Details

analyze350.0ms (6.8%)

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)

sample3.1s (59.6%)

Results

1.3s	8256×	body	128	valid
1.1s	1380×	body	1024	invalid
378.0ms	681×	body	512	invalid
176.0ms	1142×	body	128	invalid
108.0ms	335×	body	256	invalid

Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess33.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

421×	`div-sub_binary64`
418×	`associate-/l*_binary64`
293×	`associate-l_binary64`
268×	`associate-/r*_binary64`
224×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	52	44
2	119	44
3	256	44
4	668	44
5	1836	40
6	4163	40
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 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.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 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 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 2 (*.f64 (PI.f64) k)) (-.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 k (.f64 2 (PI.f64))) (*.f64 1/2 (-.f64 1 n))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 k 2)) (fma.f64 -1/2 n 1/2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 k 2)) (fma.f64 n -1/2 1/2)) (sqrt.f64 n))

Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-/l*_binary64`
544×	`associate-/r*_binary64`
257×	`associate-*l/_binary64`
214×	`unswap-sqr_binary64`
214×	`div-sub_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	140	22
4	354	22
5	958	20
6	2187	20

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

prune5.0ms (0.1%)

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

0.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.7b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
▶	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

series99.0ms (1.9%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
30.0ms	k	@	0	(/.f64 1 (sqrt.f64 k))
28.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
19.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
8.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
3.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite62.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

260×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
191×	`prod-diff_binary64`
152×	`add-sqr-sqrt_binary64`
146×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	307	51
2	3925	51

Stop Event

1×	node limit

Counts

4 → 87

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) 2) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 n (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 n (-.f64 1/2 (/.f64 k 2))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (-.f64 1/2 (/.f64 k 2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k 2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (-.f64 1/2 (/.f64 k 2)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.f64 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 k) -1) (pow.f64 (cbrt.f64 (sqrt.f64 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 k 1/4) -1) (pow.f64 (pow.f64 k 1/4) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 k) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 k -1/2)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) 2) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) 1) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) -1) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 k 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 2 (-.f64 1/2 (/.f64 k 2)))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) 1))))))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-neg_binary64`
453×	`associate-r_binary64`
390×	`associate-l_binary64`
254×	`distribute-rgt-in_binary64`
248×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	1204
1	193	1124
2	669	968
3	3849	968

Stop Event

1×	node limit

Counts

135 → 107

Calls

Call 1

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

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

prune149.0ms (2.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	96	11	107
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	11	109

Error

0.0b

Counts

109 → 11

Alt Table

Status	Error	Program
	22.1b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (-.f64 (.f64 (.f64 (.f64 1/8 k) k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)) (.f64 1/2 (.f64 k (log.f64 (.f64 n (*.f64 2 (PI.f64)))))))))))
	10.1b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) k))
	0.9b	(.f64 (.f64 (pow.f64 (pow.f64 k 1/4) -1) (pow.f64 (pow.f64 k 1/4) -1)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
	1.3b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))) 3)
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
	1.3b	(/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))) 2) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))))
	1.2b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (/.f64 k 2)))))
	1.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.8b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))

Compiler

Compiled 2799 to 2000 computations (28.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
✓	0.3b	(*.f64 (PI.f64) n)
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.4b	(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))

series22.0ms (0.4%)

Counts

3 → 12

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
5.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
2.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
2.0ms	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))
2.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))

rewrite62.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

270×	`expm1-udef_binary64`
270×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
152×	`pow1_binary64`
151×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	46
1	324	37
2	4271	37

Stop Event

1×	node limit

Counts

3 → 95

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (.f64 2 n) (PI.f64))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))) (cbrt.f64 (.f64 (.f64 2 n) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) 1/4) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) 2))) (sqrt.f64 (cbrt.f64 (.f64 (.f64 2 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) 2)) 1/2) (pow.f64 (cbrt.f64 (.f64 (.f64 2 n) (PI.f64))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) 1/2) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 2 n) (PI.f64)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (.f64 2 n) (PI.f64))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) n))) 1)))) (#(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 sqrt.f64 (pow.f64 (.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) n))))) (#(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 expm1.f64 (log1p.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 exp.f64 (log.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (PI.f64) n)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (neg.f64 (.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 (.f64 k 1/2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 (.f64 k 1/2) 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))) (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))) (.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))) (.f64 (sqrt.f64 k) (neg.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (sqrt.f64 k))) (neg.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))) 1) (.f64 (neg.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 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Outputs

