Details

analyze528.0ms (5.2%)

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)

sample156.0ms (1.5%)

Algorithm

1×

intervals

Results

27.0ms	46×	body	1024	nan
26.0ms	256×	body	128	valid
13.0ms	75×	body	128	overflowed
10.0ms	26×	body	512	nan
4.0ms	19×	body	256	nan
2.0ms	26×	body	128	nan
0.0ms	2×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify51.0ms (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

0.3b

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)

localize11.0ms (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))
✓	0.2b	(/.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)

series682.0ms (6.7%)

Counts

3 → 48

Calls

3 calls:

430.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
249.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite23.0ms (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:

7.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
5.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms	(.f64 (.f64 2 (PI.f64)) n)

simplify166.0ms (1.6%)

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

prune222.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	159	9	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	161	9	170

Error

Counts

170 → 9

Alt Table

Status	Error	Program
	0.5b	(.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))))
	19.7b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) -1/2))) (sqrt.f64 k))
	1.1b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (cbrt.f64 (sqrt.f64 k)))
	0.5b	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
	0.6b	(.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)))
	0.7b	(.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))))
	20.9b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
▶	0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

Compiler

Compiled 4324 to 2726 computations (37% saved)

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series126.0ms (1.2%)

Counts

3 → 0

Calls

3 calls:

88.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
35.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
2.0ms	(*.f64 n (PI.f64))

rewrite60.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

308×	`times-frac_binary64`
143×	`add-sqr-sqrt_binary64`
141×	`*-un-lft-identity_binary64`
141×	`add-cube-cbrt_binary64`
130×	`sqrt-prod_binary64`

Counts

3 → 267

Calls

3 calls:

12.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
7.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
3.0ms	(*.f64 n (PI.f64))

simplify374.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

743×	`associate-/r*_binary64`
350×	`fma-neg_binary64`
297×	`associate-/r/_binary64`
237×	`associate-/l/_binary64`
208×	`*-commutative_binary64`

Counts

267 → 346

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	362	12589
1	719	12274
2	2466	12046
3	3247	12046
4	4757	12046
5	5020	12046

prune512.0ms (5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	369	5	374
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	376	7	383

Error

Counts

383 → 7

Alt Table

Status	Error	Program
	19.7b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) -1/2))) (sqrt.f64 k))
	11.8b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 2 (*.f64 n (PI.f64))))))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.3b	(/.f64 1 (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))))
	0.4b	(.f64 (sqrt.f64 2) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64))))))
	0.5b	(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
▶	0.3b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)) (/.f64 (pow.f64 n (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))

Compiler

Compiled 13272 to 7688 computations (42.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series88.0ms (0.9%)

Counts

2 → 0

Calls

2 calls:

75.0ms	(/.f64 (pow.f64 n (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
13.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))

rewrite61.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

388×	`times-frac_binary64`
180×	`*-un-lft-identity_binary64`
180×	`add-sqr-sqrt_binary64`
180×	`add-cube-cbrt_binary64`
145×	`sqrt-prod_binary64`

Counts

2 → 266

Calls

2 calls:

12.0ms	(/.f64 (pow.f64 n (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
6.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))

simplify426.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

571×	`*-commutative_binary64`
499×	`associate-r_binary64`
497×	`fma-def_binary64`
404×	`fma-neg_binary64`
340×	`associate-/r/_binary64`

Counts

266 → 318

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	375	12066
1	723	11834
2	2544	11603
3	3103	11603
4	3994	11603
5	4712	11603
6	5034	11603

prune525.0ms (5.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	391	0	391
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	391	7	398

Error

Counts

398 → 7

Alt Table

Status	Error	Program
	19.7b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) -1/2))) (sqrt.f64 k))
	11.8b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 2 (*.f64 n (PI.f64))))))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
▶	0.3b	(/.f64 1 (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))))
	0.4b	(.f64 (sqrt.f64 2) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64))))))
	0.5b	(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
✓	0.3b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)) (/.f64 (pow.f64 n (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))

Compiler

Compiled 15270 to 8999 computations (41.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series84.0ms (0.8%)

Counts

1 → 0

Calls

1 calls:

84.0ms

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

rewrite234.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

1472×	`times-frac_binary64`
562×	`*-un-lft-identity_binary64`
562×	`add-sqr-sqrt_binary64`
562×	`add-cube-cbrt_binary64`
360×	`sqrt-prod_binary64`

Counts

1 → 630

Calls

1 calls:

60.0ms

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

simplify868.0ms (8.5%)

Algorithm

1×	egg-herbie

Rules

565×	`associate-/r/_binary64`
450×	`associate-/l/_binary64`
355×	`associate-/r*_binary64`
321×	`distribute-rgt-in_binary64`
242×	`fma-def_binary64`

Counts

630 → 731

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	525	37751
1	1046	34839
2	3360	33623
3	3521	33623
4	4931	33623

prune1.2s (11.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	831	1	832
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	833	6	839

Error

Counts

839 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (sqrt.f64 2) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64))))))
	0.5b	(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
	19.7b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) -1/2))) (sqrt.f64 k))
✓	0.3b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)) (/.f64 (pow.f64 n (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
	11.8b	(/.f64 1 (/.f64 (sqrt.f64 (/.f64 k (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

Compiler

Compiled 35258 to 22040 computations (37.5% saved)

regimes756.0ms (7.4%)

Accuracy

Total 0.3b remaining (74.8%)

Threshold costs 0.3b (74.8%)

Counts

153 → 1

Compiler

Compiled 14731 to 11227 computations (23.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	23	37
2	23	37

end1.0ms (0%)

Compiler: Compiled 25 to 19 computations (24% saved)

sample3.0s (29.5%)

Algorithm

1×

intervals

Results

800.0ms	1302×	body	1024	nan
774.0ms	8000×	body	128	valid
432.0ms	2354×	body	128	overflowed
291.0ms	708×	body	512	nan
89.0ms	374×	body	256	nan
76.0ms	1013×	body	128	nan
27.0ms	215×	body	128	invalid

Compiler

Compiled 187 to 141 computations (24.6% saved)

Details

analyze528.0ms (5.2%)

sample156.0ms (1.5%)

simplify51.0ms (0.5%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series682.0ms (6.7%)

rewrite23.0ms (0.2%)

simplify166.0ms (1.6%)

prune222.0ms (2.2%)

localize45.0ms (0.4%)

series126.0ms (1.2%)

rewrite60.0ms (0.6%)

simplify374.0ms (3.7%)

prune512.0ms (5%)

localize14.0ms (0.1%)

series88.0ms (0.9%)

rewrite61.0ms (0.6%)

simplify426.0ms (4.2%)

prune525.0ms (5.1%)

localize13.0ms (0.1%)

series84.0ms (0.8%)

rewrite234.0ms (2.3%)

simplify868.0ms (8.5%)

prune1.2s (11.6%)

regimes756.0ms (7.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.0s (29.5%)

Profiling