Details

analyze1.1s (12.1%)

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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.4s (49%)

Symmetry

(sort a1 a2)

Results

1.2s	1811×	body	1024	valid
1.1s	1562×	body	1024	invalid
855.0ms	5100×	body	128	valid
408.0ms	893×	body	512	valid
369.0ms	784×	body	512	invalid
148.0ms	670×	body	128	invalid
144.0ms	372×	body	256	invalid
139.0ms	451×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	58	18
3	88	18
4	115	18
5	135	18
6	152	18
7	170	18
8	172	18

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (0%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
✓	0.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series151.0ms (1.7%)

Counts

4 → 88

Calls

4 calls:

98.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
24.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
23.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
6.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite70.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`fma-def_binary64`
246×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
243×	`fma-neg_binary64`
164×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	56
1	283	54
2	3898	54

Stop Event

1×	node limit

Counts

4 → 164

Calls

4 calls:

67.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
67.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
67.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
67.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-neg_binary64`
398×	`sub-neg_binary64`
338×	`unswap-sqr_binary64`
221×	`associate-r_binary64`
193×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	2134
1	297	2126
2	859	1810
3	3448	1806

Stop Event

1×	node limit

Counts

252 → 201

prune270.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	234	7	241
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	236	7	243

Error

Counts

243 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (fma.f64 a1 a1 (*.f64 a2 a2))))
	0.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2))) (*.f64 a2 a2)))
	0.5b	(fma.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 2 -1/2) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1))))
▶	0.4b	(+.f64 (.f64 (.f64 (cos.f64 th) (pow.f64 2 -1/2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	0.4b	(/.f64 (fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 th) a2) a2))) 2)
	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 2 1/4)) (pow.f64 2 1/4)))

Compiler

Compiled 6413 to 3675 computations (42.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cos.f64 th) (pow.f64 2 -1/2))
	0.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (pow.f64 2 -1/2)) (*.f64 a1 a1))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series21.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

17.0ms	(.f64 (.f64 (cos.f64 th) (pow.f64 2 -1/2)) (*.f64 a1 a1))
4.0ms	(*.f64 (cos.f64 th) (pow.f64 2 -1/2))

rewrite40.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

838×	`log1p-expm1-u_binary64`
838×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
94×	`add-cube-cbrt_binary64`
94×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	207	22
2	2391	22

Stop Event

1×	node limit

Counts

2 → 30

Calls

2 calls:

39.0ms	(*.f64 (cos.f64 th) (pow.f64 2 -1/2))
39.0ms	(.f64 (.f64 (cos.f64 th) (pow.f64 2 -1/2)) (*.f64 a1 a1))

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-neg_binary64`
335×	`distribute-rgt-neg-in_binary64`
320×	`distribute-lft-neg-in_binary64`
278×	`associate-r_binary64`
275×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	588
1	125	580
2	425	542
3	2138	518
4	4737	518

Stop Event

1×	node limit

Counts

66 → 49

prune123.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	122	7	129

Error

Counts

129 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (fma.f64 a1 a1 (*.f64 a2 a2))))
	0.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2))) (*.f64 a2 a2)))
	0.5b	(fma.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 2 -1/2) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1))))
✓	0.4b	(+.f64 (.f64 (.f64 (cos.f64 th) (pow.f64 2 -1/2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
▶	0.4b	(/.f64 (fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 th) a2) a2))) 2)
	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 2 1/4)) (pow.f64 2 1/4)))

Compiler

Compiled 3380 to 2036 computations (39.8% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (.f64 a1 a1))
✓	0.1b	(*.f64 (cos.f64 th) a2)
✓	0.2b	(fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 th) a2) a2)))
✓	0.3b	(.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 th) a2) a2))

series85.0ms (0.9%)

Counts

4 → 88

Calls

4 calls:

55.0ms	(fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 th) a2) a2)))
15.0ms	(.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 th) a2) a2))
9.0ms	(.f64 (cos.f64 th) (.f64 a1 a1))
6.0ms	(*.f64 (cos.f64 th) a2)

rewrite55.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

369×	`prod-diff_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
210×	`log-pow_binary64`
142×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	57
1	262	54
2	3148	52

