counts

1659 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	34.2%	(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	34.3%	(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
	24.6%	(pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
✓	99.5%	(/.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 (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)))))
▶	43.8%	(/.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)))
	43.7%	(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/2 binary64))) (sqrt.f64 k))
	34.2%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	43.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	34.2%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
	34.2%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
	43.7%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
	90.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
	34.2%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	99.5%	(.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)))
	43.8%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
	43.8%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
	34.1%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 n k)))
	34.2%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
▶	34.2%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
	34.2%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	43.8%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	77.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k))))
	74.7%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))
	34.4%	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
▶	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))))
	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
✓	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 k n)))))
	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
▶	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k)))
	34.3%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
	34.4%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
	34.3%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
	34.3%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
▶	34.4%	(sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
✓	32.4%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
	32.4%	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))) #s(literal 1/2 binary64)))

Compiler

Compiled 932 to 717 computations (23.1% saved)

simplify30.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

484×	`times-frac`
380×	`-lowering-.f32`
380×	`-lowering-.f64`
292×	`/-lowering-/.f32`
292×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	182
1	59	181
2	135	181
3	334	181
4	551	181
5	754	181
6	819	181
7	825	181
0	825	181

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

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

localize486.0ms (3.4%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/2 binary64))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(/.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)))
✓	accuracy	74.3%	(PI.f64)
✓	accuracy	99.7%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
✓	accuracy	98.9%	(sqrt.f64 (PI.f64))
✓	accuracy	90.3%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n))
✓	accuracy	74.3%	(PI.f64)
✓	accuracy	99.7%	(/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	90.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k)))
✓	accuracy	74.3%	(PI.f64)
✓	accuracy	99.8%	(.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
✓	accuracy	99.6%	(/.f64 (PI.f64) k)
✓	accuracy	90.3%	(sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
✓	accuracy	74.3%	(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	74.3%	(PI.f64)

Results

392.0ms	188×	0	valid
37.0ms	68×	0	unsamplable

Compiler

Compiled 191 to 29 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-pow: 16.0ms (26.9% of total)

ival-div: 14.0ms (23.5% of total)

ival-mult: 14.0ms (23.5% of total)

ival-sqrt: 13.0ms (21.8% of total)

ival-pi: 1.0ms (1.7% of total)

const: 1.0ms (1.7% of total)

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

series96.0ms (0.7%)

Counts

21 → 360

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

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

Calls

90 calls:

Time	Variable		Point	Expression
54.0ms	k	@	inf	(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))
13.0ms	n	@	inf	(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))
7.0ms	n	@	-inf	(/ (* 2 (* (PI) n)) (* k (pow (* 2 (* (PI) n)) k)))
1.0ms	k	@	inf	(* (/ 2 k) n)
1.0ms	n	@	-inf	(/ (pow k -1/2) (pow (* 2 (* (PI) n)) -1/2))

rewrite351.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

5998×	`-lowering-.f32`
5998×	`-lowering-.f64`
3874×	`/-lowering-/.f32`
3874×	`/-lowering-/.f64`
1042×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	130
1	158	129
2	1017	129
0	8329	129

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 1627

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

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

simplify311.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

4276×	`-lowering-.f32`
4276×	`-lowering-.f64`
2808×	`+-lowering-+.f64`
2808×	`+-lowering-+.f32`
2756×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	3330
1	550	3267
2	2092	3231
3	6968	3231
0	8472	3231

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

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

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

eval346.0ms (2.4%)

Compiler: Compiled 41824 to 5905 computations (85.9% saved)

prune361.0ms (2.5%)

Pruning

46 alts after pruning (36 fresh and 10 done)

	Pruned	Kept	Total
New	2688	16	2704
Fresh	8	20	28
Picked	1	4	5
Done	0	6	6
Total	2697	46	2743

