Details

analyze353.0ms (4.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	25%	57.9%	7
18%	20.3%	61.8%	8
18.3%	16.4%	65.3%	9
18.5%	13.7%	67.8%	10
18.6%	11.5%	69.9%	11
18.7%	10%	71.3%	12
18.7%	8.9%	72.4%	13
18.7%	8.2%	73.1%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.2s (39.4%)

Results

1.3s	8256×	body	128	valid
1.1s	1360×	body	1024	invalid
404.0ms	715×	body	512	invalid
183.0ms	1148×	body	128	invalid
114.0ms	356×	body	256	invalid

Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess44.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

503×	`rule-37_binary64`
503×	`rule-38_binary64`
503×	`rule-39_binary64`
501×	`rule-40_binary64`
416×	`rule-29_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	139	44
2	517	44
3	2697	44
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

420×	`rule-16-rev_binary64`
275×	`rule-37_binary64`
275×	`rule-38_binary64`
275×	`rule-39_binary64`
274×	`rule-40_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	91	22
2	314	22
3	1550	22

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))

Compiler

Compiled 100 to 80 computations (20% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))
✓	0.3b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))
✓	0.3b	(*.f64 (PI.f64) n)

series423.0ms (5.3%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
72.0ms	n	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))
67.0ms	n	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))
66.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))
64.0ms	n	@	inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))
63.0ms	n	@	-inf	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))

rewrite67.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

267×	`rule-45_binary64`
156×	`add-sqr-sqrt_binary64`
149×	`pow1_binary64`
149×	`rules-30_binary64`
149×	`rules-31_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	350	44
2	4822	44

Stop Event

1×	node limit

Counts

3 → 110

Calls

Call 1

Inputs
(*.f64 (PI.f64) n)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) n) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) n))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) n) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 1 n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 n (/.f64 1 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (PI.f64) n)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 (PI.f64) n) 3) (pow.f64 (.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (PI.f64) n 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 n (PI.f64) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (PI.f64) n) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 2) (cbrt.f64 (.f64 (PI.f64) n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (PI.f64) n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) n)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) 2) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (sqrt.f64 k)) (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 1/2 k))) (/.f64 (pow.f64 2 (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) 2) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (/.f64 1/2 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 1 (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) (-.f64 1/2 (.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) (-.f64 1/2 (.f64 1/2 k)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 2 (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 n 2) (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (.f64 n 2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (neg.f64 (-.f64 1/2 (.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (log.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k))) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) (-.f64 1/2 (.f64 1/2 k)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 2 (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 1/2 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) n) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) n) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)) (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 1 n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 n (/.f64 1 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (PI.f64) n)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (PI.f64) n) 3) (pow.f64 (*.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (PI.f64) n 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 n (PI.f64) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (PI.f64) n) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 2) (cbrt.f64 (*.f64 (PI.f64) n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) 2) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 k)) (+.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 1/2 (*.f64 1/2 k))) (/.f64 (pow.f64 2 (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) 2) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1/2 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 1 (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2) (-.f64 1/2 (*.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2) (-.f64 1/2 (*.f64 1/2 k)))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 2 (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (*.f64 n 2) (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 n 2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (+.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (neg.f64 (-.f64 1/2 (*.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) 3) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2) (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) k))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2) (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 1/2 (*.f64 1/2 k)) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) 2) (-.f64 1/2 (*.f64 1/2 k)))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 2 (-.f64 1/2 (*.f64 1/2 k))) (pow.f64 (*.f64 (PI.f64) n) (-.f64 1/2 (*.f64 1/2 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))))))))

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

408×	`rule-19-rev_binary64`
385×	`rule-37_binary64`
385×	`rule-38_binary64`
385×	`rule-39_binary64`
381×	`rule-40_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	77	1136
1	527	1120
2	2034	1120

Stop Event

1×	node limit

Counts

158 → 132

Calls

Call 1

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

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

prune165.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	122	10	132
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	123	11	134

