Details

analyze1.2s (10.5%)

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)

sample4.6s (41.4%)

Symmetry

(sort a1 a2)

Results

1.4s	1894×	body	1024	valid
1.1s	1570×	body	1024	invalid
887.0ms	4947×	body	128	valid
423.0ms	906×	body	512	valid
347.0ms	753×	body	512	invalid
193.0ms	501×	body	256	valid
134.0ms	387×	body	256	invalid
118.0ms	642×	body	128	invalid
9.0ms	8×	body	2048	valid
4.0ms	2×	body	2048	invalid

Compiler

Compiled 68 to 47 computations (30.9% 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

prune6.0ms (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
▶	0.4b	(.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)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.1b	(.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))

series80.0ms (0.7%)

Counts

3 → 84

Calls

3 calls:

53.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
20.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
7.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite18.0ms (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:

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

simplify114.0ms (1%)

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

prune172.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	165	9	174
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	167	9	176

Error

Counts

176 → 9

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
▶	0.4b	(.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) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	1.1b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 (cbrt.f64 2)))))
	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	0.6b	(.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)))))
	0.6b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.7b	(.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)))))

Compiler

Compiled 4127 to 1933 computations (53.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
✓	0.3b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
✓	0.5b	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
✓	6.3b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series337.0ms (3%)

Counts

4 → 108

Calls

4 calls:

192.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
107.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
26.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
12.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite117.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

526×	`times-frac_binary64`
306×	`add-sqr-sqrt_binary64`
281×	`*-un-lft-identity_binary64`
281×	`add-cube-cbrt_binary64`
272×	`sqrt-prod_binary64`

Counts

4 → 401

Calls

4 calls:

31.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
9.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
3.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify360.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
353×	`associate-/r/_binary64`
280×	`*-commutative_binary64`
274×	`cancel-sign-sub-inv_binary64`
268×	`associate-/l*_binary64`

Counts

509 → 572

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	476	16630
1	1170	13399
2	3926	12746
3	4782	12746
4	4931	12746

prune461.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	571	1	572
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	572	9	581

Error

Counts

581 → 9

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
✓	0.4b	(.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) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	1.1b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 (cbrt.f64 2)))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	0.7b	(.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)))))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	0.6b	(.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)))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))

Compiler

Compiled 18147 to 7197 computations (60.3% 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))
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
✓	0.3b	(/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
✓	0.3b	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

series388.0ms (3.5%)

Counts

3 → 84

Calls

3 calls:

313.0ms

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

54.0ms

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

21.0ms

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

rewrite64.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
110×	`add-sqr-sqrt_binary64`
94×	`cbrt-prod_binary64`
90×	`*-un-lft-identity_binary64`
90×	`add-cube-cbrt_binary64`

Counts

3 → 218

Calls

3 calls:

19.0ms

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

10.0ms

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

5.0ms

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

simplify232.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-neg_binary64`
500×	`associate-/r/_binary64`
260×	`fma-def_binary64`
191×	`associate-/l*_binary64`
181×	`associate-/l/_binary64`

Counts

302 → 365

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	9806
1	697	8974
2	2581	8924
3	4583	8924
4	5353	8924

prune378.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	387	1	388
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	389	8	397

Error

Counts

397 → 8

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
✓	0.4b	(.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) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	1.1b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 (cbrt.f64 2)))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	0.7b	(.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)))))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
	0.6b	(.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)))))

Compiler

Compiled 13313 to 8404 computations (36.9% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
✓	0.3b	(/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
✓	0.4b	(.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))

series639.0ms (5.7%)

Counts

3 → 84

Calls

3 calls:

413.0ms

(*.f64 (cos.f64 th) (/.f64 (*.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))

207.0ms

(/.f64 (*.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))

18.0ms

(*.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
19×	`add-exp-log_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`

Counts

3 → 96

Calls

3 calls:

12.0ms

(*.f64 (cos.f64 th) (/.f64 (*.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))

5.0ms

(/.f64 (*.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))

4.0ms

(*.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))

simplify145.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-def_binary64`
452×	`fma-neg_binary64`
290×	`cancel-sign-sub-inv_binary64`
284×	`associate-l_binary64`
258×	`distribute-rgt-in_binary64`

Counts

180 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	4730
1	469	4129
2	1978	4012
3	4657	4010
4	4977	4010

prune198.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	182	7	189

Error

Counts

189 → 7

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
✓	0.4b	(.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 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	0.7b	(.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)))))
	0.4b	(/.f64 (.f64 (cbrt.f64 1/2) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))) (cbrt.f64 (sqrt.f64 2)))
	0.6b	(.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)))))
	1.1b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 (cbrt.f64 2)))))

Compiler

Compiled 4623 to 2774 computations (40% saved)

regimes1.4s (12.9%)

Accuracy

Total 0.4b remaining (95.9%)

Threshold costs 0.4b (95.9%)

Counts

159 → 1

Compiler

Compiled 26840 to 18271 computations (31.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	25
1	21	25
2	20	25

end129.0ms (1.2%)

Remove: (sort a1 a2)
Compiler: Compiled 213 to 154 computations (27.7% saved)

Details

analyze1.2s (10.5%)

sample4.6s (41.4%)

simplify10.0ms (0.1%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

series80.0ms (0.7%)

rewrite18.0ms (0.2%)

simplify114.0ms (1%)

prune172.0ms (1.5%)

localize13.0ms (0.1%)

series337.0ms (3%)

rewrite117.0ms (1%)

simplify360.0ms (3.2%)

prune461.0ms (4.1%)

localize12.0ms (0.1%)

series388.0ms (3.5%)

rewrite64.0ms (0.6%)

simplify232.0ms (2.1%)

prune378.0ms (3.4%)

localize12.0ms (0.1%)

series639.0ms (5.7%)

rewrite26.0ms (0.2%)

simplify145.0ms (1.3%)

prune198.0ms (1.8%)

regimes1.4s (12.9%)

simplify2.0ms (0%)

end129.0ms (1.2%)

Profiling