Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze243.0ms (2.2%)

Memory

-16.5MiB live, 179.7MiB allocated; 31ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample4.7s (42.9%)

Memory

21.3MiB live, 5 840.4MiB allocated; 2.1s collecting garbage

Samples

1.6s	8 256×	0	valid
1.3s	4 546×	1	invalid
691.0ms	1 533×	2	invalid
72.0ms	261×	0	exit
38.0ms	349×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 3.0s

ival-pow: 1.1s (37.8% of total)

ival-mult: 667.0ms (22.1% of total)

ival-div: 366.0ms (12.1% of total)

ival-sqrt: 305.0ms (10.1% of total)

adjust: 246.0ms (8.2% of total)

ival-pi: 132.0ms (4.4% of total)

ival-sub: 119.0ms (3.9% of total)

exact: 20.0ms (0.7% of total)

ival-true: 12.0ms (0.4% of total)

ival-assert: 7.0ms (0.2% of total)

Bogosity

explain231.0ms (2.1%)

Memory

3.9MiB live, 238.0MiB allocated; 22ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
4	89	(8.099404128762248e-46 7.209623289596487e+179)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	-	`k`
0	0	-	-	`n`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	93	23

Confusion

	Predicted +	Predicted -
+	4	0
-	89	163

Precision

0.043010752688172046

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	4	0	0
-	89	23	140

Precision?

0.034482758620689655

Recall?

1.0

Freqs

test

number	freq
0	163
1	93

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

59.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 13.0ms (32% of total)

ival-pow: 10.0ms (24.6% of total)

ival-div: 7.0ms (17.3% of total)

ival-sqrt: 4.0ms (9.9% of total)

ival-sub: 3.0ms (7.4% of total)

ival-pi: 2.0ms (4.9% of total)

exact: 1.0ms (2.5% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess27.0ms (0.2%)

Memory

36.0MiB live, 36.0MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	71	76
2	145	74
3	227	74
4	296	74
5	363	74
6	428	74
7	501	74
8	528	74
9	541	74
10	547	74
0	13	16
0	22	16
1	37	14
2	50	14
3	67	14
4	80	14
5	98	14
6	132	14
7	202	14
8	227	14
9	247	14
10	257	14
0	257	14

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify23.0ms (0.2%)

Memory

-27.4MiB live, 15.5MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	50	52
3	67	52
4	80	52
5	98	52
6	132	52
7	202	52
8	227	52
9	247	52
10	257	52
0	257	52

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize70.0ms (0.6%)

Memory

-15.7MiB live, 44.3MiB allocated; 15ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1796875	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.1943347811304714	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.25	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.25390625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

61.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-pow: 38.0ms (74.1% of total)

ival-mult: 5.0ms (9.8% of total)

ival-div: 3.0ms (5.9% of total)

ival-sqrt: 2.0ms (3.9% of total)

ival-pi: 1.0ms (2% of total)

ival-sub: 1.0ms (2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series74.0ms (0.7%)

Memory

37.5MiB live, 80.1MiB allocated; 12ms collecting garbage

Counts

5 → 22

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
37.0ms	n	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
22.0ms	n	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
9.0ms	n	@	inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
3.0ms	k	@	-inf	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))
3.0ms	k	@	0	((* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n))

simplify194.0ms (1.8%)

Memory

-2.5MiB live, 135.7MiB allocated; 37ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	120	502
1	378	489
2	1377	453
3	4131	453
0	8166	441

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 22

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

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

rewrite231.0ms (2.1%)

Memory

23.7MiB live, 347.4MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	38
0	22	38
1	83	35
2	446	35
3	4007	29
0	8921	29

Stop Event

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

Counts

5 → 321

Calls

Call 1

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

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

eval47.0ms (0.4%)

Memory: -24.6MiB live, 120.4MiB allocated; 17ms collecting garbage
Compiler: Compiled 7 537 to 1 169 computations (84.5% saved)

prune21.0ms (0.2%)

Memory

18.7MiB live, 65.2MiB allocated; 2ms collecting garbage

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	319	19	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	320	19	339

Accuracy

100.0%

Counts

339 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	25.9%	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
	99.3%	(.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.4%	(.f64 (pow.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	75.2%	(.f64 (pow.f64 (PI.f64) (/.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 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))
▶	99.5%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	75.2%	(.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
	75.2%	(.f64 (pow.f64 #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 n (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))
	75.1%	(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))))
▶	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	57.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (fma.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (fma.f64 (.f64 (.f64 (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64)) k (.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))) k (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))))
▶	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	50.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))))
	49.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	96.1%	(.f64 (exp.f64 (.f64 (log.f64 k) #s(literal -1/2 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	57.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (fma.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) (pow.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) #s(literal 2 binary64)) (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)) #s(literal -1/2 binary64)) (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) k) (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)))))
▶	56.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
	99.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
▶	37.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))

Compiler

Compiled 1 060 to 764 computations (27.9% saved)

simplify163.0ms (1.5%)

