Details

analyze763.0ms (14.8%)

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)

sample1.2s (23.1%)

Results

1.1s	8256×	body	128	valid
60.0ms	479×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify35.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

832×	`fma-def_binary64`
768×	`times-frac_binary64`
756×	`fma-neg_binary64`
281×	`associate-/l*_binary64`
228×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	25	20
2	51	20
3	82	20
4	166	20
5	297	20
6	488	20
7	738	20
8	1199	20
9	1800	20
10	2769	20
11	4928	20

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

24.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.6b	(/.f64 (fma.f64 y.im (neg.f64 x.re) (.f64 x.im y.re)) (fma.f64 y.re y.re (.f64 y.im y.im)))

Compiler

Compiled 69 to 35 computations (49.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y.re y.re (*.f64 y.im y.im))
✓	0.5b	(fma.f64 y.im (neg.f64 x.re) (*.f64 x.im y.re))
✓	24.1b	(/.f64 (fma.f64 y.im (neg.f64 x.re) (.f64 x.im y.re)) (fma.f64 y.re y.re (.f64 y.im y.im)))

series91.0ms (1.8%)

Counts

3 → 120

Calls

3 calls:

75.0ms	(/.f64 (fma.f64 y.im (neg.f64 x.re) (.f64 x.im y.re)) (fma.f64 y.re y.re (.f64 y.im y.im)))
9.0ms	(fma.f64 y.im (neg.f64 x.re) (*.f64 x.im y.re))
7.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

rewrite50.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`log-prod_binary64`
286×	`prod-diff_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`
175×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	226	32
2	2921	32

Stop Event

1×	node limit

Counts

3 → 94

Calls

3 calls:

48.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))
48.0ms	(fma.f64 y.im (neg.f64 x.re) (*.f64 x.im y.re))
48.0ms	(/.f64 (fma.f64 y.im (neg.f64 x.re) (.f64 x.im y.re)) (fma.f64 y.re y.re (.f64 y.im y.im)))

simplify48.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-def_binary64`
469×	`cancel-sign-sub-inv_binary64`
421×	`associate-/r/_binary64`
414×	`fma-neg_binary64`
298×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	1926
1	133	1806
2	390	1767
3	1836	1722

Stop Event

1×	node limit

Counts

214 → 128

prune85.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	122	7	129

Error

0.8b

Counts

129 → 7

Alt Table

Status	Error	Program
▶	24.7b	(.f64 (-.f64 (.f64 y.im x.re) (*.f64 x.im y.re)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 y.im y.re) 2))))
	32.2b	(-.f64 (*.f64 x.im (/.f64 (/.f64 y.re y.im) y.im)) (/.f64 x.re y.im))
✓	24.6b	(/.f64 (fma.f64 y.im (neg.f64 x.re) (.f64 x.im y.re)) (fma.f64 y.re y.re (.f64 y.im y.im)))
	40.1b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.re (*.f64 x.im y.re)) (pow.f64 (hypot.f64 y.im y.re) 2))) 3)
	37.9b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.re (.f64 x.im y.re)) (hypot.f64 y.im y.re)))
	35.8b	(-.f64 (/.f64 x.im y.re) (.f64 (/.f64 y.im (.f64 y.re y.re)) (+.f64 x.re (/.f64 (*.f64 x.im y.im) y.re))))
	32.8b	(fma.f64 (/.f64 y.im y.re) (/.f64 (neg.f64 x.re) y.re) (/.f64 x.im y.re))

Compiler

Compiled 2528 to 883 computations (65.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 y.im y.re)
✓	0.5b	(/.f64 1 (neg.f64 (pow.f64 (hypot.f64 y.im y.re) 2)))
✓	0.9b	(-.f64 (.f64 y.im x.re) (.f64 x.im y.re))
✓	24.1b	(.f64 (-.f64 (.f64 y.im x.re) (*.f64 x.im y.re)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 y.im y.re) 2))))

series145.0ms (2.8%)

Counts

4 → 144

Calls

4 calls:

106.0ms	(.f64 (-.f64 (.f64 y.im x.re) (*.f64 x.im y.re)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 y.im y.re) 2))))
19.0ms	(/.f64 1 (neg.f64 (pow.f64 (hypot.f64 y.im y.re) 2)))
10.0ms	(hypot.f64 y.im y.re)
10.0ms	(-.f64 (.f64 y.im x.re) (.f64 x.im y.re))

rewrite65.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	326	43
2	4250	43

Stop Event

1×	node limit

Counts

4 → 143

Calls

4 calls:

62.0ms	(hypot.f64 y.im y.re)
62.0ms	(/.f64 1 (neg.f64 (pow.f64 (hypot.f64 y.im y.re) 2)))
62.0ms	(-.f64 (.f64 y.im x.re) (.f64 x.im y.re))
62.0ms	(.f64 (-.f64 (.f64 y.im x.re) (*.f64 x.im y.re)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 y.im y.re) 2))))

simplify72.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

505×	`times-frac_binary64`
338×	`associate-/l*_binary64`
307×	`sub-neg_binary64`
247×	`associate-/r*_binary64`
228×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	2810
1	326	2708
2	989	2653
3	4769	2653

Stop Event

1×	node limit

Counts

287 → 217

prune144.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	214	3	217
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	215	9	224

Error

0.1b

Counts

224 → 9

Alt Table

Status	Error	Program
✓	24.7b	(.f64 (-.f64 (.f64 y.im x.re) (*.f64 x.im y.re)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 y.im y.re) 2))))
▶	32.2b	(-.f64 (*.f64 x.im (/.f64 (/.f64 y.re y.im) y.im)) (/.f64 x.re y.im))
✓	24.6b	(/.f64 (fma.f64 y.im (neg.f64 x.re) (.f64 x.im y.re)) (fma.f64 y.re y.re (.f64 y.im y.im)))
	40.1b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 y.im x.re (*.f64 x.im y.re)) (pow.f64 (hypot.f64 y.im y.re) 2))) 3)
	35.8b	(-.f64 (/.f64 x.im y.re) (.f64 (/.f64 y.im (.f64 y.re y.re)) (+.f64 x.re (/.f64 (*.f64 x.im y.im) y.re))))
	32.8b	(fma.f64 (/.f64 y.im y.re) (/.f64 (neg.f64 x.re) y.re) (/.f64 x.im y.re))
	37.8b	(.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im))))
	32.3b	(-.f64 (/.f64 y.re (*.f64 (/.f64 y.im x.im) y.im)) (/.f64 x.re y.im))
	33.1b	(-.f64 (/.f64 x.im y.re) (*.f64 (/.f64 (/.f64 y.im y.re) y.re) x.re))

Compiler

Compiled 5215 to 2333 computations (55.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 y.re y.im) y.im)
✓	1.8b	(-.f64 (*.f64 x.im (/.f64 (/.f64 y.re y.im) y.im)) (/.f64 x.re y.im))
✓	6.4b	(*.f64 x.im (/.f64 (/.f64 y.re y.im) y.im))

series123.0ms (2.4%)

Counts

3 → 108

Calls

3 calls:

52.0ms	(*.f64 x.im (/.f64 (/.f64 y.re y.im) y.im))
48.0ms	(-.f64 (*.f64 x.im (/.f64 (/.f64 y.re y.im) y.im)) (/.f64 x.re y.im))
23.0ms	(/.f64 (/.f64 y.re y.im) y.im)

rewrite68.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

295×	`fma-def_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
194×	`egg-rr`
190×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	226	30
2	3454	30

Stop Event

1×	node limit

Counts

3 → 194

Calls

3 calls:

64.0ms	(/.f64 (/.f64 y.re y.im) y.im)
64.0ms	(-.f64 (*.f64 x.im (/.f64 (/.f64 y.re y.im) y.im)) (/.f64 x.re y.im))
64.0ms	(*.f64 x.im (/.f64 (/.f64 y.re y.im) y.im))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

