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)

sample5.0s (41.6%)

Symmetry

(sort a1 a2)

Results

1.4s	1773×	body	1024	valid
1.2s	1620×	body	1024	invalid
1.0s	5106×	body	128	valid
464.0ms	908×	body	512	valid
399.0ms	776×	body	512	invalid
161.0ms	464×	body	256	valid
139.0ms	400×	body	256	invalid
138.0ms	696×	body	128	invalid
6.0ms	5×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify9.0ms (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

0.6b

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)

localize12.0ms (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))

series83.0ms (0.7%)

Counts

3 → 84

Calls

3 calls:

57.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
19.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
6.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite22.0ms (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))

simplify113.0ms (0.9%)

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

prune171.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	166	8	174
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	168	8	176

Error

0.2b

Counts

176 → 8

Alt Table

Status	Error	Program
	0.8b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	28.1b	(*.f64 (cos.f64 th) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
	0.9b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.8b	(.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))))
	1.4b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2)))) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
▶	0.6b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	1.4b	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2)))) (/.f64 (sqrt.f64 2) (cbrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1))))))

Compiler

Compiled 4145 to 1915 computations (53.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
✓	0.3b	(.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 (sqrt.f64 2) (hypot.f64 a2 a1))
✓	6.8b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series343.0ms (2.9%)

Counts

4 → 108

Calls

4 calls:

189.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
115.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
23.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
16.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite112.0ms (0.9%)

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:

29.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
8.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
5.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify368.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
355×	`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	3925	12746
3	4782	12746
4	4931	12746

prune493.0ms (4.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	567	5	572
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	573	7	580

Error

0.0b

Counts

580 → 7

Alt Table

Status	Error	Program
	0.9b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
▶	0.4b	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
	0.8b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.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) (sqrt.f64 2))) (hypot.f64 a2 a1))
	0.7b	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))))
	0.6b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1))))))
	0.9b	(.f64 (cos.f64 th) (/.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 1 (sqrt.f64 (hypot.f64 a2 a1)))) (/.f64 (sqrt.f64 2) (sqrt.f64 (hypot.f64 a2 a1)))))

Compiler

Compiled 18099 to 7144 computations (60.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a2 a1)
✓	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
	0.4b	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))

series210.0ms (1.8%)

Counts

3 → 96

Calls

3 calls:

159.0ms	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
38.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
13.0ms	(hypot.f64 a2 a1)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

3 → 96

Calls

3 calls:

7.0ms	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
3.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
0.0ms	(hypot.f64 a2 a1)

simplify117.0ms (1%)

Algorithm

1×	egg-herbie

Rules

791×	`associate-/r/_binary64`
477×	`fma-def_binary64`
298×	`cancel-sign-sub-inv_binary64`
276×	`associate-/l*_binary64`
213×	`fma-neg_binary64`

Counts

192 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	306	4690
1	808	4264
2	2930	4129
3	5130	4129

prune289.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	361	3	364
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	365	6	371

Error

Counts

371 → 6

Alt Table

Status	Error	Program
	0.9b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
✓	0.4b	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
	0.7b	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))))
▶	0.6b	(/.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (.f64 a1 a1)))))
	0.7b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
	0.7b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (hypot.f64 a1 a2))) (/.f64 (hypot.f64 a1 a2) (/.f64 (sqrt.f64 2) (sqrt.f64 (hypot.f64 a1 a2)))))

Compiler

Compiled 8810 to 4375 computations (50.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(/.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (.f64 a1 a1)))))
✓	0.4b	(/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1)))
✓	7.0b	(sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1))))

series236.0ms (2%)

Counts

3 → 84

Calls

3 calls:

190.0ms	(/.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (.f64 a1 a1)))))
27.0ms	(sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1))))
19.0ms	(/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1)))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`times-frac_binary64`
39×	`sqrt-prod_binary64`
37×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`

Counts

3 → 106

Calls

3 calls:

6.0ms	(/.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (.f64 a1 a1)))))
2.0ms	(sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1))))
2.0ms	(/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1)))

simplify114.0ms (1%)

Algorithm

1×	egg-herbie

Rules

604×	`associate-/r*_binary64`
407×	`fma-def_binary64`
363×	`associate-/r/_binary64`
339×	`associate-/l/_binary64`
270×	`cancel-sign-sub-inv_binary64`

Counts

190 → 244

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	303	5202
1	703	4747
2	2312	4657
3	5201	4657

prune258.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	320	6	326

Error

Counts

326 → 6

Alt Table

Status	Error	Program
	0.9b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
✓	0.4b	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
	0.7b	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))))
✓	0.6b	(/.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (.f64 a1 a1)))))
	0.7b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
	0.7b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (hypot.f64 a1 a2))) (/.f64 (hypot.f64 a1 a2) (/.f64 (sqrt.f64 2) (sqrt.f64 (hypot.f64 a1 a2)))))

Compiler

Compiled 8685 to 3787 computations (56.4% saved)

regimes2.6s (21.5%)

Accuracy

Total 0.4b remaining (95.1%)

Threshold costs 0.4b (95.1%)

Counts

298 → 1

Compiler

Compiled 51788 to 34373 computations (33.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	12	20
2	12	20

end104.0ms (0.9%)

Remove: (sort a1 a2)
Compiler: Compiled 177 to 114 computations (35.6% saved)

Details

analyze1.2s (10.5%)

sample5.0s (41.6%)

simplify9.0ms (0.1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series83.0ms (0.7%)

rewrite22.0ms (0.2%)

simplify113.0ms (0.9%)

prune171.0ms (1.4%)

localize13.0ms (0.1%)

series343.0ms (2.9%)

rewrite112.0ms (0.9%)

simplify368.0ms (3.1%)

prune493.0ms (4.1%)

localize9.0ms (0.1%)

series210.0ms (1.8%)

rewrite19.0ms (0.2%)

simplify117.0ms (1%)

prune289.0ms (2.4%)

localize13.0ms (0.1%)

series236.0ms (2%)

rewrite26.0ms (0.2%)

simplify114.0ms (1%)

prune258.0ms (2.2%)

regimes2.6s (21.5%)

simplify2.0ms (0%)

end104.0ms (0.9%)

Profiling