Details

analyze1.7s (19.4%)

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)

sample1.4s (15.3%)

Results

1.1s	8256×	body	128	valid
183.0ms	235×	body	8192	exit
28.0ms	224×	body	128	invalid

Compiler

Compiled 39 to 23 computations (41% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	18	18
2	22	18
3	22	18

prune3.0ms (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

23.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
▶	23.7b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))

Compiler

Compiled 104 to 54 computations (48.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y.re y.re (*.f64 y.im y.im))
✓	0.2b	(fma.f64 x.re y.re (*.f64 x.im y.im))
✓	23.3b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))

series102.0ms (1.1%)

Counts

3 → 120

Calls

3 calls:

86.0ms	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
9.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))
6.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

rewrite11.0ms (0.1%)

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`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

7.0ms	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
0.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))
0.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-def_binary64`
413×	`associate-/l/_binary64`
364×	`fma-neg_binary64`
246×	`distribute-rgt-neg-in_binary64`
245×	`distribute-lft-neg-in_binary64`

Counts

169 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	2836
1	205	2674
2	613	2590
3	2201	2542
4	5123	2542

prune100.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	9	119
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	9	121

Error

1.0b

Counts

121 → 9

Alt Table

Status	Error	Program
	38.4b	(/.f64 x.re y.re)
	24.1b	(/.f64 (.f64 (cbrt.f64 (fma.f64 x.re y.re (.f64 x.im y.im))) (cbrt.f64 (fma.f64 x.re y.re (.f64 x.im y.im)))) (/.f64 (fma.f64 y.re y.re (.f64 y.im y.im)) (cbrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)))))
	24.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))) (cbrt.f64 (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im))))) (cbrt.f64 (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))))
	34.2b	(+.f64 (/.f64 x.im y.im) (.f64 (/.f64 y.re (.f64 y.im y.im)) (-.f64 x.re (/.f64 (*.f64 x.im y.re) y.im))))
	24.0b	(.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
	14.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 y.im x.im (.f64 y.re x.re))) (cbrt.f64 (fma.f64 y.im x.im (.f64 y.re x.re)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)))
	34.7b	(fma.f64 x.im (/.f64 y.im (*.f64 y.re y.re)) (/.f64 x.re y.re))
	35.6b	(/.f64 x.im y.im)
▶	14.0b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (hypot.f64 y.im y.re)))

Compiler

Compiled 2779 to 588 computations (78.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (hypot.f64 y.im y.re)))
✓	0.5b	(fma.f64 y.im x.im (*.f64 y.re x.re))
✓	13.0b	(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series218.0ms (2.4%)

Counts

3 → 144

Calls

3 calls:

104.0ms

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

100.0ms

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

13.0ms

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

rewrite19.0ms (0.2%)

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 → 97

Calls

3 calls:

8.0ms

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

2.0ms

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

0.0ms

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

simplify202.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

735×	`times-frac_binary64`
339×	`fma-neg_binary64`
266×	`distribute-rgt-in_binary64`
259×	`fma-def_binary64`
254×	`distribute-lft-in_binary64`

Counts

241 → 221

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	186	5547
1	490	4784
2	1686	4627
3	4606	4609
4	4975	4609
5	4994	4609
6	4978	4609

prune182.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	213	8	221
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	220	10	230

Error

0.0b

Counts

230 → 10

Alt Table

Status	Error	Program
▶	13.8b	(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
	23.5b	(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (.f64 y.re y.re))) y.re (/.f64 (.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
	34.7b	(fma.f64 x.im (/.f64 y.im (*.f64 y.re y.re)) (/.f64 x.re y.re))
	44.3b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
	31.2b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
	24.0b	(.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
	41.2b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
	14.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))))
	14.1b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
	45.9b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))

Compiler

Compiled 5801 to 1595 computations (72.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
✓	0.2b	(fma.f64 x.re y.re (*.f64 y.im x.im))
✓	13.0b	(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

series227.0ms (2.5%)

Counts

3 → 144

Calls

3 calls:

112.0ms

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

106.0ms

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

9.0ms

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

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
16×	`associate-/l*_binary64`

Counts

3 → 111

Calls

3 calls:

4.0ms

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

2.0ms

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

0.0ms

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

simplify152.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

701×	`times-frac_binary64`
519×	`associate-/l*_binary64`
443×	`fma-neg_binary64`
384×	`associate-/r*_binary64`
364×	`associate-/l/_binary64`

Counts

255 → 251

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	6578
1	537	5929
2	1451	5628
3	4664	5628
4	4986	5628

prune165.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	248	3	251
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	251	10	261

Error

0.0b

Counts

261 → 10

Alt Table

Status	Error	Program
✓	13.8b	(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
	23.5b	(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (.f64 y.re y.re))) y.re (/.f64 (.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
	34.7b	(fma.f64 x.im (/.f64 y.im (*.f64 y.re y.re)) (/.f64 x.re y.re))
	44.3b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
	14.5b	(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))))
	45.8b	(/.f64 (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)) (hypot.f64 y.im y.re))
	41.2b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
	31.2b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
▶	14.1b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
	14.5b	(/.f64 1 (.f64 (hypot.f64 y.im y.re) (/.f64 (hypot.f64 y.im y.re) (fma.f64 y.im x.im (.f64 y.re x.re)))))

Compiler

Compiled 6603 to 1264 computations (80.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
	0.5b	(fma.f64 y.im x.im (*.f64 y.re x.re))
✓	5.9b	(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))
✓	7.3b	(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))

series348.0ms (3.9%)

Counts

3 → 128

Calls

3 calls:

137.0ms

(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))

107.0ms

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

103.0ms

(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))

rewrite148.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

569×	`times-frac_binary64`
364×	`add-sqr-sqrt_binary64`
292×	`*-un-lft-identity_binary64`
285×	`add-cube-cbrt_binary64`
279×	`sqrt-prod_binary64`

Counts

3 → 420

Calls

3 calls:

46.0ms

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

8.0ms

(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))

3.0ms

(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))

simplify694.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
409×	`cancel-sign-sub-inv_binary64`
350×	`associate-/l/_binary64`
325×	`associate-/l*_binary64`
315×	`associate-*l/_binary64`

Counts

548 → 592

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	441	20646
1	1204	18191
2	3743	17457
3	4839	17457
4	5166	17457

prune389.0ms (4.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	613	0	613
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	613	10	623

Error

0.0b

Counts

623 → 10

Alt Table

Status	Error	Program
✓	13.8b	(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
	23.5b	(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (.f64 y.re y.re))) y.re (/.f64 (.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
	34.7b	(fma.f64 x.im (/.f64 y.im (*.f64 y.re y.re)) (/.f64 x.re y.re))
	44.3b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
	14.5b	(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))))
	45.8b	(/.f64 (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)) (hypot.f64 y.im y.re))
	41.2b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
	31.2b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
✓	14.1b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
	14.5b	(/.f64 1 (.f64 (hypot.f64 y.im y.re) (/.f64 (hypot.f64 y.im y.re) (fma.f64 y.im x.im (.f64 y.re x.re)))))

Compiler

Compiled 22671 to 4240 computations (81.3% saved)

regimes2.6s (29.1%)

Accuracy

Total 10.0b remaining (98%)

Threshold costs 0b (0%)

Counts

192 → 2

Compiler

Compiled 20618 to 11054 computations (46.4% saved)

bsearch8.0ms (0.1%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	61
1	28	61
2	28	61

end121.0ms (1.3%)

Compiler: Compiled 276 to 144 computations (47.8% saved)

Details

analyze1.7s (19.4%)

sample1.4s (15.3%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series102.0ms (1.1%)

rewrite11.0ms (0.1%)

simplify85.0ms (0.9%)

prune100.0ms (1.1%)

localize9.0ms (0.1%)

series218.0ms (2.4%)

rewrite19.0ms (0.2%)

simplify202.0ms (2.3%)

prune182.0ms (2%)

localize8.0ms (0.1%)

series227.0ms (2.5%)

rewrite20.0ms (0.2%)

simplify152.0ms (1.7%)

prune165.0ms (1.8%)

localize12.0ms (0.1%)

series348.0ms (3.9%)

rewrite148.0ms (1.7%)

simplify694.0ms (7.8%)

prune389.0ms (4.3%)

regimes2.6s (29.1%)

bsearch8.0ms (0.1%)

simplify3.0ms (0%)

end121.0ms (1.3%)

Profiling