Memory

-28.5MiB live, 76.8MiB allocated; 22ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 k #s(literal 1/4 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	3	(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))))
cost-diff	0	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k)
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
cost-diff	0	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
cost-diff	0	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) 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	(pow.f64 k #s(literal -1/2 binary64))
cost-diff	0	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	55	453
0	93	447
1	148	437
2	258	436
3	559	436
4	1313	436
5	2568	436
6	3889	436
7	4118	436
8	4339	436
9	4649	436
10	4876	436
11	5106	436
12	5165	436
13	5203	436
14	5226	436
15	5226	436
16	5226	436
0	5226	436

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(/.f64 (*.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(PI.f64)
n
k
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
#s(literal 2 binary64)
n
(PI.f64)
(fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k)
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)))
(.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)))
(log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(*.f64 #s(literal 2 binary64) n)
n
(PI.f64)
(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
(.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)
(*.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64))
(pow.f64 k #s(literal 3 binary64))
k
#s(literal 3 binary64)
#s(literal -1/2 binary64)
(sqrt.f64 (.f64 (.f64 (PI.f64) n) k))
(.f64 (.f64 (PI.f64) n) k)
(*.f64 (PI.f64) n)
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
#s(literal 1 binary64)
(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 k #s(literal 1/4 binary64))
k
#s(literal 1/4 binary64)
#s(literal 2 binary64)
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)

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

localize186.0ms (1.7%)

Memory

-1.6MiB live, 272.4MiB allocated; 40ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1943347811304714	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.25	(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
accuracy	0.25390625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.5084762695368841	(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
accuracy	11.079881726684318	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k)
accuracy	15.077274842532907	(sqrt.f64 (.f64 (.f64 (PI.f64) n) k))
accuracy	19.366516890910386	(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
accuracy	31.90347492327141	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
accuracy	0.1796875	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
accuracy	0.1943347811304714	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
accuracy	0.25	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.25390625	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
accuracy	0.25390625	(*.f64 (PI.f64) n)
accuracy	0.4958000488422102	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	14.564720891401691	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	32.20982506812441	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
accuracy	0.0	(PI.f64)
accuracy	0.1796875	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
accuracy	0.1943347811304714	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.25390625	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

141.0ms

256×

valid

Compiler

Compiled 399 to 47 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 105.0ms

ival-pow: 47.0ms (44.9% of total)

ival-mult: 30.0ms (28.7% of total)

ival-div: 8.0ms (7.6% of total)

ival-sqrt: 8.0ms (7.6% of total)

ival-log: 3.0ms (2.9% of total)

ival-pow2: 3.0ms (2.9% of total)

ival-add: 2.0ms (1.9% of total)

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

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

exact: 1.0ms (1% of total)

adjust: 0.0ms (0% of total)

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

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

series128.0ms (1.2%)

Memory

23.4MiB live, 266.6MiB allocated; 30ms collecting garbage

Counts

25 → 58

Calls

Call 1

Inputs
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k)
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))))
(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(pow.f64 k #s(literal 1/4 binary64))
(PI.f64)
(*.f64 (PI.f64) n)
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
(sqrt.f64 (.f64 (.f64 (PI.f64) n) k))

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

Calls

6 calls:

Time	Variable		Point	Expression
41.0ms	k	@	-inf	((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (pow (pow k 1/4) 2) (* (/ 1 (pow (pow k 1/4) 2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (pow (pow k 1/4) 2)) (pow k 1/4) (PI) (* (PI) n) (* (* 2 n) (PI)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (* (* (pow k 3) (PI)) n)) (sqrt (* (* (PI) n) k)))
20.0ms	n	@	-inf	((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (pow (pow k 1/4) 2) (* (/ 1 (pow (pow k 1/4) 2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (pow (pow k 1/4) 2)) (pow k 1/4) (PI) (* (PI) n) (* (* 2 n) (PI)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (* (* (pow k 3) (PI)) n)) (sqrt (* (* (PI) n) k)))
19.0ms	k	@	0	((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (pow (pow k 1/4) 2) (* (/ 1 (pow (pow k 1/4) 2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (pow (pow k 1/4) 2)) (pow k 1/4) (PI) (* (PI) n) (* (* 2 n) (PI)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (* (* (pow k 3) (PI)) n)) (sqrt (* (* (PI) n) k)))
19.0ms	k	@	inf	((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (pow (pow k 1/4) 2) (* (/ 1 (pow (pow k 1/4) 2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (pow (pow k 1/4) 2)) (pow k 1/4) (PI) (* (PI) n) (* (* 2 n) (PI)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (* (* (pow k 3) (PI)) n)) (sqrt (* (* (PI) n) k)))
14.0ms	n	@	0	((* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (* 2 (PI)) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (PI) n) k))) (sqrt 2) (sqrt (/ (* (PI) n) k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) k) (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (pow (pow k 1/4) 2) (* (/ 1 (pow (pow k 1/4) 2)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (pow (pow k 1/4) 2)) (pow k 1/4) (PI) (* (PI) n) (* (* 2 n) (PI)) (pow (* (* 2 n) (PI)) (+ (* -1/2 k) 1/2)) (sqrt (* (* (pow k 3) (PI)) n)) (sqrt (* (* (PI) n) k)))

simplify147.0ms (1.3%)

