Details

analyze375.0ms (3.9%)

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)

sample3.3s (34.7%)

Results

1.4s	8256×	body	128	valid
1.1s	1347×	body	1024	invalid
425.0ms	693×	body	512	invalid
185.0ms	1110×	body	128	invalid
121.0ms	326×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify47.0ms (0.5%)

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
	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.4b	(/.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	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

series598.0ms (6.2%)

Counts

3 → 48

Calls

3 calls:

321.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
273.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite24.0ms (0.2%)

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:

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))
4.0ms	(.f64 (.f64 2 (PI.f64)) n)

simplify140.0ms (1.4%)

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

prune236.0ms (2.4%)

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
	0.5b	(/.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 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	0.8b	(.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))))
	0.6b	(.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))))
	23.4b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 1/2 (.f64 k (log.f64 (.f64 n (.f64 2 (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))))
	19.5b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
	0.6b	(.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)))
▶	0.4b	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
	1.1b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))

Compiler

Compiled 4419 to 2890 computations (34.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 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)) (/.f64 1 (sqrt.f64 k)))
	0.2b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
✓	0.2b	(/.f64 1 (sqrt.f64 k))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)

series333.0ms (3.4%)

Counts

2 → 12

Calls

2 calls:

317.0ms	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
16.0ms	(/.f64 1 (sqrt.f64 k))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-exp-log_binary64`
50×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
32×	`prod-exp_binary64`

Counts

2 → 119

Calls

2 calls:

11.0ms	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
3.0ms	(/.f64 1 (sqrt.f64 k))

simplify130.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-def_binary64`
657×	`times-frac_binary64`
385×	`associate-l_binary64`
297×	`distribute-rgt-in_binary64`
283×	`associate-r_binary64`

Counts

131 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	2775
1	248	2509
2	621	2509
3	1956	2470
4	4621	2470
5	4991	2470

prune301.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	219	9	228

Error

0.0b

Counts

228 → 9

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))
	0.6b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	0.6b	(.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))))
	23.4b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (-.f64 (.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (.f64 1/2 (.f64 k (log.f64 (.f64 n (.f64 2 (PI.f64)))))))))) (sqrt.f64 k))
▶	0.4b	(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	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))))
	19.5b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
	0.6b	(.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)))
	1.1b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))

Compiler

Compiled 5398 to 3677 computations (31.9% saved)

localize11.0ms (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)) (pow.f64 k -1/2))
	0.2b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)

series306.0ms (3.2%)

Counts

1 → 12

Calls

1 calls:

306.0ms

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

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
24×	`prod-exp_binary64`
14×	`pow-exp_binary64`
11×	`add-sqr-sqrt_binary64`
8×	`pow-to-exp_binary64`

Counts

1 → 45

Calls

1 calls:

8.0ms

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

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

923×	`fma-def_binary64`
629×	`associate-l_binary64`
565×	`associate-r_binary64`
256×	`distribute-rgt-in_binary64`
251×	`distribute-lft-in_binary64`

Counts

57 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1566
1	208	1442
2	618	1438
3	2336	1412
4	4425	1412
5	4933	1412

prune208.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Error

Counts

141 → 9

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))))) (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))
	0.6b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	1.1b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
▶	0.4b	(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	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))))
	19.5b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 3))
	0.6b	(.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))))
	23.4b	(.f64 (-.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64)))))) (pow.f64 k -1/2))

Compiler

Compiled 3426 to 2497 computations (27.1% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series572.0ms (5.9%)

Counts

3 → 48

Calls

3 calls:

303.0ms

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

265.0ms

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

3.0ms

(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`add-exp-log_binary64`
75×	`times-frac_binary64`
49×	`add-sqr-sqrt_binary64`
45×	`unpow-prod-down_binary64`
37×	`*-un-lft-identity_binary64`

Counts

3 → 158

Calls

3 calls:

11.0ms

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

8.0ms

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

5.0ms

(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))

simplify130.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

506×	`times-frac_binary64`
366×	`unswap-sqr_binary64`
329×	`distribute-rgt-in_binary64`
214×	`associate-l_binary64`
200×	`sqr-pow_binary64`

Counts

206 → 246

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	4783
1	694	4314
2	2363	4258
3	4914	4258

prune340.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	246	9	255

Error

Counts

255 → 9

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))))) (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))
	0.6b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.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))))
	19.5b	(cbrt.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 3))
	0.9b	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
✓	0.4b	(.f64 (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.6b	(.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))))
	23.4b	(.f64 (-.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64)))))) (pow.f64 k -1/2))

Compiler

Compiled 6318 to 4635 computations (26.6% saved)

regimes2.2s (22.5%)

Accuracy

Total 0.5b remaining (93.8%)

Threshold costs 0.5b (93.8%)

Counts

343 → 1

Compiler

Compiled 35873 to 28295 computations (21.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	13	21
2	13	21

end176.0ms (1.8%)

Compiler: Compiled 237 to 182 computations (23.2% saved)

Details

analyze375.0ms (3.9%)

sample3.3s (34.7%)

simplify47.0ms (0.5%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series598.0ms (6.2%)

rewrite24.0ms (0.2%)

simplify140.0ms (1.4%)

prune236.0ms (2.4%)

localize11.0ms (0.1%)

series333.0ms (3.4%)

rewrite25.0ms (0.3%)

simplify130.0ms (1.3%)

prune301.0ms (3.1%)

localize11.0ms (0.1%)

series306.0ms (3.2%)

rewrite12.0ms (0.1%)

simplify92.0ms (0.9%)

prune208.0ms (2.2%)

localize14.0ms (0.1%)

series572.0ms (5.9%)

rewrite41.0ms (0.4%)

simplify130.0ms (1.3%)

prune340.0ms (3.5%)

regimes2.2s (22.5%)

simplify3.0ms (0%)

end176.0ms (1.8%)

Profiling