Metrics for Migdal et al, Equation (51)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze194.0ms (1.6%)

Memory

-12.8MiB live, 131.3MiB allocated; 39ms 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)

sample4.5s (36.7%)

Memory

-75.3MiB live, 5 666.3MiB allocated; 1.9s collecting garbage

Samples

1.5s	8 256×	0	valid
1.4s	4 522×	1	invalid
580.0ms	1 464×	2	invalid
74.0ms	338×	0	invalid
48.0ms	227×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 2.8s

ival-div: 768.0ms (27.3% of total)

ival-pow: 670.0ms (23.8% of total)

ival-mult: 535.0ms (19% of total)

adjust: 265.0ms (9.4% of total)

ival-sqrt: 248.0ms (8.8% of total)

ival-sub: 147.0ms (5.2% of total)

ival-pi: 140.0ms (5% of total)

exact: 19.0ms (0.7% of total)

ival-true: 13.0ms (0.5% of total)

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

Bogosity

explain384.0ms (3.1%)

Memory

18.8MiB live, 454.8MiB allocated; 38ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
9	100	(2.874937505037429e-31 1.0344721334804931e-139)	-	`(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	108	14
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	oflow-rescue	1	0
↳	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`	overflow	1
↳	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	overflow	62

Confusion

	Predicted +	Predicted -
+	9	0
-	100	147

Precision

0.08256880733944955

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	9	0	0
-	100	14	133

Precision?

0.07317073170731707

Recall?

1.0

Freqs

test

number	freq
0	147
1	109

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

112.0ms

512×

valid

Compiler

Compiled 128 to 43 computations (66.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-pow: 27.0ms (33.6% of total)

ival-mult: 16.0ms (19.9% of total)

ival-sqrt: 15.0ms (18.7% of total)

ival-div: 12.0ms (14.9% of total)

ival-sub: 5.0ms (6.2% of total)

ival-pi: 3.0ms (3.7% of total)

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

exact: 1.0ms (1.2% of total)

adjust: 0.0ms (0% of total)

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

preprocess49.0ms (0.4%)

Memory

6.6MiB live, 59.0MiB allocated; 13ms 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: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(.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))))

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify19.0ms (0.2%)

Memory

-30.2MiB live, 17.8MiB allocated; 2ms 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)

localize41.0ms (0.3%)

Memory

35.0MiB live, 82.2MiB allocated; 1ms 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	0.23828125	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
accuracy	0.296875	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.4846658059648311	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))

Samples

31.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 5.0ms (24.3% of total)

ival-pow: 5.0ms (24.3% of total)

ival-div: 4.0ms (19.5% of total)

ival-pi: 2.0ms (9.7% of total)

ival-sqrt: 2.0ms (9.7% of total)

ival-sub: 1.0ms (4.9% 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)

series113.0ms (0.9%)

Memory

-18.0MiB live, 122.8MiB allocated; 16ms 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
51.0ms	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))
35.0ms	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))
12.0ms	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))
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))

simplify197.0ms (1.6%)

Memory

3.1MiB live, 184.5MiB allocated; 43ms 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))))

rewrite380.0ms (3.1%)

Memory

36.7MiB live, 279.7MiB allocated; 136ms 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))

eval244.0ms (2%)

Memory: 54.7MiB live, 174.7MiB allocated; 88ms collecting garbage
Compiler: Compiled 7 537 to 1 169 computations (84.5% saved)

prune70.0ms (0.6%)

Memory

-19.7MiB live, 77.3MiB allocated; 57ms collecting garbage

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	316	22	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	317	22	339

Accuracy

99.9%

Counts

339 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	26.0%	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
	98.9%	(.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))))
	99.0%	(.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))))
	99.0%	(.f64 (pow.f64 (.f64 (sqrt.f64 k) (sqrt.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))))
▶	99.1%	(.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))))
	75.1%	(.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)))
	99.0%	(.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))))
▶	98.9%	(.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))))
	95.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 (*.f64 n (PI.f64))))) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	75.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
	65.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 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))))))))))
	60.7%	(.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))))))
	99.0%	(.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)))))
	50.8%	(.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)))))
	50.2%	(.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)))))
▶	75.2%	(.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))))
	95.9%	(.f64 (exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 k) (sqrt.f64 k))) #s(literal -1/2 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	95.9%	(.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))))
	54.5%	#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)))))
▶	54.0%	#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))
	99.1%	#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))))
▶	38.8%	#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 1 254 to 910 computations (27.4% saved)

simplify165.0ms (1.3%)

Memory

24.3MiB live, 116.4MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 #s(literal 2 binary64) (/.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 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
cost-diff	0	(.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))))
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	(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 (.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))))
cost-diff	4	(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
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: 1 (0.0ms)

