Details

analyze701.0ms (12.5%)

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 (21.4%)

Results

1.1s	8256×	body	128	valid
63.0ms	502×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify9.0ms (0.2%)

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

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

31.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.9b	(/.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 66 to 32 computations (51.5% saved)

localize8.0ms (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))
✓	0.3b	(fma.f64 x.re y.re (*.f64 x.im y.im))
✓	31.3b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))

series84.0ms (1.5%)

Counts

3 → 120

Calls

3 calls:

68.0ms	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
11.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))
5.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

rewrite85.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
348×	`prod-diff_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
175×	`pow3_binary64`

Counts

3 → 97

Calls

3 calls:

83.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))
83.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))
83.0ms	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	203	32
2	2457	32
3	4976	32
4	5153	32
0	0	0
1	0	0

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-*l/_binary64`
519×	`fma-def_binary64`
472×	`associate-/r/_binary64`
341×	`fma-neg_binary64`
285×	`associate-/l/_binary64`

Counts

217 → 129

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	1830
1	112	1710
2	352	1626
3	1583	1578
4	5200	1578

prune177.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	119	10	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	10	130

Error

2.4b

Counts

130 → 10

Alt Table

Status	Error	Program
	21.2b	(.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)))
▶	20.7b	(.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)))
	38.8b	(/.f64 x.re y.re)
	36.0b	(+.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))))
	34.1b	(fma.f64 y.re (/.f64 x.re (*.f64 y.im y.im)) (/.f64 x.im y.im))
	36.1b	(/.f64 x.im y.im)
	49.8b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (/.f64 (-.f64 (.f64 (.f64 y.re y.re) (.f64 y.re y.re)) (pow.f64 y.im 4)) (-.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
	30.6b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
	32.0b	(pow.f64 (/.f64 (pow.f64 (hypot.f64 y.re y.im) 2) (fma.f64 x.re y.re (*.f64 x.im y.im))) -1)
	43.8b	(pow.f64 (/.f64 (sqrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im))) (hypot.f64 y.re y.im)) 2)

Compiler

Compiled 2643 to 941 computations (64.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 y.re y.im))
	0.3b	(fma.f64 x.re y.re (*.f64 x.im 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)))
✓	19.3b	(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (hypot.f64 y.re y.im))

series267.0ms (4.8%)

Counts

3 → 120

Calls

3 calls:

131.0ms

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

122.0ms

(*.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)))

14.0ms

(/.f64 1 (hypot.f64 y.re y.im))

rewrite102.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 127

Calls

3 calls:

99.0ms

(/.f64 1 (hypot.f64 y.re y.im))

99.0ms

(*.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)))

99.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	41
1	245	38
2	2944	38
3	5627	38
0	0	0
1	0	0

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-neg_binary64`
600×	`times-frac_binary64`
438×	`associate-/l*_binary64`
337×	`associate-/r*_binary64`
329×	`fma-def_binary64`

Counts

247 → 211

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	3272
1	376	2866
2	1282	2666
3	4741	2658
4	5167	2658

prune163.0ms (2.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	238	8	246
Fresh	7	2	9
Picked	0	1	1
Done	0	0	0
Total	245	11	256

Error

0.0b

Counts

256 → 11

Alt Table

Status	Error	Program
	46.9b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
✓	20.7b	(.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)))
	44.0b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
	36.0b	(+.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))))
	33.7b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
	34.1b	(fma.f64 y.re (/.f64 x.re (*.f64 y.im y.im)) (/.f64 x.im y.im))
	31.5b	(.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (pow.f64 (hypot.f64 y.re y.im) -2))
	30.1b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
	32.9b	(.f64 (/.f64 1 (hypot.f64 y.re y.im)) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)) 3)))
▶	20.8b	(.f64 (pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2) (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)))
	45.8b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))

Compiler

Compiled 5672 to 2114 computations (62.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 x.re y.re (*.f64 x.im y.im))
✓	0.3b	(.f64 (pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2) (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)))
✓	0.5b	(pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2)
	19.3b	(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (hypot.f64 y.re y.im))

series129.0ms (2.3%)

Counts

2 → 72

Calls

2 calls:

94.0ms	(.f64 (pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2) (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)))
34.0ms	(pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2)

rewrite60.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

254×	`prod-diff_binary64`
251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`
234×	`log-pow_binary64`
144×	`add-sqr-sqrt_binary64`

Counts

2 → 51

Calls

2 calls:

59.0ms	(.f64 (pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2) (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)))
59.0ms	(pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	298	24
2	3347	24
3	4922	24
0	0	0
1	0	0

