Details

analyze1.6s (21.9%)

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%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample234.0ms (3.2%)

Algorithm

1×

intervals

Results

63.0ms	105×	body	128	valid
57.0ms	83×	body	1024	valid
16.0ms	40×	body	512	valid
11.0ms	10×	body	2048	valid
5.0ms	18×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

667×	`div-sub_binary64`
601×	`associate-/l*_binary64`
488×	`associate-/r*_binary64`
380×	`fma-def_binary64`
279×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	123	11
5	318	8
6	1056	8
7	4350	8
8	4987	8

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	39.0b	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

Compiler

Compiled 56 to 46 computations (17.9% saved)

localize7.0ms (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))

series14.0ms (0.2%)

Counts

2 → 8

Calls

2 calls:

11.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
3.0ms	(+.f64 1 (exp.f64 x))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
4×	`sqrt-prod_binary64`
4×	`add-log-exp_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 38

Calls

2 calls:

6.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
5.0ms	(+.f64 1 (exp.f64 x))

simplify121.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
283×	`fma-neg_binary64`
235×	`fma-def_binary64`
177×	`associate-/r/_binary64`
165×	`associate-+l+_binary64`

Counts

46 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	538
1	218	494
2	595	470
3	2140	454
4	4978	454
5	4938	454
6	5008	454

prune66.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	55	2	57

Error

Counts

57 → 2

Alt Table

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

Compiler

Compiled 675 to 491 computations (27.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
✓	0.0b	(log1p.f64 (exp.f64 x))
✓	0.0b	(exp.f64 (log1p.f64 (exp.f64 x)))

series1.2s (17%)

Counts

3 → 36

Calls

3 calls:

495.0ms	(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
388.0ms	(exp.f64 (log1p.f64 (exp.f64 x)))
355.0ms	(log1p.f64 (exp.f64 x))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`exp-prod_binary64`
6×	`add-cube-cbrt_binary64`
4×	`sqrt-pow1_binary64`

Counts

3 → 43

Calls

3 calls:

3.0ms	(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
2.0ms	(exp.f64 (log1p.f64 (exp.f64 x)))
1.0ms	(log1p.f64 (exp.f64 x))

simplify112.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
323×	`fma-neg_binary64`
194×	`fma-def_binary64`
168×	`associate-+l+_binary64`
161×	`distribute-rgt-neg-in_binary64`

Counts

79 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	800
1	213	733
2	571	703
3	2170	691
4	4886	691
5	4942	691

prune101.0ms (1.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	80	2	82

Error

Counts

82 → 2

Alt Table

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

Compiler

Compiled 882 to 502 computations (43.1% saved)

regimes73.0ms (1%)

Accuracy

Total 0.0b remaining (20.3%)

Threshold costs 0.0b (20.3%)

Counts

7 → 1

Compiler

Compiled 287 to 247 computations (13.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	6	9

end1.0ms (0%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

sample3.6s (49.6%)

Algorithm

1×

intervals

Results

1.9s	2540×	body	1024	valid
505.0ms	1304×	body	512	valid
370.0ms	3211×	body	128	valid
241.0ms	280×	body	2048	valid
169.0ms	665×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 33 to 28 computations (15.2% saved)

Details

analyze1.6s (21.9%)

sample234.0ms (3.2%)

simplify58.0ms (0.8%)

prune7.0ms (0.1%)

localize7.0ms (0.1%)

series14.0ms (0.2%)

rewrite14.0ms (0.2%)

simplify121.0ms (1.7%)

prune66.0ms (0.9%)

localize10.0ms (0.1%)

series1.2s (17%)

rewrite9.0ms (0.1%)

simplify112.0ms (1.5%)

prune101.0ms (1.4%)

regimes73.0ms (1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample3.6s (49.6%)

Profiling