Iter	Nodes	Cost
0	56	444
0	96	436
1	160	426
2	277	426
3	651	426
4	2057	426
5	3683	426
6	4219	426
7	4473	426
8	4724	426
9	5400	426
10	6984	426
11	7748	426
12	7823	426
13	7859	426
14	7859	426
15	7859	426
16	7859	426
0	8386	426

Stop Event

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

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

localize367.0ms (3%)

Memory

-50.2MiB live, 451.2MiB allocated; 152ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.2109375	(*.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))))
accuracy	0.2496080827638098	(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	0.3671875	(.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))))
accuracy	14.773077834737425	(PI.f64)
accuracy	14.773077834737425	(PI.f64)
accuracy	15.189106108243944	(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
accuracy	15.404857512035088	(sqrt.f64 (.f64 (.f64 (PI.f64) n) k))
accuracy	16.43383034005583	#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	0.2578125	(.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
accuracy	0.4846658059648311	(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)))
accuracy	0.76171875	(sqrt.f64 (PI.f64))
accuracy	14.773077834737425	(PI.f64)
accuracy	0.31087875976844204	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)))
accuracy	7.388140518237951	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
accuracy	14.773077834737425	(PI.f64)
accuracy	16.74467888611289	#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	0.171875	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
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	0.4846658059648311	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	14.773077834737425	(PI.f64)

Samples

275.0ms	195×	0	valid
29.0ms	61×	0	exit

Compiler

Compiled 410 to 49 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 188.0ms

ival-pow: 131.0ms (69.5% of total)

ival-mult: 33.0ms (17.5% of total)

ival-sqrt: 9.0ms (4.8% of total)

ival-div: 6.0ms (3.2% of total)

ival-exp2: 2.0ms (1.1% of total)

ival-log: 2.0ms (1.1% of total)

ival-pi: 1.0ms (0.5% of total)

ival-add: 1.0ms (0.5% of total)

ival-sub: 1.0ms (0.5% of total)

exact: 1.0ms (0.5% of total)

adjust: 0.0ms (0% of total)

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

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

series329.0ms (2.7%)

Memory

-2.0MiB live, 394.8MiB allocated; 179ms collecting garbage

Counts

24 → 79

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

Calls

6 calls:

Time	Variable		Point	Expression
200.0ms	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)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 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 k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (sqrt (* (* (PI) n) k)) (sqrt (* (* (pow k 3) (PI)) n)) (pow (* n (PI)) (/ (- 1 k) 2)))
58.0ms	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)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 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 k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (sqrt (* (* (PI) n) k)) (sqrt (* (* (pow k 3) (PI)) n)) (pow (* n (PI)) (/ (- 1 k) 2)))
37.0ms	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)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 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 k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (sqrt (* (* (PI) n) k)) (sqrt (* (* (pow k 3) (PI)) n)) (pow (* n (PI)) (/ (- 1 k) 2)))
14.0ms	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)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 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 k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (sqrt (* (* (PI) n) k)) (sqrt (* (* (pow k 3) (PI)) n)) (pow (* n (PI)) (/ (- 1 k) 2)))
10.0ms	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)) (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (* (/ 1 (sqrt k)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (* (/ 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 k -1/2) (pow 2 (/ (- 1 k) 2))) (pow (* n (PI)) (/ (- 1 k) 2))) (* (pow k -1/2) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)) (PI) (sqrt (PI)) (pow (* (* (* n 2) (sqrt (PI))) (sqrt (PI))) (/ (- 1 k) 2)) (sqrt (* (* (PI) n) k)) (sqrt (* (* (pow k 3) (PI)) n)) (pow (* n (PI)) (/ (- 1 k) 2)))

simplify252.0ms (2%)

Memory

11.5MiB live, 392.9MiB allocated; 43ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	346	2002
1	1265	1832
2	5594	1788
0	8235	1726

Stop Event

1×	iter limit
1×	node limit

Counts

79 → 79

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

rewrite303.0ms (2.5%)

Memory

34.1MiB live, 453.9MiB allocated; 136ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	291
0	96	269
1	268	262
2	1292	262
0	8229	262

Stop Event

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

Counts

24 → 945

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 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.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 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
#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))))
(.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 (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 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(PI.f64)
(sqrt.f64 (PI.f64))
(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)))
(sqrt.f64 (.f64 (.f64 (PI.f64) n) k))
(sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n))
(pow.f64 (*.f64 n (PI.f64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))

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

eval246.0ms (2%)

