Details

analyze56.0ms (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 (83.3%)

Symmetry

(sort a x)

Results

760.0ms	1522×	body	2048	valid
565.0ms	1797×	body	1024	valid
282.0ms	3188×	body	128	valid
254.0ms	1139×	body	512	valid
93.0ms	610×	body	256	valid
11.0ms	132×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify21.0ms (0.9%)

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

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))

rewrite29.0ms (1.2%)

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:

28.0ms

(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

prune18.0ms (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
▶	15.2b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 540 to 244 computations (54.8% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	15.2b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series22.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
5.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

rewrite33.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

573×	`log1p-expm1-u_binary64`
573×	`expm1-log1p-u_binary64`
305×	`log-prod_binary64`
166×	`pow2_binary64`
118×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	156	15
2	1622	15

Stop Event

1×	node limit

Counts

2 → 50

Calls

2 calls:

32.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
32.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

simplify43.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

356×	`associate-l_binary64`
345×	`associate-r_binary64`
320×	`distribute-lft-in_binary64`
319×	`distribute-rgt-in_binary64`
286×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	48	664
1	139	664
2	428	658
3	2179	648
4	3341	622

Stop Event

1×	node limit

Counts

98 → 68

prune56.0ms (2.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	113	2	115

Error

Counts

115 → 2

Alt Table

Status	Error	Program
✓	15.2b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 1536 to 802 computations (47.8% saved)

regimes32.0ms (1.3%)

Accuracy

Total 0.0b remaining (16.7%)

Threshold costs 0.0b (16.7%)

Counts

5 → 1

Compiler

Compiled 250 to 169 computations (32.4% 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

end43.0ms (1.8%)

Remove: (sort a x)
Compiler: Compiled 39 to 27 computations (30.8% saved)

Details

analyze56.0ms (2.3%)

sample2.0s (83.3%)

simplify21.0ms (0.9%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite29.0ms (1.2%)

simplify34.0ms (1.4%)

prune18.0ms (0.8%)

localize5.0ms (0.2%)

series22.0ms (0.9%)

rewrite33.0ms (1.4%)

simplify43.0ms (1.8%)

prune56.0ms (2.3%)

regimes32.0ms (1.3%)

simplify2.0ms (0.1%)

end43.0ms (1.8%)

Profiling