Metrics for Migdal et al, Equation (51)

analyze155.0ms (1.1%)

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: 99.0ms

ival-pow: 46.0ms (46.5% of total)

ival-mult: 19.0ms (19.2% of total)

ival-div: 15.0ms (15.1% of total)

ival-sqrt: 9.0ms (9.1% of total)

ival-sub: 5.0ms (5% of total)

ival-pi: 4.0ms (4% of total)

const: 1.0ms (1% of total)

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

sample4.5s (32.5%)

Results

1.9s	4079×	5	exit
1.1s	8256×	0	valid
509.0ms	1980×	1	invalid
52.0ms	236×	0	unsamplable
42.0ms	441×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 2.6s

ival-pow: 865.0ms (33.1% of total)

ival-mult: 585.0ms (22.4% of total)

ival-div: 358.0ms (13.7% of total)

backward-pass: 298.0ms (11.4% of total)

ival-sqrt: 216.0ms (8.3% of total)

ival-sub: 144.0ms (5.5% of total)

ival-pi: 110.0ms (4.2% of total)

const: 37.0ms (1.4% of total)

Bogosity

preprocess82.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

Outputs

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

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

Call 2

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

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

explain167.0ms (1.2%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
5	216	(4.046277254145361e-264 1.617345842795287e+224)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	-	`(PI.f64)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`n`
0	0	-	-	`k`

Results

95.0ms

512×

valid

Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-pow: 23.0ms (40.3% of total)

ival-mult: 15.0ms (26.3% of total)

ival-div: 8.0ms (14% of total)

ival-sqrt: 5.0ms (8.8% of total)

ival-sub: 3.0ms (5.3% of total)

ival-pi: 2.0ms (3.5% of total)

const: 1.0ms (1.8% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.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)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize134.0ms (1%)

Localize:

Found 8 expressions of interest:

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

Results

92.0ms

256×

valid

Compiler

Compiled 105 to 21 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-pow: 17.0ms (42.6% of total)

ival-mult: 9.0ms (22.6% of total)

ival-div: 7.0ms (17.6% of total)

ival-sub: 3.0ms (7.5% of total)

ival-sqrt: 2.0ms (5% of total)

ival-pi: 1.0ms (2.5% of total)

const: 1.0ms (2.5% of total)

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

series95.0ms (0.7%)

Counts

10 → 156

Calls

Call 1

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

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

Calls

39 calls:

Time	Variable		Point	Expression
33.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
22.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
17.0ms	k	@	-inf	(/ 1 (sqrt k))
8.0ms	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)))

rewrite326.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	68
1	132	68
2	851	64
0	8618	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 0 binary64) (sqrt.f64 k))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #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 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal 1/2 binary64)) (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 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(/.f64 (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 0 binary64) (sqrt.f64 k))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k)))
(/.f64 (.f64 (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 0 binary64) (sqrt.f64 k)) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (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 0 binary64) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (*.f64 (pow.f64 #s(literal 2 binary64) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (.f64 (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 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 k))))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))))
(.f64 (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))))
(.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 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal -2 binary64))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k))))
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(.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))) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (.f64 (*.f64 n (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 (*.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 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64)) (.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (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 (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 (PI.f64) (*.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 (.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))))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))) (cbrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64))) (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64))))
(.f64 (.f64 (cbrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))))
(.f64 (.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))

simplify246.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

5256×	`-lowering-.f32`
5256×	`-lowering-.f64`
2382×	`+-lowering-+.f64`
2382×	`+-lowering-+.f32`
1472×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	2132
1	385	2104
2	1189	1816
3	4175	1732
4	7740	1732
0	8111	1732

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

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

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

eval127.0ms (0.9%)

Compiler: Compiled 21499 to 2036 computations (90.5% saved)

prune130.0ms (0.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	976	13	989
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	977	14	991

Accuracy

100.0%

Counts

991 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.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 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	96.3%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.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 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
	76.7%	(/.f64 (.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)))))) (sqrt.f64 k))
	48.8%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	99.7%	(/.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))))))
▶	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
	99.3%	(.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #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)))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	38.2%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	96.3%	(.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 488 to 360 computations (26.2% saved)

simplify58.0ms (0.4%)

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)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓	cost-diff	6528	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
✓	cost-diff	6528	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.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 1/4 binary64) (*.f64 k #s(literal 1/4 binary64))))
✓	cost-diff	6464	(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))
✓	cost-diff	6464	(/.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))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓	cost-diff	0	(.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))
✓	cost-diff	64	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 k)))
✓	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	64	(pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64))
✓	cost-diff	64	(/.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)))

Rules

398×	`-lowering-.f32`
398×	`-lowering-.f64`
368×	`fmsub-define`
352×	`fma-lowering-fma.f32`
352×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 11 (0.0ms)

Iter	Nodes	Cost
0	37	276
1	65	276
2	106	269
3	153	265
4	232	260
5	381	260
6	569	260
7	704	260
8	875	260
9	929	260
10	945	260
11	975	256
12	1048	256
13	1153	256
14	1218	256
15	1261	256
16	1303	256
17	1321	256
0	1321	256

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

localize250.0ms (1.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	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)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k))))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	94.3%	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 k)))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.7%	(/.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))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(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))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.8%	(.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))
✓	accuracy	99.7%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.7%	(*.f64 n (PI.f64))
✓	accuracy	99.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	89.2%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	99.7%	(/.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	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	77.7%	(PI.f64)

Results

128.0ms	197×	0	valid
49.0ms	59×	0	unsamplable

Compiler

Compiled 284 to 38 computations (86.6% saved)

Precisions

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

ival-pow: 71.0ms (59.3% of total)

ival-mult: 17.0ms (14.2% of total)

ival-div: 10.0ms (8.4% of total)

ival-sqrt: 8.0ms (6.7% of total)

ival-exp: 3.0ms (2.5% of total)

ival-sub: 3.0ms (2.5% of total)

ival-log: 3.0ms (2.5% of total)

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

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

const: 1.0ms (0.8% of total)

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

series56.0ms (0.4%)