Memory: -21.0MiB live, 346.2MiB allocated; 44ms collecting garbage
Compiler: Compiled 43 015 to 5 219 computations (87.9% saved)

prune34.0ms (0.3%)

Memory

18.3MiB live, 111.3MiB allocated; 6ms collecting garbage

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	1 161	13	1 174
Fresh	12	5	17
Picked	4	1	5
Done	0	0	0
Total	1 177	19	1 196

Accuracy

100.0%

Counts

1 196 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(/.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
	26.0%	(/.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 (.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64))) (sqrt.f64 k)))
▶	99.3%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64)))))
▶	50.2%	(.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)))))
	60.7%	(.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))))))
	99.0%	(.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)))))
	50.2%	(.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)))))
	99.1%	#s(approx (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k)))
	37.9%	#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))
	54.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (fma.f64 (.f64 (sqrt.f64 (.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (PI.f64)) n)) (log.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (.f64 (.f64 n (PI.f64)) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) k)))
	99.1%	#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))))
	38.7%	#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))))
	50.1%	#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))))
	38.9%	#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)))))
▶	50.2%	#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)))))
✓	38.8%	#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))))
▶	39.0%	#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))))

Compiler

Compiled 1 066 to 819 computations (23.2% saved)

simplify25.0ms (0.2%)

Memory

-18.2MiB live, 34.9MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	295
0	71	295
1	102	291
2	134	291
3	185	291
4	231	291
5	292	291
6	404	291
7	635	291
8	772	291
9	822	291
10	852	291
0	852	291

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize142.0ms (1.1%)

Memory

17.2MiB live, 203.9MiB allocated; 63ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.17578125	(*.f64 n (PI.f64))
accuracy	0.203125	(/.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
accuracy	0.4846658059648311	(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
accuracy	14.773077834737425	(PI.f64)
accuracy	0.1796875	(.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)))))
accuracy	0.3405075195368841	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	14.773077834737425	(PI.f64)
accuracy	16.833478283393802	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.25619125976844204	(*.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))
accuracy	0.31087875976844204	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k))))
accuracy	14.773077834737425	(PI.f64)
accuracy	16.74467888611289	#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)))))
accuracy	0.17578125	(*.f64 n (PI.f64))
accuracy	7.383922507187071	(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
accuracy	14.773077834737425	(PI.f64)
accuracy	16.74467888611289	#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	0.1796875	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64)))))
accuracy	0.24218750000000003	(pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64)))
accuracy	0.3632779541189607	(sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))
accuracy	14.773077834737425	(PI.f64)

Samples

66.0ms	195×	0	valid
19.0ms	61×	0	exit

Compiler

Compiled 261 to 39 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-pow: 20.0ms (33% of total)

ival-mult: 16.0ms (26.4% of total)

ival-div: 11.0ms (18.2% of total)

ival-sqrt: 10.0ms (16.5% 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)

series60.0ms (0.5%)

Memory

-9.4MiB live, 127.8MiB allocated; 21ms collecting garbage

Counts

21 → 55

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
16.0ms	n	@	0	((* (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2)))) (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2))) (sqrt (* (* n (PI)) 2)) (* (/ 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) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) n)) (sqrt 2)) (/ (pow (* (* n (PI)) 2) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* n (PI)) 2) (/ (- 1 k) 2)) (* (* n (PI)) 2) (* n (PI)) (PI) (pow (* (* n (PI)) 2) (/ k 2)))
15.0ms	n	@	-inf	((* (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2)))) (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2))) (sqrt (* (* n (PI)) 2)) (* (/ 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) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) n)) (sqrt 2)) (/ (pow (* (* n (PI)) 2) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* n (PI)) 2) (/ (- 1 k) 2)) (* (* n (PI)) 2) (* n (PI)) (PI) (pow (* (* n (PI)) 2) (/ k 2)))
14.0ms	n	@	inf	((* (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2)))) (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2))) (sqrt (* (* n (PI)) 2)) (* (/ 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) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) n)) (sqrt 2)) (/ (pow (* (* n (PI)) 2) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* n (PI)) 2) (/ (- 1 k) 2)) (* (* n (PI)) 2) (* n (PI)) (PI) (pow (* (* n (PI)) 2) (/ k 2)))
5.0ms	k	@	-inf	((* (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2)))) (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2))) (sqrt (* (* n (PI)) 2)) (* (/ 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) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) n)) (sqrt 2)) (/ (pow (* (* n (PI)) 2) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* n (PI)) 2) (/ (- 1 k) 2)) (* (* n (PI)) 2) (* n (PI)) (PI) (pow (* (* n (PI)) 2) (/ k 2)))
4.0ms	k	@	0	((* (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2)))) (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2))) (sqrt (* (* n (PI)) 2)) (* (/ 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) (sqrt (/ (PI) k)))) (sqrt 2) (* (sqrt n) (sqrt (/ (PI) k))) (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (* (sqrt (* (PI) n)) (sqrt 2)) (/ (pow (* (* n (PI)) 2) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* n (PI)) 2) (/ (- 1 k) 2)) (* (* n (PI)) 2) (* n (PI)) (PI) (pow (* (* n (PI)) 2) (/ k 2)))

simplify154.0ms (1.2%)