Error

0.0b

Counts

134 → 11

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) (sqrt.f64 k))
	25.4b	(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) 3) (pow.f64 k 3/2)))
	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	16.6b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k)) 3))
	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k)))
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k))) (sqrt.f64 k))) 2)
	0.7b	(/.f64 (pow.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 3)) (-.f64 1/2 (*.f64 k 1/2))) (sqrt.f64 k))
	0.5b	(/.f64 (.f64 (pow.f64 (PI.f64) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 n 2) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
	0.5b	(.f64 (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 1/2 k))) (/.f64 (pow.f64 2 (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))
	24.1b	(/.f64 (-.f64 (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2)))))) (.f64 1/2 (.f64 k (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (log.f64 (.f64 n (.f64 (PI.f64) 2)))))))) (sqrt.f64 k))
	0.5b	(/.f64 (/.f64 (.f64 (PI.f64) (.f64 n 2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))

Compiler

Compiled 3342 to 2316 computations (30.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))
✓	0.2b	(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
✓	0.3b	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) (sqrt.f64 k))
✓	0.3b	(.f64 (PI.f64) (.f64 n 2))

series211.0ms (2.6%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
37.0ms	n	@	0	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) (sqrt.f64 k))
35.0ms	n	@	inf	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) (sqrt.f64 k))
28.0ms	k	@	-inf	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) (sqrt.f64 k))
18.0ms	n	@	-inf	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) (sqrt.f64 k))
15.0ms	n	@	0	(/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))

rewrite45.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

173×	`add-sqr-sqrt_binary64`
166×	`pow1_binary64`
166×	`rules-30_binary64`
166×	`rules-31_binary64`
166×	`rules-32_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	398	64

Stop Event

1×	node limit

Counts

4 → 153

Calls

Call 1

Inputs
(.f64 (PI.f64) (.f64 n 2))
(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) (sqrt.f64 k))
(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
(/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (.f64 n 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (PI.f64) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (.f64 n 2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) (.f64 n 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (PI.f64) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (.f64 n 2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (.f64 n 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (PI.f64) (.f64 n 2))) (.f64 (PI.f64) (.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 1 (.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 n 2) (/.f64 1 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (.f64 n 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (PI.f64) (.f64 n 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (PI.f64) (.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (PI.f64) (.f64 n 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 n (.f64 (PI.f64) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 n 2) (PI.f64) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (PI.f64) (.f64 n 2)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) (*.f64 n 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (/.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) (pow.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) 2) (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (/.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) 2) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k)) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (/.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) 2) (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (/.f64 1/2 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k)) (sqrt.f64 k))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2) (.f64 1/2 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/2 (neg.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))) 2) (.f64 1/2 (cbrt.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 2) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 n) (pow.f64 (.f64 (PI.f64) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))) (.f64 1/2 (sqrt.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) 1/2) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (/.f64 1 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (/.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3)) 1/2) (.f64 (PI.f64) (.f64 n 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (.f64 n 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 2) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (pow.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) 2) (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) 2) (.f64 1 (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (.f64 1 (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (neg.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) 2) (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))))))))

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

808×	`rule-40_binary64`
290×	`fma-def_binary64`
256×	`fma-neg_binary64`
188×	`rule-2-rev_binary64`
183×	`rule-12_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	392
1	220	388
2	830	388
3	4431	388

Stop Event

1×	node limit

Counts

177 → 162

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
1/2
(-.f64 1/2 (.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))))
(-.f64 (+.f64 1/2 (.f64 1/4 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)))) (.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))))
(-.f64 (+.f64 1/2 (.f64 1/4 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)))) (+.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (.f64 1/12 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 3)))))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
1/2
(-.f64 1/2 (.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))))
(-.f64 1/2 (.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/2 k)))
(-.f64 (+.f64 1/2 (.f64 1/4 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)))) (.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))))
(+.f64 1/2 (-.f64 (.f64 1/4 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(-.f64 (fma.f64 1/4 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2) k)) 1/2) (.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/2 k)))
(fma.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2) (.f64 k (.f64 1/4 k)) (-.f64 1/2 (.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))))
(-.f64 (+.f64 1/2 (.f64 1/4 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)))) (+.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (.f64 1/12 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 3)))))
(+.f64 1/2 (-.f64 (.f64 1/4 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (fma.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 1/12 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 3))))))
(-.f64 (fma.f64 1/4 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2) k)) 1/2) (fma.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 3) (*.f64 1/12 (pow.f64 k 3)))))
(-.f64 (fma.f64 1/4 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)) 1/2) (fma.f64 1/2 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 1/12 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) 3)))))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))
(/.f64 1/2 (pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k))

prune579.0ms (7.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	317	7	324
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	324	11	335

