Details

analyze1.1s (12.8%)

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)

sample168.0ms (2%)

Algorithm

1×

intervals

Symmetry

(sort a1 a2)

Results

36.0ms	58×	body	1024	invalid
31.0ms	58×	body	1024	valid
16.0ms	162×	body	128	valid
8.0ms	28×	body	512	invalid
6.0ms	23×	body	512	valid
3.0ms	27×	body	128	invalid
3.0ms	13×	body	256	valid
2.0ms	13×	body	256	invalid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify14.0ms (0.2%)

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

0.4b

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
✓	0.1b	(.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))

series121.0ms (1.4%)

Counts

2 → 60

Calls

2 calls:

75.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
46.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite21.0ms (0.2%)

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:

11.0ms	(.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))

simplify112.0ms (1.3%)

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

prune170.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	146	7	153

Error

Counts

153 → 7

Alt Table

Status	Error	Program
	0.9b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))))
▶	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))))
	0.5b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	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)))))
	13.7b	(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.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 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

Compiler

Compiled 3693 to 1738 computations (52.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
✓	0.3b	(.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))))
✓	6.0b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series338.0ms (4%)

Counts

4 → 108

Calls

4 calls:

202.0ms	(.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))))
73.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
47.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
15.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite64.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

111×	`times-frac_binary64`
99×	`sqrt-prod_binary64`
86×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`
85×	`add-cube-cbrt_binary64`

Counts

4 → 212

Calls

4 calls:

20.0ms	(.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))))
8.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
5.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify282.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-neg_binary64`
363×	`associate-l_binary64`
324×	`associate-r_binary64`
236×	`associate-*r/_binary64`
233×	`*-commutative_binary64`

Counts

320 → 389

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	384	11395
1	1037	8401
2	4088	8383
3	4820	8383
4	4952	8383

prune404.0ms (4.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	389	0	389
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	389	7	396

Error

Counts

396 → 7

Alt Table

Status	Error	Program
	0.9b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))))
✓	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))))
▶	0.5b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	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)))))
	13.7b	(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.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 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

Compiler

Compiled 14782 to 8686 computations (41.2% 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))

series62.0ms (0.7%)

Counts

1 → 36

Calls

1 calls:

62.0ms

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

rewrite13.0ms (0.2%)

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:

9.0ms

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

simplify95.0ms (1.1%)

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

prune139.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	154	7	161

Error

Counts

161 → 7

Alt Table

Status	Error	Program
	0.9b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))))
✓	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))))
✓	0.5b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	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)))))
	13.7b	(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.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 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

Compiler

Compiled 3738 to 1749 computations (53.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

series97.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

66.0ms	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
31.0ms	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 51

Calls

2 calls:

6.0ms	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
5.0ms	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

simplify100.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

640×	`associate-/l*_binary64`
436×	`fma-def_binary64`
359×	`times-frac_binary64`
315×	`cancel-sign-sub-inv_binary64`
247×	`distribute-rgt-in_binary64`

Counts

123 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	2546
1	386	2329
2	1540	2260
3	4953	2258
4	5065	2258

prune104.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	105	7	112

Error

Counts

112 → 7

Alt Table

Status	Error	Program
✓	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))))
✓	0.5b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	0.9b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.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)))))
	13.7b	(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))))
✓	0.5b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
	0.4b	(/.f64 (/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 2350 to 1124 computations (52.2% saved)

regimes1.5s (17.3%)

Accuracy

Total 0.4b remaining (84.8%)

Threshold costs 0.4b (84.8%)

Counts

152 → 1

Compiler

Compiled 29720 to 20531 computations (30.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	19	42
2	19	42

end7.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 87 to 66 computations (24.1% saved)

sample3.6s (42%)

Algorithm

1×

intervals

Results

893.0ms	1752×	body	1024	valid
834.0ms	1549×	body	1024	invalid
499.0ms	4914×	body	128	valid
274.0ms	893×	body	512	valid
244.0ms	803×	body	512	invalid
89.0ms	435×	body	256	valid
82.0ms	703×	body	128	invalid
81.0ms	392×	body	256	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 191 to 137 computations (28.3% saved)

Details

analyze1.1s (12.8%)

sample168.0ms (2%)

simplify14.0ms (0.2%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series121.0ms (1.4%)

rewrite21.0ms (0.2%)

simplify112.0ms (1.3%)

prune170.0ms (2%)

localize17.0ms (0.2%)

series338.0ms (4%)

rewrite64.0ms (0.8%)

simplify282.0ms (3.3%)

prune404.0ms (4.7%)

localize11.0ms (0.1%)

series62.0ms (0.7%)

rewrite13.0ms (0.2%)

simplify95.0ms (1.1%)

prune139.0ms (1.6%)

localize9.0ms (0.1%)

series97.0ms (1.1%)

rewrite13.0ms (0.2%)

simplify100.0ms (1.2%)

prune104.0ms (1.2%)

regimes1.5s (17.3%)

simplify2.0ms (0%)

end7.0ms (0.1%)

sample3.6s (42%)

Profiling