Counts

19 → 372

Calls

Call 1

Inputs
#<alt (/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))>
#<alt (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 (* (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2)) (sqrt k)))>
#<alt (* (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2)) (sqrt k))>
#<alt (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2))>
#<alt (/ (pow (pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4))) 2) (sqrt k))>
#<alt (pow (pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4))) 2)>
#<alt (pow (* 2 (* (PI) n)) (- 1/4 (* k 1/4)))>
#<alt (/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (exp (* 1/2 (log k))))>
#<alt (exp (* 1/2 (log k)))>
#<alt (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))>
#<alt (PI)>
#<alt (* (PI) n)>

Outputs
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))))) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (* (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)>
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#<alt (* (sqrt (/ 1 k)) (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2))>
#<alt (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k)))) 2)>
#<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 (+ (* 1/8 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 2) (sqrt 2)))) (* k (+ (* -1/64 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))) (* -1/192 (* (sqrt (* n (PI))) (* (pow (log (* 2 (* n (PI)))) 3) (sqrt 2)))))))))) (* (sqrt (* n (PI))) (sqrt 2)))>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2)>
#<alt (pow (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k)))) 2)>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log n) (log (* 2 (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- 1/4 (* 1/4 k))))>
#<alt (pow (* 2 (* n (PI))) 1/4)>
#<alt (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (* k (log (* 2 (* n (PI))))))) (pow (* 2 (* n (PI))) 1/4))>
#<alt (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (* n (PI)))))) (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (* k (pow (log (* 2 (* n (PI)))) 2)))))) (pow (* 2 (* n (PI))) 1/4))>
#<alt (+ (* k (+ (* -1/4 (* (pow (* 2 (* n (PI))) 1/4) (log (* 2 (* n (PI)))))) (* k (+ (* -1/384 (* (pow (* 2 (* n (PI))) 1/4) (* k (pow (log (* 2 (* n (PI)))) 3)))) (* 1/32 (* (pow (* 2 (* n (PI))) 1/4) (pow (log (* 2 (* n (PI)))) 2))))))) (pow (* 2 (* n (PI))) 1/4))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (- 1/4 (* 1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 k))))>
#<alt (exp (* (log (* 2 (* n (PI)))) (+ 1/4 (* -1/4 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 (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 (* (+ (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 (* 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 (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
4.0ms	k	@	-inf	(/ 1 (* (pow (* 2 (* (PI) n)) (+ (/ k 2) -1/2)) (sqrt k)))
3.0ms	k	@	-inf	(pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)
3.0ms	n	@	-inf	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
2.0ms	k	@	0	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))

rewrite397.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

5750×	`-lowering-.f32`
5750×	`-lowering-.f64`
3194×	`/-lowering-/.f32`
3194×	`/-lowering-/.f64`
2578×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	182
1	234	161
2	1545	154
0	9067	154

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 1217

Calls

Call 1

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

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

simplify344.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

6926×	`-lowering-.f32`
6926×	`-lowering-.f64`
2104×	`+-lowering-+.f64`
2104×	`+-lowering-+.f32`
1354×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	411	5814
1	1336	5539
2	4994	5025
0	8538	5025

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

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

eval270.0ms (1.9%)

Compiler: Compiled 42528 to 3442 computations (91.9% saved)

prune196.0ms (1.4%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	1953	14	1967
Fresh	7	1	8
Picked	4	1	5
Done	0	1	1
Total	1964	17	1981

Accuracy

100.0%

Counts

1981 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	90.3%	(pow.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))) #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 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
	38.1%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	48.9%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	80.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
▶	39.3%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
▶	39.4%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	48.9%	(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	38.2%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	38.2%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
	38.2%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	38.2%	(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
	48.9%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	89.2%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
▶	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	36.0%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n)))) #s(literal 1/2 binary64)))

Compiler

Compiled 439 to 329 computations (25.1% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

84×	`-lowering-.f32`
84×	`-lowering-.f64`
52×	`/-lowering-/.f32`
52×	`/-lowering-/.f64`
38×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	178
1	51	177
2	74	177
3	94	177
4	107	177
5	113	177
0	113	177

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize224.0ms (1.6%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(*.f64 n (PI.f64))
✓	accuracy	99.5%	(.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	90.3%	(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.5%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	90.4%	(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.6%	(/.f64 (PI.f64) k)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	89.2%	(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.8%	(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	89.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
✓	accuracy	99.7%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	77.7%	(PI.f64)

Results

96.0ms	59×	5	exit
82.0ms	197×	0	valid

Compiler

Compiled 182 to 31 computations (83% saved)

Precisions

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

ival-pow: 31.0ms (31.2% of total)

ival-mult: 19.0ms (19.1% of total)

backward-pass: 18.0ms (18.1% of total)

ival-div: 16.0ms (16.1% of total)

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

ival-add: 2.0ms (2% of total)

const: 1.0ms (1% of total)

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

series26.0ms (0.2%)

Counts

20 → 396

Calls

Call 1

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

Calls

99 calls:

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

rewrite296.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4702×	`-lowering-.f32`
4702×	`-lowering-.f64`
3448×	`/-lowering-/.f32`
3448×	`/-lowering-/.f64`
1450×	`frac-times`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	124
1	173	122
2	1042	120
0	8415	120

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 1010

Calls

Call 1

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

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

simplify508.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

3188×	`-lowering-.f32`
3188×	`-lowering-.f64`
1960×	`fnmadd-define`
1820×	`fma-lowering-fma.f32`
1820×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	3403
1	493	3238
2	1741	3147
3	5231	3135
0	8014	3135