Error

0.0b

Counts

335 → 11

Alt Table

Status	Error	Program
	0.5b	(.f64 (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 1/2 k))) (/.f64 (pow.f64 2 (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))
	0.6b	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) 3)) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) (sqrt.f64 k))
	16.5b	(cbrt.f64 (pow.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k)) 3))
	0.4b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))) 2)
▶	0.3b	(.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k)) (sqrt.f64 k)))
	0.9b	(.f64 (cbrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (/.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) 2) (sqrt.f64 k)))
	0.5b	(/.f64 (.f64 (pow.f64 (PI.f64) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 n 2) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k)))
	0.7b	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (pow.f64 (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) 2)) (sqrt.f64 k))
	0.3b	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (sqrt.f64 n) (pow.f64 (.f64 (PI.f64) 2) 1/2))) (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) (sqrt.f64 k))
	0.5b	(/.f64 (/.f64 (.f64 (PI.f64) (.f64 n 2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))

Compiler

Compiled 10939 to 7611 computations (30.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
✓	0.2b	(/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))
✓	0.2b	(.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k)) (sqrt.f64 k)))
	0.3b	(.f64 (PI.f64) (.f64 n 2))

series234.0ms (2.9%)

Counts

2 → 0

Calls

12 calls:

Time	Variable		Point	Expression
37.0ms	n	@	0	(.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k)) (sqrt.f64 k)))
36.0ms	n	@	inf	(.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k)) (sqrt.f64 k)))
28.0ms	k	@	-inf	(.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k)) (sqrt.f64 k)))
25.0ms	k	@	-inf	(/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))
19.0ms	n	@	0	(/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (sqrt.f64 k))

rewrite39.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

173×	`add-sqr-sqrt_binary64`
166×	`pow1_binary64`
166×	`rules-30_binary64`
166×	`rules-31_binary64`
166×	`rules-32_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	66
1	398	51

Stop Event

1×	node limit

Counts

2 → 86

Calls

Call 1

Inputs

(*.f64 (+.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) k)) (sqrt.f64 k)))

(/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) k)) (sqrt.f64 k))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 0 (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (*.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (*.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) 1/2))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (*.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 0 (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (*.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (*.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k)) (/.f64 (sqrt.f64 k) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (*.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)) (*.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1/2 (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (*.f64 2 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k))) (pow.f64 (cbrt.f64 (sqrt.f64 k)) 2)) (cbrt.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3)) (*.f64 (sqrt.f64 k) (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) 1/2))) (*.f64 2 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 2) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k)) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k))) (/.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k))) 2) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (pow.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 2) (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k))) (/.f64 (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k)) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))) (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 2) (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k)) (/.f64 1/2 (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))))

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

86 → 86

Calls

Call 1

Inputs

Outputs

prune533.0ms (6.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	326	3	329
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	331	9	340

Error

Counts

340 → 9

Alt Table

Status	Error	Program
	0.9b	(.f64 (cbrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (/.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) 2) (sqrt.f64 k)))
	0.5b	(/.f64 (.f64 (pow.f64 (PI.f64) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 n 2) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k)))
	0.5b	(.f64 (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 1/2 k))) (/.f64 (pow.f64 2 (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))
▶	0.3b	(/.f64 (/.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1 (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
	0.3b	(/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k)) (/.f64 (sqrt.f64 k) (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))))
	0.4b	(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 2)
	0.7b	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (pow.f64 (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) 2)) (sqrt.f64 k))
	0.5b	(/.f64 (/.f64 (.f64 (PI.f64) (.f64 n 2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))

Compiler

Compiled 10956 to 7416 computations (32.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))
✓	0.2b	(/.f64 (/.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1 (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
✓	0.3b	(/.f64 1 (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))
	0.3b	(*.f64 (PI.f64) n)

series257.0ms (3.2%)