Memory

4.9MiB live, 199.7MiB allocated; 59ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	207	1228
1	723	1135
2	3335	1103
0	8258	1075

Stop Event

1×	iter limit
1×	node limit

Counts

58 → 58

Calls

Call 1

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

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

rewrite299.0ms (2.7%)

Memory

20.0MiB live, 384.2MiB allocated; 135ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	298
0	93	284
1	275	276
2	1461	276
0	8249	276

Stop Event

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

Counts

25 → 895

Calls

Call 1

Inputs
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k)))) k)
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 (PI.f64) n) k))))
(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(pow.f64 k #s(literal 1/4 binary64))
(PI.f64)
(*.f64 (PI.f64) n)
(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
(sqrt.f64 (.f64 (.f64 (PI.f64) n) k))

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

eval318.0ms (2.9%)

Memory: -15.0MiB live, 438.6MiB allocated; 155ms collecting garbage
Compiler: Compiled 40 902 to 4 463 computations (89.1% saved)

prune41.0ms (0.4%)

Memory

-26.5MiB live, 118.8MiB allocated; 9ms collecting garbage

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	1 092	18	1 110
Fresh	11	3	14
Picked	3	2	5
Done	0	0	0
Total	1 106	23	1 129

Accuracy

100.0%

Counts

1 129 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
	99.5%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	49.3%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	75.2%	(.f64 (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k)))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
✓	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (*.f64 #s(literal 1/2 binary64) k)))))
▶	50.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))))
	49.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	49.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
	40.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
	49.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 k #s(literal 3/8 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/8 binary64)))))
	49.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 k #s(literal 1/4 binary64)))))
	36.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
	49.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k))))
▶	37.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
	49.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
	37.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
▶	36.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 n (PI.f64)))) k))))
✓	37.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	25.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))) k))))
▶	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))

Compiler

Compiled 1 259 to 980 computations (22.2% saved)

simplify224.0ms (2%)

Memory

19.1MiB live, 205.0MiB allocated; 33ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))))
cost-diff	0	(sqrt.f64 k)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
cost-diff	2	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 n (PI.f64)))) k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 n (PI.f64)))) k))))
cost-diff	6	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))
cost-diff	0	(*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
cost-diff	0	(/.f64 (*.f64 n (PI.f64)) k)
cost-diff	0	(.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
cost-diff	0	(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
cost-diff	0	(sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))
cost-diff	0	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
cost-diff	2	(.f64 (sqrt.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	431
0	91	397
1	153	389
2	254	389
3	534	389
4	1100	389
5	1997	389
6	3240	389
7	4418	389
8	5089	389
9	6973	389
0	8129	384

Stop Event

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

Calls

Call 1

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

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

localize164.0ms (1.5%)

Memory

20.4MiB live, 206.2MiB allocated; 39ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.2109375	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.305351269536884	(.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n)))
accuracy	15.015259438585579	(PI.f64)
accuracy	16.951901240999668	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (.f64 (fma.f64 (.f64 (log.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) k) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) n))))
accuracy	0.36460878907376804	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))
accuracy	8.0448766325037	(sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) k))
accuracy	15.015259438585579	(PI.f64)
accuracy	17.056754650487964	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 n (PI.f64)))) k))))
accuracy	0.7578125	(sqrt.f64 (PI.f64))
accuracy	8.088642300984604	(sqrt.f64 (/.f64 n k))
accuracy	15.015259438585579	(PI.f64)
accuracy	17.056754650487964	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
accuracy	0.1875	(*.f64 n (PI.f64))
accuracy	8.036571669507781	(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
accuracy	15.015259438585579	(PI.f64)
accuracy	17.056754650487964	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
accuracy	0.07421875	(sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)))
accuracy	0.1875	(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
accuracy	0.19140625	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
accuracy	15.015259438585579	(PI.f64)

Samples

95.0ms	194×	0	valid
23.0ms	62×	0	exit

Compiler

Compiled 360 to 49 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 93.0ms

ival-mult: 52.0ms (55.7% of total)

ival-sqrt: 15.0ms (16.1% of total)

ival-div: 11.0ms (11.8% of total)

ival-pow: 9.0ms (9.6% of total)

ival-log: 3.0ms (3.2% of total)

ival-pi: 1.0ms (1.1% of total)

ival-add: 1.0ms (1.1% of total)

ival-sub: 1.0ms (1.1% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series119.0ms (1.1%)

