Details

analyze1.1s (14.3%)

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 (55.9%)

Symmetry

(sort a1 a2)

Results

1.2s	1851×	body	1024	valid
1.1s	1588×	body	1024	invalid
844.0ms	5017×	body	128	valid
400.0ms	919×	body	512	valid
340.0ms	778×	body	512	invalid
152.0ms	461×	body	256	valid
133.0ms	420×	body	256	invalid
114.0ms	664×	body	128	invalid
8.0ms	8×	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	53	18
3	76	18
4	103	18
5	117	18
6	132	18
7	134	18
8	136	18
9	136	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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.5b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series71.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

54.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
16.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite47.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
198×	`pow1/3_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
181×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	223	29
2	2595	29
3	5006	29

Stop Event

1×	node limit

Counts

2 → 68

Calls

2 calls:

45.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
45.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

492×	`associate-/r/_binary64`
338×	`unswap-sqr_binary64`
331×	`fma-neg_binary64`
276×	`sub-neg_binary64`
206×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	1313
1	165	1259
2	547	1215
3	2202	1173
4	4857	1173
5	5023	1173

Stop Event

1×	node limit

Counts

128 → 90

prune88.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	83	9	92

Error

0.0b

Counts

92 → 9

Alt Table

Status	Error	Program
	0.5b	(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.8b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	10.9b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4))))
✓	0.5b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 1904 to 1273 computations (33.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.2b	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
✓	0.4b	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

series136.0ms (1.7%)

Counts

3 → 84

Calls

3 calls:

76.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
45.0ms	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
14.0ms	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

rewrite87.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`log-prod_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
192×	`pow3_binary64`
191×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	247	38
2	2718	38
3	4945	38
4	4977	38
5	4943	38

Stop Event

1×	node limit

Counts

3 → 54

Calls

3 calls:

86.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
86.0ms	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
86.0ms	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
676×	`fma-def_binary64`
608×	`associate-l_binary64`
419×	`cancel-sign-sub-inv_binary64`
302×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1983
1	355	1812
2	1301	1780
3	4968	1780
4	5577	1780

Stop Event

1×	node limit

Counts

138 → 107

prune96.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	3	4	7
Picked	0	1	1
Done	1	0	1
Total	109	7	116

Error

0.0b

Counts

116 → 7

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
	10.9b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
	0.5b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	0.8b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))

Compiler

Compiled 2536 to 1644 computations (35.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
✓	0.3b	(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
✓	0.3b	(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))

series51.0ms (0.7%)

Counts

3 → 28

Calls

3 calls:

40.0ms	(.f64 (cos.f64 th) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
8.0ms	(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
4.0ms	(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))

rewrite58.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

456×	`fma-def_binary64`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
216×	`fma-neg_binary64`
143×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	38
1	299	36
2	3412	36
3	4890	36

Stop Event

1×	node limit

Counts

3 → 93

Calls

3 calls:

56.0ms	(.f64 (cos.f64 th) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
56.0ms	(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
56.0ms	(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-def_binary64`
529×	`distribute-rgt-neg-in_binary64`
495×	`distribute-lft-neg-in_binary64`
463×	`associate-l_binary64`
444×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	873
1	186	626
2	688	594
3	3349	594
4	5261	594

Stop Event

1×	node limit

Counts

121 → 110

prune96.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	109	8	117

Error

0.0b

Counts

117 → 8

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
	10.9b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
	0.5b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	0.8b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.5b	(fma.f64 (.f64 a1 (pow.f64 1/2 1/4)) (.f64 (.f64 a1 (pow.f64 1/2 1/4)) (cos.f64 th)) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (cos.f64 th)))
▶	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))

Compiler

Compiled 2752 to 1628 computations (40.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
✓	0.2b	(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
✓	0.4b	(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

series152.0ms (1.9%)

Counts

3 → 84

Calls

3 calls:

83.0ms

(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))

49.0ms

(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))

20.0ms

(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

rewrite55.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

586×	`log-prod_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
188×	`log-pow_binary64`
132×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	250	38
2	2876	38
3	5123	38

Stop Event

1×	node limit

Counts

3 → 107

Calls

3 calls:

53.0ms

(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))

53.0ms

(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))

53.0ms

(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Rules

579×	`fma-neg_binary64`
478×	`times-frac_binary64`
376×	`associate-/l*_binary64`
349×	`associate-r_binary64`
297×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	2107
1	333	2029
2	1133	1969
3	4798	1969
4	5267	1969

Stop Event

1×	node limit

Counts

191 → 158

prune125.0ms (1.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	158	8	166

Error

Counts

166 → 8

Alt Table

Status	Error	Program
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.5b	(/.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
	0.5b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	0.5b	(/.f64 (.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) (hypot.f64 a1 a2)) (sqrt.f64 2))
	0.8b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	0.5b	(*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))

Compiler

Compiled 3480 to 2194 computations (37% saved)

regimes811.0ms (10.4%)

Accuracy

Total 0.4b remaining (97.8%)

Threshold costs 0.4b (97.8%)

Counts

100 → 1

Compiler

Compiled 13314 to 10366 computations (22.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	15	21
2	15	21

Stop Event

1×

saturated

end128.0ms (1.6%)

Remove: (sort a1 a2)
Compiler: Compiled 195 to 136 computations (30.3% saved)

Details

analyze1.1s (14.3%)

sample4.4s (55.9%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series71.0ms (0.9%)

rewrite47.0ms (0.6%)

simplify73.0ms (0.9%)

prune88.0ms (1.1%)

localize8.0ms (0.1%)

series136.0ms (1.7%)

rewrite87.0ms (1.1%)

simplify73.0ms (0.9%)

prune96.0ms (1.2%)

localize10.0ms (0.1%)

series51.0ms (0.7%)

rewrite58.0ms (0.7%)

simplify50.0ms (0.6%)

prune96.0ms (1.2%)

localize9.0ms (0.1%)

series152.0ms (1.9%)

rewrite55.0ms (0.7%)

simplify76.0ms (1%)

prune125.0ms (1.6%)

regimes811.0ms (10.4%)

simplify3.0ms (0%)

end128.0ms (1.6%)

Profiling