Counts

3 → 0

Calls

15 calls:

Time	Variable		Point	Expression
37.0ms	n	@	0	(/.f64 (/.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1 (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
36.0ms	n	@	inf	(/.f64 (/.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1 (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
29.0ms	k	@	-inf	(/.f64 (/.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1 (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
24.0ms	k	@	-inf	(/.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))
21.0ms	n	@	-inf	(/.f64 (/.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1 (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))

rewrite47.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

189×	`add-sqr-sqrt_binary64`
181×	`pow1_binary64`
181×	`rules-30_binary64`
181×	`rules-31_binary64`
181×	`rules-32_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	91
1	445	91

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

Inputs

(/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))

(/.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))

(/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 1/2 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (*.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (/.f64 0 (*.f64 1 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (/.f64 0 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (*.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 1 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) 1/2))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 1 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (*.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (/.f64 0 (*.f64 1 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (/.f64 0 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (*.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (neg.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (/.f64 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (cbrt.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (*.f64 1 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (cbrt.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (*.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (cbrt.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (*.f64 (cbrt.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (cbrt.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (cbrt.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))) (cbrt.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (/.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))) (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (/.f64 (sqrt.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (*.f64 1 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (*.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (sqrt.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (sqrt.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (/.f64 (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (/.f64 1 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (*.f64 1/2 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (/.f64 1/2 (*.f64 1 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/2 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) (*.f64 1/2 (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (*.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))) (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (/.f64 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)) (+.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (*.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))) (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))) (*.f64 1 (cbrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) (*.f64 1 (sqrt.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k)) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k)) (/.f64 1/2 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k))) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (*.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))))))))

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

92 → 92

Calls

Call 1

Inputs

Outputs

prune336.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	191	9	200

Error

Counts

200 → 9

Alt Table

Status	Error	Program
	0.9b	(.f64 (cbrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k))) (/.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) 2) (sqrt.f64 k)))
	0.5b	(/.f64 (.f64 (pow.f64 (PI.f64) (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 n 2) (-.f64 1/2 (.f64 1/2 k)))) (sqrt.f64 k))
	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (.f64 1/2 k)))) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k)))
	0.5b	(.f64 (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 1/2 k))) (/.f64 (pow.f64 2 (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 k)))
✓	0.3b	(/.f64 (/.f64 1/2 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) (sqrt.f64 k))) (/.f64 1 (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
	0.3b	(/.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k)) (/.f64 (sqrt.f64 k) (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))))
	0.4b	(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) k) (sqrt.f64 k)))) 2)
	0.7b	(/.f64 (.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (pow.f64 (sqrt.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) k))) 2)) (sqrt.f64 k))
	0.5b	(/.f64 (/.f64 (.f64 (PI.f64) (.f64 n 2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))

Compiler

Compiled 7110 to 4307 computations (39.4% saved)

regimes1.2s (14.7%)

Accuracy

Total 0.4b remaining (93.6%)

Threshold costs 0.4b (93.6%)

Counts

228 → 1

Compiler

Compiled 25482 to 19618 computations (23% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	46

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (/.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k)) 0)

Outputs
(fma.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) k)) (/.f64 (+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 k)) 0)

end176.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 311 to 237 computations (23.8% saved)

Details

analyze353.0ms (4.4%)

sample3.2s (39.4%)

preprocess44.0ms (0.5%)

simplify29.0ms (0.4%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series423.0ms (5.3%)

rewrite67.0ms (0.8%)

simplify41.0ms (0.5%)

prune165.0ms (2.1%)

localize11.0ms (0.1%)

series211.0ms (2.6%)

rewrite45.0ms (0.6%)

simplify49.0ms (0.6%)

prune579.0ms (7.2%)

localize12.0ms (0.1%)

series234.0ms (2.9%)

rewrite39.0ms (0.5%)

simplify8.0ms (0.1%)

prune533.0ms (6.6%)

localize12.0ms (0.1%)

series257.0ms (3.2%)

rewrite47.0ms (0.6%)

simplify8.0ms (0.1%)

prune336.0ms (4.2%)

regimes1.2s (14.7%)

simplify1.0ms (0%)

end176.0ms (2.2%)

Profiling