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 396

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

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)))
(/ (+ (* -1/2 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 1/2)))) (* (sqrt (* k (* n (PI)))) (/ 1 (sqrt 1/2)))) k)
(/.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (.f64 k (.f64 k k))))) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))) 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)
(/.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 k (+.f64 (/.f64 (.f64 (sqrt.f64 (.f64 k (.f64 k k))) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal 1/8 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 n (*.f64 (PI.f64) k))))) (sqrt.f64 #s(literal 1/2 binary64)))))) 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)
(/.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 k (-.f64 (/.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 n (.f64 (PI.f64) k))))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 k (+.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (.f64 (sqrt.f64 (.f64 k (.f64 k k))) #s(literal -1/24 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (/.f64 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal -1/8 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 k (.f64 k k))) (.f64 #s(literal -1/2 binary64) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))))))))) k)
(* (sqrt (/ 1 k)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (log (* 2 (* n (PI)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 #s(literal -1 binary64) (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)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 #s(literal -1 binary64) (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)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 #s(literal -1 binary64) (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)) (/ (pow (sqrt -1) 2) (exp (* -1 (* (log (* 2 (* n (PI)))) (+ 1/2 (* -1/2 k)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 #s(literal -1 binary64) (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)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))))
(/.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)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
(* (sqrt (/ 1 k)) (/ 1 (exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal 1 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)) (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)))
(exp (* (+ (log n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(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 n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(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 n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(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 n) (log (* 2 (PI)))) (- (* 1/2 k) 1/2)))
(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 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(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 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(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 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(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 (PI))) (* -1 (log (/ 1 n)))) (- (* 1/2 k) 1/2)))
(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 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(exp (* (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))) (- (* 1/2 k) 1/2)))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) n))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
(* (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)))))
(+ (* 1/2 (* (* k (* (log (* 2 (* n (PI)))) (sqrt 1/2))) (sqrt (/ 1 (* n (PI)))))) (* (sqrt (/ 1 (* n (PI)))) (sqrt 1/2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))) (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* 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)))
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(/ k (* n (PI)))
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(* n (PI))
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(* 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))
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(* n (PI))
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eval230.0ms (1.7%)

Compiler: Compiled 25883 to 3569 computations (86.2% saved)

prune201.0ms (1.4%)

Pruning

48 alts after pruning (43 fresh and 5 done)

	Pruned	Kept	Total
New	1747	38	1785
Fresh	5	5	10
Picked	2	3	5
Done	0	2	2
Total	1754	48	1802

Accuracy

100.0%

Counts

1802 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
	39.4%	(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))
▶	90.3%	(pow.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))) #s(literal -1/2 binary64))
	27.1%	(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))
	39.3%	(/.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
▶	48.9%	(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
✓	99.5%	(/.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))
	38.1%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	48.9%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	38.2%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
	39.3%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	48.9%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))))
	39.2%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
	48.8%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64))))
	39.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (/.f64 k n) #s(literal 1/2 binary64))) (sqrt.f64 (PI.f64))))
	48.9%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
	39.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))))
	38.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 1/2 binary64))))
	80.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
✓	39.3%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
	39.2%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) k)) (sqrt.f64 #s(literal 1/2 binary64))))
	39.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64))))
	37.1%	(/.f64 #s(literal 1 binary64) (exp.f64 (.f64 (log.f64 (/.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
	39.4%	(*.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	48.9%	(.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64)))
	39.4%	(.f64 (pow.f64 (.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	48.9%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
✓	38.2%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	38.2%	(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n))) (sqrt.f64 (PI.f64)))
✓	38.2%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
	38.2%	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	48.9%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
	38.2%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n)) (sqrt.f64 (PI.f64)))
	38.2%	(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n))) (sqrt.f64 #s(literal 2 binary64)))
▶	38.3%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
	38.3%	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) (/.f64 k #s(literal 2 binary64))))
	89.2%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
✓	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1 binary64) n)))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k n) (/.f64 #s(literal 1 binary64) (PI.f64)))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k)))
	38.3%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
	38.3%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
▶	38.3%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
	37.1%	(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 2 binary64))) #s(literal -1/2 binary64)))

Compiler

Compiled 1187 to 937 computations (21.1% saved)

simplify36.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

556×	`-lowering-.f32`
556×	`-lowering-.f64`
432×	`associate-r`
366×	`times-frac`
354×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	178
1	58	178
2	125	178
3	258	178
4	544	178
5	995	178
6	1118	178
0	1118	178

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize268.0ms (1.9%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.5%	(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n))) (sqrt.f64 (PI.f64)))
✓	accuracy	98.8%	(sqrt.f64 (PI.f64))
✓	accuracy	89.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))
✓	accuracy	89.2%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal 2 binary64) k) n)
✓	accuracy	99.6%	(.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64))
✓	accuracy	89.2%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
✓	accuracy	77.7%	(PI.f64)
✓	accuracy	99.9%	(/.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))
✓	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	90.3%	(pow.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))) #s(literal -1/2 binary64))
✓	accuracy	77.7%	(PI.f64)

Results

126.0ms	59×	5	exit
90.0ms	197×	0	valid

Compiler

Compiled 188 to 29 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 129.0ms

ival-pow: 53.0ms (41.2% of total)

ival-div: 35.0ms (27.2% of total)

backward-pass: 15.0ms (11.7% of total)

ival-mult: 14.0ms (10.9% of total)

ival-sqrt: 9.0ms (7% of total)

ival-pi: 2.0ms (1.6% of total)

const: 1.0ms (0.8% of total)

series92.0ms (0.7%)

