Details

analyze704.0ms (17.2%)

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)

sample2.7s (66.8%)

Results

1.5s	2678×	body	1024	valid
446.0ms	1409×	body	512	valid
403.0ms	3146×	body	128	valid
164.0ms	740×	body	256	valid
163.0ms	283×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 41 to 35 computations (14.6% saved)

simplify24.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

390×	`fma-neg_binary64`
270×	`rules-42_binary64`
267×	`fma-def_binary64`
261×	`rules-41_binary64`
260×	`rules-40_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	65	13
2	151	13
3	401	13
4	932	13
5	11	13

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 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

Compiler

Compiled 39 to 28 computations (28.2% 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)))

series57.0ms (1.4%)

Counts

2 → 24

Calls

2 calls:

49.0ms	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
8.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

rewrite57.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

664×	`log1p-expm1-u_binary64`
664×	`expm1-log1p-u_binary64`
208×	`prod-diff_binary64`
120×	`log1p-udef_binary64`
83×	`egg-rr`

Counts

2 → 83

Calls

2 calls:

55.0ms	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
55.0ms	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	159	24
2	1952	24
3	4955	24
0	0	0
1	0	0

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

970×	`fma-neg_binary64`
470×	`rules-40_binary64`
470×	`rules-41_binary64`
470×	`rules-42_binary64`
470×	`rules-43_binary64`

Counts

107 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	372
1	369	358
2	1646	358
3	5357	358

prune76.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	2	101

Error

Counts

101 → 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 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3)))

Compiler

Compiled 1945 to 657 computations (66.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series42.0ms (1%)

Counts

3 → 36

Calls

3 calls:

20.0ms

(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3)

14.0ms

(sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3)))

8.0ms

(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3))

rewrite75.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

808×	`log1p-expm1-u_binary64`
808×	`expm1-log1p-u_binary64`
244×	`prod-diff_binary64`
142×	`egg-rr`
85×	`rules-40_binary64`

Counts

3 → 142

Calls

3 calls:

72.0ms

(sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3)))

72.0ms

(pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3)

72.0ms

(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	208	38
2	2374	38
3	5689	38
0	0	0
1	0	0

simplify44.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

595×	`rules-40_binary64`
595×	`rules-41_binary64`
595×	`rules-42_binary64`
595×	`rules-43_binary64`
417×	`rules-15-rev_binary64`

Counts

178 → 168

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	67	550
1	483	527
2	2149	527
3	5502	527

prune130.0ms (3.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	225	2	227

Error

Counts

227 → 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 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) 3)))

Compiler

Compiled 5040 to 1781 computations (64.7% saved)

regimes45.0ms (1.1%)

Accuracy

Total 0.0b remaining (4.3%)

Threshold costs 0.0b (4.3%)

Counts

13 → 1

Compiler

Compiled 510 to 404 computations (20.8% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	7	13

end45.0ms (1.1%)

Compiler: Compiled 39 to 27 computations (30.8% saved)

Details

analyze704.0ms (17.2%)

sample2.7s (66.8%)

simplify24.0ms (0.6%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series57.0ms (1.4%)

rewrite57.0ms (1.4%)

simplify39.0ms (0.9%)

prune76.0ms (1.9%)

localize10.0ms (0.2%)

series42.0ms (1%)

rewrite75.0ms (1.8%)

simplify44.0ms (1.1%)

prune130.0ms (3.2%)

regimes45.0ms (1.1%)

simplify1.0ms (0%)

end45.0ms (1.1%)

Profiling