Details

analyze341.0ms (5.7%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample3.7s (61.3%)

Results

1.6s	1990×	body	1024	valid
846.0ms	4415×	body	128	valid
562.0ms	1080×	body	512	valid
274.0ms	233×	body	2048	valid
191.0ms	538×	body	256	valid
135.0ms	399×	body	128	invalid
21.0ms	29×	body	1024	invalid
1.0ms	4×	body	256	invalid
1.0ms	2×	body	512	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
577×	`div-sub_binary64`
534×	`cancel-sign-sub-inv_binary64`
519×	`fma-neg_binary64`
467×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	57	45
2	153	37
3	394	37
4	1347	37
5	4048	37
6	4614	37
7	5259	37

prune5.0ms (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

28.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	47.3b	(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 (+.f64 eps -1)) x) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))
▶	28.1b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Status

Error

Program

47.3b

(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 (+.f64 eps -1)) x) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))

▶

28.1b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 172 to 133 computations (22.7% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 eps) x)
✓	0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
✓	0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
✓	2.4b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series84.0ms (1.4%)

Counts

4 → 92

Calls

4 calls:

45.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
18.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
16.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
4.0ms	(*.f64 (+.f64 1 eps) x)

rewrite73.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64`
80×	`exp-neg_binary64`
80×	`frac-times_binary64`
60×	`exp-diff_binary64`
60×	`neg-sub0_binary64`

Counts

4 → 191

Calls

4 calls:

16.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
12.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
12.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
6.0ms	(*.f64 (+.f64 1 eps) x)

simplify907.0ms (15.1%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-neg_binary64`
538×	`associate-l_binary64`
535×	`associate-r_binary64`
518×	`fma-def_binary64`
273×	`distribute-rgt-in_binary64`

Counts

283 → 340

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	575	12489
1	1523	11687
2	4721	11687
3	5065	11687

prune423.0ms (7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	338	2	340
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	339	3	342

Error

0.0b

Counts

342 → 3

Alt Table

Status	Error	Program
	18.2b	(/.f64 (-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) 2) (*.f64 x x)) 2)
✓	28.1b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
▶	0.3b	(/.f64 (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x)))) 2)

Compiler

Compiled 17426 to 12996 computations (25.4% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x))))
✓	0.0b	(*.f64 x (exp.f64 (neg.f64 x)))

series8.0ms (0.1%)

Counts

2 → 21

Calls

2 calls:

5.0ms	(+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x))))
3.0ms	(*.f64 x (exp.f64 (neg.f64 x)))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`associate-*r/_binary64`
14×	`exp-neg_binary64`
9×	`frac-add_binary64`
7×	`exp-diff_binary64`
7×	`neg-sub0_binary64`

Counts

2 → 47

Calls

2 calls:

8.0ms	(+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x))))
7.0ms	(*.f64 x (exp.f64 (neg.f64 x)))

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

966×	`fma-neg_binary64`
499×	`fma-def_binary64`
392×	`cancel-sign-sub-inv_binary64`
318×	`unswap-sqr_binary64`
241×	`*-commutative_binary64`

Counts

68 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	995
1	272	795
2	948	726
3	2833	719
4	4432	719
5	4928	719

prune63.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	89	2	91

Error

Counts

91 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (/.f64 (fma.f64 x 2 2) (exp.f64 x)) 2)
✓	28.1b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Status

Error

Program

▶

0.3b

(/.f64 (/.f64 (fma.f64 x 2 2) (exp.f64 x)) 2)

✓

28.1b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 1737 to 981 computations (43.5% saved)

localize6.0ms (0.1%)

prune2.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

2 → 2

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (/.f64 (fma.f64 x 2 2) (exp.f64 x)) 2)
✓	28.1b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Status

Error

Program

✓

0.3b

(/.f64 (/.f64 (fma.f64 x 2 2) (exp.f64 x)) 2)

✓

28.1b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 42 to 34 computations (19% saved)

regimes166.0ms (2.8%)

Accuracy

Total 0.5b remaining (95.4%)

Threshold costs 0.5b (95.4%)

Counts

36 → 1

Compiler

Compiled 3588 to 2776 computations (22.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	7	13

end53.0ms (0.9%)

Compiler: Compiled 64 to 52 computations (18.8% saved)

Details

analyze341.0ms (5.7%)

sample3.7s (61.3%)

simplify65.0ms (1.1%)

prune5.0ms (0.1%)

localize18.0ms (0.3%)

series84.0ms (1.4%)

rewrite73.0ms (1.2%)

simplify907.0ms (15.1%)

prune423.0ms (7%)

localize9.0ms (0.1%)

series8.0ms (0.1%)

rewrite18.0ms (0.3%)

simplify84.0ms (1.4%)

prune63.0ms (1%)

localize6.0ms (0.1%)

prune2.0ms (0%)

regimes166.0ms (2.8%)

simplify2.0ms (0%)

end53.0ms (0.9%)

Profiling