Accuracy

100.0%

Counts

2743 → 46

Alt Table

Click to see full alt table

Status	Accuracy	Program
	34.2%	(pow.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	34.3%	(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
	24.6%	(pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
	34.1%	(/.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)))
	43.8%	(/.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)))
	34.9%	(/.f64 (pow.f64 (.f64 k k) #s(literal -1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)))
✓	99.5%	(/.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 (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)))))
✓	43.8%	(/.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)))
	43.7%	(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/2 binary64))) (sqrt.f64 k))
	43.8%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/2 binary64)))
	34.2%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	43.8%	(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/2 binary64)))
✓	43.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	43.8%	(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 k (PI.f64))))
	34.2%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
	34.2%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 1/2 binary64)))
	34.2%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
	43.7%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
	34.2%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	99.5%	(.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)))
	43.8%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
	1.7%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	43.8%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n)))
	34.2%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
✓	34.2%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
	34.2%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	34.1%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
	43.8%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	34.3%	(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
	74.7%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 k (*.f64 (PI.f64) n))))
	34.4%	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
	90.4%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (/.f64 n (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))) (/.f64 k (PI.f64))))
	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
✓	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
✓	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k)))
	34.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (.f64 (/.f64 #s(literal 1 binary64) n) k))))
	34.4%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
	34.3%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
	34.3%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
✓	34.4%	(sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
✓	32.4%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))
	32.4%	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))) #s(literal 1/2 binary64)))

Compiler

Compiled 1473 to 696 computations (52.7% saved)

regimes126.0ms (0.9%)

Counts

72 → 1

Calls

Call 1

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

Calls

4 calls:

56.0ms	(.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))))
23.0ms	k
22.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
19.0ms	n

Results

Accuracy	Segments	Branch
99.8%	1	`k`
99.8%	1	`n`
99.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes81.0ms (0.6%)

Counts

66 → 1

Calls

Call 1

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

Outputs
(/.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))

Calls

4 calls:

20.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
19.0ms	n
18.0ms	k
17.0ms	(.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
99.5%	1	`k`
99.5%	1	`n`
99.5%	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))))`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes73.0ms (0.5%)

Counts

60 → 1

Calls

Call 1

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

Outputs
(/.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)))))

Calls

4 calls:

19.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
17.0ms	k
17.0ms	n
14.0ms	(.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
99.5%	1	`k`
99.5%	1	`n`
99.5%	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))))`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes36.0ms (0.3%)

Counts

52 → 1

Calls

Call 1

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

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

2 calls:

17.0ms	k
15.0ms	n

Results

Accuracy	Segments	Branch
99.5%	1	`k`
99.5%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes33.0ms (0.2%)

Counts

50 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

15.0ms	k
14.0ms	n

Results

Accuracy	Segments	Branch
56.6%	2	`k`
47.5%	2	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes33.0ms (0.2%)

Counts

49 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

15.0ms	n
14.0ms	k

Results

Accuracy	Segments	Branch
43.8%	1	`n`
46.0%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes15.0ms (0.1%)

Counts

28 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

13.0ms

Results

Accuracy	Segments	Branch
46.0%	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 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n k)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(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 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 k n)) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64)) k)))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 k n)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
(/.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 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (.f64 (/.f64 #s(literal 1 binary64) n) k))))
(pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))

Outputs

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

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
46.0%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts

25 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
46.0%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes15.0ms (0.1%)

Counts

20 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

7.0ms	n
6.0ms	k

Results

Accuracy	Segments	Branch
34.4%	1	`n`
36.6%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes14.0ms (0.1%)

Accuracy

Total -0.2b remaining (-0.5%)

Threshold costs -0.2b (-0.5%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	n
6.0ms	k

Results

Accuracy	Segments	Branch
34.4%	1	`n`
34.4%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch25.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
23.0ms	5.816631862750443e-63	1.6340152393702783e-56

Results

14.0ms

128×

valid

Compiler

Compiled 247 to 201 computations (18.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 3.0ms (30.9% of total)

ival-pow: 3.0ms (30.9% of total)

ival-div: 2.0ms (20.6% of total)

ival-pi: 1.0ms (10.3% of total)

ival-sub: 1.0ms (10.3% of total)

ival-sqrt: 1.0ms (10.3% of total)

const: 0.0ms (0% of total)

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

bsearch18.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	3.752431117592849e+209	4.248774622769554e+211

Results

12.0ms

112×

valid

Compiler

Compiled 247 to 164 computations (33.6% saved)

Precisions

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

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

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

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

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

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

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

const: 0.0ms (0% of total)

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

bsearch22.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	3.752431117592849e+209	4.248774622769554e+211

Results

15.0ms

112×

valid

Compiler

Compiled 247 to 164 computations (33.6% saved)

Precisions

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

ival-div: 5.0ms (46% of total)

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

ival-pow: 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 (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	3.752431117592849e+209	4.248774622769554e+211

Results

12.0ms

112×

valid

Compiler

Compiled 247 to 164 computations (33.6% saved)

