Details

analyze1.0s (13.8%)

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)

sample4.3s (57.8%)

Symmetry

(sort a1 a2)

Results

1.2s	1851×	body	1024	valid
1.1s	1588×	body	1024	invalid
839.0ms	5017×	body	128	valid
386.0ms	919×	body	512	valid
337.0ms	778×	body	512	invalid
156.0ms	461×	body	256	valid
122.0ms	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)

simplify9.0ms (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

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

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))

series73.0ms (1%)

Counts

2 → 60

Calls

2 calls:

49.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
23.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite45.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
182×	`pow3_binary64`
181×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	224	29
2	2744	29

Stop Event

1×	node limit

Counts

2 → 65

Calls

2 calls:

44.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
44.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

488×	`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	201	1259
2	604	1215
3	2757	1173

Stop Event

1×	node limit

Counts

125 → 87

prune88.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Error

0.0b

Counts

89 → 9

Alt Table

Status	Error	Program
	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 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
	0.5b	(/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (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))))
	11.1b	(expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
	0.5b	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))

Compiler

Compiled 1862 to 1249 computations (32.9% saved)

localize10.0ms (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))

series144.0ms (1.9%)

Counts

3 → 84

Calls

3 calls:

81.0ms	(.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)))
17.0ms	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

rewrite50.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	247	38
2	2876	38

Stop Event

1×	node limit

Counts

3 → 54

Calls

3 calls:

48.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
48.0ms	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
48.0ms	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-def_binary64`
605×	`associate-l_binary64`
419×	`cancel-sign-sub-inv_binary64`
302×	`times-frac_binary64`
228×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1983
1	389	1812
2	1408	1780

Stop Event

1×	node limit

Counts

138 → 107

prune100.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	109	7	116

Error

0.0b

Counts

116 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
	11.1b	(expm1.f64 (log1p.f64 (/.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))))
	0.8b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
▶	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))))

Compiler

Compiled 2548 to 1658 computations (34.9% saved)

localize11.0ms (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))

series55.0ms (0.7%)

Counts

3 → 28

Calls

3 calls:

47.0ms	(.f64 (cos.f64 th) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
4.0ms	(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
4.0ms	(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))

rewrite56.0ms (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	300	36
2	3793	36

Stop Event

1×	node limit

Counts

3 → 89

Calls

3 calls:

54.0ms	(.f64 (cos.f64 th) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
54.0ms	(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
54.0ms	(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-def_binary64`
456×	`associate-l_binary64`
440×	`associate-r_binary64`
374×	`cancel-sign-sub-inv_binary64`
310×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	873
1	212	626
2	770	594
3	4668	594

Stop Event

1×	node limit

Counts

117 → 106

prune87.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	105	8	113

Error

0.0b

Counts

113 → 8

Alt Table

Status	Error	Program
	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 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (cos.f64 th))))
✓	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))))
	0.5b	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
	0.8b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	11.1b	(expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
▶	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))

Compiler

Compiled 2680 to 1517 computations (43.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
✓	0.2b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	0.3b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
✓	0.4b	(/.f64 a1 (sqrt.f64 2))

series81.0ms (1.1%)

Counts

4 → 60

Calls

4 calls:

59.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
8.0ms	(/.f64 a1 (sqrt.f64 2))
7.0ms	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
7.0ms	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)

rewrite61.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`expm1-udef_binary64`
252×	`log1p-udef_binary64`
222×	`fma-neg_binary64`
143×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	286	47
2	4127	47

Stop Event

1×	node limit

Counts

4 → 115

Calls

4 calls:

59.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
59.0ms	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
59.0ms	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
59.0ms	(/.f64 a1 (sqrt.f64 2))

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1250
1	196	1250
2	598	1076
3	2745	1046

Stop Event

1×	node limit

Counts

175 → 134

prune112.0ms (1.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	134	8	142

Error

0.0b

Counts

142 → 8

Alt Table

Status	Error	Program
	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 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (cos.f64 th))))
✓	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))))
	0.5b	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
	0.8b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	11.1b	(expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))

Compiler

Compiled 3061 to 1999 computations (34.7% saved)

regimes823.0ms (11%)

Accuracy

Total 0.3b remaining (95.5%)

Threshold costs 0.3b (95.5%)

Counts

101 → 1

Compiler

Compiled 13931 to 10821 computations (22.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	16	23

Stop Event

1×

saturated

end132.0ms (1.8%)

Remove: (sort a1 a2)
Compiler: Compiled 218 to 156 computations (28.4% saved)

Details

analyze1.0s (13.8%)

sample4.3s (57.8%)

simplify9.0ms (0.1%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

series73.0ms (1%)

rewrite45.0ms (0.6%)

simplify44.0ms (0.6%)

prune88.0ms (1.2%)

localize10.0ms (0.1%)

series144.0ms (1.9%)

rewrite50.0ms (0.7%)

simplify45.0ms (0.6%)

prune100.0ms (1.3%)

localize11.0ms (0.1%)

series55.0ms (0.7%)

rewrite56.0ms (0.7%)

simplify40.0ms (0.5%)

prune87.0ms (1.2%)

localize10.0ms (0.1%)

series81.0ms (1.1%)

rewrite61.0ms (0.8%)

simplify40.0ms (0.5%)

prune112.0ms (1.5%)

regimes823.0ms (11%)

simplify2.0ms (0%)

end132.0ms (1.8%)

Profiling