Details

analyze2.6s (9.6%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
1.6%	98.3%	0.1%	12
1.6%	98.3%	0.1%	13
2.3%	97.5%	0.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample17.1s (62.8%)

Symmetry

(sort a1 a2)

Results

12.9s	4710×	body	8192	exit
1.4s	1770×	body	1024	valid
1.0s	5035×	body	128	valid
618.0ms	792×	body	1024	invalid
502.0ms	963×	body	512	valid
294.0ms	401×	body	512	invalid
182.0ms	482×	body	256	valid
82.0ms	185×	body	256	invalid
42.0ms	181×	body	128	invalid
7.0ms	6×	body	2048	valid

Compiler

Compiled 45 to 31 computations (31.1% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
29×	`*-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	58	18
3	88	18
4	115	18
5	135	18
6	154	18
7	174	18
8	176	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

0.5b

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

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series215.0ms (0.8%)

Counts

3 → 64

Calls

3 calls:

197.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
11.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))
7.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite24.0ms (0.1%)

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-l_binary64`

Counts

3 → 97

Calls

3 calls:

9.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

simplify750.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

496×	`associate-*l/_binary64`
407×	`associate-/l*_binary64`
394×	`distribute-lft-in_binary64`
394×	`distribute-rgt-in_binary64`
223×	`fma-def_binary64`

Counts

161 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	3037
1	496	2817
2	1835	2706

prune144.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	146	7	153
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	148	7	155

Error

0.0b

Counts

155 → 7

Alt Table

Status	Error	Program
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2))))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))))
	0.4b	(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (fma.f64 a1 a1 (.f64 a2 a2)))
▶	0.4b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	0.5b	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
	0.9b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))) (fma.f64 a1 a1 (*.f64 a2 a2)))
	0.4b	(.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))) (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))))
	0.4b	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2)))) (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))))

Compiler

Compiled 3504 to 1737 computations (50.4% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

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

series94.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

72.0ms	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
22.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite16.0ms (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-l_binary64`

Counts

2 → 85

Calls

2 calls:

6.0ms	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
4.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify1.2s (4.4%)

Algorithm

1×	egg-herbie

Rules

589×	`associate-r_binary64`
584×	`associate-l_binary64`
372×	`associate-*l/_binary64`
360×	`associate-/l*_binary64`
321×	`associate-*r/_binary64`

Counts

145 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3670
1	425	3364
2	1462	2960

prune305.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	173	6	179

Error

Counts

179 → 6

Alt Table

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

Compiler

Compiled 4015 to 1876 computations (53.3% saved)

localize12.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a2 a2 (*.f64 a1 a1))
✓	0.2b	(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
✓	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 2))

series128.0ms (0.5%)

Counts

3 → 96

Calls

3 calls:

73.0ms	(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 2))
39.0ms	(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
16.0ms	(fma.f64 a2 a2 (*.f64 a1 a1))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

7.0ms	(/.f64 (.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 2))
5.0ms	(.f64 (cos.f64 th) (fma.f64 a2 a2 (.f64 a1 a1)))
0.0ms	(fma.f64 a2 a2 (*.f64 a1 a1))

simplify925.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

436×	`fma-def_binary64`
373×	`associate-/l/_binary64`
368×	`times-frac_binary64`
345×	`cancel-sign-sub-inv_binary64`
266×	`distribute-lft-in_binary64`

Counts

157 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	2838
1	451	2592
2	1924	2523

prune133.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	133	6	139

Error

Counts

139 → 6

Alt Table

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

Compiler

Compiled 2879 to 1356 computations (52.9% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

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

series36.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

11.0ms	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
11.0ms	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
9.0ms	(/.f64 a2 (sqrt.f64 2))
5.0ms	(/.f64 (sqrt.f64 2) a1)

rewrite47.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

194×	`times-frac_binary64`
131×	`add-sqr-sqrt_binary64`
123×	`*-un-lft-identity_binary64`
123×	`add-cube-cbrt_binary64`
70×	`sqrt-prod_binary64`

Counts

4 → 234

Calls

4 calls:

9.0ms	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
8.0ms	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
4.0ms	(/.f64 a2 (sqrt.f64 2))
4.0ms	(/.f64 (sqrt.f64 2) a1)

simplify979.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

587×	`associate-/r*_binary64`
524×	`*-commutative_binary64`
233×	`associate-/r/_binary64`
223×	`associate-/l/_binary64`
207×	`associate-*r/_binary64`

Counts

258 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	289	4181
1	610	3952
2	2195	3820
3	3713	3764
4	4928	3764

prune288.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	308	0	308
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	308	6	314

Error

Counts

314 → 6

Alt Table

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

Compiler

Compiled 7663 to 4929 computations (35.7% saved)

regimes2.1s (7.5%)

Accuracy

Total 0.4b remaining (93%)

Threshold costs 0.4b (93%)

Counts

185 → 1

Compiler

Compiled 32671 to 22927 computations (29.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
0×	`distribute-lft-neg-in_binary64`
0×	`distribute-rgt-neg-in_binary64`
0×	`distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	17	25

soundness9.0ms (0%)

Compiler: Compiled 325 to 238 computations (26.8% saved)

end111.0ms (0.4%)

Remove: (sort a1 a2)
Compiler: Compiled 194 to 135 computations (30.4% saved)

Details

analyze2.6s (9.6%)

sample17.1s (62.8%)

simplify19.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0%)

series215.0ms (0.8%)

rewrite24.0ms (0.1%)

simplify750.0ms (2.8%)

prune144.0ms (0.5%)

localize9.0ms (0%)

series94.0ms (0.3%)

rewrite16.0ms (0.1%)

simplify1.2s (4.4%)

prune305.0ms (1.1%)

localize12.0ms (0%)

series128.0ms (0.5%)

rewrite16.0ms (0.1%)

simplify925.0ms (3.4%)

prune133.0ms (0.5%)

localize13.0ms (0%)

series36.0ms (0.1%)

rewrite47.0ms (0.2%)

simplify979.0ms (3.6%)

prune288.0ms (1.1%)

regimes2.1s (7.5%)

simplify3.0ms (0%)

soundness9.0ms (0%)

end111.0ms (0.4%)

Profiling