Metrics for Migdal et al, Equation (51)

analyze176.0ms (1.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
50%	25%	25%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
50%	25%	25%	0.1%	0%	50%	0%	6
51.6%	25%	23.4%	0.1%	0%	50%	1.6%	7
52.5%	25%	22.6%	0.1%	0%	50%	2.3%	8
53.8%	25%	21.5%	0.1%	0%	50%	3.5%	9
54.5%	25%	20.9%	0.1%	0%	50%	4.1%	10
55.3%	25%	20.2%	0.1%	0%	50%	4.8%	11
55.7%	25%	19.9%	0.1%	0%	50%	5.1%	12

Compiler

Compiled 19 to 14 computations (26.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

ival-pow: 37.0ms (42.5% of total)

ival-mult: 19.0ms (21.8% of total)

ival-div: 14.0ms (16.1% of total)

ival-sqrt: 7.0ms (8% of total)

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

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

const: 1.0ms (1.1% of total)

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

sample4.5s (32.6%)

Results

1.9s	3965×	5	exit
1.2s	8256×	0	valid
533.0ms	2029×	1	invalid
43.0ms	458×	0	invalid
38.0ms	256×	0	unsamplable

Precisions

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

ival-pow: 669.0ms (26.7% of total)

ival-mult: 459.0ms (18.3% of total)

ival-div: 399.0ms (15.9% of total)

backward-pass: 356.0ms (14.2% of total)

ival-sqrt: 339.0ms (13.5% of total)

ival-sub: 150.0ms (6% of total)

ival-pi: 91.0ms (3.6% of total)

const: 40.0ms (1.6% of total)

Bogosity

preprocess93.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	92
1	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)))

explain208.0ms (1.5%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
2	221	(5.228279852726265e+174 3.3767424528362692e+90)	-	`(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

141.0ms

512×

valid

Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions

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

ival-pow: 31.0ms (51.8% of total)

ival-mult: 10.0ms (16.7% of total)

ival-div: 8.0ms (13.4% of total)

ival-sqrt: 5.0ms (8.4% of total)

ival-sub: 3.0ms (5% of total)

ival-pi: 2.0ms (3.3% of total)

const: 1.0ms (1.7% 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
▶	99.7%	(/.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))
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Status

Accuracy

Program

▶

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))

▶

99.6%

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

Compiler

Compiled 34 to 25 computations (26.5% saved)

simplify15.0ms (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)

localize133.0ms (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	99.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	accuracy	99.7%	(*.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	99.7%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Results

102.0ms

256×

valid

Compiler

Compiled 105 to 21 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-pow: 15.0ms (34% of total)

ival-div: 14.0ms (31.7% of total)

ival-mult: 8.0ms (18.1% of total)

ival-sub: 3.0ms (6.8% of total)

ival-sqrt: 2.0ms (4.5% of total)

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

const: 1.0ms (2.3% of total)

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

series77.0ms (0.6%)

Counts

10 → 156

Calls

Call 1

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

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

Calls

39 calls:

Time	Variable		Point	Expression
32.0ms	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)))
9.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	k	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite359.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	68
1	132	68
2	857	64
0	8650	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 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 k #s(literal -1 binary64)))) (.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 k #s(literal -1 binary64)))) (*.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 (.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 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64))) (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64))))
(.f64 (.f64 (cbrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))))
(.f64 (.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)))

simplify293.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

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

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

eval155.0ms (1.1%)

Compiler: Compiled 21499 to 2035 computations (90.5% saved)

prune119.0ms (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
▶	99.7%	(/.f64 (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	82.0%	(/.f64 (pow.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (/.f64 (+.f64 k #s(literal -1 binary64)) #s(literal -4 binary64))) (sqrt.f64 k))
✓	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))
	96.7%	(/.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))))
	99.6%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64))))
	99.7%	(/.f64 (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	99.6%	(/.f64 (/.f64 #s(literal 1 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 k))
▶	44.9%	(/.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)))
	99.7%	(/.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))))))
	99.6%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (+.f64 (/.f64 k #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
▶	36.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 474 to 344 computations (27.4% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

