Details

analyze765.0ms (16.2%)

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 (24%)

Results

1.1s	8256×	body	128	valid
61.0ms	488×	body	128	invalid

Compiler

Compiled 40 to 24 computations (40% saved)

preprocess41.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

905×	`fma-def_binary64`
532×	`associate-/l*_binary64`
381×	`fma-neg_binary64`
305×	`div-sub_binary64`
300×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	140
1	122	140
2	243	140
3	398	140
4	872	140
5	1687	140
6	3097	140
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 19 to 11 computations (42.1% 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

28.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.4b	(/.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)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 y.im (neg.f64 x.re) (*.f64 x.im y.re))
✓	27.9b	(/.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)))

series83.0ms (1.8%)

Counts

2 → 96

Calls

24 calls:

12.0ms	(/.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)))	x.im	0
11.0ms	(/.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)))	x.im	inf
11.0ms	(/.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)))	x.re	inf
9.0ms	(/.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)))	x.re	-inf
9.0ms	(/.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)))	x.im	-inf

rewrite45.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	226	25
2	2902	25

Stop Event

1×	node limit

Counts

2 → 65

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	1722
1	133	1638
2	390	1599
3	1836	1554

Stop Event

1×	node limit

Counts

161 → 92

prune59.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Error

0.7b

Counts

93 → 9

Alt Table

Status	Error	Program
▶	28.6b	(.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))))
	40.8b	(/.f64 x.im (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) y.re))
	33.6b	(-.f64 (/.f64 x.im y.re) (*.f64 (/.f64 y.im y.re) (/.f64 x.re y.re)))
	32.1b	(-.f64 (.f64 (/.f64 (/.f64 y.re y.im) y.im) (+.f64 x.im (/.f64 (.f64 y.re x.re) y.im))) (/.f64 x.re y.im))
	37.9b	(/.f64 x.im y.re)
	36.5b	(.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)))
	44.6b	(sqrt.f64 (pow.f64 (/.f64 (fma.f64 y.im x.re (*.f64 x.im y.re)) (pow.f64 (hypot.f64 y.im y.re) 2)) 2))
	30.5b	(fma.f64 x.im (/.f64 (/.f64 y.re y.im) y.im) (/.f64 (neg.f64 x.re) y.im))
	38.0b	(-.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))))

Compiler

Compiled 1968 to 719 computations (63.5% saved)

localize10.0ms (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)))
✓	0.7b	(-.f64 (.f64 y.im x.re) (.f64 x.im y.re))
✓	27.7b	(.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))))

series149.0ms (3.1%)

Counts

4 → 144

Calls

36 calls:

17.0ms	(.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))))	x.im	inf
16.0ms	(.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))))	x.im	-inf
15.0ms	(.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))))	x.re	inf
15.0ms	(.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))))	x.re	0
14.0ms	(.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))))	x.im	0

rewrite63.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
161×	`add-sqr-sqrt_binary64`
157×	`pow1_binary64`
155×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	327	43
2	4259	43

Stop Event

1×	node limit

Counts

4 → 143

simplify77.0ms (1.6%)

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

prune143.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	212	5	217
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	217	9	226

Error

0.1b

Counts

226 → 9

Alt Table

Status	Error	Program
✓	28.6b	(.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))))
	33.6b	(-.f64 (/.f64 x.im y.re) (*.f64 (/.f64 y.im y.re) (/.f64 x.re y.re)))
	32.1b	(-.f64 (.f64 (/.f64 (/.f64 y.re y.im) y.im) (+.f64 x.im (/.f64 (.f64 y.re x.re) y.im))) (/.f64 x.re y.im))
	31.4b	(-.f64 (/.f64 y.re (*.f64 (/.f64 y.im x.im) y.im)) (/.f64 x.re y.im))
▶	26.3b	(-.f64 (.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im)))) (/.f64 x.re (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) y.im)))
	36.5b	(.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)))
	34.5b	(-.f64 (fma.f64 (/.f64 x.im y.im) (/.f64 y.re y.im) (/.f64 y.re (/.f64 (pow.f64 y.im 3) (*.f64 y.re x.re)))) (/.f64 x.re y.im))
	34.5b	(-.f64 (/.f64 x.im y.re) (*.f64 (/.f64 (/.f64 y.im y.re) y.re) x.re))
	28.4b	(/.f64 (neg.f64 (-.f64 (.f64 y.im x.re) (.f64 x.im y.re))) (pow.f64 (hypot.f64 y.im y.re) 2))