Memory

5.1MiB live, 141.3MiB allocated; 19ms collecting garbage

Counts

25 → 49

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
41.0ms	k	@	0	((* (sqrt (* (* n 2) (PI))) 1) (/ (* (sqrt (* (* n 2) (PI))) 1) (* (pow (* (* n 2) (PI)) (/ k 2)) (sqrt k))) (sqrt (* (* n 2) (PI))) (* (* n 2) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI)))) (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI))) (* (sqrt (* n (PI))) (sqrt (* n (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (sqrt (* n (PI))) (sqrt (* n (PI)))) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (sqrt (/ (* (sqrt (* n (PI))) (sqrt (* n (PI)))) k)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))))
32.0ms	n	@	0	((* (sqrt (* (* n 2) (PI))) 1) (/ (* (sqrt (* (* n 2) (PI))) 1) (* (pow (* (* n 2) (PI)) (/ k 2)) (sqrt k))) (sqrt (* (* n 2) (PI))) (* (* n 2) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI)))) (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI))) (* (sqrt (* n (PI))) (sqrt (* n (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (sqrt (* n (PI))) (sqrt (* n (PI)))) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (sqrt (/ (* (sqrt (* n (PI))) (sqrt (* n (PI)))) k)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))))
18.0ms	n	@	-inf	((* (sqrt (* (* n 2) (PI))) 1) (/ (* (sqrt (* (* n 2) (PI))) 1) (* (pow (* (* n 2) (PI)) (/ k 2)) (sqrt k))) (sqrt (* (* n 2) (PI))) (* (* n 2) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI)))) (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI))) (* (sqrt (* n (PI))) (sqrt (* n (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (sqrt (* n (PI))) (sqrt (* n (PI)))) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (sqrt (/ (* (sqrt (* n (PI))) (sqrt (* n (PI)))) k)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))))
13.0ms	n	@	inf	((* (sqrt (* (* n 2) (PI))) 1) (/ (* (sqrt (* (* n 2) (PI))) 1) (* (pow (* (* n 2) (PI)) (/ k 2)) (sqrt k))) (sqrt (* (* n 2) (PI))) (* (* n 2) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI)))) (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI))) (* (sqrt (* n (PI))) (sqrt (* n (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (sqrt (* n (PI))) (sqrt (* n (PI)))) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (sqrt (/ (* (sqrt (* n (PI))) (sqrt (* n (PI)))) k)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))))
8.0ms	k	@	-inf	((* (sqrt (* (* n 2) (PI))) 1) (/ (* (sqrt (* (* n 2) (PI))) 1) (* (pow (* (* n 2) (PI)) (/ k 2)) (sqrt k))) (sqrt (* (* n 2) (PI))) (* (* n 2) (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (/ (* n (PI)) k) 2)) (* (/ (* n (PI)) k) 2) (/ (* n (PI)) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI)))) (sqrt 2) (* (sqrt (/ n k)) (sqrt (PI))) (* (sqrt (* n (PI))) (sqrt (* n (PI)))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (sqrt (/ (* (sqrt (* n (PI))) (sqrt (* n (PI)))) k))) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (* n (PI)) (sqrt (/ n k)) (sqrt (PI)) (sqrt (/ (* (sqrt (* n (PI))) (sqrt (* n (PI)))) k)) (* (* (+ (* (* (log (* (* 2 n) (PI))) k) -1/2) 1) (sqrt 2)) (sqrt (* (PI) n))))

simplify137.0ms (1.2%)

Memory

-29.2MiB live, 165.5MiB allocated; 31ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	211	1043
1	747	988
2	3226	959
0	8633	936

Stop Event

1×	iter limit
1×	node limit

Counts

49 → 49

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

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

rewrite210.0ms (1.9%)

Memory

10.1MiB live, 197.0MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	301
0	91	266
1	262	249
2	1237	249
0	8173	249

Stop Event

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

Counts

25 → 1 056

Calls

Call 1

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

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

eval277.0ms (2.5%)

Memory: 4.5MiB live, 324.4MiB allocated; 55ms collecting garbage
Compiler: Compiled 43 645 to 5 524 computations (87.3% saved)

prune60.0ms (0.6%)

Memory

1.5MiB live, 120.4MiB allocated; 25ms collecting garbage

Pruning

29 alts after pruning (25 fresh and 4 done)

	Pruned	Kept	Total
New	1 368	18	1 386
Fresh	9	7	16
Picked	3	2	5
Done	0	2	2
Total	1 380	29	1 409

Accuracy

100.0%

Counts

1 409 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
	76.9%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) k)))
	99.5%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	76.9%	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (neg.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
▶	49.3%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	76.6%	(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) k))) (sqrt.f64 (/.f64 n k)))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	49.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	49.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
	40.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
	36.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) n) k)) (sqrt.f64 (PI.f64))))
▶	36.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
	49.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	41.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))))
	49.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
	49.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
▶	49.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
	49.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
	41.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))))))
✓	36.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 n (PI.f64)))) k))))
✓	37.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
	25.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))) k))))
	27.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (-.f64 (/.f64 (.f64 (PI.f64) n) k) (/.f64 (.f64 (PI.f64) n) k))))
✓	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
	36.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
▶	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))