Memory

17.9MiB live, 202.5MiB allocated; 32ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	221	1287
1	803	1213
2	3455	1140
0	8392	1110

Stop Event

1×	iter limit
1×	node limit

Counts

55 → 55

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

rewrite232.0ms (1.9%)

Memory

35.8MiB live, 414.9MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	228
0	71	231
1	199	205
2	838	205
3	7804	205
0	8141	205

Stop Event

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

Counts

21 → 1 381

Calls

Call 1

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

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

eval259.0ms (2.1%)

Memory: -15.6MiB live, 410.5MiB allocated; 82ms collecting garbage
Compiler: Compiled 43 342 to 5 374 computations (87.6% saved)

prune631.0ms (5.1%)

Memory

-126.2MiB live, 175.9MiB allocated; 1.1s collecting garbage

Pruning

35 alts after pruning (31 fresh and 4 done)

	Pruned	Kept	Total
New	1 544	23	1 567
Fresh	5	8	13
Picked	2	3	5
Done	0	1	1
Total	1 551	35	1 586

Accuracy

100.0%

Counts

1 586 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.0%	(/.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
	26.0%	(/.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 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
	42.7%	(.f64 (pow.f64 (.f64 k k) #s(literal -1/4 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	49.7%	(.f64 (pow.f64 k #s(literal -1/4 binary64)) (.f64 (pow.f64 k #s(literal -1/4 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
	99.0%	(.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)))))
▶	50.2%	(.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)))))
	50.2%	(.f64 #s(approx (pow k -1/2) (sqrt.f64 (/.f64 #s(literal 1 binary64) k))) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	49.8%	(neg.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))))))
	99.1%	#s(approx (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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))))
	77.8%	#s(approx (* (pow k -1/2) (/ (sqrt (* (* n (PI)) 2)) (pow (* (* n (PI)) 2) (/ k 2)))) (.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))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (sqrt.f64 k))))
	49.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k)))
	37.9%	#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))
	99.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (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.f64 (/.f64 #s(literal 1 binary64) k))))
▶	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n)))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
	50.2%	#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))))
	38.7%	#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))))
	50.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k))))
▶	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 k))))
	50.1%	#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))))
	38.9%	#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)))))
	50.2%	#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 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64))) k)))))
✓	50.2%	#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)))))
✓	38.8%	#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))))
	25.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 (.f64 (PI.f64) n) k (.f64 k (.f64 (PI.f64) n))) (.f64 k k))))
	38.7%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (.f64 n (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))) k) #s(literal 2 binary64))))
✓	39.0%	#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))))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
	38.8%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))))
▶	38.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))

Compiler

Compiled 1 808 to 1 431 computations (20.9% saved)

simplify38.0ms (0.3%)

Memory

6.5MiB live, 50.2MiB allocated; 6ms 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 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #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)) #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	(PI.f64)
cost-diff	0	(sqrt.f64 (PI.f64))
cost-diff	0	(.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 k)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 k))))
cost-diff	0	(/.f64 (PI.f64) k)
cost-diff	0	(sqrt.f64 (/.f64 (PI.f64) k))
cost-diff	0	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n)))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))))
cost-diff	0	(PI.f64)
cost-diff	0	(.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))
cost-diff	0	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
cost-diff	0	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
cost-diff	0	(*.f64 (PI.f64) n)
cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	298
0	70	298
1	105	290
2	135	290
3	178	290
4	227	290
5	330	290
6	522	290
7	628	290
8	717	290
9	754	290
10	759	290
0	759	290

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize159.0ms (1.3%)

Memory

-1.7MiB live, 331.0MiB allocated; 72ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.234375	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
accuracy	0.3405075195368841	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	14.773077834737425	(PI.f64)
accuracy	16.833478283393802	#s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.2623825195368841	(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k))
accuracy	0.76171875	(sqrt.f64 (PI.f64))
accuracy	14.773077834737425	(PI.f64)
accuracy	16.74467888611289	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 k))))
accuracy	0.21875	(/.f64 (PI.f64) k)
accuracy	0.2421875	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n)))
accuracy	14.773077834737425	(PI.f64)
accuracy	16.74467888611289	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))))
accuracy	0.171875	(.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))
accuracy	7.383922507187071	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
accuracy	14.773077834737425	(PI.f64)
accuracy	16.74467888611289	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
accuracy	0.1953125	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
accuracy	0.24218750000000003	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
accuracy	0.3632779541189607	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
accuracy	14.773077834737425	(PI.f64)

