Details

analyze345.0ms (3.9%)

Algorithm

1×

Search

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.2s (36.3%)

Results

1.3s	8256×	body	128	valid
1.1s	1419×	body	1024	invalid
350.0ms	645×	body	512	invalid
189.0ms	1199×	body	128	invalid
115.0ms	347×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify60.0ms (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%)

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
▶	0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.4b	(.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	(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)

series711.0ms (8%)

Counts

3 → 48

Calls

3 calls:

457.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
250.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite158.0ms (1.8%)

Algorithm

3×	egg-rewrite

Rules

56×	`egg`
51×	`egg`
37×	`egg`

Counts

3 → 144

Calls

3 calls:

62.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
48.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
45.0ms	(.f64 (.f64 2 (PI.f64)) n)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	121	8
2	1359	8
3	5038	8
0	13	20
1	273	20
2	3155	20
3	5471	20
0	11	15
1	229	15
2	2504	15
3	4938	15

simplify62.0ms (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

192 → 161

Iterations

Useful iterations: 3 (0.0ms)

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

prune189.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	154	7	161
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	156	7	163

Error

0.0b

Counts

163 → 7

Alt Table

Status	Error	Program
	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))))
	0.5b	(.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)))
	0.5b	(/.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) n)) (fma.f64 k -1/2 1/2)) (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))))
	24.6b	(/.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))
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
▶	0.2b	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (sqrt.f64 k))

Compiler

Compiled 3588 to 2472 computations (31.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)))
✓	0.1b	(sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))
✓	0.2b	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (sqrt.f64 k))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)

series126.0ms (1.4%)

Counts

3 → 12

Calls

3 calls:

77.0ms

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

35.0ms

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

12.0ms

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

rewrite204.0ms (2.3%)

Algorithm

3×	egg-rewrite

Rules

61×	`egg`
39×	`egg`
30×	`egg`

Counts

3 → 130

Calls

3 calls:

93.0ms

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

66.0ms

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

43.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	296	22
2	3650	20
3	4958	20
0	7	10
1	141	10
2	1567	10
3	4988	10
0	12	26
1	250	17
2	2889	15
3	4989	15
4	4925	15

simplify95.0ms (1.1%)

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

142 → 137

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

prune393.0ms (4.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	247	4	251
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	251	7	258

Error

Counts

258 → 7

Alt Table

Status	Error	Program
	0.5b	(.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) 1/4) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) 1/4)))
	24.6b	(/.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))
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
▶	0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))))
	0.3b	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) 1) (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 k)))
	0.4b	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n (sqrt.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 2 (PI.f64))))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (sqrt.f64 k))

Compiler

Compiled 6232 to 4211 computations (32.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2)))
	0.1b	(sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))
✓	0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)

series348.0ms (3.9%)

Counts

2 → 12

Calls

2 calls:

270.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2)))
78.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))))

rewrite207.0ms (2.3%)

Algorithm

2×	egg-rewrite

Rules

63×	`egg`
50×	`egg`

Counts

2 → 113

Calls

2 calls:

144.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))))
60.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	302	29
2	3861	29
3	4993	29
4	5000	29
5	5041	29
0	12	19
1	255	19
2	3091	19
3	5451	19

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

680×	`exp-prod_binary64`
571×	`fma-neg_binary64`
526×	`exp-sum_binary64`
319×	`distribute-rgt-in_binary64`
294×	`distribute-lft-in_binary64`

Counts

125 → 117

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	336
1	89	312
2	185	312
3	687	276
4	2327	228
5	4543	228
6	5001	228

prune317.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	258	3	261
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	262	6	268

Error

Counts

268 → 6

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 (/.f64 k (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))))
	0.5b	(.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)))
	0.3b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))))
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	8.9b	(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 k (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))))
	0.4b	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n (sqrt.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 2 (PI.f64))))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (sqrt.f64 k))

Compiler

Compiled 6751 to 4580 computations (32.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1)
	0.1b	(sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))
✓	0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 (/.f64 k (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)

series358.0ms (4%)

Counts

2 → 24

Calls

2 calls:

259.0ms	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1)
98.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 (/.f64 k (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))))

rewrite128.0ms (1.4%)

Algorithm

2×	egg-rewrite

Rules

52×	`egg`
48×	`egg`

Counts

2 → 100

Calls

2 calls:

73.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 (/.f64 k (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))))
53.0ms	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	29
1	303	26
2	3772	26
3	5074	26
0	10	14
1	210	13
2	2380	13
3	5304	13

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

720×	`cancel-sign-sub-inv_binary64`
365×	`neg-mul-1_binary64`
358×	`neg-sub0_binary64`
296×	`fma-neg_binary64`
270×	`distribute-rgt-neg-in_binary64`

Counts

124 → 110

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	495
1	141	455
2	359	374
3	1778	373
4	4227	333
5	5109	333

prune307.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	254	6	260

Error

Counts

260 → 6

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 (/.f64 k (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))))
	0.5b	(.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)))
	0.3b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))))
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	8.9b	(sqrt.f64 (/.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 k (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) k) -1))))
	0.4b	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 n (sqrt.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 2 (PI.f64))))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2))) (sqrt.f64 k))

Compiler

Compiled 6279 to 4403 computations (29.9% saved)

regimes1.3s (15.1%)

Accuracy

Total 0.3b remaining (81.5%)

Threshold costs 0.3b (81.5%)

Counts

260 → 1

Compiler

Compiled 26183 to 20610 computations (21.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	18	28
2	18	28

end113.0ms (1.3%)

Compiler: Compiled 168 to 130 computations (22.6% saved)

Details

analyze345.0ms (3.9%)

sample3.2s (36.3%)

simplify60.0ms (0.7%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series711.0ms (8%)

rewrite158.0ms (1.8%)

simplify62.0ms (0.7%)

prune189.0ms (2.1%)

localize11.0ms (0.1%)

series126.0ms (1.4%)

rewrite204.0ms (2.3%)

simplify95.0ms (1.1%)

prune393.0ms (4.4%)

localize11.0ms (0.1%)

series348.0ms (3.9%)

rewrite207.0ms (2.3%)

simplify64.0ms (0.7%)

prune317.0ms (3.6%)

localize12.0ms (0.1%)

series358.0ms (4%)

rewrite128.0ms (1.4%)

simplify67.0ms (0.8%)

prune307.0ms (3.5%)

regimes1.3s (15.1%)

simplify2.0ms (0%)

end113.0ms (1.3%)

Profiling