Compiler

Compiled 1 432 to 1 121 computations (21.7% saved)

simplify22.0ms (0.2%)

Memory

-13.9MiB live, 31.6MiB allocated; 3ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	304
0	66	304
1	105	298
2	140	298
3	174	298
4	219	298
5	277	298
6	394	298
7	618	298
8	756	298
9	806	298
10	836	298
0	836	298

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize138.0ms (1.3%)

Memory

-12.5MiB live, 179.3MiB allocated; 16ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1875	(*.f64 (PI.f64) n)
accuracy	0.3786125488422101	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	15.015259438585579	(PI.f64)
accuracy	17.149613700427558	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.24837875976844204	(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
accuracy	0.3623237793053261	(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
accuracy	15.015259438585579	(PI.f64)
accuracy	17.056754650487964	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
accuracy	0.7578125	(sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	8.088642300984604	(sqrt.f64 (/.f64 n k))
accuracy	15.015259438585579	(PI.f64)
accuracy	17.056754650487964	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
accuracy	0.19921875	(.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))
accuracy	8.036571669507781	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64)))
accuracy	15.015259438585579	(PI.f64)
accuracy	17.056754650487964	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
accuracy	0.1875	(*.f64 (PI.f64) n)
accuracy	0.19140625	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
accuracy	0.3786125488422101	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	15.015259438585579	(PI.f64)

Samples

63.0ms	194×	0	valid
18.0ms	62×	0	exit

Compiler

Compiled 260 to 38 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 19.0ms (32.6% of total)

ival-sqrt: 14.0ms (24% of total)

ival-pow: 13.0ms (22.3% of total)

ival-div: 8.0ms (13.7% of total)

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

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

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series50.0ms (0.5%)

Memory

7.3MiB live, 94.4MiB allocated; 13ms collecting garbage

Counts

21 → 43

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	n	@	inf	((/ (* (sqrt (* (PI) n)) (sqrt 2)) (* (pow (* (* n 2) (PI)) (/ k 2)) (sqrt k))) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ n k)) (PI))) (* (* 2 (/ n k)) (PI)) (* 2 (/ n k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ n k)) (sqrt (* (PI) 2))) (sqrt (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (sqrt (* (PI) 2)))
13.0ms	n	@	-inf	((/ (* (sqrt (* (PI) n)) (sqrt 2)) (* (pow (* (* n 2) (PI)) (/ k 2)) (sqrt k))) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ n k)) (PI))) (* (* 2 (/ n k)) (PI)) (* 2 (/ n k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ n k)) (sqrt (* (PI) 2))) (sqrt (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (sqrt (* (PI) 2)))
10.0ms	n	@	0	((/ (* (sqrt (* (PI) n)) (sqrt 2)) (* (pow (* (* n 2) (PI)) (/ k 2)) (sqrt k))) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ n k)) (PI))) (* (* 2 (/ n k)) (PI)) (* 2 (/ n k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ n k)) (sqrt (* (PI) 2))) (sqrt (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (sqrt (* (PI) 2)))
5.0ms	k	@	-inf	((/ (* (sqrt (* (PI) n)) (sqrt 2)) (* (pow (* (* n 2) (PI)) (/ k 2)) (sqrt k))) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ n k)) (PI))) (* (* 2 (/ n k)) (PI)) (* 2 (/ n k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ n k)) (sqrt (* (PI) 2))) (sqrt (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (sqrt (* (PI) 2)))
2.0ms	k	@	0	((/ (* (sqrt (* (PI) n)) (sqrt 2)) (* (pow (* (* n 2) (PI)) (/ k 2)) (sqrt k))) (* (sqrt (* (PI) n)) (sqrt 2)) (sqrt (* (PI) n)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (* 2 (/ n k)) (PI))) (* (* 2 (/ n k)) (PI)) (* 2 (/ n k)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ n k)) (sqrt (* (PI) 2))) (sqrt (/ n k)) (/ n k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k))) (sqrt 2) (/ (sqrt (* (PI) n)) (sqrt k)) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (PI) (sqrt (* (PI) 2)))

simplify128.0ms (1.2%)

Memory

34.3MiB live, 133.3MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	188	892
1	648	851
2	2661	796
0	8253	778

Stop Event

1×	iter limit
1×	node limit

Counts

43 → 43

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

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

rewrite191.0ms (1.7%)

Memory

-20.8MiB live, 255.0MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	217
0	66	208
1	196	197
2	884	165
0	8403	165

Stop Event

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

Counts

21 → 2 171

Calls

Call 1

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

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

eval288.0ms (2.6%)

Memory: 42.0MiB live, 364.4MiB allocated; 86ms collecting garbage
Compiler: Compiled 46 616 to 4 977 computations (89.3% saved)

prune101.0ms (0.9%)

Memory

-21.2MiB live, 172.1MiB allocated; 25ms collecting garbage

Pruning

26 alts after pruning (22 fresh and 4 done)