Samples

58.0ms	195×	0	valid
30.0ms	61×	0	exit

Compiler

Compiled 254 to 38 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-mult: 27.0ms (42.6% of total)

ival-sqrt: 15.0ms (23.7% of total)

ival-div: 9.0ms (14.2% of total)

ival-pow: 8.0ms (12.6% of total)

ival-pi: 1.0ms (1.6% of total)

ival-sub: 1.0ms (1.6% 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)

series56.0ms (0.5%)

Memory

17.8MiB live, 155.4MiB allocated; 16ms collecting garbage

Counts

22 → 48

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
15.0ms	n	@	-inf	((/ (sqrt (* 2 (* (PI) n))) (* (pow (* 2 (* (PI) n)) (* k 1/2)) (sqrt k))) (sqrt (* 2 (* (PI) n))) (* 2 (* (PI) n)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (PI) (* n (/ 2 k)))) (* (PI) (* n (/ 2 k))) (PI) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* 2 n))) (sqrt (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (PI)) (/ (sqrt (* 2 n)) (sqrt k))) (sqrt (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* 2 (* (PI) n)) (* k 1/2)) (/ (sqrt (* 2 n)) (sqrt k)) (* (sqrt (* (PI) n)) (sqrt 2)))
14.0ms	n	@	inf	((/ (sqrt (* 2 (* (PI) n))) (* (pow (* 2 (* (PI) n)) (* k 1/2)) (sqrt k))) (sqrt (* 2 (* (PI) n))) (* 2 (* (PI) n)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (PI) (* n (/ 2 k)))) (* (PI) (* n (/ 2 k))) (PI) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* 2 n))) (sqrt (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (PI)) (/ (sqrt (* 2 n)) (sqrt k))) (sqrt (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* 2 (* (PI) n)) (* k 1/2)) (/ (sqrt (* 2 n)) (sqrt k)) (* (sqrt (* (PI) n)) (sqrt 2)))
11.0ms	n	@	0	((/ (sqrt (* 2 (* (PI) n))) (* (pow (* 2 (* (PI) n)) (* k 1/2)) (sqrt k))) (sqrt (* 2 (* (PI) n))) (* 2 (* (PI) n)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (PI) (* n (/ 2 k)))) (* (PI) (* n (/ 2 k))) (PI) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* 2 n))) (sqrt (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (PI)) (/ (sqrt (* 2 n)) (sqrt k))) (sqrt (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* 2 (* (PI) n)) (* k 1/2)) (/ (sqrt (* 2 n)) (sqrt k)) (* (sqrt (* (PI) n)) (sqrt 2)))
9.0ms	k	@	-inf	((/ (sqrt (* 2 (* (PI) n))) (* (pow (* 2 (* (PI) n)) (* k 1/2)) (sqrt k))) (sqrt (* 2 (* (PI) n))) (* 2 (* (PI) n)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (PI) (* n (/ 2 k)))) (* (PI) (* n (/ 2 k))) (PI) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* 2 n))) (sqrt (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (PI)) (/ (sqrt (* 2 n)) (sqrt k))) (sqrt (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* 2 (* (PI) n)) (* k 1/2)) (/ (sqrt (* 2 n)) (sqrt k)) (* (sqrt (* (PI) n)) (sqrt 2)))
3.0ms	k	@	0	((/ (sqrt (* 2 (* (PI) n))) (* (pow (* 2 (* (PI) n)) (* k 1/2)) (sqrt k))) (sqrt (* 2 (* (PI) n))) (* 2 (* (PI) n)) (* (PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt (* (PI) (* n (/ 2 k)))) (* (PI) (* n (/ 2 k))) (PI) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (/ (PI) k)) (sqrt (* 2 n))) (sqrt (/ (PI) k)) (/ (PI) k) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (* (sqrt (PI)) (/ (sqrt (* 2 n)) (sqrt k))) (sqrt (PI)) (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/ 1 (sqrt k)) (sqrt k) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (pow (* 2 (* (PI) n)) (* k 1/2)) (/ (sqrt (* 2 n)) (sqrt k)) (* (sqrt (* (PI) n)) (sqrt 2)))

simplify198.0ms (1.6%)

Memory

30.6MiB live, 271.7MiB allocated; 19ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	203	983
1	704	953
2	2876	894
3	7678	888
0	8005	864