152×	`-lowering-.f32`
152×	`-lowering-.f64`
90×	`sum3-define`
76×	`fma-lowering-fma.f32`
76×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	229
1	72	227
2	108	226
3	150	221
4	200	221
5	248	221
6	314	221
7	363	221
8	423	221
9	427	221
0	427	221

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

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

localize439.0ms (3.2%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 n (PI.f64))
✓	accuracy	99.6%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
✓	accuracy	99.5%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64))))
✓	accuracy	75.4%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))))
✓	accuracy	99.8%	(/.f64 (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	accuracy	99.7%	(/.f64 (*.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n))
✓	accuracy	75.4%	(PI.f64)
✓	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	99.8%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	accuracy	99.7%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	accuracy	75.4%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (*.f64 n (PI.f64)) k)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	91.3%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	75.4%	(PI.f64)
✓	accuracy	99.8%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	99.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	75.4%	(PI.f64)

Results

212.0ms	65×	5	exit
138.0ms	191×	0	valid

Compiler

Compiled 241 to 40 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 167.0ms

ival-mult: 41.0ms (24.5% of total)

backward-pass: 39.0ms (23.3% of total)

ival-pow: 39.0ms (23.3% of total)

ival-div: 17.0ms (10.2% of total)

ival-sqrt: 16.0ms (9.6% of total)

ival-pi: 10.0ms (6% of total)

ival-sub: 3.0ms (1.8% of total)

const: 1.0ms (0.6% of total)

series54.0ms (0.4%)

Counts

23 → 360

Calls

Call 1

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

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

90 calls:

Time	Variable		Point	Expression
11.0ms	k	@	-inf	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
10.0ms	n	@	0	(sqrt (* 2 (* (PI) n)))
4.0ms	n	@	0	(pow (* (pow (* 2 (* (PI) n)) k) k) 1/2)
2.0ms	n	@	-inf	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))
2.0ms	n	@	inf	(/ (sqrt (* 2 (* (PI) n))) (pow (* (pow (* 2 (* (PI) n)) k) k) 1/2))

rewrite350.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4394×	`-lowering-.f32`
4394×	`-lowering-.f64`
2592×	`/-lowering-/.f32`
2592×	`/-lowering-/.f64`
2166×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	158
1	222	148
2	1441	143
0	8356	143

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 1054

Calls

Call 1

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

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

simplify300.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

5294×	`-lowering-.f32`
5294×	`-lowering-.f64`
2882×	`+-lowering-+.f64`
2882×	`+-lowering-+.f32`
966×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	249	4286
1	768	4148
2	2797	3742
3	6547	3694
0	8191	3694

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

eval235.0ms (1.7%)

Compiler: Compiled 33787 to 3706 computations (89% saved)

prune177.0ms (1.3%)

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	1757	19	1776
Fresh	8	0	8
Picked	2	3	5
Done	0	1	1
Total	1767	23	1790

Accuracy

100.0%

Counts

1790 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	36.8%	(pow.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal -1/2 binary64))
	91.3%	(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
✓	99.7%	(/.f64 (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	99.7%	(/.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))
	44.9%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))) (sqrt.f64 k))
✓	44.9%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	45.0%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
	36.7%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) #s(literal 1/2 binary64)))
	36.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	36.8%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶	44.9%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	36.7%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	44.9%	(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
▶	36.5%	(*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	36.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	36.5%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n)) (/.f64 #s(literal -1 binary64) k))) (sqrt.f64 #s(literal 2 binary64)))
	36.5%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	45.0%	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (/.f64 #s(literal 2 binary64) k) #s(literal 1/2 binary64)))
▶	45.0%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
▶	91.4%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
▶	36.6%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
	36.6%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	34.3%	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)))

