Details

analyze750.0ms (13.7%)

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.1s (20.8%)

Results

1.0s	8256×	body	128	valid
62.0ms	498×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

26.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

Compiler

Compiled 70 to 36 computations (48.6% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
✓	26.2b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series86.0ms (1.6%)

Counts

2 → 96

Calls

2 calls:

78.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
8.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

rewrite54.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`fma-def_binary64`
244×	`fma-neg_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
134×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	264	25
2	3782	25

Stop Event

1×	node limit

Counts

2 → 94

Calls

2 calls:

49.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
49.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify39.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-*l/_binary64`
519×	`fma-def_binary64`
455×	`associate-/r/_binary64`
341×	`fma-neg_binary64`
284×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	1626
1	114	1542
2	358	1458
3	1828	1410

Stop Event

1×	node limit

Counts

190 → 119

prune88.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	6	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Error

2.2b

Counts

120 → 7

Alt Table

Status	Error	Program
✓	26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
	19.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x.re y.re (.f64 x.im y.im))) 2) (hypot.f64 y.re y.im)) (/.f64 (cbrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im))) (hypot.f64 y.re y.im)))
	35.7b	(/.f64 x.re y.re)
	38.7b	(pow.f64 (/.f64 (sqrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im))) (hypot.f64 y.re y.im)) 2)
▶	19.3b	(.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)))
	37.2b	(/.f64 x.im y.im)
	23.2b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (.f64 (/.f64 y.re (fma.f64 y.im y.im (*.f64 y.re y.re))) x.re))

Compiler

Compiled 2522 to 802 computations (68.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x.re y.re (*.f64 x.im y.im))
✓	0.0b	(hypot.f64 y.re y.im)
✓	0.3b	(.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)))
✓	17.9b	(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (hypot.f64 y.re y.im))

series199.0ms (3.6%)

Counts

4 → 168

Calls

4 calls:

94.0ms	(.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)))
85.0ms	(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (hypot.f64 y.re y.im))
11.0ms	(hypot.f64 y.re y.im)
8.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))

rewrite61.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`log-prod_binary64`
254×	`prod-diff_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
200×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	246	43
2	3155	43

Stop Event

1×	node limit

Counts

4 → 153

Calls

4 calls:

58.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))
58.0ms	(hypot.f64 y.re y.im)
58.0ms	(.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)))
58.0ms	(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (hypot.f64 y.re y.im))

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

585×	`times-frac_binary64`
422×	`associate-/l*_binary64`
319×	`fma-def_binary64`
314×	`associate-/r*_binary64`
293×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	3496
1	373	3040
2	1300	2876

Stop Event

1×	node limit

Counts

321 → 244

prune194.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	295	6	301
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	300	8	308

Error

0.0b

Counts

308 → 8

Alt Table

Status	Error	Program
	44.1b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
	23.2b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (.f64 (/.f64 y.re (fma.f64 y.im y.im (*.f64 y.re y.re))) x.re))
▶	19.3b	(/.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (hypot.f64 y.re y.im) (fma.f64 x.re y.re (*.f64 x.im y.im))))
	45.0b	(.f64 (/.f64 1 (hypot.f64 y.re y.im)) (fma.f64 (.f64 (/.f64 x.re y.re) (*.f64 (/.f64 y.im y.re) y.im)) -1/2 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
	44.5b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
✓	26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
	31.1b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
	32.4b	(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))

Compiler

Compiled 6919 to 2567 computations (62.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x.re y.re (*.f64 x.im y.im))
	0.0b	(hypot.f64 y.re y.im)
✓	0.3b	(/.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (hypot.f64 y.re y.im) (fma.f64 x.re y.re (*.f64 x.im y.im))))
✓	17.9b	(/.f64 (hypot.f64 y.re y.im) (fma.f64 x.re y.re (*.f64 x.im y.im)))

series143.0ms (2.6%)

Counts

2 → 96

Calls

2 calls:

92.0ms	(/.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (hypot.f64 y.re y.im) (fma.f64 x.re y.re (*.f64 x.im y.im))))
51.0ms	(/.f64 (hypot.f64 y.re y.im) (fma.f64 x.re y.re (*.f64 x.im y.im)))

rewrite52.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

281×	`prod-diff_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
207×	`log-pow_binary64`
127×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	252	31
2	3382	31

Stop Event

1×	node limit

Counts

2 → 79

Calls

2 calls:

50.0ms	(/.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (hypot.f64 y.re y.im) (fma.f64 x.re y.re (*.f64 x.im y.im))))
50.0ms	(/.f64 (hypot.f64 y.re y.im) (fma.f64 x.re y.re (*.f64 x.im y.im)))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

534×	`cancel-sign-sub-inv_binary64`
533×	`fma-def_binary64`
280×	`associate-/l/_binary64`
239×	`times-frac_binary64`
239×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	3924
1	511	3324
2	2362	3100

Stop Event

1×	node limit

Counts

175 → 143

prune185.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	291	0	291
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	291	8	299

