Details

analyze2.1s (24.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.5s (17.4%)

Results

1.2s	8256×	body	128	valid
193.0ms	270×	body	8192	exit
31.0ms	231×	body	128	invalid

Compiler

Compiled 39 to 23 computations (41% saved)

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1070×	`fma-neg_binary64`
881×	`fma-def_binary64`
768×	`times-frac_binary64`
551×	`cancel-sign-sub-inv_binary64`
514×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	25	20
2	47	20
3	78	20
4	149	20
5	228	20
6	324	20
7	500	20
8	694	20
9	867	20
10	999	20
11	2422	20
12	3920	20
13	4950	20

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

21.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	21.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
▶	21.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

Compiler

Compiled 107 to 55 computations (48.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
✓	0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
✓	21.1b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series110.0ms (1.3%)

Counts

3 → 120

Calls

3 calls:

93.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
9.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
7.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 64

Calls

3 calls:

6.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
3.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
3.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

514×	`fma-def_binary64`
396×	`fma-neg_binary64`
392×	`times-frac_binary64`
348×	`associate-/l*_binary64`
235×	`associate-*l/_binary64`

Counts

184 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	3114
1	413	2977
2	1392	2931
3	4837	2930
4	5047	2930

prune107.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	136	9	145
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	138	9	147

Error

1.3b

Counts

147 → 9

Alt Table

Status	Error	Program
	39.0b	(/.f64 (-.f64 (.f64 (.f64 x.im y.re) (.f64 x.im y.re)) (.f64 (.f64 x.re y.im) (.f64 x.re y.im))) (.f64 (fma.f64 y.im y.im (.f64 y.re y.re)) (fma.f64 x.re y.im (*.f64 y.re x.im))))
	36.5b	(neg.f64 (/.f64 x.re y.im))
	21.7b	(.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (/.f64 1 (fma.f64 y.im y.im (.f64 y.re y.re))))
▶	12.1b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
	38.3b	(.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (hypot.f64 y.im y.re)) (/.f64 (sqrt.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
	39.2b	(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (.f64 (.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
	12.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (hypot.f64 y.im y.re)))
	37.6b	(/.f64 x.im y.re)
	38.6b	(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (.f64 x.re (.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))

Compiler

Compiled 3729 to 791 computations (78.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 y.re x.im) (.f64 x.re y.im))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
✓	11.3b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (hypot.f64 y.im y.re))

series239.0ms (2.8%)

Counts

3 → 108

Calls

3 calls:

118.0ms

(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))

112.0ms

(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

9.0ms

(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`

Counts

3 → 106

Calls

3 calls:

10.0ms

(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))

10.0ms

(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

3.0ms

(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

simplify144.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

747×	`times-frac_binary64`
528×	`fma-neg_binary64`
402×	`fma-def_binary64`
254×	`cancel-sign-sub-inv_binary64`
230×	`distribute-rgt-in_binary64`

Counts

214 → 211

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	5757
1	607	4941
2	2096	4883
3	4765	4882
4	5102	4882

prune162.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	204	7	211
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	208	12	220

Error

1.2b

Counts

220 → 12

Alt Table

Status	Error	Program
	12.2b	(.f64 (.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (/.f64 1 (hypot.f64 y.im y.re)))
	44.5b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.im (/.f64 (.f64 x.re y.im) y.re)))
	12.3b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
	36.5b	(neg.f64 (/.f64 x.re y.im))
	12.1b	(.f64 (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (/.f64 1 (hypot.f64 y.im y.re)))
	17.1b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re)) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))))
	38.5b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (/.f64 (sqrt.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (hypot.f64 y.im y.re)))))
	39.2b	(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (.f64 (.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
	12.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (hypot.f64 y.im y.re)))
▶	12.0b	(/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
	37.6b	(/.f64 x.im y.re)
	38.6b	(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (.f64 x.re (.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))

Compiler

Compiled 6034 to 1718 computations (71.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
	0.2b	(-.f64 (.f64 y.re x.im) (.f64 x.re y.im))
	11.3b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (hypot.f64 y.im y.re))

series115.0ms (1.3%)

Counts

1 → 48

Calls

1 calls:

115.0ms

(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 73

Calls

1 calls:

6.0ms

(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))

simplify388.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

566×	`times-frac_binary64`
497×	`fma-neg_binary64`
471×	`associate-/l*_binary64`
471×	`associate-/l/_binary64`
359×	`div-sub_binary64`