Compiler

Compiled 549 to 441 computations (19.7% saved)

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

280×	`-lowering-.f32`
280×	`-lowering-.f64`
226×	`times-frac`
186×	`/-lowering-/.f32`
186×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	183
1	53	179
2	108	179
3	233	179
4	368	179
5	457	179
6	457	179
0	457	179

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize351.0ms (2.5%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n))
✓	accuracy	99.5%	(*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	91.3%	(sqrt.f64 (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) n)) k))
✓	accuracy	75.4%	(PI.f64)
✓	accuracy	99.8%	(sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	accuracy	99.8%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	accuracy	99.6%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
✓	accuracy	75.4%	(PI.f64)
✓	accuracy	99.9%	(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
✓	accuracy	99.7%	(/.f64 (PI.f64) k)
✓	accuracy	99.6%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
✓	accuracy	75.4%	(PI.f64)
✓	accuracy	99.8%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	accuracy	99.7%	(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
✓	accuracy	91.3%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
✓	accuracy	75.4%	(PI.f64)
✓	accuracy	99.9%	(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k)))
✓	accuracy	99.8%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	accuracy	91.4%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
✓	accuracy	75.4%	(PI.f64)

Results

158.0ms	65×	5	exit
93.0ms	191×	0	valid

Compiler

Compiled 191 to 29 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

backward-pass: 20.0ms (22.5% of total)

ival-pow: 19.0ms (21.3% of total)

ival-sqrt: 16.0ms (18% of total)

ival-mult: 16.0ms (18% of total)

ival-div: 15.0ms (16.9% of total)

ival-pi: 2.0ms (2.2% of total)

const: 1.0ms (1.1% of total)

series58.0ms (0.4%)

Counts

18 → 312

Calls

Call 1

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

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

Calls

78 calls:

Time	Variable		Point	Expression
20.0ms	n	@	inf	(/ (* (PI) (* n 2)) (* k (pow (* (PI) (* n 2)) k)))
17.0ms	k	@	-inf	(/ (* (PI) (* n 2)) (* k (pow (* (PI) (* n 2)) k)))
5.0ms	n	@	-inf	(/ (* (PI) (* n 2)) (* k (pow (* (PI) (* n 2)) k)))
2.0ms	n	@	0	(/ (* (PI) (* n 2)) k)
1.0ms	k	@	inf	(sqrt (* (/ (PI) k) 2))

rewrite340.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

5996×	`-lowering-.f32`
5996×	`-lowering-.f64`
4022×	`/-lowering-/.f32`
4022×	`/-lowering-/.f64`
986×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	118
1	146	115
2	954	114
0	8535	114

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 1345

Calls

Call 1

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

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

simplify403.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

4302×	`-lowering-.f32`
4302×	`-lowering-.f64`
2812×	`+-lowering-+.f64`
2812×	`+-lowering-+.f32`
2756×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	3014
1	519	2919
2	2112	2883
3	6993	2883
0	8482	2883

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

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

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

eval396.0ms (2.9%)

Compiler: Compiled 34300 to 5166 computations (84.9% saved)

prune317.0ms (2.3%)

Pruning

39 alts after pruning (34 fresh and 5 done)

	Pruned	Kept	Total
New	2195	27	2222
Fresh	7	7	14
Picked	2	3	5
Done	2	2	4
Total	2206	39	2245

