Details

analyze709.0ms (14.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.1%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample3.2s (66.5%)

Results

1.7s	2678×	body	1024	valid
483.0ms	1409×	body	512	valid
415.0ms	283×	body	2048	valid
379.0ms	3146×	body	128	valid
154.0ms	740×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 41 to 35 computations (14.6% saved)

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

667×	`div-sub_binary64`
601×	`associate-/l*_binary64`
488×	`associate-/r*_binary64`
380×	`fma-def_binary64`
279×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	123	11
5	318	8
6	1056	8
7	4350	8
8	4987	8

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 30 to 24 computations (20% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	0.0b	(+.f64 1 (exp.f64 x))

series6.0ms (0.1%)

Counts

2 → 8

Calls

2 calls:

5.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))

rewrite51.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
357×	`unpow-prod-down_binary64`
232×	`log-prod_binary64`
140×	`pow2_binary64`

Counts

2 → 100

Calls

2 calls:

49.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
49.0ms	(+.f64 1 (exp.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	117	14
2	1314	14
3	5001	14
0	0	0
1	0	0

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
661×	`associate-/l*_binary64`
268×	`fma-neg_binary64`
177×	`associate-/r/_binary64`
159×	`fma-def_binary64`

Counts

108 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	180
1	131	166
2	430	142
3	1778	130
4	4971	130
5	4989	130

prune85.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Error

Counts

114 → 2

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
	0.0b	(sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3)))

Compiler

Compiled 1537 to 1122 computations (27% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
✓	0.0b	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

series26.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

15.0ms	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
10.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

rewrite46.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

703×	`log1p-expm1-u_binary64`
703×	`expm1-log1p-u_binary64`
208×	`prod-diff_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Counts

2 → 70

Calls

2 calls:

45.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
45.0ms	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	148	24
2	1804	24
3	4982	24
0	0	0
1	0	0

simplify32.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
666×	`associate-/l*_binary64`
272×	`fma-neg_binary64`
179×	`associate-/r/_binary64`
159×	`fma-def_binary64`

Counts

94 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	372
1	152	358
2	456	334
3	1834	322
4	5032	322

prune38.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	87	2	89

Error

Counts

89 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
▶	0.0b	(sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3)))

Compiler

Compiled 1254 to 502 computations (60% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3)))
	0.0b	(+.f64 1 (exp.f64 x))
✓	0.0b	(pow.f64 (+.f64 1 (exp.f64 x)) 3)
✓	0.0b	(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))

series14.0ms (0.3%)

Counts

3 → 28

Calls

3 calls:

7.0ms	(pow.f64 (+.f64 1 (exp.f64 x)) 3)
5.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3)))
2.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))

rewrite91.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

670×	`log1p-expm1-u_binary64`
670×	`expm1-log1p-u_binary64`
157×	`fma-def_binary64`
123×	`expm1-udef_binary64`
123×	`log1p-udef_binary64`

Counts

3 → 109

Calls

3 calls:

89.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3)))
89.0ms	(pow.f64 (+.f64 1 (exp.f64 x)) 3)
89.0ms	(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	163	23
2	1725	23
3	4890	23
4	4854	23
0	0	0
1	0	0

simplify36.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
661×	`associate-/l*_binary64`
268×	`fma-neg_binary64`
237×	`fma-def_binary64`
178×	`associate-+l+_binary64`

Counts

137 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	334
1	167	311
2	514	285
3	1987	273
4	5182	273

prune205.0ms (4.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	194	2	196

Error

Counts

196 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓	0.0b	(sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3)))

Compiler

Compiled 2747 to 2001 computations (27.2% saved)

regimes92.0ms (1.9%)

Accuracy

Total 0.0b remaining (13.4%)

Threshold costs 0.0b (13.4%)

Counts

36 → 1

Compiler

Compiled 981 to 845 computations (13.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	7	13

end46.0ms (1%)

Compiler: Compiled 36 to 26 computations (27.8% saved)

Details

analyze709.0ms (14.9%)

sample3.2s (66.5%)

simplify44.0ms (0.9%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite51.0ms (1.1%)

simplify55.0ms (1.2%)

prune85.0ms (1.8%)

localize5.0ms (0.1%)

series26.0ms (0.5%)

rewrite46.0ms (1%)

simplify32.0ms (0.7%)

prune38.0ms (0.8%)

localize6.0ms (0.1%)

series14.0ms (0.3%)

rewrite91.0ms (1.9%)

simplify36.0ms (0.8%)

prune205.0ms (4.3%)

regimes92.0ms (1.9%)

simplify2.0ms (0%)

end46.0ms (1%)

Profiling