Details

analyze607.0ms (6.6%)

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)

sample4.9s (53.1%)

Results

2.1s	8256×	body	128	valid
1.6s	1336×	body	1024	invalid
659.0ms	717×	body	512	invalid
289.0ms	1190×	body	128	invalid
169.0ms	336×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify85.0ms (0.9%)

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

prune7.0ms (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

0.4b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series510.0ms (5.5%)

Counts

3 → 48

Calls

3 calls:

300.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
205.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
5.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite87.0ms (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:

85.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
85.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
85.0ms	(.f64 (.f64 2 (PI.f64)) n)

Iterations

Useful iterations: 0 (0.0ms)

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

simplify53.0ms (0.6%)

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 → 99

Iterations

Useful iterations: 3 (0.0ms)

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

prune145.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	93	8	101

Error

0.0b

Counts

101 → 8

Alt Table

Status	Error	Program
	0.7b	(/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) n)) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.6b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
	0.4b	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
▶	0.3b	(/.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))
	21.0b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2)) (*.f64 k -1/2)))) (sqrt.f64 k))
	0.7b	(.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 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))

Compiler

Compiled 2487 to 1743 computations (29.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series111.0ms (1.2%)

Counts

3 → 12

Calls

3 calls:

63.0ms

(/.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))

39.0ms

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

8.0ms

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

rewrite79.0ms (0.9%)

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 → 87

Calls

3 calls:

77.0ms

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

77.0ms

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

77.0ms

(/.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))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	67
1	296	49
2	3652	45
3	4904	45

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
452×	`distribute-rgt-neg-in_binary64`
449×	`distribute-lft-neg-in_binary64`
443×	`associate-r_binary64`
374×	`associate-l_binary64`

Counts

99 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	508
1	125	476
2	434	416
3	2240	399
4	4904	399
5	5000	399
6	4973	399

prune222.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	134	8	142

Error

Counts

142 → 8

Alt Table

Status	Error	Program
✓	0.3b	(/.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))
	0.4b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)))) (sqrt.f64 k))
▶	0.3b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)))
	9.4b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 2 (PI.f64)) n)))))
	0.6b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
	0.7b	(.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 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))

Compiler

Compiled 3321 to 2273 computations (31.6% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)))
	0.2b	(sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.4b	(.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2))

series137.0ms (1.5%)

Counts

2 → 0

Calls

2 calls:

90.0ms	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)))
46.0ms	(.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2))

rewrite123.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Counts

2 → 36

Calls

2 calls:

121.0ms	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)))
121.0ms	(.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	297	39
2	3455	37
3	5851	37

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune220.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	102	7	109

Error

Counts

109 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.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))
▶	0.4b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)))) (sqrt.f64 k))
	0.6b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (pow.f64 (.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) 1/4) (pow.f64 k -1/4)) 2))
✓	0.3b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)))
	9.4b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 2 (PI.f64)) n)))))
	0.6b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))

Compiler

Compiled 2664 to 1985 computations (25.5% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 n (PI.f64)))
✓	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)))) (sqrt.f64 k))
✓	0.3b	(*.f64 n (PI.f64))
✓	0.3b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2))))

series189.0ms (2%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)))) (sqrt.f64 k))
57.0ms	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2))))
10.0ms	(sqrt.f64 (*.f64 n (PI.f64)))
4.0ms	(*.f64 n (PI.f64))

rewrite113.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

286×	`expm1-udef_binary64`
286×	`log1p-udef_binary64`
161×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`

Counts

4 → 103

Calls

4 calls:

109.0ms	(sqrt.f64 (*.f64 n (PI.f64)))
108.0ms	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)))) (sqrt.f64 k))
108.0ms	(*.f64 n (PI.f64))
108.0ms	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	73
1	336	67
2	4100	67
3	4961	67

simplify120.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
452×	`distribute-rgt-neg-in_binary64`
449×	`distribute-lft-neg-in_binary64`
443×	`associate-r_binary64`
374×	`associate-l_binary64`

Counts

115 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	508
1	125	476
2	434	416
3	2240	399
4	4904	399
5	5000	399
6	4973	399

prune226.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	129	6	135

Error

Counts

135 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (*.f64 k -1/2))) (pow.f64 k -1/2)))
	0.6b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (pow.f64 (.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) 1/4) (pow.f64 k -1/4)) 2))
✓	0.3b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (pow.f64 k -1/2)))
	9.4b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 2 (PI.f64)) n)))))
✓	0.3b	(/.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))
	0.6b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))

Compiler

Compiled 3310 to 1935 computations (41.5% saved)

regimes910.0ms (9.8%)

Accuracy

Total 0.3b remaining (81.3%)

Threshold costs 0.3b (81.3%)

Counts

113 → 1

Compiler

Compiled 9538 to 7586 computations (20.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	19	32
2	19	32

end221.0ms (2.4%)

Compiler: Compiled 179 to 139 computations (22.3% saved)

Details

analyze607.0ms (6.6%)

sample4.9s (53.1%)

simplify85.0ms (0.9%)

prune7.0ms (0.1%)

localize25.0ms (0.3%)

series510.0ms (5.5%)

rewrite87.0ms (0.9%)

simplify53.0ms (0.6%)

prune145.0ms (1.6%)

localize9.0ms (0.1%)

series111.0ms (1.2%)

rewrite79.0ms (0.9%)

simplify80.0ms (0.9%)

prune222.0ms (2.4%)

localize24.0ms (0.3%)

series137.0ms (1.5%)

rewrite123.0ms (1.3%)

simplify11.0ms (0.1%)

prune220.0ms (2.4%)

localize25.0ms (0.3%)

series189.0ms (2%)

rewrite113.0ms (1.2%)

simplify120.0ms (1.3%)

prune226.0ms (2.4%)

regimes910.0ms (9.8%)

simplify2.0ms (0%)

end221.0ms (2.4%)

Profiling