Counts

21 → 396

Calls

Call 1

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

Outputs
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (/ (+ (* -1 (* (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 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (/ (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (sqrt 2))))))) k)>
#<alt (/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (/ (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (sqrt 2)))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (/ (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* 1/3 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* k (pow (sqrt 2) 2)))))) (sqrt 2))))))))) 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 (* (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 (* 1/2 (/ k (* n (PI))))>
#<alt (* k (+ (* 1/2 (/ (* k (log (* 2 (* n (PI))))) (* n (PI)))) (* 1/2 (/ 1 (* n (PI))))))>
#<alt (* k (+ (* k (+ (* 1/4 (/ (* k (pow (log (* 2 (* n (PI)))) 2)) (* n (PI)))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* n (PI)))))) (* 1/2 (/ 1 (* n (PI))))))>
#<alt (* k (+ (* k (+ (* 1/2 (/ (log (* 2 (* n (PI)))) (* n (PI)))) (* k (+ (* 1/12 (/ (* k (pow (log (* 2 (* n (PI)))) 3)) (* n (PI)))) (* 1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* n (PI)))))))) (* 1/2 (/ 1 (* n (PI))))))>
#<alt (* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))>
#<alt (* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))>
#<alt (* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))>
#<alt (* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))>
#<alt (* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))>
#<alt (* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))>
#<alt (* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))>
#<alt (* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log n) (log (* 2 (PI))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log n) (log (* 2 (PI))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log n) (log (* 2 (PI))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log n) (log (* 2 (PI))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* n (PI))))>
#<alt (* 1/2 (/ (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* n (PI))))>
#<alt k>
#<alt (* k (+ 1 (* k (log (* 2 (* n (PI)))))))>
#<alt (* k (+ 1 (* k (+ (log (* 2 (* n (PI)))) (* 1/2 (* k (pow (log (* 2 (* n (PI)))) 2)))))))>
#<alt (* k (+ 1 (* k (+ (log (* 2 (* n (PI)))) (* k (+ (* 1/6 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/2 (pow (log (* 2 (* n (PI)))) 2))))))))>
#<alt (* k (pow (* 2 (* n (PI))) k))>
#<alt (* k (pow (* 2 (* n (PI))) k))>
#<alt (* k (pow (* 2 (* n (PI))) k))>
#<alt (* k (pow (* 2 (* n (PI))) k))>
#<alt (* k (pow (* 2 (* n (PI))) k))>
#<alt (* k (pow (* 2 (* n (PI))) k))>
#<alt (* k (pow (* 2 (* n (PI))) k))>
#<alt (* k (pow (* 2 (* n (PI))) k))>
#<alt (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (* k (exp (* k (+ (log n) (log (* 2 (PI)))))))>
#<alt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))>
#<alt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log n) (log (* 2 (PI))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))>
#<alt 1>
#<alt (+ 1 (* k (log (* 2 (* n (PI))))))>
#<alt (+ 1 (* k (+ (log (* 2 (* n (PI)))) (* 1/2 (* k (pow (log (* 2 (* n (PI)))) 2))))))>
#<alt (+ 1 (* k (+ (log (* 2 (* n (PI)))) (* k (+ (* 1/6 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/2 (pow (log (* 2 (* n (PI)))) 2)))))))>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (pow (* 2 (* n (PI))) k)>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* (sqrt (/ (* n (PI)) k)) (sqrt 2))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ (* n (PI)) k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (* 2 (/ n k))>
#<alt (/ 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)) (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 (/ 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 (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<alt (/ k n)>
#<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)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (sqrt 2))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))>
#<alt (sqrt (/ 1 (* n (PI))))>
#<alt (sqrt (/ 1 (* n (PI))))>
#<alt (sqrt (/ 1 (* n (PI))))>
#<alt (sqrt (/ 1 (* n (PI))))>
#<alt (sqrt (/ 1 (* n (PI))))>
#<alt (sqrt (/ 1 (* n (PI))))>
#<alt (sqrt (/ 1 (* n (PI))))>
#<alt (sqrt (/ 1 (* n (PI))))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))>
#<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

99 calls:

Time	Variable		Point	Expression
26.0ms	n	@	inf	(pow (/ (* k (pow (* 2 (* (PI) n)) k)) (* 2 (* (PI) n))) -1/2)
17.0ms	n	@	0	(sqrt (/ 2 (/ k n)))
12.0ms	n	@	inf	(/ (* k (pow (* 2 (* (PI) n)) k)) (* 2 (* (PI) n)))
6.0ms	k	@	-inf	(pow (/ (* k (pow (* 2 (* (PI) n)) k)) (* 2 (* (PI) n))) -1/2)
6.0ms	n	@	-inf	(/ (* k (pow (* 2 (* (PI) n)) k)) (* 2 (* (PI) n)))

rewrite379.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

5728×	`-lowering-.f32`
5728×	`-lowering-.f64`
2358×	`/-lowering-/.f32`
2358×	`/-lowering-/.f64`
1310×	`frac-times`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	135
1	165	135
2	1064	126
0	8263	126

