Details

analyze1.4s (13%)

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)

sample139.0ms (1.3%)

Algorithm

1×

intervals

Symmetry

(sort a1 a2)

Results

30.0ms	60×	body	1024	valid
21.0ms	44×	body	1024	invalid
17.0ms	153×	body	128	valid
9.0ms	22×	body	512	invalid
6.0ms	20×	body	512	valid
5.0ms	23×	body	256	valid
3.0ms	26×	body	128	invalid
2.0ms	9×	body	256	invalid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify14.0ms (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

prune5.0ms (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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.7b	(.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.3b	(.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))

series94.0ms (0.9%)

Counts

3 → 84

Calls

3 calls:

62.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
24.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
8.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 95

Calls

3 calls:

10.0ms	(.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))
0.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

simplify144.0ms (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

179 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3607
1	368	3275
2	1296	3231
3	4370	3231
4	5109	3231

prune191.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	168	6	174
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	168	8	176

Error

Counts

176 → 8

Alt Table

Status	Error	Program
	17.5b	(.f64 (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))) (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))))
	0.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.7b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
✓	0.7b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.9b	(.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)))))
	38.1b	(.f64 (cos.f64 th) (/.f64 (cbrt.f64 (pow.f64 (fma.f64 a2 a2 (.f64 a1 a1)) 3)) (sqrt.f64 2)))
	0.7b	(.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))))
	0.7b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 4084 to 1899 computations (53.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.4b	(.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))

series95.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

63.0ms	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
32.0ms	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))

rewrite13.0ms (0.1%)

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:

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

simplify110.0ms (1%)

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

prune124.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	128	8	136

Error

Counts

136 → 8

Alt Table

Status	Error	Program
	38.1b	(.f64 (cos.f64 th) (/.f64 (cbrt.f64 (pow.f64 (fma.f64 a2 a2 (.f64 a1 a1)) 3)) (sqrt.f64 2)))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
✓	0.7b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
✓	0.7b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.9b	(.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)))))
	17.5b	(.f64 (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))) (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))))
	0.7b	(.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))))
▶	0.7b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 2852 to 1367 computations (52.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series112.0ms (1%)

Counts

3 → 84

Calls

3 calls:

62.0ms

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

26.0ms

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

24.0ms

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

rewrite272.0ms (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:

63.0ms

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

13.0ms

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

7.0ms

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

simplify702.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
722×	`associate-/r/_binary64`
428×	`associate-/l/_binary64`
297×	`associate-/l*_binary64`
226×	`associate-l_binary64`

Counts

790 → 700

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	474	27472
1	1079	24440
2	3065	23626
3	4504	23572
4	5188	23572

prune892.0ms (8.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	722	1	723
Fresh	2	3	5
Picked	0	1	1
Done	1	1	2
Total	725	6	731

Error

Counts

731 → 6

Alt Table

Status	Error	Program
	0.7b	(.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	17.5b	(.f64 (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))) (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
▶	0.7b	(.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))))
✓	0.7b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
✓	0.7b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

Compiler

Compiled 24396 to 14234 computations (41.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.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)))
✓	0.4b	(.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))))
✓	6.2b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series353.0ms (3.2%)

Counts

4 → 108

Calls

4 calls:

211.0ms	(.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))))
74.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
53.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
16.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite69.0ms (0.6%)

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:

22.0ms	(.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))))
6.0ms	(/.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)))

simplify321.0ms (2.9%)

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

prune491.0ms (4.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	389	0	389
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	389	6	395

Error

Counts

395 → 6

Alt Table

Status	Error	Program
	0.7b	(.f64 (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	17.5b	(.f64 (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))) (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
✓	0.7b	(.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))))
✓	0.7b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
✓	0.7b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

Compiler

Compiled 14662 to 8603 computations (41.3% saved)

regimes1.9s (17.2%)

Accuracy

Total 0.4b remaining (95.1%)

Threshold costs 0.4b (95.1%)

Counts

170 → 1

Compiler

Compiled 34284 to 24968 computations (27.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	16	36
2	16	36

end7.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 75 to 57 computations (24% saved)

sample3.5s (31.5%)

Algorithm

1×

intervals

Results

918.0ms	1850×	body	1024	valid
744.0ms	1538×	body	1024	invalid
481.0ms	4816×	body	128	valid
282.0ms	910×	body	512	valid
224.0ms	758×	body	512	invalid
87.0ms	422×	body	256	valid
76.0ms	662×	body	128	invalid
76.0ms	391×	body	256	invalid
3.0ms	2×	body	2048	valid

Compiler

Compiled 178 to 129 computations (27.5% saved)

Details

analyze1.4s (13%)

sample139.0ms (1.3%)

simplify14.0ms (0.1%)

prune5.0ms (0%)

localize9.0ms (0.1%)

series94.0ms (0.9%)

rewrite21.0ms (0.2%)

simplify144.0ms (1.3%)

prune191.0ms (1.7%)

localize10.0ms (0.1%)

series95.0ms (0.9%)

rewrite13.0ms (0.1%)

simplify110.0ms (1%)

prune124.0ms (1.1%)

localize12.0ms (0.1%)

series112.0ms (1%)

rewrite272.0ms (2.5%)

simplify702.0ms (6.4%)

prune892.0ms (8.1%)

localize17.0ms (0.2%)

series353.0ms (3.2%)

rewrite69.0ms (0.6%)

simplify321.0ms (2.9%)

prune491.0ms (4.5%)

regimes1.9s (17.2%)

simplify3.0ms (0%)

end7.0ms (0.1%)

sample3.5s (31.5%)

Profiling