Details

analyze1.1s (10.1%)

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)

sample154.0ms (1.5%)

Algorithm

1×

intervals

Symmetry

(sort a1 a2)

Results

41.0ms	62×	body	1024	invalid
24.0ms	49×	body	1024	valid
15.0ms	159×	body	128	valid
10.0ms	33×	body	512	valid
5.0ms	17×	body	512	invalid
3.0ms	15×	body	256	valid
2.0ms	12×	body	256	invalid
2.0ms	14×	body	128	invalid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify10.0ms (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

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 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (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)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize10.0ms (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))

series85.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

63.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
21.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite89.0ms (0.8%)

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:

17.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
6.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify175.0ms (1.7%)

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 → 151

Iterations

Useful iterations: 2 (0.0ms)

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

prune158.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	143	8	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	145	8	153

Error

Counts

153 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.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 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.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))))
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
▶	0.4b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	1.1b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))

Compiler

Compiled 3799 to 1794 computations (52.8% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series60.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

60.0ms

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

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`associate-l_binary64`
20×	`times-frac_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 44

Calls

1 calls:

8.0ms

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

simplify100.0ms (1%)

Algorithm

1×	egg-herbie

Rules

454×	`associate-l_binary64`
393×	`unswap-sqr_binary64`
389×	`associate-r_binary64`
331×	`fma-neg_binary64`
310×	`times-frac_binary64`

Counts

80 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2273
1	324	2099
2	994	1695
3	3622	1695
4	5155	1695

prune145.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	156	6	162

Error

Counts

162 → 6

Alt Table

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

Compiler

Compiled 3739 to 1751 computations (53.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
✓	0.2b	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) 1) (*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
✓	0.5b	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))
✓	7.3b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series338.0ms (3.2%)

Counts

4 → 120

Calls

4 calls:

228.0ms	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) 1) (*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
73.0ms	(*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
23.0ms	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))
14.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite63.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`times-frac_binary64`
56×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
47×	`add-cube-cbrt_binary64`
41×	`add-exp-log_binary64`

Counts

4 → 155

Calls

4 calls:

15.0ms	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) 1) (*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
13.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))
8.0ms	(*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
3.0ms	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))

simplify220.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
335×	`fma-neg_binary64`
284×	`associate-r_binary64`
251×	`associate-/l*_binary64`
237×	`associate-l_binary64`

Counts

275 → 324

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	7290
1	963	6314
2	3747	6206
3	5008	6206

prune312.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	324	0	324
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	324	6	330

Error

Counts

330 → 6

Alt Table

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

Compiler

Compiled 9901 to 4894 computations (50.6% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series107.0ms (1%)

Counts

3 → 84

Calls

3 calls:

59.0ms

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

25.0ms

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

23.0ms

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

rewrite265.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

1137×	`sqrt-prod_binary64`
1119×	`times-frac_binary64`
624×	`add-sqr-sqrt_binary64`
577×	`*-un-lft-identity_binary64`
577×	`add-cube-cbrt_binary64`

Counts

3 → 706

Calls

3 calls:

47.0ms

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

13.0ms

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

6.0ms

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

simplify781.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

671×	`associate-*r/_binary64`
576×	`fma-neg_binary64`
417×	`associate-/r/_binary64`
386×	`associate-/l/_binary64`
288×	`associate-*l/_binary64`

Counts

790 → 818

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	474	28065
1	1125	25081
2	2454	23711
3	4642	23711
4	5159	23711

prune903.0ms (8.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	817	1	818
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	818	6	824

Error

Counts

824 → 6

Alt Table

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

Compiler

Compiled 28049 to 16460 computations (41.3% saved)

regimes1.9s (18.1%)

Accuracy

Total 0.3b remaining (86.4%)

Threshold costs 0.3b (86.4%)

Counts

179 → 1

Compiler

Compiled 33310 to 22861 computations (31.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	30
1	20	30
2	19	30

end8.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 66 to 51 computations (22.7% saved)

sample3.5s (33.2%)

Algorithm

1×

intervals

Results

868.0ms	1755×	body	1024	valid
749.0ms	1492×	body	1024	invalid
496.0ms	4795×	body	128	valid
302.0ms	995×	body	512	valid
244.0ms	784×	body	512	invalid
91.0ms	451×	body	256	valid
75.0ms	377×	body	256	invalid
65.0ms	615×	body	128	invalid
3.0ms	4×	body	2048	valid

Compiler

Compiled 170 to 122 computations (28.2% saved)

Details

analyze1.1s (10.1%)

sample154.0ms (1.5%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series85.0ms (0.8%)

rewrite89.0ms (0.8%)

simplify175.0ms (1.7%)

prune158.0ms (1.5%)

localize11.0ms (0.1%)

series60.0ms (0.6%)

rewrite12.0ms (0.1%)

simplify100.0ms (1%)

prune145.0ms (1.4%)

localize14.0ms (0.1%)

series338.0ms (3.2%)

rewrite63.0ms (0.6%)

simplify220.0ms (2.1%)

prune312.0ms (3%)

localize13.0ms (0.1%)

series107.0ms (1%)

rewrite265.0ms (2.5%)

simplify781.0ms (7.5%)

prune903.0ms (8.6%)

regimes1.9s (18.1%)

simplify3.0ms (0%)

end8.0ms (0.1%)

sample3.5s (33.2%)

Profiling