Stop Event

1×	node limit

Counts

4 → 72

Calls

4 calls:

53.0ms	(.f64 (cos.f64 th) (.f64 a1 a1))
53.0ms	(*.f64 (cos.f64 th) a2)
53.0ms	(fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 th) a2) a2)))
53.0ms	(.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 th) a2) a2))

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
597×	`associate-l_binary64`
564×	`associate-r_binary64`
488×	`cancel-sign-sub-inv_binary64`
201×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	1758
1	310	1624
2	1113	1459

Stop Event

1×	node limit

Counts

160 → 111

prune105.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	112	6	118

Error

Counts

118 → 6

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (sqrt.f64 2) (fma.f64 (cos.f64 th) (.f64 a1 a1) (.f64 (cos.f64 th) (.f64 a2 a2)))) 2)
	0.5b	(fma.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 2 -1/2) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1))))
	0.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2))) (*.f64 a2 a2)))
✓	0.4b	(+.f64 (.f64 (.f64 (cos.f64 th) (pow.f64 2 -1/2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
▶	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 2 1/4)) (pow.f64 2 1/4)))

Compiler

Compiled 3190 to 1788 computations (43.9% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.3b	(/.f64 (sqrt.f64 2) (cos.f64 th))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

series65.0ms (0.7%)

Counts

3 → 64

Calls

3 calls:

52.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
8.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
5.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite52.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

569×	`log-prod_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
185×	`log-pow_binary64`
156×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	230	32
2	2981	32

Stop Event

1×	node limit

Counts

3 → 111

Calls

3 calls:

50.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))
50.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
50.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

338×	`unswap-sqr_binary64`
331×	`fma-neg_binary64`
276×	`sub-neg_binary64`
245×	`associate-r_binary64`
222×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1449
1	236	1409
2	713	1051
3	3152	1047

Stop Event

1×	node limit

Counts

175 → 139

prune133.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	139	6	145

Error

Counts

145 → 6

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (sqrt.f64 2) (fma.f64 (cos.f64 th) (.f64 a1 a1) (.f64 (cos.f64 th) (.f64 a2 a2)))) 2)
	0.5b	(fma.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 2 -1/2) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1))))
	0.5b	(*.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 (hypot.f64 a1 a2) (/.f64 1 (cos.f64 th))))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
✓	0.4b	(+.f64 (.f64 (.f64 (cos.f64 th) (pow.f64 2 -1/2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (/.f64 (.f64 (.f64 (cos.f64 th) a2) a2) (pow.f64 2 1/4)) (pow.f64 2 1/4)))

Compiler

Compiled 2688 to 1615 computations (39.9% saved)

regimes1.8s (20.1%)

Accuracy

Total 0.5b remaining (96.2%)

Threshold costs 0.5b (96.2%)

Counts

203 → 1

Compiler

Compiled 36007 to 26348 computations (26.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	17	30

Stop Event

1×

saturated

end255.0ms (2.8%)

Compiler: Compiled 213 to 150 computations (29.6% saved)

Details

analyze1.1s (12.1%)

sample4.4s (49%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series151.0ms (1.7%)

rewrite70.0ms (0.8%)

simplify59.0ms (0.7%)

prune270.0ms (3%)

localize13.0ms (0.1%)

series21.0ms (0.2%)

rewrite40.0ms (0.4%)

simplify48.0ms (0.5%)

prune123.0ms (1.4%)

localize31.0ms (0.3%)

series85.0ms (0.9%)

rewrite55.0ms (0.6%)

simplify40.0ms (0.4%)

prune105.0ms (1.2%)

localize11.0ms (0.1%)

series65.0ms (0.7%)

rewrite52.0ms (0.6%)

simplify41.0ms (0.5%)

prune133.0ms (1.5%)

regimes1.8s (20.1%)

simplify2.0ms (0%)

end255.0ms (2.8%)

Profiling