Details

analyze339.0ms (5.4%)

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)

sample3.0s (48.4%)

Results

1.3s	8256×	body	128	valid
1.0s	1302×	body	1024	invalid
359.0ms	668×	body	512	invalid
165.0ms	1115×	body	128	invalid
113.0ms	345×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-/l*_binary64`
544×	`associate-/r*_binary64`
257×	`associate-*l/_binary64`
214×	`unswap-sqr_binary64`
214×	`div-sub_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	140	22
4	354	22
5	958	20
6	2187	20

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (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 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

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

series483.0ms (7.7%)

Counts

3 → 48

Calls

3 calls:

262.0ms	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
219.0ms	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
2.0ms	(*.f64 (PI.f64) n)

rewrite56.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`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	40
1	274	40
2	3319	40

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

55.0ms	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
55.0ms	(*.f64 (PI.f64) n)
54.0ms	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
433×	`associate-r_binary64`
373×	`associate-l_binary64`
176×	`distribute-rgt-in_binary64`
172×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1144
1	183	984
2	587	828
3	3443	826

Stop Event

1×	node limit

Counts

130 → 99

prune118.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	95	6	101

Error

0.0b

Counts

101 → 6

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
	21.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (fma.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 k k)) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 k -1/2)))))) (sqrt.f64 k))
▶	0.5b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
	0.7b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
	0.5b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))

Compiler

Compiled 2393 to 1640 computations (31.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series497.0ms (7.9%)

Counts

3 → 48

Calls

3 calls:

280.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
211.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
6.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite52.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`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	44
1	274	44
2	3212	44

Stop Event

1×	node limit

Counts

3 → 60

Calls

3 calls:

51.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
51.0ms	(.f64 n (.f64 2 (PI.f64)))
51.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
433×	`associate-r_binary64`
373×	`associate-l_binary64`
176×	`distribute-rgt-in_binary64`
172×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1180
1	183	1020
2	587	864
3	3443	862

Stop Event

1×	node limit

Counts

108 → 78

prune89.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	79	5	84

Error

0.0b

Counts

84 → 5

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n)))) (pow.f64 k -1/2))
	0.8b	(.f64 (.f64 (pow.f64 (*.f64 n 2) (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))
	21.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (fma.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (.f64 k k)) (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 k -1/2)))))) (sqrt.f64 k))
	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
▶	0.5b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))

Compiler

Compiled 1934 to 1381 computations (28.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series99.0ms (1.6%)

Counts

3 → 12

Calls

3 calls:

56.0ms

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

33.0ms

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

10.0ms

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

rewrite58.0ms (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`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	67
1	298	49
2	3841	45

Stop Event

1×	node limit

Counts

3 → 87

Calls

3 calls:

56.0ms

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

56.0ms

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

56.0ms

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

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
451×	`distribute-rgt-neg-in_binary64`
449×	`distribute-lft-neg-in_binary64`
437×	`associate-r_binary64`
372×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	508
1	127	476
2	460	416
3	2920	414

Stop Event

1×	node limit

Counts

99 → 96

prune141.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	135	6	141

Error

0.0b

Counts

141 → 6

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))
	9.8b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 2 (.f64 (PI.f64) n))))))
▶	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))
	0.5b	(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n)))) (pow.f64 k -1/2))
	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) 2)) (sqrt.f64 k))

Compiler

Compiled 3259 to 2078 computations (36.2% saved)

localize15.0ms (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))))

series113.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(/.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))))
12.0ms	(sqrt.f64 (*.f64 n (PI.f64)))
6.0ms	(*.f64 n (PI.f64))

rewrite71.0ms (1.1%)

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	339	67
2	4334	67

Stop Event

1×	node limit

Counts

4 → 103

Calls

4 calls:

69.0ms	(sqrt.f64 (*.f64 n (PI.f64)))
69.0ms	(/.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))
69.0ms	(*.f64 n (PI.f64))
69.0ms	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2))))

simplify32.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
451×	`distribute-rgt-neg-in_binary64`
449×	`distribute-lft-neg-in_binary64`
437×	`associate-r_binary64`
372×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	508
1	127	476
2	460	416
3	2920	414

Stop Event

1×	node limit

Counts

115 → 112

prune127.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	129	5	134

Error

Counts

134 → 5

Alt Table

Status	Error	Program
	0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) (.f64 2 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) -1)))) (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))
	0.5b	(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n)))) (pow.f64 k -1/2))
	10.4b	(sqrt.f64 (/.f64 (.f64 (.f64 n (PI.f64)) (.f64 2 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k) -1))) k))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) 2)) (sqrt.f64 k))

Compiler

Compiled 3294 to 2027 computations (38.5% saved)

regimes653.0ms (10.4%)

Accuracy

Total 0.2b remaining (68.3%)

Threshold costs 0.2b (68.3%)

Counts

144 → 1

Compiler

Compiled 12570 to 10074 computations (19.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	21	31

Stop Event

1×

saturated

end99.0ms (1.6%)

Compiler: Compiled 151 to 114 computations (24.5% saved)

Details

analyze339.0ms (5.4%)

sample3.0s (48.4%)

simplify18.0ms (0.3%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

series483.0ms (7.7%)

rewrite56.0ms (0.9%)

simplify47.0ms (0.7%)

prune118.0ms (1.9%)

localize11.0ms (0.2%)

series497.0ms (7.9%)

rewrite52.0ms (0.8%)

simplify46.0ms (0.7%)

prune89.0ms (1.4%)

localize9.0ms (0.2%)

series99.0ms (1.6%)

rewrite58.0ms (0.9%)

simplify30.0ms (0.5%)

prune141.0ms (2.3%)

localize15.0ms (0.2%)

series113.0ms (1.8%)

rewrite71.0ms (1.1%)

simplify32.0ms (0.5%)

prune127.0ms (2%)

regimes653.0ms (10.4%)

simplify2.0ms (0%)

end99.0ms (1.6%)

Profiling