Details

analyze397.0ms (5.5%)

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 (45.3%)

Results

1.3s	8256×	body	128	valid
1.2s	1419×	body	1024	invalid
370.0ms	645×	body	512	invalid
185.0ms	1199×	body	128	invalid
131.0ms	347×	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

0.3b

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)

series546.0ms (7.5%)

Counts

3 → 48

Calls

3 calls:

289.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
254.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite75.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

82× egg-rr

Counts

3 → 82

Calls

2 calls:

74.0ms	((.f64 (.f64 2 (PI.f64)) n) (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

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

simplify51.0ms (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

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

prune129.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	7	101

Error

0.0b

Counts

101 → 7

Alt Table

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

Compiler

Compiled 2391 to 1669 computations (30.2% 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)

series131.0ms (1.8%)

Counts

3 → 12

Calls

3 calls:

80.0ms

(/.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)))

12.0ms

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

rewrite72.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

87× egg-rr

Counts

3 → 87

Calls

2 calls:

70.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

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

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

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

prune195.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Error

0.0b

Counts

141 → 7

Alt Table

Status	Error	Program
	8.5b	(.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)))))
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	0.5b	(.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)))
✓	0.2b	(/.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))
	0.5b	(/.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))
	0.4b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) -1)
▶	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))

Compiler

Compiled 3239 to 2211 computations (31.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(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))))

series138.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(/.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))
39.0ms	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2))))
9.0ms	(sqrt.f64 (*.f64 n (PI.f64)))
2.0ms	(*.f64 n (PI.f64))

rewrite85.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

103× egg-rr

Counts

4 → 103

Calls

2 calls:

82.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

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

simplify74.0ms (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

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

prune154.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	128	7	135

Error

Counts

135 → 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)))
	8.9b	(sqrt.f64 (/.f64 (.f64 (.f64 n (PI.f64)) (.f64 2 (pow.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) k) -1))) k))
✓	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))
	0.5b	(/.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))
▶	0.4b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) -1)
	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)
✓	0.3b	(/.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))

Compiler

Compiled 3412 to 2016 computations (40.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series820.0ms (11.3%)

Counts

2 → 24

Calls

2 calls:

473.0ms	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) -1)
347.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))

rewrite101.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

82× egg-rr

Counts

2 → 82

Calls

2 calls:

98.0ms	((/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) -1))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	313	40
2	3499	40
3	4977	40
4	5750	40
0	0	0
1	0	0

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

813×	`exp-sum_binary64`
475×	`exp-prod_binary64`
400×	`distribute-rgt-in_binary64`
382×	`distribute-lft-in_binary64`
331×	`fma-neg_binary64`

Counts

106 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	732
1	92	708
2	173	516
3	699	516
4	2894	516
5	5056	516

prune164.0ms (2.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	145	7	152

Error

Counts

152 → 7

Alt Table

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

Compiler

Compiled 3354 to 2366 computations (29.5% saved)

regimes498.0ms (6.9%)

Accuracy

Total 0.3b remaining (81.8%)

Threshold costs 0.3b (81.8%)

Counts

97 → 1

Compiler

Compiled 9081 to 7422 computations (18.3% 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

end127.0ms (1.7%)

Compiler: Compiled 182 to 140 computations (23.1% saved)

Details

analyze397.0ms (5.5%)

sample3.3s (45.3%)

simplify50.0ms (0.7%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series546.0ms (7.5%)

rewrite75.0ms (1%)

simplify51.0ms (0.7%)

prune129.0ms (1.8%)

localize9.0ms (0.1%)

series131.0ms (1.8%)

rewrite72.0ms (1%)

simplify73.0ms (1%)

prune195.0ms (2.7%)

localize11.0ms (0.2%)

series138.0ms (1.9%)

rewrite85.0ms (1.2%)

simplify74.0ms (1%)

prune154.0ms (2.1%)

localize10.0ms (0.1%)

series820.0ms (11.3%)

rewrite101.0ms (1.4%)

simplify51.0ms (0.7%)

prune164.0ms (2.3%)

regimes498.0ms (6.9%)

simplify2.0ms (0%)

end127.0ms (1.7%)

Profiling