770×	`times-frac_binary64`
637×	`associate-/l/_binary64`
393×	`associate-/l*_binary64`
241×	`associate-l_binary64`
211×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	1200
1	27	1200
2	52	1200
3	117	1200
4	327	1200
5	1181	1200

Stop Event

1×	node limit

Counts

302 → 202

prune111.0ms (2.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	198	4	202
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	201	10	211

Error

0.1b

Counts

211 → 10

Alt Table

Status	Error	Program
▶	31.1b	(fma.f64 (/.f64 y.re y.im) (*.f64 (/.f64 1 y.im) x.im) (/.f64 (neg.f64 x.re) y.im))
✓	24.7b	(.f64 (-.f64 (.f64 y.im x.re) (*.f64 x.im y.re)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 y.im y.re) 2))))
	32.3b	(-.f64 (/.f64 x.im (*.f64 y.im (/.f64 y.im y.re))) (/.f64 x.re y.im))
	35.8b	(-.f64 (/.f64 x.im y.re) (.f64 (/.f64 y.im (.f64 y.re y.re)) (+.f64 x.re (/.f64 (*.f64 x.im y.im) y.re))))
✓	24.6b	(/.f64 (fma.f64 y.im (neg.f64 x.re) (.f64 x.im y.re)) (fma.f64 y.re y.re (.f64 y.im y.im)))
	31.2b	(fma.f64 (/.f64 x.im (pow.f64 (cbrt.f64 y.im) 2)) (/.f64 (/.f64 y.re y.im) (cbrt.f64 y.im)) (/.f64 (neg.f64 x.re) y.im))
	33.4b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 (*.f64 x.im y.re) y.im) y.im)) 3) (/.f64 x.re y.im))
	32.8b	(fma.f64 (/.f64 y.im y.re) (/.f64 (neg.f64 x.re) y.re) (/.f64 x.im y.re))
	32.3b	(-.f64 (/.f64 y.re (*.f64 (/.f64 y.im x.im) y.im)) (/.f64 x.re y.im))
	33.1b	(-.f64 (/.f64 x.im y.re) (*.f64 (/.f64 (/.f64 y.im y.re) y.re) x.re))

Compiler

Compiled 4193 to 1137 computations (72.9% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 y.im) x.im)
✓	3.6b	(fma.f64 (/.f64 y.re y.im) (*.f64 (/.f64 1 y.im) x.im) (/.f64 (neg.f64 x.re) y.im))

series32.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

27.0ms	(fma.f64 (/.f64 y.re y.im) (*.f64 (/.f64 1 y.im) x.im) (/.f64 (neg.f64 x.re) y.im))
5.0ms	(*.f64 (/.f64 1 y.im) x.im)

rewrite95.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

351×	`prod-diff_binary64`
257×	`egg-rr`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
184×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	248	18
2	3377	18

Stop Event

1×	node limit

Counts

2 → 257

Calls

2 calls:

85.0ms	(*.f64 (/.f64 1 y.im) x.im)
85.0ms	(fma.f64 (/.f64 y.re y.im) (*.f64 (/.f64 1 y.im) x.im) (/.f64 (neg.f64 x.re) y.im))

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

789×	`times-frac_binary64`
602×	`associate-/l/_binary64`
398×	`associate-/l*_binary64`
241×	`associate-l_binary64`
202×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	768
1	27	768
2	51	768
3	115	768
4	320	768
5	1173	768

Stop Event

1×	node limit

Counts

329 → 263

prune173.0ms (3.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	262	1	263
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	264	9	273