Accuracy

100.0%

Counts

2245 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	36.8%	(pow.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal -1/2 binary64))
	36.6%	(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 n (/.f64 k (PI.f64)))) #s(literal -1/2 binary64))
▶	91.3%	(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
	25.7%	(pow.f64 (*.f64 (/.f64 (PI.f64) (/.f64 (/.f64 k #s(literal 2 binary64)) n)) (/.f64 (PI.f64) (/.f64 (/.f64 k #s(literal 2 binary64)) n))) #s(literal 1/4 binary64))
	36.6%	(/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
✓	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))
	45.0%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))
	45.0%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
	36.5%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 n (/.f64 k (PI.f64)))) #s(literal 1/2 binary64)))
	36.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	36.4%	(.f64 (pow.f64 (/.f64 (.f64 n #s(literal 2 binary64)) k) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
	36.8%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	45.0%	(.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64)))
	27.1%	(.f64 (pow.f64 (.f64 n n) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	38.6%	(.f64 (pow.f64 (.f64 k k) #s(literal -1/4 binary64)) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))
	44.9%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) n))))
✓	44.9%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	45.0%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 n #s(literal -1/2 binary64))) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
▶	44.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	36.5%	(*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1 binary64) n))) (sqrt.f64 #s(literal 2 binary64)))
✓	36.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	36.5%	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) (/.f64 #s(literal -1 binary64) n)) (/.f64 #s(literal -1 binary64) k))) (sqrt.f64 #s(literal 2 binary64)))
	36.5%	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	45.0%	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
✓	45.0%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
▶	45.0%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
	36.6%	(sqrt.f64 (/.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) n)) k))
	36.6%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) n)))
	36.6%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
	36.6%	(sqrt.f64 (/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (/.f64 #s(literal 2 binary64) k)) (/.f64 #s(literal -1 binary64) n)))
✓	91.4%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
	36.6%	(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
	36.6%	(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
	36.6%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	36.6%	(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))))
	36.6%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
	36.6%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
▶	36.6%	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n)))
	34.3%	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)))

Compiler

Compiled 912 to 728 computations (20.2% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

116×	`-lowering-.f32`
116×	`-lowering-.f64`
60×	`sum3-define`
60×	`/-lowering-/.f32`
60×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	170
1	58	168
2	95	168
3	133	168
4	153	168
5	166	168
6	183	168
7	211	168
8	275	168
9	290	168
10	297	168
0	297	168

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize281.0ms (2%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	accuracy	99.7%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.8%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))
✓	accuracy	99.5%	(*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))
✓	accuracy	99.5%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.7%	(/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	accuracy	99.7%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	accuracy	78.3%	(pow.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal 2 binary64) k) n)
✓	accuracy	99.5%	(.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n))
✓	accuracy	79.6%	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n)))
✓	accuracy	99.9%	(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))
✓	accuracy	99.8%	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k))
✓	accuracy	99.7%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	accuracy	91.4%	(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))

Results

215.0ms

256×

valid

Compiler

Compiled 181 to 29 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

ival-pow: 46.0ms (52.9% of total)

ival-mult: 21.0ms (24.2% of total)

ival-sqrt: 9.0ms (10.4% of total)

ival-div: 8.0ms (9.2% of total)

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

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

const: 1.0ms (1.2% of total)

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

series23.0ms (0.2%)

Counts

18 → 324

Calls

Call 1

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

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

Calls

81 calls:

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

rewrite348.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

6176×	`-lowering-.f32`
6176×	`-lowering-.f64`
2498×	`/-lowering-/.f32`
2498×	`/-lowering-/.f64`
1390×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	112
1	157	112
2	907	112
0	8430	112

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 1293

Calls

Call 1

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

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

simplify270.0ms (2%)

Algorithm

1×	egg-herbie

Rules

6424×	`-lowering-.f32`
6424×	`-lowering-.f64`
1410×	`+-lowering-+.f64`
1410×	`+-lowering-+.f32`
1186×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	3080
1	395	3037
2	1304	2874
3	4437	2832
0	8212	2832

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 324

Calls

Call 1

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

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

eval597.0ms (4.3%)

Compiler: Compiled 31440 to 4250 computations (86.5% saved)

prune261.0ms (1.9%)

Pruning

38 alts after pruning (30 fresh and 8 done)

	Pruned	Kept	Total
New	2000	11	2011
Fresh	10	19	29
Picked	1	4	5
Done	1	4	5
Total	2012	38	2050

