Details

analyze595.0ms (8.9%)

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%	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)

sample88.0ms (1.3%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
22.0ms	37×	body	1024	nan
12.0ms	69×	body	128	overflowed
7.0ms	17×	body	512	nan
3.0ms	36×	body	128	nan
3.0ms	11×	body	256	nan
0.0ms	3×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify50.0ms (0.8%)

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

0.3b

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)

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

rewrite20.0ms (0.3%)

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)

series758.0ms (11.3%)

Counts

3 → 48

Calls

3 calls:

379.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
368.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))
11.0ms	(.f64 (.f64 2 PI.f64) n)

simplify143.0ms (2.1%)

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

prune219.0ms (3.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	274	10	284
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	276	10	286

Error

Counts

286 → 10

Alt Table

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

Compiler

Compiled 4310 to 2732 computations (36.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`

Counts

3 → 67

Calls

3 calls:

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

series92.0ms (1.4%)

Counts

3 → 0

Calls

3 calls:

74.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n PI.f64)))) (sqrt.f64 k))
9.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
8.0ms	(*.f64 n PI.f64)

simplify114.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

568×	`associate-/l*_binary64`
546×	`times-frac_binary64`
546×	`fma-def_binary64`
459×	`associate-l_binary64`
372×	`fma-neg_binary64`

Counts

67 → 113

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	117	1597
1	220	1379
2	753	1379
3	3940	1379
4	4587	1379
5	4952	1379
6	4965	1379

prune155.0ms (2.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	139	10	149

Error

Counts

149 → 10

Alt Table

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

Compiler

Compiled 3210 to 1785 computations (44.4% saved)

localize10.0ms (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 n PI.f64)
	0.2b	(*.f64 n PI.f64)
✓	0.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (sqrt.f64 k))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64`
22×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`

Counts

1 → 49

Calls

1 calls:

7.0ms

(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (sqrt.f64 k))

series40.0ms (0.6%)

Counts

1 → 0

Calls

1 calls:

40.0ms

(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (sqrt.f64 k))

simplify142.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
609×	`div-sub_binary64`
534×	`associate-/l*_binary64`
470×	`associate-/l/_binary64`
331×	`distribute-rgt-in_binary64`

Counts

49 → 67

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	82	1265
1	129	1203
2	278	1203
3	780	1203
4	2461	1203
5	2377	1203
6	2849	1203
7	3405	1203
8	3108	1203
9	3845	1203
10	4691	1203

prune140.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	243	4	247
Fresh	6	2	8
Picked	1	0	1
Done	0	1	1
Total	250	7	257

Error

Counts

257 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n PI.f64)))) (sqrt.f64 k))
	12.1b	(.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 2 (.f64 n PI.f64)) k)))
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n PI.f64))) (sqrt.f64 k)))
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n PI.f64)))))
▶	0.3b	(.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 n PI.f64)) (sqrt.f64 k))))
	0.6b	(/.f64 (pow.f64 (*.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))

Compiler

Compiled 3210 to 1745 computations (45.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`times-frac_binary64`
52×	`add-sqr-sqrt_binary64`
48×	`sqrt-prod_binary64`
36×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

11.0ms	(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 n PI.f64)) (sqrt.f64 k)))
6.0ms	(/.f64 (sqrt.f64 (*.f64 n PI.f64)) (sqrt.f64 k))

series72.0ms (1.1%)

Counts

2 → 0

Calls

2 calls:

43.0ms	(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 n PI.f64)) (sqrt.f64 k)))
29.0ms	(/.f64 (sqrt.f64 (*.f64 n PI.f64)) (sqrt.f64 k))

simplify200.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1038×	`associate-/l/_binary64`
858×	`fma-def_binary64`
813×	`fma-neg_binary64`
409×	`distribute-rgt-in_binary64`
332×	`sqr-pow_binary64`

Counts

106 → 149

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	128	2334
1	249	2200
2	749	2200
3	2128	2200
4	2093	2200
5	2291	2200
6	2844	2200
7	4079	2200
8	4194	2200
9	5761	2200

prune155.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	773	0	773
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	773	7	780

Error

Counts

780 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (fma.f64 k -1/2 1/2)))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n PI.f64)))) (sqrt.f64 k))
	12.1b	(.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 2 (.f64 n PI.f64)) k)))
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n PI.f64))) (sqrt.f64 k)))
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n PI.f64)))))
✓	0.3b	(.f64 (pow.f64 (.f64 2 (.f64 n PI.f64)) (.f64 k -1/2)) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 n PI.f64)) (sqrt.f64 k))))
	0.6b	(/.f64 (pow.f64 (*.f64 2 PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))

Compiler

Compiled 4382 to 1948 computations (55.5% saved)

regimes565.0ms (8.4%)

Accuracy

Total 0.4b remaining (96.1%)

Threshold costs 0.4b (96.1%)

Compiler

Compiled 12001 to 8878 computations (26% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	18	31
2	18	31

end1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

sample3.0s (45.3%)

Algorithm

1×

intervals

Results

816.0ms	8000×	body	128	valid
779.0ms	1286×	body	1024	nan
400.0ms	2233×	body	128	overflowed
265.0ms	635×	body	512	nan
119.0ms	321×	body	256	nan
76.0ms	1045×	body	128	nan
29.0ms	254×	body	128	invalid

Compiler

Compiled 186 to 140 computations (24.7% saved)

Details

analyze595.0ms (8.9%)

sample88.0ms (1.3%)

simplify50.0ms (0.8%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite20.0ms (0.3%)

series758.0ms (11.3%)

simplify143.0ms (2.1%)

prune219.0ms (3.3%)

localize13.0ms (0.2%)

rewrite18.0ms (0.3%)

series92.0ms (1.4%)

simplify114.0ms (1.7%)

prune155.0ms (2.3%)

localize10.0ms (0.1%)

rewrite10.0ms (0.1%)

series40.0ms (0.6%)

simplify142.0ms (2.1%)

prune140.0ms (2.1%)

localize13.0ms (0.2%)

rewrite24.0ms (0.4%)

series72.0ms (1.1%)

simplify200.0ms (3%)

prune155.0ms (2.3%)

regimes565.0ms (8.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.0s (45.3%)

Profiling