Details

analyze567.0ms (4.1%)

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%	37.5%	12.6%	7
50%	37.5%	12.6%	8
50%	31.2%	18.8%	9
50%	31.2%	18.8%	10
50%	28.1%	22%	11
50%	28.1%	22%	12
50%	26.5%	23.5%	13
50%	26.5%	23.5%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample10.2s (74%)

Results

5.3s	4986×	body	1024	valid
1.7s	2020×	body	1024	invalid
1.1s	1735×	body	512	valid
673.0ms	449×	body	2048	valid
574.0ms	1005×	body	512	invalid
279.0ms	684×	body	256	valid
216.0ms	544×	body	256	invalid
156.0ms	710×	body	128	invalid
88.0ms	402×	body	128	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify104.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

626×	`associate-/l*_binary64`
509×	`div-sub_binary64`
462×	`times-frac_binary64`
386×	`sub-neg_binary64`
367×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	22	18
2	49	18
3	111	18
4	208	17
5	362	17
6	692	17
7	1513	17
8	3726	17
9	4287	17
10	4857	17
11	4749	17

prune5.0ms (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

58.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	58.0b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

Compiler

Compiled 53 to 38 computations (28.3% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 re)
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
✓	6.4b	(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

series37.0ms (0.3%)

Counts

3 → 40

Calls

3 calls:

31.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
4.0ms	(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
3.0ms	(cos.f64 re)

rewrite150.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

524×	`prod-diff_binary64`
473×	`log-prod_binary64`
198×	`fma-def_binary64`
178×	`expm1-udef_binary64`
178×	`log1p-udef_binary64`

Counts

3 → 138

Calls

3 calls:

145.0ms	(cos.f64 re)
145.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
145.0ms	(-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	251	27
2	2461	23
3	4888	23
4	5310	23
0	0	0
1	0	0

simplify116.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-def_binary64`
469×	`sub-neg_binary64`
397×	`distribute-rgt-neg-in_binary64`
257×	`neg-mul-1_binary64`
254×	`associate-l_binary64`

Counts

178 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	809
1	309	787
2	1026	754
3	3725	754
4	4666	754
5	4962	754

prune158.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	172	2	174

Error

0.1b

Counts

174 → 2

Alt Table

Status	Error	Program
✓	58.0b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
▶	0.9b	(.f64 (cos.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))

Compiler

Compiled 3237 to 1809 computations (44.1% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 re)
✓	0.1b	(.f64 (cos.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
✓	0.1b	(*.f64 (pow.f64 im 3) -1/6)

series46.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

40.0ms	(.f64 (cos.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
5.0ms	(*.f64 (pow.f64 im 3) -1/6)

rewrite115.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

511×	`log-prod_binary64`
367×	`fma-def_binary64`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`
172×	`fma-neg_binary64`

Counts

2 → 81

Calls

2 calls:

110.0ms	(.f64 (cos.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
110.0ms	(*.f64 (pow.f64 im 3) -1/6)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	242	20
2	2661	20
3	4982	20
4	4850	20
0	0	0
1	0	0

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

389×	`fma-def_binary64`
328×	`sub-neg_binary64`
327×	`associate-l_binary64`
282×	`associate-r_binary64`
273×	`distribute-rgt-neg-in_binary64`

Counts

117 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	549
1	174	545
2	610	523
3	2562	519
4	4987	519

prune168.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	120	8	128

Error

0.0b

Counts

128 → 8

Alt Table

Status	Error	Program
	19.4b	(.f64 (pow.f64 (sqrt.f64 (cos.f64 re)) 2) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
✓	58.0b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	1.1b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 re) 3)) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
✓	0.9b	(.f64 (cos.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	1.3b	(.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 re)))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 re))))) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	1.5b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 re)) 3) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	1.2b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 re)))) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
▶	1.0b	(.f64 (log1p.f64 (expm1.f64 (cos.f64 re))) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))

Compiler

Compiled 2425 to 1472 computations (39.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (log1p.f64 (expm1.f64 (cos.f64 re))) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	0.1b	(*.f64 (pow.f64 im 3) -1/6)
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 re)))
✓	0.6b	(expm1.f64 (cos.f64 re))

series49.0ms (0.4%)

Counts

3 → 48

Calls

3 calls:

41.0ms	(.f64 (log1p.f64 (expm1.f64 (cos.f64 re))) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
5.0ms	(expm1.f64 (cos.f64 re))
3.0ms	(log1p.f64 (expm1.f64 (cos.f64 re)))

rewrite98.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

549×	`log-prod_binary64`
379×	`fma-def_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
183×	`fma-neg_binary64`

Counts

3 → 114

Calls

3 calls:

