Details

analyze375.0ms (5.8%)

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)

sample3.5s (53.3%)

Results

1.5s	8256×	body	128	valid
1.2s	1399×	body	1024	invalid
408.0ms	672×	body	512	invalid
196.0ms	1173×	body	128	invalid
123.0ms	321×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify48.0ms (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`

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

Stop Event

1×	node limit

Counts

1 → 2

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

0.4b

Counts

3 → 2

Alt Table

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

localize10.0ms (0.2%)

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

series483.0ms (7.4%)

Counts

3 → 48

Calls

3 calls:

244.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
236.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite60.0ms (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`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

58.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
58.0ms	(.f64 (.f64 2 (PI.f64)) n)
58.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

simplify52.0ms (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`

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

130 → 100

prune123.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	95	7	102

Error

0.0b

Counts

102 → 7

Alt Table

Status	Error	Program
	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)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
	0.5b	(/.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 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.6b	(.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)))
	21.4b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (fma.f64 1/8 (.f64 (.f64 k k) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) k)) (.f64 1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3))))))) (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 2504 to 1763 computations (29.6% saved)

localize14.0ms (0.2%)

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

series227.0ms (3.5%)

Counts

1 → 12

Calls

1 calls:

227.0ms

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

rewrite50.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

640×	`log-prod_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
221×	`log-pow_binary64`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	274	21
2	3021	21
3	5027	21

Stop Event

1×	node limit

Counts

1 → 18

Calls

1 calls:

50.0ms

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

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Rules

884×	`exp-prod_binary64`
511×	`exp-sum_binary64`
353×	`unsub-neg_binary64`
252×	`exp-neg_binary64`
237×	`exp-diff_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	372
1	72	372
2	139	276
3	484	276
4	1884	276
5	4240	276
6	4805	276
7	4937	276

Stop Event

1×	node limit

Counts

30 → 22

prune98.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Error

0.0b

Counts

85 → 7

Alt Table

Status	Error	Program
	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)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
▶	0.5b	(/.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 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.6b	(.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)))
	21.4b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (fma.f64 1/8 (.f64 (.f64 k k) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) k)) (.f64 1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3))))))) (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 2060 to 1549 computations (24.8% saved)

localize13.0ms (0.2%)

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	(/.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))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.4b	(sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))

series97.0ms (1.5%)

Counts

3 → 12

Calls

3 calls:

57.0ms

(/.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))

29.0ms

(*.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))

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`

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 87

Calls

3 calls:

65.0ms

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

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

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

simplify79.0ms (1.2%)

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`

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

Stop Event

1×	node limit

Counts

99 → 96

prune131.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	136	7	143

Error

Counts

143 → 7

Alt Table

Status	Error	Program
	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)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
✓	0.5b	(/.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 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.6b	(.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)))
▶	0.6b	(/.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 (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 3289 to 2244 computations (31.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
✓	0.2b	(*.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))))
✓	0.4b	(sqrt.f64 (*.f64 n (PI.f64)))

series97.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(/.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))
31.0ms	(.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))

rewrite75.0ms (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`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 103

Calls

4 calls:

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

simplify75.0ms (1.2%)

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`

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

Stop Event

1×	node limit

Counts

115 → 112

prune131.0ms (2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	4	0	4
Picked	0	1	1
Done	0	2	2
Total	129	6	135

Error

Counts

135 → 6

Alt Table

Status	Error	Program
	11.8b	(sqrt.f64 (/.f64 (.f64 (.f64 n (PI.f64)) (.f64 2 (pow.f64 (pow.f64 (.f64 (*.f64 n (PI.f64)) 2) k) -1))) k))
✓	0.5b	(/.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 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
✓	0.6b	(/.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 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2))))
	0.6b	(.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 k -1/2)))

Compiler

Compiled 3299 to 1922 computations (41.7% saved)

regimes539.0ms (8.3%)

Accuracy

Total 0.4b remaining (88.4%)

Threshold costs 0.4b (88.4%)

Counts

114 → 1

Compiler

Compiled 10862 to 8598 computations (20.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	20
1	19	20
2	18	20

Stop Event

1×

saturated

end109.0ms (1.7%)

Compiler: Compiled 154 to 116 computations (24.7% saved)

Details

analyze375.0ms (5.8%)

sample3.5s (53.3%)

simplify48.0ms (0.7%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series483.0ms (7.4%)

rewrite60.0ms (0.9%)

simplify52.0ms (0.8%)

prune123.0ms (1.9%)

localize14.0ms (0.2%)

series227.0ms (3.5%)

rewrite50.0ms (0.8%)

simplify66.0ms (1%)

prune98.0ms (1.5%)

localize13.0ms (0.2%)

series97.0ms (1.5%)

rewrite67.0ms (1%)

simplify79.0ms (1.2%)

prune131.0ms (2%)

localize13.0ms (0.2%)

series97.0ms (1.5%)

rewrite75.0ms (1.2%)

simplify75.0ms (1.2%)

prune131.0ms (2%)

regimes539.0ms (8.3%)

simplify2.0ms (0%)

end109.0ms (1.7%)

Profiling