Counts

121 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	4368
1	440	4066
2	1093	3872
3	4104	3805
4	5309	3805

prune224.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	230	5	235
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	236	11	247

Error

1.2b

Counts

247 → 11

Alt Table

Status	Error	Program
	36.5b	(neg.f64 (/.f64 x.re y.im))
▶	12.1b	(/.f64 (.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (/.f64 1 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
	38.6b	(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (.f64 x.re (.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
	15.3b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (cbrt.f64 (hypot.f64 y.im y.re))) (cbrt.f64 (hypot.f64 y.im y.re))))
	43.9b	(/.f64 x.im (hypot.f64 y.im y.re))
	44.5b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.im (/.f64 (.f64 x.re y.im) y.re)))
	12.2b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
	39.2b	(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (.f64 (.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
	12.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (hypot.f64 y.im y.re)))
	38.3b	(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (/.f64 (sqrt.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
	37.6b	(/.f64 x.im y.re)

Compiler

Compiled 6549 to 1428 computations (78.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (/.f64 1 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
	0.2b	(-.f64 (.f64 y.re x.im) (.f64 x.re y.im))
✓	11.4b	(.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (/.f64 1 (hypot.f64 y.im y.re)))

series231.0ms (2.7%)

Counts

2 → 96

Calls

2 calls:

118.0ms	(/.f64 (.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (/.f64 1 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
113.0ms	(.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (/.f64 1 (hypot.f64 y.im y.re)))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
14×	`times-frac_binary64`
13×	`associate-r_binary64`

Counts

2 → 75

Calls

2 calls:

8.0ms	(.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (/.f64 1 (hypot.f64 y.im y.re)))
8.0ms	(/.f64 (.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (/.f64 1 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))

simplify161.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

398×	`fma-def_binary64`
394×	`fma-neg_binary64`
343×	`associate-/l/_binary64`
328×	`associate-/r/_binary64`
249×	`cancel-sign-sub-inv_binary64`

Counts

171 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	4671
1	541	3918
2	1879	3858
3	4616	3856
4	4992	3856
5	4968	3856

prune148.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	195	11	206

Error

1.2b

Counts

206 → 11

Alt Table

Status	Error	Program
	36.5b	(neg.f64 (/.f64 x.re y.im))
✓	12.1b	(/.f64 (.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (/.f64 1 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
	38.6b	(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (.f64 x.re (.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
	15.3b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im)) (cbrt.f64 (hypot.f64 y.im y.re))) (cbrt.f64 (hypot.f64 y.im y.re))))
	43.9b	(/.f64 x.im (hypot.f64 y.im y.re))
	44.5b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.im (/.f64 (.f64 x.re y.im) y.re)))
	12.2b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
	39.2b	(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (.f64 (.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
	12.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (hypot.f64 y.im y.re)))
	38.3b	(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 y.re x.im) (.f64 x.re y.im))) (/.f64 (sqrt.f64 (-.f64 (.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
	37.6b	(/.f64 x.im y.re)

Compiler

Compiled 4984 to 1460 computations (70.7% saved)

regimes2.6s (29.7%)

Accuracy

Total 9.2b remaining (85%)

Threshold costs 0b (0%)

Counts

213 → 2

Compiler

Compiled 26722 to 13966 computations (47.7% saved)

bsearch11.0ms (0.1%)

Compiler: Compiled 19 to 11 computations (42.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	59
1	32	59
2	46	59
3	54	59
4	59	59
5	60	59
6	60	59

end135.0ms (1.6%)

Compiler: Compiled 333 to 161 computations (51.7% saved)

Details

analyze2.1s (24.3%)

sample1.5s (17.4%)

simplify67.0ms (0.8%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series110.0ms (1.3%)

rewrite15.0ms (0.2%)

simplify102.0ms (1.2%)

prune107.0ms (1.2%)

localize10.0ms (0.1%)

series239.0ms (2.8%)

rewrite33.0ms (0.4%)

simplify144.0ms (1.7%)

prune162.0ms (1.9%)

localize10.0ms (0.1%)

series115.0ms (1.3%)

rewrite15.0ms (0.2%)

simplify388.0ms (4.5%)

prune224.0ms (2.6%)

localize10.0ms (0.1%)

series231.0ms (2.7%)

rewrite23.0ms (0.3%)

simplify161.0ms (1.9%)

prune148.0ms (1.7%)

regimes2.6s (29.7%)

bsearch11.0ms (0.1%)

simplify4.0ms (0%)

end135.0ms (1.6%)

Profiling