Accuracy

100.0%

Counts

2050 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	36.8%	(pow.f64 (/.f64 (/.f64 (*.f64 k #s(literal 1/2 binary64)) (PI.f64)) n) #s(literal -1/2 binary64))
	36.6%	(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 n (/.f64 k #s(literal 2 binary64)))) #s(literal -1/2 binary64))
	26.2%	(pow.f64 (/.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 4 binary64)) #s(literal -1/4 binary64))
	36.6%	(pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 n (/.f64 k (PI.f64)))) #s(literal -1/2 binary64))
	36.6%	(pow.f64 (/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) k) (.f64 (PI.f64) (*.f64 n #s(literal -2 binary64))))) #s(literal -1/2 binary64))
✓	91.3%	(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64))
	36.8%	(pow.f64 (*.f64 (/.f64 k #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) n)) #s(literal -1/2 binary64))
	36.6%	(/.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 k n) #s(literal 1/2 binary64)))
	45.0%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 k (PI.f64)) #s(literal 1/2 binary64)))
	45.0%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
	36.5%	(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 n (/.f64 k (PI.f64)))) #s(literal 1/2 binary64)))
	36.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	36.8%	(.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	44.9%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
✓	44.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	36.5%	(*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1 binary64) n))) (sqrt.f64 #s(literal 2 binary64)))
✓	36.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	36.4%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
	36.5%	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	45.0%	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64))))
	45.0%	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
	45.0%	(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
✓	45.0%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
✓	45.0%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
	91.3%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
	36.6%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) (/.f64 #s(literal 1 binary64) n)))
	36.6%	(sqrt.f64 (/.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) n))))
✓	91.4%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
	36.6%	(sqrt.f64 (/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 k n)))
	36.6%	(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
	36.6%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	36.6%	(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))))
	36.6%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))) n))
	36.6%	(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64)))))
	36.6%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n)))
✓	36.6%	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n)))
	36.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
	34.3%	(exp.f64 (.f64 (log.f64 (/.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k)) #s(literal 1/2 binary64)))

Compiler

Compiled 1300 to 614 computations (52.8% saved)

regimes111.0ms (0.8%)

Counts

72 → 1

Calls

Call 1

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

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:

36.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
26.0ms	(.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))))
22.0ms	k
20.0ms	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)

regimes84.0ms (0.6%)

Counts

70 → 1

Calls

Call 1

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

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

Calls

4 calls:

20.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
20.0ms	n
19.0ms	k
18.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
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)

regimes82.0ms (0.6%)

Counts

65 → 1

Calls

Call 1

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

4 calls:

20.0ms	k
18.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms	n
17.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.7%	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)

regimes38.0ms (0.3%)

Counts

56 → 2

Calls

Call 1

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

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

Calls

2 calls:

17.0ms	k
16.0ms	n

Results

Accuracy	Segments	Branch
99.7%	2	`k`
91.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes34.0ms (0.2%)

Counts

46 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

16.0ms	k
14.0ms	n

Results

Accuracy	Segments	Branch
45.0%	1	`n`
47.9%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes16.0ms (0.1%)

Counts

44 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

12.0ms

Results

Accuracy	Segments	Branch
47.9%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes24.0ms (0.2%)

Counts

25 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

9.0ms	k
7.0ms	n

Results

Accuracy	Segments	Branch
36.8%	1	`n`
39.8%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes17.0ms (0.1%)

Counts

23 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	k
7.0ms	n

Results

Accuracy	Segments	Branch
36.8%	1	`n`
36.8%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0.1%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	k
4.0ms	n

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	k
3.0ms	n

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch17.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	2.6068840081518665e-57	1.1266383539092325e-56

Results

12.0ms

96×

valid

Compiler

Compiled 185 to 149 computations (19.5% saved)

