Details

analyze368.0ms (5.4%)

Algorithm

1×

Search

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.1s (46%)

Results

1.3s	8256×	body	128	valid
1.1s	1359×	body	1024	invalid
377.0ms	702×	body	512	invalid
179.0ms	1203×	body	128	invalid
110.0ms	344×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify50.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-/l*_binary64`
625×	`associate-/r*_binary64`
461×	`div-sub_binary64`
445×	`distribute-frac-neg_binary64`
288×	`distribute-rgt-neg-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	65	22
3	129	22
4	280	22
5	634	20
6	1332	20
7	3121	20
8	4914	20
9	4550	20

prune4.0ms (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

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.9b	(.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)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.7b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series418.0ms (6.2%)

Counts

3 → 48

Calls

3 calls:

221.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
194.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite61.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

657×	`log-prod_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
222×	`log-pow_binary64`
132×	`add-sqr-sqrt_binary64`

Counts

3 → 82

Calls

3 calls:

59.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
59.0ms	(.f64 (.f64 2 (PI.f64)) n)
59.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	273	43
2	3155	43
3	5471	43

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
455×	`distribute-rgt-neg-in_binary64`
454×	`distribute-lft-neg-in_binary64`
435×	`associate-r_binary64`
375×	`associate-l_binary64`

Counts

130 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1180
1	181	1020
2	524	864
3	2685	862
4	5113	862

prune117.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	92	8	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Error

0.0b

Counts

102 → 8

Alt Table

Status	Error	Program
	1.2b	(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
▶	0.7b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))) (sqrt.f64 k))
	1.0b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	11.7b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) 2) k)))
	23.9b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (fma.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 k -1/2)))))) (sqrt.f64 k))
	0.8b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	0.8b	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))

Compiler

Compiled 2498 to 1757 computations (29.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))) (sqrt.f64 k))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))
✓	0.6b	(sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))

series267.0ms (3.9%)

Counts

3 → 24

Calls

3 calls:

200.0ms

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

55.0ms

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

12.0ms

(sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))

rewrite67.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

263×	`log-pow_binary64`
256×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`
144×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`

Counts

3 → 91

Calls

3 calls:

65.0ms

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

65.0ms

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

65.0ms

(sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	296	46
2	3652	44
3	4904	44

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-neg_binary64`
711×	`cancel-sign-sub-inv_binary64`
375×	`exp-prod_binary64`
282×	`distribute-rgt-neg-in_binary64`
276×	`distribute-lft-neg-in_binary64`

Counts

115 → 104

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	536
1	147	504
2	389	436
3	1931	431
4	4287	422
5	5040	422

prune204.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	144	8	152

Error

Counts

152 → 8

Alt Table

Status	Error	Program
	11.7b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) 2) k)))
	23.9b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (fma.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2)) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 k -1/2)))))) (sqrt.f64 k))
	0.8b	(.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (pow.f64 k -1/2)))
	0.8b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
▶	0.7b	(/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))) (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n))) (sqrt.f64 k))
	1.2b	(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
	0.9b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) 1/4) 2)) (sqrt.f64 k))
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))

Compiler

Compiled 3706 to 2568 computations (30.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (.f64 2 (PI.f64)) n)
	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))
✓	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) k)
	0.6b	(sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))

series192.0ms (2.8%)

Counts

1 → 24

Calls

1 calls:

192.0ms

(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)

rewrite40.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

742×	`log1p-expm1-u_binary64`
742×	`expm1-log1p-u_binary64`
150×	`expm1-udef_binary64`
150×	`log1p-udef_binary64`
84×	`add-sqr-sqrt_binary64`

Counts

1 → 20

Calls

1 calls:

39.0ms

(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) k)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	167	11
2	1938	11
3	4978	11

simplify106.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

767×	`unswap-sqr_binary64`
551×	`associate-+l+_binary64`
467×	`associate-+r+_binary64`
433×	`*-commutative_binary64`
264×	`unsub-neg_binary64`

Counts

44 → 32

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	455
1	126	411
2	310	329
3	1430	329
4	3509	329
5	5230	329

prune274.0ms (4.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	153	8	161

Error

Counts

161 → 8

Alt Table

Status	Error	Program
	0.8b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	0.8b	(/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 k))
▶	0.8b	(.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (pow.f64 k -1/2)))
✓	0.7b	(/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))) (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n))) (sqrt.f64 k))
	1.2b	(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
	0.9b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) 1/4) 2)) (sqrt.f64 k))
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	11.7b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) 2) k)))

Compiler

Compiled 5893 to 4161 computations (29.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (pow.f64 k -1/2)))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)
	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))
	0.6b	(sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))

series48.0ms (0.7%)

Counts

1 → 0

Calls

1 calls:

48.0ms

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

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

786×	`log-prod_binary64`
263×	`log-pow_binary64`
255×	`expm1-udef_binary64`
255×	`log1p-udef_binary64`
145×	`add-sqr-sqrt_binary64`

Counts

1 → 18

Calls

1 calls:

56.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	297	23
2	3459	23
3	5841	23

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune164.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	119	8	127

Error

Counts

127 → 8

Alt Table

Status	Error	Program
	0.8b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
	0.8b	(/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 k))
✓	0.8b	(.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (pow.f64 k -1/2)))
	0.9b	(.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64)))) (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (pow.f64 k -1/2)))
✓	0.7b	(/.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))) (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n))) (sqrt.f64 k))
	1.2b	(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
	0.9b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) 1/4) 2)) (sqrt.f64 k))
	11.7b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) 2) k)))

Compiler

Compiled 3098 to 2291 computations (26% saved)

regimes862.0ms (12.7%)

Accuracy

Total 0.5b remaining (94.3%)

Threshold costs 0.5b (94.3%)

Counts

151 → 1

Compiler

Compiled 16384 to 13095 computations (20.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	16	27
2	16	27

end178.0ms (2.6%)

Compiler: Compiled 250 to 196 computations (21.6% saved)

Details

analyze368.0ms (5.4%)

sample3.1s (46%)

simplify50.0ms (0.7%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series418.0ms (6.2%)

rewrite61.0ms (0.9%)

simplify57.0ms (0.8%)

prune117.0ms (1.7%)

localize9.0ms (0.1%)

series267.0ms (3.9%)

rewrite67.0ms (1%)

simplify69.0ms (1%)

prune204.0ms (3%)

localize16.0ms (0.2%)

series192.0ms (2.8%)

rewrite40.0ms (0.6%)

simplify106.0ms (1.6%)

prune274.0ms (4.1%)

localize13.0ms (0.2%)

series48.0ms (0.7%)

rewrite57.0ms (0.8%)

simplify6.0ms (0.1%)

prune164.0ms (2.4%)

regimes862.0ms (12.7%)

simplify2.0ms (0%)

end178.0ms (2.6%)

Profiling