94.0ms	(.f64 (log1p.f64 (expm1.f64 (cos.f64 re))) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
94.0ms	(log1p.f64 (expm1.f64 (cos.f64 re)))
94.0ms	(expm1.f64 (cos.f64 re))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	261	21
2	2851	21
3	5171	21
0	0	0
1	0	0

simplify104.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

511×	`fma-def_binary64`
456×	`sub-neg_binary64`
388×	`distribute-rgt-neg-in_binary64`
383×	`associate-l_binary64`
370×	`distribute-lft-neg-in_binary64`

Counts

162 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	673
1	255	661
2	846	633
3	3323	624
4	4945	624
5	5101	624

prune424.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	162	8	170

Error

0.0b

Counts

170 → 8

Alt Table

Status	Error	Program
	1.2b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 re)))) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	2.1b	(.f64 (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 (cos.f64 re))) 3)) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
▶	1.1b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 re) 3)) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
✓	0.9b	(.f64 (cos.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	1.3b	(.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 re)))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 re))))) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	1.5b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 re)) 3) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
✓	58.0b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	19.4b	(.f64 (log1p.f64 (pow.f64 (sqrt.f64 (expm1.f64 (cos.f64 re))) 2)) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))

Compiler

Compiled 3187 to 1906 computations (40.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 re) 3)) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	0.1b	(*.f64 (pow.f64 im 3) -1/6)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 re) 3))
✓	0.3b	(pow.f64 (cos.f64 re) 3)

series57.0ms (0.4%)

Counts

3 → 40

Calls

3 calls:

44.0ms	(.f64 (cbrt.f64 (pow.f64 (cos.f64 re) 3)) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
10.0ms	(pow.f64 (cos.f64 re) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 re) 3))

rewrite107.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

561×	`log-prod_binary64`
380×	`fma-def_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
177×	`log-pow_binary64`

Counts

3 → 116

Calls

3 calls:

97.0ms	(.f64 (cbrt.f64 (pow.f64 (cos.f64 re) 3)) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
97.0ms	(cbrt.f64 (pow.f64 (cos.f64 re) 3))
97.0ms	(pow.f64 (cos.f64 re) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	265	22
2	2881	22
3	5170	22
0	0	0
1	0	0

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-def_binary64`
402×	`sub-neg_binary64`
352×	`associate-l_binary64`
347×	`distribute-rgt-neg-in_binary64`
331×	`distribute-lft-neg-in_binary64`

Counts

156 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	601
1	230	589
2	765	559
3	3015	553
4	5208	553

prune251.0ms (1.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	160	9	169

Error

0.0b

Counts

169 → 9

Alt Table

Status	Error	Program
	1.2b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (cos.f64 re)))) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	2.1b	(.f64 (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 (cos.f64 re))) 3)) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
✓	1.1b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 re) 3)) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
✓	0.9b	(.f64 (cos.f64 re) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	1.1b	(.f64 (.f64 (cbrt.f64 (cos.f64 re)) (pow.f64 (pow.f64 (cos.f64 re) 2) 1/3)) (+.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) -1/6)))
	1.5b	(.f64 (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 re) 3)))) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
	1.5b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 re)) 3) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))
✓	58.0b	(.f64 (.f64 1/2 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	19.4b	(.f64 (log1p.f64 (pow.f64 (sqrt.f64 (expm1.f64 (cos.f64 re))) 2)) (+.f64 (neg.f64 im) (.f64 (pow.f64 im 3) -1/6)))

Compiler

Compiled 3078 to 1913 computations (37.8% saved)

regimes539.0ms (3.9%)

Accuracy

Total 0.8b remaining (89.8%)

Threshold costs 0.8b (89.8%)

Counts

53 → 1

Compiler

Compiled 4929 to 3888 computations (21.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	16	19
2	16	19

end283.0ms (2%)

Compiler: Compiled 181 to 146 computations (19.3% saved)

Details

analyze567.0ms (4.1%)

sample10.2s (74%)

simplify104.0ms (0.8%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series37.0ms (0.3%)

rewrite150.0ms (1.1%)

simplify116.0ms (0.8%)

prune158.0ms (1.1%)

localize15.0ms (0.1%)

series46.0ms (0.3%)

rewrite115.0ms (0.8%)

simplify69.0ms (0.5%)

prune168.0ms (1.2%)

localize21.0ms (0.2%)

series49.0ms (0.4%)

rewrite98.0ms (0.7%)

simplify104.0ms (0.7%)

prune424.0ms (3.1%)

localize20.0ms (0.1%)

series57.0ms (0.4%)

rewrite107.0ms (0.8%)

simplify76.0ms (0.5%)

prune251.0ms (1.8%)

regimes539.0ms (3.9%)

simplify4.0ms (0%)

end283.0ms (2%)

Profiling