Error

0.1b

Counts

273 → 9

Alt Table

Status	Error	Program
✓	24.6b	(/.f64 (fma.f64 y.im (neg.f64 x.re) (.f64 x.im y.re)) (fma.f64 y.re y.re (.f64 y.im y.im)))
	31.1b	(fma.f64 (/.f64 y.re y.im) (pow.f64 (cbrt.f64 (/.f64 x.im y.im)) 3) (/.f64 (neg.f64 x.re) y.im))
✓	31.1b	(fma.f64 (/.f64 y.re y.im) (*.f64 (/.f64 1 y.im) x.im) (/.f64 (neg.f64 x.re) y.im))
✓	24.7b	(.f64 (-.f64 (.f64 y.im x.re) (*.f64 x.im y.re)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 y.im y.re) 2))))
	32.3b	(-.f64 (/.f64 x.im (*.f64 y.im (/.f64 y.im y.re))) (/.f64 x.re y.im))
	35.8b	(-.f64 (/.f64 x.im y.re) (.f64 (/.f64 y.im (.f64 y.re y.re)) (+.f64 x.re (/.f64 (*.f64 x.im y.im) y.re))))
	32.8b	(fma.f64 (/.f64 y.im y.re) (/.f64 (neg.f64 x.re) y.re) (/.f64 x.im y.re))
	32.3b	(-.f64 (/.f64 y.re (*.f64 (/.f64 y.im x.im) y.im)) (/.f64 x.re y.im))
	33.1b	(-.f64 (/.f64 x.im y.re) (*.f64 (/.f64 (/.f64 y.im y.re) y.re) x.re))

Compiler

Compiled 10139 to 3806 computations (62.5% saved)

regimes1.5s (29.2%)

Accuracy

Total 11.9b remaining (97.2%)

Threshold costs 0b (0%)

Counts

77 → 6

Compiler

Compiled 6448 to 4159 computations (35.5% saved)

bsearch81.0ms (1.6%)

Steps

Iters	Range		Point
5	5.90120665875336e+62	2.0807438758843815e+63	1.8454883815855177e+63
7	5.1314403485896385e-111	1.7559298781140565e-109	1.700724934216277e-110
11	-1.2788452108889373e-88	-6.1878964206463e-110	-1.7029803518844395e-105
0	-1.7014204412768508e+24	-1.693526029288618e+24	-1.6974732352827345e+24
10	-1.447572801113306e+53	-2.3291054698633433e+41	-5.174874392946877e+44

Compiler

Compiled 5 to 4 computations (20% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

29×	`distribute-rgt-neg-in_binary64`
22×	`cancel-sign-sub-inv_binary64`
22×	`neg-sub0_binary64`
21×	`neg-mul-1_binary64`
20×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	141
1	65	140
2	84	140
3	103	138
4	140	138
5	173	138
6	199	138
7	214	138
8	238	138
9	269	138
10	281	138

Stop Event

1×

saturated

end134.0ms (2.6%)

Compiler: Compiled 350 to 189 computations (46% saved)

Iter	Nodes	Cost
0	47	141
1	65	140
2	84	140
3	103	138
4	140	138
5	173	138
6	199	138
7	214	138
8	238	138
9	269	138
10	281	138

Iter	Nodes	Cost
0	47	141
1	65	140
2	84	140
3	103	138
4	140	138
5	173	138
6	199	138
7	214	138
8	238	138
9	269	138
10	281	138

Details

analyze763.0ms (14.8%)

sample1.2s (23.1%)

simplify35.0ms (0.7%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series91.0ms (1.8%)

rewrite50.0ms (1%)

simplify48.0ms (0.9%)

prune85.0ms (1.6%)

localize11.0ms (0.2%)

series145.0ms (2.8%)

rewrite65.0ms (1.3%)

simplify72.0ms (1.4%)

prune144.0ms (2.8%)

localize8.0ms (0.1%)

series123.0ms (2.4%)

rewrite68.0ms (1.3%)

simplify45.0ms (0.9%)

prune111.0ms (2.2%)

localize8.0ms (0.2%)

series32.0ms (0.6%)

rewrite95.0ms (1.9%)

simplify39.0ms (0.8%)

prune173.0ms (3.4%)

regimes1.5s (29.2%)

bsearch81.0ms (1.6%)

simplify10.0ms (0.2%)

end134.0ms (2.6%)

Profiling

Iter	Nodes	Cost
0	47	141
1	65	140
2	84	140
3	103	138
4	140	138
5	173	138
6	199	138
7	214	138
8	238	138
9	269	138
10	281	138