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

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	60
1	5	60

Stop Event

1×

saturated

Counts

107 → 96

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))

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))

prune189.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	140	7	147

Error

Counts

147 → 7

Alt Table

Status	Error	Program
	0.8b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
	0.7b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 (.f64 k 1/2) 1/2))))
	10.1b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) k))
	0.6b	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))) (sqrt.f64 (*.f64 (PI.f64) n))))
▶	0.5b	(/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))) (pow.f64 k -1/2)) (neg.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))))
	1.1b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))

Compiler

Compiled 3349 to 2224 computations (33.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 (.f64 2 n) (PI.f64)) (*.f64 k 1/2))
✓	0.3b	(.f64 (.f64 2 n) (PI.f64))
✓	0.3b	(.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 2 n) (PI.f64)))) (pow.f64 k -1/2))
✓	0.4b	(sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))

series11.0ms (0.2%)

Counts

4 → 36

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	n	@	0	(.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 2 n) (PI.f64)))) (pow.f64 k -1/2))
1.0ms	k	@	0	(.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 2 n) (PI.f64)))) (pow.f64 k -1/2))
1.0ms	n	@	-inf	(.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 2 n) (PI.f64)))) (pow.f64 k -1/2))
1.0ms	k	@	-inf	(.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 2 n) (PI.f64)))) (pow.f64 k -1/2))
1.0ms	n	@	inf	(.f64 (neg.f64 (sqrt.f64 (.f64 (*.f64 2 n) (PI.f64)))) (pow.f64 k -1/2))

rewrite57.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

246×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
236×	`log-pow_binary64`
156×	`add-sqr-sqrt_binary64`
149×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	320	47
2	3828	47

Stop Event

1×	node limit

Counts

4 → 102

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (neg.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 2 n)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 2) (pow.f64 (.f64 n (PI.f64)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 n)) (neg.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64))))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 (.f64 2 n))) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 -1 (cbrt.f64 (.f64 2 (.f64 n (PI.f64))))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 -1 (sqrt.f64 (.f64 2 n))) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2)) (+.f64 0 (fma.f64 2 (.f64 n (PI.f64)) (.f64 0 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 n (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 2 (.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (.f64 2 n)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (pow.f64 (exp.f64 (PI.f64)) (.f64 2 n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (+.f64 1 (expm1.f64 (.f64 2 (.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 2 n) 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (.f64 2 n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 2 n)) k) (pow.f64 (sqrt.f64 (PI.f64)) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (PI.f64)) k) (pow.f64 (sqrt.f64 (.f64 2 n)) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 k 4)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 k 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (.f64 k 1/2)) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (.f64 k 1/2)) (pow.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 k 1/2)) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 k 1/2)) (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) 1/2))))))

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-+l+_binary64`
542×	`associate-+r+_binary64`
179×	`unswap-sqr_binary64`
170×	`associate-l_binary64`
154×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	632
1	139	596
2	408	510
3	2140	506

Stop Event

1×	node limit

Counts

138 → 116

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

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

prune156.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	137	7	144

Error

Counts

144 → 7

Alt Table

Status	Error	Program
	0.8b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
	0.7b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 (.f64 k 1/2) 1/2))))
	10.1b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 2 (-.f64 1/2 (/.f64 k 2)))) k))
▶	0.6b	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))) (sqrt.f64 (*.f64 (PI.f64) n))))
✓	0.5b	(/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))) (pow.f64 k -1/2)) (neg.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))))
	1.1b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k 2))))

