Details

analyze58.0ms (2.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (78.7%)

Symmetry

(sort a x)

Results

714.0ms	1485×	body	2048	valid
567.0ms	1806×	body	1024	valid
276.0ms	3122×	body	128	valid
265.0ms	1189×	body	512	valid
99.0ms	654×	body	256	valid
15.0ms	171×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify19.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

440×	`unswap-sqr_binary64`
329×	`associate-l_binary64`
275×	`associate-+l+_binary64`
252×	`associate-r_binary64`
201×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	16	6
2	23	6
3	35	6
4	70	6
5	175	6
6	556	6
7	2331	6

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.2%)

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	(expm1.f64 (*.f64 a x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))

series5.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(expm1.f64 (*.f64 a x))

rewrite28.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

405×	`log1p-expm1-u_binary64`
405×	`expm1-log1p-u_binary64`
342×	`pow1_binary64`
285×	`unpow-prod-down_binary64`
236×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	96	6
2	1123	6

Stop Event

1×	node limit

Counts

1 → 36

Calls

1 calls:

27.0ms

(expm1.f64 (*.f64 a x))

simplify34.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

882×	`fma-def_binary64`
844×	`distribute-lft-out_binary64`
307×	`*-commutative_binary64`
300×	`unswap-sqr_binary64`
172×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	284
1	87	284
2	242	278
3	1040	262
4	3195	248
5	4880	248

Stop Event

1×	node limit

Counts

60 → 45

prune20.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	2	46

Error

Counts

46 → 2

Alt Table

Status	Error	Program
▶	18.2b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 560 to 254 computations (54.6% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 a x) 3)
✓	0.2b	(.f64 1/2 (.f64 a a))
✓	3.8b	(fma.f64 x (.f64 1/2 (.f64 a a)) a)
✓	8.0b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (.f64 1/6 (pow.f64 (.f64 a x) 3)))

series38.0ms (1.5%)

Counts

4 → 84

Calls

4 calls:

17.0ms	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
10.0ms	(pow.f64 (*.f64 a x) 3)
8.0ms	(fma.f64 x (.f64 1/2 (.f64 a a)) a)
2.0ms	(.f64 1/2 (.f64 a a))

rewrite54.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

605×	`log-prod_binary64`
272×	`prod-diff_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
195×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	271	49
2	3098	49

Stop Event

1×	node limit

Counts

4 → 104

Calls

4 calls:

52.0ms	(pow.f64 (*.f64 a x) 3)
52.0ms	(.f64 1/2 (.f64 a a))
52.0ms	(fma.f64 x (.f64 1/2 (.f64 a a)) a)
52.0ms	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (.f64 1/6 (pow.f64 (.f64 a x) 3)))

simplify111.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

937×	`fma-def_binary64`
755×	`unswap-sqr_binary64`
535×	`*-commutative_binary64`
350×	`sqr-pow_binary64`
164×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	1158
1	63	1122
2	171	1076
3	681	1056
4	1605	1032
5	3289	1032
6	3482	1032
7	3681	1032
8	3862	1032
9	4198	1032
10	4415	1032
11	4709	1032

Stop Event

1×	node limit

Counts

188 → 119

prune71.0ms (2.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	119	2	121

Error

Counts

121 → 2

Alt Table

Status	Error	Program
✓	18.2b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 2724 to 1471 computations (46% saved)

regimes40.0ms (1.6%)

Accuracy

Total 0.0b remaining (10.4%)

Threshold costs 0.0b (10.4%)

Counts

8 → 1

Compiler

Compiled 495 to 319 computations (35.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Stop Event

1×

saturated

end42.0ms (1.7%)

Remove: (sort a x)
Compiler: Compiled 49 to 32 computations (34.7% saved)

Details

analyze58.0ms (2.3%)

sample2.0s (78.7%)

simplify19.0ms (0.7%)

prune5.0ms (0.2%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite28.0ms (1.1%)

simplify34.0ms (1.4%)

prune20.0ms (0.8%)

localize10.0ms (0.4%)

series38.0ms (1.5%)

rewrite54.0ms (2.2%)

simplify111.0ms (4.4%)

prune71.0ms (2.8%)

regimes40.0ms (1.6%)

simplify2.0ms (0.1%)

end42.0ms (1.7%)

Profiling