Compiler

Compiled 5275 to 2354 computations (55.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im))))
✓	4.5b	(/.f64 x.re (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) y.im))
✓	19.3b	(/.f64 y.re (fma.f64 y.re y.re (*.f64 y.im y.im)))
✓	20.2b	(/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) y.im)

series148.0ms (3.1%)

Counts

4 → 120

Calls

30 calls:

18.0ms	(.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im))))	x.im	-inf
16.0ms	(/.f64 x.re (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) y.im))	x.re	-inf
15.0ms	(/.f64 x.re (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) y.im))	x.re	0
14.0ms	(.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im))))	x.im	0
14.0ms	(.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im))))	x.im	inf

rewrite62.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
191×	`log-pow_binary64`
175×	`log-div_binary64`
140×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	50
1	237	46
2	3358	46

Stop Event

1×	node limit

Counts

4 → 133

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

496×	`times-frac_binary64`
406×	`associate-/l*_binary64`
313×	`associate-/r*_binary64`
237×	`sub-neg_binary64`
226×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	2568
1	266	2520
2	844	2397
3	4723	2397

Stop Event

1×	node limit

Counts

253 → 189

prune147.0ms (3.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	188	10	198

Error

0.1b

Counts

198 → 10

Alt Table

Status	Error	Program
✓	28.6b	(.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))))
	33.6b	(-.f64 (/.f64 x.im y.re) (*.f64 (/.f64 y.im y.re) (/.f64 x.re y.re)))
	32.1b	(-.f64 (.f64 (/.f64 (/.f64 y.re y.im) y.im) (+.f64 x.im (/.f64 (.f64 y.re x.re) y.im))) (/.f64 x.re y.im))
	31.4b	(-.f64 (/.f64 y.re (*.f64 (/.f64 y.im x.im) y.im)) (/.f64 x.re y.im))
✓	26.3b	(-.f64 (.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im)))) (/.f64 x.re (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) y.im)))
	36.5b	(.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)))
	34.5b	(-.f64 (fma.f64 (/.f64 x.im y.im) (/.f64 y.re y.im) (/.f64 y.re (/.f64 (pow.f64 y.im 3) (*.f64 y.re x.re)))) (/.f64 x.re y.im))
	34.5b	(-.f64 (/.f64 x.im y.re) (*.f64 (/.f64 (/.f64 y.im y.re) y.re) x.re))
	28.4b	(/.f64 (neg.f64 (-.f64 (.f64 y.im x.re) (.f64 x.im y.re))) (pow.f64 (hypot.f64 y.im y.re) 2))
▶	16.9b	(-.f64 (.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im)))) (/.f64 x.re (+.f64 y.im (*.f64 (/.f64 y.re y.im) y.re))))

Compiler

Compiled 5243 to 1928 computations (63.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 y.re y.im) y.re)
	3.8b	(.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im))))
✓	4.5b	(/.f64 x.re (+.f64 y.im (*.f64 (/.f64 y.re y.im) y.re)))
	19.3b	(/.f64 y.re (fma.f64 y.re y.re (*.f64 y.im y.im)))

series62.0ms (1.3%)

Counts

2 → 60

Calls

15 calls:

13.0ms	(/.f64 x.re (+.f64 y.im (*.f64 (/.f64 y.re y.im) y.re)))	x.re	-inf
12.0ms	(/.f64 x.re (+.f64 y.im (*.f64 (/.f64 y.re y.im) y.re)))	x.re	0
12.0ms	(/.f64 x.re (+.f64 y.im (*.f64 (/.f64 y.re y.im) y.re)))	x.re	inf
3.0ms	(/.f64 x.re (+.f64 y.im (*.f64 (/.f64 y.re y.im) y.re)))	y.re	inf
3.0ms	(/.f64 x.re (+.f64 y.im (*.f64 (/.f64 y.re y.im) y.re)))	y.im	0

rewrite48.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

857×	`prod-diff_binary64`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`
129×	`fma-neg_binary64`
97×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	181	18
2	2740	18