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

743×	`fma-neg_binary64`
512×	`distribute-neg-frac_binary64`
332×	`times-frac_binary64`
272×	`associate-/l*_binary64`
224×	`cancel-sign-sub-inv_binary64`

Counts

123 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	1890
1	249	1802
2	809	1702
3	3499	1694
4	5198	1694

prune192.0ms (3.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	219	12	231

Error

0.0b

Counts

231 → 12

Alt Table

Status	Error	Program
	46.9b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
✓	20.7b	(.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)))
	44.0b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
	36.0b	(+.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))))
	33.7b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
	34.1b	(fma.f64 y.re (/.f64 x.re (*.f64 y.im y.im)) (/.f64 x.im y.im))
	31.5b	(.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (pow.f64 (hypot.f64 y.re y.im) -2))
▶	30.1b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
	45.8b	(*.f64 (pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
	32.9b	(.f64 (/.f64 1 (hypot.f64 y.re y.im)) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)) 3)))
✓	20.8b	(.f64 (pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2) (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)))
	45.8b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))

Compiler

Compiled 5448 to 2261 computations (58.5% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.8b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))

series29.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

29.0ms

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

rewrite49.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

532×	`log-prod_binary64`
278×	`prod-diff_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`
166×	`log-pow_binary64`

Counts

1 → 30

Calls

1 calls:

48.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	191	14
2	2584	14
3	5095	14
0	0	0
1	0	0

simplify130.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

984×	`associate-/r/_binary64`
976×	`*-commutative_binary64`
624×	`times-frac_binary64`
533×	`associate-/l/_binary64`
434×	`unswap-sqr_binary64`

Counts

78 → 35

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	660
1	20	660
2	37	588
3	83	588
4	202	588
5	611	588
6	2273	588
7	3120	588
8	3121	588
9	3275	588
10	3464	588
11	3600	588
12	3944	588
13	4798	588
14	4793	588

prune22.0ms (0.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	34	1	35
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	34	13	47

Error

0.0b

Counts

47 → 13

Alt Table

Status	Error	Program
	46.9b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
✓	20.7b	(.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)))
	44.0b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
	36.0b	(+.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))))
	33.7b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
	34.1b	(fma.f64 y.re (/.f64 x.re (*.f64 y.im y.im)) (/.f64 x.im y.im))
	31.5b	(.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (pow.f64 (hypot.f64 y.re y.im) -2))
✓	30.1b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
	45.8b	(*.f64 (pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
	30.6b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))) 2))
	32.9b	(.f64 (/.f64 1 (hypot.f64 y.re y.im)) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)) 3)))
✓	20.8b	(.f64 (pow.f64 (pow.f64 (hypot.f64 y.re y.im) -1/2) 2) (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (hypot.f64 y.re y.im)))
	45.8b	(*.f64 (/.f64 1 (hypot.f64 y.re y.im)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))

Compiler

Compiled 800 to 253 computations (68.4% saved)

regimes1.7s (30.4%)

Accuracy

Total 11.8b remaining (98.7%)

Threshold costs 0b (0%)

Counts

113 → 5

Compiler

Compiled 10313 to 6204 computations (39.8% saved)

bsearch77.0ms (1.4%)

Steps

Iters	Range		Point
9	3.627282684220053e+113	6.1617923709117596e+119	2.2666934726198564e+115
7	9.859358158521771e-48	2.1916706673406483e-46	1.0144811947290463e-47
6	-3.9297576502057126e-51	-7.667654871302878e-52	-7.788909268214381e-52
8	-4.3144961082925656e+88	-3.793265380744982e+85	-7.484249059006481e+87

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	117
1	47	117
2	46	117

end171.0ms (3%)

Compiler: Compiled 414 to 219 computations (47.1% saved)

Details

analyze701.0ms (12.5%)

sample1.2s (21.4%)

simplify9.0ms (0.2%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series84.0ms (1.5%)

rewrite85.0ms (1.5%)

simplify56.0ms (1%)

prune177.0ms (3.2%)

localize9.0ms (0.2%)

series267.0ms (4.8%)

rewrite102.0ms (1.8%)

simplify93.0ms (1.7%)

prune163.0ms (2.9%)

localize14.0ms (0.2%)

series129.0ms (2.3%)

rewrite60.0ms (1.1%)

simplify64.0ms (1.1%)

prune192.0ms (3.4%)

localize10.0ms (0.2%)

series29.0ms (0.5%)

rewrite49.0ms (0.9%)

simplify130.0ms (2.3%)

prune22.0ms (0.4%)

regimes1.7s (30.4%)

bsearch77.0ms (1.4%)

simplify3.0ms (0.1%)

end171.0ms (3%)

Profiling