Details

analyze823.0ms (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
0%	50%	50%	5
3.1%	43.7%	53.2%	6
3.1%	40.6%	56.3%	7
4.7%	35.9%	59.4%	8
4.7%	33.6%	61.8%	9
5.5%	30.8%	63.7%	10
5.5%	29.5%	65.1%	11
5.9%	28%	66.1%	12
5.9%	27.3%	66.9%	13
6%	26.5%	67.4%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample9.1s (60.5%)

Results

5.6s	2813×	body	8192	exit
1.5s	8256×	body	128	valid
1.2s	1407×	body	1024	invalid
440.0ms	723×	body	512	invalid
169.0ms	915×	body	128	invalid
139.0ms	362×	body	256	invalid

Compiler

Compiled 37 to 31 computations (16.2% saved)

simplify46.0ms (0.3%)

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%)

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

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize10.0ms (0.1%)

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)
✓	0.4b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series589.0ms (3.9%)

Counts

3 → 48

Calls

3 calls:

303.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
282.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite26.0ms (0.2%)

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:

7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
7.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
5.0ms	(.f64 (.f64 2 (PI.f64)) n)

simplify128.0ms (0.8%)

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

prune208.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	161	7	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	7	170

Error

0.0b

Counts

170 → 7

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))
	0.7b	(.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))))
	20.5b	(/.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 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	0.4b	(.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))))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))

Compiler

Compiled 4351 to 2824 computations (35.1% saved)

localize10.0ms (0.1%)

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)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))
✓	0.1b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
✓	0.3b	(.f64 n (.f64 2 (PI.f64)))
✓	0.4b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))

series161.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))
52.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
14.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
3.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`times-frac_binary64`
51×	`add-sqr-sqrt_binary64`
43×	`sqrt-prod_binary64`
40×	`add-exp-log_binary64`
38×	`*-un-lft-identity_binary64`

Counts

4 → 145

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))
8.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
5.0ms	(.f64 n (.f64 2 (PI.f64)))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

simplify180.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

482×	`associate-/l*_binary64`
441×	`*-commutative_binary64`
366×	`fma-def_binary64`
350×	`associate-*r/_binary64`
319×	`associate-*l/_binary64`

Counts

157 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	4123
1	362	3862
2	1318	3834
3	3693	3834
4	4499	3834
5	4953	3834
6	4942	3834

prune296.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	240	6	246

Error

0.0b

Counts

246 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k)))))
▶	0.3b	(.f64 (pow.f64 n (.f64 k -1/2)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))

Compiler

Compiled 6976 to 4294 computations (38.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2))
	0.1b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
	0.3b	(.f64 n (.f64 2 (PI.f64)))
	0.4b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))

series5.0ms (0%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-exp-log_binary64`
4×	`pow1_binary64`
2×	`pow-exp_binary64`
2×	`pow-pow_binary64`
1×	`sqr-pow_binary64`

Counts

1 → 17

Calls

1 calls:

3.0ms

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

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

937×	`fma-neg_binary64`
724×	`cancel-sign-sub-inv_binary64`
380×	`unswap-sqr_binary64`
361×	`exp-prod_binary64`
286×	`distribute-rgt-neg-in_binary64`

Counts

29 → 27

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	472
1	124	423
2	386	411
3	1788	404
4	4004	400
5	4960	400
6	4999	400

prune188.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	149	6	155

Error

0.0b

Counts

155 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
▶	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k)))))
✓	0.3b	(.f64 (pow.f64 n (.f64 k -1/2)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))

Compiler

Compiled 4791 to 3111 computations (35.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
✓	0.3b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k)))
	0.3b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))

series104.0ms (0.7%)

Counts

2 → 8

Calls

2 calls:

53.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k)))
51.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))

rewrite130.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

874×	`sqrt-prod_binary64`
756×	`times-frac_binary64`
370×	`*-un-lft-identity_binary64`
370×	`add-sqr-sqrt_binary64`
370×	`add-cube-cbrt_binary64`

Counts

2 → 491

Calls

2 calls:

19.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
8.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k)))

simplify859.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

721×	`times-frac_binary64`
538×	`sub-neg_binary64`
510×	`associate-/l*_binary64`
477×	`div-sub_binary64`
465×	`associate-/l/_binary64`

Counts

499 → 445

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	366	23792
1	749	22517
2	1267	21005
3	3031	20489
4	3191	20462
5	3915	17753
6	4329	16583
7	4507	16391
8	5250	16391

prune689.0ms (4.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	523	1	524
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	524	6	530

Error

Counts

530 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))) (sqrt.f64 (sqrt.f64 k))))
	0.5b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	0.4b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k)))))
✓	0.3b	(.f64 (pow.f64 n (.f64 k -1/2)) (.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))

Compiler

Compiled 19576 to 10444 computations (46.6% saved)

regimes1.2s (8.1%)

Accuracy

Total 0.4b remaining (89.6%)

Threshold costs 0.4b (89.6%)

Counts

242 → 1

Compiler

Compiled 27410 to 20380 computations (25.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

end141.0ms (0.9%)

Compiler: Compiled 196 to 147 computations (25% saved)

Details

analyze823.0ms (5.4%)

sample9.1s (60.5%)

simplify46.0ms (0.3%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series589.0ms (3.9%)

rewrite26.0ms (0.2%)

simplify128.0ms (0.8%)

prune208.0ms (1.4%)

localize10.0ms (0.1%)

series161.0ms (1.1%)

rewrite44.0ms (0.3%)

simplify180.0ms (1.2%)

prune296.0ms (2%)

localize12.0ms (0.1%)

series5.0ms (0%)

rewrite4.0ms (0%)

simplify73.0ms (0.5%)

prune188.0ms (1.2%)

localize13.0ms (0.1%)

series104.0ms (0.7%)

rewrite130.0ms (0.9%)

simplify859.0ms (5.7%)

prune689.0ms (4.6%)

regimes1.2s (8.1%)

simplify3.0ms (0%)

end141.0ms (0.9%)

Profiling