Details

analyze538.0ms (8.2%)

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
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	40.6%	9.5%	7
50%	39%	11%	8
50%	33.6%	16.5%	9
50%	32.4%	17.7%	10
50%	29.5%	20.6%	11
50%	28.8%	21.3%	12
50%	27.3%	22.8%	13
50%	26.9%	23.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample4.5s (68%)

Results

1.4s	2061×	body	1024	valid
1.1s	2035×	body	1024	invalid
703.0ms	4647×	body	128	valid
389.0ms	998×	body	512	valid
370.0ms	1034×	body	512	invalid
149.0ms	544×	body	256	valid
137.0ms	527×	body	256	invalid
107.0ms	746×	body	128	invalid
9.0ms	6×	body	2048	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

preprocess43.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

692×	`times-frac_binary64`
480×	`fma-def_binary64`
341×	`associate-/r/_binary64`
306×	`associate-/l/_binary64`
305×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	36
1	50	36
2	135	36
3	273	34
4	361	34
5	489	34
6	837	34
7	2180	34
8	4821	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

778×	`unswap-sqr_binary64`
455×	`associate-/r*_binary64`
357×	`associate-/l*_binary64`
346×	`times-frac_binary64`
315×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	28	18
2	71	18
3	140	17
4	185	17
5	252	17
6	430	17
7	1107	17
8	3311	17
9	3702	17
10	4192	17

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 53 to 38 computations (28.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
✓	0.0b	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

series16.0ms (0.3%)

Counts

2 → 36

Calls

9 calls:

3.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))	im	inf
3.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))	re	0
3.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))	im	-inf
2.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))	re	-inf
2.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))	re	inf

rewrite42.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

635×	`prod-diff_binary64`
176×	`log1p-udef_binary64`
131×	`add-sqr-sqrt_binary64`
128×	`pow1_binary64`
127×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	257	20
2	3669	20

Stop Event

1×	node limit

Counts

2 → 56

simplify36.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
517×	`fma-def_binary64`
246×	`distribute-rgt-neg-in_binary64`
244×	`sub-neg_binary64`
228×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	735
1	245	670
2	799	646
3	3336	645

Stop Event

1×	node limit

Counts

92 → 83

prune68.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	4	84

Error

Counts

84 → 4

Alt Table

Status	Error	Program
	1.1b	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))
	32.7b	(log.f64 (pow.f64 (pow.f64 (exp.f64 1/2) (sin.f64 re)) (*.f64 2 (cosh.f64 im))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
▶	0.3b	(.f64 (.f64 1/2 (sin.f64 re)) (cbrt.f64 (pow.f64 (*.f64 2 (cosh.f64 im)) 3)))

Compiler

Compiled 1603 to 874 computations (45.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (cbrt.f64 (pow.f64 (*.f64 2 (cosh.f64 im)) 3)))
✓	0.0b	(cosh.f64 im)
✓	0.0b	(pow.f64 (*.f64 2 (cosh.f64 im)) 3)
✓	0.3b	(cbrt.f64 (pow.f64 (*.f64 2 (cosh.f64 im)) 3))

series64.0ms (1%)

Counts

4 → 60

Calls

15 calls:

9.0ms	(pow.f64 (*.f64 2 (cosh.f64 im)) 3)	im	inf
7.0ms	(pow.f64 (*.f64 2 (cosh.f64 im)) 3)	im	-inf
7.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (cbrt.f64 (pow.f64 (*.f64 2 (cosh.f64 im)) 3)))	im	inf
6.0ms	(cbrt.f64 (pow.f64 (*.f64 2 (cosh.f64 im)) 3))	im	inf
6.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (cbrt.f64 (pow.f64 (*.f64 2 (cosh.f64 im)) 3)))	im	-inf

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`log-prod_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
185×	`pow3_binary64`
173×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	275	26
2	2905	26

Stop Event

1×	node limit

Counts

4 → 119

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-neg_binary64`
529×	`fma-def_binary64`
257×	`sub-neg_binary64`
246×	`associate-r_binary64`
244×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1028
1	289	971
2	903	946
3	3665	946

