Details

analyze1.5s (10.8%)

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)

sample118.0ms (0.8%)

Algorithm

1×

intervals

Results

34.0ms	73×	body	1024	valid
26.0ms	47×	body	1024	invalid
14.0ms	151×	body	128	valid
6.0ms	22×	body	512	invalid
5.0ms	19×	body	512	valid
3.0ms	13×	body	256	valid
2.0ms	12×	body	256	invalid
2.0ms	17×	body	128	invalid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify12.0ms (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`

Counts

1 → 2

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

prune6.0ms (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)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.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))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

2 → 85

Calls

2 calls:

7.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
3.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series145.0ms (1%)

Counts

2 → 60

Calls

2 calls:

101.0ms	(.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))

simplify119.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-l_binary64`
410×	`associate-r_binary64`
396×	`fma-neg_binary64`
332×	`associate-/l*_binary64`
299×	`sub-neg_binary64`

Counts

145 → 284

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3315
1	365	3012
2	1289	2968
3	4359	2968
4	5076	2968

prune140.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	278	6	284
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	279	7	286

Error

0.0b

Counts

286 → 7

Alt Table

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

Compiler

Compiled 3727 to 1760 computations (52.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
✓	0.5b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
✓	5.0b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`sqrt-prod_binary64`
72×	`times-frac_binary64`
65×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-cube-cbrt_binary64`

Counts

4 → 162

Calls

4 calls:

9.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
5.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
3.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series339.0ms (2.5%)

Counts

4 → 120

Calls

4 calls:

258.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
44.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
23.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
14.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify244.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-def_binary64`
376×	`cancel-sign-sub-inv_binary64`
345×	`associate-l_binary64`
317×	`sub-neg_binary64`
308×	`fma-neg_binary64`

Counts

282 → 535

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	347	7564
1	936	6108
2	3364	6008
3	4799	6003
4	4932	6003
5	5038	6003

prune291.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	532	3	535
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	535	7	542

Error

Counts

542 → 7

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (*.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (sqrt.f64 2)))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 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)))
▶	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))

Compiler

Compiled 9301 to 3958 computations (57.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)
	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
✓	5.2b	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`

Counts

3 → 90

Calls

3 calls:

7.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
2.0ms	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))
2.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)

series185.0ms (1.3%)

Counts

3 → 84

Calls

3 calls:

136.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
29.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)
19.0ms	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))

simplify153.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

767×	`times-frac_binary64`
619×	`fma-neg_binary64`
488×	`cancel-sign-sub-inv_binary64`
293×	`associate-r_binary64`
260×	`associate-l_binary64`

Counts

174 → 334

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	5151
1	752	4553
2	2741	3865
3	5000	3865
4	5283	3865

prune216.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	433	3	436
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	437	6	443

Error

Counts

443 → 6

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 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
	0.4b	(.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 (/.f64 1 2)))
▶	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))))
	0.5b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))

Compiler

Compiled 7783 to 3468 computations (55.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
	0.5b	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))
✓	0.5b	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))
✓	5.2b	(sqrt.f64 (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`add-sqr-sqrt_binary64`
114×	`times-frac_binary64`
74×	`*-un-lft-identity_binary64`
74×	`add-cube-cbrt_binary64`
61×	`sqrt-prod_binary64`

Counts

3 → 172

Calls

3 calls:

22.0ms

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

6.0ms

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

3.0ms

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

series165.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

114.0ms

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

28.0ms

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

24.0ms

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

simplify215.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-def_binary64`
508×	`associate-/l/_binary64`
506×	`associate-/r*_binary64`
375×	`fma-neg_binary64`
320×	`*-commutative_binary64`

Counts

244 → 445

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	222	6086
1	609	5425
2	1901	4983
3	4309	4947
4	5111	4947

prune327.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	553	0	553
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	553	6	559

Error

Counts

559 → 6

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 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
	0.4b	(.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 (/.f64 1 2)))
✓	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))))
	0.5b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))

Compiler

Compiled 11304 to 5938 computations (47.5% saved)

regimes3.1s (22.5%)

Accuracy

Total 0.3b remaining (91.8%)

Threshold costs 0.3b (91.8%)

Compiler

Compiled 34295 to 22843 computations (33.4% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	15	24
2	15	24

end13.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 57 to 36 computations (36.8% saved)

sample6.4s (46.1%)

Algorithm

1×

intervals

Results

1.7s	1788×	body	1024	valid
1.4s	1552×	body	1024	invalid
909.0ms	4894×	body	128	valid
522.0ms	873×	body	512	valid
491.0ms	833×	body	512	invalid
165.0ms	441×	body	256	valid
142.0ms	379×	body	256	invalid
123.0ms	655×	body	128	invalid
6.0ms	4×	body	2048	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 157 to 105 computations (33.1% saved)

Details

analyze1.5s (10.8%)

sample118.0ms (0.8%)

simplify12.0ms (0.1%)

prune6.0ms (0%)

localize9.0ms (0.1%)

rewrite14.0ms (0.1%)

series145.0ms (1%)

simplify119.0ms (0.9%)

prune140.0ms (1%)

localize12.0ms (0.1%)

rewrite27.0ms (0.2%)

series339.0ms (2.5%)

simplify244.0ms (1.8%)

prune291.0ms (2.1%)

localize13.0ms (0.1%)

rewrite17.0ms (0.1%)

series185.0ms (1.3%)

simplify153.0ms (1.1%)

prune216.0ms (1.6%)

localize15.0ms (0.1%)

rewrite41.0ms (0.3%)

series165.0ms (1.2%)

simplify215.0ms (1.6%)

prune327.0ms (2.4%)

regimes3.1s (22.5%)

simplify8.0ms (0.1%)

end13.0ms (0.1%)

sample6.4s (46.1%)

Profiling