	Pruned	Kept	Total
New	1 610	14	1 624
Fresh	12	8	20
Picked	3	2	5
Done	2	2	4
Total	1 627	26	1 653

Accuracy

100.0%

Counts

1 653 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 k #s(literal 1/2 binary64))))
	99.7%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 k #s(literal 1/2 binary64)))))
	99.5%	(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
	76.9%	(.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (neg.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sqrt.f64 k)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
	99.6%	(.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 k #s(literal 1/2 binary64))))))
	9.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 k n (*.f64 n k))) (fabs.f64 k)))
	49.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
	10.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
✓	36.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
	9.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64))))
	49.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	49.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
	49.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))))
	10.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
	49.4%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
	8.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k))))
	9.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
	27.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (-.f64 (/.f64 (.f64 (PI.f64) n) k) (/.f64 (.f64 (PI.f64) n) k))))
	4.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
✓	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
✓	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
	4.6%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (PI.f64))))
	9.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
	37.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))

Compiler

Compiled 2 483 to 829 computations (66.6% saved)

regimes77.0ms (0.7%)

Memory

29.6MiB live, 178.6MiB allocated; 12ms collecting garbage

Counts

70 → 1

Calls

Call 1

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

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

Calls

4 calls:

20.0ms	k
20.0ms	n
19.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
15.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes87.0ms (0.8%)

Memory

-63.2MiB live, 111.4MiB allocated; 65ms collecting garbage

Counts

47 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 k n (*.f64 n k))) (fabs.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (-.f64 (/.f64 (.f64 (PI.f64) n) k) (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 n (PI.f64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (neg.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 k #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))

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

Calls

4 calls:

46.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
14.0ms	k
12.0ms	n
11.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 23 to 23 computations (0% saved)

regimes94.0ms (0.9%)

Memory

-8.2MiB live, 88.2MiB allocated; 9ms collecting garbage

Counts

44 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 k n (*.f64 n k))) (fabs.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (-.f64 (/.f64 (.f64 (PI.f64) n) k) (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 n (PI.f64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (neg.f64 (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))

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

Calls

4 calls:

34.0ms	(.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))))
34.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
12.0ms	n
11.0ms	k

Results

Accuracy	Segments	Branch
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.5%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.5%	1	`k`
99.5%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes72.0ms (0.7%)

Memory

10.0MiB live, 55.5MiB allocated; 4ms collecting garbage

Counts

38 → 2

Calls

Call 1

Inputs
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) n) k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 (PI.f64) k) n) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 k n (*.f64 n k))) (fabs.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) n) k)) (sqrt.f64 (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (-.f64 (/.f64 (.f64 (PI.f64) n) k) (/.f64 (.f64 (PI.f64) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 #s(approx (* (sqrt 2) (+ (* (* (log (* (* 2 n) (PI))) (sqrt (* (* (pow k 3) (PI)) n))) -1/2) (sqrt (* (* (PI) n) k)))) (.f64 (sqrt.f64 (.f64 (*.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))) k))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) (.f64 n (PI.f64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) n) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 n (PI.f64)))) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 (PI.f64) n)))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 n)) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) k))))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))

Outputs

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

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

Calls

4 calls:

42.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
10.0ms	n
10.0ms	k
9.0ms	(.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
52.6%	3	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
74.4%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
74.2%	2	`k`
52.6%	3	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes13.0ms (0.1%)

Memory

26.3MiB live, 26.3MiB allocated; 0ms collecting garbage

Counts

22 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

6.0ms	k
6.0ms	(.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
51.2%	2	`k`
51.2%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes11.0ms (0.1%)

Memory

-37.6MiB live, 13.1MiB allocated; 6ms collecting garbage

Counts

21 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
51.2%	2	`k`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes11.0ms (0.1%)

Memory

21.7MiB live, 21.7MiB allocated; 0ms collecting garbage

Counts

18 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

5.0ms	k
5.0ms	(.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
51.2%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
51.2%	2	`k`

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes47.0ms (0.4%)

Memory

-10.4MiB live, 34.1MiB allocated; 4ms collecting garbage

Counts

15 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

4 calls:

32.0ms	n
5.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	k
4.0ms	(.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
37.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
37.1%	1	`n`
40.7%	3	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
39.0%	2	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes9.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated; 0ms collecting garbage

Counts

13 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

4.0ms	k
4.0ms	(.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
37.1%	1	`k`
38.9%	2	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes14.0ms (0.1%)

Memory

-24.3MiB live, 21.9MiB allocated; 2ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	n
3.0ms	k
3.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
37.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
37.1%	1	`k`
37.1%	1	`n`
37.1%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes9.0ms (0.1%)

Memory

18.3MiB live, 18.3MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	n
2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	k
2.0ms	(.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
37.1%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
37.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
37.1%	1	`k`
37.1%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes8.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
2.0ms	k
2.0ms	(.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
9.1%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
9.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
9.1%	1	`k`
9.1%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes6.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

4 calls:

1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	n
1.0ms	k
1.0ms	(.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
4.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
4.6%	1	`k`
4.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
4.6%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes6.0ms (0.1%)

Memory

-30.6MiB live, 15.7MiB allocated; 2ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	k
1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
1.0ms	n

Results

Accuracy	Segments	Branch
4.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
4.6%	1	`n`
4.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
4.6%	1	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.0136190524626947e-124

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch23.0ms (0.2%)

Memory

-21.8MiB live, 34.6MiB allocated; 3ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	3.304379966409038e+163	1.8538092426120492e+171

Samples

13.0ms

144×

valid

Compiler

Compiled 505 to 396 computations (21.6% saved)

Precisions

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

ival-div: 2.0ms (21.1% of total)

ival-mult: 2.0ms (21.1% of total)

ival-pow: 2.0ms (21.1% of total)

ival-sub: 1.0ms (10.6% of total)

ival-sqrt: 1.0ms (10.6% of total)

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

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	3.304379966409038e+163	1.8538092426120492e+171

Compiler

Compiled 505 to 396 computations (21.6% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	3.304379966409038e+163	1.8538092426120492e+171

Compiler

Compiled 505 to 396 computations (21.6% saved)

bsearch1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.0696404179341306e+154	5.719905382542293e+156
0.0ms	0.0	1.0136190524626947e-124

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0696404179341306e+154	5.719905382542293e+156

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify79.0ms (0.7%)

Memory

1.8MiB live, 47.9MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	100	617
1	121	571
2	146	571
3	184	571
4	248	571
5	365	571
6	568	571
7	865	571
8	953	571
9	1060	571
10	1133	571
11	1155	571
12	1163	571
13	1173	571
14	1194	571
15	1220	571
16	1244	571
17	1273	571
18	1303	571
19	1315	571
20	1325	571
21	1329	571
22	1330	571

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 k #s(literal 1/2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(if (<=.f64 (.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)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (-.f64 (/.f64 (.f64 (PI.f64) n) k) (/.f64 (.f64 (PI.f64) n) k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))))
(if (<=.f64 k #s(literal 34000000000000001083568463219533558794073418729127208589339158830301777681777136741137747448217459074980048844160181709770983389513275922354668752895056901283250176 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k)))))
(if (<=.f64 k #s(literal 34000000000000001083568463219533558794073418729127208589339158830301777681777136741137747448217459074980048844160181709770983389513275922354668752895056901283250176 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k)))))
(if (<=.f64 k #s(literal 34000000000000001083568463219533558794073418729127208589339158830301777681777136741137747448217459074980048844160181709770983389513275922354668752895056901283250176 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k)))))
(if (<=.f64 (.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)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k)))) (if (<=.f64 (.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)))) #s(literal 20000000000000000738950913761164530819618359659685376903845557104301087318694439194433026219410816654893023507374465334628674006699146808342092384896548864 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 k n (*.f64 n k))) (fabs.f64 k)))))
(if (<=.f64 (.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)))) #s(literal 20000000000000000738950913761164530819618359659685376903845557104301087318694439194433026219410816654893023507374465334628674006699146808342092384896548864 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 k n (*.f64 n k))) (fabs.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))

Outputs
(/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (.f64 k #s(literal 1/2 binary64)))))
(/.f64 #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (sqrt.f64 k))
(if (<=.f64 (.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)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (-.f64 (/.f64 (.f64 (PI.f64) n) k) (/.f64 (.f64 (PI.f64) n) k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 #s(literal 0 binary64))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))))
(if (<=.f64 k #s(literal 34000000000000001083568463219533558794073418729127208589339158830301777681777136741137747448217459074980048844160181709770983389513275922354668752895056901283250176 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))) (sqrt.f64 k))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k)))))
(if (<=.f64 k #s(literal 34000000000000001083568463219533558794073418729127208589339158830301777681777136741137747448217459074980048844160181709770983389513275922354668752895056901283250176 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k)))))
(if (<=.f64 k #s(literal 34000000000000001083568463219533558794073418729127208589339158830301777681777136741137747448217459074980048844160181709770983389513275922354668752895056901283250176 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k)))))
(if (<=.f64 (.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)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k)))) (if (<=.f64 (.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)))) #s(literal 20000000000000000738950913761164530819618359659685376903845557104301087318694439194433026219410816654893023507374465334628674006699146808342092384896548864 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 k n (*.f64 n k))) (fabs.f64 k)))))
(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 0 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 k n (.f64 n k)) (.f64 k k)))) (if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 20000000000000000738950913761164530819618359659685376903845557104301087318694439194433026219410816654893023507374465334628674006699146808342092384896548864 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 k n (*.f64 n k))) (fabs.f64 k)))))
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(if (<=.f64 (.f64 (pow.f64 (sqrt.f64 k) #s(literal -1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))) #s(literal 20000000000000000738950913761164530819618359659685376903845557104301087318694439194433026219410816654893023507374465334628674006699146808342092384896548864 binary64)) #s(approx ( (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (fma.f64 k n (*.f64 n k))) (fabs.f64 k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (/.f64 n k)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) k))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (PI.f64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (+.f64 (PI.f64) (PI.f64))))

derivations1.0s (9.5%)

