Details

analyze535.0ms (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%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample133.0ms (2%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
19.0ms	32×	body	1024	nan
13.0ms	74×	body	128	overflowed
7.0ms	19×	body	512	nan
3.0ms	29×	body	128	nan
2.0ms	8×	body	256	nan
1.0ms	5×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify45.0ms (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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.7b	(.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))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series538.0ms (8.1%)

Counts

3 → 48

Calls

3 calls:

274.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
261.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 108

Calls

3 calls:

5.0ms	(.f64 (.f64 2 (PI.f64)) n)
5.0ms	(/.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))

simplify120.0ms (1.8%)

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

prune229.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	158	10	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	160	10	170

Error

0.0b

Counts

170 → 10

Alt Table

Status	Error	Program
	0.8b	(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	24.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (sqrt.f64 k))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (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))
	0.6b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	0.6b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	19.3b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
	25.3b	(/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

Compiler

Compiled 4321 to 2832 computations (34.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series328.0ms (4.9%)

Counts

4 → 36

Calls

4 calls:

231.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 k -1/2))
80.0ms	(/.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))
13.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
3.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
21×	`pow1_binary64`
14×	`prod-exp_binary64`
14×	`add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 86

Calls

4 calls:

9.0ms	(/.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))
6.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 k -1/2))
4.0ms	(.f64 n (.f64 2 (PI.f64)))
3.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

731×	`associate-/l*_binary64`
452×	`distribute-rgt-in_binary64`
447×	`distribute-lft-in_binary64`
206×	`associate-/l/_binary64`
177×	`fma-def_binary64`

Counts

122 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2583
1	374	2257
2	1377	2245
3	5515	2245

prune242.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	166	9	175

Error

Counts

175 → 9

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
	0.8b	(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
	0.7b	(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	24.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (sqrt.f64 k))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
	0.6b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	19.3b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/2 k))) 3))
	25.3b	(/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

Compiler

Compiled 4552 to 2896 computations (36.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series70.0ms (1.1%)

Counts

1 → 0

Calls

1 calls:

70.0ms

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

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64`
8×	`prod-exp_binary64`
6×	`associate-/l*_binary64`
6×	`sqrt-prod_binary64`
6×	`times-frac_binary64`

Counts

1 → 33

Calls

1 calls:

10.0ms

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

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Rules

487×	`fma-neg_binary64`
439×	`times-frac_binary64`
362×	`associate-/r*_binary64`
326×	`associate-l_binary64`
287×	`fma-def_binary64`

Counts

33 → 36

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	83	1317
1	153	1128
2	521	1128
3	2809	1128
4	4628	1128
5	5053	1128

prune210.0ms (3.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	153	9	162

Error

Counts

162 → 9

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
	0.8b	(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
	0.7b	(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	24.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (sqrt.f64 k))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
▶	0.6b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
	0.6b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	19.3b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/2 k))) 3))
	25.3b	(/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

Compiler

Compiled 4522 to 3027 computations (33.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))
✓	0.4b	(sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64)))))
✓	0.4b	(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))

series29.0ms (0.4%)

Counts

3 → 8

Calls

3 calls:

13.0ms	(sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64)))))
9.0ms	(.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))
6.0ms	(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`pow1_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
15×	`pow-prod-down_binary64`
12×	`associate-l_binary64`

Counts

3 → 64

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64))))
6.0ms	(.f64 (sqrt.f64 n) (.f64 2 (PI.f64)))
5.0ms	(sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64)))))

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-def_binary64`
386×	`associate-*l/_binary64`
336×	`*-commutative_binary64`
267×	`associate-*r/_binary64`
206×	`log-div_binary64`

Counts

72 → 79

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	77	846
1	167	750
2	548	750
3	795	750
4	994	750
5	2504	750
6	3798	750
7	4957	750
8	4998	750
9	4955	750

prune136.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	109	9	118

Error

Counts

118 → 9

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
	0.8b	(.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
	0.7b	(/.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	24.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (sqrt.f64 k))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
✓	0.6b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
	0.6b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	19.3b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/2 k))) 3))
	25.3b	(/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

Compiler

Compiled 3250 to 1882 computations (42.1% saved)

regimes506.0ms (7.6%)

Accuracy

Total 0.4b remaining (83.9%)

Threshold costs 0.4b (83.9%)

Counts

108 → 1

Compiler

Compiled 10888 to 8277 computations (24% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	23	31
2	22	31

end1.0ms (0%)

Compiler: Compiled 21 to 16 computations (23.8% saved)

sample3.2s (47.4%)

Algorithm

1×

intervals

Results

833.0ms	1318×	body	1024	nan
771.0ms	8000×	body	128	valid
412.0ms	2312×	body	128	overflowed
313.0ms	649×	body	512	nan
175.0ms	315×	body	256	nan
76.0ms	947×	body	128	nan
25.0ms	229×	body	128	invalid

Compiler

Compiled 232 to 181 computations (22% saved)

Details

analyze535.0ms (8%)

sample133.0ms (2%)

simplify45.0ms (0.7%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series538.0ms (8.1%)

rewrite20.0ms (0.3%)

simplify120.0ms (1.8%)

prune229.0ms (3.4%)

localize14.0ms (0.2%)

series328.0ms (4.9%)

rewrite25.0ms (0.4%)

simplify78.0ms (1.2%)

prune242.0ms (3.6%)

localize12.0ms (0.2%)

series70.0ms (1.1%)

rewrite13.0ms (0.2%)

simplify66.0ms (1%)

prune210.0ms (3.2%)

localize13.0ms (0.2%)

series29.0ms (0.4%)

rewrite22.0ms (0.3%)

simplify97.0ms (1.5%)

prune136.0ms (2%)

regimes506.0ms (7.6%)

simplify2.0ms (0%)

end1.0ms (0%)

sample3.2s (47.4%)

Profiling