Details

analyze346.0ms (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)

sample3.4s (48.2%)

Results

1.4s	8256×	body	128	valid
1.2s	1384×	body	1024	invalid
392.0ms	658×	body	512	invalid
202.0ms	1205×	body	128	invalid
110.0ms	328×	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`

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)

localize10.0ms (0.1%)

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

series547.0ms (7.9%)

Counts

3 → 48

Calls

3 calls:

287.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
257.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`

Counts

3 → 108

Calls

3 calls:

7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
4.0ms	(.f64 (.f64 2 (PI.f64)) n)

simplify120.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

405×	`distribute-rgt-in_binary64`
399×	`distribute-lft-in_binary64`
243×	`fma-neg_binary64`
211×	`associate-/l*_binary64`
162×	`associate-l_binary64`

Counts

156 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	4057
1	428	3712
2	1390	3636
3	4506	3636
4	4960	3636

prune226.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	8	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	162	8	170

Error

0.0b

Counts

170 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
▶	0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))
	0.5b	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	0.2b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)))
	0.5b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	24.3b	(/.f64 (-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
	0.5b	(.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)) (sqrt.f64 k)))
	0.4b	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))

Compiler

Compiled 4386 to 2760 computations (37.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series133.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))
37.0ms	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
12.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
2.0ms	(*.f64 n (PI.f64))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64`
18×	`pow1_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`prod-exp_binary64`
13×	`add-cbrt-cube_binary64`

Counts

4 → 98

Calls

4 calls:

9.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))
7.0ms	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
4.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
3.0ms	(*.f64 n (PI.f64))

simplify105.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

875×	`fma-def_binary64`
334×	`distribute-rgt-in_binary64`
332×	`distribute-lft-in_binary64`
280×	`associate-/r*_binary64`
269×	`associate-*l/_binary64`

Counts

110 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2985
1	365	2651
2	1373	2611
3	4679	2603
4	5478	2603

prune212.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	166	7	173

Error

Counts

173 → 7

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
	0.5b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	0.4b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))
	0.4b	(.f64 (sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))))
	0.5b	(.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)) (sqrt.f64 k)))
	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 4747 to 2638 computations (44.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series100.0ms (1.4%)

Counts

2 → 0

Calls

2 calls:

85.0ms	(.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
15.0ms	(/.f64 1 (sqrt.f64 k))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`add-exp-log_binary64`
56×	`prod-exp_binary64`
36×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`

Counts

2 → 111

Calls

2 calls:

14.0ms	(.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
8.0ms	(/.f64 1 (sqrt.f64 k))

simplify107.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-/r*_binary64`
505×	`unswap-sqr_binary64`
501×	`fma-def_binary64`
390×	`associate-/l/_binary64`
343×	`associate-/r/_binary64`

Counts

111 → 127

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	116	2714
1	212	2475
2	703	2475
3	1685	2475
4	4073	2475
5	5385	2475

prune238.0ms (3.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	191	6	197

Error

Counts

197 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))
	0.5b	(.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (/.f64 (/.f64 1 (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 k))))
	0.5b	(.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)) (sqrt.f64 k)))
▶	0.3b	(.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 (sqrt.f64 n) (.f64 (PI.f64) (sqrt.f64 n)))))) (/.f64 1 (sqrt.f64 k)))
	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 5524 to 3205 computations (42% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.2%)

Counts

2 → 8

Calls

2 calls:

8.0ms	(*.f64 (PI.f64) (sqrt.f64 n))
5.0ms	(.f64 (sqrt.f64 n) (.f64 (PI.f64) (sqrt.f64 n)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`associate-l_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 n) (.f64 (PI.f64) (sqrt.f64 n)))
4.0ms	(*.f64 (PI.f64) (sqrt.f64 n))

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

648×	`log-div_binary64`
528×	`associate-/l/_binary64`
469×	`associate-/l*_binary64`
393×	`cube-div_binary64`
305×	`times-frac_binary64`

Counts

55 → 58

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	59	608
1	116	461
2	304	461
3	501	461
4	629	461
5	846	461
6	1545	461
7	3414	461
8	4652	461
9	5014	461

prune157.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	129	6	135

Error

Counts

135 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))
	0.5b	(.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (/.f64 (/.f64 1 (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 k))))
	0.5b	(.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)) (sqrt.f64 k)))
✓	0.3b	(.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 (sqrt.f64 n) (.f64 (PI.f64) (sqrt.f64 n)))))) (/.f64 1 (sqrt.f64 k)))
	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 3998 to 2032 computations (49.2% saved)

regimes908.0ms (13.1%)

Accuracy

Total 0.3b remaining (87.6%)

Threshold costs 0.3b (87.6%)

Counts

179 → 1

Compiler

Compiled 20086 to 15114 computations (24.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	18	31
2	18	31

end116.0ms (1.7%)

Compiler: Compiled 186 to 134 computations (28% saved)

Details

analyze346.0ms (5%)

sample3.4s (48.2%)

simplify48.0ms (0.7%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series547.0ms (7.9%)

rewrite22.0ms (0.3%)

simplify120.0ms (1.7%)

prune226.0ms (3.2%)

localize11.0ms (0.2%)

series133.0ms (1.9%)

rewrite28.0ms (0.4%)

simplify105.0ms (1.5%)

prune212.0ms (3.1%)

localize11.0ms (0.2%)

series100.0ms (1.4%)

rewrite35.0ms (0.5%)

simplify107.0ms (1.5%)

prune238.0ms (3.4%)

localize15.0ms (0.2%)

series13.0ms (0.2%)

rewrite13.0ms (0.2%)

simplify82.0ms (1.2%)

prune157.0ms (2.3%)

regimes908.0ms (13.1%)

simplify2.0ms (0%)

end116.0ms (1.7%)

Profiling