Error

0.0b

Counts

299 → 8

Alt Table

Status	Error	Program
	44.1b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
▶	23.2b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (.f64 (/.f64 y.re (fma.f64 y.im y.im (*.f64 y.re y.re))) x.re))
✓	19.3b	(/.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (hypot.f64 y.re y.im) (fma.f64 x.re y.re (*.f64 x.im y.im))))
	45.0b	(.f64 (/.f64 1 (hypot.f64 y.re y.im)) (fma.f64 (.f64 (/.f64 x.re y.re) (*.f64 (/.f64 y.im y.re) y.im)) -1/2 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
	44.5b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
✓	26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
	31.1b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
	32.4b	(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))

Compiler

Compiled 7591 to 3177 computations (58.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (.f64 (/.f64 y.re (fma.f64 y.im y.im (*.f64 y.re y.re))) x.re))
✓	4.0b	(.f64 (/.f64 y.re (fma.f64 y.im y.im (.f64 y.re y.re))) x.re)
✓	17.0b	(/.f64 y.re (fma.f64 y.im y.im (*.f64 y.re y.re)))
✓	18.5b	(/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re)))

series207.0ms (3.8%)

Counts

4 → 132

Calls

4 calls:

120.0ms	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (.f64 (/.f64 y.re (fma.f64 y.im y.im (*.f64 y.re y.re))) x.re))
59.0ms	(.f64 (/.f64 y.re (fma.f64 y.im y.im (.f64 y.re y.re))) x.re)
16.0ms	(/.f64 y.re (fma.f64 y.im y.im (*.f64 y.re y.re)))
12.0ms	(/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re)))

rewrite55.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

359×	`prod-diff_binary64`
210×	`expm1-udef_binary64`
210×	`log1p-udef_binary64`
195×	`log-pow_binary64`
117×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	64
1	229	59
2	3067	59

Stop Event

1×	node limit

Counts

4 → 117

Calls

4 calls:

53.0ms	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (.f64 (/.f64 y.re (fma.f64 y.im y.im (*.f64 y.re y.re))) x.re))
53.0ms	(.f64 (/.f64 y.re (fma.f64 y.im y.im (.f64 y.re y.re))) x.re)
53.0ms	(/.f64 y.re (fma.f64 y.im y.im (*.f64 y.re y.re)))
53.0ms	(/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re)))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

443×	`times-frac_binary64`
364×	`associate-/l*_binary64`
310×	`sub-neg_binary64`
301×	`associate-/r*_binary64`
279×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	3318
1	281	3210
2	891	3069
3	4633	3069

Stop Event

1×	node limit

Counts

249 → 183

prune133.0ms (2.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	183	8	191

Error

0.0b

Counts

191 → 8

Alt Table

Status	Error	Program
	44.1b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
✓	23.2b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (.f64 (/.f64 y.re (fma.f64 y.im y.im (*.f64 y.re y.re))) x.re))
✓	19.3b	(/.f64 (/.f64 1 (hypot.f64 y.re y.im)) (/.f64 (hypot.f64 y.re y.im) (fma.f64 x.re y.re (*.f64 x.im y.im))))
	45.0b	(.f64 (/.f64 1 (hypot.f64 y.re y.im)) (fma.f64 (.f64 (/.f64 x.re y.re) (*.f64 (/.f64 y.im y.re) y.im)) -1/2 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
	44.5b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
✓	26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
	31.1b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
	32.4b	(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))

Compiler

Compiled 4693 to 1876 computations (60% saved)

regimes1.7s (30.2%)

Accuracy

Total 10.8b remaining (98.7%)

Threshold costs 0b (0%)

Counts

128 → 5

Compiler

Compiled 11803 to 7189 computations (39.1% saved)

bsearch79.0ms (1.4%)

Steps

Iters	Range		Point
4	3.5965325781940086e+140	5.90931478180851e+140	3.6360166068854995e+140
9	2.634451215286903e-71	3.60595376629138e-65	2.670610561569208e-71
8	-2.4141280899525958e-105	-1.8387138583883085e-108	-1.1965629553159867e-107
10	-1.1215020233833144e+95	-3.5217700334405997e+83	-1.1090419202097725e+95

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	121
1	52	121
2	59	119
3	66	119
4	69	119
5	70	119

Stop Event

1×

saturated

end121.0ms (2.2%)

Compiler: Compiled 325 to 168 computations (48.3% saved)

Details

analyze750.0ms (13.7%)

sample1.1s (20.8%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.2%)

series86.0ms (1.6%)

rewrite54.0ms (1%)

simplify39.0ms (0.7%)

prune88.0ms (1.6%)

localize9.0ms (0.2%)

series199.0ms (3.6%)

rewrite61.0ms (1.1%)

simplify58.0ms (1.1%)

prune194.0ms (3.5%)

localize9.0ms (0.2%)

series143.0ms (2.6%)

rewrite52.0ms (0.9%)

simplify61.0ms (1.1%)

prune185.0ms (3.4%)

localize10.0ms (0.2%)

series207.0ms (3.8%)

rewrite55.0ms (1%)

simplify74.0ms (1.3%)

prune133.0ms (2.4%)

regimes1.7s (30.2%)

bsearch79.0ms (1.4%)

simplify5.0ms (0.1%)

end121.0ms (2.2%)

Profiling