Precisions

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

ival-div: 2.0ms (25.1% of total)

ival-mult: 2.0ms (25.1% of total)

ival-pow: 2.0ms (25.1% of total)

ival-sub: 1.0ms (12.5% of total)

ival-sqrt: 1.0ms (12.5% of total)

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

const: 0.0ms (0% of total)

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

bsearch21.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	3.752431117592849e+209	4.248774622769554e+211

Results

15.0ms

112×

valid

Compiler

Compiled 247 to 164 computations (33.6% saved)

Precisions

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

ival-pow: 5.0ms (44.4% of total)

ival-div: 2.0ms (17.7% of total)

ival-mult: 2.0ms (17.7% of total)

ival-sub: 1.0ms (8.9% of total)

ival-sqrt: 1.0ms (8.9% of total)

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

const: 0.0ms (0% of total)

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

bsearch32.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
30.0ms	1.949067078118768e+197	2.7619313481982565e+202

Results

24.0ms

144×

valid

Compiler

Compiled 302 to 197 computations (34.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 3.0ms (29% of total)

ival-pow: 3.0ms (29% of total)

ival-div: 2.0ms (19.3% of total)

ival-pi: 1.0ms (9.7% of total)

ival-sub: 1.0ms (9.7% of total)

ival-sqrt: 1.0ms (9.7% of total)

const: 0.0ms (0% of total)

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

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary64`
16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	246
1	91	246
2	105	246
3	115	246
4	123	246
5	126	246

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (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 (.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 (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 (.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 795081179150273/441711766194596082395824375185729628956870974218904739530401550323154944 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (/.f64 (pow.f64 (.f64 k k) #s(literal -1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))))
(if (<=.f64 k #s(literal 450000000000000032900346982464683657002271791066892281519006930998500590007006783343913534564735835700424809599863934064007062562223593701017461087137813475697687592244249131301031077100345964516650481818271744 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 1249999999999999945391752965158318717377708037220933940969484798597472749263080492067398912002145397645303397843737246150132378540044504116343285269146577043963969969567615785105701190194704832116499408714989568 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 k (PI.f64)))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 2150000000000000011192446930087686031382251619354718504007498660594473929277094058755225981131617069046153017043465114278146503664491691518378207443422203995359345154056114047707763344395396761149800372351533056 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 19500000000000001133685503045649131143730128181413354072657009212693856676568639466015975796449866810639988491682334223607198231652980325826679544941277218725396137868362420974917020848624701657084239241675800576 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 254999999999999993981587741203796938972680596208930632207714441649886617748884134853492054486728119028790163909467114281310300478627913384939485735159124854681574089273393979838773690603984479481495552 binary64)) (sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))

Outputs
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (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 (.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 (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 (.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 795081179150273/441711766194596082395824375185729628956870974218904739530401550323154944 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (/.f64 (pow.f64 (.f64 k k) #s(literal -1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))))
(if (<=.f64 k #s(literal 450000000000000032900346982464683657002271791066892281519006930998500590007006783343913534564735835700424809599863934064007062562223593701017461087137813475697687592244249131301031077100345964516650481818271744 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 1249999999999999945391752965158318717377708037220933940969484798597472749263080492067398912002145397645303397843737246150132378540044504116343285269146577043963969969567615785105701190194704832116499408714989568 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 k (PI.f64)))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 2150000000000000011192446930087686031382251619354718504007498660594473929277094058755225981131617069046153017043465114278146503664491691518378207443422203995359345154056114047707763344395396761149800372351533056 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 19500000000000001133685503045649131143730128181413354072657009212693856676568639466015975796449866810639988491682334223607198231652980325826679544941277218725396137868362420974917020848624701657084239241675800576 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 19500000000000001133685503045649131143730128181413354072657009212693856676568639466015975796449866810639988491682334223607198231652980325826679544941277218725396137868362420974917020848624701657084239241675800576 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(if (<=.f64 k #s(literal 254999999999999993981587741203796938972680596208930632207714441649886617748884134853492054486728119028790163909467114281310300478627913384939485735159124854681574089273393979838773690603984479481495552 binary64)) (sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))) (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))) #s(literal 1/4 binary64)))
(sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))

soundness2.2s (15.3%)