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 1471

Calls

Call 1

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

Outputs
(exp.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #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)) (+.f64 k #s(literal -1 binary64)))) #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)) (+.f64 k #s(literal -1 binary64))))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))))) #s(literal -1/4 binary64)) (.f64 (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))))) #s(literal -1/4 binary64))))
(pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #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)) (+.f64 k #s(literal -1 binary64)))) #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)) (+.f64 k #s(literal -1 binary64))))))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (.f64 (PI.f64) n)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (.f64 (PI.f64) n)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64)) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/4 binary64)) (.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (.f64 (PI.f64) n)) #s(literal -1/4 binary64)) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64))))
(.f64 (pow.f64 k #s(literal -1/4 binary64)) (.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/4 binary64)) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/2 binary64)) (pow.f64 k #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 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal -1/4 binary64)) (.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)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64))))
(.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/8 binary64)) (.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/8 binary64)) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64))))
(.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k)) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal 2 binary64) k)) #s(literal -1/2 binary64)) (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 k (.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) n) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (.f64 #s(literal 2 binary64) (PI.f64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (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 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64))) (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) #s(literal -1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64)) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal -1/4 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (.f64 (PI.f64) n)) #s(literal -1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/4 binary64)) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/8 binary64))) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/8 binary64)))
(exp.f64 (log.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64))) (neg.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))))))
(neg.f64 (neg.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))))))
(neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))))))
(neg.f64 (.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal 2 binary64) k)) (/.f64 #s(literal -1 binary64) (.f64 (PI.f64) n))))
(neg.f64 (.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 0 binary64) (/.f64 k n))))
(neg.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal 2 binary64) k)) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))))))
(neg.f64 (/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 k #s(literal -2 binary64))) (.f64 (PI.f64) n)))
(/.f64 k (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))))
(/.f64 k (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))))
(/.f64 k (.f64 (/.f64 (.f64 (PI.f64) n) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal 2 binary64)))
(/.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 #s(literal 1 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))))))
(/.f64 #s(literal 1 binary64) (exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))))))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (*.f64 (PI.f64) n)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 (.f64 (PI.f64) n) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(/.f64 #s(literal 1 binary64) (/.f64 n (/.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (.f64 #s(literal 2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 n (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal 2 binary64) k)) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal 2 binary64) k)) n)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))))))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n))))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k)) (.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) k) (.f64 (/.f64 (.f64 (PI.f64) n) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal -2 binary64)))
(/.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 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (*.f64 (PI.f64) n)) (/.f64 #s(literal 2 binary64) k))
(/.f64 (/.f64 #s(literal 1 binary64) n) (.f64 (/.f64 #s(literal 2 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (PI.f64)))
(/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal 2 binary64) k)) (*.f64 (PI.f64) n))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (.f64 (/.f64 #s(literal 2 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) n))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 k #s(literal -2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 (PI.f64) n)))
(/.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) (.f64 (/.f64 #s(literal 2 binary64) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (-.f64 #s(literal 0 binary64) n)))
(/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (*.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 n k))
(/.f64 (.f64 (/.f64 k #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (.f64 (PI.f64) n))
(/.f64 (/.f64 k (/.f64 (.f64 (PI.f64) n) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))) #s(literal 2 binary64))
(/.f64 (/.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (.f64 #s(literal 2 binary64) (PI.f64))) n)
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal 2 binary64) k)) (PI.f64)) n)
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal 2 binary64) k)) n) (PI.f64))
(/.f64 (exp.f64 (log.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 (exp.f64 (log.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k)))) (exp.f64 (log.f64 (.f64 (*.f64 (PI.f64) n) #s(literal -2 binary64)))))
(/.f64 (exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (/.f64 #s(literal 2 binary64) k)))) (*.f64 (PI.f64) n))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) k) #s(literal 1 binary64)) (.f64 #s(literal -2 binary64) (/.f64 (.f64 (PI.f64) n) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) (/.f64 k (.f64 (PI.f64) n))))
(/.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) #s(literal -1 binary64)) (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 n (-.f64 #s(literal 0 binary64) k))))
(/.f64 (.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) #s(literal -1 binary64)) (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64)))
(/.f64 (.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k)) #s(literal 1 binary64)) (.f64 (.f64 (PI.f64) n) #s(literal -2 binary64)))
(/.f64 (.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (-.f64 #s(literal 0 binary64) k)) #s(literal -1 binary64)) (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
(/.f64 (.f64 k (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) n)) (.f64 #s(literal 2 binary64) (PI.f64)))
(/.f64 (.f64 k (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (PI.f64))) (.f64 #s(literal 2 binary64) n))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (.f64 #s(literal -2 binary64) (/.f64 (*.f64 (PI.f64) n) k)))
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(.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 (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 (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 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (PI.f64) n)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)))
(/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) n)))
(/.f64 (-.f64 #s(literal 0 binary64) n) (/.f64 #s(literal -1 binary64) (PI.f64)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) n)) #s(literal -1 binary64))
(pow.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n)) #s(literal -1 binary64))
(*.f64 (PI.f64) n)
(*.f64 (PI.f64) (pow.f64 (/.f64 #s(literal 1 binary64) n) #s(literal -1 binary64)))
(*.f64 (PI.f64) (pow.f64 n #s(literal 1 binary64)))
(*.f64 (PI.f64) (exp.f64 (log.f64 n)))
(*.f64 n (PI.f64))
(*.f64 n (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))))
(.f64 (.f64 (PI.f64) n) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) n))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 (sqrt.f64 (PI.f64)) n) #s(literal 1 binary64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (*.f64 (sqrt.f64 (PI.f64)) n) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 (PI.f64) n)))
(.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (.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 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) n)))
(.f64 (cbrt.f64 (PI.f64)) (.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) n)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (cbrt.f64 (PI.f64)) n))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (.f64 (cbrt.f64 (PI.f64)) n) #s(literal 1 binary64)))
(.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (.f64 (*.f64 (cbrt.f64 (PI.f64)) n) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) n) (-.f64 #s(literal 0 binary64) (PI.f64)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 (PI.f64) n)) #s(literal -1 binary64))
(.f64 (pow.f64 (.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) 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 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) n) #s(literal -1 binary64)) (PI.f64))
(*.f64 (pow.f64 n #s(literal 1 binary64)) (PI.f64))
(.f64 (pow.f64 (.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (pow.f64 (.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (exp.f64 (log.f64 n)) (PI.f64))
(.f64 (.f64 n (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))) n)
(.f64 (.f64 #s(literal 1 binary64) (*.f64 n (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) n)
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 n (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 n (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 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (*.f64 n (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/3 binary64))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(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)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (PI.f64)) #s(literal -1/2 binary64))))
(fabs.f64 (sqrt.f64 (PI.f64)))
(fabs.f64 (neg.f64 (sqrt.f64 (PI.f64))))
(sqrt.f64 (PI.f64))
(/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal -1/2 binary64))))
(pow.f64 (PI.f64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) #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)))

simplify310.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

3900×	`-lowering-.f32`
3900×	`-lowering-.f64`
2990×	`fma-lowering-fma.f32`
2990×	`fma-lowering-fma.f64`
1622×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	3776
1	606	3714
2	2205	3649
3	6142	3648
0	8233	3648

