Details

analyze337.0ms (4.7%)

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)

sample3.3s (46.4%)

Results

1.3s	8256×	body	128	valid
1.1s	1419×	body	1024	invalid
465.0ms	711×	body	512	invalid
194.0ms	1100×	body	128	invalid
108.0ms	340×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify51.0ms (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

0.3b

Counts

3 → 2

Alt Table

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

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

series446.0ms (6.3%)

Counts

3 → 48

Calls

3 calls:

237.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
201.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
7.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite74.0ms (1%)

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 → 85

Calls

3 calls:

72.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
72.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
72.0ms	(.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

simplify52.0ms (0.7%)

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

133 → 102

Iterations

Useful iterations: 3 (0.0ms)

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

prune125.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	95	7	102
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	7	104

Error

0.0b

Counts

104 → 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))
	0.8b	(.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)))
	0.9b	(.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))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
	0.7b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
	22.6b	(/.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 2 (.f64 n (PI.f64)))) 2)) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 k -1/2)))))) (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 2516 to 1753 computations (30.3% 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)))
✓	0.1b	(sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))
✓	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)

series98.0ms (1.4%)

Counts

3 → 12

Calls

3 calls:

59.0ms

(/.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))

30.0ms

(*.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))

rewrite70.0ms (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 → 89

Calls

3 calls:

68.0ms

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

68.0ms

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

68.0ms

(/.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

simplify73.0ms (1%)

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

101 → 98

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

prune135.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	139	6	145

Error

Counts

145 → 6

Alt Table

Status	Error	Program
	0.9b	(.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))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 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)))
▶	0.4b	(/.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))
	0.7b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.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 3336 to 2275 computations (31.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (*.f64 n (PI.f64)))
✓	0.2b	(/.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))))

series111.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(/.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))
32.0ms	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2))))
6.0ms	(sqrt.f64 (*.f64 n (PI.f64)))
2.0ms	(*.f64 n (PI.f64))

rewrite86.0ms (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 → 106

Calls

4 calls:

84.0ms	(sqrt.f64 (*.f64 n (PI.f64)))
84.0ms	(/.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))
84.0ms	(*.f64 n (PI.f64))
84.0ms	(.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

simplify73.0ms (1%)

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

118 → 115

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

prune155.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Error

Counts

138 → 6

Alt Table

Status	Error	Program
	0.9b	(.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))))
▶	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 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)))
✓	0.4b	(/.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))
	0.7b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.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 3522 to 2082 computations (40.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 k))
✓	0.2b	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
✓	0.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
	0.3b	(*.f64 n (PI.f64))

series428.0ms (6%)

Counts

3 → 28

Calls

3 calls:

227.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
197.0ms	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
4.0ms	(sqrt.f64 (/.f64 1 k))

rewrite62.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

679×	`log-prod_binary64`
249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
239×	`log-pow_binary64`
144×	`add-sqr-sqrt_binary64`

Counts

3 → 76

Calls

3 calls:

60.0ms	(sqrt.f64 (/.f64 1 k))
60.0ms	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
60.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	44
1	307	39
2	3283	39
3	5477	39

simplify48.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

104 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	900
1	174	820
2	515	648
3	2667	646
4	5080	646

prune119.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	108	6	114

Error

Counts

114 → 6

Alt Table

Status	Error	Program
	0.9b	(.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))))
✓	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 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)))
✓	0.4b	(/.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))
	0.7b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (*.f64 2 (PI.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 2383 to 1659 computations (30.4% saved)

regimes1.1s (15.3%)

Accuracy

Total 0.3b remaining (86.4%)

Threshold costs 0.3b (86.4%)

Counts

209 → 1

Compiler

Compiled 20746 to 16337 computations (21.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	19	31
2	19	31

end132.0ms (1.9%)

Compiler: Compiled 187 to 144 computations (23% saved)

Details

analyze337.0ms (4.7%)

sample3.3s (46.4%)

simplify51.0ms (0.7%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series446.0ms (6.3%)

rewrite74.0ms (1%)

simplify52.0ms (0.7%)

prune125.0ms (1.8%)

localize9.0ms (0.1%)

series98.0ms (1.4%)

rewrite70.0ms (1%)

simplify73.0ms (1%)

prune135.0ms (1.9%)

localize11.0ms (0.2%)

series111.0ms (1.6%)

rewrite86.0ms (1.2%)

simplify73.0ms (1%)

prune155.0ms (2.2%)

localize11.0ms (0.2%)

series428.0ms (6%)

rewrite62.0ms (0.9%)

simplify48.0ms (0.7%)

prune119.0ms (1.7%)

regimes1.1s (15.3%)

simplify2.0ms (0%)

end132.0ms (1.9%)

Profiling