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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

rewrite173.0ms (1.4%)

Memory

-25.8MiB live, 261.7MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	227
0	70	219
1	190	204
2	870	163
0	8693	163

Stop Event

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

Counts

22 → 1 850

Calls

Call 1

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

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

eval457.0ms (3.7%)

Memory: 22.1MiB live, 617.5MiB allocated; 153ms collecting garbage
Compiler: Compiled 54 748 to 6 624 computations (87.9% saved)

prune143.0ms (1.2%)

Memory

-0.5MiB live, 215.9MiB allocated; 23ms collecting garbage

Pruning

35 alts after pruning (28 fresh and 7 done)

	Pruned	Kept	Total
New	2 065	18	2 083
Fresh	16	10	26
Picked	1	4	5
Done	1	3	4
Total	2 083	35	2 118

Accuracy

100.0%

Counts

2 118 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.0%	(/.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 k))
	26.0%	(/.f64 (pow.f64 (*.f64 #s(literal 0 binary64) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 8 binary64))) (sqrt.f64 k))
	46.9%	(/.f64 (pow.f64 (.f64 #s(literal -2 binary64) n) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/4 binary64) k))) (sqrt.f64 k))
	99.2%	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
	97.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (pow.f64 (+.f64 n n) (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
✓	99.3%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
	42.7%	(.f64 (pow.f64 (.f64 k k) #s(literal -1/4 binary64)) #s(approx (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 #s(literal 2 binary64)))))
	99.0%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) #s(approx (pow ( (* 2 (PI)) n) (/ (- 1 k) 2)) (pow.f64 (.f64 (.f64 (PI.f64) n) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
✓	50.2%	(.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)))))
	77.8%	#s(approx (/ (sqrt (* 2 (* (PI) n))) (* (pow (* 2 (* (PI) n)) (* k 1/2)) (sqrt k))) (.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))))
	99.1%	#s(approx (* (pow k -1/2) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.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))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 k))))
	99.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (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.f64 (/.f64 #s(literal 1 binary64) k))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (pow.f64 (.f64 (PI.f64) (PI.f64)) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) n)) (sqrt.f64 k))))
	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))))
✓	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 (.f64 n (PI.f64)))))
	11.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 n)))
	50.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n)))
	50.2%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k))))
	38.7%	#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))))
✓	50.1%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 k))))
✓	38.8%	#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))))
	9.3%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (/.f64 (fma.f64 n k (.f64 k n)) (.f64 k k))))
✓	39.0%	#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))))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
	9.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 n k) #s(literal 2 binary64))))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 (PI.f64) n))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
	9.5%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)))
	39.0%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))
	4.9%	#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (/.f64 (sqrt.f64 (PI.f64)) k) #s(literal 2 binary64)))))

Compiler

Compiled 2 947 to 1 069 computations (63.7% saved)

regimes124.0ms (1%)

Memory

9.3MiB live, 144.8MiB allocated; 18ms collecting garbage

Counts

77 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

46.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
35.0ms	n
22.0ms	k
16.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.3%	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))))`
99.3%	1	`k`
99.3%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes80.0ms (0.6%)

Memory

2.5MiB live, 106.5MiB allocated; 11ms collecting garbage

Counts

62 → 1

Calls

Call 1

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

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

Calls

4 calls:

29.0ms	n
17.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
15.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
15.0ms	k

Results

Accuracy	Segments	Branch
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.3%	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))))`
99.3%	1	`k`
99.3%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes119.0ms (1%)

Memory

-34.3MiB live, 101.4MiB allocated; 12ms collecting garbage

Counts

52 → 1

Calls

Call 1

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

Outputs

#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))))

Calls

4 calls:

46.0ms	k
16.0ms	n
13.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) 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
99.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
99.1%	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))))`
99.1%	1	`k`
99.1%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes51.0ms (0.4%)

Memory

30.4MiB live, 82.9MiB allocated; 8ms collecting garbage

Counts

43 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

16.0ms	k
11.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms	n
10.0ms	(.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
66.3%	7	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
95.8%	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))))`
95.9%	2	`k`
66.3%	7	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes44.0ms (0.4%)

Memory

-5.6MiB live, 86.3MiB allocated; 5ms collecting garbage

Counts

39 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

12.0ms	k
11.0ms	n
10.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
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
50.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
50.3%	1	`n`
52.9%	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))))`
52.9%	2	`k`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes10.0ms (0.1%)

Memory

15.8MiB live, 15.8MiB allocated; 0ms collecting garbage

Counts

15 → 2

Calls

Call 1

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

Outputs

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

Calls

2 calls:

5.0ms	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
52.9%	2	`k`
52.9%	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)

regimes27.0ms (0.2%)