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 396

Calls

Call 1

Inputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(/ (+ (* -1 (* (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 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (/ (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (sqrt 2))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (/ (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (sqrt 2)))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (/ (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* 1/3 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* k (pow (sqrt 2) 2)))))) (sqrt 2))))))))) 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)))
(* (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))))
(* 1/2 (/ k (* n (PI))))
(* k (+ (* 1/2 (/ (* k (log (* 2 (* n (PI))))) (* n (PI)))) (* 1/2 (/ 1 (* n (PI))))))
(* k (+ (* k (+ (* 1/4 (/ (* k (pow (log (* 2 (* n (PI)))) 2)) (* n (PI)))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* n (PI)))))) (* 1/2 (/ 1 (* n (PI))))))
(* k (+ (* k (+ (* 1/2 (/ (log (* 2 (* n (PI)))) (* n (PI)))) (* k (+ (* 1/12 (/ (* k (pow (log (* 2 (* n (PI)))) 3)) (* n (PI)))) (* 1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* n (PI)))))))) (* 1/2 (/ 1 (* n (PI))))))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log n) (log (* 2 (PI))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log n) (log (* 2 (PI))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log n) (log (* 2 (PI))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log n) (log (* 2 (PI))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* n (PI))))
(* 1/2 (/ (* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))) (* n (PI))))
k
(* k (+ 1 (* k (log (* 2 (* n (PI)))))))
(* k (+ 1 (* k (+ (log (* 2 (* n (PI)))) (* 1/2 (* k (pow (log (* 2 (* n (PI)))) 2)))))))
(* k (+ 1 (* k (+ (log (* 2 (* n (PI)))) (* k (+ (* 1/6 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/2 (pow (log (* 2 (* n (PI)))) 2))))))))
(* k (pow (* 2 (* n (PI))) k))
(* k (pow (* 2 (* n (PI))) k))
(* k (pow (* 2 (* n (PI))) k))
(* k (pow (* 2 (* n (PI))) k))
(* k (pow (* 2 (* n (PI))) k))
(* k (pow (* 2 (* n (PI))) k))
(* k (pow (* 2 (* n (PI))) k))
(* k (pow (* 2 (* n (PI))) k))
(* k (exp (* k (+ (log n) (log (* 2 (PI)))))))
(* k (exp (* k (+ (log n) (log (* 2 (PI)))))))
(* k (exp (* k (+ (log n) (log (* 2 (PI)))))))
(* k (exp (* k (+ (log n) (log (* 2 (PI)))))))
(* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n)))))))
(* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(* k (exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n)))))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log n) (log (* 2 (PI))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
(exp (* k (+ (log (* -2 (PI))) (* -1 (log (/ -1 n))))))
1
(+ 1 (* k (log (* 2 (* n (PI))))))
(+ 1 (* k (+ (log (* 2 (* n (PI)))) (* 1/2 (* k (pow (log (* 2 (* n (PI)))) 2))))))
(+ 1 (* k (+ (log (* 2 (* n (PI)))) (* k (+ (* 1/6 (* k (pow (log (* 2 (* n (PI)))) 3))) (* 1/2 (pow (log (* 2 (* n (PI)))) 2)))))))
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(pow (* 2 (* n (PI))) k)
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(* 2 (/ n k))
(/ 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)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (* (sqrt -2) (sqrt -1))))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(* 2 (/ (* n (PI)) k))
(/ 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))
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(/ k n)
(* (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)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (sqrt 2))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(sqrt (/ 1 (* n (PI))))
(sqrt (/ 1 (* n (PI))))
(sqrt (/ 1 (* n (PI))))
(sqrt (/ 1 (* n (PI))))
(sqrt (/ 1 (* n (PI))))
(sqrt (/ 1 (* n (PI))))
(sqrt (/ 1 (* n (PI))))
(sqrt (/ 1 (* n (PI))))
(* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 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))

Outputs
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/ (+ (* -1 (* (sqrt (* (pow k 3) (* n (PI)))) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* (sqrt (* k (* n (PI)))) (sqrt 2))) k)
(/.f64 (-.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (.f64 (sqrt.f64 (.f64 (.f64 (.f64 k (.f64 k k)) (PI.f64)) n)) (/.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (/ (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (sqrt 2))))))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (.f64 (.f64 k k) (-.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 k (.f64 n (PI.f64))))) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))) k)
(/ (+ (* (sqrt (* k (* n (PI)))) (sqrt 2)) (* (pow k 2) (+ (* -1 (* (sqrt (/ (* n (PI)) k)) (/ (log (* 2 (* n (PI)))) (sqrt 2)))) (* k (+ (* -1/2 (* (sqrt (/ 1 (* k (* n (PI))))) (/ (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (sqrt 2)))) (* -1/2 (* (sqrt (/ k (* n (PI)))) (/ (+ (* -1 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (+ (* -1 (* (log (* 2 (* n (PI)))) (+ (* -2 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))) (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2)))))) (+ (* 1/3 (* n (* (PI) (pow (log (* 2 (* n (PI)))) 3)))) (/ (* n (* (PI) (pow (log (* 2 (* n (PI)))) 2))) (* k (pow (sqrt 2) 2)))))) (sqrt 2))))))))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (.f64 (.f64 k k) (-.f64 (.f64 (.f64 k #s(literal -1/2 binary64)) (+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64))) k)) #s(literal -1 binary64)) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 (.f64 n (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (+.f64 (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64)) #s(literal 1/3 binary64)) (/.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 k #s(literal 2 binary64))))) #s(literal 0 binary64)) (/.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))) k)
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ (* n (PI)) (* k (pow (* 2 (* n (PI))) k)))) (* (sqrt -2) (sqrt -1)))
(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 n k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 n k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 n k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log n) (log (* 2 (PI))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 n k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 n k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 n k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 n k)))))
(* (sqrt (/ (* n (PI)) (* k (exp (* k (+ (log (* 2 (PI))) (* -1 (log (/ 1 n))))))))) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (/.f64 (.f64 n (PI.f64)) k) (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k) (pow.f64 n k)))))
(* -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)))
(* 1/2 (/ k (* n (PI))))
(.f64 (/.f64 k (.f64 n (PI.f64))) #s(literal 1/2 binary64))
(* k (+ (* 1/2 (/ (* k (log (* 2 (* n (PI))))) (* n (PI)))) (* 1/2 (/ 1 (* n (PI))))))
(.f64 k (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) (.f64 (/.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 n (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))))
(* k (+ (* k (+ (* 1/4 (/ (* k (pow (log (* 2 (* n (PI)))) 2)) (* n (PI)))) (* 1/2 (/ (log (* 2 (* n (PI)))) (* n (PI)))))) (* 1/2 (/ 1 (* n (PI))))))
(.f64 k (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) (.f64 k (+.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) (.f64 #s(literal 1/4 binary64) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 k (.f64 n (PI.f64)))))))))
(* k (+ (* k (+ (* 1/2 (/ (log (* 2 (* n (PI)))) (* n (PI)))) (* k (+ (* 1/12 (/ (* k (pow (log (* 2 (* n (PI)))) 3)) (* n (PI)))) (* 1/4 (/ (pow (log (* 2 (* n (PI)))) 2) (* n (PI)))))))) (* 1/2 (/ 1 (* n (PI))))))
(.f64 k (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))) (.f64 k (+.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) (.f64 k (+.f64 (.f64 (.f64 k (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 1/12 binary64) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 n (PI.f64))))))))))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(/.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (*.f64 n (PI.f64)))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(/.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (*.f64 n (PI.f64)))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(/.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (*.f64 n (PI.f64)))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(/.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (*.f64 n (PI.f64)))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(/.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (*.f64 n (PI.f64)))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(/.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (*.f64 n (PI.f64)))
(* 1/2 (/ (* k (pow (* 2 (* n (PI))) k)) (* n (PI))))
(/.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)) (*.f64 n (PI.f64)))
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(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (/ (* n (PI)) k)) (sqrt 2))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* (sqrt (/ (* n (PI)) k)) (sqrt 2)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(* (sqrt (/ 1 k)) (* (sqrt -2) (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(sqrt (/ 1 (* n (PI))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(sqrt (/ 1 (* n (PI))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(sqrt (/ 1 (* n (PI))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(sqrt (/ 1 (* n (PI))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(sqrt (/ 1 (* n (PI))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(sqrt (/ 1 (* n (PI))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(sqrt (/ 1 (* n (PI))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(sqrt (/ 1 (* n (PI))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64))))
(* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(* (sqrt (/ 1 (* n (PI)))) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.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))
(* n (PI))
(*.f64 n (PI.f64))

eval400.0ms (2.9%)