Memory

19.1MiB live, 925.4MiB allocated; 80ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	301
0	91	266
1	262	249
2	1237	249
0	8173	249
0	120	502
1	378	489
2	1377	453
3	4131	453
0	8166	441
0	55	298
0	93	284
1	275	276
2	1461	276
0	8249	276
0	13	38
0	22	38
1	83	35
2	446	35
3	4007	29
0	8921	29
0	42	217
0	66	208
1	196	197
2	884	165
0	8403	165

Stop Event

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

Compiler

Compiled 607 to 101 computations (83.4% saved)

preprocess95.0ms (0.9%)

Memory: -5.6MiB live, 130.5MiB allocated; 10ms collecting garbage
Compiler: Compiled 1 246 to 228 computations (81.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Iter	Nodes	Cost
0	31	88
1	71	76
2	145	74
3	227	74
4	296	74
5	363	74
6	428	74
7	501	74
8	528	74
9	541	74
10	547	74
0	13	16
0	22	16
1	37	14
2	50	14
3	67	14
4	80	14
5	98	14
6	132	14
7	202	14
8	227	14
9	247	14
10	257	14
0	257	14

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	50	52
3	67	52
4	80	52
5	98	52
6	132	52
7	202	52
8	227	52
9	247	52
10	257	52
0	257	52

Iter	Nodes	Cost
0	42	304
0	66	304
1	105	298
2	140	298
3	174	298
4	219	298
5	277	298
6	394	298
7	618	298
8	756	298
9	806	298
10	836	298
0	836	298

Iter	Nodes	Cost
0	31	88
1	71	76
2	145	74
3	227	74
4	296	74
5	363	74
6	428	74
7	501	74
8	528	74
9	541	74
10	547	74
0	13	16
0	22	16
1	37	14
2	50	14
3	67	14
4	80	14
5	98	14
6	132	14
7	202	14
8	227	14
9	247	14
10	257	14
0	257	14

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	50	52
3	67	52
4	80	52
5	98	52
6	132	52
7	202	52
8	227	52
9	247	52
10	257	52
0	257	52

Iter	Nodes	Cost
0	42	304
0	66	304
1	105	298
2	140	298
3	174	298
4	219	298
5	277	298
6	394	298
7	618	298
8	756	298
9	806	298
10	836	298
0	836	298

start0.0ms (0%)

analyze243.0ms (2.2%)

sample4.7s (42.9%)

explain231.0ms (2.1%)

preprocess27.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify23.0ms (0.2%)

localize70.0ms (0.6%)

series74.0ms (0.7%)

simplify194.0ms (1.8%)

rewrite231.0ms (2.1%)

eval47.0ms (0.4%)

prune21.0ms (0.2%)

simplify163.0ms (1.5%)

localize186.0ms (1.7%)

series128.0ms (1.2%)

simplify147.0ms (1.3%)

rewrite299.0ms (2.7%)

eval318.0ms (2.9%)

prune41.0ms (0.4%)

simplify224.0ms (2%)

localize164.0ms (1.5%)

series119.0ms (1.1%)

simplify137.0ms (1.2%)

rewrite210.0ms (1.9%)

eval277.0ms (2.5%)

prune60.0ms (0.6%)

simplify22.0ms (0.2%)

localize138.0ms (1.3%)

series50.0ms (0.5%)

simplify128.0ms (1.2%)

rewrite191.0ms (1.7%)

eval288.0ms (2.6%)

prune101.0ms (0.9%)

regimes77.0ms (0.7%)

regimes87.0ms (0.8%)

regimes94.0ms (0.9%)

regimes72.0ms (0.7%)

regimes13.0ms (0.1%)

regimes11.0ms (0.1%)

regimes11.0ms (0.1%)

regimes47.0ms (0.4%)

regimes9.0ms (0.1%)

regimes14.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

bsearch23.0ms (0.2%)

bsearch2.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

simplify79.0ms (0.7%)

derivations1.0s (9.5%)

preprocess95.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	31	88
1	71	76
2	145	74
3	227	74
4	296	74
5	363	74
6	428	74
7	501	74
8	528	74
9	541	74
10	547	74
0	13	16
0	22	16
1	37	14
2	50	14
3	67	14
4	80	14
5	98	14
6	132	14
7	202	14
8	227	14
9	247	14
10	257	14
0	257	14

Iter	Nodes	Cost
0	13	54
0	22	54
1	37	52
2	50	52
3	67	52
4	80	52
5	98	52
6	132	52
7	202	52
8	227	52
9	247	52
10	257	52
0	257	52

Iter	Nodes	Cost
0	42	304
0	66	304
1	105	298
2	140	298
3	174	298
4	219	298
5	277	298
6	394	298
7	618	298
8	756	298
9	806	298
10	836	298
0	836	298