Stop Event

1×	node limit

Counts

2 → 57

simplify35.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

555×	`fma-def_binary64`
521×	`associate-/r/_binary64`
383×	`fma-neg_binary64`
291×	`associate-/l/_binary64`
200×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	1032
1	118	1032
2	365	975
3	1890	936

Stop Event

1×	node limit

Counts

117 → 76

prune136.0ms (2.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	166	10	176

Error

0.0b

Counts

176 → 10

Alt Table

Status	Error	Program
✓	28.6b	(.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))))
	33.6b	(-.f64 (/.f64 x.im y.re) (*.f64 (/.f64 y.im y.re) (/.f64 x.re y.re)))
	32.1b	(-.f64 (.f64 (/.f64 (/.f64 y.re y.im) y.im) (+.f64 x.im (/.f64 (.f64 y.re x.re) y.im))) (/.f64 x.re y.im))
	31.4b	(-.f64 (/.f64 y.re (*.f64 (/.f64 y.im x.im) y.im)) (/.f64 x.re y.im))
✓	26.3b	(-.f64 (.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im)))) (/.f64 x.re (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) y.im)))
	35.9b	(-.f64 (.f64 x.im (pow.f64 (/.f64 (sqrt.f64 y.re) (hypot.f64 y.re y.im)) 2)) (/.f64 x.re (+.f64 y.im (.f64 (/.f64 y.re y.im) y.re))))
	34.5b	(-.f64 (fma.f64 (/.f64 x.im y.im) (/.f64 y.re y.im) (/.f64 y.re (/.f64 (pow.f64 y.im 3) (*.f64 y.re x.re)))) (/.f64 x.re y.im))
	34.5b	(-.f64 (/.f64 x.im y.re) (*.f64 (/.f64 (/.f64 y.im y.re) y.re) x.re))
	28.4b	(/.f64 (neg.f64 (-.f64 (.f64 y.im x.re) (.f64 x.im y.re))) (pow.f64 (hypot.f64 y.im y.re) 2))
✓	16.9b	(-.f64 (.f64 x.im (/.f64 y.re (fma.f64 y.re y.re (.f64 y.im y.im)))) (/.f64 x.re (+.f64 y.im (*.f64 (/.f64 y.re y.im) y.re))))

Compiler

Compiled 4408 to 1496 computations (66.1% saved)

regimes1.1s (24%)

Accuracy

Total 4.4b remaining (95.6%)

Threshold costs 0b (0%)

Counts

71 → 3

Compiler

Compiled 6713 to 4074 computations (39.3% saved)

bsearch61.0ms (1.3%)

Algorithm

2×	binary-search

Calls

2 calls:

56.0ms	y.re
2.0ms	y.re

Steps

Iters	Point		Range
-3.9696921097903e-311	∈ [	-2.4589133606071e-308	,	5.141751627714131e-306	]
-7.579958549150986e+153	∈ [	-1.3891652471045586e+155	,	-4.1192307090218054e+152	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	89
1	36	89
2	45	89
3	49	89
4	52	89
5	53	89

Stop Event

1×

saturated

end129.0ms (2.7%)

Stop Event

1×

fuel

Compiler

Compiled 329 to 174 computations (47.1% saved)

Details

analyze765.0ms (16.2%)

sample1.1s (24%)

preprocess41.0ms (0.9%)

simplify35.0ms (0.7%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series83.0ms (1.8%)

rewrite45.0ms (1%)

simplify46.0ms (1%)

prune59.0ms (1.3%)

localize10.0ms (0.2%)

series149.0ms (3.1%)

rewrite63.0ms (1.3%)

simplify77.0ms (1.6%)

prune143.0ms (3%)

localize11.0ms (0.2%)

series148.0ms (3.1%)

rewrite62.0ms (1.3%)

simplify70.0ms (1.5%)

prune147.0ms (3.1%)

localize12.0ms (0.2%)

series62.0ms (1.3%)

rewrite48.0ms (1%)

simplify35.0ms (0.7%)

prune136.0ms (2.9%)

regimes1.1s (24%)

bsearch61.0ms (1.3%)

simplify4.0ms (0.1%)

end129.0ms (2.7%)

Profiling