Compiler: Compiled 38569 to 4973 computations (87.1% saved)

prune275.0ms (2%)

Pruning

49 alts after pruning (43 fresh and 6 done)

	Pruned	Kept	Total
New	2482	14	2496
Fresh	9	29	38
Picked	3	2	5
Done	1	4	5
Total	2495	49	2544

Accuracy

100.0%

Counts

2544 → 49

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	90.3%	(pow.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))) #s(literal -1/2 binary64))
	39.4%	(pow.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal -1/2 binary64))
	90.1%	(pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) k) #s(literal -1/2 binary64))
	27.1%	(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))
	39.3%	(/.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
	48.9%	(/.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal -1/2 binary64)))
	39.3%	(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 k n)))
	38.1%	(/.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 1/2 binary64)))
	48.9%	(/.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (pow.f64 (*.f64 (PI.f64) n) #s(literal -1/2 binary64)))
	48.9%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
	39.3%	(/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k (*.f64 #s(literal 2 binary64) n))))
	38.2%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))) #s(literal -1/2 binary64)))
	39.3%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
	48.9%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) n))))
	39.2%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))
	48.9%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
	39.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal -1/2 binary64))))
	80.5%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
✓	39.3%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
	39.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64))))
	39.4%	(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 2 binary64)) #s(literal -1/2 binary64))))
	39.4%	(*.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	48.9%	(.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64)))
	39.4%	(.f64 (pow.f64 (/.f64 k (.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64)) (sqrt.f64 (PI.f64)))
	39.4%	(.f64 (pow.f64 (.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1 binary64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	38.2%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	38.2%	(.f64 (sqrt.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k)) (sqrt.f64 (PI.f64)))
✓	38.2%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
	38.2%	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	48.9%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) (sqrt.f64 n))
	38.2%	(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1 binary64) k) n))) (sqrt.f64 #s(literal 2 binary64)))
	38.3%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 (/.f64 #s(literal 1 binary64) n) (PI.f64))))
	38.3%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)))))
✓	38.3%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
	38.3%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) n))))
	89.2%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k n) (PI.f64))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) n) (/.f64 (PI.f64) k))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))))
✓	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1 binary64) n)))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 (/.f64 k n) (/.f64 #s(literal 1 binary64) (PI.f64)))))
	38.3%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) n)) k)))
	38.3%	(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
	38.3%	(sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) (PI.f64)))
	38.3%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
	38.3%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
	37.1%	(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 2 binary64))) #s(literal -1/2 binary64)))

Compiler

Compiled 1579 to 768 computations (51.4% saved)

regimes160.0ms (1.2%)

Counts

81 → 1

Calls

Call 1

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

Calls

4 calls:

62.0ms	(.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))))
25.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
25.0ms	k
24.0ms	n

Results

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

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes103.0ms (0.7%)

Counts

78 → 1

Calls

Call 1

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

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

Calls

4 calls:

27.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
23.0ms	n
23.0ms	k
22.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.5%	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)

regimes47.0ms (0.3%)

Counts

65 → 1

Calls

Call 1

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

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:

21.0ms	k
18.0ms	n

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes45.0ms (0.3%)

Counts

64 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

20.0ms	n
19.0ms	k

Results

Accuracy	Segments	Branch
99.6%	2	`k`
92.6%	2	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes46.0ms (0.3%)

Counts

63 → 2

Calls

Call 1

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

Outputs

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

2 calls:

22.0ms	k
19.0ms	n

Results

Accuracy	Segments	Branch
48.9%	1	`n`
51.9%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts

47 → 2

Calls

Call 1

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

15.0ms

Results

Accuracy	Segments	Branch
51.9%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes21.0ms (0.1%)

Counts

25 → 2

Calls

Call 1

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

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

2 calls:

9.0ms	k
8.0ms	n

Results

Accuracy	Segments	Branch
39.4%	1	`n`
42.4%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts

24 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	n
7.0ms	k

Results

Accuracy	Segments	Branch
39.4%	1	`n`
39.4%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	n
3.0ms	k

Results

Accuracy	Segments	Branch
38.3%	1	`k`
38.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
38.3%	1	`n`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes4.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

Calls

2 calls:

2.0ms	n
2.0ms	k

Results

Accuracy	Segments	Branch
38.3%	1	`k`
38.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes30.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

Inputs
(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))

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

Calls

2 calls:

28.0ms	n
2.0ms	k

Results

Accuracy	Segments	Branch
38.3%	1	`k`
38.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	n
1.0ms	k

Results

Accuracy	Segments	Branch
38.3%	1	`k`
38.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch19.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
17.0ms	4.281385925887549e-64	6.262246924677472e-58

Results

13.0ms

112×

valid

Compiler

Compiled 233 to 185 computations (20.6% saved)

Precisions

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

ival-pow: 3.0ms (32% of total)

ival-div: 2.0ms (21.3% of total)

ival-mult: 2.0ms (21.3% of total)

ival-sub: 1.0ms (10.7% of total)

ival-sqrt: 1.0ms (10.7% of total)

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

const: 0.0ms (0% of total)

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

bsearch45.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
42.0ms	3.0893868461131727e+183	1.7292010191563186e+186

Results

38.0ms

128×

valid

Compiler

Compiled 295 to 193 computations (34.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-div: 23.0ms (68.8% of total)

ival-pow: 5.0ms (14.9% of total)

ival-mult: 3.0ms (9% of total)

ival-pi: 1.0ms (3% of total)

ival-sub: 1.0ms (3% of total)

ival-sqrt: 1.0ms (3% of total)

const: 0.0ms (0% of total)