Rules

5998×	`-lowering-.f32`
5998×	`-lowering-.f64`
5664×	`-lowering-.f32`
5664×	`-lowering-.f64`
5256×	`-lowering-.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	241	3825
1	812	3583
2	2752	3515
3	6157	3515
0	8245	3515
0	37	181
1	235	160
2	1611	158
0	8262	158
0	26	124
1	164	120
2	1156	117
0	8192	117
0	28	130
1	158	129
2	1017	129
0	8329	129
0	139	2132
1	409	2094
2	1221	1806
3	4209	1722
4	7799	1722
0	8149	1722
0	13	14
1	33	14
2	50	14
3	72	14
4	93	13
5	116	13
6	152	13
7	191	13
8	217	13
9	231	13
10	232	13
0	232	13
0	20	68
1	135	68
2	873	64
0	8718	64

Stop Event

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

Compiler

Compiled 783 to 480 computations (38.7% saved)

preprocess299.0ms (2.1%)

Compiler: Compiled 532 to 176 computations (66.9% saved)

Iter	Nodes	Cost
0	20	98
1	41	98
2	61	98
3	81	98
4	103	92
5	132	92
6	173	92
7	205	92
8	234	92
9	238	92
0	238	92

Iter	Nodes	Cost
0	26	205
1	45	205
2	75	205
3	105	205
4	132	205
5	162	202
6	189	202
7	211	202
8	237	202
9	260	202
10	266	202
11	269	202
0	269	202

Iter	Nodes	Cost
0	28	182
1	59	181
2	135	181
3	334	181
4	551	181
5	754	181
6	819	181
7	825	181
0	825	181

Iter	Nodes	Cost
0	20	98
1	41	98
2	61	98
3	81	98
4	103	92
5	132	92
6	173	92
7	205	92
8	234	92
9	238	92
0	238	92

Iter	Nodes	Cost
0	26	205
1	45	205
2	75	205
3	105	205
4	132	205
5	162	202
6	189	202
7	211	202
8	237	202
9	260	202
10	266	202
11	269	202
0	269	202

Iter	Nodes	Cost
0	28	182
1	59	181
2	135	181
3	334	181
4	551	181
5	754	181
6	819	181
7	825	181
0	825	181

analyze191.0ms (1.3%)

sample4.3s (30.2%)

preprocess99.0ms (0.7%)

explain182.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.1%)

localize119.0ms (0.8%)

series81.0ms (0.6%)

rewrite413.0ms (2.9%)

simplify277.0ms (1.9%)

eval108.0ms (0.8%)

prune107.0ms (0.7%)

simplify47.0ms (0.3%)

localize245.0ms (1.7%)

series70.0ms (0.5%)

rewrite413.0ms (2.9%)

simplify360.0ms (2.5%)

eval290.0ms (2%)

prune218.0ms (1.5%)

simplify23.0ms (0.2%)

localize223.0ms (1.6%)

series206.0ms (1.4%)

rewrite410.0ms (2.9%)

simplify375.0ms (2.6%)

eval284.0ms (2%)

prune176.0ms (1.2%)

simplify30.0ms (0.2%)

localize486.0ms (3.4%)

series96.0ms (0.7%)

rewrite351.0ms (2.4%)

simplify311.0ms (2.2%)

eval346.0ms (2.4%)

prune361.0ms (2.5%)

regimes126.0ms (0.9%)

regimes81.0ms (0.6%)

regimes73.0ms (0.5%)

regimes36.0ms (0.3%)

regimes33.0ms (0.2%)

regimes33.0ms (0.2%)

regimes15.0ms (0.1%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

regimes15.0ms (0.1%)

regimes14.0ms (0.1%)

bsearch25.0ms (0.2%)

bsearch18.0ms (0.1%)

bsearch22.0ms (0.2%)

bsearch21.0ms (0.1%)

bsearch21.0ms (0.1%)

bsearch32.0ms (0.2%)

simplify14.0ms (0.1%)

soundness2.2s (15.3%)

preprocess299.0ms (2.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	20	98
1	41	98
2	61	98
3	81	98
4	103	92
5	132	92
6	173	92
7	205	92
8	234	92
9	238	92
0	238	92

Iter	Nodes	Cost
0	26	205
1	45	205
2	75	205
3	105	205
4	132	205
5	162	202
6	189	202
7	211	202
8	237	202
9	260	202
10	266	202
11	269	202
0	269	202

Iter	Nodes	Cost
0	28	182
1	59	181
2	135	181
3	334	181
4	551	181
5	754	181
6	819	181
7	825	181
0	825	181