Precisions

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

ival-mult: 4.0ms (44.2% of total)

ival-pow: 2.0ms (22.1% of total)

ival-sub: 1.0ms (11% of total)

ival-div: 1.0ms (11% of total)

ival-sqrt: 1.0ms (11% of total)

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

const: 0.0ms (0% of total)

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

bsearch30.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
28.0ms	1.946416692058409e+182	4.361982320574098e+184

Results

24.0ms

112×

valid

Compiler

Compiled 247 to 178 computations (27.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-pow: 14.0ms (70.9% of total)

ival-div: 2.0ms (10.1% of total)

ival-mult: 2.0ms (10.1% of total)

ival-pi: 1.0ms (5.1% of total)

ival-sub: 1.0ms (5.1% of total)

ival-sqrt: 1.0ms (5.1% 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	1.946416692058409e+182	4.361982320574098e+184

Results

16.0ms

112×

valid

Compiler

Compiled 233 to 164 computations (29.6% 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)

bsearch19.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	2.8463550885016907e+181	1.946416692058409e+182

Results

12.0ms

96×

valid

Compiler

Compiled 203 to 143 computations (29.6% saved)

Precisions

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

ival-pow: 3.0ms (36.1% of total)

ival-mult: 2.0ms (24.1% of total)

ival-sub: 1.0ms (12% of total)

ival-div: 1.0ms (12% of total)

ival-sqrt: 1.0ms (12% of total)

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

const: 0.0ms (0% of total)

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

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	184
1	101	184
2	118	184
3	128	184
4	135	184
5	137	184

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k) k) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.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 4858829428140557/441711766194596082395824375185729628956870974218904739530401550323154944 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 5500000000000000001112615672791674008335849414915695813879613266759179352606775112567667825371643480516115567983725672897910554595965438431471460187304213799166726245161756052030488576 binary64)) (.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(if (<=.f64 k #s(literal 13999999999999999488200872873259531261006537466839649673931576440417852664425477525768950502016612665932831648823287957176266634776478629675029449123393548866774268883225918543887335424 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))) (pow.f64 (/.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(if (<=.f64 k #s(literal 122000000000000000206945069304328391037479375308131602444203639585043067237355702224727162332864553356062456485332753131226840868773532689116559942759070386640449377263008022716743680 binary64)) (pow.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(pow.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (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 (.f64 (PI.f64) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.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 4858829428140557/441711766194596082395824375185729628956870974218904739530401550323154944 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 4858829428140557/441711766194596082395824375185729628956870974218904739530401550323154944 binary64)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 5500000000000000001112615672791674008335849414915695813879613266759179352606775112567667825371643480516115567983725672897910554595965438431471460187304213799166726245161756052030488576 binary64)) (.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(if (<=.f64 k #s(literal 5500000000000000001112615672791674008335849414915695813879613266759179352606775112567667825371643480516115567983725672897910554595965438431471460187304213799166726245161756052030488576 binary64)) (.f64 (pow.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) n) #s(literal 1/2 binary64))) (pow.f64 (/.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(if (<=.f64 k #s(literal 13999999999999999488200872873259531261006537466839649673931576440417852664425477525768950502016612665932831648823287957176266634776478629675029449123393548866774268883225918543887335424 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))) (pow.f64 (/.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(if (<=.f64 k #s(literal 13999999999999999488200872873259531261006537466839649673931576440417852664425477525768950502016612665932831648823287957176266634776478629675029449123393548866774268883225918543887335424 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) (pow.f64 (/.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(if (<=.f64 k #s(literal 122000000000000000206945069304328391037479375308131602444203639585043067237355702224727162332864553356062456485332753131226840868773532689116559942759070386640449377263008022716743680 binary64)) (pow.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(if (<=.f64 k #s(literal 122000000000000000206945069304328391037479375308131602444203639585043067237355702224727162332864553356062456485332753131226840868773532689116559942759070386640449377263008022716743680 binary64)) (pow.f64 (/.f64 k (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (.f64 (/.f64 k (.f64 (PI.f64) n)) (/.f64 k (*.f64 (PI.f64) n))) #s(literal 4 binary64)) #s(literal -1/4 binary64)))
(pow.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 k (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) k))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))

soundness1.8s (13.3%)