Memory

-21.1MiB live, 24.8MiB allocated; 4ms collecting garbage

Counts

14 → 3

Calls

Call 1

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

Calls

4 calls:

14.0ms	k
4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	n
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
39.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
39.0%	1	`n`
41.6%	2	`k`
43.3%	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))))`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes8.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated; 0ms collecting garbage

Counts

11 → 2

Calls

Call 1

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

Outputs

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

Calls

2 calls:

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
39.0%	1	`k`
40.6%	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)

regimes10.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated; 0ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

Calls

3 calls:

3.0ms

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

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
39.0%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
39.0%	1	`n`
39.0%	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 22 to 21 computations (4.5% saved)

regimes32.0ms (0.3%)

Memory

-56.9MiB live, 8.7MiB allocated; 10ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

25.0ms	(.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
38.9%	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))))`
38.9%	1	`k`
38.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
38.9%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes8.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB 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 (/.f64 #s(literal 2 binary64) k) n)))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.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 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))

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

Calls

4 calls:

2.0ms	k
2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
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
9.5%	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))))`
9.5%	1	`k`
9.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
9.5%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

regimes6.0ms (0%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

Accuracy

Total -3.1b remaining (-5.4%)

Threshold costs -3.1b (-5.4%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Calls

4 calls:

1.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
1.0ms	k
1.0ms	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))))

Results

Accuracy	Segments	Branch
9.5%	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))))`
9.5%	1	`k`
9.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
9.5%	1	`n`

Compiler

Compiled 23 to 23 computations (0% saved)

bsearch20.0ms (0.2%)

Memory

14.5MiB live, 14.5MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	55481269269179.1	138437233205634290.0

Samples

12.0ms

128×

valid

Compiler

Compiled 323 to 290 computations (10.2% saved)

Precisions

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

ival-pow: 3.0ms (32.8% of total)

ival-div: 2.0ms (21.9% of total)

ival-mult: 2.0ms (21.9% of total)

ival-pi: 1.0ms (10.9% of total)

ival-sub: 1.0ms (10.9% of total)

ival-sqrt: 1.0ms (10.9% 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)

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	3.7070830632752696e-131

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	3.7070830632752696e-131

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.673112066407306e+153	1.780459542943999e+155
0.0ms	0.0	3.7070830632752696e-131

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.673112066407306e+153	1.780459542943999e+155

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify32.0ms (0.3%)

Memory

-0.3MiB live, 45.5MiB allocated; 3ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	538
1	126	508
2	149	508
3	172	508
4	189	508
5	208	508
6	242	508
7	304	508
8	335	508
9	368	508
10	378	508

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 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))))
(if (<=.f64 k #s(literal 7500000000000000 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) (/.f64 (pow.f64 (.f64 #s(literal -2 binary64) n) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/4 binary64) k))) (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 (fma.f64 n k (.f64 k n)) (.f64 k k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))))
(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 n k (.f64 k n)) (.f64 k 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)))))
(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 n k (.f64 k n)) (.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 5000000000000000184737728440291132704904589914921344225961389276075271829673609798608256554852704163723255876843616333657168501674786702085523096224137216 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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 n)))))
(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 5000000000000000184737728440291132704904589914921344225961389276075271829673609798608256554852704163723255876843616333657168501674786702085523096224137216 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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.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 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)))

Outputs
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (pow.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 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))))
#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 (pow.f64 k #s(literal -1 binary64)))))
(if (<=.f64 k #s(literal 7500000000000000 binary64)) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))) (/.f64 (pow.f64 (.f64 #s(literal -2 binary64) n) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/4 binary64) k))) (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 (fma.f64 n k (.f64 k n)) (.f64 k k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))))
(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 n k (.f64 k n)) (.f64 k k)))) #s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) (sqrt.f64 n))))
(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 n k (.f64 k n)) (.f64 k 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)))))
(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 n k (.f64 k n)) (.f64 k 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)))))
(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 n k (.f64 k n)) (.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 5000000000000000184737728440291132704904589914921344225961389276075271829673609798608256554852704163723255876843616333657168501674786702085523096224137216 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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 n)))))
(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 n k (.f64 k n)) (.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 5000000000000000184737728440291132704904589914921344225961389276075271829673609798608256554852704163723255876843616333657168501674786702085523096224137216 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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 n)))))
(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 5000000000000000184737728440291132704904589914921344225961389276075271829673609798608256554852704163723255876843616333657168501674786702085523096224137216 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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 n))))
(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 5000000000000000184737728440291132704904589914921344225961389276075271829673609798608256554852704163723255876843616333657168501674786702085523096224137216 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 (/.f64 #s(literal 2 binary64) k)) (sqrt.f64 n))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (.f64 (/.f64 n k) (PI.f64)) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (.f64 (PI.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 n k) #s(literal 2 binary64))))
#s(approx (* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2))) (sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) k) n)))

derivations1.0s (8.3%)

