Details

analyze1.0s (11.6%)

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
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)

sample129.0ms (1.5%)

Algorithm

1×

intervals

Symmetry

(sort a1 a2)

Results

27.0ms	54×	body	1024	valid
19.0ms	38×	body	1024	invalid
17.0ms	156×	body	128	valid
11.0ms	34×	body	512	valid
9.0ms	34×	body	512	invalid
2.0ms	12×	body	256	valid
1.0ms	15×	body	128	invalid
1.0ms	7×	body	256	invalid

Compiler

Compiled 48 to 34 computations (29.2% 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

prune5.0ms (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
▶	0.5b	(.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)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 th)
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.5b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series84.0ms (1%)

Counts

3 → 64

Calls

3 calls:

61.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
21.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
2.0ms	(cos.f64 th)

rewrite19.0ms (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 → 94

Calls

3 calls:

8.0ms	(.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))
1.0ms	(cos.f64 th)

simplify109.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-l_binary64`
420×	`associate-r_binary64`
337×	`unswap-sqr_binary64`
336×	`associate-/l*_binary64`
276×	`associate-*r/_binary64`

Counts

158 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	3431
1	398	3117
2	1373	3069
3	4414	3069
4	5205	3069

prune149.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	163	5	168
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	164	6	170

Error

Counts

170 → 6

Alt Table

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

Compiler

Compiled 3938 to 1841 computations (53.3% saved)

localize12.0ms (0.1%)

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))))
✓	0.1b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
✓	0.2b	(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))
✓	0.3b	(.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))

series287.0ms (3.3%)

Counts

4 → 108

Calls

4 calls:

111.0ms	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
67.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
66.0ms	(.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
42.0ms	(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
70×	`times-frac_binary64`
61×	`add-exp-log_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

4 → 181

Calls

4 calls:

15.0ms	(.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
13.0ms	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
7.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
3.0ms	(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))

simplify180.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

517×	`cancel-sign-sub-inv_binary64`
363×	`fma-neg_binary64`
266×	`associate-r_binary64`
250×	`associate-l_binary64`
250×	`associate-*r/_binary64`

Counts

289 → 309

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	9877
1	938	7509
2	3617	7422
3	5079	7422

prune297.0ms (3.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	309	0	309
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	309	6	315

Error

Counts

315 → 6

Alt Table

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

Compiler

Compiled 10413 to 6827 computations (34.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series193.0ms (2.2%)

Counts

3 → 84

Calls

3 calls:

104.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
69.0ms	(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
21.0ms	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
23×	`associate-r_binary64`

Counts

3 → 110

Calls

3 calls:

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

simplify98.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

731×	`associate-/l*_binary64`
669×	`times-frac_binary64`
233×	`fma-def_binary64`
218×	`associate-/l/_binary64`
166×	`associate-r_binary64`

Counts

194 → 177

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	4340
1	586	4018
2	2016	3928
3	5092	3928

prune152.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	194	6	200

Error

Counts

200 → 6

Alt Table

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

Compiler

Compiled 4645 to 2481 computations (46.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series236.0ms (2.7%)

Counts

3 → 96

Calls

3 calls:

106.0ms	(/.f64 (.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (hypot.f64 a2 a1))) (sqrt.f64 2))
80.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (hypot.f64 a2 a1)))
50.0ms	(*.f64 (hypot.f64 a2 a1) (hypot.f64 a2 a1))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 81

Calls

3 calls:

6.0ms	(/.f64 (.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (hypot.f64 a2 a1))) (sqrt.f64 2))
5.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (hypot.f64 a2 a1)))
3.0ms	(*.f64 (hypot.f64 a2 a1) (hypot.f64 a2 a1))

simplify100.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

614×	`times-frac_binary64`
429×	`associate-/r*_binary64`
399×	`fma-def_binary64`
301×	`cancel-sign-sub-inv_binary64`
240×	`associate-/r/_binary64`

Counts

177 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	3276
1	440	2877
2	1648	2721
3	4780	2711
4	4987	2711

prune143.0ms (1.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	168	6	174

Error

Counts

174 → 6

Alt Table

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

Compiler

Compiled 3535 to 1658 computations (53.1% saved)

regimes2.0s (23.6%)

Accuracy

Total 0.3b remaining (89%)

Threshold costs 0.3b (89%)

Counts

189 → 1

Compiler

Compiled 31178 to 21092 computations (32.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	15	24
2	15	24

end16.0ms (0.2%)

Remove: (sort a1 a2)
Compiler: Compiled 57 to 36 computations (36.8% saved)

sample3.3s (37.7%)

Algorithm

1×

intervals

Results

845.0ms	1815×	body	1024	valid
723.0ms	1506×	body	1024	invalid
478.0ms	4849×	body	128	valid
260.0ms	899×	body	512	valid
223.0ms	767×	body	512	invalid
84.0ms	431×	body	256	valid
71.0ms	376×	body	256	invalid
63.0ms	634×	body	128	invalid
5.0ms	6×	body	2048	valid

Compiler

Compiled 164 to 115 computations (29.9% saved)

Details

analyze1.0s (11.6%)

sample129.0ms (1.5%)

simplify9.0ms (0.1%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

series84.0ms (1%)

rewrite19.0ms (0.2%)

simplify109.0ms (1.3%)

prune149.0ms (1.7%)

localize12.0ms (0.1%)

series287.0ms (3.3%)

rewrite57.0ms (0.7%)

simplify180.0ms (2.1%)

prune297.0ms (3.4%)

localize12.0ms (0.1%)

series193.0ms (2.2%)

rewrite24.0ms (0.3%)

simplify98.0ms (1.1%)

prune152.0ms (1.8%)

localize8.0ms (0.1%)

series236.0ms (2.7%)

rewrite19.0ms (0.2%)

simplify100.0ms (1.2%)

prune143.0ms (1.6%)

regimes2.0s (23.6%)

simplify2.0ms (0%)

end16.0ms (0.2%)

sample3.3s (37.7%)

Profiling