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

bsearch31.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
27.0ms	3.0893868461131727e+183	1.7292010191563186e+186

Results

23.0ms

128×

valid

Compiler

Compiled 279 to 185 computations (33.7% saved)

Precisions

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

ival-pow: 5.0ms (40.1% of total)

ival-mult: 3.0ms (24.1% of total)

ival-div: 2.0ms (16% of total)

ival-pi: 1.0ms (8% of total)

ival-sub: 1.0ms (8% of total)

ival-sqrt: 1.0ms (8% 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
20.0ms	9.302897865704024e+181	1.7304009997137673e+183

Results

16.0ms

112×

valid

Compiler

Compiled 247 to 164 computations (33.6% saved)

Precisions

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

ival-pow: 6.0ms (49.6% of total)

ival-div: 2.0ms (16.5% of total)

ival-mult: 2.0ms (16.5% of total)

ival-sub: 1.0ms (8.3% of total)

ival-sqrt: 1.0ms (8.3% of total)

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

const: 0.0ms (0% of total)

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

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	216
1	94	216
2	102	216
3	108	216
4	113	216
5	115	216

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 #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 (.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 8480865910936245/14134776518227074636666380005943348126619871175004951664972849610340958208 binary64)) (.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) k) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 12200000000000000551407972920962091762716550482288473029612410579566241964139581194513614069682387660217816376641539498641674325578518957941894457859081002617996629334023683409870585856 binary64)) (.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 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 420000000000000003515838310305492699037969028946533944802553395294737721813795827001189327021242640408618575352992476422629874197113583389103806623325769628810399323660257774563596697600 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 549999999999999976523996412144533949323868810314889013157203699073165257909388134721615767586234022513319524438005270155613711517322513219580992081700467426407708553061825332394328064 binary64)) (pow.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal -1/2 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)))
(pow.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))

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 #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 (.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 8480865910936245/14134776518227074636666380005943348126619871175004951664972849610340958208 binary64)) (.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64))) k) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 8480865910936245/14134776518227074636666380005943348126619871175004951664972849610340958208 binary64)) (.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64))) (pow.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 12200000000000000551407972920962091762716550482288473029612410579566241964139581194513614069682387660217816376641539498641674325578518957941894457859081002617996629334023683409870585856 binary64)) (.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 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 12200000000000000551407972920962091762716550482288473029612410579566241964139581194513614069682387660217816376641539498641674325578518957941894457859081002617996629334023683409870585856 binary64)) (.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) n) #s(literal 1/2 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 420000000000000003515838310305492699037969028946533944802553395294737721813795827001189327021242640408618575352992476422629874197113583389103806623325769628810399323660257774563596697600 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 420000000000000003515838310305492699037969028946533944802553395294737721813795827001189327021242640408618575352992476422629874197113583389103806623325769628810399323660257774563596697600 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 549999999999999976523996412144533949323868810314889013157203699073165257909388134721615767586234022513319524438005270155613711517322513219580992081700467426407708553061825332394328064 binary64)) (pow.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal -1/2 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)))
(pow.f64 (/.f64 k (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (/.f64 (.f64 (PI.f64) n) k) #s(literal 2 binary64)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 (.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) (PI.f64)))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 #s(literal 2 binary64) n) k)))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n)) (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) (/.f64 k n))))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)) n))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n) (PI.f64)))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))

soundness2.3s (16.8%)

Rules

5750×	`-lowering-.f32`
5750×	`-lowering-.f64`
5728×	`-lowering-.f32`
5728×	`-lowering-.f64`
5664×	`-lowering-.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	187	3776
1	606	3714
2	2205	3649
3	6142	3648
0	8233	3648
0	13	14
1	30	14
2	47	14
3	69	14
4	90	13
5	113	13
6	149	13
7	188	13
8	214	13
9	228	13
10	229	13
0	229	13
0	37	182
1	234	161
2	1545	154
0	9067	154
0	139	2132
1	385	2104
2	1189	1816
3	4175	1732
4	7740	1732
0	8111	1732
0	20	68
1	132	68
2	851	64
0	8618	64
0	28	135
1	165	135
2	1064	126
0	8263	126
0	30	124
1	173	122
2	1042	120
0	8415	120

Stop Event

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

Compiler

Compiled 672 to 426 computations (36.6% saved)

preprocess110.0ms (0.8%)

Compiler: Compiled 472 to 174 computations (63.1% saved)

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

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

analyze155.0ms (1.1%)

sample4.5s (32.5%)

preprocess82.0ms (0.6%)

explain167.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize134.0ms (1%)

series95.0ms (0.7%)

rewrite326.0ms (2.4%)

simplify246.0ms (1.8%)

eval127.0ms (0.9%)

prune130.0ms (0.9%)

simplify58.0ms (0.4%)

localize250.0ms (1.8%)

series56.0ms (0.4%)

rewrite397.0ms (2.9%)

simplify344.0ms (2.5%)

eval270.0ms (1.9%)

prune196.0ms (1.4%)

simplify9.0ms (0.1%)

localize224.0ms (1.6%)

series26.0ms (0.2%)

rewrite296.0ms (2.1%)

simplify508.0ms (3.7%)

eval230.0ms (1.7%)

prune201.0ms (1.4%)

simplify36.0ms (0.3%)

localize268.0ms (1.9%)

series92.0ms (0.7%)

rewrite379.0ms (2.7%)

simplify310.0ms (2.2%)

eval400.0ms (2.9%)

prune275.0ms (2%)

regimes160.0ms (1.2%)

regimes103.0ms (0.7%)

regimes47.0ms (0.3%)

regimes45.0ms (0.3%)

regimes46.0ms (0.3%)

regimes18.0ms (0.1%)

regimes21.0ms (0.1%)

regimes18.0ms (0.1%)

regimes8.0ms (0.1%)

regimes3.0ms (0%)

regimes4.0ms (0%)

regimes30.0ms (0.2%)

regimes3.0ms (0%)

bsearch19.0ms (0.1%)

bsearch45.0ms (0.3%)

bsearch31.0ms (0.2%)

bsearch22.0ms (0.2%)

simplify12.0ms (0.1%)

soundness2.3s (16.8%)

preprocess110.0ms (0.8%)

end0.0ms (0%)

Profiling

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