Memory

0.8MiB live, 814.5MiB allocated; 101ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	228
0	71	231
1	199	205
2	838	205
3	7804	205
0	8141	205
0	56	291
0	96	269
1	268	262
2	1292	262
0	8229	262
0	13	38
0	22	38
1	83	35
2	446	35
3	4007	29
0	8921	29
0	44	227
0	70	219
1	190	204
2	870	163
0	8693	163
0	120	502
1	378	489
2	1377	453
3	4131	453
0	8166	441

Stop Event

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

Compiler

Compiled 538 to 106 computations (80.3% saved)

preprocess123.0ms (1%)

Memory: -28.5MiB live, 115.6MiB allocated; 16ms collecting garbage
Compiler: Compiled 1 108 to 238 computations (78.5% 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	44	295
0	71	295
1	102	291
2	134	291
3	185	291
4	231	291
5	292	291
6	404	291
7	635	291
8	772	291
9	822	291
10	852	291
0	852	291

Iter	Nodes	Cost
0	44	298
0	70	298
1	105	290
2	135	290
3	178	290
4	227	290
5	330	290
6	522	290
7	628	290
8	717	290
9	754	290
10	759	290
0	759	290

Iter	Nodes	Cost
0	103	538
1	126	508
2	149	508
3	172	508
4	189	508
5	208	508
6	242	508
7	304	508
8	335	508
9	368	508
10	378	508

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	44	295
0	71	295
1	102	291
2	134	291
3	185	291
4	231	291
5	292	291
6	404	291
7	635	291
8	772	291
9	822	291
10	852	291
0	852	291

Iter	Nodes	Cost
0	44	298
0	70	298
1	105	290
2	135	290
3	178	290
4	227	290
5	330	290
6	522	290
7	628	290
8	717	290
9	754	290
10	759	290
0	759	290

Iter	Nodes	Cost
0	103	538
1	126	508
2	149	508
3	172	508
4	189	508
5	208	508
6	242	508
7	304	508
8	335	508
9	368	508
10	378	508

start0.0ms (0%)

analyze194.0ms (1.6%)

sample4.5s (36.7%)

explain384.0ms (3.1%)

preprocess49.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify19.0ms (0.2%)

localize41.0ms (0.3%)

series113.0ms (0.9%)

simplify197.0ms (1.6%)

rewrite380.0ms (3.1%)

eval244.0ms (2%)

prune70.0ms (0.6%)

simplify165.0ms (1.3%)

localize367.0ms (3%)

series329.0ms (2.7%)

simplify252.0ms (2%)

rewrite303.0ms (2.5%)

eval246.0ms (2%)

prune34.0ms (0.3%)

simplify25.0ms (0.2%)

localize142.0ms (1.1%)

series60.0ms (0.5%)

simplify154.0ms (1.2%)

rewrite232.0ms (1.9%)

eval259.0ms (2.1%)

prune631.0ms (5.1%)

simplify38.0ms (0.3%)

localize159.0ms (1.3%)

series56.0ms (0.5%)

simplify198.0ms (1.6%)

rewrite173.0ms (1.4%)

eval457.0ms (3.7%)

prune143.0ms (1.2%)

regimes124.0ms (1%)

regimes80.0ms (0.6%)

regimes119.0ms (1%)

regimes51.0ms (0.4%)

regimes44.0ms (0.4%)

regimes10.0ms (0.1%)

regimes27.0ms (0.2%)

regimes8.0ms (0.1%)

regimes10.0ms (0.1%)

regimes32.0ms (0.3%)

regimes8.0ms (0.1%)

regimes6.0ms (0%)

bsearch20.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

simplify32.0ms (0.3%)

derivations1.0s (8.3%)

preprocess123.0ms (1%)

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	44	295
0	71	295
1	102	291
2	134	291
3	185	291
4	231	291
5	292	291
6	404	291
7	635	291
8	772	291
9	822	291
10	852	291
0	852	291

Iter	Nodes	Cost
0	44	298
0	70	298
1	105	290
2	135	290
3	178	290
4	227	290
5	330	290
6	522	290
7	628	290
8	717	290
9	754	290
10	759	290
0	759	290

Iter	Nodes	Cost
0	103	538
1	126	508
2	149	508
3	172	508
4	189	508
5	208	508
6	242	508
7	304	508
8	335	508
9	368	508
10	378	508