Details

analyze64.0ms (2.2%)

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)

sample2.2s (73.9%)

Symmetry

(sort a x)

Results

764.0ms	1510×	body	2048	valid
662.0ms	1770×	body	1024	valid
294.0ms	3174×	body	128	valid
276.0ms	1154×	body	512	valid
101.0ms	648×	body	256	valid
13.0ms	147×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify108.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
455×	`*-commutative_binary64`
440×	`unswap-sqr_binary64`
344×	`associate-l_binary64`
274×	`associate-+l+_binary64`

Counts

1 → 2

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	160	6
6	432	6
7	1564	6
8	3490	6
9	4954	6
10	4993	6
11	4874	6

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	(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))

rewrite71.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

736×	`log1p-udef_binary64`
405×	`log1p-expm1-u_binary64`
405×	`expm1-log1p-u_binary64`
342×	`pow1_binary64`
287×	`unpow-prod-down_binary64`

Counts

1 → 36

Calls

1 calls:

71.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	95	6
2	1080	6
3	4662	6
4	5883	6

simplify56.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1324×	`distribute-lft-out_binary64`
882×	`fma-def_binary64`
423×	`associate-/l/_binary64`
368×	`*-commutative_binary64`
362×	`associate-/r/_binary64`

Counts

60 → 44

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	284
1	86	284
2	234	278
3	888	262
4	2148	248
5	2915	248
6	3566	248
7	5038	248

prune20.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	2	45

Error

Counts

45 → 2

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	24.9b	(+.f64 (.f64 a x) (.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))))

Compiler

Compiled 546 to 250 computations (54.2% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.6b	(+.f64 (.f64 a x) (.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))))
✓	14.6b	(*.f64 (pow.f64 a 2) (pow.f64 x 2))

series24.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

14.0ms	(+.f64 (.f64 a x) (.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))))
10.0ms	(*.f64 (pow.f64 a 2) (pow.f64 x 2))

rewrite58.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

534×	`log-prod_binary64`
467×	`fma-def_binary64`
238×	`fma-neg_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`

Counts

2 → 88

Calls

2 calls:

56.0ms	(+.f64 (.f64 a x) (.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))))
56.0ms	(*.f64 (pow.f64 a 2) (pow.f64 x 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	238	21
2	2615	21
3	5012	21

simplify146.0ms (5%)

Algorithm

1×	egg-herbie

Rules

816×	`fabs-mul_binary64`
743×	`unswap-sqr_binary64`
743×	`cube-prod_binary64`
718×	`sqr-pow_binary64`
361×	`pow-sqr_binary64`

Counts

94 → 91

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	60
1	23	60
2	48	60
3	141	60
4	539	60
5	783	60
6	791	60
7	879	60
8	984	60
9	1093	60
10	1208	60
11	2300	60
12	2264	60
13	2510	60
14	2722	60
15	3039	60
16	3466	60
17	3758	60
18	3940	60
19	4155	60
20	4368	60
21	4643	60
22	4864	60

prune74.0ms (2.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	91	2	93

Error

Counts

93 → 2

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	24.9b	(+.f64 (.f64 a x) (.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))))

Compiler

Compiled 1538 to 827 computations (46.2% saved)

regimes83.0ms (2.8%)

Accuracy

Total 0.0b remaining (1.1%)

Threshold costs 0.0b (1.1%)

Counts

20 → 1

Compiler

Compiled 1290 to 784 computations (39.2% 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
2	6	6

end41.0ms (1.4%)

Remove: (sort a x)
Compiler: Compiled 45 to 31 computations (31.1% saved)

Details

analyze64.0ms (2.2%)

sample2.2s (73.9%)

simplify108.0ms (3.7%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite71.0ms (2.4%)

simplify56.0ms (1.9%)

prune20.0ms (0.7%)

localize7.0ms (0.3%)

series24.0ms (0.8%)

rewrite58.0ms (2%)

simplify146.0ms (5%)

prune74.0ms (2.5%)

regimes83.0ms (2.8%)

simplify2.0ms (0.1%)

end41.0ms (1.4%)

Profiling