Details

analyze757.0ms (20.7%)

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)

sample2.4s (66.4%)

Results

1.3s	2762×	body	1024	valid
406.0ms	1354×	body	512	valid
328.0ms	3137×	body	128	valid
195.0ms	690×	body	256	valid
177.0ms	313×	body	2048	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 28 to 24 computations (14.3% saved)

preprocess25.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

590×	`associate-/l*_binary64`
477×	`associate-/r*_binary64`
380×	`fma-def_binary64`
281×	`distribute-rgt-in_binary64`
270×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	127	11
5	349	8
6	1345	8
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify19.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

590×	`associate-/l*_binary64`
477×	`associate-/r*_binary64`
380×	`fma-def_binary64`
281×	`distribute-rgt-in_binary64`
270×	`associate-/l/_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	127	11
5	349	8
6	1345	8

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	(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))

series5.0ms (0.1%)

Counts

2 → 8

Calls

6 calls:

2.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))	x	0
1.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))	x	inf
1.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))	x	-inf
1.0ms	(+.f64 1 (exp.f64 x))	x	0
0.0ms	(+.f64 1 (exp.f64 x))	x	inf

rewrite38.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

550×	`pow1_binary64`
512×	`add-log-exp_binary64`
512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
500×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	118	14
2	1423	14

Stop Event

1×	node limit

Counts

2 → 58

simplify26.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	180
1	132	166
2	456	142
3	1993	130

Stop Event

1×	node limit

Counts

66 → 71

prune35.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	2	72

Error

Counts

72 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	0.6b	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))

Compiler

Compiled 863 to 609 computations (29.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.6b	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))

series142.0ms (3.9%)

Counts

1 → 12

Calls

3 calls:

71.0ms	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))	x	inf
70.0ms	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))	x	-inf
1.0ms	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))	x	0

rewrite41.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

545×	`pow1_binary64`
500×	`add-log-exp_binary64`
500×	`expm1-log1p-u_binary64`
499×	`log1p-expm1-u_binary64`
488×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	131	8
2	1428	8

Stop Event

1×	node limit

Counts

1 → 21

simplify42.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

477×	`associate-/l/_binary64`
398×	`distribute-lft-out_binary64`
395×	`fma-def_binary64`
362×	`*-commutative_binary64`
243×	`unswap-sqr_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	24	139
1	62	139
2	146	137
3	421	123
4	1443	120
5	2293	119
6	3095	119
7	3347	119
8	3976	119

Stop Event

1×	node limit

Counts

33 → 29

prune15.0ms (0.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	29	2	31

Error

Counts

31 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	0.6b	(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))

Compiler

Compiled 294 to 221 computations (24.8% saved)

regimes32.0ms (0.9%)

Accuracy

Total 0.0b remaining (19%)

Threshold costs 0.0b (19%)

Counts

6 → 1

Compiler

Compiled 262 to 222 computations (15.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	9	8

Stop Event

1×

saturated

end38.0ms (1%)

Stop Event

1×

done

Compiler

Compiled 25 to 21 computations (16% saved)

Details

analyze757.0ms (20.7%)

sample2.4s (66.4%)

preprocess25.0ms (0.7%)

simplify19.0ms (0.5%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite38.0ms (1%)

simplify26.0ms (0.7%)

prune35.0ms (1%)

localize5.0ms (0.1%)

series142.0ms (3.9%)

rewrite41.0ms (1.1%)

simplify42.0ms (1.1%)

prune15.0ms (0.4%)

regimes32.0ms (0.9%)

simplify2.0ms (0%)

end38.0ms (1%)

Profiling