Details

analyze1.1s (10.5%)

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%	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)

sample170.0ms (1.6%)

Algorithm

1×

intervals

Results

45.0ms	41×	body	1024	nan
43.0ms	256×	body	128	valid
24.0ms	73×	body	128	overflowed
22.0ms	20×	body	512	nan
5.0ms	8×	body	128	invalid
4.0ms	27×	body	128	nan
3.0ms	8×	body	256	nan

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify52.0ms (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

0.2b

Counts

3 → 2

Alt Table

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

rewrite19.0ms (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	(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)

series1.1s (10.2%)

Counts

3 → 48

Calls

3 calls:

595.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
464.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))
11.0ms	(.f64 (.f64 2 PI.f64) n)

simplify140.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

418×	`distribute-rgt-in_binary64`
412×	`distribute-lft-in_binary64`
223×	`exp-sum_binary64`
211×	`associate-/l*_binary64`
170×	`fma-def_binary64`

Counts

156 → 284

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	4057
1	428	3712
2	1383	3642
3	4520	3642
4	5214	3642

prune210.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	276	8	284
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	278	8	286

Error

Counts

286 → 8

Alt Table

Status	Error	Program
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))))
	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)))
▶	0.3b	(/.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)))))
	23.9b	(/.f64 (-.f64 (.f64 (sqrt.f64 (.f64 n PI.f64)) (sqrt.f64 2)) (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (.f64 n PI.f64))))) (sqrt.f64 (*.f64 n PI.f64))))) (sqrt.f64 k))
	0.3b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 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))))
	0.5b	(.f64 (/.f64 (pow.f64 (.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (sqrt.f64 k))))

Compiler

Compiled 4300 to 2724 computations (36.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite95.0ms (0.9%)

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)))))
6.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n PI.f64))))
3.0ms	(*.f64 n PI.f64)

series125.0ms (1.2%)

Counts

3 → 0

Calls

3 calls:

75.0ms	(/.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)))))
42.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n PI.f64))))
7.0ms	(*.f64 n PI.f64)

simplify430.0ms (4.1%)

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 → 474

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

prune538.0ms (5.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	518	3	521
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	522	7	529

Error

Counts

529 → 7

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))
	0.4b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (.f64 n PI.f64))))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 k -1/2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n PI.f64)))))
	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 (/.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))))
	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (sqrt.f64 k))))
	10.5b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 2 (*.f64 n PI.f64)))))

Compiler

Compiled 13263 to 7696 computations (42% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
32×	`sqrt-prod_binary64`
24×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64`
21×	`add-exp-log_binary64`

Counts

3 → 99

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))
4.0ms	(pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))
2.0ms	(sqrt.f64 (/.f64 1 k))

series740.0ms (7.1%)

Counts

3 → 28

Calls

3 calls:

372.0ms	(pow.f64 (.f64 2 (.f64 n PI.f64)) (fma.f64 k -1/2 1/2))
364.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))
4.0ms	(sqrt.f64 (/.f64 1 k))

simplify133.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

409×	`distribute-rgt-in_binary64`
403×	`distribute-lft-in_binary64`
351×	`*-commutative_binary64`
237×	`cancel-sign-sub-inv_binary64`
232×	`fma-neg_binary64`

Counts

127 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	3052
1	328	2830
2	1000	2684
3	3018	2684
4	4850	2684
5	5056	2684

prune213.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	256	1	257
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	257	7	264

Error

Counts

264 → 7

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))
▶	0.3b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))
	0.4b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (.f64 n PI.f64))))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 k -1/2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n PI.f64)))))
	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 (/.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))))
	10.5b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 2 (*.f64 n PI.f64)))))

Compiler

Compiled 4173 to 2935 computations (29.7% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite8.0ms (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:

6.0ms

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

series375.0ms (3.6%)

Counts

1 → 12

Calls

1 calls:

374.0ms

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

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Rules

857×	`fma-def_binary64`
668×	`associate-l_binary64`
588×	`associate-r_binary64`
247×	`distribute-rgt-in_binary64`
242×	`distribute-lft-in_binary64`

Counts

57 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1607
1	208	1505
2	624	1445
3	2336	1417
4	4470	1417
5	4952	1417

prune161.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	234	7	241

Error

Counts

241 → 7

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))
✓	0.3b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))
	0.4b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (.f64 n PI.f64))))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 k -1/2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n PI.f64)))))
	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 (/.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))))
	10.5b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 2 (*.f64 n PI.f64)))))

Compiler

Compiled 2961 to 2042 computations (31% saved)

regimes1.5s (14.4%)

Accuracy

Total 0.4b remaining (91.6%)

Threshold costs 0.4b (91.6%)

Compiler

Compiled 31390 to 23820 computations (24.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	33
1	20	33
2	20	33

end1.0ms (0%)

Compiler: Compiled 23 to 17 computations (26.1% saved)

sample3.2s (30.7%)

Algorithm

1×

intervals

Results

922.0ms	1377×	body	1024	nan
790.0ms	8000×	body	128	valid
444.0ms	2321×	body	128	overflowed
280.0ms	669×	body	512	nan
80.0ms	975×	body	128	nan
75.0ms	321×	body	256	nan
27.0ms	234×	body	128	invalid

Compiler

Compiled 201 to 155 computations (22.9% saved)

Details

analyze1.1s (10.5%)

sample170.0ms (1.6%)

simplify52.0ms (0.5%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite19.0ms (0.2%)

series1.1s (10.2%)

simplify140.0ms (1.3%)

prune210.0ms (2%)

localize12.0ms (0.1%)

rewrite95.0ms (0.9%)

series125.0ms (1.2%)

simplify430.0ms (4.1%)

prune538.0ms (5.1%)

localize14.0ms (0.1%)

rewrite19.0ms (0.2%)

series740.0ms (7.1%)

simplify133.0ms (1.3%)

prune213.0ms (2%)

localize11.0ms (0.1%)

rewrite8.0ms (0.1%)

series375.0ms (3.6%)

simplify101.0ms (1%)

prune161.0ms (1.5%)

regimes1.5s (14.4%)

simplify4.0ms (0%)

end1.0ms (0%)

sample3.2s (30.7%)

Profiling