Details

analyze317.0ms (4.8%)

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)

sample3.1s (47.1%)

Results

1.3s	8256×	body	128	valid
1.1s	1399×	body	1024	invalid
366.0ms	672×	body	512	invalid
175.0ms	1173×	body	128	invalid
106.0ms	321×	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 (pow.f64 (.f64 2 (.f64 (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)

localize9.0ms (0.1%)

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

series445.0ms (6.7%)

Counts

3 → 48

Calls

3 calls:

240.0ms	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
204.0ms	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
2.0ms	(*.f64 (PI.f64) n)

rewrite53.0ms (0.8%)

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:

52.0ms	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
52.0ms	(*.f64 (PI.f64) n)
52.0ms	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))

simplify44.0ms (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

prune113.0ms (1.7%)

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
	12.1b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
	11.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
	0.5b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
▶	0.5b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	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))
	1.1b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 2) 1) (/.f64 (cbrt.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 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))

Compiler

Compiled 2423 to 1666 computations (31.2% saved)

localize12.0ms (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))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))

series432.0ms (6.5%)

Counts

3 → 48

Calls

3 calls:

228.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
202.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite50.0ms (0.7%)

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:

48.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
48.0ms	(.f64 n (.f64 2 (PI.f64)))
48.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))

simplify43.0ms (0.6%)

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

prune91.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Error

0.0b

Counts

85 → 7

Alt Table

Status	Error	Program
	12.1b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
	11.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
	0.5b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
✓	0.5b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
▶	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))
	0.5b	(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	0.6b	(.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) (pow.f64 k -1/2))

Compiler

Compiled 1992 to 1430 computations (28.2% saved)

localize13.0ms (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))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.4b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

series99.0ms (1.5%)

Counts

3 → 12

Calls

3 calls:

60.0ms

(/.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))

31.0ms

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

8.0ms

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

rewrite56.0ms (0.8%)

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:

54.0ms

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

54.0ms

(/.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))

54.0ms

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

simplify31.0ms (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

prune133.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	137	6	143

Error

Counts

143 → 6

Alt Table

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

Compiler

Compiled 3225 to 2059 computations (36.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series665.0ms (10%)

Counts

3 → 48

Calls

3 calls:

270.0ms

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

212.0ms

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

182.0ms

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

rewrite58.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
150×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`
144×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	56
1	343	49
2	3910	49

Stop Event

1×	node limit

Counts

3 → 102

Calls

3 calls:

56.0ms

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

56.0ms

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

56.0ms

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

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

484×	`fma-neg_binary64`
311×	`associate-r_binary64`
283×	`associate-l_binary64`
229×	`unswap-sqr_binary64`
167×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	1312
1	216	997
2	594	975
3	3106	975

Stop Event

1×	node limit

Counts

150 → 123

prune155.0ms (2.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	142	6	148

Error

Counts

148 → 6

Alt Table

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

Compiler

Compiled 3559 to 2365 computations (33.5% saved)

regimes504.0ms (7.6%)

Accuracy

Total 0.4b remaining (88.2%)

Threshold costs 0.4b (88.2%)

Counts

117 → 1

Compiler

Compiled 9998 to 8038 computations (19.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	25	24
2	31	24
3	35	24
4	36	24

Stop Event

1×

saturated

end103.0ms (1.6%)

Compiler: Compiled 153 to 122 computations (20.3% saved)

Details

analyze317.0ms (4.8%)

sample3.1s (47.1%)

simplify18.0ms (0.3%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

series445.0ms (6.7%)

rewrite53.0ms (0.8%)

simplify44.0ms (0.7%)

prune113.0ms (1.7%)

localize12.0ms (0.2%)

series432.0ms (6.5%)

rewrite50.0ms (0.7%)

simplify43.0ms (0.6%)

prune91.0ms (1.4%)

localize13.0ms (0.2%)

series99.0ms (1.5%)

rewrite56.0ms (0.8%)

simplify31.0ms (0.5%)

prune133.0ms (2%)

localize12.0ms (0.2%)

series665.0ms (10%)

rewrite58.0ms (0.9%)

simplify46.0ms (0.7%)

prune155.0ms (2.3%)

regimes504.0ms (7.6%)

simplify2.0ms (0%)

end103.0ms (1.6%)

Profiling