Stop Event

1×	node limit

Counts

179 → 163

prune129.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	164	3	167

Error

Counts

167 → 3

Alt Table

Status	Error	Program
	21.7b	(cbrt.f64 (pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3))
▶	1.1b	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 2728 to 1703 computations (37.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2)))
✓	0.0b	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))
✓	0.1b	(*.f64 (sin.f64 re) (pow.f64 im 2))

series42.0ms (0.6%)

Counts

3 → 15

Calls

18 calls:

7.0ms	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))	im	inf
3.0ms	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))	re	0
3.0ms	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))	re	inf
3.0ms	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))	re	-inf
3.0ms	(.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2)))	re	-inf

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

971×	`prod-diff_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`
107×	`add-sqr-sqrt_binary64`
103×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	215	36
2	2674	36

Stop Event

1×	node limit

Counts

3 → 66

simplify32.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-def_binary64`
360×	`sub-neg_binary64`
341×	`distribute-rgt-neg-in_binary64`
341×	`cancel-sign-sub-inv_binary64`
337×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	60	435
1	193	387
2	729	333
3	3816	333

Stop Event

1×	node limit

Counts

81 → 93

prune64.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	93	3	96

Error

Counts

96 → 3

Alt Table

Status	Error	Program
▶	21.7b	(cbrt.f64 (pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3))
✓	1.1b	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 1819 to 983 computations (46% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cosh.f64 im) (sin.f64 re))
	0.0b	(cosh.f64 im)
✓	0.3b	(pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3)
✓	21.7b	(cbrt.f64 (pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3))

series98.0ms (1.5%)

Counts

3 → 72

Calls

18 calls:

12.0ms	(pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3)	im	inf
10.0ms	(pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3)	re	0
9.0ms	(pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3)	im	-inf
9.0ms	(pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3)	re	-inf
8.0ms	(cbrt.f64 (pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3))	re	0

rewrite42.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

779×	`pow1_binary64`
727×	`log1p-expm1-u_binary64`
727×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
81×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	191	27
2	2043	27

Stop Event

1×	node limit

Counts

3 → 77

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

805×	`associate-l_binary64`
328×	`cancel-sign-sub-inv_binary64`
215×	`fma-def_binary64`
187×	`distribute-rgt-in_binary64`
171×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	2196
1	483	2084
2	2014	2043

Stop Event

1×	node limit

Counts

149 → 96

prune83.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	132	3	135

Error

Counts

135 → 3

Alt Table

Status	Error	Program
✓	21.7b	(cbrt.f64 (pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3))
✓	1.1b	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 2555 to 1434 computations (43.9% saved)

regimes462.0ms (7.1%)

Accuracy

Total 0.0b remaining (15.9%)

Threshold costs 0.0b (15.9%)

Counts

80 → 1

Compiler

Compiled 6029 to 4668 computations (22.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	11	14

Stop Event

1×

saturated

end66.0ms (1%)

Stop Event

1×

done

Compiler

Compiled 59 to 46 computations (22% saved)

Details

analyze538.0ms (8.2%)

sample4.5s (68%)

preprocess43.0ms (0.7%)

simplify34.0ms (0.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series16.0ms (0.3%)

rewrite42.0ms (0.6%)

simplify36.0ms (0.5%)

prune68.0ms (1%)

localize8.0ms (0.1%)

series64.0ms (1%)

rewrite48.0ms (0.7%)

simplify47.0ms (0.7%)

prune129.0ms (2%)

localize6.0ms (0.1%)

series42.0ms (0.6%)

rewrite48.0ms (0.7%)

simplify32.0ms (0.5%)

prune64.0ms (1%)

localize7.0ms (0.1%)

series98.0ms (1.5%)

rewrite42.0ms (0.6%)

simplify59.0ms (0.9%)

prune83.0ms (1.3%)

regimes462.0ms (7.1%)

simplify2.0ms (0%)

end66.0ms (1%)

Profiling