Rules

6176×	`-lowering-.f32`
6176×	`-lowering-.f64`
5996×	`-lowering-.f32`
5996×	`-lowering-.f64`
5664×	`-lowering-.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	39	158
1	222	148
2	1441	143
0	8356	143
0	20	68
1	132	68
2	857	64
0	8650	64
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	28	118
1	146	115
2	954	114
0	8535	114
0	139	2132
1	385	2094
2	1192	1806
3	4167	1722
4	7737	1722
0	8108	1722
0	28	112
1	157	112
2	907	112
0	8430	112

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

Compiler

Compiled 570 to 386 computations (32.3% saved)

preprocess63.0ms (0.5%)

Compiler: Compiled 408 to 176 computations (56.9% 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	39	229
1	72	227
2	108	226
3	150	221
4	200	221
5	248	221
6	314	221
7	363	221
8	423	221
9	427	221
0	427	221

Iter	Nodes	Cost
0	28	170
1	58	168
2	95	168
3	133	168
4	153	168
5	166	168
6	183	168
7	211	168
8	275	168
9	290	168
10	297	168
0	297	168

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	39	229
1	72	227
2	108	226
3	150	221
4	200	221
5	248	221
6	314	221
7	363	221
8	423	221
9	427	221
0	427	221

Iter	Nodes	Cost
0	28	170
1	58	168
2	95	168
3	133	168
4	153	168
5	166	168
6	183	168
7	211	168
8	275	168
9	290	168
10	297	168
0	297	168

analyze176.0ms (1.3%)

sample4.5s (32.6%)

preprocess93.0ms (0.7%)

explain208.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.1%)

localize133.0ms (1%)

series77.0ms (0.6%)

rewrite359.0ms (2.6%)

simplify293.0ms (2.1%)

eval155.0ms (1.1%)

prune119.0ms (0.9%)

simplify22.0ms (0.2%)

localize439.0ms (3.2%)

series54.0ms (0.4%)

rewrite350.0ms (2.5%)

simplify300.0ms (2.2%)

eval235.0ms (1.7%)

prune177.0ms (1.3%)

simplify21.0ms (0.2%)

localize351.0ms (2.5%)

series58.0ms (0.4%)

rewrite340.0ms (2.5%)

simplify403.0ms (2.9%)

eval396.0ms (2.9%)

prune317.0ms (2.3%)

simplify19.0ms (0.1%)

localize281.0ms (2%)

series23.0ms (0.2%)

rewrite348.0ms (2.5%)

simplify270.0ms (2%)

eval597.0ms (4.3%)

prune261.0ms (1.9%)

regimes111.0ms (0.8%)

regimes84.0ms (0.6%)

regimes82.0ms (0.6%)

regimes38.0ms (0.3%)

regimes34.0ms (0.2%)

regimes16.0ms (0.1%)

regimes24.0ms (0.2%)

regimes17.0ms (0.1%)

regimes8.0ms (0.1%)

regimes11.0ms (0.1%)

bsearch17.0ms (0.1%)

bsearch30.0ms (0.2%)

bsearch22.0ms (0.2%)

bsearch19.0ms (0.1%)

simplify15.0ms (0.1%)

soundness1.8s (13.3%)

preprocess63.0ms (0.5%)

end0.0ms (0%)

Profiling

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

Iter	Nodes	Cost
0	39	229
1	72	227
2	108	226
3	150	221
4	200	221
5	248	221
6	314	221
7	363	221
8	423	221
9	427	221
0	427	221

Iter	Nodes	Cost
0	28	170
1	58	168
2	95	168
3	133	168
4	153	168
5	166	168
6	183	168
7	211	168
8	275	168
9	290	168
10	297	168
0	297	168