Details

analyze808.0ms (5%)

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
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	50%	0.1%	7
50%	50%	0.1%	8
50%	50%	0.1%	9
50%	50%	0.1%	10
50%	50%	0.1%	11
50%	50%	0.1%	12
50%	50%	0.1%	13
50%	50%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample13.5s (83.1%)

Symmetry

(sort a b)

Results

10.5s	7977×	body	8192	exit
1.5s	1954×	body	1024	valid
624.0ms	4584×	body	128	valid
441.0ms	996×	body	512	valid
177.0ms	193×	body	2048	valid
144.0ms	529×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

29.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	6.1b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series320.0ms (2%)

Counts

2 → 48

Calls

2 calls:

316.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite47.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
71×	`add-sqr-sqrt_binary64`
68×	`add-log-exp_binary64`

Counts

2 → 60

Calls

2 calls:

46.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
46.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	137	18
2	1701	18
3	4952	18
0	0	0
1	0	0

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

630×	`fma-neg_binary64`
407×	`associate-+l+_binary64`
328×	`fma-def_binary64`
238×	`times-frac_binary64`
222×	`associate-+r+_binary64`

Counts

108 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	746
1	244	742
2	857	714
3	3662	710
4	4952	710
5	4990	710

prune51.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	2	92

Error

0.0b

Counts

92 → 2

Alt Table

Status	Error	Program
▶	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
✓	29.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 1415 to 693 computations (51% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (exp.f64 a))
✓	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(+.f64 1 (exp.f64 a))

series161.0ms (1%)

Counts

3 → 20

Calls

3 calls:

142.0ms	(log1p.f64 (exp.f64 a))
17.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
1.0ms	(+.f64 1 (exp.f64 a))

rewrite49.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

761×	`expm1-log1p-u_binary64`
760×	`log1p-expm1-u_binary64`
140×	`log1p-udef_binary64`
108×	`prod-diff_binary64`
93×	`egg-rr`

Counts

3 → 93

Calls

3 calls:

47.0ms	(log1p.f64 (exp.f64 a))
47.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
47.0ms	(+.f64 1 (exp.f64 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	157	20
2	1951	20
3	5140	20
0	0	0
1	0	0

simplify59.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
574×	`distribute-rgt-neg-in_binary64`
513×	`distribute-lft-neg-in_binary64`
477×	`associate-l_binary64`
384×	`associate-r_binary64`

Counts

113 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	194
1	131	186
2	353	174
3	984	159
4	3103	159
5	4619	159
6	5026	159

prune61.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	112	3	115

Error

Counts

115 → 3

Alt Table

Status	Error	Program
▶	0.7b	(+.f64 (expm1.f64 (log1p.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))
✓	29.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
✓	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1781 to 955 computations (46.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (exp.f64 a))
✓	0.0b	(expm1.f64 (log1p.f64 (log1p.f64 (exp.f64 a))))
✓	0.0b	(log1p.f64 (log1p.f64 (exp.f64 a)))
	0.0b	(+.f64 1 (exp.f64 a))

series527.0ms (3.2%)

Counts

2 → 24

Calls

2 calls:

385.0ms	(log1p.f64 (log1p.f64 (exp.f64 a)))
141.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (exp.f64 a))))

rewrite76.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

366×	`expm1-log1p-u_binary64`
364×	`log1p-expm1-u_binary64`
328×	`add-log-exp_binary64`
319×	`pow1_binary64`
221×	`unpow-prod-down_binary64`

Counts

2 → 73

Calls

2 calls:

75.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (exp.f64 a))))
75.0ms	(log1p.f64 (log1p.f64 (exp.f64 a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	92	12
2	978	12
3	4863	12
4	5000	12
0	0	0
1	0	0

simplify59.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

718×	`associate-/l*_binary64`
599×	`fma-neg_binary64`
515×	`cancel-sign-sub-inv_binary64`
485×	`associate-/r*_binary64`
200×	`associate-/r/_binary64`

Counts

97 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	305
1	138	305
2	399	288
3	1549	282
4	4610	282
5	4973	282
6	4969	282

prune101.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	160	3	163

Error

Counts

163 → 3

Alt Table

Status	Error	Program
✓	0.7b	(+.f64 (expm1.f64 (log1p.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))
✓	29.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
✓	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 2962 to 1649 computations (44.3% saved)

regimes121.0ms (0.7%)

Accuracy

Total 0.5b remaining (51.7%)

Threshold costs 0.5b (51.7%)

Counts

23 → 1

Compiler

Compiled 1865 to 1418 computations (24% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	13	16
2	12	16

end197.0ms (1.2%)

Compiler: Compiled 82 to 56 computations (31.7% saved)

Details

analyze808.0ms (5%)

sample13.5s (83.1%)

simplify6.0ms (0%)

prune2.0ms (0%)

localize5.0ms (0%)

series320.0ms (2%)

rewrite47.0ms (0.3%)

simplify67.0ms (0.4%)

prune51.0ms (0.3%)

localize6.0ms (0%)

series161.0ms (1%)

rewrite49.0ms (0.3%)

simplify59.0ms (0.4%)

prune61.0ms (0.4%)

localize10.0ms (0.1%)

series527.0ms (3.2%)

rewrite76.0ms (0.5%)

simplify59.0ms (0.4%)

prune101.0ms (0.6%)

regimes121.0ms (0.7%)

simplify3.0ms (0%)

end197.0ms (1.2%)

Profiling