Compiler

Compiled 3854 to 2768 computations (28.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (PI.f64) n)
	0.3b	(.f64 (.f64 2 n) (PI.f64))
✓	0.3b	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))) (sqrt.f64 (*.f64 (PI.f64) n))))
✓	0.4b	(sqrt.f64 (*.f64 (PI.f64) n))

series8.0ms (0.2%)

Counts

2 → 0

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	n	@	-inf	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))) (sqrt.f64 (*.f64 (PI.f64) n))))
1.0ms	k	@	0	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))) (sqrt.f64 (*.f64 (PI.f64) n))))
1.0ms	n	@	0	(sqrt.f64 (*.f64 (PI.f64) n))
1.0ms	n	@	inf	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))) (sqrt.f64 (*.f64 (PI.f64) n))))
1.0ms	k	@	inf	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))) (sqrt.f64 (*.f64 (PI.f64) n))))

rewrite62.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

177×	`add-sqr-sqrt_binary64`
174×	`pow1_binary64`
173×	`*-un-lft-identity_binary64`
164×	`add-log-exp_binary64`
164×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	364	33
2	4815	33

Stop Event

1×	node limit

Counts

2 → 70

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (cbrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) n)) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) 1/4) (pow.f64 (*.f64 (PI.f64) n) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) n) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) n))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))) (cbrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))) (cbrt.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))) (sqrt.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))))))))) (#(struct:change 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(/.f64 (pow.f64 2 1/4) (pow.f64 (*.f64 (PI.f64) n) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 2) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))) (cbrt.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))) (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))))) (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))) 1) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))) (cbrt.f64 (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))) (pow.f64 (*.f64 (PI.f64) n) 1/4)) (pow.f64 (*.f64 (PI.f64) n) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)))) (sqrt.f64 (PI.f64))) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k))) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (sqrt.f64 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (/.f64 (*.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) k)) (*.f64 (PI.f64) n))))) 1))))))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

70 → 70

Calls

Call 1

Inputs

Outputs

prune121.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	108	6	114

Error

Counts

114 → 6

Alt Table

Status	Error	Program
	0.8b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1/2 (*.f64 k 1/2))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (-.f64 1/2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (/.f64 k 2)))))
	0.5b	(.f64 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) k)))) (sqrt.f64 (PI.f64))) (sqrt.f64 n))
✓	0.6b	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))) (sqrt.f64 (*.f64 (PI.f64) n))))
✓	0.5b	(/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64)))) (pow.f64 k -1/2)) (neg.f64 (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (.f64 k 1/2))))
	9.9b	(sqrt.f64 (/.f64 2 (/.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) k)) (.f64 (PI.f64) n))))

Compiler

Compiled 2592 to 1600 computations (38.3% saved)

regimes414.0ms (8%)

Accuracy

Total 0.4b remaining (96.7%)

Threshold costs 0.4b (96.7%)

Counts

140 → 1

Compiler

Compiled 2928 to 1957 computations (33.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	35
1	31	35
2	43	35
3	53	35
4	58	35
5	60	35

Stop Event

1×

saturated

Calls

Call 1

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

Outputs

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

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

end119.0ms (2.3%)

Stop Event

1×

fuel

Compiler

Compiled 174 to 136 computations (21.8% saved)

Details

analyze350.0ms (6.8%)

sample3.1s (59.6%)

preprocess33.0ms (0.6%)

simplify18.0ms (0.4%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

series99.0ms (1.9%)

rewrite62.0ms (1.2%)

simplify45.0ms (0.9%)

prune149.0ms (2.9%)

localize11.0ms (0.2%)

series22.0ms (0.4%)

rewrite62.0ms (1.2%)

simplify8.0ms (0.2%)

prune189.0ms (3.7%)

localize13.0ms (0.3%)

series11.0ms (0.2%)

rewrite57.0ms (1.1%)

simplify31.0ms (0.6%)

prune156.0ms (3%)

localize13.0ms (0.3%)

series8.0ms (0.2%)

rewrite62.0ms (1.2%)

simplify7.0ms (0.1%)

prune121.0ms (2.4%)

regimes414.0ms (8%)

simplify3.0ms (0.1%)

end119.0ms (2.3%)

Profiling